Formal Semantics: The Essential Readings (Linguistics: The Essential Readings)

Fot-r

I

The Essential Readings

Edited by

Paul Portner

and

Barbara H. Partee Blackwell Publishing

1

Formal Semantics

Limguistics: Tlme Essential Readings consists of comprcliensivc collectio~~s of classic and contemporary reprinted articlcs in a wide range of fields within linguistics. Thc primary works presented throughout each book in the serics arc complcn~entcdby outstanding- editorial material by key figures in tlze field. Each volume stands as an excellent resource on its own, as n-ell us an ideal companion to an introductory tcxt. 1 Phono/o'yr'c,n/ T h e o q ~ :The Essc~zrilrlRtnr/l'ngs, edited by John :I. Goldsmith 2 fimilctl Stnrarrric-.v: T/IP Essential R~uding.~,cdited by Paul Postncs an3 Hasbara H. Partee

Formal Semantics The Essential Readings Edited by

Paul Portner and Barbara H. Partee

Blackwell Publishers

i' 2002 b! Ulack~vcllPublishers 1-tcl a Bl~lcliwcllPublishing conipanq

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Contents

Acknowledgments Introcluction Paul Portner and Barbara H. Partee

1 The Proper Treatment of

in Ordinary English

Richard Montague

2 A Unified rlnalysis of the Englisll Bare Plural Greg N. Carlson

3

Generalized Quantifiers and Natural Language Jon Barwise and Robin Cooper

4 The Logical Analysis of Plurals and Mass Terms: A Lattice-thcoretical Approach Godehard Link

5 Assertion Robert C. Stalnaker

6 Scorekeeping in a IJanguage Game David Lewis

7 Adverbs of Quantification David Lewis

8 A Theorj- of Truth and Sen~anticRepresentation Hans Kamp

9 File Change Scnlantics and the Familiarity Theory of 1)cfiniteness lrene Heim

10 On the Projection Problem for Presuppositions lrene Heim

1 I Toward a Semantic Analysis of Verb Aspect and the English "Imperfective" Progressive David R. Dowty

viii Contents 12 T h e Notional Catcgory of Modality Angelika Kratzer

1.3 The Algebra of Ei-cnts Emmon Bach

1-1 Gencsalized Conjui~ctioiland Type Ambiguity Barbara H. Partee and Mats Rooth

15 Noun Phrasc Interpretation and Type-shifting Principles Barbara H. Partee

16 Syntax and Seinantics of Questions Lauri Karttunen

17 Type-shifting Rules and the Seii~anticsof Interrogatives Jeroen Groenendijk and Martin Stokhof

18 O n the Notion Afictitle in thc Analysis of Ncgatil-c-polarity Items William A. Ladusaw Index

Acknowledgments

The editors and publishers gratefully ackno\~ledgethe following for permission to reproduce copyright material: l
,!z

Walter dc Gruyter 8i Co. for: "The Logical Analysis of Plurals and h;lass Terms: A 1,iittice-theoretical Approach," by Godehard Link (from Raincr Uiiuerle, Christoph Schmarze and -4rnim yon Stechow (eds), lMcntring, LGe arld 1Iti7 Itzte/pr-t1n~ior7of' Lu~zg~ragc, pp. 303-23, 1983 Walter de Gruyter & Co.); "File Change Semantics and the Familial-itp Theory of Dcfinitencss," by Irene I-Jeim (fi-on1 Rainer Rli~ierle, C:hristoph Schwarze and Arnim von Stecho~v((els), rtleanifrg, L i s p rrnd tlrr Itt~crprc~u~ior~ of'/,llrr~.liugc,pp. 1 6 4 00, 1983 Walter de Gruytcr & Co.); "The Notional Category of hlodalitjl," b!" Angelilia Kratzer (from H.-J. Eikmeyer and M. Kicser (eds), CCitrrls, Il'orldx, rr17J Cnittrsts. Lbi~vr~ :qppronl.hes to R'oril Semnntil-s, pp. 38-74, :(-~:198 1 \&'alter de

(c,

x Acknowledgments Grupter 81 Co.); and "Generalized Conjunction and TJpc Ambiguity," by Barbara H. Partee and Mats Root11 (from Rainer Ha~~erle, Christopli Scli\varze and Arnim von Stechow (eds), ~Mraning,CJ.w nnd ~ h Irlterpr~tatiorr r ~ ~ ' L N ~ S Ipp. I I I301-03, ~P, !(: 1983 Walter de Gruyter & Co.); Acadc~nicPress for "Assertion," by Robert C:. Stalnakel- (from Pctcr Cole (ed.), Prllginnlit.~,pp. 3 15-32, I:(_;) 1978 Academic Press Inc.); rcprintcd by permission of the publisher; Cambridge University Press for "Adverbs of @lantification," by David 1,ewis (from E. L. Keenan (cd.), Forrrznl Sew7awtics of'N~~turil/ L,(lngrr(lp, pp. 3 1 5, LC'! 1975 Cambridge University Press); reprinted with the permission of Cambridge University Press; Foris Publications for "A Theory of Truth and Semantic Reprcscntation," by I-lans Kamp (from Jeroen Groenendijk, Theo Janssen and Martin Stokhof (eds), T'ril~h, In/erpretcrtion, I~zjbrma~ion (GRASS 2 ) , pp. 1-41, >Jy 1984 Foris Publications, originally publislled in Jcroen Groenendijk, Theo Janssen and hlartin Stokhof (eds), For~~lu/ M~'t/ro~I's ill thr Stu4)t r!/'I,a11guage, Mathematische Centrum, Uni~ersityof Amsterdam, 135); and "Noun Phrase Interpretation and Type-shifting Principles," by Barbara M. Partee (from J. Groenendjik, D. de Joi~ghand Rfl. Stokhof (eds), Stlrilits ilr Di.s~~rntrl:ve R~~pres~wtutio~z Theo?)~arzd the Th~'o/:yqf Genercl/i:ed @iant[/i~.rs, pp. 11.5 -43, 1086 1'~- Foris Publications); ((''1

Irene Heim for "On the Projection Probleni for Presuppositions" (from hZ. Barlow, D. Flickingcr and kl. Wescoat (eds), ITCCFL 2: Second rlnnttal W ~ s tCULLS/ Co~!fl~rcnce on Formal LinLquisti~.s, pp. 114-25, :'(::I 1983 Irene EIeim); William Ladusabv for "On the Notion 'Affective' in the Analysis of Negative Polarity L P1-1 ' . ~0, , (!: 1080 William L,adusatv). Items" (Jountal q/ Lirzguzstic R L ~ S ~ C I, '

1

T h e publislicrs apologize for any errors or oii~issionsin the above list and would be grateful to be notified of any corrections that should be incorporated in the next edition or reprint of this book.

Introduction

Our purpose here has been to put together a collection of "classics" that have shaped the field of formal semantics in linguistics which can serve both as a reader for graduate-level semantics courses and as a reference collection for researchcrs in semantics and related fields. These works are widely recommcndcd to virtually evcry student of formal semantics, and we believe they are of value for anyone interested in the semantics of natural language.

What Is Formal Semantics? The roots of formal semantics lie in logic and the philosophv of language. Its first appearance as part of a theory extending to natural language semantics was in the form of "hlontague grammar," originally developed by the logician Richard M o n t a g ~ ~ e (1930-71) and subsequen~lymodified and extended hy linguists, philosophers, and logicians. It quick]! became influential in linguistics, and linguists have played il large role in its evolution into contemporary formal semantics. T h e most constant 6eatur.e~of the theory ovcr time have been the focus on truth-conditional aspects of meaning, a model-theoretic conception of semantics, and the methodological centrality of the Principle oJ'Cornpositiunality: "The meaning of a whole is a function of thc mcanings of its parts and their mode of syntactic con~bination." Formal semantics contrasts on a number of dimensions with other aypl.oaches to meaning within linguistics, psycl~olog.y,and philosophy. 1;ormal semantics originates within the non-psychologistic tradition of "objective" (though abstract) meanings (1;regc 1982; Tarski 1944; Carnap 1956; Montague 1970b), which contrasts wit11 thc psj-chologistic view of meanings "in the head" (Fodor 197.5; Jackcndoff 1983, 190h; Higginbotham 1985; Lakoff 1987, and all psychologists). Do expressions rckr to objects or to concepts? Is semantics a branch of mathematics, or is it (as on thc Chomshj-an view of all of linguistics) a branch of psychology? Classical formal scmanticists, n-11o took 1-he first disjunct in these choices, distinguished scmantics from knowledge of semantics (I,ew+is 1975b; Cresswell 1978), making semantic competence

2 Introduction interestinglj- different from syntactic competence. Many today seek an integration of these two perspectives b y studying inind-internal intuitions of inind-external relations such as reference and truth conditions (see Chierchia and McConnell-Ginet 1900). Formal semantics diflers from most previous linguistic thcorics of semantics on another dinlension as well: it is model-theoretic rather than representational. Many linguists have thought of semantics in terms of a "level of reprcscntation" of' cxprcssions analogous to a syntactic or phonological le\rel, and this mas the way semantics was approached in the theories of Katz and Fodor (1963), Katz and Postal (1964), in generative sen~anticsand interpretive semantics (see Newn~cyer1980; Harris 199.1)) and in later work positing a level of "Logical Form" within gcncrati\:c grammar (Higginbotham 1983b; May 1985; Larson and J3udlow 1993). Psychologists, who generally think of semantics as relating expressions to concepts, often regard concepts as something like elements of a "languagc of' thought." A representational kiew of semantics is quite congenial to the popular coml.>utationaltheory of mind (Jachcndoft' 1983). A pure model-theoretic view sees semantic interpretation relating expressions to elements of models (possibly mental models) defined in terms of constituents such as possible situations, entities, properties, truth-values, etc. Intensional objects may be modeled, for instance, as functions from possible worlds or situatiot~sto extensions. T h e question of the mental representation of such model-theoretic constructs is o$cn (see Johnson-Laird 1983); the inclusion of h4arrian "2 $ - I 1 sltetches" in Conceptual Structure in Jackendoff (1987) suggests the possibility of mixed approaches. And Iieim (1982) and many other formal semanticists have found it fruitful to ivork within a Chomskyan syntactic framework that does include a syntactic level of "Logical Form" or "LF" w-hich is then taken as thc input to the kind of modcl-theo~aeticcomposilional senlantics characteristic of formal semantics. Many current rcscarchers seek an integration of model-theoretic and representational approaches, and not all contenlporary formal semanticists emphasize a inodel-theorctic pcrspcctivc in tlreir worh.

Historical Perspective Formal semantics as a part of linguistic theory was born of two parents: philosophical logic and generative grammar. Like any child, this child inherits some features from each parent, learns others from the parents during life, follows its peers in certain ways, and eventuallj- develops an independent personality and makes its own uniqiic contributions. This volume provicles a highlight-album style view o i classics that mark the , early development of the field, fi-om the end of the 1000s to the late 1980s, emphasizing the linguistically important developments, while recognizing the crucial interconnectedness of linguistic, philosophical, and logical perspectives. As such, it is explicitly about a variety of linguistic topics, drawn from among thosc for \vhich this approacll to the study of meaning has proven particularly insightf~~l, and implicitly about the foundations and history of the field itself As mentioned above, the approach to the analysis of meaning nhich is pivsued in formal semantics has its origin in the development of formal logic. The ~nilestoncssct 1 by Frege, Tarski, Carnap, Dat-idson, Kriplce, Kanger, Hintikka, Montaguc, Kaphn, and others developed the ideas of a truth-conditional, modcl-thcorctic, and intcnsioilal 1

~

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Introduction 3 seniantics for formal languages. T h e classics of this literature may be found in tlie many excellent readers on philosophy of language, and so we have not reproduced them here. The idea that the techniques developed for artificial formal languages could he applied to natural language was first pursued systematically in the late 1960s and early 1970s by Richard Montague (Montaguc 1970a, b, 1973), David Lewis (Lewis 1970), Max Cresswell (C:rcsswell 1973), and Terence Parsons (Parsons 1972). O n l ) the most influential of these works, hlontague's paper on "The proper trcatment of qui~ntificationin ordinary English" (Montague 1973), is reproduced here, but it shoulcl be stressed that the others also made significant contributions to the basic form which formal semantic theories take. Montague's paper is hcrc because it is a historically important starting point for Montague grammar and hence for formal semantics, and is not available except in tlie out-of-print collection (Montague 1974). It is not easy to read, however. (Introductions to its content can be found in Dowty et al. (1981), Gamut (1991), Link (1979), and Partee (1973, 197%)) A more readable and also important early work is Lewis (1970), which is more widely available and hence not included licrc. At thc most basic level, a formal semantic analysis postulates a compositional, hnctional pairing between syntactically analyzed sentences of il language and their truth-conditional meaning. From the time of these earliest works, including Montague's, it has becn usual (though by no means universal) for the expression of truth a~nditionsto be mediated by an intensional logic (such as Montaguc's own typed intensional language 11,) with an underlying model structure utilizing thc notion of possible worlds. In its reliance on having an explicit syntactic analysis for each sentence under anal!-sis, a semantic theoly requires some sort of syntactic theorj- to build on. Wontaguc's o\vn ivork followed the logicians' tradition of stating the sFntnx in the form of a reciusivc definition of the set of wcll-formed expressions of each syntactic category. 'Thc "analysis trees" corresponding to the steps of the derivation of particular sentences provided the syntactic structilrcs that were the input to the compositional semantic interpretation. While some linguists follo\ved up on the development of some aspects of Montague's syntax, such as his use of a modified categorial grammar (see Bach ct al. 1987), othcr linguists preferred to scek ways to integrate Montague's semantics svith the kinds of approaches to syntax that had bccn developed within linguistics in the 1960s and 1970s (Partee 1973, 197%; Cooper 1975; Bach and Cooper 1978; Bach 1979). Explicit comparisons between Montaguc grammar and generative semantics, as well as the earliest systematic attention to thc lexicon in formal semantics, can be found in Dovvty (1979). Montague was doing his work on natural language a t the height of the "linguistic wars" bctwcen generative and interpretive semantics (see Fodor 1980; Newrneycr 1980; Harris 1993), though Montague and the semanticists in linguistics had no am-arencss of one another. (A4ontague was aware of Chomsk~'swork and respected its aim for rigor but was skeptical about the fruitfulness of stuclying syntax in isolation from semantics.) -4s a]-gued by Partee (1973, 1975b), one of thc potential attractions of Montague's work for linguistics was that it offcred an interestingly different view of thc relation between syntax and semantics that might be able to accommodate the best aspccts of both of the warring approaches. T h e instantiation of Wontaguc's algebraic theory in Montaguc (1973) illustrates what Bach (1976) christcncd the "rule-by-rule"

4 Introduction approach to syntax-semantics correspondence: syntactic ri~lcsput exprcssions (or : bracketed expressions; see Partee 197%) together to form more complex expressions, i and corresponding semantic rules interpret the whole as ;l function of the interpretations of the corresponding parts. ?'his is quite different from both gencrativc and 1 interpretive semantics, which were framed in terms of the prevailing conception of 1 syntactic derivations from some kind of phrase-structure-gcneratcd ul~derlyingstructures via transformations to surface structures, with the debate centered on which level(s) of syntactic representations provided the basis for s e l ~ ~ i ~intcrpretation. ~~tic Cooper and Parsons (1976) providcd "conversioi~algorithn~s"to sl~owthe descriptivc equivalence and theoretical differences among (particular versions of) A/fontague grarnmar, generative semantics, and interpretive semantics wit11 respect to the fvagment of English generated in Montague (1973). Once it was shown hour productively the basic ideas of a formal semantics for natural languagc could be applied, a flurry of work started in the 1970s as many scholars tried to see what insights were to be gained by looking at a widc variety of linguistic phenomena. At first, the theoretical forinat used was typically closcly modeled on Montague's, and the theory as a whole was k n o w as "Montague grainniar." Some important figures from this era arc Michael Bennett, Barbara Pnrtee, Greg Carlson, Robin Cooper, David Dowry, Lauri Karttuncn, Richmond 'I'liomason, and Lmmon Bach; the earliest collections were Kodman (1972) and Partec (1976). 13ou.t~-ct al.'s (1981) classic textbook Introduction to Mowtrigue Scrnnntir.~includes iln extensive bibli, papers by C~arlson, ography of work in this framcworli. Within the prescnt ~ o l u m e thc Dowty, and K,~rttunenrepresent this pcriod. Related independent work was done by Edward keenan, hl. J. Cresswcll, Terence Parsons, C:. I,. Hamblin, Kenatc Bartsch, and others. A4ontague's compositionality requirement mas in principle compatible wit11 many different forms of syiitactic thcory, and linguists soon began to explore a range of options that were opened up by the h c t that with a morc powerful semantics, a less pow-erfirl syntax might be adequate. For instance, therc have been intercsting dcbates about whether control of infinitival complements is to be analyzed by having an cinpty category PRO as subject of' an embedded clause (the classic syntactic view, successor to "Equi-NP deletion"), or with a bare infinitival complenient plus a theory of control as a semantic entailment associated uith the embedding verb (Cl~ierchia1984; 13owty 1985). Similar issues arise with "Raising" and other "NP-nioveinent" rilles (Sag 1982; Jacobson 1990); Dowty (1978) in fact argued that all "gotcrncd transti)rinationsl' should be recast as lexical rules, with lexico-syntactic effects on the argument structure of the governing item and a corresponding con~positionalchange in its semantics. A nunlbcr of new syntactic theorics developed as a part of this trend. Gcneralizcd Phrase Structure Grammar (GPSG: Gazdar 1982; Gazdar et ill. 1985) was the first of a number of proposals for "monostratal" (lion-transforrnation;ll) gr;imniars conibined with coi~lpositionalformal semantics. Other proposals for monostratal syntax to be combined w-ith compositional formal senlantics inclucled extensions of C:atcgorii~l Grammar (CG: Rach 1984; Chicrchia 1984; Rach ct al. 1987), Heacl-Uriken P11rasc Structure Grammar (IIPSG: Pollard and S;lg 1994), and t11c morc recent TrccAdjunction Grammars (TAGs: Joshi 1985). T A G s wcre originally motivated by purely syntactic consideratioils b ~ l twere later cstended to includc con~l>ositio~ial scrnantics,

I

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Introduction 5 both clirectly (Subrahmanyam 1989; Joshi and Vi jay-S hanker 1999) ancl via the simultaneous derivation of' an LF-like representation which can serve as input to modeltheoretic interpretation (Schabes and Shieber 1994). An independent but in some ways related line of development is found in Bresnan and Kaplan's Lexical Functional Grammar (Brcsnan 1982; Kaplan and Bresnan 1995). While debilt~sconcerning the notion of LLautonomoussyntax" (including debates about what the tcrm should bc taken to mean) have continued since the issues were raised by Chomsky in thc 1970s (Chornsky 1975; Partee 1975a), and similarly fi)r the status of the compositionalitv constraint (Partee 1984; Janssen 1997), most lii~guistsby the end of the 1980s werc agreed that proposals for syntax must be judged at least in part by their compatibility ivith a coherent semantics and vice ircrsa. In the meantime, other scmanticists found new ways to integrate formal scmantics with mainstream Chomshyan approaches to syntax. Hein1 (1982) combined innovativc formal semantic proposals with innovations in a GB-style lcvel of l~,ogical Form, making it clear for the first time how these approaches could be fit together. Kooth (1985) proposed that the syntactic operation of Quantifier Raising ((LR) was triggered by tvpe mismatch, i.e. by the impossibility of interpreting quantiticational NPs in ordinary argument positions. In general, semantic ~vorkof this kind raises issues of tradeoffs t~etweenthe use of a semantic module enrichcd with devices such as typeshifting (Partee and Rooth 1983; Partee 1986) versus the crucial use of ;-I level of Logical Form distinct fiom surfacc syntax (cf. Heim and ICratzer 1998). A second major movement that paralleled the development of formal scmantics is the dcvclopinent of formal pragmatics; the two movements often influenced one anothcr and a number of scholars contributed to both. Within philosophy, the works by Stalnaker (1978) and Lewis (1979) reprinted in this volume, as well as others by, for csample, Montague, Michael Bennett, Kaplan, and Soames (see Davis 1991), were to have a trerncndous in~pacton semantic theory. Within linguistics, pragmatics grew greatly as a separate subfield closelj- tied to both semantics and syntax, a development which was to some extent launched by generative semanticists like James McCawlcy, Georgia Green, Jerry Morgan, and Larry Horn, and also ineludcd scholars with a more direct intcrest in pragmatics like killen .Prince and Gerald Gazdar. Some of thc work was closely ticd to Montague grammar, like that of Lauri Karttunen and Stanley Peters on lxesupposition (Karttuncn and Peters 1979); Keenan's earlies work on presupposition reflects a similar interest in thc semantics-pragmatics interf~ce(Keenan 1971). Reseilrch at the hordes bctwccn linguistics and philosophj on such topics as prcsupposition, implicature, indexicality, and speech acts continues to have an important iinpact on the ficld of formal scmantics. One effect of the subsequent tlevelopn~entof d y n i ~ m i ~ scmantics, discussed bclom-, \\.-asto bring formal semantics and formal pragmatics closer together, as can bc seen in such works as Heiln (1983b), included here. The late 1070s and early 1980s saw a grcat expansion and diversification in thc rangc of theoretical frameworks which fall into the formal semantics tradition. Montague grammar evolved into a less monolithic thcorctical framework, with formal semanticists modifying or replacing various aspects of the syntax, the scmantics, or the architecture of the interface, while continuing to use many of the tools from Montaguc's "toolbox." 'I'his time saw the de\~elopmentof dynamic approaches to meaning, that is an;~l!ses n-hich vie\$-meaning as the contribution which an expression can make to the increase

6 Introduction of information in a context. This trend was inspired by Stalnakcr's (1978) work on pragmatics and Lewis's (19753) on adverbial quantification, both included here, ils well as by linguistic and philosophical work on anaphora and the sen~anticsof indefinite and dcfinite noun phrases (Evans 1977, 1980; Fodor and Sag 1982), and especially the problems of discourse anaphora (Karttuncn 1976; Wcbber 1979). Stalnakcr's contrihution was crucial because he developed the basic ideas of the evolving conversational context which allows tlie dynamic view to be formalized; JJewis's work led to a better understanding of the seniantics of indefinite noun phrases and anaphora, tlie crucial laboraton for most of the progress within the dynamic franictvork. l,etvis (1979), illso included Ilere, opened broader perspectives on the range of phenomena for which a dynamic perspective could be iniportant. Dynamic semantics also had iniportailt predecessors in the fields of' psychologp (Clark and Clark 1977), the semlntics of programniing languages (Scott 1982), and pragniaties (in particular, tlie scholarship on presupposition). T h e foundational work within linguistics and philosophy was done indcpendentl! by IJans Kanip and Irene Hcim, represented in this volunle bj- Hcim (1983a) and Knmp (1984). An important later framework, dynamic logic, was developed by Jcroen Groenendijk ancl Martin Stokhof (1990, 1991). Throughout the 1980s and I990s, a trcmenclous amount of research on inter- and intra-sentcntial anaphora dt.e\v upon the richncss of the dynamic approach to meaning. We include Heim (1983b), which deals with the particularly natural relation between anaphora and presupposition in a dynamic semantic approach, and simultaneously illustrates the essential integration of scmantics and some parts of pragn~aticson this approach. Another important theoretical framcn-ork de\leloyed during this period uas Situation Semantics (Barwise 1981; Rarwisc ancl Perry 198 1, 1983). 13arwisc and Pcrry's Situation Semantics was in many ways within the formal semantics tradition, and added nevir insights about the value of positing "situations" as a net+ basic type, scrving for instaiicc as the objects of "naked infinitive" perception reports. But it diffcrcd markedly in some of its (onto-)logical underpinnings. In particular, although it is also model-theoretic, it does not make use of the possiblc worlds-based n~odeltheory developed by klontaguc and others; rather it constructs n notion of "possiblc situations" through quite different, set-theorctic, means. Another fran~euorkwhich rcjccts the possible \s-orlds-based model theory, and in Fact rejects model thcory altogether in flvor or' absolute t r ~ ~ tconditions, h is "l>avidsonian Semantics," after Davidson (1967b). This aplwoach produced important scholarship as well (I-ligginbotham 1983a, 1986; Schein 1993; Larson and Segal 1995) and has had a particularly strong follo\ving among a generation of Oxford philosophers (1~;vansand h4cil)owell 1976). Throughout the history of fbrrnal semantics, there has been an incrcasing trend tol~ardsgreater empirical diversity in thc topics which researchers have been interested in. Our collection manages to partiall!- reflect this greater brc;ldth in terms of tlie variety of linguistic constructions treated, but it unfortunately rcflects a historical tendencj- to focus on English. A great deal of recent rcscarch hi~sbegun to erase this bias, but our desire to create a reader of'the essential "classics" of tlie field has meant that none was to be included lierc. (A few early norlis that did address issues in lang~~ages other than English included Cooper (197.5, with a chapter on corrclative

Introduction 7 relative clauses in I-Iittitc), Siege1 (1976a,b), Karttunen and Karttuncn (lO76), Johnson (1977), Link (1979), Gunji (198 l), Miyara (198 11, and Stein (l98l).) Another respect in which the field has developed significantly over the years is in inno\;ations in thc model-theoretic structures in terms of which the semantics is articulated and the increasing sophistication with which the model-theorctic tools of the trade arc deployed. Ladusavv's work on thc role of monotone decreasing functions in the explanation of the distribution of negative polarity items (reprcscntcd hcrc by Ladusaw 1980) was an important step in that direction, as were the innovations in a number of the other papers included here, including Link (1983), Hach (1986), and Kratzer (198 1). A third respect in which thc fielcl has developect significantly since thc ivorlis included here is in tile move away from fully explicit "fiagments" of English or othcr languages to proposals for more general constraints (such as type-driven interpretation; Klcin and Sag 1985) that should interact with a minimal spccification of languageparticular "parametcrs." I11 this respect, developments in semantics have paralleled deirelopments in syntax (although semanticists still tend toward greater explicitness). And it should be noted that within the presently tlourishing area of computational semantics (see Rosncr and Johnson 1992; Nerbonne 199h), explicitness in both syntax and semantics can still be found. All of thcse developments reflect increasing success in blending the perspecti\~esof philosophers and linguists to form a unified field of tornla1 natural language semantics. More 011 the background, historical development, and content of formal semantics in linguistics can be found in o\;ervie\v articles (Janssen 1983; Pastee 1987, 1996, 1097), textbooks (Link 1979; Dowtv et al. 1981; Bach 1989, Chierchia and McConncll-Ginet 1990; Gamut 1991; Heim and Kratzcr 1498), and handbooks (von Stcchow and Wunderlich 1991; Lappin 1996; van Hcnthem and ter Meulen 1997). Major journals in the field are Li~1puistii:~ rind P/tilosop/i,)~ (thrce of our selections, by Karttuncn, L>owty, and Carlson, are fi-om its first volume), and the newer Narurcil Lnr~gutige,J'PIII(IP~/IL.S (too nen- to include "classics", since its first volume was publishcd in 1993).

Selection and Organization of Contents 'The total length of the volume had to be limited so that it could be published at a reasonable cost, and unfortunately this has ineant that we have had to go through the very difficult process of selecting only this small set of papers for inclusion. We have tried to balance a number of competing recluirements and desires, knowing ti-om the beginning that nrc would not be able to include all of the papers that wc ant1 our colleag~~es rccognizc as classics in the field, nor even all of the authors who havc urrittcn articles or dissertations that are considcrcd classics. we started by askins a 131-gc number of colleagues for their suggestions, and then thought and rethought our decisions as we xvorked our way from an initial list of about fifty indisputably classic \vorks down to the present collection of eighteen. We regret every omission, but hope that our colleagues will agree that we have assembled a good collection of outstanding papers that balance the various criteria that are important for a volume like this onc.

8 Introduction Some of the issues we have considered in making our selection arc tlic following: we wantecl papers which have been broadly influential for a number of' ?cars, papers covering a variet~-of empirical domains and formal tools, papers representative of the field's historical development, ant1 ideally papers that are not too long (so as not to displace too many others). Some classics are dissertations or other longer works, but we made a conscious decision to include only complete articles ancl not cscerpts, since it is usually very difficult to react anything in formal semantics without starting at tlic beginning, and the "results" are likely to come near tlic end. Other things being equal, we gave preference to papers that are not already easily accessible (in major journals or in accessible collected voluines such as this one). And because there already exist many fine anthologies of the philosophy of language (see, for instance, Martinich 2000) and very few if any in linguistic semantics, that last consideration eliminated a number of' classic background papers in the philosoplip of language which are alrcady widely anthologized, such as Davidson (1967a), Lewis (1970). and Kaplan (1978, 1979). Tlic volume is therefore unevenly tilted toward the linguistic side of the linguistics and philosophy interaction, and the table of contents does not reprcscnt the degree to which the early development of fornial semantics resulted from the combined efforts and fiuitful interaction of linguists and philosophers. But omission of most philosophical classies also helped us to narrow down the time span of our contributions, increasing their coherence: the earliest paper in the collection is Moiitague (1973), and the latest is Groenendij h and StokhoC ( 1989). Dcspite our efforts to cover a broadly representative range of topics in ous choices of' classics, soine important areas of research remain unrepresentcd or only tangentially represented here. We would have liked to include works on the scnlantics of adjectives and adverbs, such as the classic papers by 'I'homason m d Stalnakcr (1973) and Kainp (1975). Another underrepresented area is intensionality: while i i ~ u c of l ~ thc important work in that area is well represented in collet.tions in the philosophy of langui~gc,it m.ould have bcen nice to be able to include more hcrc, such as Cresswell and von Steclion~(1982), Chierchia (1982, 1985), and Chierchia and T ~ ~ r n (1988). cr Work by formal semanticists on the semantics and pragmatics of f ~ c u s a, major research in more recent Fears, was just getting started near the cnd of the period of our "classics" with the dissertation of Rooth (1985); the later payers by krifka (1992) and Root11 (1992), which are quite accessible, gi1.e a good picture of progress in thc first scvcral years of research on tlic semantics of focus. We have organized our volume more or less bq topic. Of course, ho\vevcr one dividcs 1113 the topics, there will he a great deal of o\-erlap. T h e groupings w-e have come up wit11 are listed below. we have already said a few words ahove about some of thcsc papers and their place in the development of'the field; we add atlditional coinn~entsbcloiv.

1 'The beginnings, representecl by Moiitaguc (1973). All of Montaguc's papers in formal semantics and pragmatics, as well as his work in the dcvclopmciit of intcnsioiial logic, are collected in nllontague (1974), u~liichnlso inclucles an important introductory essaj by Richmond Thoniason. 2 Noun phrase semantics: Carlson (1077), Uarwise and C;ooper (lC)81), and Idink (1983). h4ontaguc (1973) could certainly be included hcrc as well, since it aiid

Introduction 9 Lewis (1970) were the first works to propose that noun phrases should be intcrpretcd as generalized quantiiiers (properties of propcrties, rather than as in a firstordcr sjstcm like predicate logic); Barwise and Coopcr elevate this idea to thc level of claimed universal, suggcsting that all noun phrases denote gcneralizcd quantifiers. Thcy also propose a wide variety of potential applications, thus launching thc sub-field of seniantics known as Generalized Quantifier Thcory, including a first attempt at formalizing the weak/strong distinction among determiners that \vas argued for by hlilsarh (1977) in llis treatment of existential sentenccs in 1.nglish. Carlson's paper focuscs on the interpretation of bare plurals; bare plurals present a variety of semantic puzzles which have long exercised linguists, and these puzzles intersect with many othcr important issues like quantification and genericity. In particular, Carlson's work is important for having introduced, and demonstrated the linguistic relevance of, the distinction between prcdicatcs which express more or less transient properties (stage-level predicates) and those which cxpscss morc or less permanent ones (individual-level predicates). Idink's paper represents an influential step in our ullderstatiding of plurals and mass terms, adding e-type plural entities and mass entities alongside the more familiar singular atoniic entities, and introducing a homomorphism between count and inass domains. At the thcoretical level, it shows the relevance of abstract algebraic structures to thc study of natural language, introducing a mathematical perspective which has rcniained influential. Philosophical pr;~gn~atics: Stalnaker (1978) and Lewis (1979). These papers niahe foundational contributions to the embedding of truth conditional semantics into a broader franicwork of semantics and pragmatics. Stalnahes introduces the notion of "conimon ground" (the set of possible worlds compatible with what speaker and hearer can bc presumed to take for granted at a given point in a conversation), and analyzes the core pragmatic concepts of assertion and presupposition in ternis of tlie wav utterances both depend on and affect the common ground as it evolvcs during a conversation. Lea-is extends this perspective with his "scorekeeping" mctaphos to show that the evolving context on which many aspects of interpretation dcpend includes not only prcs~~pyositions but also indications of such things as the current salience of various entities being talked about, standards of precision, graded modal relations, and perspectives relevant to indexicality. In terms of their iiiipact on linguistics, they la)- tlie groundwork for work in dynamic semnn~ics,thc next section. Dynamic scmantics: Lcwis (1975a), Kamp (1981), and Heim (19$3a, b). We discussed this work, and the further development of dynanlic scmantics in the ~vorkof Groenendijk and Stolthof, and others, above. Thc semantics of thc inflcctional/auxiliary system, i.e. tense, aspect, and modality. This diverse field is quite inadequately represented by Doivt~;(1977), Kratzcr (1981), and Bach (1986). Dowty's paper is onc of the most influential \vol-ks o ~ i an aspectual construction, in this case the English progressive. Bilcli's paper has to do with the progressil-e as well, which is nrl.1~it is includcd in this scction, hut it is also note\\-orthy for its connectioiis to Link's research on bare plurals; it also allows tlie readcr to be introduced to the important role of the notion of "evcnt." Kratzcr's

10 Introduction work from the late 1970s and early 1980s has long been the standard for our understanding of modality. 6 Conjunction and type-shifting: Partee and Rooth (1983) and Partee ( 1986). 'l'ypeshifting is a theoretical tool which allows an explanation of phenomena which indicate that a particular phrase can have a variety of different n~eaningswhich are nevertheless closely related in a logical sense. T h e Partee and Rooth paper, which builds o n earlier w-ork by Gazdar (1980) and others on non-transforn~atio~lal treatments of cross-categorial phrasal conjunction, is usually cited as containing the first systematic proposals for some general principles of type-shifting. Partee (1986) applies the technique to the treatment of noun phrases, and of'fers among other things a w-ay to reconcile gcneralized quantifier theory with the non-uniform NP semantics proposed by lcamp and Heim. 7 Questions: Karttunen (1975) and Groenendijk and Stokhof (1989). Clausc types other than declaratives raise an obvious issue for truth-conditional theories of meaning: how can one think of thc semantics of a question in terms of what would nlake it true? T h e solution to this puzzle involves understanding the meaning of questions in terms of the truth conditions of their answers, and various scholars have worked out this perspective in different ways. Karttunen's papcr, a highly influential early work on the topic, argues that thc meaning of a question is the sct of propositions espressii~gits true anskvers. Groenendijk and Stokhof point out that theories like Karttunen's take answers to be uniformly propositional (Q: I/b'/lo k j t A: May11 lefi.),argue that constituent answers (-4:Mar)?) must be considered as well, and work out a synthesis utilizing type-shifting. (The choice of this particular paper by Groenendijk and Stokhof might be somewhat surprising, as it is not their mostcited work on the topic, but we find it most suitable because it incorporates many of their important ideas while being quite self-contained.) 8 Negative polarity: Ladusaw (1980). Ladusaw's work on negativc polarity was tllc first to show the linguistic significance of a purely model-theorctic property, onc that has no analog as a structural property of a syntactic rcprescntation, even at a level of "logical form." It thus establishes the importance of formal semantic analysis tbr understanding the distribution of linguistic forms.

Acknowledgments Finall!;, we would like to express our thanks to somc of those who contributed LO putting togctlicr this volume. First of ;ill n-e extend our thanks to Stexc Smith, Tanii Kaplan, and Sal-;ih Coleman, as wcll as their collc;igues at Blackwell. for their support and assistance, to all of our many collcagucs who responrled to an e-mail solicitation with liclpful aclvicc about what papcrs they nould lilic to scc in such a book, and to Anna Oxbury for. overseeing the copy-editing and prooii.cading. Wc arc g~.ateli~I to Barbara's research assistants Paul de I,acy for managing and compiling thc responses to our initial c-mails and Ji-yung Kim for co-managing the indexing projcct, and to Paul's rescarch assist.ants Simon Maucli, Matt Baucl., and S h i m Felling for hanclling photocopies and col>! right permissions. Thanks also to tlic indexing team members Luis F. Xlonso Ovallc, Xlaho I lirot;ini, Eva Juarros, hlahoto Kadaffaki, Minjoo Kim, Xlcredith I,andn-ran, and hlil~.cinMorzqcLi. Paul Portner and Barbara 11. Partcc Gcorgeto-I$n and !!nihcl.sr

Introduction 11

References Dach, Emmon. 1976. An extension of classical transformational grammar. In I'r~obli~rtrs?/'I,itrgirrs~il. .d/!~~b(/f/ll'Ol:~J: hoc.e~diir$sr ! / ' ~ k e1976 Con/l.r.en~-P, 1:ast Lansing, Mich.: Michigan State Uni\crsity Linguistics Dcparttnent. Bach, Emmon. 1979. C:ontrol in Mo~ltaguegrammar. Lir~~yuictir /nq1411:1/10: 5 1 5-3 1 . Dach, Enln~on.1984. Some generalizations of categorial grammars. In Frcd Landman and Fr;~nl\ Veltman (eds), ?/jzri~tIesc!f'Formrnl Sctmuntics, Dordrccht: Foris, 1-24. Bach, Emnlon. 1986. T h e algebra of cvcnts. Lrnp.lris/is nr7d Phrlosophlr 9; 5-16. Hach, Einnlon. 1989. In/hrnurl 1,i~~rurrs ~ F Forrnnl I Senrantits. Neiv York: State University of Ncw- York Press. Bach, Lmmon and Robin Cooper. 1'378. T h e NP-S analysis of relative clai~scsand compositional semantics. Lzng~~~I.c/i~r\. NIICI P11ilo~op~1)l 2: 145-50. Bach, Emmon, Richard Oehrle, and Ilcirdre FVheeler (ctls). 1987. C i ~ / ~ > ~ y oGr~rrrrrrrrrr:v ri(tl c111rlh;r/rrrirI Llrr~glrir,~t~ .S~rrvc.turi~s. Dordrecht: D. Reidel. Hartvise, Jon. 1981. Scenes and other situations. Juurntrl c!f'P/rilosopl~,)~ 50: 369-06. Bar\$-isc,Jon and Robin Choper. 1981. Generalized quantifiers and natul.al language. Lirrgrrrs~i(sI I I ~ L I Plrilosop~~.~~ 4: 1 59-2 19. Barwise, Jon and John Pcrry. 1981. Situatiotls and attitudes. Journal r!/'Philosopig! 78: 068-01. Barwisc, Jon and John Perry. 1983. Sitlcutio~zst r r d . i t ~ l r ~ d c sCambridge, . Mass.: XIIT Prcss. 13rcsnai1, Joan (ed.). 1982. Tlrt Mrnrlrl Repr~~.cetz/u~iolrr ~ ! f ' C l v n ~ n ~ ( l /Ri>/rttio~s. ii.i~l Can~\)ridge,&l;li\ss.: hflT Prcss. Carlson, Greg. 1977. A unified analysis of the English bare plural. L r ~ i ~ q ~ r i (rrrd c ~ i cP~k i / o s o p / ! ~1 ~: 413-58. Carnap, R. 1956. Mrtrnitrp trrztl N ~ ~ i . c s s i 2nd / ) ~ , edn with supplements. C:hicago, Ill.: Univctsit! of' Chicago Press. Chierchia, Cknnaro. 1982. Nominalization and htontaguc grammar. Lrnc~rrI~x/ii:~ (rnll Plril~soj)ltl,5: 303-54. C:hicrchia, Gennaro. 1984. Topics in the S!-ntax and Semantics of Infinitives and Gcruntls. Ph.1). dissertation, University of hIassachusetts, Amherst. Chierchia, Gennaro. 1985. Formal semantics and the grammar of predication. IJin,yr/istic Irrqrrir:)~16: 417-43. Chicrchia, Gennilro and Sally McConncll-Ginet, 1'490. M ~ c r r ~ i rt ~t rgd Grntnrtur~..--irr Irrtro~/rr~.riorr10 Sorrrrrr~ii~s. Cambridge, Mass.: h l I T Press. Chicrchia, Gcnnaro and Raymond Turner. 1988. Semantics and property theory. I,irrg.uis/ir..x rrrrJ Pl~ilosopi?y1 1 : 26 1-.302. (:hornsky, Noam. 1975. Qucstio~lsof form and interpretation. 1,irrgrlistic. .lrrn/l~sis1: 75-105). Rcpr. in R. Austcrlitz (ed.), Tlre S L V ~I Y ! / ' ~ ~ ~ I P I . ILitlgrli.~~il.~ ~(L~I (Lissc: Peter dc Riddcr Press, 1075), 159--96. Clark, Herbert and Etlc Clark. 1977. Psj/r.hulog)~arrtl Cunplrtrpr. New York: Narcourt Rmcc Jovailot~ich. Cooper, Robin. 1975. hlontague's Semantic Theory and Transformational S!ntizx. Ph.11. disscrration, University of Massachusetts, Amhcrst. Co01>cr,Robin and Tercnee Parsons. 1976. Mnntague grammar, generative semantics, and interpreti ~ semantics. c l n R. Partce (ed.j, il/lori/tr~lteC;rtlrrrrr?(rr.,Nctv Yorli: Aci~dcn~ic Press, 31 1-62. Crcsstvell, h.1. J. 1973. L ~ ~ c i nrr~l c s L~rtlgliages.London: Methuen. Crcsstvell, M.J. 1978. Sen~anticcompetence. In F. Guenthner and M. Guenthner-Kcuttcr (ccls). 44rlrnil1'~arirl Tr~rnslrntror~: Philnsuph~ct~l orrrl Linguistii. .-lppro~r~./ri~, Idondon: Uiick~vorth,0-43. C;rcssnell, h4. J , and Arnini \;on S t c c h o ~ 1982. . Ilc re belief genct-illizcd.Lrrrgui.v~ic.virrrrl Phi1osol)lr~)~ 5: 503-35. Ilavidson, Don;~ltl.1065a. T h e logical form of action scntcnccs. In Nicholas Kcscher (cd.), '771~1Lo>qil. r!/'Dn.t.\.lol~(11711.-lcfion, Pittsburgh, Pa.: Pittsburgh Universit\- Press, 81-95.

12 Introduction Davidson, Donald. 1967b. Truth and meaning. .!?yn~hest. 17: 004-23. Rcpr. in M'lrtinich 2000. Davis, Stcvcn (cd.). 1991. Prn~n~otics: RP(I~('I.. Oxfor~l:0xSi)rd University Press. Dowty, David. 1977. Totvard a semantic anal\-sis of verb aspect and the ICnglish "impcrfectivc" 1: 15-77. progressive. Liligulstlcs and Philosopl~,)~ Doivtj-, ]]avid. 1978. Governed transformations as lexical rules in a Montaguc grammar. I,ilrg~risirc Iirquir)~9: 393- 426. I>o\vty, David. 1979. 1Pi)rd Mcanilzg ~ i i c Moiitrrjirl~ l Grtlit~lii[ir.T / I PS P ~ I N ~I!/' I I1 I, iL~ r, I~[ri~d ~ ~ Ti7tw.v ill G~rlrrir~ii!r Se?rrnntj~.sand in Mot~trlgut~i PTQ. Dordrecht: D . Reidel. Don-t!-, David. 1985. On recent analyses of the scniantics of control. Li~~,~rrlstir.s rrlirl Philosopl~)~ 8: 291-3.31, Donty, David, Robert E. Wall, and Stanley Peters, Jr. 1981. I ~ i l ~ o d u i ~ i10o nM o r i / r r ~ uS(~t7zon1rr.s. ~ Dordrecht: D . Reidel. Evans, Garetli. 1977. Pronouns, quantifiers and rclativc clauses. (,'(r~~ai/iirn Jourrirll c!/'Phi/osop/q~7 : 467-536. Evans, tiareth. 1980. Pronouns. Li~iguIstil.Inqzriry 1 1: 337-62. E\-ans, Garetl) and J. McDonell (eds.). 1976. T m l h arzd .I.lcurri~~g:L.YS[~,)W rii Stm~tit/c.i.Oxtord: Ctarendon Press. Fodor, Janet D. 1980. Srinarit~r.~:TIzeories qf'Merrni?~g.sin Gcizer.irirz.r Crrr~inriar.Cambridge, Mass.: Harvard University Press. Fodor, Janet D . and Ivan A . Sag. 1982. Referential and quantificational indctinitcs. Lingz/isrir.s rrlrd Plcilost~ph.)l5 : 3 55-9s. Fodor, Jerr!. -4. 197-5. The Lnnc~u~zgt (I/'T/zo~dc~,./r~. Cambridge, Mass.: Har\larcl University Prcss. Frcge, Gottlob. 1892. Uhcr Sinn und Bedeutung. Z~>i/sc/rriJi J i r Phikoso/~l~ie rind philos~tpl~iV~~I~e Krilik 22-50. Trans, as Frege, On sense and nominatum, in P. Cicach and M. Black (cds), Tr(rnsl~r/ro?rs fi-(~rr~ rhr Philosophicnl CYrrlrli~s(!/'Gottlo/~F r ~ g Rlackivell, ~. Oxforrl, 1980. Rcpr. in A. P. Martinich (ed.). Tlie Philosoplgf c!/'Larzfiur&ge,4th edn, Oxford: Oxford University Prcss. 2000. Gamut, L. T. F. 1991. Lo.qr(, Lrc~i~zrage, (in(/ A4eal11lig,\-01. 2 , Inr~.r/si(~ll(rl Logic (rnrfLogi1.(11G ~ i l ~ n n i t ~ r . C1lici1g.0, Ill.: University of Chicago Press. Gazdar, Gerald. 1980. A cross-categorial semantics for conjunction. L~rigurs~irs riiirl P / ~ i l o s o p 3: l ~ 407--0. ~~ Gazdar, Gerald. 1982. Phrase structure grammar. In Paulinc Jacobson and Geoffrey Pull~un(cds), Thc hirrtrd~.c/![.S')r~fai.licRl?pr~,.~c~t~~(r/~on, Dordrecht: Reidel, 13 1-86. Gazdar, Gcrald, ]<wan 1Clein. Geoffrcy Pulliun, and Ivan Sag. 198.5. G)PIIPI.~IIICL'(I P h ~ o . sS1rri1.1111-e ~ Gnrrtztr~t1r.Oxford: Hlackwell. Grocncndijk, Jeroen and Martin Stokhof. 1989. Tyl~c-shiftingrules and the semantics of intcrrogatives. In Gcnnaro Cliierchia, Barbara H. Partee, and Raymond Turner (eds), P I . O ~ L ~ ~TI)I~' p~e~(sI ISI I,/ Alrurriri,ys, vol. 2, Semantic. Isnres, Dordrecht: Kluwcr, 21-68. Groenendijk, Jcroen and hlartin Stokhof'. 1990. Dynaniic Montaguc glainm;lr. In I.. Kilman ant1 I,. PGlos (eds), Pr~persfrom he Sei.anr/ Sllntposiunl o ~ lLosi(. trirr/ L~trgrra~r, 13ud~pcst:A4cli~kkmi;li Kiadb, 3-48. Groenendijk, Jcroen and Martin Stokhol', 1991. Dynamic prcdicatc logic. Litr~y~is~i(~.$ oirrl Philost~ph)! 14: 30-100. Gunji, 'lakao. 1981. A Phrase Structural Analysis of the Japanese Language. h l . A . thesis, University of Ohio. Harris, Rand! -411en. 1093. Tlzr Ll~rgrris~~(.s Tjirrs. New York: Oxford Universit~Prcss. JIciin, Irene. 1982. T h e Semantics of Definite and Illdefinite Noun Phrascs. P1i.D. dissertation, Unir-crsit?; of hIassachusctts, ;iiiiherst. Hcini, Ircnc. 1983~.File change selnantics and the f61nlili:lrity theory of ddinitc~.tess.In .Mccrnit~~, iL,-p ant/ rlri. Inlerprrln~ion(!/'Lat~g.urr,ye,Rcrlin: Walter dc tiruylcr, 164-90. I-Ieim, Irene. 1983h. On the projection problem tbr presuppositions. In R1. Barlow, D. Flichingcr and 41. \Vescoat (eds), II'CCFI, 1:Scr.oiril.it~~~rra/ ll,i~i/ Cousl Con/i~rc.nt.roji F'clr-tiicrl Lrt~~yrri.$/r(~s, StanLi~rtl, Calif.: Stanford Uni~crsity,1 1 t 2 5 . T-leim, Ircnc and Angclikn Kratzcr. 1998. Sn~i(~titrcs it, C ~ c ~ t ~ c ~ rG'lanr~i~rrr. ( i i i z ~ ~ London: IIlac1,wcll.

Introduction 13 I-Iigginbotllam, James. 1083~1.T h e logic of perceptual reports: an cstcnsional alternative to Siti~arion Semantics. Joul-rrlrl c!/'P/ti/osopl!)l80: 100-27. Higginbotham, Jamcs. 1983b. L.ogical form, binding, and nominals. Lingui.vtic Irlqrrir)~14: 39.5-420. I-Iigginbotham, James. 1 985. On semantics. L ~ ~ I ~ UII~S II ~~ LL16: L. ~547-93. I:~ I-Iigginbotham, Jamcs. 1986. Linguistic thcory and Davidson's program in semantics. In Ernest L,cPore (ed.), Truth u i ~ dIrrterpwtrrtiotr: Per.vpt~i-tirtson the Phil~~sopIlj~ c!/'Doirtrltl Dacirlsoit, Owl'ord: Blacka ell, 29-48. Cognirioir. Ch-nbridgc, Mass.: M I T Prcss. Jackendoff, Ray. 1983. Stwarr?rLir.s t Mnid. Cambridge, Mass.: MIT Press. Jackendoff, Ray. 1987. Corisi.iousness o r ~ d~ h Cori~pr~tationiil Jackendoff, Ra). 1996. Seinantics and cognition. In Shalom Lappin (ed.), Tht Htrrtdbo~)kc!/'Corrlnrrporrlr:)l Semirntjc Tizenr:)l, Oxford: Blachwell, 539-59. Ji~cobson,Pauline. 1090. Raising as function conlposition. I,inguI.F11i.slrlri/ Pi~tIosoph)~ 13: 423-76. Jnnssen, Theo \,I V..1983. F'orrnri'utions rrnd .Ifiplir.c~tio~rs I!/' Movtogue Granrnrilr. Amsterdam: Mathematisch Centrum, University of Amstesdan~. Janssen, Theo M. V. 1997. Compositionality. In ]ohan van Bcntllem and Alice tcr hlculcn (eds), Hirwr/l)ook qf l o g c r (l12d Ltrngzr(r,gt~,Arnsterdan?: Elsevier, 417-70. Johnson. Marion Rose. 1977. A Semantic Analy~sisof Kik~~!~u 'fense and .4spcct. P11.11). tlissertation, University of Ohio. lohnson-Laircl, Philip N. 1983. hlen~crlh/lo~lt/s.Cambridge: <:ambridge University Press. loshi, Aravind K. 1985. Tree adjoining gramm,lrs: how much contest-sensitivity is rcquirecl to psovicle rcasonablc structural descriptions? ln Lauri Karttui~en,Arnold h4. Zwichy, and Ilavicl R . Dojvty (ccls), !Y(ILLIY~/ Lnngutrji~I'/crsii~i, Cambridge: Cambridge University Press, 206-50. Joshi, Aravind K. and K. Vijay-Shanker. 1999. Compositional semantics with 1,cxicalizcd 'I'rce-4djoining Grammar (LTAG): how much uilclerspecification is necessary.; In I I. C:. Runt and 1;. Ci. C. Thijsse (eds), P i . o ~ . t ~ r / ~q/' ~ / g/he s 7'11it.ll I ~ r / e r . i ~ r ~ t i ola'orkshop ~il~l on Coirrptrt(r/ioiilrI .S'~,trrairiii.s ( I I K " - 3 ) , Tilburg, 1314.5. Kamp, Hans. 1975. T w o theorics about adjectives. In Edward L. Keenan (ed.), Formal .S~~ittirrtii~.s I//' nblzrrltl /,~lnptlage,Cambridge: Chnlbridge University Press, 123-55. Ka~np,Hans. 1984. A theory of truth and semantic representation. In Jcrocn Grocncndijk, 'l'hco Janssen, and Martin Stobhof (eds), Tl-w~it,In~erprr~aii~liz, ln/brr7raiion, GRASS 2, Uordrccht : Foris 2-41. Originall! published 1081 in Jeroen Groenendijli, Theo Jansscn, and Martin Stokhof (cds). I.'~)rtiralM ~ t h o d sirr tlre S'trlc/)r I!/' L ~ ~ ~ z g u i t A4msterdam: pz, ;Llathematisch C:cntrun~, Unircrsit!. of Anlsterdam, 13.5. Kaplan, llavid. 1978. Dthat. In Pcter Cole (ed.), Prtr~rnatics(J1)lnta.v trnB Seintrnti~.s,vol. 9), New York: -4cadcmic Prcss. Rcpr. in A. P. Martinich (ed.) 2000. Titc P h i l ~ ~ s o p i!/'l,rrn,r(.u(~gp, h,~ 4th ccln, Uiford: Oxford University Press. Kaplan, David. 1979. On the logic ot'den~onstratives.In Pctc~'.A. French, Thcodorc IC. Lchling, Jr., and Howard K.Wettstein (eds), Conien~porizr)lPerspec~ri~rs rn 1/14? P l r i / u s ~ ) p l~!/'Lurrgurigr, ~~)~ Minncpoli is, AlIinn.: Universitj- of Minnesota Prcss. Also in Jorlrirrrl c!/'l)lri/osoplzir~iILogrr. 1070, X: X 1-98. Laplan, Ronald &ilncl I, Joan Hresnan. 1995. Lexical-functional grammar: a fi)snlal system for gramn~aticalrepresentation. In Mary Dalrymple, Ronald M. Kaplan, John T. 12~Iaxmcll,111, ilnd .-hie Zaenen (eds), Forirtn/ Is.srles tit L t ~ s i c i ~ / - F i r n e ~ iGrartlr?rnr, o ~ r ~ ~ / St;lnfosd, Calif.: CSLI. Karttunen, Lauri. 1970. Discourse referents. In J. !bIcC:awlcy (cd.), ib'o~r.s/iu/rr/hr Lirr,quistii I 'irrii~i.grorrttd ( S ~ ~ t r / ~~liztl r . vScrttrrtt/ic.s. vol. 7). Ncw York: Academic Press, 303-85. liarttunen, Lai11.i. 1077. Syntax and semantics of questions. L ~ i ~ , g l l / . art(/ ~ i / r Pitilo.s~)phy .~ 1: 3-44. liasttuncn, 1,auri and Frances Karttuncn. 1976. T h e clitic -kt?//-ktriir~in Finnish. In Pl/pcr~,/~OIi/ t1ri8 Trctirsirtltrnlii. T i / ~ ~ z i .Cs lO~I ! / ~ J T ( , ITr,\ws I ~ C : Liizg~ii\'ttL. ror111it vo1. .5, .4ustin, Tex.: 1Ic~)nrtiiiciitof Linguistics, 'LTniversitg of Tesas at Austin, 89-1 18. Karttuncn, Lauri ant1 Stanle! Peters. 1979. Conventional implicature. In C;hoon-Iiyu 011 ant1 David Dinnecn (eds), P r ~ s t ~ p p o s i ~ i(.Syn/rrs or~ i ~ / ~ rJ'er~lairtirs, / bo1. 1 1). New Yorh, ?cadcmic Press, 1-56. K'ltz, Jcrry J and Jcrry A. Fodor. 1063. T h e structure of a semantic theory. I,~~n~grrti,qt~ 30: 120 210.

14 Introduction Katz, J e r r ~, and Paul Post:il. 1964. .jri Iii~c~gr.n~eJ T h ~ o r :c!/'I,irig.rruri~ )~ D~siripr~orrs. Canihridgc, hlnss.: h,IIrT Press. Kccnan, Edward. 1971. T w o kinds of presupposition in natural language. In C:, Fillmore and 'r. Lnnpencloen (eds), Sllrili~sin Lirrgclisiir. Setr~nnrrc.~, Ncw E'ork: Holt, Rincliart CSr Winston, 45 54. Klein, En--an and Ivan A. Sag. 1985. Type-driven translation. Li~r~yuls/ii~s clrirl Phrlosnpl~,)~ 8: 163-201. Kratzer. Angelika. 108 I . T h e notional category of modalit!. In FI.-J. Eikme! cr ancl H. Ricser (cds), l h ~ r r l . ~Ilbrlrl.~, , r l t ~ C~ lO ~ I I P I .IV.~'JP I S . ~ ( J ) P ~ o ( ~ L . /toI ( ~I1,h~d s . S C I I I ~ I I IBerlin: I ~ ( . S , Walter tle Gruytcr, -38- 74. Krifk;~,hlanfrcd. 1992. A framework for Lbcus-sensitive quantilication. In Chris Barbcr and David Dontj- (eds), Proi.ec.r/i~igsuf'tlle .'?eroni/ (,'or!fi~lunt.t>on Scrnrr1~11c.smrid I,in,yrirslic 7 ~ 1 i ~ o(.s.iLT r)~ I)), Colunibus, Ohio: Oliio State University, 21 5-36 I.adus;~n,\tTilliam, 1980. On the notion "affective" in the analysis of ncgativc polrlrit!. items. Jo;,rrrtr~/ of'Liir~~rrz.I l~~tticc'-thcor~'tici~I ii1~p1.oach. In 1%. Haucrlc, C. Schwarzc, and "I. von S t e c l ~ o \(eds), ~ /l.l~~(rrrirrg-, lisi. irrril /he l i ~ / t ~ r p t - t ~ / ((!/' //ioi~ Ltrrrgirape, Berlin: Waltcr de Gruyter. Rcpr. in Linb, tiodehard. 1008. :I[yc~hriric .Sei/rirniii~sin Lntlgulrgc' (iirl/ Philo.~oplt)~, CSLI lecture notes no. 74. Stanford, C:i~lif.,:CSI .I I'ublicl~tions, 1 I--34. Rlartinich, 11. P . (ed.). 20O0. Tlir /Jlrr/osoplr,)~o/'i,rrng~rtrgc:,4th cdn. Oxf'orcl: Oxford University Prcss. &la!-, Robert. 1985. Lop.il.rr/ For/rr: Iis S/rvi.iurc lrrzrl Dcri~.tr/ron.C;arnhridgc, Mass.: M I T Press. hqilsark, Gary. 1977. Tornard an explanation of ccrtain peculiarities of tllc existenti;il construction in English. Lirig~~istir .-liicrllvis 3: 1-29. hliyara, Sl~insho. 1081. Complex Preclicatcs, C:asc XIizrhing and Scrambling in J;tyancsc. Ph.U. dissertation. University of ?Vlassachusetts, Amhcrst. klontague, Richard. 1970a. English ss a formal language. In B r ~ ~ nViscntini o 1.1 irl. (cds), Lingrrl~~gi r~cll~r Soc~'e/ric nc,/l~rTcc.irrtn, Milan: Erlizioni di (:omuniti, 180-224. Repr. in hlo11t;lguc 1074, 188--22 1. Montayue, Richard. 1970b. Universal grammar. Tllr~orirr 36: 3'73-98. Rcpr. in Alontaguc 1074, 222-46. hlonraguc, Richard. 1973. T h e proper rrcatmci~tof quantification in ortlinal*!. English. In I(.J. J. Mintihka. J . M. L. hioravusik, and P. Suppcs (eds), .ippioaclii~slo Nu/irr~(r/I , ~ I I I R I ~Dorilrccht: ~I~c>, D . Reidel, 221-42. Repr. in Alontague 1954, 247-70. hfontague, Richard. 1974. F o n ~ i r ~Plrilosopl~)~. I S'tkc./c~rlPapers .vI/'Ric~lrrrrlli \ 1 o t r / 1 1 ~ 1 t i cditcd ~, and u irh ;in introcluction by Richmoncl 13. Thoniason. New I-Iavcn, C:onn.: Yalc Uni\,crsity I'rcss.

Introduction 15 Ncrbonne, John. 1900. C:omputational scn~antics linguistics and processing. In Shalom T,i~ppin (ed.), Tlre H~irrr/l)ookr!/'Corr/enipoia~:)f .S~.rrrrrn/ir.T ~ I L ~ Oxford: ~ I : ) ~ , Hlack~vcll,401-84. Ncwmcycr, Fretlcrick. 1980. Lirigrrrsrl(~Tl7cor:)firr z-17~rrr.ir.~i: Tlie F11:rr Qnrir/er-Cr~~r/vr:)~ I!/' 7j.,rli.~/;)r.rrrlr/rorrul G P I I C ~ ( IG/ ~I I~~' C ~ ~ I NCMI I I ( IYork: ~ . 14cademic Press. I'arsons, Tcrcncc. 1972. An Outline of a Sanantics of English. Ms. thcsis, Lnivcrsit!! of h1assach~1sctts, Amherst. Partec, Barbara. 1073. Some transf'orniational ex~cnsionsot' Montaguc grammar. .?o~irnril I ! / ' Philosoplrinil Logic 2: 509-31. Repr. in Partee 1976, 5 1-76. Partce, Barbara. 197.5a. Comments on C . J. Fillmore's and N. C.hon~sk!;'s papers. In R. Austcrlitz (cd.), Tllr Scopr ( ! / ' , - ~ I N P I . ~ CLtr~guistit.~, ~I~ Lisse: Peter de Ridder Press, 197-209. Partec, Uarbara. l075b. Montaguc grammar and transformation;~l yrammar. I,ingiiis/ir 11rqii11:)l0: 203-300. Partec, Barbara (ect.). 1976. Monl(rfiiie Gn~nrtn(rr.Nccv York: A4cademicPress. Partce, Rurbara. 1984. Compositionality. In Fred Landman and Frank ITcltman (cds), I irrii,/res ( I / Forrtrrrl LSenrontrr~s, I~orclrccht:Foris, 281-312. Partcc, Harbara. 1987. Possible worlds in model-theoretic semantics: a linguistic perspective. In Sture A411en(ed.), P~tssihlc bbi)r/r/.~rrr Hlirnrirr ilits, ijr/s, (r irtl Sr,ier~r.~s. Proi.~rrlr~~gs I!/' oh^/ .5')~111posirii1i 0.7, ljcrlin: Wattcr clc Gru! ter, 93-123. Partcc, Barbara. 1986. Noun phrase intupretation and type-shifting principles. In J. Groencndijk, L). de Jongh, and M. Stokhof (cds), Srul1ie.r iir L ) I S I . ~ I I IR S Pr p w . ~ ~ ~ ~ r r irlreol:)' t i o ~ r rrrrrl 111t T I I I ~ o (!/' I:)~ G~rr~nrli:ci/ Q~rorr~!/ild'rr~, Dordrecht: roris, 115-43. Partcc, Harbara. 1996. T h e detelopment of formill semantics in linguistic theory. In Shalom 1,appin (cd.), Tlic, Hrrndl~~tok ~!/'C~ont~rrrpn~.rtr:)~ ,S~~nrrrn/ir. rlizor:)~,Oxford: Black\\-ell, 1 1-38. Pmtcc, Barbara, and Mats Rooth. 1983. Generalized conjunction ancl type ambiguity. In Raincr Biucrlc, Christoph Schwarzc, ancl Arnim von Stechoa (cds), Mnrairrx, Zlsr, r//i(lIn/erpr.i~tlr/irrrr01' Lri~rgurrp,Rcrtin: Wattel. dc Gruj-tcr, 361-83. Pvtcc, Barbara H. with Herman L. \V. Hendriks. 1997. Montague glamnlar. In Johan van R e ~ l t h c n ~ and Alice ter !vIeulen (eds), Hanr//)ook I ! / Logii. r r ~ r i / Lr~rrgutr~qe,.4mstcrctan1/C:arnbridgc, klass.: I
16 Introduction Stein, .Mark. 1981. Quantification in Thai. Ph.D. dissertation, Department of Linguistics, University of Massachusetts, hmherst (available from GLSA, UMass, L A i i i l ~ ~ r ~ t ) . Subrahmanyam, Ramesh. 1989. Scmantic interprctation in tree adjoining grammar. In Joyce Poncrs and Kenneth de Jong (cds), ESCOL 5: A-oc.et~clirrgsc!/'thi~5th E l ~ s t ~LS/n/es r ~ i Cou/iv-lwr.~ O I I Ll~~gujs~rrs, Columbus, Ohio: Ohio State University. Tarski, i2lfrcd. 1944. The semantic conception of' truth and the foundntions of scmantics. Philnsnph~~ unlf Pl~enom~~nokogrl~rrl' ResearcY~ 4: 341-75. Repr. in Martinich 2000. Tlion~ason,Richmond and Robert Stalnaher. 1973. A semantic theory of advcrhs. I;in~ll~.s/jc l n q i r r ~4:) ~ 195-220. L a n C y u ( ~ Arnsterclam y~. van Benthem, Johan and Alice ter Mculen (cds). 1997. H l ~ ~ ~ d h oofo k Clambridge, Mass.: Elsevier M I T Press. \-on Stechow, - h i m and Dieter Wunderlich (eds). 1991. Sarrrcrtr~iX*:Ein i r ~ ~ e r ~ r a ~ i o iH~ ~u l~r ~ s( ~ (Ier /JIu/I :.til~e?zir,sis~lzen Fonchuirg [Sew~antir.s:.An Itr/em(~tion~rl Hr~ndhook~ ? / ' C o t l / e ~ r ~ p oReserrr.~.lr]. mty Berlin: Walter de Gruyter. Webher, Ronnie. 1979. -4 For,nl~aI,4ppro(r~.hl o Disr.our:~e.41?(rphortr.New Yorh: Garland.

The Proper Treatment of Quantification in Ordinary English Richard Montague

The aim of this paper is to present ill a rigorous way the syntax and seniantics of a certain fragment of a certain dialect of English. For expository purposes the fragment has been made as simple and restricted as it can be while accommodating all the more puzzling cases of quantification and reference with which I am acquaintcd. 1 Patrick Suppes claims, in a paper prepared for the present \vorkshop [the 1970 Stanford Workshop on Graninlar and Semantics], that "at the presenr time the semantics of natural languages are less satisfactorily fbrmulated than the grammars ... [and] a complctc grammar for any significant fragment of natural language is yet to be written." This claim would ofcourse be accurate if restricted in its application to thc attempts emanating from the hlassachusetts Institute of Technology, but Fails to take into account the syntactic and semantic treatments proposed in Montague (1970a, b). T h u s the present paper cannot claim to present the first coinplete syntax (or grammar, in Suppes' terminology) and semantics for a significant fragment of natural language; and it is perhaps not inappropriate to sketch relations between the earlier proposals and the one given bcloiv. Montague (197Ob) contains a general theory of languages, their interpsetations, and the inducing of interpretations by translation. T h e treatment given below, as well as that in hlontague (1970a) and the trcatmcnt of a fragment of Cnglish proposed at the end of Montague (1970b), can all easily be construed as special cases of that general theory. T h e fragment in Montague (1970a) was considerably more restricted in scopc than those in Montagiie (l970b) or the present paper, in that although it admitted indirect discourse, it failed to accommodate a number of more con~plexintensional locutions, for instalice, those involving interz.sionn1 zrerhs (that is, verbs like seelts, worships, conceives). T h e fragment in Montague (1970b) did indeed include intensional verbs but excluded certain intensional locutions involving pronouns (for instance, the sentence John wishes to catch a fish and eat it, to which a number of linguists have recently drawn attention). The present treatment is capable of accounting for such examples, as well as a number of other heretofore unattempted puzzles, for instance, Professor Partee's t h e t e m p e r a t u r e is ninety b u t i t is rising and the problem of intensional prepositions. On the other hand, the present treatment, unlike that in Vontague (1970b), will not directly accommodate such sentences as J. M. E. hloravcsik's a unicorn a p p e a r s to be approaching,

18 Richard Montague in which an indefinite tern1 in subject positioi? would have a nonrcfercntial reading, bur must treat thein indirectly as paraphrases (of, in this casc, it a p p e a r s t h a t a unicorn is approaching or t h a t a uilicorn is approaching a p p e a r s to be true), On thcir common domain of' applicability the three treatments essentially agrce in the troth and entailment conditions imposed on sentences.' Further, when only LC/nr.athlr sentences come into consideration, it is the construction of such conditions that (Suppes notwithstanding) should count as the central concern of syntax and semantics.' Nevcstheless, the details of thc present development possess certain aesthetic merits, of coherence and corlccptual simplicitj-, not to bc found in the treatment of English in Montague ( 1 9'70b). (It is in ordcr to preserve these mcrits that I hcre hrgo il dircct account of such sentences as -Moravcik's.)

1 The Syntax of a Fragment of English Let P and r be two fixed objects (0 and 1, sax) that arc distinct and neither ordered pairs nor ordcred triples. Then Cot, or. the set of l.strgorlcs of English, is to bc the sinallcst set X such that (1) t. and t are in X , and (2) whenever ./I and B arc in X, :I/B and ..4//8 (that is, (0, A, B) and (l,.ii, B) respectively) arc also in ,Y. It should be pointed out that our categories are not sets of expressions but wili instead serve as inrl'icus of such sets. We regard r and I as the categories of entit) expressions (or individual ex;prcssions) and truth valuc expressions (or declarative sentences) respecti\-ely. Wc shall regard the categories A/B and .-I//B as playing tht same semantical but different syntactical I-oles.An cxpression of either category is to bt such that \\-hen it is cornbilled (in some as yet unspecified way, and indeed in differq n~aj-sfix the two categories) with an expression of category 3, an expl-ession of categor! A is produced. (The precise character of the categories l J / B and A//B is unimportant we require only two different kinds of ordered pair.) It will be observed that our syntactic categories diverge from those of Ajdukicwic: (1960) only in our intl-oduction of two compound categories ( d 4 / Band .Ll//B) whcrc Ajdukiewicz would have had just onc. T h c fiact that we necd only two copies is merel: an accident of English or perhaps of our limited hagmcnt; in connection with othc 4 languages it is quite conceivable that il larger number would be requircd. Keeping in mind the intuitive roles described above, we ma!. sin& o ~ as~ follofv t certain traditional syntactic categories.

IV, or the categorv of intransitive verb phrases, is to bc t/e. T , or the category of terms, is to be t/IV. TV, 01- thc category of transitive verb phrases, is to bc IV/T. IAV, or the category of IV-modifying adverbs, is to bc IV/IV. CN, or the category of common noun phrases, is to be t//c. T h c fi)llowil~gcategorics will also be exemplified in our fragment although no special symbol u-ill be introduced for them. t / t is the category of scntcnce-modifying adverbs. IAV/T is the category of IAV-making prcpositioi~s.

The Proper Treatment of Quantification 19 IV/t is the category of sentence-taking verb phrases. IV//IV is the category of IV-taking verb phrases.

By BA4is understood the set of bnsic c.sprt.ssions of the category A; the notion is characterized as follows.

BI\-= {run, walk, talk, rise, change) H..1 - {John, Mary, Bill, ninety, heo, h e l , hez, . . .) B,l-v= {find, Iose, eat, love, date, be, seek, conceive) BI.\\. = {rapidIy, slowIy, voIuntarily, allegedly) BC:h= { m a n , w o m a n , park, fish, pen, unicorn, price, t e m p e r a t u r e } B,:, = {necessarily) BIAI.p-= {in, a b o u t ) BIVlt= {believe t h a t , assert t h a t ) RI~~ll= l \ {try to, wish to) B,4 = L (that is, the empty set) if A is an; category other than those mentioned above. (In particular, thc sets B, of basic entity expressions and Bt of basic declarative sentences are empty .)

BY a bnsic e.t.p~eaionof the present fragment is understood a member of U-i,c,,,,13.1. BY PA is understood the set of phrases of the categorj- A. (We may read "Pc:n", "Pel,\"', and the like as "the set of common noun phrases", "the set of transitive verb phrases", and so on.) These sets are introduced, in a sense to be made precise below, by the following rules, S 1-S 17.

Syntactic rules S1. U 4 PA for every category A. S2. If i E PCN then Fo(<),Fl (i), Fl(<)t P-I., )

ivherc Fo([) = every <, F l ( i ) = t h e i, F2(<)is a ior a n [ according as the first \vord in itakes a or a n . wl~creF3,n(;94) = [ s u c h t h a t SO. If it and 4 E P,, then F3,,(i? 4) E 4'; and d)' comes from (j5 by replacing each occirrrence of he,, or him,, by

{ ) }:{ Fe

or

respectively according as the first B.:.

in

<

is of

neuter

2 E Ptjl\-and 6 E PI\, then F+('r,d) t Pr, where F+(a,d) = rh' and h' is the result of replacing the first wrb (i.e.; member of RlY, Brl.\, HI\./,, or B1\ in 6 by its third person singular present.

S4. If

20 Richard Montague

S5. If (5 E PIl /.I. and /IE PI., thcn F5(S,p) E PI\,, whcre P5(S,[I) = tSP it'P does not have the form he,, and Fs(fS, he,) = 6 him,,. S6. If d E PIrlvI,I'and /? E P.17, then F5(6,P) E PI,l\,. S5. If 6 E PI\ /, and E P,, then F6(ci,/3) E PIv, where F(,(cj,1,') = SP. 58. If 6 E and E PI\., then Fb(O,P ) E PI\;. S9. I f 6 E P,!, and /I E P,, then f.i,(S,P) E P,. S 10. If (S E Pli /n'and fi E PIV,thcn Fi(S, P ) E Ply, where F j ( 6 , /I) = Ph.

Sl I . If 4, Id/ E P,, then F8(4. $), F o ( ~$) , E P,, where F8(C),$) = rf, and !I/, F(,((I,,lI/) = 4)or $. S12. If:l,6 EP,\-, then rx(7j,(5),F9(;~,6)~ PI\-. S13. If 2,/I E Psi,, then FO(a, p) E Pvl..

S14. If x E PT and 4 E P,, then Flcl,,,(a,4) t P,, whcre citlicr (i) a does not have the form hel., and Flo,,,(a,4) comes from 4 by replacing the first occurrence of he,, or him,, by a and all other occurrences of he,, or him, by

}!F{ }::{ or

wspectively, i~ccordingas the gende~of t1.c

}

C

masc. first B~:. or B , in ~ a is {fern. , or neuter (ii) a = heLp, and Flo,,,(a,4) comes fioni ciJ by replacing all occurrences of he,, or him,, by hek,or himk respectively. S15. If a E Prr and i E PCN,then Flo, ,,(a,i)E PCN S16. If z E PT and 0 E Plv, then Fill, ,,(a,6) E Ply.

Rl~lesqf lense and si'qt~ S17. If a E PT and 6 E Ply, then TI (a, d), F12('%, O), F13(a,S), P14(a,d), F15(a,6 ) E P,, where: F1I (a, 0 ) = ah' and 6' is the result of replacing thc first verb in 6 by its negativc third person singular present; Flz(a,6) = adf' and 6" is the result of replacing thc first rcrb in 6 by its third person singular future; Flj(a,d) = adf'' and 6"' is the result of replacing the first verb in 6 by its negative third person singular Suture; FI4(a,8) = xd"" and dJfJfis the result of replacing the first verb in ;5 by its third person singular present perfect; and finally, F15(a,6) = aiS""' and 6""' is the result of replacing the first verb in 6 by its negative third person singular present perfect.

The Proper Treatment of Quantification 21 The precise characterization of the sets P,\, for '4 a category, is accon~plishedils follows. We first define the auxiliary notions occurring in the rules above in an obvious and rlrtir.lr tnkrtr traditional way: the R C I I ~ Cof~ an arbitrary member of BT U BCN,the ~rri/ third person si~~~qrrkrr presewt, the rhird person singulur % f b t u wthe , ncy(itiz1c t h i d penon si?~~qlllr~r firtrrve, the tizi)~ripersonsingukm presetat prt;fir.t, and thc n~>gntjzte tlijri/pcrsot~singrrlarpr~sc~n~ pfi;fict of an arbitrary verb. Then we may regard SlLS17 as constituting a sin~ultaneous inductive definition of the sets P:l. Since, however, inductive definitions of this form are somewhat unusual, it is perhaps in order to state a corresponding explicit definition: the sets P I (for A E Cat) arc the smallest sets satisfying SlLS17; that is to say, (P,l),E(;~,, is the unique fanlily of sets indexed by Cat such that (1) (PA)-4c(:,,satisfies S 1- -S17, and (2) whenecer (P\)A4,c,, is a family of sets indexed by Cat, if ( P i ) satisfies S 1--S17, then P,\ C P i for all A E Cat. (It is easily shown, using an idea I believe to have originated with Dr. Perry Smith, that there is exactly one family of sets satisfying these conditions.) By a rneirrzingfi~Ie.~pressionof the present fragment of English we may understand il member of any of the sets PA for A E Cat. As an example, let us sho~vthat every man loves a woman such that she Ioves h i m is a declarative sentence (that is, member of P,). By S1, love E P,rs and he,, E P.1.. Hence, by S5, love himo E Prv. Therefore, by S1 and S4, hel lovcs himr)E P,. Thus, by S I and S3, woman such that she love hin10 f Therefore, hy 52, a woman such that she loves himo E PT. Hence, by S1 and S5, love a woman such that she loves him* E PIv.Therefore, by S 1 and S4, heo loves a woman such that she loves himo E P,. Also, by S1 and S2, every m a n E P.1.; and hence, by S 14, every man Ioves a woman such that she loves h i m E P,. We nlay indicate the way in which this sentence has just been constructed by means of the following 1rnn1l1si.v trpee: every m a n loves a woman such that she loves him, 10, 0 every man, 0

/

man

he,, loves a woman such that she lovcs him,,, 4

/

love a woman such that she loves him,,, 5

I

woman such that she lovcs him,,, 3, 1 woman love him,,, A

love

22 Richard Montague T o each node we attach a meaningful expression, together, in casc that expression is not basic, tvith the index of that structural operation among I;;,-fi, F3,0,F3, 1, . . . , P4-F9, rlo, o, Flo,1 , . . . ,F1I - F 1 5 (as characterized above, within S l -51.7) which we understand as having been applied in obtaining the expression in question; thc nodes dominated by an? node are to be occupied by the expressions to which the structural operation is uilderstood as having been applied in obtaining the expression occupying the superior nodc. (For example, the nunlbers 10,0 attached to the top node of the tree above indicate that thc expression attached to that node is regarded as the value of the operation as applied to certain arguments; and the nodes beneath indicate that thosc arguments are understood to be the expressions every man and heclloves a woman such that she loves himcl.)A precise characterization of an ~ i ~ ~ n / ) 1rue ~ s i sin the sense of these remarks \vould be routine and will not be given hcre; for such a characterization in an analogous content the reader might consult A4ontague (1970a). Now there are other ways of constructing the sentence under consideration, and hence other analysis trees for it; indeed, it can be shown that eyer? declarati~csentence of our fragment has infinitely many analysis trecs. But in the case considered, the various analysis will differ only inessentially; that is to say, they will all lead to the same scmantical rcsults. There arc other cases, however, of which this cannot be said. 17or instance, thc sentence

rlr,,o

John seeks a unicorn has two essentially different analyses, representcd by the following two trecs:

Tohn sceks a unicorn, 4

4 seek a unicorn, 5

Tohn

a unicorn, 2

seek

I

I

unicorn John seeks a unicorn, 10, 0 /

au

n

I

i

unicorn

c

c

him,,, 4

>eks

A seck him,,, 5

John

A

seek he,,

As we shall see, the first of these trees corresponds to the c/e diltilo (or nonrefcrential) reading of the sentence, and the second to the de re (or referential) reading. Thus our fragment admits genuinely (that is, scmanticallp) ambiguous sentences. If' it were desired to construct a corresponding unambiguous language, it ~vouldbc convcnient to take the analysis trees themselves as the exprcssions of that language; it

,

The Proper Treatment of Quantification

23

would then be obvious how to characterizc (in keeping with MIontague (1970b)) the structural operations of that language and the correspondence relation betneen its expressions and those of ordinary English.' For present purposes, houever, no such construction is neccssary .

2 Intensional Logic We could (as in Montague ( 1970a)) in trod uce the senlan tics of our fragment dircctl j.; but it is probably more perspicuous to proceed indirectly, by ( 1 ) setting up a certain simple artificial language, that of tensed intensional logic, (2) giving the sen~anticsof that language, and (3) interpreting English indirectlj- by showin%in a rigorous way how to translate it into the artificial language. l h i s is the procedure we shall aclopt; accordingly, I shall now present the syntax and semantics of a tensed variant of the intensional logic 1 have discussed on earlier occasions." Let s be a fixed object (2, say) distinct from P and r and not an ordered pair or triplc. The ljyc, or the set of (Ipes, is the smallest set Y such that (1) e,l t Y, (2) whenever cl,h E E',( ~ i , bt ) Y , and (3) whenever a E Y, ( s , ~ E) Y. Uic shall employ denumerably many variables and infinitely many constants of each t y e . In particular, if n is any natural number and a F Type, wc understand hy I),,~,, the ,rr" I-arinblc of type o, and by Con,, the set of constants of type o. (The prccisc cardinality of Coti, need not concern us, providcd only that it hc infinite.) By ME,, is understood the set of metrnin'q-fillr.~pressio?isof type I r ; this notion has the following recursive definition:

1 Evcry variable and constant of type is in NIE,. 2 If a E hlE,, and u is a variable of type 6, then i,rrx E ME(hl,,). 3 If x E and p f hk,, then a@) t ME,,. 4 l f a , / j ME;,, then a = j? E 1\4L<,. !. If Si,,~,!iE ME, and z.r is a variable, then ]4,Irl,r,$J,[&v1[/~l,I~/) 11/.1,[(1) t) 1/11) V nq!!,A u 4 , Oq5, lV41,H4 E ME,. 6 If % E MEI,, then [^lr;l E ME!,,,,. 7 If a E ME(,,,,:, then ['a1 E ME,,. 8 Nothing is in any set ME,, except as required by 1-7.'

-

By a nr~~unit~gfi~l e-~plussiclr~ of intensional logic is understood a member of C]ilE7'i#pr, A,IJ<(,. If l i is a variable of type n , then i u o l is understood as denoting that function f1.0111 objects of type N \vl~ichtakes as value, for any such object s, the object denoted bv x nhcn u is understood as denoting .r. T h e expression %(I$) is as usual understood as daloting the value of thc function denoted by a for the arguinent denoted by /I. The equalit!- spil~bol=, the negation synlbol 1,the conjunction symbol 11, thc disjunction s! mbol v, the conditional symbol +, the biconditional symbol ++,the existential quantifier V, and the universal quantilier A are all understood in the usual way. Tllc symbols 0 , Pt', H mily be read "it is necessar! that," "it will be the case that," "it has been the case that," respectively. T h c expression ["a] is regarded as dcnoting (or

24 Richard Montague having as its extension) the I'nln~sionof the expression a. T h e expression ['nJ is meaningful only if a is an expression that denotes an intension or sense; in such a. case ['a] denotes the corresponding extension. We could have donc with a nluch smaller stock of primitive symbols, as in Montague (1970b); but there is no point in considering here the relevant rcductions. In the presentation of actual expressions of intensional logic square brackets will sometimes for pcrspicuity be omitted, and sometiines gratuitously inserted. Let A, 1,J be any sets, which we may for the moment regard ns the set of entities (or individualsx), the set of possible worlds, and the set of moments of time respectively. In addition, let cr. be a type. Then Dl,, , 1 7, or the set of possibkt clenotarions of type a corresponding to A, I,J, may be introduced by the following recursive definition. (If X and Y are any sets, thcn as usual we understand by X' the set of all fu~lctionswith prolllllc~of X and Y (that is, the domain Y and valucs in X, and by ,Y x Y the C(~r/i~silz~~ set of all ordered pairs (x,.)/) such that ,v f X and , ) I E Y). Further, we identify thc truth values falsehood and truth with the numbers 0 and 1 respectively.) %.

U y S,,,,,~,I, J , or the set of senses of type a corresponding to A, I , .7; is understood D;.,,,),.I, r , , ~ that . is, D!:.;)!,!,~. By an interpretation (or intensional model) is understood a quintuple (-4, I,.j', ,I.') such that (1) -4, I , J arc nonempty sets, (2) 5 is a simple (that is, linear) ordering having J as its field, (3) F is a function having as its domain the set of all constants, and (4) whenever n E Type and a E Con,, F ( r ) E S,,, , , J , J . Suppose that A is an interpretation having the for111 (..4, I , J , , F). Suppose also (of values to variables), that is, a function having as its donlain that p is a n A-ns.sig,tz~r~ent the set of all variables and such that g(tr) E D,,, r,r,g w-henever 11 is a variablc of tj-pe [ I . If a is a rncaninpful expression, we shaIl understand by xA,,: the i n ~ ~ n s i o rofr a with respect to A and g; and if (i,,,) E I x J thcn rA*'?l,Lis to be the ~>.r/~vr~io~, of rr with respect to A, i , l , and g-that is, aA,'((i,.j)) or the function value of the intension of '2whcn applied to the point of referenec (i,j ) . Thesc notions may be introduced by the f'ollowing- recursive definition.

<

<

1 If x is a constant, then is r(,x). is g(n). 2 If r is a variable, then nA?J)lr,c 3 If n E ME, and u is a variithle of type b, thcn [halAy'?-''5sthat function /I with domain Dh, ~ , I , -such J that whenever s is in that domain, h ( x ) is & ~ ' ~ f where ) ~ ' , g' is the A-assignment like g except for the possible difference thilt $ ( u ) is .v. 4 If a E M E , , , , and /I E ME,,, then [ X ( ~ ) ] ~ is) ' ~ J ~ ~ ~ (that is, the value of the function aAli,~7"for the argument /jA,',/)'), 5 i f u,/3 E ME,,, then [a = is 1 if and only if a A ~ ' ~is/ , ~ e h If Q, E ME,, then J / ~ ] ~ * ' ) . ' ) %1s if and only if gA7'7'7^ is 0; and similarly for A,b,

+

, w.

The Proper Treatment of Quantification 25

9 If 4 t ME, and rr is a variable of type a, then [ ~ s q 5 ] ~ ? ' 7is~ 1, , ' if and only if thcrc exists r. t D,,,-J,J,.J such that 4A7'*'7i is 1, where g' is as in 3; and sirnibrlg fi)r

a

e

Aucb. 8 If d) E ME,, then [ ~ d ] ~ ~ ' " ) " sI if and only if c,!?7").i'7" is 1 for all 1' E I and j t -7;' 1I V J ~~ * ' , ~is, v1 if and only if ' 3 " 7 ~1sfor some j' such that .j j'; and j # j'; and [ H + ] ~ , ' , J is , L 1 if and only if q"A7'71'7ris 1 for some I' such that j' j and./' # . j . - ' ~ "lo 9 If a E ME,,, then [ ^ x ] ~ ~ 'is~ xA,f. 10 If C( E ME(,,,/),then ["a l A ~ ' ~ ' . y is ~ ~ ~ ~ ' ~ j ~ ~ ( i , , j ) ) .

<

n

<

I1

h e e

If $ is a/i,mruln (that is, member of ME,), then 4 is rrur with respect to A, i , j if mrl only if q5A)i,i,ris I for every A-assignment g. It will be useful to call attention to some particular meaningful expressions of intensional logic. If 11E MEi,,,) and a E h,fE,,, then denotes (that is, has as its estension) a set (or really the characteristic function of a set) of objccts of type a, and we may regard the formula ;'((Y),which denotes truth exactly in case the object dcnoted by r is a mcinber of that set, as assertir~gthat the object denoted by a is a mcinbel- of the set dcnoted by 11.If y E MEi,, (by,) ) ) cz E ME,,, and t ME,,, thcn may be regardcd ~LSdenoting a (two-place) rclntion, and ;?(by a) is to be the expression ;l(r)(fi), which asserts that the objects dcnoted by- /I and x stanif in that relation. If 7 E ME:(,, : and r E ME,; thcn ;: denotes a prfiperty, and y{a) is to bc the expression I'll](a), which asserts that thc object denoted b y r has that pnjperty. If 1. E ME(, (,,, (,,,,) i , n E ME, and (1' E ME,,, then y may be regarded as denoting a rtl~ltion-in-i?lteiuion,and ;I{/$,a$ is to bc the exprcssion [':.](P, a), ~vhichasserts that the objects denoted hg /I imcl n stand in that relation. If tr is a variable of type (1 and 4 a formula then licl, is to bc i.1~14, which denotes the set of all objects of type n that satisfy 6 (with respect to the place rnt~rkedb~ a), and u$ is to be ( iiq!~],which denotes the property of' objects of type a cxprcsscd by (/I. If r E IME,, then a* is to be P f P { n 8 ~ )wherc ], P is r?,, i,,(;, ,a ;I

;I

) )

n

)

r )

,.

3 Translating English into Intensional Logic We first introduce a mapping J from the categories of English to the types of intensional logic. Accordingly, f is to be a function having Cat as its donlain and such that ~ ' ( L= J )e, = L,

l'(if/B) = .[(il//B) = ((s,.[(B)) ,./'(A))whenever A, B E Cat. The intention is that English expressions of any category A arc to translate into expressions of type .Kg/. In all that follows let g be a fixed biunique function such that ( 1 ) the domain ofg is the set of basic expressions of our fragment of English other than be, necessarily, and the members of Br, and (2) whenever .4 E CLU,a E B.,, and r/. is in the domain of g, ~ ( x E) C O ? ! ~ (Let . ~ )j,. m, 6, ?I be particular distinct members of Con,.. (If u-e had

''

26 Richard Montague introduced a definite well-ordering of the constants of intensional logic, we could at this point have explicitly defined g, j, m, h, and r1. Such details would, however, be irrelevant to our present concerns.) Let 21, u be the particular individual wariablcs ~ 0r ,, r l l , ,, respectively; r, y, x,, be the particular individual-concept variables ol,.(., ,,), 03, (s, l,!, 112~, ,( ), respecti~ely(for any natural number n); p be the proposition variable 110,(,., /:;; P, Q b e the variables uo, is, 1, 111, i(s,l,),,) ), which range over properties of individual concepts; 3 be the variable vo,,,( ( (, 1 (, ,), ,) !,,) i , which ranges over propertics of properties of individual concept; M be the variable t)O, (,, (,,,,)), which ranges over properties of individuals; S be the variable oo, (, (,,(,, ,)) ), which ranges over two-place relations-in-intension between individuals; and G be the variable "0, (,, (r,,.u1 1 )) ) . VCTc shall now consider some rules of translation, TlLT17, which will be seen to col-respond to the syntactic rules S 1-S 17 respcctively and to constitute, in a sense to be made precise below, a definition of the translation relation. (,$,

Translation rules Basic rules TI. (a) If x is in the domain of g, then translates into g(a). (b) be translates into i3;1x3{,jl['s = : ) I ) ) . (c) necessarily translates into j l ' p ] . (d) John, Mary, BilI, ninety translate into,;", ni", h", rtQ respectively. ( e ) he,, translates into P P{x,,}. T2. If [ E PCN and i translatcs into [I, thcn every i translates into PA .Y[['(.v) -t P{x)], the i translates into PV,y[A .\.I ['(.z.) -i s = ,111 n P{.y) I, F2(<) translates into P V rl it(s) P{L~).l. TR. If*i t PcN, Q E P,, imd (, Q translate into i t , (bt respectivcly, tllen fi,,,(i, g)) A

A

A

A

translates into .?,,[('(s,,A)4 f 1. 12

Rules qf :firncriorzal application T4.

If 6 E P,,iIy, fi E Ply, and 6, fl translate into h', /I'respectively, then F+((>,P)

translates into 6'("13'). T5. If 0 E PI\;-I., /I E PVr-,and (5, fi translate into (5') /I' rcspccti\lel!-, then P5(6,li) tr;lnslates into St('[?). rcspectivelv, thcn F5(S,Ij) T6. If 6 E PIliv/,I.,/3 E P.I., and 6, /j translate into (it, /I' translates into hl("P'). T7. If 6 E Plvi,, /iE P,, and 6, fl translate into 6')fit respectivelj, thcn F,((j,/l) translates into 6'("pf). TX. I f S E PIv//Iv,11 E PI\^, and 6, /) translatcs into 6'. [I' respectivcly, then F'(,((j,/j) trinslales into 8'("/1'). T9. If 6 E I?,/,, P E P,, and 5, [j translatcs into 6', [j' respecti\elj*, then Fb(6,/i) translates into S 1 ( ^ / j ' ) . TIO. If 6 t PIv,qv, E P I \ , and 6, /I translatcs into (5'. B' respcctively, then F7(0, fi) rans slates into 6'(A/1').

The Proper Treatment of Quantification 27

S 7

e

f s r C

If ( j , t,b E P, and 6 , ~,btranslate into gh', $' respectively, then cf, and I/! translates into [4 A $1, (/, or !,/I translates into [$ v $1. T12. If ;!, (5 E PTvand 71, (5 tra~lslatesinto I?', S' respectively, thcn ;' and 6 translates into .i.kf(.v) A df(s)l,;> or 6 translates into F[-)"(x) fit(x)]. T13. If a, /Ic P r l - and x,3!, translate into x', P' respectively, then or [l translates into i [ d ( v~[I'P ) j].

T11.

\/

1

Rules qf'yua~trJii.aiion 1'14. If a E P.l., d) t P,, and n, 4 translate into a', (11' sespectirely, then Pl0,,,(n,(1)) translates into a'(.?,, (/I/). T15. If a t PT, [ E PC;\,and n, i translate into n', i'respectively, then Flll,,,(r,i) translates into ?,),x'(.i',,[<'(5~)]). 1 1 If y. E Prl., 6 E PI\, and n, A translate into r',6' respectirely, then Flu,,,(n,li) translates into jla'(.~,,[6'(y)l).

Rules

uf'tpi?sr 111111 ~ i g n

1'1 7. If x E Prr.,ci t PlV,and x, S translate into a', Fl (a, 6) translatcs into /a'(^~5~), F1?(a, 0 ) translates into ~ r x ' ( ~ b ' ) , F 13('x,b) translates into / C'C'CX'(' S'), F14(a,6 ) translates into ~ x ' ( ^ h ' j , F1;('%,6) translates into ]13a'(^b1).

1

1

1

1

1

cj'

rcspectivcl\i, thcn

'l'he precise import of the rules T1-TI7 is that the translation relation nlay be defined as thc smallest binary rclation satisfying them; that is to say, an cxpressioo is characterized as tmnslrrting into an expression 4' if the pair {(b, 4') is a membcr of cvcrybinarv relation R such that T1-TI7 hold (with the condition that one expression translates into another replaced by the condition that the rclation R holds between thc tno expressions). The translati011 relation is of course not a function; a meaningful expression of' English may translate into several different expressions of intensional logic. We could, however, speak of rhr 1ra~ulntior7of a given meaningful cxyression of English corrcsponding to any given analysis trce for that expression; the rathcr obvious definition of this notion will be omitted Ilere. The interpretations of intensional logic may, by way of the translation relation, be made to play a second role as interpretations of ~ n g l i s h . ' " Not all interpretations of intensional logic, however, would bc reasonable candidates for interpretations of English. In particular, it would be reasonable in this coi~tcxtto restrict attention to those interpretations of intensional logic in which the following formulas are true (uith respect to all, or equivalently some, worlds and momcnts of time):

28 Richard Montague

1 2 3

4

5 6 7 8

9

V I ~ O I I= I a], where x isJ, rrr, 6, or n, 0[6(.v) 4 Vu.v = ^ u ] , where d translates any member of RCh other than price or temperature, VII/IAw~-O [6(.~) M { " s ) ] ,where 6 translates any-member of ElIb other than rise or change, V.S'A.t.A3Ol6(.r, 3) ++ 3{jS{'s, :)!)}I, where 6 translates find, lose, eat, love, o r date, A3VAMAvrO[d(s, 3) rl4{',x')], where 6 translates seek or conceive, A PV-hfA.rO[G(r,p) * hl{'s)J,where b translates believe t h a t or assert that, A PVMAL~OIG(x, P ) * IZZ{'x}J, where 6 translates t r y t o or wish to, VGA3A QAv~r0[6(3)(Q)(x) 3{,j~[['G](".)1)(Q)(.r)1) J, where 6 translates in, q IseekJ(x,3) try-to' (.v,^[findJ(3)])], where seek', try-to', find' translate seek, t r y to, find respectively.

-

-

-

T h e truth of (1) guarantees that proper nouns rill be "logically dcterminate" according to the interpretations under eonsidcration, that is, will have extensions invariant with respect to possible worlds and moments of time. In view of ( 2 ) , "ordinary" common nouns (for example, horse) will denote sets of COMS~CIIIIindividual concepts (for example, the set of constant functions on woslds and moments having horses as their values; from an intuitive viewpoint, this is no different from the set of horses). It would be unacceptable to impose this condition on such ''extraordinary)' common nouns as price or t e m p e r a t u r e ; the individual concepts in their extensions would in the most natural cases be fi~nctionswhose values vary with their temporal arguments. T h e truth of (3) is the natural requirement of e.v/ensionalitll for intransitive verbs, that of (4) the condition of extensionality (or extensional first-order reducibility) for transitive verbs, and that of (8) the condition of extensionality (or estel~sionalfirstorder reducibility) for prepositions. T h e intrnsionul (or nonextensional) transitive verbs seek and conceive, as well as the verbs believe t h a t , assert: t h a t , t r y to, wish to of other categories, are nevertheless extensional i~~it/l Y L ( S ~ t~oC sllly'ect ~ posilion, and this is expressed by imposing conditions (5)-(7). Condition (9) is thc natural definition of seek as t r y t o find. Several notions of a logically possible interpretation map reasonably come into consideration, depending on whether, and if so how m a n s conditions analogous to (1)-(9), stemming from our intended system of translation, are to be imposed. For prescnt purposes we may perhaps resol\-e the matter as follows: by a /ogical/y possihlr in&erpreratlonunderstand an interpretation of intensional logic in which fornlulas (1)(9) are true (with respect to all worlds and moments of time). Logical truth, logical consequence, and logical equivalence, for formulas of intensional logic, arc to be characterized accordingly. For instance, a formula cj, of intc~lsionallogic is construed as Iogi~.flytrue if it is true in every logically possible interpretation, with respect t o all worlds and moments of time of that interpretation; and two formulas cj, and II/ ol' intensional logic are logic all)^ cyuicalr~ztif and only if the biconditional rkl is logically true. If 6 is an expression of intensional logic of such type as to translate il transitive or intransitive verb, then 6% is to be an expression designating the set of individuals or reliltion between individuals that n a t u ~ l l ycorresponds to the set or relation designated

-

The Proper Treatment of Quantification 29

r r r

:

' 1

; i

hy S. In particular, if S E then S r is to be the expression iiS(lAu]); and if 6 E ME/.(,l.Vl,then 6% is to be iuGG(lAu],[*v*]). Notice that since J'(C:N) = J'(IV), this characterization is also applicable in the case in which 6 translates a common noun. It is a consequence of principles ( 2 ) , (3), (4) that if 6 is among the constants involved in those principles (that is, constants translating "ordinary" common nouns or "extcnsional" transitii-e or intransitive verbs), then 6 is definable in terms of cS%. 12.lorc exactly, the following formulas are logically true: IJ[6(s) * SS('.V)],ifh translates any membcr of Hc5 or RIJ. other than price, t c m perature, rise, or change; IJ[h(x, 3) ++ 3{.1;6s(".v,:y))l, if 0 translates any menlber of other than seek or conceive. Hrl-~-

Notice that although the verb b e (or its translation) is not covered by principle (4), it is by the Iast principle above. T h e reason why the extensionality of be was not cxplicitl\assumed is that it can be proved. (A4ore precisely, the analoguc of (4) in u-hich 0 is the expression translating b e is true in a11 interpretations (with respect to all worlds and moments).)

4 Examples I

;

' i

I I

-

:

1

I

'

Thc virtues of the present treatment can perhaps best he appreciated by considering ~xuticularEnglish sentences and the preciseIy interpreted sentences of intensional logic that translate them. I shall give a list of such examples. It is understood that each English scntcnce listed below translates into some formula logically equivalent to each of the onc or more formulas of intensional logic listed with it, and that every formula into svhich thc English sentence translates is logica11~-equivalent to one of those formulas. It should be emphasized that this is not a matter of vaguc intuition, as in elementary logic courscs, but an assertion to wrhich nrc have assigned exact significance in preceding sections and which can be rigorously prinwl. (The constants of intensional logic that translate various basic expressions of English at-c designated beloii~hy primed variants of those expressions.) The first five exan~plesindicate that in simple extensional cascs symbolizations of the expected forms are obtained.

Bill waIks : walk; (b) a man walks : V~r[mani,(u) n walki(u)] every m a n walks : Au[mank(u) + walkk(u)] the m a n walks : Vv{Au [[mani(u) u = I!] P, walli;(u)] John finds a unicorn : Va [unicorn;(u) n find:(.j, u)]

-

The next sentence, though superficially like thc last, is ambiguous and has two essentially different sy-n~holizationscorresponding to the two analysis trees prescntccf above; thc first gives the AP dicto reading; and the second thc cjc re.

30 Richard Montague John seeks a unicorn :

seek'(:j, ~ ~ u [ u n i c o r n k (neP{^a}I) ) Vu[unicorni(rl) n seekk(j, r,)]

T h e source of the ambiguity of John seeks a unicorn will perhaps be clarified if cvc compare that sentence with thc intuitively sgnonymous John tries t o find a unicorn, which contains no intensional verbs but only the extensional verb find and the "higher-order" verb try to. Here, though perhaps not in John seeks a unicorn, the an~biguitpis clearlq- a matter of scope, and indcccl depends on the possibility of regarding either the conlponcnt find a unicorn or the whole sentence as thc scope of the enistcntial quantification indicated by a unicorn. John tries t o find a u n i c o r n :

try-tot(;j,. j!~lr[unicorn&(u) n findL(Iy, LI)II) Vu[unicornL(rr) A try-tof('j,.i; /I))]

It might be suggested, as in Quine (1960) or Moiltague (1 969), that intensional verbs be allow~edonly as paraphrases of more tractable locutions (such us try t o find).14 Such a proposal, how-ever, would not be naturally applicable, for uant of a paraphrase, to such intcilsional verbs as conceive and such iiitcnsional prepositions as about; and I regard it as one of the principal virtues of the present treatment, as well as the one in Montague (1970b), that it enables us to deal directly with intcnsional locutions. The next cxample accordingly concerns a b o u t and gives us, as intuition demands, one rcading of John talks a b o u t a unicorn that does not entail that tlierc are unicorns. John talks a b o u t a u n i c o r n :

C

aboutf(~Vulunicorn:(,r) n P( ' u } l)('talkl)(''j) Vz~lunicornk(u)n about'(^rr*)(^talkf)(:j) I

T h e next two examples indicate that our uniform symbolixation of b e will adequately cover both the is of identity and the i s of predication; views along this linc, though not the rather complicated analysis of be given here, may be found in (&line (1960). Bill i s M a r y : h = rn Bill i s a Inan : manL(6) T h c next few exainplcs concern an interesting pi~zzledue to 13arl)nr~Hall I'artcc in\-olving a ltind of intensionality not previously ohscr\,cd bq philosophers. From thc ~x-emisest h e t e m p e r a t u r e is ninety and t h e t e m p e r a t u r e rises, the conclusion ninery rises would appear to follow bj- normal principles of logic; yet thcrc are occasions on which both premises are true, but none on which the conclusion is. .According to the following symbolizations, ho~vcvcr,the argument in question turns out not to be valid. (Tlze reason, speaking very loosely, is this. T h e t e m p e r a t u r e "denotes" an iildividual concept, not an individual; i111d rise, utllikc most vcrhs, depends for its applicability on the full behavior of individual concepts, not just on their extensions n-ith respect to the actual worltl and (what is more relevant herc)

The Proper Treatment of Quantification 31 moment of time. Yet the scntencc t h e t e m p e r a t u r e is ninety asserts the identity not of two individual concepts but only of' their exteasions.) the temperature is ninety : V.),[A x[temperaturel(s) ++ .Y = ,111 I, [:I/] = t? I the temperature rises : V,Y[{A x[temperaturel(,r) ++w = A risel(y)l ninety rises : rise'(*n) We thus see thc virtue of having intransitive verbs and common nouns dcnotc sets of individual concepts rather than sets of indil-iduals - a consequence of our general development that might at first appear awkward and unnatural. It would be possible to treat the Partee argument itself without introducing this feature, but not certain analogous arguments involving indefinite rather than definite terms. Notice, for instance, that a price rises and every price i s a n u m b e r must not be allowcd to entail a number rises. Indccd they do not according to our treatment; to scc this, perhaps it is enough to consider the first premise, which, unlike a m a n waIks, requires individual-concept variables (and not simply individual variables) for its symbolization. a price rises :{V.r[price'(.r) A rise' (s)]

The next example shows that ambiguity can arise even when therc is no clcmcnt of' intensionality, simply because quantifying terms may be introduced in more than one ordcr.

-

V I ~ [ W O ~ ~ A~Av[manL(r~) ;(U) lovek(u, u)11

woman loves every m a n :

Au[rnank(o)

+

Vu[womank(u) A lovek(u, v)] 1

The next example indicates the necessity of allowing verb phrascs as well as sentences to be conjoined and quantified. Without such provisions the scntencc John wishes t o find a unicorn a n d e a t it \vould (unacceptably, as scvcral linguists have pointed out in connection with parallel examples) have only a "rcf'crential" reading, thal is, one that entails that there are ilnicorns. John wishes t o find a unicorn a n d e a t it : vu[unicorn:(u) A wish-tol(i,,~[findk("j~, u) n eat;(>:

s)l)l

'The next example is somewhat simpler, in that it docs not involvc conjoining or quantifying verb phrascs; but it also illustrates the possibility of a nonrcferential rcading in the prcsence of a pronoun.

Mary believes t h a t John finds a unicorn a n d h e e a t s i t : ( ~n[unicorn:(u) n believe-thatl(^m, ^[find:(j, u ) A eat;(.j, u)])]

32 Richard Montague O n the other hand, in each of the following examples only one reading is possible, and that the referential: (1) John seeks a unicorn a n d M a r y seeks it, (2) John tries t o find a unicorn a n d wishes t o eat it, ~u[unicorn:(u) A try-to'(:j,.l; [find:(:)/, N) . I r, wish-tof(:j,.l; (Ieata ( ' ' J , u )J)I This is, according to my intuitions (and, if I guess corrcctly from ren-rarks in Partcc (1970), those of Barbara Partee as well), as it should be; but David Kaplan would differ, at least as to (2). Let him, however, and those who might sympathizc with him consider the following variant of (2) and attempt to make nonrefcrontial sense of it:

(2') John wishes t o find a unicorn a n d tries t o eat it. Of course there arc other uses of pronouns than the ones treated in this paper - for instance, their use as what have been called in Geach (1962, 1967) and Partee (1970) pr/)11otm.s u ~ ' ~ ~ ~ z ~ ? zthat P s . sis, , as "standing for" longer terms bearing a somewhat indcfinite relation to other expressions in the sentence in question (or preceding sentenccs within the discourse in question). For instance, it is not impossible to construe it in (2) as standing for t h e unicorn h e finds (that is, the unicorn s u c h that h e finds it), a unicorn he finds, or every unicorn he finds, and in this way to obtain a nonreferential reading of that sentence; but this is not a reading with which David Kaplan would be content.

Notes Much of' the content reported here was supported by Unitcd States National Science k'oundation Grant GS-2785. 1 am indebted to Mr. Michael Bcnnett. Mr. Harry Dcutsch, and Mr. Daniel Gallin for helpfi~lcomments.

1

The mediekal ant1 twentieth-century philosophical literature has pointcd out a nun~berof such difticultics, most of them involving so-called intensional contexts. I am indebted to 13arbalu Hall Partec for pointing out others, both in conversation and in her provocative paper IJartee (1970). (This remark should not, hon-ever, be takcn as implying aprccment with a l l of Professor Partce's conclusions.) 2 iVit11 the exception that in Monraguc (1970b) a numhcr of intuitively pl;iusihlc arnbiguitics &ere for simplicity ruled out. 3 In connection with imperatives and interrogatives truth and entailment conditions arc of course inappropriate, and would be replaccd by fulfilment conditions and n characterization of the semantic content of a correct answer. 4 It was perhaps the failure to pursue the possibilit! of s~ntacticallysplitting categories originally conceivetl in semantic terms that accounts for the fact th;it Ajduliicnicz's pl-oposals have not previousl!: led to a successful s3ntas. They have, ho~vcver,been cmploycd semantically in Mon~aguc(1970a) and, in a modified version, in 1,en.i~(1970). 5 This tva! of constructing ;In underlying unan~biguousIangui~ge,though convcnicnt here, nrould I)c unsuitable in connection with fragments of natural language eshibiting greater syntactical complcsitics of certain sorts.

The Proper Treatment of Quantification 33 0

7

8

9 10

In particular, in talks belore the Southern California 1,ogic C:olloqui~~n~ and the Association li)r Sjnlbolic Logic in April and May of 1969, and in the paper hlontiague (1970b). The :lddition of tenses is rather routine in the light of tlie discussion in Montaguc (1908); and it would he possible to replace the tensc operators by prcdicatcs. thus prescrring exactly tlie language in Montague (1970b), in the manner indicatcd in Montaguc (1970~). Clause (8) is of course vague but can be elinlinated in a familiar way. T o bc exact, the recursi\c definition given above can be replaced by the following explicit definition: ME,, is the set of all objects x such that xRc7, whcrc R is the smallest relation such that clauses (1)-(7) hold (wit11 all parts of the form " p E ME,," replaced by "BRn"). Or possible individuals. If there are individuals that are only possible but not actual, .-l is to contain them; but this is an issue on which it would be unethical for me as a logician (or linguist or grammarian or semanticist, for that matter) to take a stand. [Richmond H. Thomason's note: EIcrc, is interpreted in the sense of "necessarily always."] [Richmond 11. Thomason's note: T h e form of this delinition is not quite correct, since (xA>"s undefined when x is not a conslant. But thc intention is clear; what is to be defined recursively is a A l ! ~ / Clauses ~? (1) and (0) should bc rcviscd to read as follows. s (1) I f r is a constant then r A l ' . l * ~F(x)((i,j)). If Q f ME,, then [-ajA.'>i-x is that function h with domain I x 3 such that whcnever (9) ( i ~ )E I x -7, h((i,,;)) = x A ~ ' ~ l ~ ~ q . The irr/~>nvon xAl!: of a rclativc to A and g is then defined explici~ly: ~ ~ 9 " sthat function Ir with domain I x 3 such that whencvcr (i,.j) E I x 3.Ir((i,,)} = a A ~ ' ~ / l ~ . It then follows as a corollar!l that [Aa]A11317x = xA'? for all (i,j) E I x 3.1

11 The simplicity and uniformity of the present correspondence stands in rcmal.kable contrast to the rill hor character of the type assignment in Montaguc (1970b). 12 [Richmond H. Thomason's note: T o avoit1 collision of varinhles, the translation must be ,i,,j[~'(,v,,l) ,I $1, u-here $ is the result of replacing all occurrences of .v, in cp' by occurrcnccs of .r,,,, wlicrc rn is the least even number such that s,,,has no occurrcnccs in either or (p'.] 13 Alternatives arc possible. For instance, we could instead consider cliwc.1 interpretations of lcnglish induced by interprcvations of intensional logic in conjunction with our translation procedure; the yrccisc gcncral construction is given in Montaguc (1970b). Though this would probably bc the best approach from a general viewpoint, it would introduce slight conlplications that need not be considered in thc present paper. 1-1 Strictly speaking, this ~vouldmean, within tlie fran1cnrol.h of the prescnt paper, introducing ;I syntactic operation r such that, for example, F (John tries to find a unicorn) = Jolin seeks a unicorn, a syntactic rule to the effect that F ( 4 ) t P, whene\-cr Ci, E l',, and a corrcspon~ling translation rille that whenever Q, E P, and 4 translates into (,/I F((/))trallslatcs into cl,'.

c'

Notes 9, 10, and 12 are reprocluced by pcrnlission of Yale University I'ress from Richard klontaguo, Fornlai Pliilosopl~~)~. .Stier.~erlPoprrs (!/Riiknid L140t/ti~C~fi~, edited and with an introduction h j Richmond H. Thomason. New Haven, Conn.: Yale Univcrsitj- Press, 1071.

References r\jduliicwicz, klai'imicrz. 1960. *jf!.z:),k i Po.:ni/~lrt [Langrruge ~ i n dK ~ o ) ~ ~ l byarsari: ~ ~ ~ / g I';IIIS~WOM~ ~~l. U'j;dau n. .Sonic .,I/I~i/irz.(i/(/?/I/:\lor/r,r11 Grach, Peter T . 1962. R~$reni,c. irncj G(~ncnziitj~: -411 E.vnrniria/rotr T11~~oriil.c. Ithaca, N.Y .: Corncll University Press.

34 Richard Montague Geach, Peter T. 1967. Inten~ionalidentity. Journal r!f'Plzilosopl~)t64: 027-32. Ixwis, David. 1970. General seman~ics.Syr~tliesc22: 18-67. Montaguc, Richard. 1968. Pragmatics. In Ra)-mend Klibansky (ed.), C o ~ z ~ c n ~ p 1'111/1isop/~ll: o r . ~ ~ : ~ ~ .-1 S u r z q ~ vol. , 1, Florence: La nuova Italia. Repr. in Montaguc 1071. Montague, Richard. 1969. On the nature of certain philosophical entities. il;lorrisl 53: 161-94. Repr. in Montague 1974. hlontague, Richard. 1970a. Universal grammar. Th~oriu36: 373-98. Repr. in Montague 1974. Montague, Richard. 1970b. English as a formal language. In B. Viscntini et al. (cds), LingriagLqlnclirr Sol-ietri e nclli~Tecnira, Milan. Repr. in Montague 1974. Montague, Richard. 1970c. Pragmatics and intensional logic. S)arrlrc~sc22: 68-94. Rcpr, in _Monii~gl~c 1974. St~ltrrcdPapers (!/Richard Morrlrr~uc,edited and with an Montaguc, Richard. 1974. Forr~znlP/zilo.soph~)~. introduction by Richmond H. Thoniason. New Haven, Conn.: Yalc University Press. Partee, Barbara H. 1970. Opacity, coreference, and pronouns. Synrh~.rc21: 359-85. Quine, Willard Van Orman. 1960. ITord ( ~ n d0hjer.l. Cambridge, Mass.: M I T Press.

A Unified Analysis of the English Bare Plural Greg N. Carlson

ABSTRACT.It is argued that the English "bare plural" (an NP with plural head that lacks a determiner), in spite of its apparently diverse possibilities of interpretation, is optimally represented in the grammar as a unified phenomenon. The chief distinction to be dealt with is that between the "generic" use of the bare plural (as in "Dogs bark") and its existential or "indefinite plural" use (as in "He threw oranges at Alice"). The difference between these uses is not to be accounted for by an ambiguity in the NP itself, but rather by explicating how the context of the sentence acts on the bare plural to give rise to this distinction. A brief analysis is sketched in which bare plurals are treated in all instances as proper names of kinds of things. A subsidiary argument is that the null determiner is not to be regarded as the plural of the indefinite article a.

0 Introduction This study deals with the English "bare plural" construction, by which I mean plural Noun Phrases of English which exhibit no quantifier or determiner before the head noun (like "dogs", "ineffective arguments", or "old white houses that have been painted dozens of times"). For ease of reference, however, I will speak of thesc NP's as containing a null determiner, and leave open the question of whether there is any determiner present at all. This construction has long posed a semantic puzzle for grammarians and philosophers alike, chiefly because of the diversity of its possible interpretations. Although there is no agreed-upon inventory of distinct uses, there seems to be a basic split between the "generic" and "existential" uses, with further subdivisions among the generic uses. The generic is most naturally regarded as something like a universal quantifier, as would seem appropriate for representing the truth-conditions of (la); however, in

36 Greg N. Carlson many cases this "universal" admits of exceptions, and appears to have tlic forcc of "most", as in the examples of (lb).

( I ) (a) Ilorses are mammals/creatures/material objects. (b) Horses are smart/larger than mules/good pets. These uses may be opposed to the use of the generic exemplified in (2), where it is clear that a universal quantifier or the quantifier "niost" tvould simply bc inappropriate.

(2) (a) Horses are widespread. (b) Iiorscs are extinct. (c) Horses are indigenous to eastern Chile. Perhaps other sorts of generic uses can be distinguished, but these exa~iiplesshould suffice to illustrate the variety of generic interpretations that arise. There is another quire distinct use of the bare plural which has been conlmonly referred to as the "indefinite plural", since in many cases it seems to be the semantic plural of the NP's determined by the singular indefinite article a ( n ) . 'l'his use of the bare plural lacks the universal flavor of the generics and seems to be most appropriately modeled by an existential quantifier having essentially the force of sullze. A few exaniples are given in (3).

(3) (a) DOC~OKT tried to save the dying boy. (b) Knute threw rollen p~achesat the library. (c) Mice will come out of that ~ i ~ aifl l you pound on it. It ~ i i l lbe my chief contention here that these apparently distinct uses of the hare plural (henceforth referred to as S N P ) are merely facets of a syntactically and scmantically unified phenomenon, and that in all cases the differing interpretations can bc attributed in an entirely predictable manner to some aspect of the context in which that particular instance of (bNP occurs.' If this hypotllcsis is correct, and the null determiner is in fact unambiguous, then we can gcIlerate thc (/)NP in a rather straightforward manner syntactically, assigning it a constant interpretation in all instances. 2 Though this goal of unification may seem desirable on general esthetic grounds, I wish to argue that a unified analysis is motivated by data unco~-ercdin examining 4 N P ; that is, a unified analysis is not only desirable, but necessary, if we are to havc a complete account of this construction. I will proceed in a rather roundi~bout fashion, first attacking the notion that (/, serves as the plural counterpart of' a, and thereby elucidi~tingsome interesting semantic properties of t/)NP. I will then argue that the indefinite plural use of (bNP is not distinct from the generic uses, and that the generic uses are not distinct from each othcr. I conclude by sketching a ratha. programmatic analysis of the semantics of thc bare plural, one which allo\vs for the seeming variet~-of interpretations but assigns ;I constant interpretation lo ill1 occurrences.

A Unified Analysis of the English Bare Plural 37

1 The Indefinite Plural ?'he notion that the null determiner is the plural counterpart of a is bolstered by certain parallelisms in their distributions. For example, both a and cj~have generic uses, as in

(4).

(4) (a) A nznrnmal bears live young. (b) Mammals bear live young. Both also appear as singular-plural counterparts in predicate-nonlinals, as in (5).

(5) (a)

Gerry is an c~nitrznl. (b) Gerry and Muneie are nrrinznls.

Despite this rather inviting pattern, it has by no means been universally assumed that & is the plural of a. Sweet (1898) and Stockwell et al. (1973), for example, posit the unstressed variant of sornr (often written "sm") as the true indefinite plural. 13ut a number of others have held that c , is the proper candidate." In Chomsky (1965), for example, there is a base rule introducing Articles in the following way:

Art

-+

[ f Definite1

Thc I+ Definite] article is the, which occurs before both singulars and plurals. Tlie I- Definite] article is IL, which is deleted before plurals by transformational rule. Thus, the indefinite plural use of "houses" is derived from the underlying NP "a house".

1.1 Anticipated semantics

I

If in fact 4 serves as the plural counterpart of the indefinite article Q ,we would expect that the two would share all relevant semantic properties except for those attributable to thc presencc or absence of plurality.4 Let us agree to interpret thc indefinite singular as an esistcntial quantifier which also asserts singularity (rcprcsented here by "Esg"), and the plural 4 as an existential quantifier that also asserts plurality ("Epl"). J,ct us assume that "singular" means "one", and that "plural" means "two or more". Hoth of these quantifiers range over the same set of objccts. T h e relationship between semantic intcrpretation and syntactic form is presumed to be of the sort prcscnted in Montague (1952). 'The crucial fcature of this system for us is that quantifier scopc phenomena arc handlcd by syntactic rules "quantifying in" an NP and by associated rulcs of semantic interpretation which assign that NP scope in the semantic representation.' Though the details of this analysis may bc debatable, it gives reasonable semantic representations and should serve our purposcs here for instance, the sentences of (6) cvould be represented senlantically as the corresponding expressions in (7). (h) (a) A clog chased Marvin down the street. (b) Dogs chased Marl-in down the street.

38 Greg N. Carlson (7)

(a) (Esg x) (Dog (x) & x chased M. down the street) (b) (Epl x) (Dog(x) & x chased M. down the street)

We construe (7a) as true just in case there is at least one individual from the domain of objects such that the sentence following the quantifier is true when that individual is assigned as the value of x. (7b) is true just in case there are two or more distinct individuals from the domain such that the sentence Eollou~ingthe quantifier is truc that each of the inctividuals assigned ils the value of x. T h u s (7a) and (7b) tlo appear to represent closely the truth-conditions of (6a) and (6b), respectively.

1.2 Opacity phenomena In the presence of an opacity-inducing operator or predicate, the indefinitc siilg~llar exhibits a rather clear ambiguity. Consider (8) as an example.

(8) Minnie wishes to talk with a young psychiatrist. On one reading, there is some particular young- psychiatrist that Minnic has in mind, and she wishes to speak with him. Let us, following Quine (1960), call this the transparent reading. On the other reading, the opaque reading, Minnie's desires are fulfilled b-! talking to anyone, so long as that person is a youi~gpsychiatrist. The transparent reading is most readily modclcd by having thc existential cli~antifier outside the scope of thc opacitj--inducing predicate "\vish", whilc the opacluc reading is coi~ventionallyrendered by a formula having thc existential quantifier isithin its scope. Thus, (8) may have at least the following two semantic structures associated with it. (8')

(a)

(h)

(Esg x) (young psych. (x) & All. wishes hll. talk with x) bl.wishes (Esg x) (young psych. (x) & h t . talk with x)

We would therefore expect the indefinite plural to show the sanle ambiguity. 'That is, we should find the readings of (9a) and (b), corresponding to (8a) and (8b), for sentence (10). (9) (a) (Epl x) (young psych. (x) & M. wishes M. talk with x) (b) hl. wishes (Epl (s)(young psych. (x) 8i M, talk with x) (10) Minnie wishes to talk with young psychiatrists.

However, (10) does not have both of these readings; the transparent reading represented by (9a) is absent. This is most clearly seen if (10) is compared with (1 I), which does exhibit both readings of (9). (1 1) Minnie wishes to talk with sm young psychiatrists For some reason, the reading of (10) with a wide-scope quantifier is rulcd out, although the parallel reading, (8'a), is allowed for sentence (8) containing the indefinite singular.

A Unified Analysis of the English Bare Plural 39 It is clear that the responsibility for this state of afFairs cannot rcst solely with the plurality marlier, for witness again (1 I), which contains a plural NP. 0 s su\>stitutcfi)r s ~ i rtlic quantifiers rnlrny, all, tme/?le, aiid others that take a plural head noun. All thc resulting sentences exhibit a similar scope ambiguity.

Neither can somc cranky property of the verb i ~ i s hbe held accountable, for ~irtually ;In\.. opacity-inducing operator has the same effect: the singular wit11 a shows an opaque-transparent ambiguity, but the plural with 4 gives rise to only an opilquc reading. Compare the following pairs of sentences, where the opacitj--inducing p1-edicate is italicized. Mas Oeli~i~es a Commie to have robbed Macy's. i'vlax helieces Commies to have robbed Mac y's. A drunk is likely to win the annual potato-sack race. Drunks are lihe/y to win thc annual potato-sack race. hlas is seeking a unicorn. hlax is seeking unicorns. Gerald Tnust talk to a congressman before noon today. Gerald tnust talk to congressmen before iiooii totlay. Ij'a woman were sent to the Supreme Court, busing would end. I/'w-omen were sent to the Supreme Court, busing would end. These fclcts are clearly not predicted by any analysis which analyzes cf, as the plural counterpart of a.

1.3 Narrow scope phenomena ."Zclated set of fiacts comes to light when we examine the relative scope properties of 4 in the presence of negation and other quantified NP's. Consider the followiiig argumen t.

(18) A cat is in this room. ?4 cat is in the next sooii1. Therefore: A cat is in this room and a cat is not in this room. I

The conclusion of (18) is an ambiguous sentence. One reading is a contradiction, being of the form A G -A.

40 Greg N. Carlson (18')

(Esg x) (cat (x) & x is in this room) & -(Esg x) (cat (x) 131 x is in this room)

This reading arises when the existential quantifier is within the scope of the negative. A more likely way of saying (18') in English would be (19). (19) There is a cat in this room and there isn't a cat in this room. However, (18) on another reading sccms to be a reasonable argument. This reading has the existential quantifier outside thc scope of the negative, ancl the resulting formula is not of the form G -.,4 (nor equivalent to it), and thus is not a contradiction. Its representation would be (18"). ( 1 8 ) (Esg x) (Cat (x) & x is in this room) & (Esg x) (Cat (x) & -(x is in this room) A clearer rendering of ( 1 8") would be (20). (20) There is a cat in this room and there is a cat not in this room. If cf, is the plural counterpart of a, then we would expect the conclusion of (21) to exhibit a similar ambiguity. (2 1) Cats are in this room. Cats are in the next roorn. Therefore: Cats are in this room and cats aren't in this room. T h e conclusion of (21) has only the contradictory reading. Apparently there is no semantic structure that may be associated with the conclusion of (21) that is like that of (18")' where the existential quantifier has wider scope than the negative. Only a narrow-scope reading is allo\ved, which is the contradictory reading parallel to that of (18')." A further example of the scopc restriction on 4 , assuming it to bc an existential, is illustrated by the following facts. (22) is ambiguous with respect to the relativo scope oE the existential and universal quantifiers. (22) Everyone read a book on caterpillars. On the reading where the universal quantifier has wider scope than the existential each indi~idualneed not have read the same particular book. IIowcvcr, on the rcading where the existential has wider scope than the universal, it is thc same hook that every pesson read. These readings nppcar as (22'a) and (22'b) rcspcctivcly. (Rook (y) Si x read y)) (22') (a) ('v'x) (Person (x) -+ (3) (b) (3y) ('v'x) (Hook (y) & (Person (z)-+x reacl y ) )

A Unified Analysis of the English Bare Plural 41

We would therefore cxpcct (23) to be similarly ambiguous.

(23) Everyone read books oil caterpillars. (23) howevcr lias no reading in which the existential quantifier has wide sa)pc with rcspcct to thc unii-ersal. This is a general phenomenon. (24a)-(28a) all contain occurrences of cr and all exhibit a scope ambiguity with respect to some other quantifying expressioil (indicatccl by italics) in thc sentence. T h e corresponcling (b) sentences have the bare plural in place of a but exhibit no such scope ambiguity.

1

(2.1)

I

I

(4 (b)

1

(25) (a)

I

(b)

'

I

(26) (4 (b)

(27) (a)

I

('4 I

i

,

(28) (a) (b)

John saw a dog on his lawn u t 3, 430, 6, and 7 : 15. John saw dogs on his lawn a1 3, 3:30, 6, ~ n 7d : 15. A goat didn 't run across my lawn. Goats didn't run across my lawn. A whale lias attacked this ship ow t m l ~ l eorcnsions. Whales have attacked this ship an tn~elzleoccasions. Max saw an actor in eceql scene. Max sa\17actors in czler-1/ scene. A movie was seen by wrost pzoplc. h4ovies wcre seen by most people.

In none of these is there a reading of the q5NP which would bc appropriately represented by usc of an existential quantifier having wide scope. This is not predicted by- anv - analysis holding that b, is the plural counterpart of a. One could conceivably maintain that q5 is "really" the indefinite plural article, but that some idiosyncratic property of its semantics restricts it to having narrow scope only. It is not clear how a defense of this nature might proceed, but in any case it becomes untenable when we examine the ncxt set of data, where the scope possibilities of i~ and q5 are differentiated, and it is not the case that one exhibits simply a subset of the readings a l l o ~ - e dby the other.

1.4 Differentiated scope phenomena Lncler certain circumstances b,NP can havc narrower scope than the indefinite singular 110ssihl!l can, assuming that we continue to model 4 as an existential. Consider (29).

(29) A dog was everywhere. It is my clear intuition that (29) has only a bizarre reading, in which the same dog pops I

' I

I

up in every location. '.There is no rcadiilg in which the universal quantifier of the predicate has wider scope than thc existential of tlie subject (which rcading is clearly possible in "There was a dog evcrywhere"). Howcver, (30) does l~avc the reading that would be represented by the universal having widc scope. Entirely missing is the reading analogous to (29), in which it is tlie same group of dogs in c\-cry place.

42 Greg N. Carlson (30) Dogs were everywhere. Here is a case where the singular and plural have no readings in common, The plural cannot have narrower scope than is possible for the singular, and this is dit'fcrent from the previous examples, where plurality seemed to restrict the 4NP to a subset of the possibilities already present in the singular. 11 similar phenomenon is seen in the difference perceived betwecn (31) and (32), which serves to raise yet another difficulty for the hypothesis under considcration. (31) An accident happened today at 3 , 1 : 30, and 6. (32) Accidents happened today at 3, 4 : 30, and 6. In (3 l), we are asked to imagine a recurring accident, one which happens three times on the same day. (32), on the other hand, might be used by a local radio announccr to report the happenings of the afternoon. In this latter case, we are not asked to imagine recurring accidents. T h e semantic formulae for (31) and (32) would be of the following approximate forms. (31') (32')

(3) (Accident (x) & x happened at, 3, 4 ~ 3 0 and , 6). At 3, 4:30, and 6 ((3~) (Accident (x) & x happened)).

Here again the plural can have narrower scope than the singular. In this particular example we see further that the notion of plurality fails us. (32) could very easily be used to report the occurrence of one accident at each of the timcs mentioned, although the possibility of more is left open. But this ought not to be a possible state of affairs if 4 carried the information of "two or more", as would scem to follow from any analysis that treats 4 as the plural of (6.' A particularly interesting construction is given much attention in Dowty (1972), wherefor time adverbials are analyzed in some depth. An example of this construction is seen in (33).

-

(33) Marge sat on the coucl~j b v nifze hours. Dowty's analysis treats fir time adverbials as a universal quantification ranging over a given range of time points. Roughly, the semantics of (33) would be that of (33'). (33') 'it: t E 9 hrs ( A T (Marge sat on the couch, t)) (33') asserts that (33) is true just in case "Marge sits on the couch" is truc for each (relevant) time-point in some nine-hour period. One of t-hemore puzzling facts about these adverbials is that they are quite strange with a certain class of verbs ("achievement" verbs), unless the subject or dircct object of thc verb is a bare plural or an unquantified mass noun. For example, (31) appears to describc a rather unusual state of affairs, while (35) has a much more ilatural reading.

A Unified Analysis of the English Bare Plural 43

(34) Max discovered a rabbit in his yard f'or two hours. (35) Max discovered rabbits in his yard for two hours.

If wc use Dowty's analysis, the readings of (31) and (35) could be represented by thc following.

(34') (3x) (Rabbit (x) & Vt: t E 2 hrs ( A T (M. discover x in his yard, t))) (35') Vt: t E 2 hrs. (3x (Rabbit (x) & A T (M. discover x in his yard, t))) (34'), the reading in which the existential has wider scope,' asscrts that the same rabbit is discovered and rediscovered, which would be a strange statc of affairs. In (3Sf), however, we find no such assertion. T h e universal 1x1s wider scopc than the existential, so the same rabbits need not (but, of coursc, may) be discovered time and again. So once more cfi appears to be capable of narrower scope than 0. Thcre are a number of other time adverbials which behave in much thc same fashion, allowing Q, to have narrower scope than is possible for the putative singular countcrpart. The following (a) examples indicate a strange state of affairs, while the (b) esamples need not. In each case, we can attribute the difference to the narrow-scope possibilities of 6. (36) (a) (b) (37) (a) (b) (38) (a) (b)

Kent killed a mouse until Ruidwz~znarriued. Kent killed mice until Raidnratl n ~ r i ~ e d . Chester killed a fly repercteci/y last night. Chester killed flies uepeatedy last night. Leon has killed a cow since before the depression. Leon has killed cows since Iwfi)re the depr.e.ssion.

Aspectual verbs appear to play much the same role, and the exainples pattern similarly. (39) Harvey continued to kill

{

a rabbit i t

1.

(40) The North American Bread Eater tends to eat And evcn the morphologically simple "generic" statements scem to have the same characteristics.

(41) Abner rcpairs

1 1

{ }

for a living.

Similar results are obtained when the NP in question is in subject position. Consider the pairs of sentences in (42)-(44). In the (a) vcrsions, where the subject is the indefinite singular, the existential quantifier is interpreted as being outside the scopc

44 Greg N. Carlson of the time adverbial, and thus it is the same object that is spoken of at all timepoints in that period. In the (b) versions, the "indefinitc plural" is apparently intcrpreted as being within the scope of the quantifying expression implicitly prescnt in the time adverbial, and thus the objects need not remain constant ovcr the period of time. (42) (a) (b) (43) (a) (b) (44) (a) (b)

A dog hung around my valet all last year. Dogs hung around my valet all last year. A cat has been here since Columbus landed. Cats have been here since Colun~buslanded. A11 epileptic ruled Serenia for 200 years. Epileptics ruled Serenia for 200 years.

T h e quantifier need not in all cases arise from a time adverbial. One rather intriguing type of sentence is exemplified in (45); the (a) version has no rcasonaldc reading, but the (b) version has a quite normal interpretation. (45) (a) A wolf gets bigger as you go north from here. (b) Wolves get bigger as you go north from hcre. While (45a) asserts that a wolf in thc back seat of your car uill g 1 . o ~if you head a certain direction, (4%) asserts that northern wolves are larger than southern wolves (and it has an interpretation similar to that of (45a) as well). Though I do not pretend to understand (45), its readings arc clearly not predicted by any analysis that posits (,!I as the plural counterpart of a. One final example of differentiated scopc may be drawn from cleft sentences. (463) lacks the reading of (46b) which allows each pcrson to cat his on-11 tomato. In (46a) the tomato is shared by- all. (46) (a) It was a tomato that everyone ate. (b) Everyone ate a tomato. With ONP matters are different, and (47a) and (47b) are virtually synonymous. (47) (a) It was tomatoes that everyone ate. (b) Everyone ate tomatoes. So far the contrast in differentiated scope has been between and a. But therc is il deeper, and more important, distinction to be inndc herc. As mattcrs turn out, differentiated scope scts apart 4 not only from (1, but from a / / othcr quantifiers and determiners, with the uneven exception of thr and the unstresscd demonstratives in some cases. I cite one example from many to illustrate thc point. Rccall that with f i r time adverbials, a yields a strange reading in sentences like (34), but 4 doesn't. If we substitute other quantifiers and determiners into this context, wc find that they, too, pattern like a in giving old? strange readings. This puts (I!, virtually in a class by itself.

A Unified Analysis of the English Bare Plural 45

(48) Max discovered

se\.cral lots of those many all most twenty few sn~ etc.

rabbits in his yard for two hours.

All the other examples of differentiated scope yield similar results. I further note that (1) is the only quantifier or determiner among the indefinites that fiails to exhibit scopc ambiguities or opaque-transparent distinctions. If $J is an indefinite, it is a special one indeed. The 4 "indefinite plural" thcn, is semantically not the parallel of the singular form 11. Though there is a great deal of semantic overlap between the two, it is clearly not the case that their semantics are coextensive up to differences that can be attributed to the presence or absence of plurality.

1.5 Anaphoric processes A sentence such as (49), as has been mentioned before, is ambiguous between transparent and opaque readings.

(39) Kelly is seeking a unicorn.

In the larger context of (SO), however, the ambiguity disappears, in spite of thc fact that (19) is wholly contained within (50). This lack of ambiguity can be traced to the definite pronominal form found in the second conjunct, here assumed to refer to the objcct NP of the first conjunct."

(50) Kelly is seeking a unicorn, and Millie is seeking it, too. In (.iO), Kelly and Millie must both be seeking the same unicorn. There is no reading in which each is looking for different unicorns, nor is there a reading in which both are engaged in some gcneral activity of unicorn-seeking. Such readings are allowcd in ( 5 I), where thc pro-form ''one" scrves as thc pronoun.

(51) ICelly is seeking a unicorn, and hlillie is seeking one, too. Neither of the readings of (51) are found in (50). We would expect that the I$NP in this position urould not allow any dcfinite pronominalization to take place in a subsequent conjunct, sinee mrc have secn that SNP allows only an opaque reading in sucll contexts. Since only the transparent reading of (49) is found in the context of (N), not the opaque reading, and since cb

46 Greg N. Carlson rules out a transparent rcading, it should be impossible to obtain a reading for the following sentencc (with lhenz meaning "unicorns"). (52) Queenie is seeking unicnrus, and Phil is seeking them, too. Surprisingly, (52) does have a perfectly legitimate rcadi~lg,although it is not thc rcading to he found in (501, but rather one of the readings of (5 I), the opaquc rcading. There is no sense in n-hich Phil and Queenie are seeking the same group of imicorns. It scems to mean only that they are both engaged in some general activity of unicorn-seeking, despite the definite pronominalization in the second conjunct. I must hasten to point out rhat this result is not clue to any difference b e t w e n them and if beyond pluralit!.; rather it is due to the nature of the antecedent. 11s the rei~dermay have noticed, inass nouns with 4 determiners hehave almost identically to QNP with respect to the phenomena notcd." in (53) we find pronominalization resulting in the definite pronoun it, but here, in contrast to (50), the opaque reading of the first conjuilct remains. Cedrick and Hiran1 need not be seeking the same articles of furniture. (53) Cedrick is seeking furniture, and Hiram is seeking ir, too. If i/ can ha\:e this property in (53) then why not in (SO)?T h c answer is simply that it is the nature of the antecedent, and not the form of the pronoun, which gives rise to this property. 1 I It appears that this particular set of facts does not depend on the presence of an opaque context. In (54), the italicized NP's are not in opaque or intensional contexts, but srill Harsiet need not catch the same rabbits as Ozzie, nor must I drink the same beer Dad did. (54) (a) Harriet caught rabbits yesterday, and Ozzie caught thorn today (b) Dad drank heel. slowly, and I drank it fiast. Compare (51a) and the following.

( 5 5 ) Harriet caught

a

rnhhit today, and Ozzie caught it yesterday.

Here again we see Q, behaving in a manner quitc different fiom rr. Similar sorts of results are obtained when deletion occurs in coordinate structures rather than pronominalization. First let us consider the case with the indefinite sin. gulai. a. (56)

A buildi~zgwill collapse in Berlin tomorrow, and u buililirzg will burn down ir Boston the day after.

Clearly, (56) leaves the impression that two different buildings arc being spoken of However, if the subject of the second conjuilct is deleted "on identity with" the subjec of the first, a stranger tale is told in which the same building will collapse and burn i r two different places. This is the only reading of (57).

A Unified Analysis of the English Bare Plural 47 l down in 13oston (57) A building will collapse in Berlin tomorrow, a n d t ~ . i l bur11 the day after. Using the "indefinite plural", we find that (58) means sonlething very close to (56). The difference arises when we remove the subject of the second conjunct, and find that it still means the same as (58). (59) need not denote an extremely unusual statc of affairs, and hence it is like (56) rather than (57).

(58) Buildings will collapse in Berlin tomorrow, and buildings will burn in Boston thc day ilfter. (59) Buildings ~villcollapse in Berlin tomorrow, and day after.

will burn in Boston the

A someivhiit different phenomenon, which hits much the samc flavor as those just discussed, involves reference to the complement of a set. T o illustrate \*-hatI mean, let us examine (60). (60) Jack is hunting h r a unicorn, and Frank is looking for another/some more/some others.

NP's like aizotl~erand sonrf tnol-e, in (60), involve s o n ~ cnotion like "one of the unicorns that Jiick is not looking for", or "some unicosns beyond those that Jack is already

sccliing". There is at least an implicit rcfercnce to the unico~.nsthat Jiick is not seeking. We find that in (60), there is no opaque reading for the first conjunct, in spite of the [act that the first conjunct in isolation exhibits the transpiircnt/opaque distinction quite clearly. One apparently cannot refer to the complelllent set of something that is "down in'' an intensional context, a fact r\-hich seems to inake clear intuitive sense. Since the $NP only to opaque readings in opaque contexts, we would naturally antiuipiitc that sentences such as (61) would be ill-formed. And indeed, (61) lacks an interpretation whcre Jack and Frank are seeking different unicorns. 1

I \

1

(61) Jack is hunting fbr unicorns, and Frank is hunting for ??another/??others/ ??somemore/ ??some others. This result is erpccted. What is unexpected is that similar results ;ire obtained with (/)NP ewn when it appears in extensional contexts. T h e sentences of (02) arc all strange in the sanle way as (61), yet none of the uilderlined NP's are in opaque or intensional contexts. last night, and fed (some) others. (62) (a) ??lMas trapped 1~ecrr~i:r (b) ??Dogsjust ran across my lawn, and some more found their way into 111y kitchen. (c) ??George walhed down the street with kiltcns, and Henry David \valked dojvn the street with (somc) others. Compare (62) with (63), M-herethe NP's differ in their determiners. I vastly pset'er the scntcnces of (63) to those of (62).

48 Greg N. Carlson

(63)

(a) Max trapped (b) (c)

{

dog S m dogs

{

(some) others some more

beaver(s) last night. and k d

}

just ran across my lawn, and (somc) others found their way into my kitchen. sm kittens George walked down the street with , and I-Icnry a kitten David walked down the street with

i i

I

(some) others some more

1.

None of these facts are predicted by any analysis that assumes (/, to be thc plural counterpart of the indefinite singular o.

1.6 Status of the "indefinite plural" T h e facts presented above indicate that 4 simply cannot be the plural of a in any semantically relevant n-ay.12 I therehre conclude that (/) should be stricken from the list of candidates for this position, if in fact there is such a slot in the granlmar. 'l'he unstressed variant of "some" appears to be the most likely candidate, but I will lcave the matter unresolved here as it is not at all germane to the point of this study. I will continue to allotl: myself the liberty of referring to this usc of c/,NP as the "indefinite plul-al", but merely as a convenicilt label n~ithouttheoretical significance. Let us herc sum up some of the properties of (/jNP that havc bcen notcd so far. 1:isst of all, we noted that it had only opaque readings in opilque contexts, ncvcr transyarcnt ones. T h e n it .c~-asshown that (bNP does not participate in quantificr scopc anlbiguitics, but always seems to take narrowest scopc. We then found that c/)hP could actually achieve scnlantically namou-er scope than the other determiners and quantifiers. In matters oS pronominalization and anaphora, we found that thiilgs were also diffcrcnt from what might be expected. Definite pronominalization and coordinate deletion, rules n~hichnormally have quitc strict coreference rcsrsictions, behaved more like "identity of sense" anaphora (o?!c.-pronominali~ltion or VP-11t.letion). I think all thcse properties call be summarized by one short statement about the indcfir~ite plulal use of (/)UP: it fails to pick out a g~oopthat persists tl~roiightinlc and spacc in its membesship. Yet, this doesn't seem quite right, either, since in sentences like (44) it seeins that a group really is in somc scnse, being set 1113 and rcfert-cd to. Othern-ise, n e would simply have no undesstanding of whj- some gives us such a nice paraphrase.

,

(44) Arlene found

sguirn~ls in her attic. XOlllP squil'r~h

2 Generics and the "Indefinite Plural" Now that we have determined that (/I cannot bc the plural of iz, its relationship to thc rest of thc grammar becomes much less clear. 1I:e must ask once ;]gain what it is related I to, and how this relationship is represented in thc grammar. 11

A Unified Analysis of the English Bare Plural 49

A certain amount of evidencc indicates that the indefinite plural use of S N P is not to be distinguished from its generic uses. I,et us for the moment considcr thc hypothesis that there are at least two distinct detcrnliner elements of English, both of which just happen to be pronounced "4".T h e first is like an existential quantifier (but not quite), and accounts for the "indefinite plural"; the second is like a universal (but not quite) and accounts for at lcast one of the "generic" uses of (/,NP (there may hc a number of generic determiners, all pronullced 4, so we let the onc posited represent possibly n whole class of determiner elernents).'"~~ hppothcsis curries with it the claim that 4 N P is systematically ambiguous. I-Iowever, in most cases this is not bornc out bj. the facts (as has been noted previously, for example in Dahl (1975)). Consider the following sentences: (65) Smokers are rude. (66) Dogs bark. (67) Elephants are easily trained. These sentences cshihit the gcneric, or "universal" reading." Hut what is missing is the indefinite plural, or "existential" reading. Why don't (65-67) mean (65'-6'7') as well, if cj, is really systematically ambiguous? (65') Some smokcrs are rude. (66') Some dogs bark. (67') Some elephants are easily trained. Thesc readings are clearly plausible pragmatically, but they are rulcd o ~ l tfol- some reason. Again, why don't we judge the italicized d)NP's of the following sentelices to be ambiguous? Either reading should be possible, but only the "universal" emerges.

(68) Mark really loves puppies. (09) Kris hates smull 1dg1~crentures. (70) The man over thcre believes Te.rans to be friendly And thc following appear to be ilnambiguously existential, even though a universal, or near-universal, would be rcasonable. (71) Sir Snooter slew ~ l r ~ c for ~ o the ~ ~ Baron. s (as an "event"). (72) Pl~rmhersstormed into the convention demanding Ionger lunch breaks. (73) Alice personally knows ilrtresscs. These facts require further explanation uncles an analysis which treats & as an ambiguous determiner. In a number of contexts, an ambiguity does appear. Consider the following ambiguous sentence.

(71) Dinosaurs ate kelp.

50 Greg N. Carlson One reading posits kelp-eating as a characteristic of most, or all, dinosaurs. Another reading of the sentence, one which reports a kelp-eating event of long ago (more readily seen if the sentence is continued " . . . while Grog watched"), refers only to some dinosaurs. So here we have an ambiguity of the type predicted by the hypothesis under consideration. However, these sentences are ambiguous even when the subject of the seiltence is not a $NP, but an N P that is not normally regarded as being ainbiguous in any relevant way. Witness (75):

( Maxwell

(75)

I

Lots of conductors T h e old fireman A few scientists

I

ate kelp.

)

(75) can still be interpreted either ils reporting a past kelp-eating event, or as reporting a past characteristic of the subject of the sentence. These two readings have quite distinct truth-conditions, and thus the distinction drawn coi~stitutcsil genuine ambiguity. Virtuallj any N P in subject position in such a sentence will produce a similar ambiguity, and it is plain that the ambiguity has little to do with the nature of thc subject itself. ate kelp" is already two-ways ; ~ n ~ b i ~ u oregardless os'~ of the Given that "nature of the subject, and nssuining that 6 is itself at least two-ways ambiguous, then (74) ought to be at least four-ways ambiguous. But it is not. T h e existential reading alone appears with the "event" reading, and the universal alone ilppcars with the "characteristic" rcading of the predicate. 'There itre 110 "n~ixti~res"(c.g. it bciilg a past characteristic of some dinosaurs that they ate kelp regul;~rly).Here we see that thc context itself selects certain readings of 4 and disallows others. This is different from the situation with regard to the generic and specific uses of the definite article. An NP such as "the horse" may refer to the species of horses, or to il particular horse (say, Holding Pattern). Sentences such as (76) are ambisuous with ~ h o , but not so with 4,which allows onlj- the "generic" reading. T h e horse \vorks Horses work

quite hard.

'I'he generalization that falls out of this line of inquiry is that the generic and indefinite plural uses of (/, are in complementary distribution. In fact, I wish to rmke the stronger claim that these readings of cjNP arc not only in coinplementarq distrihution, but that their distributions are wholly predictable froin context. cb itself, then, is never ambiguous in a given context. If there is an apparent ambiguity, it can be tsaced to the environment. is in Gct anlbiguous but that thc reasonable counterargument might be that semantic properties of the distinct readings of arc s u c l ~that they- may only rarely, if ever, appear in the same environment. A rather weak ill~illogy might be used to illustrate thc hypothesis. Tlle NP "a crow" is at least two ways anlbiguous, onc reading denoting a large black bird, and thc other denoting the characteristic sound of a rooster at claybreak. Yet the instances of the N P "a crow" in t11c fi)llowing sentences are virtually unambiguous.

A Unified Analysis of the English Bare Plural 51

(77) A '?'Om perched on my doorstep. (78) The rooster rared back and let go with

(1

(lorrd)

CYOII~.

Yet 1 would not wish to claim that the NP "a crow" is unambiguous. 'Thcscforc, complementary distribution of' readings for $NP cannot be used to show conclusivelqthat SNP is unambiguous. However, nonambiguity, though not sufficient argument for a unified analysis, is clearly a necessary one. I nowr turn to other arguments.

2.1 More anaphora Onc of the major differences between the putative ambiguities of QINP and the cxan~plc mentioned above is that different interpretations of 4 may stand in an anaphoric relationship, but not those of "a crow". T h e following sentence cannot be interpreted readily as referring to a large black bird in the first clause, and to thc characteristic noise of a rooster in the second. \

I

I

(79) My rooster lets go with a

1.1'0171

when he sees it near the llouse.

If NP's exhibiting a null determiner were similarly an~bigiious,wc v~ouldnot expect a generic instance of 4 N P to serve as antecedent for an indcfinite plural use, or vicc\-ersa.The use of (/,NP cxempiified in (SO) should not be able to stand in an anaphoric relationship with the use exemplified in (81); the result should bc sotncthing like that of

(79). (80) Le1iz1wit7g.rare protected by law (81) Mick traps k ~ ~ ~ ~ ~ t z i r r ~ s . Hocvet-cr, this state of afhirs can hold, as wc see in (82). (82) (a) NIick traps luwttnir~gseven thoi~ghhe knows full well that r/tqy arc protected by law. are protected by law, but Mick goes ahcad and traps thcnr an!.(b) Lenzvrri~g.~

In (82a), we find an indefinite plural serving as antecedent for a generic use; in (8%) we scc that a generic may serve felicitouslj, as antecedent for an existential. A great number of other such examples can be constructed, and a few are listed here. M y mother hates t-~~crootzs because I ~ Z L stole ; ~ her sweet corn last summer. (b) Rnl.coons have stolen my mothcr's sweet corn every >-eiw,so shc really hates I / ? P ~a Ilot. 4 ) (3) Ally brother thinks s~iclkesare nasty creatures, l>ut that hasn't stopped nic from hai-ing tllrtji as pets m j n;hole life. (b) I've had sncikes as pets my wholc life, but my brother still thinks tl7i;)l're nast creatures. (85) (a) Martha told me that Eetitrs don't grow as well in this ulimatc, but tl7ey grew well for me last year.

(83) (a)

52 Greg N. Carlson B~irnsgrew quite well for me last season in spite of .Martha's warning that thyy can't grow in this climate. (86) (a) I didn't believe that goats liked ti11 l a n s until I actually saw ihenz eating /hem last week. (b) Before I actually saw goats eating /in rairs last week, I didn't believe ~ h t y liked them. (b)

In all these cases, we see a generic (or a universal) serving as antecedent for an indefinite plural (or an existential), and vice-versa. It is not at all clear how this would be possible if (p were at least two-ways ambiguous. There is a complicating Factor here (among a number of others), which I think in the end also argues for a unified analysis. T h e reference of the pronominal form in (87) is ambiguous. (87) -Mark knows ten linguists, and Freddie knows six of them. Ignoring thc rcadings where the pronoun refers to some extra-sentential objects, (87) might have either of the following meanings. (87') (a) (b)

. .. and Freddie lrllows six of the ten linguists lllot ,Mark knows . .. and Freddie knows six (of) lingz4i.st.s.

It appears that the pronoun in (87) may have as its antcccdcnt il subpart of the whole NP tell fi?~,o.u~sts of the form firzguists, or something of the form 4NP. Now this particular antecedent-psonoun relationship can be used to account fix cases of the following sort.

q extinct. ~ (88) Spaceman u-ants to see some gf~/r.sbefore ~ h i1l.e Since the11 stands in a position in this sentence characteristic of generic NP's, its antecedent illust be a generic. Howel-er, examples like (88) can also he constructed in which the pronoun is more like an indefinite plural; e.g.. (89).

(89) Max killed very few r(zBl~it.s,but IHiram killed thcvlr in great abundance. (80) does not require that we imagine some resurrected rabbits. Let us assume that the 4 determiner is ambiguous, that thc NP underlying the pronoun in (88) (or the pronoun's antecedent, as I wish to remain neutml on the deep structure status of pronouns) is something of the form V N o l n , and that in (89) it is solmething of the form ENum (where b' and E are the generic and indefinite pliual markers respectively, and Nom stands for "nominal"). T h e antecedent in (89) then must "contain" an indefinite plural, and the antecedent NP in (88) must "contain" a gencric. This would mean that an NP of the form "three cats" would he at least twoways ambiguous, depending on whether or not it contained ENorn or 'dNora.It is not at all clear that such an ambiguity can be explicated in any reasonable way. Hut our assunlptions would have the further undesirable conscqucnce of allocti-~ga gencric to

A Unified Analysis of the English Bare Plural 53 contain an indefinite plural (be of the form VENorrr) and an indefinite ~>luralto contain a generic (Eb'h7om) in order to account for (83--86). Not only is it hard to make scnsc of the prolific an~biguitiespredicted by such an analysis, but the syntactic slipperiness of' thc invisible elements 'v' and E (pronounced 4 and (/I, respectively) is discon~fortingils well. I know of no othcr determincrs or q~~antifiers that could apycar in all thc positions allowed foi. thcse. However, 4 is a vcry difficult item to find in a sentence, and without spcclfic claiims about its syntactic and semantic properties, it is virtually impossihlc to show that q5 isn't really there. I do not wish to overstate the case that can be inadc from pronominalization, for the processes involved remain very poorly undcrstood, and only in thc framew-ork of solnc definitive analysis can thcse arguments be evaluated adequately. But insof'zir as current theories account fbr these phenorncna, an analysis claiming d'NP to be unambiguous would not suffer from the difficulties of the amhipuity analysis. In all of the cases ;lbove the antecedent of the pronoun is sin~plyof the form (/)NP, and its particular intcrprctation is predictable from context. In any event, an ambiguity analysis of (/) has to face most of' the same problems of' context as il unificd analysis does, so thc rcfcrence to contcxt I rnakc here is not sonlething that can bc avoided cvcn with an ambiguous cb.

2.2 NP's denoting kinds of things I belicve that the strongest argumcnt for a unified analysis of 4 N P conles from the fact that contextual factors that give rise to the gencric and indefinite plural interpretations are independently motivated and are needed elsewhere in the grammar to account tor interpretations of ccrtain constructions that are wholly distinct s!;ntactically fi-om 4 N P . 'I'his class of constructions - NP's that refer overtly to kinds of things - points the path tocvards a correct analysis of the bare plural construction. We might offhand think of kinds of things (I will henceforth simply use thc locution "kinds") as being really quite abstract, as opposed to say, particular individuals. 13ut NP's denoting kinds inny appear as the subject of sentences that predicate vcry concrete things of the subject. They can bt tall, hn7v mings, or even hc sillirzg nrsi 10 w t in rht thrrr/cr.' "

(90) (a) This kind of animal is tall. certain kind of lizard has wings. (b) (c)

Some kind of duck was sitting ncxt to me in the theliter.

If we compiirc the behavior of thcse NI"s denoting kinds to other NP's that are chasacterized as being abstract (iikc c/emol-r.al:y, or 1l7e s p c ~ J(!/' lighl), we find that, grammatically, the NP's making reference to abstract kinds appear cluitc concrete. NP's denoting kinds, such as those in (go), have a number of properties in common with the indefinite plural (/)NP. Let us fix the reference of "this kind of animal" as your f;norite kind of animal, and examine a sentence liLc (91). to have eaten his pet spongc. (91) hlax believes this kind c/J'a~~ili~(il

54 Greg N. Carlson There is no reading of this sentence in which Max believes of any particular indi\~idual that it ate his pet sponge. If Rover ate thc spongc, for example, it does not follow that Max believes that Rover ate his pet sponge, on ail!- reading of the sentence. Conipare this with (911), where there is a reading having this entailment. i

(91')

Adax believes

nlz

animal o$f/zls kird to have eaten his pet sponge.

If we were to entertain the llppothesis that "this kind of animal" refers to certain individual animals, we might be led then to think of (91) as exhibiting only an opaque reading. T h e same follows for the sentences of (92) if we think of this NP as referring to a group of animals. On this false hypotl~csis,we would then think of'(92) as exhibiting only opaque readings.

(92) (a) Max is seeking this kind of animal. Minnie wishes to talk with this kind of animal. This kind of anilnal is likely to win the race. (c) (b)

Ho~~rever, since thcse NP's do not refer to indiiriduals, but to thc kinds then~selves,1 the question of opacity vs. transparent!- wit11 rcspcct to particular ii~di~iduals si~nply does not arise. When such a distinction does arise wit11 N1"s dcnoting kinds, it is a question of transparency vs. opacity with respect to kinds themsclucs, and not wilh respect to individuals. In (93), tl~ereis one reading on which there is a particular kind, e.g. "the kind of animal George has", which is believed by Adax to have eatcn his pet sponge, and there is another reading on which Max's belief is not about any particular kind.

(93) Max belicves

soune

k i d qf'anirtrc~lto have eaten his yet sponge.

If we continue to slippose for the moment that NP's denoting kinds refer to individuals, we find that the NP "this kind of animal" exhibits only narrow scolx. Consider the case of (94), recalling that we agreed to fix the reference of'the subject NP as your favorite kind of animal. (94)

This kind of animal is in this room. This kind of' animal is in the next room. Therefore: This kind of animal is in this room, and this kind of aniinal i s not in this room.

T h e premises of (94) could very well be true, but the conclusion has only a contradictory reading. This is so in spitc of the F~ct that the particulat. indii~iduals in the two roonls are in a11 liltelihood quite distinct. So if we cvcrc thinking of "this kind of animal" as referring to individuals, it ~vouldappear to h~lveonlj narrot+ scope. We also find that the sentences of (95) cxhil~itonly narrow scope l-eadings.

A Unified Analysis of the English Bare Plural 55 (95) (a) Everyone saw this kind of animal. (b) This kind of animal has attacked the ship on tlvclve occasions. (c) John saw this kind of animal in every scene of the movie. In (95,)' h r instance thcre is no reading on which everyone saw thc same particular animals. So we see here "nasrow scope only" alongside "opacity only". Continuing our false notion that NP's denoting kinds refer to particular individuals, we find that they can exhibit differentiated scope as well. Recall that in the context of (96) the appearance of any quantified NP yields a bizarre reading, whcreas 6 N P yields a more natural interpretation. (96) -be everywhere. However, NP's referring overtly to kinds likewise yield quite natural readings. (97) This kind of aniinal was everywhere. In cach place there need be only some animal of this kind; the same particular individuals necd not appear in more than one place. If we put NP's denoting kinds into the contests that were defined in 1 .I as differentiated scopc (or perhaps "to narrow scope"), we find that in all cases a natural interpretation appears. I list a few niorc esamples.

(98) (a) Max discovered this kind of animal in his yarcl for tu-o hours. (b) This kind of animal ruled Serenia for 500 years. (c) It was this kind of animal that cveryone ate.

Thus wc see that these NP's may be thought of as exhibiting differentiated scopc. Given that only an opaque reading seems to occur with NP's denoting kinds, KC see that in (99) definite prol~on~inalization is allowcd, but it docs not yield a reading on which Kelly and Horace arc seeking the same particular individual animals. 17 (99) Kelly is seeking this kind of animal, and Horace is seeking idthen1 as well.

If' we thought of (99) as making reference to particular animals, this ~vouldbe a semantic curiosity indeed. NP's denoting kinds also pattern like indefinite plural (IJNP with respcct to the othcr anaphora phenomena. In ( 100) and ( I 0 1) identity of particular individuals is ilot preserved.

(100) Harriet caught this kind of animal yesterday, and Max caught it/theni earlier today. (101) This kind of structure will burn dourn in Berlin tomorrow, and collapse in Boston the day after.

- will

56 Greg N. Carlson T h e same particular animals need not be caught, nor must thc same particular structures burn and collapse. Reference to the complement is also forbidden with kinds. (102) is strange if one is speaking of the animals that weren't trapped. (102)

Marv trapped this kind of animal last night and fed (some) othcrs/some morc.

((102) is of course fine if this is ref'crence to other kinds. But then so are (61) and (62)). So we sec that with respect to anaphora, NP's dcnoting kinds pattern like the indefinite plural 4NP. NP's denoting kinds also appear to have "generic" and "indefinite plural" intcrpretations. In (103)' for instance, we appear to be speaking of all animals of that kind. (103) This kind of animal is a vertebrate. In (104), howcver, it appears to follow that there are some animals of that kind which Max shot; clearly there is no reference to all animals of that kind. (104) Last night, Max shot this kind of animal. Thus, that NP's denoting kinds also have an "indefinite plural" reading. It would be questionable indeed to account for the existential reading of "this kind of animal" in (104) postulating an ambiguous invisible dcterminer. This becomes even less likely when we note that NP's denoting kinds come in a wide variety of syntactic shapes.'' Evcry one of thc sentences in (10.5) has a perfectly natural reading, provided wc interpret the subject N P as referring to a kind or kinds. (10.5)

This cignretle (yes, thc one 1 am tapping on the table, putting in my mouth, and non- lighting) is made in nine different countries. q~ bird is now extinct. (b) E z ~ e /icclhe~lrss (c) Alo rcfitilcs arc indigenous to the Philippines. (d) Mnn.11 mec.hnnicn1 i/ez:ic-csulcrc invented by mistake. (a)

These, too, may have existential or "indefinite plural" interpretations. (106)

(a) Carter sells this animal in his pet shop (meaning "this kill[/ of animal") in it. (b) This zoo has ez3eqtpal.i~,lrd~v+f?t ( c ) Severcll bircEs were discovered in Spitsbergen by the I>arscn expedition. (d) M.11 (lug has been known to attack leopards.

T h e sentences of (106) are ambiguous as to whether thc italicized NP's denote individuals or kinds. On the "kincl" reading, thc sentence speaks of sotne of that kind, rather than all or most. This is thc "inclefinitc plural". T h u s the hypothesis of an ambigious 4 dcterminer to account for generic vs. indefinite plural interpretations of (/2NP would be difficult to extend to this widc variety of NP's denoting kinds. A l ~ d positing an ambiguous 4 determiner for ~ I N but P some other mechanisnl for the same

A Unified Analysis of the English Bare Plural 57 variation ~ - i t hthe other NP's would be to miss an obvious generalization. l'his all suggests strongly that q5 is not to be represented semantically as an ambiguous determiner.

3 A Brief Excursus on the Diversity of Generic j'NP As mentioned above, a number of "generic" uses of d, might be distinguished. 13ut here, too, positing an ambiguous determiner or quantifier for r j suffers from the same objections that have been raised against the generic/indefinite plural distinctlon. Let us suppose for the momeilt that there are at least three 4 determiners. 'The first would be a strict universal, as in (107). (107) Dogs are mammals. The second kvould be much like a universal but would allow exceptions. (108) Dogs are good pets.

The third as in (109), does not lend itself to interpretation as a quantifier a t all. (109) Plants are \videspreacf/cxtinct/numerous.

The first problem is that these NP's simply do not appear to be ambiguous. (108), for example, does not seeill to be true a n one reading, fialse on another, and true or f'alsc on yet another. It's simply true. I dispense with further examples as the generic scntences presented herein speak for themselves in this respect. We find that thcse various "interpre~ations" of (/,NP can be mixed in antecedentpronoun relationships (and all of these may, in turn, be associated with the indefinite plural). Consider the follo\\ling. (110) (a) Dinosaurs ;are extinct because thqy ate kelp. J difficult to (b) Trzlcks hrrfiling r(ynarnite are illegal in Nevada because I I I ~ are manuever in heavy traffic. (c) W0lz.e~eat only kosher deer, so rbq are less nurnerous than the?; woulcl be if rhey weren't so choosy. (d) Elfphanls are not widespread in spite of the fiict that thy)! are quite largc and strong.

So pronominalization fiacts do not effect a separation among different generic uses. Finally, NP's overtly referring to kinds or types would havc to be distinguished in the same variety of ways. They, too, appear to have the same "readings". 'This kind of animal This animal

is a mammal.

58 Greg N. Carlson This kind of animal This animal

is a good pet/barks.

i

This kind of ani~nal is widespread/extinct/i~umerous. This animal So the ambiguities posited for #NP would have to be allowed in these cases as wcll, if generality is to be preserved at all. There is one further danger inherent in positing an ambiguous (/I determiner to account for the varying truth-conditions associated with the barc plural, namely that one would end up positing a large number of cb's to cover all the desired cases. We have already seen three, but therc would have to be a q!!rc,,,,, to account for "mamma/s givc milk to their young", a #,,,I, to account for L'liop7s have manes", a Onlatu1.e for "birils reproduce annually" a d~,~,,,, for "bees reproduce by laying eggs", and so forth. I do not believe that positing distinct 4's in each of these cases would serve an!. useful purpose, as it seems clear that they would not be modeling anything that iiltuitivelv we would call an ambiguity. These quantifiers would rcflcct more Izow we find out the truth or F~lsit?of generic statements; this is tantamount to building a theory of epistemology into the semantics, something not at all easily done. 'll~erefore,it appears that the various uses of the gencric # arc likenrise contcxtdcterrnined, and that a unified analysis is thercfore desirable. I now turn to a brief description of a program for accomplishing this unified analysis. A great deal of what follows must be termcd speculative, but the general line of' i n q ~ ~ i rappears y to he capable of solving a number of difficulties raised so far.

4 Towards a Solution 4.1 Generic statements about individuals Let 11s bcgin b!; presenting a means of interpreting thc generic uses of c/)NP, which incorporates a unified analysis but ~vhichnevertheless allo\s.s for a wide rangc of different uses. This task is best begun bv drawing somc analogics. Generic statcments can also bc made of individuals. 'l'hcsc statements, too, have notoriously erratic truth-conditions. Consider (1 12).

( 1 12) Jake mows his neighbor's lawn. This clearly does not mean that Jake's days and nights arc spent mowing. \Vc might hypothesize that (1 12) is truc just in case it is Jake, most of the time, who mows the lawn. T h e lawn must furthermore be mowed regularly (onc mowing cvcry tivc years wrould not do). Jake is allolved to be sick occasionally, or to be on vacation, etc. Comparc this line of thought with thc one that emerges from an examination of (1 13).

(1 13) Kenney bcats small children.

A Unified Analysis of the English Bare Plural 59 -

-

A great deal of regularity is not required for (1 13) to count as true; nor must Kcnney be the one who beats children largely to the exclusion of other maniacs. He necd not beat children a t every opportunity, nor every time a child needs a beating. A very few childbcating instances would suffice for (1 13) to be true. 'I'he reader may take issue with certain aspects of these remarks, but this is not entirely germane to the point at hand. These generic statements about individuals clearlv vary greatly in truth-conditions. Consider the following, asking for each h o ~ many times Jake must do whi~tif the sentence is to be true.

(I 14) (a) Jake wears contact lenses. (b) (c) (d) (c)

Jake runs to school. Jake runs the mile in 3:58.2. Jake is a drunk. Jake is a failure.

(f)

Jake writ-es

Careful examination will reveal a maze of factors to be taken into account in cases such as these. 'I'herc is a means at our disposal of allowing for all this variation while retaining a cohcrent scinantics. If we fi>llowa semantic theory of the sort proposcd in Montagiie (1972), the truth of hlsity o f a sentence is detern~inedby finding out whcther or not the property attributed to the subject of the sentence is in the set of propertics that the subject of the sentence has. (We might also talk equivalently in terms of the predicate naming a set, and finding out if the subject of thc sentcncc is in that set.) So, for example, (1 1 -#a) is true just in case the property of wearing contact lenses is in the sct of properties associated ~vithJake, and (1 14d) is true if being a drunk is in that property set. How do we know whether or not these set membership relations hold? In a modeltheorctic semantics, the nlodel kt-ill tell you, so the determination of truth or thlsity i s simply a matter of consulting the model. If we think of thc real world as being the model m-e consult, matters become a good deal more complicated. We no longel- just need to be able to read off some information that is given to us; wc ~ ~ c also c d to bc ablc to perocive, to compute, remember, make i~lductiorrs and deductions of startling complexity, and go through a host of othcr cognitive processes to tell if sonlcone is a drunk, or \\;ears contact lenses, \ V h t is suggested, then, is that thc apparent variation in the truth-conditions of'(114) can be attributed to our strategies of investigation and not to any inherent semantic marker in the sentence (in particular, a qui~ntificr). Let us return now to the question of the proper interpretation of the bitre plural. Wc have already noted the semantic relationship that holds between 4 N P and kinds. T h e suggestion herc is that w-e treat the bare plural in all cases as denoting il kind of thing. In particular, we suppose that the bare plural acts as the proper name of a kind, and that kinds are to be construed as individuals. Of course, these individuals arc a little different from more normal individuals in that kinds can hc hcrc and there, n-hereas normal individuals are generally confined to one location (though it might bc il big location) at a given time. 'That is, while hlark Spitz at a given time is spatially quite

60 Greg N. Carlson confined (he can only be in one place, roughly), bees can be in 111ilny locations (wherever there are one or more bees). (Zemach (1975) makes a siinilar point.) Postal (1969) notes a striking similarity between bare plurals and proper names with respect to the "so-called" construction. Consider (1 15).

(1 15) (a) Slim is so-called because of his slender build. (b) Cnr(1itzuls are so-called because of their eolor. "Those cardinals 'All cardinals are so-called because of their color. *No cardinals "The cardinals ctc. Quantified or determinccl NP's are cxcludcd, leaving $NP, proper names (and the generic definite "the cardinal"). TActus agree then to treat 4 N P as a proper name of a kind, and let us think of kinds as being abstract individuals. Tn this treatnlent, 4NP's arc treated semantically as if they were unanalyzable wholes. This assuinption is clearly incorrect in many cases, but this does not affect the point of the anal?-sis sketcl~edhere. Generic s ~ a t e n ~ e nfor t s bare plurals are then handled cxaetly as they arc for regular proper names. ( 1 16a) is true just in case the individual Bossie has in her property set the propcrty "eats hay", and (1 16b) is true just in case "cats ha!-" is in the property set of the individual Cows. ( 1 16) (a) Hossie eats hay. (b) Cows eat hay.

HOJDwe go abo~itdeciding whether a given property is in a property set is not a semantic issue.'" In this way we avoid dealing with thc extremely recalcitrant problem of the widely-varying truth conditions of sentences like (I lob) in the same way that we do in the case of generic statements about particillar individuals. This, then, is how we go about accounting for the various uses of the generic 4 N P . It is not ambiguous, but it may take on the appearance of ambiguity when we assign different properties to the individual in question. Tf we assign the predicate "lives in caves" to the individual "bats", our strategies for determining whether or not that property is in their property set let us tolerate the exceptions. If we assign "reproduces by giving live birth" to LLrabbit~", our strategies deterininc that wc nced not take into account the male rabbits. Thcse strategies are not so different from those we nced for determining the truthvalue of generic statements about individuals, as in (1 14) above. Those for kinds may bc a bit more complex, but it is clear that the proeesscs involved are closely related to one another. T h e relationship between particular individuals and these "kind-level" individuals is, I believe, a tighter one than might be imagined. For example, I know of no predicates that can be assigned to particular individuals that cannot also be assigned to kinds. And the predicates that cannot be assigned to particular individuals (or groups of particular individuals) but which may be assigned to kinds arc not numerous.

(I 17)

A Unified Analysis of the English Bare Plural 61

1

*Fred "All goats Goats This kind of animal

} { Ze )

~ ~ ? i d e s j r ~c lt /u ~ n e r uTs , I ; mre/ ~.ommon/irzcligenous to . .

The predicates of (1 17) represent a saml~leof what appears to me to be a rather exclusive class. I now leave the problem of the generic use of (I,NP and turn my attention to its indefinite plural use.

4.2 The indefinite plural \Ve still must account for the indefinite plural interpretation of $NP. In light of previous discussion, one may wonder why we single out this particular interpretation for analysis. Why shouldn't it be treated in the same simplistic fashion as the generic interpretations? That is, could (1 18) be construed as being true just in case "he sitting on my lawn" is one of thc properties of the individual "dogs"? (I 18) Dogs are sitting on nly law-n.

It would then follow that the "indefinite plural" interpretation would be, in a certain sense, illusory, and not really an existential statement at all. I do not believe, however, that such an approach is entirely justified. Fos one thing, there seeins intuitively to be a rather clear distinction bctween the generic and indefinite plul-a1 uses of 4NP. T h e generic secms to speak of tendencies, dispositions, characteristics, and thc like; thc indefinite plural does not have this flavol- at all. There is a more important reason for wishing to split off the indefinite plural scnsc from the other senses of $NP and treat it as a semantically distinct phenomenon. Onc of the chief aims of semantic theory is to represent correctly the entailment relations that hold between sentences. As matters turn out sentences with the indefinite plural md sentences with the generic sense of $NP have quite distinct ent;~ilrnents."' Consider the argunlent presented in (1 19). (119) Dogs arc sitting on my lawn. All dogs arc n~an-~mals. Therefore: Mammals are sitting on my lawn. The infcrence of (1 19) appears to be valid, and could easily be shown to he correct if thc indefinite plural wcre represented by an existential quantifier. Contrast this with (1 20), nherc the bare plural has the generic scnsc. (120) Dogs are good pets. All dogs are rnainmals Therefore: Mammals arc good pets.

62 Greg N. Carlson This invalid argument is a case of overgcneralization, as would he clearly demonstrable were thc generic to be construed here as a universal quantifies. Clearly the indefinite plural and generic senses of Q)NP give rise to different entailments and are thercfol-e distinct. But here I seem to be arguing the contrary of what I havc argued fils at lenglh a bit earlier - that the generic and the indefinite plural arc not to bc differentiated syntactically or semantically. I seem to be sitting atop a paradox. 1 am not really; the remainder of this work is devoted to thc resolution of this contradictor)- state of affairs. I11 thc following discussion I will consider only Q)NP in subject position, as matters arc clearest there. No doubt the reader has noted that therc is another diffcrcnce betwecn (1 19) and (120), namely in the tense, or aspect of the scntcnce. This diffcrcnce cr)uld be the ultimate source of the difference in entailment rclations between (110) and (120). 1h ~ i s h in the end to claim that essentially this is so. Let US begin by asking ourselves about the relationship between the two sentences of (121). (121) (a) Max is being clei-cr. (b) Max is clever. Both appear to be predications concerning thc same individual. (121a) says son~cthing about ~24ax'scurrent actions, m.hereas (121b) says i ery little about his current actions (he ma; ill fact be making an utter fool of himself when this is uttered) hut speaks more of a disposition or characteristic. T h e generic is, in a sense, timeless, whilc the present progressive refers to a particular period of timc. We have seen that thc simple past tense may yield eithcr of these interpretations. A sentence suc11 as (122) is ambiguous, one reading being akin to that of (l2la), and the other being like that of (12 1b).

(122) Jake ate kelp. There is one reading that refers to a particular stretch of time, and another which attributes morc or less timeless characteristics to Jake. T h e same holds for the "filturc" tense. (123) Jake will eat kelp.2' In all these cases, the reading that is "timeless" and sycaks of characteristics and the likc is the one that unambiguously sclects the "universal" reading of ONP. tind that reading of (1 19)-(123) which l ~ a referencc s to a particular stsetch of timc, and intuitively secms to be reporting events, unambiguously sclects thc "existential" reading of the hare plural. For instance, (121a) selects the existential and (124b) selects the universal or generic. (124) (a) Dogs are running around in circles. (b) Dogs run around in circlcs.

A similar sort of phenomenon can be observcd in the casc of English adjectives. Somc adjectives select the indefinite plural existential reading, and others select only

,

,

I

1

1

A Unified Analysis of the English Bare Plural 63 -

-

the genenc. In A4ilsark (1974) and in Siegcl (1976), two classes of adjectives are isolated, the chief diagnostic being whether 01. not a given adjective will fit into the types of content cited in (125). (125) (a) Jules caught the girls . (b) There were five dalmatians Into these contexts may go only those predicates that Milsark calls "states" (which may be rozlglily characterized as being fairly temporary), as opposed to those predicates he calls "properties" (which are roughly more permanen t sorts of things). Among the states are adjectives such as "hungry", "sleeping", "awake", "drunk", "availal~le" and the like. _4mong the properties wc find adjectives such as "fat", "tall", "clever", "obnoxious", etc. As Milsark noted, when the subject is a 4 N P the "propcrties" select the generic or universal reading, while the "states" unambiguously select the indefinite plural reading. Compare the "states" of (126) to the "properties" of (127)."

(126) (a) (b) (c) (127) (a) (b) (c)

Soldiers were available. Dentists \\-ere drunk. Frogs are awake. Soldiers are brave. Dentists were tall. Frogs are clever.

In (126), the only possible interpretation of the subject is the indefinite plural, whereas in (127) only the generic readii~gis possible. We find one particularly interesting contrast in the case of the adjective "sick". This has two senses; the first, a state, is physical illness, and the second, a "property", indicates mental instability. Notc that in the context of (125), only the physically ill reading is to be found.

(125') (a) Jules caught the girls sick. (b) There were five dalmatians sick. In (128), however, this predicatc is ambiguous, but here the physically ill reading sclccts the indefinite plural reading of bNP, while the mentally ill reading selects only thc generic.

(128) Girls are sick. Among the other predicates, we find that predicate nominals unambiguously refer to "properties", while most prepositional phrases (especially those of location) refer to thc "~tates".~" And wc find, as expected, that predicate nominals select the generic reading \vhilc prepositional phrases select the indefinite plural. (129) (a) Dogs are sivect animals. (b) Dentists are book collectors.

64 Greg N. Carlson (130) (a) Dogs are in the next room. (b) Children were without pasents. (129) is generic, while (130) is existential. In all of these cases, one might hypothesize roughly that the predicates selecting the "indefinite plural" arc predicating something of an individual for a short period of time, while the predicates selecting the generic leave the implication that what is predicated of the individual is of a more permanent nature. Though this is most assuredly on the right path, time as the crucial fiactor does not satisfactorily distinguish c4 states'' from "properties". For exan~ple,one can be physicallj ill for several years, and mentally ill for only a few w-eeks. O r one can be "in the next room" for a lot longer than one is "a butcher". I wish to look at things in a slightly different wrap. Suppose that the "states" and "properties" are being predicated of dzfirent sorts qf'things. Suppose we take an individual, Jake, and look at him as being composed of a set of Jake-stages, or temporallybounded portions of Jake's existence. T l ~ e r eis more to Jake, howcvcr, than a set of stages. There is whatever it is that ties all these stages together to make them stages of the same tl~ing.Let us call this whatever-it-is the individual Jake. Those predicates we have been calling "states" then are not predicated of individuals, but of stages of individuals; and those we have been calling "properties" (in the sensc of Milsnrk) are predicated of the individual, or the thing that ties all the stagcs together. Now thcso "stages" can be short or long in duration, but they are nonetheless perceived as parts of a whole. Thus the apparently temporary nature of such predication. It is not at all clear that anything of a temporal nature falls out of the characterization proposed for thc "properties", but since they are predicated of the individual, no doubt the permanence of the "properties" arise from this notion. Perhaps a cautionary note on the intuitive idea of "stages" is in order here. I do not see them simply as clips of film of an individual's lifetime that are taken out and examined, w7ith the sum of the clips of film being the individual. T h e individual is more than the sum of the parts, and the stages are not static sorts of things. T h e stages aren't simply things that are; they are more akin to things that hr~ppen.That is, stages are conceived of as being much more closely related to ejrenrs than to objects. I think this characterization can be taken quite scriousl?;, but rather than try to mect possible objections the readcr may have at this point, I will leave matters quitc open regarding the ontological aspects of this proposal and move on to the formalism. Let us take the individual as basic, and define "stages" in terms of an individual. An individual's set of stages is denoted by the follon-ing formula (exemplified here for Jake):

This may be read as "the set of all things, x, such that .x bears the relation R to Jake". (1 henceforth assume the reader to be familiar with the notation used in such places as Montaguc (1972)). 'rhc predicate R ma! bc thought of, roughly, as "rcalizes". 'l'ho stages then may bc callcd "rcalizations" of an individual. When one prcdicatcs a "state" of an individual, intuitively I urish to say that one claims that that state is in

A Unified Analysis of the English Bare Plural 65 the property set (in the scnse of Montague (1972)) of a realization, or stage, of that individual, rather than in the individual's property set directly. The "properties" (in Milsark's sense) are asserted to be in the property set of an individuaI, rather than in the property set of one of that individual's realizations. Let us exe~nplifythis with somc formulae. First I will present "Jake is intelligent", ignoring tense. I will treat be as semantically null; it won't show up directly in any of the translations. "Jake" translates as: ),PP{j) "be intelligent": I' 'tJake is intelligent" is: APP{ j)(^J1) This formula reduces to the following: I(j) is predicated of the individual Jake ( j ) . I,et us compare this with the tral~sla~ion of the sentence "Jake is sick" in the physically ill sense, which is a "state".

Here, we find that I ("intelligent")

"be sick" translates as: Il,r3y[R(y,s) & sick'(y)] "Jake is sick" ivould then have the following semantic representation: /ZPP{j)(^A.viI)! [R(,y,.r) &- sickJ(,)/)] This formula reduces to: j)11R( ,-j) 8: s i c k l ( j ~ ) ~ This illustrates formally what was said in words above. Being "intelligent" is a property of Jake, but being "sick" (physically) is a property not of Jake but of one of his realizations. This invites a characterization of the function of the English progressive marker. No doubt a far more sophisticated treatment is ultimately required,'4 but among other things t l ~ eprogressive seems to have the function of predicating a verb of a stagc, but not of an individual. Let us give the following translation of thc progressii~emarker, which is of the category IV/IV, or something that takes IV-phrases (or Verb Phrases) and turns them into other IV's. T h e progressive, then, turns a "property" into a LL~tate".

I then compare "Jake runs" with "Jake is running". "Jake runs": RPP{ j ) (^Axrunl(s)) Which is equivalent to: run1(j ) "Jake is running": ; I P P { j ) ( A L P 1 l . x ~ y [ R (& . YP'{y)](^),z Y~) runl(.z))) This reduces to: ?ylR(.)/,j) & run'(.y)] In the case where "runs" is predicated directly of Jake, it may be intcsprcted v:~riablp as a habit, or a disposition, or an occupation of Jake's. Thcsc various characterizations arc not distinguished under this analysis, though closer examination may rcvcal that ccrtain distinctions will have to be made.

66 Greg N. Carlson Another problem raised here is that individuals and stages appear to be of the same type, as run' may be predicated of either. These should be distinguished at some level, and can be, but to do so would require a certain amount of additional notation (introduced by Terry Parsons in class lectures, spring 1976), so I leave the matter unresolved here. Intuitively, if run' is predicated of something that realizes an individual, it means something like: "running is a characteristic of this event-like thing, il realization of an individual". I now turn to the matter of 4 N P and the indefinite plural interpretation. Formally it is a rather simple matter to incorporate 6 N P into this framework if we treat it as a proper name of abstract individuals. T h e translation of "dogs" would be very much like that of "Jake". (We ignore the obvious internal structure which the N P dogs exhibits.) (a) "Dogs" translates as: ilPP(d}. If we construct the proposed translations of the following sentences, we can see how the "indefinite plural" reading arises. T h e translations are given in their reduced forms. "Dogs "Dogs "Dogs "Dogs

are intelligent": I(d) are sick" (physically): 3x[.R(.r,d ) & sick' (x)] run": run' (d) are running": 3x[R(s,8 ) & run' (x)]

T h e indefinite plural reading- arises whenever it is a dog-stagc that something is predicated of. A dog-stage, or a realization of the hind dogs, thcn, is whatever realizes the kind dogs at a time and a place. That is, it is a temporally and spatially bounded appearance of a kindVz5Particular individuals are by definition spatially bounded (i.e. can only be in one place at a time) but not temporally bounded (can exist at different times), so the main difference between kinds and individuals is that kinds are not sparially bounded, but individuals are. A realization of a kind, appearing at il time and place, would be simply one or inore of that kind. As an individual may be thought of as whatever it is that ties a bunch of stages of an individual together, so might a kind be thought of as whatever it is that ties a buncl~of things of that liind together, maliing them realizations of the same thing.2" T h e notion that a realization of a kind should be a subset of' the set of individuals of that bind might run counter to the feeling of some that a realization of a kind should instead be a11 of the individuals of that kind. But we simply do not speak that way. If we say "Marvin owns that kind of do%'' we clearly do not mean that he has a monopoly on the ownership of that kind of dog, but only that he owns at least some of that kind. Or, if we say "that hind of animal is found in India and is also found in Pakistan", we do not mean that all of that kind of animal are found in each place, only that s o m 2 are fbund in one place, and some in the other. If there are some of a kind present, then this counts as the presence of that kind. With this in mind, we see that the indefinite plural does indeed have an existential quantifier associated with it, but that the source of the existential quantifier is not the determiner of t11c 4 N P , hut rather what is being predicated of it at the time. Thus, the

A Unified Analysis of the English Bare Plural 67 existential quantifier itself vvill have constant scope, and in fact will have "narrowest" scope. This clearly accounts for the lack of interaction between the existential quantifier and other predicates in the sentence. We will conclude by showing how this way of looking at things can account for the opacity, narrow scope, and differentiated scope phenomena discussed earlier. Let us first look at what is proposed to bc the difference between the sentences in (131) and (132).

(131) Max believcs some dogs are here. (132) Max believes dogs are here.

1

'

The question we are concerned with is why (131) exhibits a transparent reading, but (132) does not. T h e transparent reading of (13 1) would be derived by introducing the NP "somc dogs" outside the scope of "believes". This structure would bc represented as follows. '[be here" translates as: ;lx3y[R(y,x) & Here1(j~)] "belie~es" is: Bell "Max" is: iLPP{m} "Some dogs" is: ; ~ 3 s ( D o ~ ' ( x&) " ~ ( x )(I] ignore plurality) "Max believes some dogs are here" translates as: (131') 3r[Dog1(x)& [Bell(cjJ~[R(.y, x) & He~-e'(,~/)l)(uw)]] Substituting the NP "dogs" for "somc dogs" in this structure and translating "dogs" as ~.PP{IJ),u7e arrive at the follon-ing representation:

(132') A~[Bel'('3,~[R(~~t, x) & He~-e'(.~!)])(rn)](d) What this says is that the individual denoted by d is believed by Max to have a stage that is here. Since d is a kind of thing, there is no reference M-hatsoever in this formula to any particular dogs. Hence, Max's belief has nothing at all to do with particular canines. Our impression that sentence (132) has only the narrow scope reading derives from the fact (which in a full formalism would be explicitly stated) that any stage of 11 (the kind) also has to be a stage of some particular individual of that kind. In making this inference, though, we find that the expression denotes thc stages in question appears in an intensional context, being part of the predicate itself, and not part of the NP. As no particular stages are referred to here due to the intensional context, these stages need not be associated with any particular dogs. I11 extensional contexts, as for example in "Dogs are here" the specific stages may be associated with specific dogs. In this way the notion arises that (132) and he like exhibit only opaque readings. It should also be noted that if we consider d to be a rigid designator (as Montaguc considered proper names to he) the formula in (132') would be equivalent to the following.

68 Greg N. Carlson So the logic makes the claim that sentences like (132') are not ambiguous with respect to scope possibilities. As is well-known, this might not be exactly correct. In any casc, the claim made here is that whatever ambiguity proper names may exhibit in intcnsional contexts, bare plurals will exhibit the same sort of ambiguity. I think a littlc reflection will show that this is reasonable. Compare (13Ba) and (133b). (133)

(a) Max believes that Bossit has horns. (b) Max believes that conls have horns.

It sce~nswhatever anlbiguity can be attributed to (133a) may also be attributed to (133b), though the judgments here are notoriously subtle. T h e treatment of barc plurals as proper names also leads us to an account of thc narrow scope phenomena. Recall that a sentence like (134) has only a contradictory reading.

(134) Cats are here and cats are not here, If we look at the second conjunct alone and introduce the NP "oats" outside the scope of the negative, we come to the following representation:

But because c is treated as being a proper name, this formula is equivalent to thc follow-ing.

Thus, the representation of sentence (134) will always be equivalent to somcthing ofthc forin A & -A, or a contradiction. T h e same equivalence will account for all the othcr cases of narrow scope. T h e other quantifiers in the sentence will always, in the cascs exemplified, have wider scope than thc existential cluantifier that is a part of thc predicate itself, and the relationship between the other quantifiers and thc bare plural is irrelevant since proper names do not show scope behavior. T h e sentence ( 1 31) is a contradiction for the same reason that a sentence like "Fred is here and Fred is not here" is a contradiction. And a sentence like "everyone saw movies" fails to exhibit relative scope ambiguity for the same rcason that "everyone saw Fred" fails to exhibit that sort of ambiguity. We will conclude this section by presenting a brief analysis of differentiated scope, which once again cxploits the analysis of barc plural NP's as proper names. An examination of the sentences of (135) reveals that (a) and (b) cannot receive ilorrnal literal interpretations (though a hyperbolic usage of (1351)is heard on occasion, a matter I disregard for the time being). T h e proposed translations of these sentences r e ~ c a lwhy it is that the first two are strange in a way that (135c) is not. (13 5 )

Jake is everywhere. (b) Some dog is everywhcrc. (c) Dogs are everywhere. (a)

A Unified Analysis of the English Bare Plural 69 "Jake" translates as: %PP{ j) "Some dog" translates as: IP3.lel~Dog1(x)& P { x ) ] "Dogs" translates as: 'PP(cl) "be evcrywhere'' transIates as:

"Jake is everywhere":

"Some dog is ever~where":

"Dogs are everywhere"

In these cases, we see that a felicitous transIation results with $NP in spite of the fact that the universal in the predicate is always restrictcd to being within the scope of any quantifiers present in the subject NP. In the case of (135a), the assertion is that in cvery relevant placc there is a Jake-stage. Since Jake is an individual of the type that can be in only one placc at a time, this sentence, taken literally, speaks of'a worlcl we simply don't live in (but if "Jake" were the name of a god, for example, the sentence would make a bit more sense). Likewise, w-ith "some dog" in (135b), it is realizations of the samc animal that must appear ever~rwhereif the sentence is to bc true (supposing that the phrase means some particular individual dog, and ignoring thc well-formcd "kind" rcading for now). This sentence encounters the samc problems as "Jake is everywhere". Note that I am not claiming that these sentences are either syntactically or scmantieally ill-formed, only that they are strangc in our ~ o r l dIn . the case of ( 1 3 5 ~we ) exploit the notion that 1-ealizationsof a kind consist of sofile of that kind, appeasing at a time and a place. It is asserted that the same individual is everywhere, just as with Jake, but this individual is not of the type that can be in only one place at a timc. Whatever it is that ties all individual dogs together as a kind - thc abstract individual "dogs" has the propert! of having sonic realization in every relevant placc. 'This, then, is a means of accounting for differentiated scope. Ilue to thc programmatic nature of this formalization, I leave undiscussed a number of other difficulties with 4NP that have been raised here. T h e analysis proposcd can handle some of these quite readily; others at this time remain unresolved. A number of othcr issues raised by the proposecl analysis have not been notcd here, and I do not wish to pretend that it is u-ithout its difficulties.

70 Greg N. Carlson

5 Conclusion T began by noting that the analysis of the semantics of the English bare plural was full of difficulties because of its apparently diverse uses. Hen-ever, there was reason to believe that the divisions noted were not so clearly distinct after all, and that a unified analysis LWSfound to be desirable, if not necessary. A unified analysis was then psoyosed which allows a constant translation of (bNP in all cascs, existential and generic, and which seems to be able to account for some of the surpsising semantic characteristics of the "indefinite plural" use of this construction. Ally number of directly related matters have been left untouched, but tbs which this analysis of the bare plural, if adequate, would have direct consequences. For example, a striking similarity was noted between bare pli~ralsancl Illass nouns that have no cletermi~lerassoeated with them (see Cartwright (1975) for similar observations). In addition, the singular generics with rr and the were left untouchcd, though the relationship bctween a, the, and d, is a mast interesting (and difficult) one. I hope tliat this analysis of the bare plural will be able to shed some more light on such matters.

Notes This paper represents a major revision and extension of my h.3.L4.thesis written at the Univcrsit! of Iowa in the fall of 1973 under the direction of Larry Martin. I nish to thank Lisa Sclkirk, E n ~ n ~ o n Rach, Edwin Williains, 1,arry Martin, and Barbara H. Partcc For reatling and criticizing earlier versions of this paper, and for their constant interest and encouragcnicnt. T h e quality of the contents has been enhanced reniarkablp by their comments; of coursc nonc ncccssarily bclicvc anything contained herein, and I am alonc responsible for errors. In addition, I rcccived man! fine coninlcnts from the anonvmous rekree which contributed grc;ltly to the tinislicd product. 1

This hypothesis appcnretl in t\vo publications in the coursc of' niy work on this topic. See Schachtcr (1976) and Burton-Roberts (1976). 2 E:xcluded from consideration arc the predicate noniinals, though an extension of the suggested analysis may be able to cover them as well. 3 T o mcntion but 3 f~ 5 - ,Dowty (1972), Gough (l069), a11d Do~lgI~crt!.and 13elonnc (1072) worked under this assuniption. I do not intend to claim that thcrc ~ i ~ c c s ~ n1s.r;1i lplural ~ counterpart for the indefinite article: only that if there is one, it is not the null determiner. 4 That is, the differences we find in other singular-plural pairs such as /hrw-/hr.\., he sp ancl 1Itc pl, that-lhose, r r ~ y sg, and nr!)! pl (thc quantilier, not the polarity itcni), and I - sg and some -t pl (the quantifier). 5 T h c gcncral prediction is tliat any NP in any contcrt mily gct t1icl.e cithcr b y direct introduction or by quantifj-ing in, and if it makes a difference in the ultiniate semantic rcprescntation, tlierc will be an ambiguity. However, thcrc are many cascs \\~llerepredicted ambiguities clo not ilplJf3di". Sometin~esit depends on the nature of the YP itself:

+

+

+

+

, ,

I

A Unified Analysis of the English Bare Plural 71 (i) Bart wants to slio\v Jcnnie ( I gaoi/ ?trozq~~. (ii) Bart wants to show Jcnnie rr A-oocl tiirrr. (ii), unlihc (i) docs not appear to bc ambiguous with respect to relative scopc of' thc italicized NP. In other cases, the nature of ~ h predicate c is responsible. (iii) Bart wants to have LI I I I I S I ~ C S S . Note that (iii) is not nmhiguous with any other NP's in place of the italicized expression either.

(iv) Bart wants to have

6

7

8

0 10

I 1 lots of twenty set-cral

1?:: 1

mistresses.

I assunic that certain predicates like "have" reyuirc a lcsical direct object, h;~nning.rluantjfving in, and that certain NP's, like "a good time" cannot be quantified in. It is not clelir to me how to sure thcso restrictions formally. The sentence "there aren't cats in this room" is really quite awkward, if not ungramma~ical.I believe [his stcnls from the fact that the ncgative here negates the quantifier on the subject N1' and not the \\-hole sentencc. If there is no quantifier present, as may he thc case \\ith dNP, this result is expected. This lict conflicts with our feeling that "cats are here" means that Inore than onc cat is here. At this time, I think it rrwans one or more, but inlpljes morc than one; if ?-ou knew there was just onc there, you'd say so. Thc fact that the existcnti;il must hold wider scopc is nor predicted by Ilo\~-ty'sanalysis, and an! ,~tlccluateanalysis of.fi,r tinic adverbials should reflect this observation. Pcrl~aps/ i ) r time advcrbiills are verb modifiers and not VY or sentence modifiers. This is discussed in hlnntague (1972), Partcc (1970) and references citccl. Unquantified Inass nouns exhibit unambiguousl~opaclue readings, narrow scope, and dillkrcntiatcd scope as wcll. (i) Jack belicvcs that .furniture is kept in Ncll's attic. (ii) Ever>-onctll-nnk water thri~~r,os.fi~arir/~ited. (iii) Chloritrc gas was e\.eryw here.

11 This problem is discussed in Cartmright (1965). 12 One readcr notcd that it cvould be possible to assign scope after the translation from the object language into the language that is to be intcrprctcd, and that is r~rouldbc possible thcn for the singul~rand plural ( I and 0, to participate in diffcrcnt scope-assignment rulcs, bur remilin singular ilnd plural counterparts nonetheless. I mean to exclude this logical possibilitl as violating the very assuniption I started out with, that singular and plural shoultl bcha\-e ;dike up to thosc differences that can he attributed to plurality. Attributing differential scope beha\-ioi to pluralit! per se is not possible, sincc so t"ir as I know it has no inrlcpendcnt motivation clsewhere in the grammar. T h e differential scope behavior \voiild then be retluccd ro sonic ,~rbitrarj-property of thc bare plural, and not simply the h c t that il is n plural. generic quantifier or article, though I clon't know 13 I know of no languages that have an e~i.lrr.uz~e/,~ whether this is universall\; so. Smith (1964) notes that generic NP's of ICnglish arc gcncmtcd s!-ntacticall!- just lihc non-generic NP's, requiring no special rulcs ; ~ tall. I suspect that all languages pattern liken-ise. 14 I assilnlc some notion of "normal intonation", and T ;111i 11ot responsible for M-hath~lppenswhen additional stress is added to some constituent. For examylc, "smokcrs .4RL rudc" can apparently

72 Greg N. Carlson mean that some smokers are rude. I doubt that it can bc maintained that such scntcnccs in\-olve a simple existential claim howevcr, for the following seem cstre~nclc.strange to rncb, even if existentially true.

(i) (??)Smokers .4REChincse. (ii) (??)Trccs ARE 350 feet tall. (iii) (??)Babies ARE six-toed. It seems thc stress has to do with disposition or some similar notion in this case, having some sorts of behavioral implications. 15 T h c p~.escnceof the mass noun "kelp" cannot be held rcsponsiblc, for "chirpcd", "walked without stumbling" and other VP's having no dircct object cxhibit the same iunbiguit!.. 16 This is similar to referring to. say, all the members of a team by calling them "the team". In (a)(c), the predicate is true of each team member individually. (a) T h c team is m-caring red shirts. (b) T h e tcaln died in the plane crash. (c) T h e tcam is quite tall. Hov.cver, "the team" can be used to rcfcr to something more than thc sun1 of'its parts: (d) Thc tcam has ~ v o n22. pennants over the last 40 years. (c) T h c team has becn in continuous cxistcncc for 100 years.

I do not wish to push the analogy too far, but kinds arc a bit like tcanls in this respect. I thank Barbara Partee for his obser~ation. 17 I am not sure rvhy this variation of pronominal fbrm is roleratccl, but sometimes one, and then thc other, seems preferable. In fact, "sm" alone appears to disallow any reference to hinds, while all the rest allow it. 18 (a) ""Sin birds are \videspread.

19

I do not mean to discount as a possible line ofliguistic inquiry an investigation of ~ h relationship c belween binds and individuals of that kind. For example it scems to me that thc fiict that (a) below can mean that linguists, collectively, have .30.000 books in print but th;~t(h) cannot mean t h a ~linguists, collectively, have 62,344 legs (even though (b), on a collccti~ebasis, m i ~ h bc t true) is a fact that needs to be accounlcd for within a semantic aniilysis.

j

7

;; 1

, I

(a) 1,inguisls lla\-e over 30,000 books in print. (b) Linguists have 62,.744 legs.

20 21

I do mcan to excludc from a semantic analysis hen-c\cr, the q ~ ~ c s t i oofn whcthcr 200 out of 000 birds born without wings t~louldfalsify "bircls have wings". This is a different cluestion li-om the above, thoug1:ll I grant that the dividing line is not al~vaysclear it1 any given casc. I wish to separate linguistic knowledge from the act of recognizi~lgficts about the world. This sort of analysis might also bc uscd to investigate abstract individuals such ;IS "honestj", bL democracy", and the like. These arc csscntially mass nouns, lihc "water" and "tire". Noted in Lawler (1972). Will also give rise to a very natural third reading, indicating present clisposition. as in: (a) Water r~v'llboil at 100°C.

22

kIilsiirk also notes that his "states" are predictablc of NP's detcr~nincclhy ~ h ~~nstresscd c "sm" and b! the non-generic "a", but that the "propcrtics" only sclect thc generic "a" (assuming

1

: I

j

A Unified Analysis of the English Bare Plural 73 there to be a distinction, which there may or ma>-not be, bctaeen generic ant1 existential "a") and ;ire not acceptable when predicated of an N P determined by "sm".

(a) A soldier nas available Sm soldiers were a\;ailablc (a "state") (b) ,4 soldier was tall, (generic only) "Sm soldiers were tall (a "property") Though I have no account of thcsc distributional facts at this time, they may be uscd (at least in subject position) to test \diether the predicate is a "state" or a "property". 2.1 1 exclude those cascs whcrc it is thc hr of identity that precedes the predicate nominal. These are quite different, for they allow an indefinite plural reading: (a) Children were thr z?rr.tims(![/he nssliult. (b) Horses were /he p n n ~ sin /tic parnr.

24 For example, we ~vouldwant it to entail that john hadn't finished crossing the street in (a): (1)

John was crossing the strcct (when he was flattened by a truck)

See Bennett and Partee (1972) for some problems and suggested solutions. of translation 2.5 This sort of notion may be what Quine (1960) had in mind in his clisc~~ssion procedures, but whether or not this is true, it served as the sourcc of thc line of thought l~ursucd herein. 26 We night try, then, to define a "gcncric sentence" as any sentence that attributes a property to thc individual that s e r ~ e sas the subject of the sentence, and not to one of that individual's realizations.

References Iknnett, Michacl. 1975. Some extensions of a Montaguc fragment of English. Ph.11. dissertation, UCLA. Rcpr, by the Indiana Linguistics Club. llcnnett, Michael and Barbara H. Partee. 1972. Toward the Logic of Tensc and Aspect in Ilnglish, unpublished manuscript. Ilurton-Roberts, Noel. 1976. On the generic indefinite article. Llrlrgt/n~r52(2): 427-48. C;arlson, Greg N . 1973. Superficially Unquantificd Plural Count Nowl Ph1-ases in llnglish. M . 4 . thesis, University of Iowa. Cartwight, Elelen. 1965. Heraclitus and the bathwatcr. Philosopliir~rrlR P Z ~ C71: J ) 406-85. ~ (;artwright, Helen. 1975. Some remarlcs on mass nouns and plurality. . S ' ) ~ t ~ / h31: ~ ~ s39.5-410. e (:honisky, Noam. 1945. .-lsj)i~i.tsoJ/lre T11ror:yr![S')~nta.\.,Cambridge, Mass.: M1T Press. Chonisk~~, Noarn. 1975. Questions of form and interpretation. Lrng~ris~tc .41z~!j~sI.s 1: I. Ilahl, &ten. 1975. O n generics. In Edward Keenan (cd.), Fonnirl Se~rrtrr~tr~..~ q/',V(~~trnrl /,an,qr,rrg(~, (:ambridge: Cambridge University Press. Uelorme, ICvclyn and Ray Dougherty. 1972. ,4ppositive N P constructions. F'or4nrlnlioi1s ( ? / ' I , l i ~ i , y ~ ~ o , y ~ ~ 8: I . Dowt!, David R. 1972. Stttdrrs irr the Logic. of' I'i.rb -4spi>c/~rnd 7 i m i ~Rq/i,rerne ill EtrK/islr. I'h.11. dissertation, L ~ n i v c r s i tof ~ Texas, Austin. Rcpr. in Stztdirs in Li~zpuis/ic.s,University of Texas, Austin. Gough, James, Jr. 1969. T h e syntax-based semantics of the English determiners a, /he, and 0. Pcrptr:\. itr Ling 14is1il.s1: 1 . Lawler, John. 1972. Generic to a h u h . In Paul h4. I'eranteau, Judith N. Levi, and Gloria (:. l'liarcs (eds), Prlpers#i-om /hc Eigh~hRiyio,lwtrl i2.lrrtin.~c!f /lzr Clril.npo Lin,y~rtslit.S o r i i ~ i )Chicago, ~, Ill.: (:I ,S.

74 Greg N. Carlson J,ewis, David. 1975. "Adverbs of Quantification", in Edward Keenan (ed.). firr~jal S1~nrrrnrli.sr!/' ;Virlurul Licnguage, Cambridge: Cambridge University Press. McCawley. James D . 1970. Where do noun phrases conic from?. In Roderick 11.Jacobs and Pctcr S . Rosenbaum (eds), Rua(litrgs in Englzsh T ~ ~ I ~ ~ I MGrrrrnnrur, I I I I J OWallham, ?? Mass.: Ginn and Co. Milsarli, Gary. 1974. Cxistcntial senlcnces in English. P11.D. thesis, MIT. Montague. Richard. 1972. T h e proper treatment of quantification in ordinary Cnglish. In Richard 11. Thomason (ed.j, (1974) for~ri~cl Pfzi/ost~ph.)f. Stlerted P(zpers r!/'Rirhrlr-d.Mon/~lgrr~, New I Iat en: Yalc University Press. Parsons, Tercnce. 1970. An analysis of mass and amount terms. Fourtd~r~ions c![Lrrlaguugi~6: 363-88. Partee, Barbara H. 1970. Opacity, coreference, and pronouns. Slln~ki~se 21. Partee. Barbara H. 1975. Deletion and variable binding. In Edward Keenan (ed.) Forrttnl Sem(mlics I!/' Naturul Language, Cambridge: Cambridge University Press. Perlmutter, David. 1970. On the article in English. In hlanfrcd Rierm-isch and karl Erich Heidolph (eds), Progress 212 Lirtguistic-s. The Hague: Moutton. Poslal, Paul. 1969. Anaphoric islands. In Robert I. Rinnick et al. (cds), P(ipe,:rJ h m the I;i/ih Rqionrrl Mertrng of ~ h Chicago t Linguistil- Socirt.11. Chicago, Ill.: CLS. Q ~ ~ i nWillard e, van Orman. 1960. IVoril irl~dOl!;ect, Cambridge, hlass.: MIT Press. Schachter, Paul. 1976. A nontransformational account of gerundive nominals in English. Lin~rris~ic. Inquit:)/7: 2 . Siegcl, hlufft E. A. 1976. Capturing the adjective. Ph.D. dissertation, University of Massachusetts, ,4mhcrst. Smith, Carlotta. 1964. Determiners and relative clauses in a generative grammar of English. Langmii,~e 40: 1. S~ockwell,Robert P., P. Schachtm, and B. H. Parlcc. 1973. The /Mr!;or- .Synr~rc.ll'lSlruclur~,sc!f'Erzg/ish. Ncw '170rk: Holt, Rinehart, and Winston. S~veel,Henry. 1898. -4 ~ V e mE n ~ j i s hGnlmnrur. Oxford. Zemach, Eddq-. 1975. On the adequacy of a type ontolog!.. Sy~rrhesc31: 509-15.

Generalized Quantifiers and Natural Language Jon Barwise and Robin Cooper

0 Introduction In 1957, the Polish logician Andrej Mostowski pointed out that there arc many mathematically interesting quantifiers that are not definable in terms of the firstorder ti, 3 and initiated study of so-called generalized quantifiers (cf. Mostowski 1957). Since then logicians have discovered and studied a large number of gencralizcd quantifiers. At last counl there were well over 200 research papers in this area. Most of this work has been directed toward cardinality quantifiers (e.g. Keisler 1969) and topological quantifiers (e.g. Sgro 1977) which are not particularlj? relevant to natural language, but even so, it has fbrced logicians to rethink the traditional theory of quantification. The quantifiers of standard first-order logic (as presented in elementary logic textbooks) arc inadequate to treat the quantified sentences of natural languages in at least two respects. First, there are sentences which simply cannot be symbolized in a logic which is restricted to the first-order quantifiers b' and 3. Second, the syntactic sti-uctureof quantified sentences in predicate calculus is completely different from the syntactic structul.e of quantified sentences in natural language. T h e work on generalized quantifiers referred to above has led to net+-insights into the nature of quantifiers, insights which permit logical syntax to correspond inore closely to natural language syntax. These insights, we argue, may also make a significant contribution to linguistic theory. Section 1 discusses the nature of generalized quantifiers and thcir relationship to the syntax of English in general terms. Section 2 develops a logic containing generalized quantifiers. Section 3 shows how this logic may be formally related to a fragment of a syntax for English. Section 4 is the main section of the paper. In it we discuss some of the general implications of the notion of generalized quantifier for a theory of natural language of the kind that is interesting to linguists. Our conclusion, in secrion 5, attempts to draw some general conclusions about thc relationship between syntax, semantics and logic.

76 Jon Barwise and Robin Cooper 'Thc papcr has four appendices. Appendix A contains additions to the fragn~entin section 3 which are suggested by the results in $ 4 . Appendix 13 contains sol~lcpossible semantic postulates on the meaning of non-logical dctcrminers. Appendix C contains the proofs of the Facts about quantificrs asserted in the body of the paper. Appendix D consists of a chart classifying English determiners according to the semantic categorics introduced in $ 4. Some (but not all) of the points made in section 1-3 of this paper are implicit or explicit in A4ontaguc (1 974), especially in PTQ, "The Proper Treatment of Qyantification in Ordinary English". (Some of the suggestions in 1-3 are also similar to suggestions in other papers: e.g. Fenstad (1978); Peacocke (1 979)). Our hope is to develop h4ontague's treatment of noun phrases further in a straightforward way (without lambdas), and to show some of its implications for a theory of natural language.

1 Generalized Quantifiers and Noun Phrases 1.1 Some examples of generalized quantifiers Viewed from a modern perspective, the familiar b' and 3 are extremely atypical quantifiers. They have special properties which arc entirely misleading when one is concerned with quantifiers in gcncral. JVc begin this paper by discussing some simple examples of generalized quantifiers froin mathematics to draw out some of the general features of quantifiers. Consider the following examples. (1) (a) (b) (2) (a) (b) (3) (a) (b)

There are only a finite number of stars. No one's heart will beat an infinite number of times. More than half of John's arrows hit the targct. More than half the people voted for Carter. Most of John's arrows hit the target. Most people voted for Carter.

1.2 Many quantifiers are not definable using first-order 'd and 3 There is no doubt that in any human language in which modern science can bc formulated, sentences like (1) and (2) can be expressed. We suspect that sentences with quantifiers like those in (2) and (3) can be cxpresscd in any human language. But tlie quantifiel-s in (1)-(3) cannot be expressed in terms of tlie first-order quantifiers b',r(. . . ,v . . . ) and 3x( . . . .t. . . . ). It is not just that we do not see how to express them in terms of b' and 3; it simply- cannot be done. Thus, a semantic theory for natural language cannot be based on the predicate calculus alone. First, before sceing just what thc problcms arc, Ict us abstract out thc quantifiers at \vorli in (1)-(3) as follows. (1') (2') (3')

Finitely many things s satisfy q ( s ) , or., Inore .\:ymho/ic.a/l)/,1;inite xlcp(.v)l. More than half the x such that $(r) satisfy cp(.v), or, (more than t~b).rlq~(.v)]. A/lost ,I? such that II/(.v)satisfy cp(x), or (most rl/).~[rp(.v)l.

Generalized Quantifiers and Natural Language 77

Let E be an arbitrary non-empty set of things (individuals, entities, call tlicm what !.ou will) over which our variables range. First-order logic only a l l o ~ squantification over objects in E, not over arbitrary sets of things, functions from things to things or other sorts of abstract objects not in E. Within this framework, it is easy to prove that none of the quantifiers used in (1)-(3) is definable in terms of the ordinary 'v' and 3. Consider the case of "more than half'. It is a routine application of familiar tcchniques in first-order logic to prove that this cannot be defined from 'v' and 3; that is, that there is no fixed definition that works even in all finite domains. 'This is proved in Appendix C (C12). One has to leave traditional first-order logic in oiie of two ways. One possibility is to expand he domain E of quantification to a bigger domain E U .#I,where .4 includes numbers and funetions fiom subsets of E to numbers. That is, one might mirror the high-order set-theoretic definition of "more than half' in thc semantics by forcing every domain E to contain all of the abstract apparatus of modern set-theory. A different approach, oiie that model-theorists have found more profitable, is to keep the formal definition as part of the metalanguage, and treat generalized quantifiers without bringing all the problems of set theory into the syntax and semantics of the logicper se. We'll see just how this is done in a moment. T h e point to make here is that, once we make this move, it also gives us a way to treat determiners like "niost", "many", "few" and others.

1.3 Quantifiers correspond to noun-phrases, not'to determiners We have bccn at some pains no/ to call "inost" ancl "more than half" quantifiers. T o see why, note for example that there is no way to define "morc than half of John's arrows" from "more than half of all things", i.e., it cannot be formalized as sonietl~inglike "More than half s( . . . x . . . ),' . This is why, in (2')' we symbolized the quantifier with (I/ built into thc quantifier prefix. What this means, semantically, is that "more than half" is not acting like a quantifier, but like a determiner.l It combines with a set expression to produce a quantifier. On this view, the structure of the quantifier may be represented as below. Quantifier

/"',

Determiner

,

, 1

Set expression

If we compare this structure with the syntactically simple sentence (313) we can see that the structure of the logical quantifier corresponds in a precise n-av to the structure of the English noun-phrase (NP) as represented in:

Det

ANoun

78 Jon Barwise and Robin Cooper For exactly the same reason, "most" must be treated as a determiner, not as a quantifier. It is the NP "most people" that is the quantifier. There is no way to paraphrase a sentence like (3b) that begins "most things are such that if they are people then. .. ". This can be proved, given reasonable assumptions about tlie meaning of L< most", in the same ways as for "more than half".

1.4 Quantifiers are not necessarily logical symbols 'There is a mistaken notion that the meaning of the quantifiers nlr~stbe built into the logic, and hence that it cannot vary from one model to another. This is mistaken on several counts even for mathematical examples. Unfortunately, the most convincing examples of this are outside the scope of this papcr. For example, the rncaning of tlie quantifier Q~cp(x)wl~icliasserts that {x 1 (p(.~))contilins a 11011-empty open set (studied by Sgro 1977) is determined not by logic, but by somc underljring notion of distance, or, more precisely, by an underlying "topology". T o interpret such a quantifier, me need not just an ordinary model, but also a topology to make the quantifier precise. 'The same idea can be applied to the determiner "more than half" when onc turns to infinite sets. hleasures have been developed in which (4) :u~d( 5 ) makes perfectly good sense. More than half the integers are not prime. ( 5 ) More than half the real numbers bctn-een 0 and 1, expressed in dccilnal notation, do not begin with 7.

(4)

However, the truth or falsity of (4), ( 5 ) will depend not on rr priori logic but on which underlying measure of infinite sets one is using.-his measure must be includccl as part of the model before the sentences have any truth value whatsoever. One of the simplifying assumptions often made in the model theory is that one hiis a fixed context whieh determines the meaning of the basic csprcssions. We can think of this context as providing an intcrpretation for non-logical dcterrniners in the above examples. In this paper we shall assume throughout that thcrc is a rich context held fixcd that determines the precise meaning for basic expressions, even those like "most", "niany" and "few". We refer to this as the.fised ~'orttr.vtassu~ilplz'or~. It should bc pointed out, however, that even with this assumption the interpretation of quantifiers, even those like "every man", will vary fro111 model to model since the interpretation of "man" is clctcrmined by the model. T h e difference between "cvcry man" and "nlost men" is this. T h e interpretation of both "most" and "man" depend on t l ~ cmodel whereas the interpretation of "ever!;" is the same for e\~erj-model. "Every", unlike "open", "niorc than half" and "most", is a logical quantifier. T h e fixed context assumption is our way of finessing the vagueness of non-logical determiners. We think that a thcory of vagueness like that given by Kamp (1975) for other kinds of basic expressions could be superimposed on our theory.4 We do not do this here, to keep things managcable.

1.5 Quantifiers denote families of sets Quantifiers are used to assert that a set has some property. 3.\-(p(.z)asserts that the set of things which satisfy q(.r) (informally {,vlq(s)} or, in our formal notation .i'[(p(.z')l) is a

Generalized Quantifiers and Natural Language 79 nonempty set. That is, the set of individuals having property cp contains at least onc member. b'.vcp(.v) asserts that the set contains all individuals. Finite ,v(p(.~) asserts that the set its finite. It is clear that a quantifier map be seen as dividing up or partitioning the fimily of sets provided by the model. When combined with sonlc scts i t will produce the value "true" and when combined with others it will produce the value "false". In ordcr to capture this idca formally, quantifiers are taken to denote thc fhmily ofscts for which they yield the value "true". T h e truth of a sentence QPvlcp(s.)jis the11 determined by whether or not the set .i[cp(,v)-Iis a member of the quantifier denotation. The denotation IlQII, of a quantifier symbol can be specified informally as follows for some of the quantifiers we have discussed. (Wc Ict E represent the set of entities provided by the model.) 11311 = { X It'7'II

=

L E I -x# 4 )

{El

J(Finitel1= {X C E X is finite} contains more than half of the Ns} lMore than half of NII = {X 2 E 1 Ilhlost NII = {X & E I X contains most Ns} To e~nphasizcthe role of the set, we will write Q,i.Lcp(,v)Jrather than just Qr[rp(.\:) 1 in the logic developed in section 2. If cp is a simple set expression we may write QW

1.6 Proper names and other noun-phrases are natural language quantifiers

I

Wc are now in a position to examine the notorious mismatch between the syntas of noun phrases in a natural language like English and their usual representations in traditional predicate logic. To review the mismatch, notice that thc sentcnccs in (6) arc all to be analyzed as consisting of a noun phrasc followcd hy il verb-phrase as represerlted by the labelled brackets.

(6) (a) [HarryJkp[sneezed]\ (b) [Some person],p[si~eezed]\.l, (c) [Every man],,[sneezed]\ (cl) [Most babies]Np[~ncc~e]\:l., There is strong evidence that the phrases labelled as NP's here belong to a singlc syntactic category. For examplc, they may occur not only as the subjccts of intransitive verbs (as in (6)) but also as the objects of transitive verbs (7) and of prepositions

(8) Harry some pel-son (7) Susan kissed every man ( most babies

80 Jon Barwise and Robin Cooper

( Harry (8) I saw Susan with

some person every man ( most babies

This constituent structure is not reflected in the translation of sentenccs containing NP's into predicate calculus. (6a-c) might be represented, ignoring tense, as (9a~c) respectively. (9) (a) (b) (c) (d)

sneeze (h) 3.r[person (,r) sneeze (,x)] 'v'.r[n~ai~ (x) + sneeze (x)] (There is no predicate calculus reprcsentation for ((id))

While (9a) contains a representatioi~of the English NP Hurq), (9b) and (9c) do not eontain constituents representing the NP's some person and e o e ~ n2an. : ~ Furthermore these two expressio~lscontain open sentences joined by two place connectives which do not correspond to constituents of thc English sentences. T h e corrcct choicc of thc connective depends on the quantifier which is to be prefixed to the open sentence. From our discussion of generalized quantifiers we can see that the mismatch bctwcen (ha-d) and (9a-d) is not necessary. (9b) is not really a translation of (6b), but of the logically equivalent, but linguistically quite different, sentence: (10) Something was a person and sneezed. What is wanted, to translate (6b-d), is (in our notation): (1 1 )

(a) ( S o m e person) .i- [sneeze (s)] (c) (Every m a n ) ,i.[sneeze (s)] [sneeze * (.v)]. (d) (Most babies) ,i

Or, more simply, (12) (b) ( S o m e person) (sneeze) (c) (Every man) (sneeze) (d) (Most babies) (sneeze). These sentences will be true just in case the set of sneczcrs (~+epresented either by .i, [sneeze (s)] or by sneeze) contains some p c r s o ~ ~every , man, or most b~bies, respectively. All that is left to make the treatment of NP's ;IS quantifiers uniform is the observation that even proper nanles can be treated as quantifiers. In our logic, (13) may bc translated as (14), or rather, something like (14) in structure.

(13) Harry knew he had a cold. (13)

I-Iarry i[x knew s had a cold].

Generalized Quantifiers and Natural Language 81 - -

-

~p

(14) must be truc just in case Harry is a illember of the set. Hence the quantifies represented by the NP H~i1.1.y can be taken as denoting the family of sets which eontain I-Iarry. T o hare our cake and cat it too (preserving the intuition that proper narnes denote individuals, rather than scts of sets) we will let the lexical item or word Hur-?)I denote an individual. However, the NP containing just this word, represented by [HarryjNp,will denote the family of sets containing Harry.

1.7 Quantifiers can degenerate in some models As mentioned above, we can think of a noun phrase as dividing the sets corresponding to verb phrases into t\vo classes correspoi~dingto those which make it truc and those which make it hlse. As a denotation of the noun phrase, we choose the set of those whicl~ make it true. It seems the most natural way to formalize the intuitions. Thus noun phrases act, semantically, like tlte logician's generalized quantifiers. In some interpretations (models) however, thesc NP denotations ma>-degenerate in one of three ways. The) may denote the cmpty set, the set of all sets, or, the worst case, hi1 to denote any set at all. T h e first two types of degeneracies are discussed in S 4.5. To see how a noun phrase can fail to denote, notice that determiners will be interpreted as functions from common noun deilotations (scts of things) to noun phrase denotations (sets of sets). Ho~vever,functions have domains and a set may fail to be in the do~nainof function u-hich serves as the denotation of a given detel-miner. In particular, the determiners the, boll1 and rreitlrer havc domains which are special. The l~londtncin, for example, does not denote anything at all unless there is a unique blond man in the state of affairs represented bj- the model. Any attempt to assign it a11 (lr/ ~ I J L denotation is bound to give rise to some incorrect infcrcnces. Thus, we treat the determiner Ithell as a function wit11 domain the set of scts with esactly one element. llbothll and llneitherl are dcfined on those sets with exactly two elements. (?'his treatment is siinilar to some presuppositional treatments that havc been proposed in the literature.) We now turn to spelling out the ideas of section 1 formally. Some readers might prcfer to turn directly to section 4 to see tRe kind of applications we have in n ~ i n d . -

2 A Logic with Generalized Quantifiers: L (GQ) The logic developed here has no basic quantifier symbols. All quantifiers are built up by applying some basic determiner sj.mbol D to some set tcrm 17.

2.1 Logical symbols Thc logical symbols of L ( G Q ) include: propositional connectives: A, v, (b) variables: s , y, Z , xu, . . . (c) n distinguished srl / e m : thing ( d ) parenthesis: (, ), brackets: [, 1, and a c r ~ psymbol:

(a)

^

82 Jon Barwise and Robin Cooper (e) an equality symbol: = (f) sonic of the following logical i1~7/ernzirzers: some, every, no, both, neither, 1,2, 3, ... , !l, !2, !3, . .. ,the 1, the 2, the 3, ...

The semantics of L ( G Q will be defined so that thing alw-ays denotes the set E of things in our model, i.e., the set of individuals or objects. The semantics of the numerical determiners will be defined so that 3 m e n run will mean that at least three men run; !3 men r u n will nlean that exactly three men run; the 3 men run, following I .7, will only have a meaning in those models where thcrc are cxactly three men. In such models it will be true if they- all run.

2.2 Nonlogical symbols Thesc include: some sct (possibly empty) of constan/ s)nnbols, say c, d , .. . (b) for each 12 = I , 2, . . ., sonie set (possibly empty) of n-ary ~.clu/ion.synzj,ols, say R, S, .. . The I -ary relation symbols are also called pl-errlilatc .\:lrmi~ois. say D l , Dz,. . . . These may (c) some set (possibly empty) of now-/ogil.sl ~l~~terrnine~s? include most, m a n y , few, a few, etc. (a)

'Thus L ( G Q ) is not just one language, but is rathcr a whole fin~ilyof languages, dcpcnding on the choiccs made in 2. If and 2.2.

2.3 Syntactic formation rules There are six syiltactic fbrn~ationrules which, together, provide an inductive definition of thc three kinds of expressions of L ( G Q ) , namely set terms, r/ul~?7t?fiers, and/i)rn~zr/ris. These rules are given in Rl-R6 bclo\v-. R1. Atzy preu'ic.ilte synbol is B sel 1er.w. R2. I f q is a Jorv~ulnarrd 14 I s rr zlnriahle tllelr i1.qJ zs a set trrni. R3. I[ D is a rleter-nliilrr rln~l11 is n set tertll the72 D (11) is rn quuntifi~~r. R4. I[ R is an tz-rir:y relnrion sy??1bol and tl, . . . ,t, (11-c conslunls or- i>(/~-i(~bits //IP~ R(tl, . . . ,t,) is a jbrmuln. Sirnilur/)/,!/'11 is 11 srt irrtrr irrrtl I 15 (1 z*~rrirrl?Ic. or. rbonstrzn/ tllerr q(t) is aJi)rrnrd/a. R5. I/' Q Is a qunrntijiri- l~nliq Is a sel tel-rrz Q(II) is rr /i)n?1rr/~r.Wc lcave off' thc parentheses if no confusion is likely. R6. The ~ ; ) T N I L I / L ELII'P S c/o.\-ed untier t/ie pl,opnsilionr// ~.orlr.rcl.tii~es ,A (i~nd),v (or) and (not). N

Some remarks and then some examplcs. 1;ormulas are built up by R4-R6. Set tcrms arc built up by R l and R2. Quantifiers are built by R3. In particulas, RS givcs 11sthe quantifiers: every (thing), (dcnotcd in accordance with tradition by V), some(t11ing) (denoted by 31,and no(thing). Gi\-cn a set term rl we u-rite t h e (11) for the quantifier the 1 (11). In R1, t ~ ( t is ) used rather than thc more customary ( t E I!), just becausc it

Generalized Quantifiers and Natural Language 83 makes the formulas neater. We will abbreviate the formula (1,

= (11, t l )

(given by R4)bl;

= h).

2.4 Some examples In the examples below we assume that our language L ( G Q has the determincrs displayed in addition to the obvious stock of relation symbols. Below each sentcncc of L ( G Q ) we write an appropriate rendering in English and, whcre possible, a predicate calculus equivalent.

(18)

(a) (b)

(4 [19)

(4 (b)

(4 (20) (a) (b)

(4

Some (thing) run. Something runs. 3x[run (.E^)]. Every (man) sneeze. Every nlan sneezes. b'x[man (s)4 sneeze (,r)]. 5(woman)i [the (man).?[kiss (s,.)l)]l. Five (or more) women kiss the man. 3.~1 3 . ~ ~ 3 ~. r~~3 . x - # ~ [xz x ~ # " ~ 3 . . . r\ woman n woman (x2)fi . . . 3y[man (y) n b'zlman ( z ) + , ) I = z.1 A kiss (.q, y) n kiss (sz,.p) r\ . . . n kiss (.t'j,,)r)] No (woman) .? [run (x) r\ sneeze (x)]. No woman runs and sneczes. 3,r[woman (x) n run (x) n sneeze (s)]. Some (woman)j j [most (men) .i.[kiss (s?y )1). Most men kiss a (particular) won~an. (No predicate calculus equivalent for rrrost.) Many (men) i [ see (.v, h)]. -Many men don't see Iiarry. (No predicate calculus equivalent for ~rrlrn.y.)

(XI )

I.

N

2.5 The semantics of L(GQ) A model for L ( G Q is a function &I which assigns interpretations to expressions of tho language that need interpretations. It assigns to thing some nun-empty set E and it assigns to each basic symbol S an interpretation (ISI( satisfying S1-S6 below. (To cxhibit the important parts of M separately, we sometimes identify M with the ordered pair (E, I1 I\}.)

SI. IJti.sa l~onstarrtorvnriablr., tlzrn lltll E E. S2. ((thing// = E. / = (1 = ( ( a , ~ ) l aE E ) (i.e., thc equality rclation on E). S3. S4. If'R is un n-uqy rr/c~tion.y~rnbolthert I(R(I C E x . . . x E (n-1it11r.s).Sivrilorl)/. !/' U is n basil set PI-nz (2.2b) then 1 I U / 1 C E.

84 Jon Barwise and Robin Cooper \ ) S o m e ( ) is the #bnction ~ ~ h i c assigns h to crrch & L i11t IurnIl~ llsornell (A) = { X E I X n l / l # 0). (b) IIEveryll i.s the j i ~ n ~ . t i o tI~ N S S J ~ ~ tS u erlch ..I C E I/U ,/i~~ijljt IIEvery)((A) = {X C E124 X ) . (c) llnoll i.s the ./irrzclion L P ~ I ' C ~assigns t u tach - . I C E the /iinlily llnoll (A) = {X 2 E I A n X = 4 ) . (d) For erich natural r~ulnber n, Inll, Il!nll, cznd 11 t h e rill arc /i{t~r.tinn.sorz sels defined by:

S5. (a)

I > 71) I X n24 I = n)

llnll (A) = (X

g El I X

Iln!ll ( 4 = (X

El

nil

\\every11 (A) undefined llbothll (14) = llthc2)1 ( A )

/ ) t h en J /(_,I) =

llneitherll (A) =

if 1-41= 11 otherwise

{l~noll(-4)

if/.,,=?

undefined

otherwise

rvhere I Y I is /he i.nrd?nu/il.~lqf'tlze set Y. Note that for each of these determiners D , llDl[ (-4)is a fimily of sets Q with the property that X E Q if and only if (X n L 4 )t Q. That is, wlicthcr or not ,Y is a member of I D I (-4) depcnds only on -Y n This property is described by saying that the quantificr ID11 (A) /ive.s on A. It is a universal semantic feature of determiners that thcj- assign to any set -4 a quantifier (i.e. family of sets) that lives on A. When nre turn to non-logical determiners, it is the only condition we impose as part of the /ogt'c. T h e other properties will bc determined by the meaning of thc determiner in question in a given context, just like with other non-logical symbols. Just as with other non-logical symbols, we may place non-logical semantic constraints on their interpretations. We will discuss somc of their constraints in Appendix A.

S6. [f D Is a non-loLgica/rlt~erminersyn~holthe71 ID11 ~ ~ ~ j g 1101~~(1l.h s .(Pi (!/'sets that lizqes o r z A.

sorrre /i,nzillt

If more than one model is around, we can keep track of the modcl M by writing [ I S1"' for the denotation of S with respect to M . Givcn a model M = ( E , 11 11)) a variable 11 and an n f E, we let M(::)= (E, 11 11' ) ) be the model n~liich is just like M except that llull' = a . We use this notation belo\v to assign interpretations to all expressions of our logic by extending the function 11 1 . We use 1 for "true", 0 for "false" below. (Formally speaking, rules S7-Sll constitute a definition of I ~ S I I by " ' recursion on expressions S of I.(GQ), simultaneously for all models A I . )

Generalized Quantifiers and Natural Language 85

Similarly, if rl is a set term then

D is I / ~leleriniratr1twl1 q a set /rl.~nrhe~zthe qlrnntz/ier D(q) ~/etlot~.sthc rcslrlt (!/' S9. If ~~pp/jling the ~kt~zot~ltiofl ?/'D to file l/enotcbtion 1!/')7; i.e. lID(v)lI = IlDllcllvlIl).

It is a family of sets that lives on (Irjll 017 S10. I f Q i s (1 quantlfie~mad I./( is a set tern thcrz Q$ dttzotcs t r u ~or~/ill.wcI'i'~,enr/i~g i~hrrhrror mot the denoration of'll/ is one qj'the sets in the ~lt>notation of'Q i.e.,

T l l e u . s u ~ ~ / ~ r l i t h ~ r c h k ~ ~ . z ~ / e s-., / i )L.g. rn,v,

Sll.

if II(PII = lli4l = 1 otherwise. We arc only interested in models where our quantifiers turn out to he defined. However, to make things definite, we might use the conventions of Klcene (1952) 111s logic of "true", "false" and "undefined" on p. 344, extended in thc usual ways. A formula g is said to be tnie in A4 !/ I I ~ I ( ~=" 1. -

3 Application to English Syntax The similarity of the structure of the logical expression in the examples (15)(20) at the end of 2.4 to thc strucrure of their corresponding English expressions should be evident. To makc this relationship explicit we characterize a small fragment of English 2nd define a translation relation between the English fragn~cntand L(GQ), thereby inducing a semantics onto the fragment. T h e fragment will be extendcd in Appendix A.

FRAGMENT 1

3.1 Lexicon NP N

{.John, Harry, Sus(iir, so~rzcfhirzg,e v ~ ~ ) f t k i nlg~, e ( I~I L, J ~., . .) - {person, miln, woman, hook, thing) -

86 Jon Barwise and Robin Cooper ITP- {sneeze, vun) IT- {kiss, see, read}

3.2 Syntactic rules SD of structurlif ~/escri'tions (phrase structure trees) by

IVe define the set means of an inductive (i.e., recursive) definition. We say jr is an S D rather than the more accurate: a is a member of SD.

3.2. I

Le.ril.al inserrion

SDO. If a is a word listed in the lexicon under A (where -4 is NP, N , etc.) then I a]A4 is .%

an S D . [a], may be identified with the tree / . X

3.2.2 Phlzlse structure mlts SD1. N P - + D e t N. (In words, if a, /3 are SDs of forms [S],,, [illr\; respectively then [a/31KPmay be identified with the tree NP.)

is an S1>.

A

(NP

SD3.

SD.1. SD5.

S-{

N R

VP

N P do not VP S and S

-+

S or S NR

-+

that I'P

SD1 and SD5 are used to generate rudinienrary relative clauses, as in ez3tr:)l7rzutz /hu/ runs. Of course, these two rules do not present anything like a coinpletc treatment- of' English relative clauscs.

Generalized Quantifiers and Natural Language 87

3.2.3 Q~rm~tification rule

C(NP, hc/she/ it)

n

This is shorthand for: If [[INl, and [t],are SDs and if'c contains at least one occurrence of hr; then thc result of replacing the first in by and subsecluent occurrences of I I ~ by , he, she, or it (depending on the gender of [ ( l N p ] is ) a n SI).

<

3.3 Morphological rules We need additional morphological rules to obtain the correct forms of pronouns and verbs. We shall not specifjr these here. See Cooper (1978) for details.

3.4 Examples

I

We give structural descriptions of the English esn~nplesin 2.4. (15')

(a) [[S0?t~elh27?g']~~ [uunIvpIs ( b ) [[Sor?~e]~,,,[thing]~

PIS.

The two SD's obtained for sonzethifzg may be regarded as alternatives for the analysis of this n~ordor as making the claim that English contains a word sorn~thi~rg with stress on the first svllable in addition to the phrase S V V I P thing with stress oil the second syllable. T h e truth co~~ditional semantics of the tv*o a]-e sho\vn to bc the same by our translation procedure. Similar remarlis can bc made about ~z~e?:y~//ir/g and eolJql rking.

To get the SD's for 2.1 (19) and (20) whose derivation rcflects the desired scope dependencies we must usc the quantification rule.' (19')

[ [ a ],], , [ ~ ~ 0 1 ? ~ ~ l ? -k ' Z L[[ml~st]~),,[~l(/nl~]~~,l.[k~.\.l~,[~l~~)~~~*1\ ]~]~~~ PIS

(20!)

+[ [ l l ~ o s / ][~m, n, n ] ~ ] ~ l ~ [ [ k i s s ] ~ ~ [ [ ~ ~ ] l ~ c ~ [ ~ ~ ~ o ~ ~ ~ n n ] N ] N P ] \ ~ P ~ S [ [ r n i ~ ~ ~ ~ ] ~ )lN]ll, , , [ n ~+l r[n[ h ~ l do ] ~not ~ ) L[sc.e]\ [ H ~ r l - r : )IS~ I ~ ~ ] ~ ~ ~

0

I

ih lZot [ [ s P Y ] ~ [ H L c Y ~ ~ ~ ] ~ ~ ] ~

[ [ Y ? I Q ? Z ) ~ ] [ ) , , [ ~ ~ ~ ] ~ ] ~ ~ ,

88 Jon Barwise and Robin Cooper

3.5 The translation of fragment 1 into L(GQ) Wc define a relation a' is n tra~zslution? f a by induction on derivations of structural descriptions a by means of rules T g T 4 below. We will use d to vary over translations of a, keepii~gin mind that a' is not necessarily uniquely determined by a (due to rule SD6). z' is uniquely determined by a derivation of a . The Lexicon. On thc left we list lexical items x of Fragment 1, on the right their translation a' in L ( G Q )

NP

VP V Det

John, fIarvy, Susan something, eceglt hing hc, person, man, momarz, book, thing sneeze, run kiss\., see. rend IL, somr t're4y. emh, a1/ the no, neither one, tlvo, LJZWP hot h rtzost, ! I I C ~ ~ )fin), ~, (i fl.111

j, h, s (constant sj-mbols) some(thing), every(thing) person, m a n , w o m a n , book, t h i n g (predicate symhols) sneeze, r u n (predicate symbols) kiss, see, r e a d (relation s ~ m b o l s ) some every t h e (i.c. t h c 1) 110, neither 1, 2, 3 both m o s t , many, few, a few

TO. If' a is an SD of the form [ q ] , , u-here q is in the lexicon, then a' is t ~ 'as given in the above table u~z/es.sX is NP and g is a proper namc or pronoun, in ~vhichcase a' is the quantifier t h e .i,[ll = I?']. Let us explain the exception in the above rule. 'The denotation (in a model M = ( E , I I ) ) of the lexical item Hur?)~is the denotation of its translation h , namely Ilhll or Harry. However, the nounphrase [Harry lK, dcnotes {X El IlhI t X ) . To see this we sinlply compute:

-

I t h e .Yf[.)) = hlll = Ilt~~ell(ll.i.ll.l' hill) IIthell({ llhlll) = {X C El{llhll} =

= {X

C El

CX )

since I(II11II)I

=

1

llhli E X}.

This set of sets is called the prim.ip~/z~/trr~filte~generated bp Ilhll. T h c coinputatio~i sholvs the logical validity of thc following: t h e (?[]I = [I) .? [ c p ( x ) )

cp(r)

(as long as t is not a bound variable of cp(,r)). We could have used a special notation, say h*, fix such quantifiers in our logic. T h e present treatment has the virlue of pointing

Generalized Quantifiers and Natural Language 89 out the relationship of proper names to definite dcscriptions. Many languages cmplo) definite determiners with propcr namcs (e.g., German L r Hetzs, Spanish r l . p ~ o n ) . Pronouns are vanslated similarly: Ire; and are translated .Y,and as the .711 .11 = .r, 1, respectivclp. translated as S'(ql), a quantifier. (We suppress the labelled brackets in translations for ease of reading.)

translates as .+[pl(x)A ql(x)l

If the cluantifiel- Q is a translation of lplNr,then translates as .i[Q(
There would be a closer correspondencc between the structure of this kind of phrase and its translation if we were to adopt Montague's treatment in P T Q , of intensional verbs like seek. Under his treatment the translation would be (" " Q)where " " " is a11 intensional operator). We avoid this here because we are not presently concerned with the semantics of intensional contexts. T h e translation we have provided corresponds to Montague's rule of VP-quantification. 11'

translates as if(<')

translates as

[UNPc/o

not

rV

[jr(<')l

[51vr translates as

(['A

tl)

^

90 Jon Barwise and Robin Cooper translates as (('A <')

translates i [ q ' ( s )A <'(b4)]

translates as

['

that

T6. Suppose a is an SD that comes via the quantification rulc

Then x' is (['.?,[<']). We lcave it to the reader to check that if a is an! of (15')-(20') above, tlicn a' is the corresponding formula of 2.4. This is true except in thc cases of (19') and (20')) kvhcre thc quantifier rule is used. The actual translation 01 (?Ot), for example, turns out to be

many (men),i[ N the

(illy

= h]),? [see

I

i'

1

I

(X,J,)~].

T o get the formula (20). you need to use the logical validity of the scheme t h e (.?[.I, = tl) .i I (~(.1'>1 ( ~ ( f ) pointed out in the cliscussion of translation rule TO.

4 Generalized Quantifiers and Linguistic Theory Linguistic theory is concerned, in part, with nntural l ~ r ~ ~ ' q r aeirerrr~is, ~igc ficts \vhicli llold for all naturally occurring liilman languages and which disringuish them from other logically possible languages In this section we suggest some potential univcrslls which relate to the theory of generalized quantifiers. In discussing these universals we

1

1 11 i

Generalized Quantifiers and Natural Language 91 shall restrict ourselves largely to siwlple NP's of English: Proper nouns, a singlc determiner clement followed by a common count noun and basic count words like (1 n2eH and ez'eyybody .

4.1 The universality of noun-phrases There is a strong intuition that every natural language has a syntactic category which should be labelled NP. This category includes proper names and is also the locus of detcrmincrs such as errgl, most, one. If the language has pronouns and dcfinite or indefinite articles (tkr or a), they also occul* insicle NP's. IIowever, thcrc is no simple way to give a universal syntactic definition of NP. NP's in the world's languages having varying internal structure and the positions in which they can occur in a sentence vary from language to language. This is just the sort of situation rvherc semantics can contl.ibutc to syntactic theory. The kind of semailtics we arc suggesting allows us to proposc thc follorr-ing univcrsal for consideration:

U1. NP-Quantifier universal: Every narural l u n ~ u c ~ ghas e .qvrtac./il. c.unsii~u~vrr.v (called noun-phrases) 1s7hosc serjzantii- -fi~nctir,nis to e.rpress gcn~nrlizedyum~~/~/icl:s o iwr tile dorm/iw of dis~.nzrt-j~>. It would probably be wrong to claim that NP's are thc only quantifiers in natural language. (It seems possible, for cxample, that tcmporal adverbs should cxpress quantifiers over moments or intervals of time as has been suggested by Partee (1073); Dow-ty (1979) and others). It docs seem reasonable, however, to claim that the noiutiyhrascs of a language are all and only the quantifiers over the domain of discourse, i.c. the set E of things provided by the model. The quantifier universal not only allows us to consider something which mil! be true of all natural languages but also scrr-es to distinguish natural languages from some other languages like the standard formulation of first-order prcdicatc calculus. -

4.2 Scope involves whole NP's, not just determiners In readings for natural language sentences, it is alcvays the interpretations associated with whole NP's that cnter into scope relationships, rznt simply the detcrniincr interpretation. This is one of the mismatches between standard predicate calculus and natural languages. O n a generalized quantifier analysis, rvherc NP's function as genesalized quantifiers, this fact about natural language would follow from thc univcrsal fict that quantifiers ma; be given different scope interpretations.

4.3 Dislocated phrases It has been proposcd recently (e.g Karttunen 197'7; Ciwper 1978; Gazdar 1970; Chomsky 1980) that somc phetlonicna (\vhich in a tranditional transformatiotial grammar would bc accounted for bv means of mor7ement rules) arc associated with

92 Jon Barwise and Robin Cooper seinailtic rules having to do with the binding of variables by quantifiers. An example is the rule of wh-movement, which woulcl be involved in dcriving the sentence who (lid Jo/rn .stJe. O n the traclitioi~al analysis who has been moved from its deep structure position after see. It seems significant that many such rules involve the movement of NP's. In order not to prejudice the issue of whether such sentences are to bc accounted for by a nlovemcnt rule IYC will adopt the term p l ~ n ~ sinc il2slocat~)d position (due to Stanley Peters) and proposc the following as a candidate for a univcrsal:

U2. Dislocated phrase universal. I f IL litnzguuge i ~ l / o p~ l~~ ns ~ s etos occtrr in rr. disfucntcdposiiion a.ssol.iated zuith a I.u/~ql'zlari(rbli>birding, then rrt /cast NP's (i.c. the syntactic category corresponding to quantifiers over the domain of discourse) r ~ i /occur / in this position. We would not expect to find a natural language in which adjectives or prepositional phrases, but not noun-phrases, OCCLLI. in dislocated positions associated with variable binding. In particular we would not espect a language to allow dislocated determiners if it did not also allow dislocated NP's. If determiners were regarded as qilantifiers one inight expect the opposite to bc true.

4.4 The property "Lives on" Quantifiers denote hmilies of subsets of the domain E of discourse. In this and future sections we will often refer to thc families as yurrnt!ficrs-, rather than as quantifier or NP rlenoiatio~zs,and use Q a s a variable over such quantificrs, It should always be clcar from the context what is meant by the term yuan~zfier. In a modcl /tl = ( E , 11 II), a quantifier Qfizwon a set C h' if Q is il set of subsets of E \vitlz thc property that, for any ,XC E,

X

E Q iff

(X n -4)E Q.

English examples u-hich illustrate this notion are the following equivalences Many men run tt Many men are men who run Few U ~ O ~ I C Isneeze I +-+ Fcw wonien are women who sneeze John loves hilary --t John is John and loves -Mary. T h e quantifiers represented hp the subjccts of the sentcnccs livc on the set of mcn, women and the singleton set containing John, respectively. ?'he peculiarity of the sentences on the right hand side of the biconditioi~alsis presumably due to thc fict that they arc oh\-iously I-edundant. LVc know of no counterexamples in the world's languages to the fbllowing requirement.

contrri~~s husic e.rprcssions, (called U3. Determiner universal. Ere?))nrrtui~alItrn~l~ugr determiners) ruhose senzaniic.fik~z~~tinn is to N S S Z ~ I ?to co?n?r~olrcount noun r/enotatinns (i.c., sets) 2-1 n gzlnnt~fiprtlzrst /ires on -4.

Generalized Quantifiers and Natural Language 93

4.5

Proper quantifiers as "sieves"

We think of a quantifier Q on a model IM = ( E , (1 (1) as separating ("sifting") thc VP denotations into those that do and those that do not combine with it to makc il true sentence. There are situations, I~owevcr,wherc this sifting process is degenerate: \chcn it lets ~'z'etyset through (i.e. Q = {X I X C E ) , called Pow(E)) and when Qdoesn't let an)! sct through (i.e. Q = 4).We call Q a prtjpe?. quantiji~>r denotation or skoe if neither of thcse hay yen, i.e., if Q i s a non-empty proper subset of Pow(E). Notice that this is a property that applies to cluantifiers as NP denotations, not to NP's themselves. I.e., it is a semantic property. For example, 11 inany inell [I= q5 in exactly those models where there aren't many men. 11 Every man I = Pow(E) in exactly those models wherc thcre aren't any men. Table 1 shows conditions under which various NP's can fail to denote proper quantifiers. We work in a fixed model 11/1 = (E, I I ) . T h e first column indicates by ayes" or uno" whether the quantifier can ever be 4. T h c second column indicates whether it can ever be Pow(E). T h e ncxt two columns give equivalent conditions for the quantifier to bc proper; column three a formal description, column four an informal description. It is often assumed in normal conversation that noun-phrases denote sieves. For example, given the utterance (2 1) we could naturally assume thc truth of (22). I Iotve\*er,this assumption may be explicitly contradicted as in (23). (21) No boy at the party kissed Mary. (22) T11ere were boys at thc psrty. (23) No boy at the party kissed Mary since therc \verenlt any boys at the part!. With some NP's it is harder to contradict the assumption that the denotation is a sicvc. For examl~lc,(24a) invites the assumption (24b) and the explicit denial in (24c) soiul~ds quitc odd. (24) (a) Every nlan at the party kissed Mar!(b) There were men at the party. (c) ?Every man at the party kissed Mary, but only because thcre weren't any men at the party. In column 5 of our chart we indicate our judgement as to whether it is easy or hard to interpret the NP as denoting an improper cluantifier (i.c., a non-sieve). 111 thc next section we find an independent semantic characterization of these classes. Column 6 has t o do with that characterization. Note that, according to our analysis, the n 17, both 17, and neither v1 will always denote a proper quantifier when they denote an! thing at all. \Vc suggest that these arc special cases of a general phenomenon which we attempt to capture with U4.

U4. Constraint on determiners that call create undefined NP's. scrrt u simple J t t e m i n e r such //?at 11 D 11 (A) is so?ne/ii?zesundcjinrrl.

/,LV L) fillre-

Table 1 --

-

-

(5)

When does it denote a sieve?

(4) Informal description of 3

Easy or hard to interpret as a non-sieve?

(6) Strong or weak determiner

hard easy hard easy easy easy

strong weak strong weak weak weak

easy easy impossible

weak weak strong

impossible

strong

impossible

strong (-1

always

There is some 11 There is some 1 There is some rl There are many 11's (There are few 11's) There is an 17, i.e. (There are no 11's) There are 317's There are 311's Undefined unless there is exactly one 11 Undefined unless there are exactly two 11's Undefined unless there are exactly two 11's always

impossible

strong (the y [ y = j l )

(1) Can NP denote 47

(2)

(3)

Can NP denote Pow(E)?

1. Every r l 2. Some 11 3. Most 4. Many rl 5. Few 11 6, No 11

No Yes No Yes No No

Yes No Yes No Yes Yes

7. 3 1 ~ 8. !3 17 9. The 1 tl

Yes Yes No

-

10. Both I/

11. Neither 11 12. John

NO

Generalized Quantifiers and Natural Language 95 1.

2.

R'lzerterc~r(1 D (1 (A) is c/
This suggests that the partial determiners D function semantically just likc their completions D' with the added import that they clenotc sieves. A completion of the n and hot12 is ez~er1t.The completion of neither is no. By U4, we would not expect to find a language with a word for nrithrr without one for no. Similarly, we predict that no natural language has a simple NP D men with the same meaning as ez5ri:ymnri except that it would be undefined only if there were more than 2 men, D men would be defined but improper if there were no men. This contrasts with The 2 men which is undefined unless there are exactly two men. Finally, note that no determiner has a "yes" in both column (1) and column (2). It would bc logically possible to have a determiner D which sometimes fiailed to be a sieve by having D(g) denote 4 for some q and Pow(E) for other q. It appears to be a rather trivial universal that ~zonaturr~llrrngiinge delev?niner mill' h ~ i v ethis propert)f. An even more trivial universal is that no (letrr?iziner is rrlr~~rqts tri-~~i~l.

4.6 Weak, strong and definite determiners In this section we dcfinc, semantically, a division of the determiners into "weak" ancl strong". We then make a hrther division by defining thc definite determiners as a subset of the strong determiners. LC

PROPOSITION. [f'n quantiJier Q o n M = (E, 11 (Cf. Appcndix C , C1 for the proof.)

I

11)

l t ' ~ )on ~ sA then .A E IQ ~ [ f E' E Q.

DEFINITION. A determiner D I,\.posilizle strong (or rregurk~i~ strong, resp.) if for evcry model M = ( E , 11 11) ancl every A E, if the quantifier IIDII(A) is defined then rl E IIDII(A). (Or A $ IIDJl(rl),resp.). If D is not (positive or negativc) strong then 13 is wei~k. To classify a determiner D as (1) positive strong, (2) negativc strong or (3) weah, you form a simple sentencc of the form

ancl sec if it is judged (1) automatically valid, (2) contradictory or (3) contingent on the interpretation. For examples, ez!eql gnu is (1 gnu is true in every model, ~ e i l h e g?zu r is n p i 4 is false in every model in which it is definecl and ??tanygnus ore gizr4s will bc true just in case there are many gnus. These judgemeilts classify rrpyy, l~cilherand riuztqt as positive strong, negative strong, and weak, 1-espectil-cly.'Table 2 presents our classification of the determiners we are considering. The terms "weak" ancl "strong" (though not the dcfinitiuns) are borrowed from Milsark (1977). Weak determiners for _Milsark are those which create noun-phrases which sound good after tlzCri~zs or there arc. (Such NP's are called indefinite in earlier literature.)

96 Jon Barwise and Robin Cooper Table 2 Weak

Strong

a some one, two, three many a few few no

the 1, the 2 , ... both all every each most neither (negative strong)

Note that a theory of demonstratives (this, that, thue, those) should work out so that they are strong determiners, since they sound odd in chere is contexts. Note also that the weak determiners are exactly the ones marked "easy" in colun~n5 of Table 1. We can use our definition to explain tvhy noun-phrascs with strong determiners sound strange in tlzew-sentences:

A sentence of the form there is/nw NP can be intcrpretcd as meaning that thc set of individuals in the model (E) is a member of thc quantifier denoted by the NP. For any positive strong determ~nerthe result will be a tautology, since to say that E is in the quantifier is the same as to say that A is in the quantifier. For negative strong determiners, the result will be a contradiction. While tautologies and contradictions are not ungrammatical they are not very informative and are normally restrictccl to use in special situations construcd as set phrases. For example, to say llzrre'.v John (in the existential, not the locative sense) is to say something that could not possibly be false sincc our semantics will require that John has a denotation, whatever the model.7 T h e sentence is therefore used in a special kind of situation with special intonation as in the following dialogue: Who coulcl possibly play Hamlet? Well, there's John. T h e speaker is using a tautology here to avoid making the direct assertion that John could play Hamlet but nevertheless implicating that this is a possibility. We can also gain some insight into the dichoton~yobserved in the previous section. NP's constructed m-it11 strong determiners sound much inore peculiar than those with weak determiners when they do not denote a proper quantifier (sieve). For an NP Dy \vhei.e D is weak, the "sieve-hood" of IDilll is contingent on whether I(rlJI E II/hlI or not. On the other hand, with strong determiners, Iqll f llDqll is always true (except for the negative strong, ~lihercit is always false). Thus in the case of weak determiners wc arc ablc to cancel the implicature that Dq is a sievc by saying soincthing like r h ~ wis (n't)/ilvr ( n ' ~ )Dq whereas this is not possible in the case of strong determiners. This hardly- constitutes an cxplanation of the dichotomy, but the meak/strong distinction is

Generalized Quantifiers and Natural Language 97 clearly relevant to any explanation of this phenomenon. 'l'he exact match between columns 5 and 6 of Table 1 ean hardly be an accident. Wc now turn to definite drtc~mine~s. Of the determiners we are considcring, the definite ones are thc n and both. DEFINITION. A determiner D is defhile if for every model .M = (E, 11 1 ) and every A for which j(D(((_.l)is dcfined, there is a non-empty set B, so that ((D(I(;f)is the sievc {X El B C _XI.(Hence, I Dl1(A) is what is usually called the principal filter gcncrated by B.) PROPOSITION. If.D is d
(We suppose that in the case of demonstratives, one would have only nllDyl( 2 IIqII.) We suspect that it is this ability to ~ ~ n i q u e deterrninc ly the generator from the NP that allows the N P to play the role of a common noun and recombine ivith a determiner. The additional information being supplied by the definite determiner is just that the set being quantified ~ \ ~isenon-null. r We shall interpret ofNI' in the abovc construction as the intersection of the quantifier denoted by the N P and apply certain detcrn~incrsto the result. An implemeneation of these suggestions for the treatment of /heve scntenccs and definite determiners can be found in Fragment 2 in Appendix A. Note that wc have no explanation of the contrast between ortr of tlzr two rnerl and "ol-16 c!f'both nwn since we arc treating the ~ J T ~and O both as equivalent.

4.7 Monotone quantifiers In this section we discuss two subclasses of quantifiers suggested by work in moclcl theory and recursion theory. T h e classes seem equally important for linguistic theory.

1

I

r)

DEFINITION. A quantifier Q is nronorowr inrreasitig (mon if X E Q and -X Y C E implies Y E Q (i.e. for any set € Q, Q also contains all the superscts of X.) Q is ~noncitnnedecrrasing (n-lon 1.) if X E Q and Y C X C E implies Y E Q (i.c. for any set X E Q,Q also contains all the subsets of X).A determiner D is moi/otoizr increasing (or decreasing) if it al\vays gives rise to monotonc increasing (or decreasing) quantifiers IlDl((_4).T o test an N P for monotonicity we take two verb-phrases, Vl'] and

98 Jon Barwise and Robin Cooper VP2 such that the denotation of VPI is a subset of the denotation of VP2 and then check whether either of the following seem logically valid.*

I f ' N P VPI, then N P VP2. ( N P is mon IJNP VP2, thew NP VP1. (NP is moll

1')

1)

LXAMPLES. Take VPI to be entered the race eady and VP2 to bc entered the race. T h e following are valid:

(30)

some Republican every linguist o n most peanut farmers many inen

If

)entered

the race early,

some Republican every linguist entered thc race most peanut farmers many men Notice that the reverse implications do not hold, since these clearly could be people who entered the race but did not enter early. T h e validity of these implications follow from the fact that the NP's are mon '/. T o exhibit somc mon 1 NP's, we note the validity of:

l3 If

{

no plumber few linguists }entered the race, neither Democrat no plumber entered thc race early. neither Dcmocrar

By considering such examples one comes to the following fiairly clcar judgements of monotonici ty: hlonotone increa.sing: he, John, men, a man, some man, some men, somcbody, the 0 man/men, these/those men, most men, many men, several men, either man, at least two men. Monotone &creasirig: no m a d m e n , few men, neither man, nobody, nonc, nothing, at most two men. Not monolone: exactly two men, exactly half thc men. There are some NP's which could arguably be regardcd as bcing able to denote both monotone and non monotone quantifiers. If ir .fern is used to mean some but no1 mnn,y, then n.)m men is not monotone. If it is used to mean ul 1erl.s~r z j i ~ itl ~is mon 1'. It is likely that the man T reading is the only one that should be accountecl for by the semantics, conversational implicature explaining the illusion of a non-monotone

I

,

1.

II II

Generalized Quantifiers and Natural Language 99 I.'

reading. (Cf. Grice 1975; Horn 1976.) Similar remarks apply to sez'rrml, qlrile a Ji)i7 and tmo. The first thing that strikes one about the above list is that there are Car fewer rnon 1 NP's than rnon T. What decreasing ones there are have traditionally- been trcatcd ils negations of increasing quantifiers (no man of n man,j>m ?Tienof mnaql ?nenor perhaps of sezleral men). We can state a general relationship between rnon T and rnon 1 quantifiers, once we define Q and Q -.

-

DEFINITION:

Given a quantifier Q on E, define nenr quantifiers

-- -

Note that Q and Q are sieves just in case Q is a sieve and that if Q i s not a S~CVC, then Q = Q . Q corresponds to negating a sentence beginning with (c.g. no/ one nrnn r~zn).Q corresponds to negating the VP following Q (e.g. onc man didn't run). N

a

N

--

then Q and PROPOSlTlON. Negation rez~erstsmmol2otonicity. 1. I j - Q is won Q ure mon 1. 2. If Q is nzvn .1 then Q and Q arc Inon T. Further Q = Q = Q --, (See C9 in Appendix C.) It follows that we can think of any nlonotone decreasing quantifier as Q for some moil .T Q. This together with our discussion of weak determiners in section 4.6 allows us to consider the following potential language universal. N

N

-

US. -Monotonicity correspondence universal. There is a sirnple iClP n7lril.h expresses the rnon 1 yuant$fier Q af nlzd onZy $t/~ercis a sitnple N P with a nwak non-cardinal dtterwliner whic.h expresses the rnon T yuantzfier Q. This potential universal suggests the following relationship between English determiners. Corresponding mon no man/men neither man

some man (men) a man

fen- men

many men several men

nobody

TQ

some person etc.

This proposal would predict that no language would have basic determiners meaning no/ nrost, not eveq, or not the since most, czlery and the are strong. It would also predict that no language would have a basic determiner nleaning not (at lt.as/) tnlo since two is a cardinal determiner. Thus, such a proposal, if correct, puts real constraints on the set of basic determiners in a human language. Another significant aspect of this kind of

I!

100 Jon Barwise and Robin Cooper universal is that we can talk in semantic (i.e., model theorctic) tcsn~s.We do not havc to assumc, for example, that.f?n. is the same as not macy at any syntactic lcvcl.

4.8 A Monotonicity constraint on simple NP's

1 1

There do nor seem to be any simple NP's in English which could not conceivably be 1 analyzed a s monotone quantifiers or as a conjunction of monotone quantiticrs. Rr example, if we claim that a fin, ,nm has a non-monotone reading, wc a ) ~ ~say l d that it 1 expresses the same quantifier as the conjunction some men hui no1 n m q lmen. Sinlili~rly,I a non-monotone reading of t r ~ omen could be the same as at Icasl tn?o inell hut fit IIIOSI two 1 mrn. (Semantically, conjoining NP's is simply intersection of quantifiers and will he taken up in section 4.) These observations suggest the following candidate for a ! universal.

1

1

e U6. Monotonici ty constraint. The sin~pltl NP s! c! f' an.)! r~llfzrrnlI ( ~ n g u a ~il,rpnss nlonolone quant?fiers or rcoi~junrrionsof nzou~otonequtznt!/ier-.s. This proposed universal has the effect of ruling out many logically possible quantifiers as simple NP denotations. Examples arc the denotations of [ I N ~ ~ r enurnher ll ~!f??zcn, e.vnctly t h ~ e eor esuctly . .live men, all but olre mun. It seems unlikcly that any natural languagc would havc a basic cletern~incrmeaning u n ereu nlcrnber o/,. L J X ~ L ' I ~I ~h r e ror e.ractly.fi~)eor 011 hul one. If the monotonicity constraint is true, it seems to be more than an arbitrary restriction on the quantifiers found in human languages. Rather, it seems to be related to the way people understand quantified sentences. We take this up in the next section. Recall our discussion of strong and weak determines from section 4.6. D is positive strong just in case A E IIDII(A) is always true. It does not follow from this that D is monotone increasing. For example, we could define an artificial determiner D which was strong but not mon 1. by

11 D1((,4)= {X

Card(X - A) is finite and even).

A E IlDII(A) and if n , b ~ ; 4 , a # I ? then - { I , E ( 4 ) but (A {u)) $! 1D(1(,4). However, there do not seem to bc an>- such determiners that arise in natural language. This leads us to propose anothcr possible ~~niversal.

Then -

U7.

Strong determiner constraint. In n~riurizllr~ir'q-~~agn, po.sitiz:r slrovz'q ~/~~lermin~.rs ar-r morrnlonr ~zcreasing.Nrg~z~irt. slrong ~/eterrni?zersarc t~Jonolo?lcr/eec.r-casing.

This proposal makes some predictions as to rhc logical behavior of st]-ong determiners. T o see just what the>-are, we note the following proposition, PROPOSITION. [f D zs pusitit:e strong aird inonotonr inrreasirr'y then ,fill. un)t wiorlcl IZI = (E, (1 (1) and nn.y sets A, B in M :

B

E 11D11(-r2 n B).

Generalized Quantifiers and Natural Language 101 Ij'D is n e g ~ t i c estrong und nzonotane decr,ensirig then nw huz~cB 6 IIDII(A n B). (C;f'. C8 in Appendix C.) Thus, U7 predicts that if D is a (natural language) positive strong determiner then any sentence of the form

Dek

N

D a

A

shoulcl be judged valid (since its translation is true in M just in case

which is equivalent to

IIP'II

l l ~ l l ~ l l ~ ' nl l ll/j'll).)

This prediction is borne out by the following examplcs.

men that love Mary, love Mary. T h e three

("I

{ :::'

}man that loves Mary, loves Mary.

T h e corresponding prediction for negative strong determiners is that such scntcnccs are judged contradictory, as in (34). (34) Neither man that loves Mary, loves Mar?-. When one carries out the same test with weak determiners the results ilre odd and certainly not universally valid as the examples in (35) and (36) show. (a) No nlan (c) (At least) three inen (d) Exactly threc lncn

that love(s) Mary, love(s) Mary.

102 Jon Barwise and Robin Cooper (36)

{

(a) Many men (b) Few men (c) A fccw men

}

that love Mary, love Mary.

We judge the examples in (35) to be logicall? equivalent to those in (37) but it is not I clear that the same holds fbr (36) and (38).

(37)

( (a) No

man ome man (c) At least three men ( (d) Exactly three men

I

lovc(s) Mary.

)

Accepting these equivalences amounts to asserting that weak determiners satisfy the intefiection con~izr'ilion.

i I

DEFINITION. = (E,

)I 11)

D satisfies the intevse~.tion~~on(iition if for all models

and all X,-,.l

E,

x E 11011(.4) iff x E 11011(--l n s). do i n ~ satisfit i ti7c inlrnecliorr l.orrditior?. (Cf (26.) PROPOSITION. Strotzg ck'tet.m~~zt>rs

T h e second author is inclined to think that weak determiners rrll satisfy the intersection condition but it violates the first author's intuitions for mar^)^ a11d.fl.n). It would say, for example, that 117arl.)/could not mean something approximately like the following in a model h l containing one thousand men: (

4

)={

E

1Y

4

1

1A

and I X n -4

I>

30)

Here the nurnber that counts as "many" gets smaller the sinaller / I is, but nothing smallcr than 30 ever counting as "man!;" men. If rlznny is interpreted in this way in somc model, and if 35 men love Mary ill the model, then Mi~n,yinen l o z ~M[zry is hlse, but il/l[rrr,lmer~[hilt love A.1211:)1, 107'~MLII;)~ is true. T h e issue hangs on the one's interpretation of the fixed context constraint in rclation to relative clausc constructions. It can probably only bc resol\.ed by working out a (Kamp-like?) theory of the vagueness to superimpose on o u r tl-catmcnt, and seeing \vhich interpretation of the constraint provides the smoother theory. (This samc issue coines up in deciding whether ~ r ~ c l nisy persistent, as defined in thc next section.) Sentences involving determiners that satisfi- the intersection conditioil can be expressed, up to logical equivalence, in a number of waj-s, due to the follo~vingfacts.

Generalized Quantifiers and Natural Language 103

(CE Appendix C, C4 and C5 for proofs.) The right hand of the first biconditional corresponds to the semantics for the there is/are sentences, as in (37'). T h e right hand side of (2) corresponds to switching the verb and noun as in (37").

( (a) no man Thcre is/are

(37")

some man (c) at lcast thrce mcn ( (d) exactly three men

I

that love(s) ~Marg

)

(a) No one that lovcs Mary is a man. (b) Sorneonc that loves Mary (c) At lcast thrce pcople that love Mary are men. (d) Exactly three people that love h4ary

The proposition predicts that corresponding sentences in (37), (37') and (37") i~rc equivalent. And, as above, the equivalence of the sentences in (38), (38') and (38") is much less clear.

(38')

(38'')

There are

{

(a) manj- men (b) few men (c) a few- men

}

that love Mary.

i

(a) Man]- people that love Mary (b) Feu. people that love NIary (c) R few people that love h4al.y

4.9 Processing quantified statements _An objection that could be leveled against Montague's treatment of NP's is that it would seem to make cl~eckingthe truth of a simple sentence like John rlnns wcll nigh impossible. For, the argument might go, one tvould first have to "calculate" thc denotation of namely, the family of all sets X to which John belongs, and then see if the set of runners is one of these sets. 13ut this clcarly corresponds in no way to the reasoning process actual1~-used by a native speaker of English. Using the monotonicity constraint, we wish to show that something very much like an intuitive checking procedure is always possible for simple NP's. The procedure rests on thc notion of mitness sets. DEFINITION. A witness sct for a quantifier such that m E D(24).

D (A) living on ,/i is any subset a, of '4

EXAMPLES. T h e only ivitncss set for 113ulznl is {John). A witness set for 1111 woman1 is any nonempty set of women. R witness set for Ili~zosl)~,orlz~i?(( is any set

104 Jon Barwise and Robin Cooper of women which contains most women. A witness set for I[/ir~n?omen)lconsists of any set of women which contains only few women. A witness sct for Il(c.zac.tl)l)ljoo a~o~nerall is any set of exactly tw-o women. PROPOSITION.

Let m range over a~ktrresssets /or the qutzntqier

I f D(A) is mon T then .fhr nny X, X E D(14) ?ff3w[m C .X] (ii) I f L44) is mon the??- f i r ntz.), iY, E D(A) $f ~ P [ ( xn '1)

lizing o ~ A. t

(i)

x

cII~.

(Cf. C11 in Appendix C for the proof.) We can paraphrase this Proposition as follows: To e z ~ a l l ~ nX f c E D(.4) do tlw ~7)/lomi~1g:

1 Take some subset r1) of A which you ltnow to be in D (A). 2 (i) For mon D(/4), check rv C X. (ii) For mon J, D(A), check (X n A) 2 113. 3 If there is such a m, the sentence is true. Otherwise it is false. These procedures are not totally unlike some computational models for the verification of quantified sentences which have been suggested in the psychological literature. (See Clark 1976.) We imagine it might bc possible to design experiments which check the predic~ionsof a psychological theory based on witness sets. For example, we predict that response latencies for verification tasks involving decreasing cluantitiers would be somewhat greater than for increasing quantifiers, and that fix the nun-monotonc it would be still greater. These predictions are based on the complexity of the checking procedure we have suggested above.

EXAMPLE. Imagine a yard full of animals, including some dogs. 1,et us imagine a dog Fido that looks like a spaniel, but we're not sure if it is a spaniel. Iinaginc deciding which of the followiilg are true. (a)

(b) (c) (d) (c)

Fido is in the yard. Some spaniels are in the yard. No spaniel is in the yard. hxactly one spaniels is in the yard. An even number of spaniels are in the yard.

In all of these the set X = {,)/I.)1 is in the yard) is the set .Ydenoted by the VP. For (a), the only witness set is {Fido). M7e check to scc if Fido E AY.For (b), we need to find some non-empty set n? of spaniels, 1~ C_ _X.For (c), the only \1-itncss set is 0.We must see if A- n llspanielsll = 4.This will causc us no problems if there is a clear cut spanicl in the yard, for then clearly S n I)spanicls)l# (b, so (c) is fillst w~l~ctl~cr Fido is in the vard or not. If Fido E X but no clcar cut spaniel is in .Y then ivc won't be able to compute the truth or falsity of (c) without deciding wl~etherFiclo is a spaniel. For (d),

Generalized Quantifiers and Natural Language

105

we must do two things to scc that it is true; find some spailiel in A- and show tliat tllerc is at most one spaniel in X. This corresponds to breaking down e.t.ar*t/)~ O I I P sp~~?/icI into sorrzc sprtniel and nr tnosr otle spnrri~~l. For (e), we niust decide whether X n I(spaniclsl( contains an even number of things. We will not be able to do this without deciding whether Fido is a spaniel. There is another distinction, related to monotonicity, that seems to affect processing of quantifiers, and is bound to interact with processing requirements by nionotonieity.

DEFINITION. A determiner D is ~ C V . S Z S ~ P ifI I ~ for all M = ( E , 11 I ) , and all A i B i E, if E IlDll(A) thenX E IlDll(B). (On the other hand, D is crtzti-pcr:vis/e,~/ if nl 2 B C E and X E IlDll(B) implies X E 11011(.4).) T h e idea here is tliat if D is persistent then once you see that X E 11D11(-4)then you know that X E (IDII(B) for any set B that contains '4. For example, if B = {x I x is a man that left the party before IOPM) and .?l = {x I x a man that left the party beforc 9PM) then A C_ B so that for persistent determines D. (39) D men

that

lcfi the p~krtyhefire 9Ph4 n m t hotlae

will imply

(10)

D met? that Iefl /he port]/ befire IOPM went konze.

Logical (and mathematical) examples of persistent determillers are solize, ai /(>as/I?, (infilile/y ITULI!~~, uizcoun/nh()l IT/LE~)I). Other determiners that seem to function as persistent dctermiliers are .sever[~l, and rnnr/j/ (??). For anti-persistent deterillincrs D,the inlplication goes the other way, from (40) to (39). Thesc include PZIPP)I, IIU, f r 1 7 7 (?), C L ~ most n, .fini/t>lyununy. Other determiners are neither persistent nor antipersistent. A glance at the table in appendix 2) table suggests another proposition for consideration as a univessal. (See also C7 in Appendix C.)

U8. Persistent d e t e r m i n e r universal. Ez!ery pvv.si.steitt ~/tternzine~c!J' Izzinlcrrl Inrrgullge i s lnon

und m m k .

Since it is not difficult to construct artificial determiners which Fail U8, (ct: Appendix C ) , this would, if truc, provide another constraint on the class of human languages among the class of all possible languages. In terms of witness sets, pel-sistence works as follows. If D is persistent and if n? is a witness set for D (A) then 1~ will be a witness set for any B that contains .-l (,-I C B). It seems clear that between monotone quantifiers D l , D2, which arc otherwise comparable, if D l is persistent and D2 isn't, then Dl should be easier to process, especially when the universe is too large to pcrceii-e all a t once, since a \$-itnussset for D l ( @ may bc able to be found on the basis of some manageable A C B. Continuing the above examples, it should be easier to verify (f) than (g), since any witness set for (g) must contain most dogs in the yard, whereas for (f) it might suffice to have a witness sct for .scz:~r~~l dogs in /he .vnrd t~/~il-lr are closc enough / o see.

I

106 Jon Barwise and Robin Cooper (f) Several dogs in the yard are spaniels. (g) Most dogs in the yard are spaniels.

Persistent determiners were introduced in Barwise (1978). Ladusaw (1979) has put them to excellent use in his discussions of polarity items. They turn out to be important for the logic of perception (Barwise 1980).

4.10 Monotonicity and NP-conjunction An advantage of treating natural language NP's as generalized quantifiers is that we can treat NP-conjunction (instances of N P and NP, N P or NP, NP hut NP, etc.) directly. NPlorNP2 denotes the intersection of IJNP111 and IJNP211, NPI or NP2 denotes the union of the two quantifiers. We may similarly extend the logic l,(Ci(B to L(GQ,) by adding a formation rule R8.

R8. If Q 1 nlzd Q 2 are qutrntjfifiersso are

(a a ) , (av a ) . A

T h e corresponding semantic rule is S13:

This logic allows us to represent new quantifiers but provides no real strengthening of the logic, since

are logically valid. That is, we cannot express any sentences that were not already represented, up to logicnl equivalence. Not all instances of NP-conjunction are acceptable in English. In general, it seems to be difficult to use a.nd or or between two NP's if they represent quantifiers of different monotonicity . Examples are given in (32). (32)

+

(a) inc~eczsing increasing: a man and thrcc women, several men and a few women. the professor or some student, most men and any woman (could lift this piano) (b) de~-reasi?zg decrecrsing: no man and fcw wonien (could lift this piano), no violas or few violins (are playing in tune) (c) mixed: *John and no woman, *few women and a few mcn (could lift this piano), *two violas ancl few violins (are playing in tune).'"

+

T h e unacceptability of the mixed conjunctions is not simply due to the peculiarity of the message \vliich would be expressed by sentences containing them, l'here are acceptable sentential conjunctions which would express the samc proposition.

Generalized Quantifiers and Natural Language 107

(33) (a) John was invited and no woman was, so he went home alonc again. *John and no woman was invited, so he went home alone again. (b) Few mathematicians have worked on natural language conjunction and a few linguists have - so I don't think you have the right to illakc thcse unfounded statements. *Few mathematicians and a few linguists have worked on natural language conjunction .. . (c) Whcn two violas are playing in tune and few violins are, Berlioz begins to sound like Penderecki. riVhen two violas and few violins are playing in tune, . . . This restriction on NP-conjunction could be related to the preservation of properties of monotonicity. T h e conjunction or disjunction of two increasing quantifiers will be another increasing quantifier and sin~ilarlyfor the decreasing quantifiers. T h c conjunction or disjunction of an increasing and decreasing quantifier will normally not bc a monotone quantifier. For example, the putative conjunction John lznd no wornan would have the denotation represented in (34).

(.34)

{X I John E

X and 171 n {woman)

=

4).

This would for example contain the set {John) but not all of its superscts or subsets. Not all instances of NP-conjunction demand monotonicit!- in the way we have suggested. It is possible to conjoin an increasing and a decreasing quantifier wit11 hut as illustrated in (35).

(35) (a) John but no woman was invited. (b) Few mathen~aticiansbut

{

linguists have worked on natural lin-

guage conjunction. (c) T w o violas but

{ }

violins ase playing in tune.

In fact, in order to use hut in this way it seems necessary or at least prefcrable to mix increasing and decreasing quantifiers. Comparc the sentences in (36). (36) (a) (b)

(c)

*John but a woman

{ze }

invited.

*Few mathematicians but no linguists have worked on natural language conjunction. ?Two violas but three violins arc playing in tune.

We assume that the interpretation of hut is the samc as that of und for the purposc of truth conditional semantics. However, there are important ways in which it behaves differently from and. Conjunction with and can be repeated indefinitely many times. This is not possible with But no matter how one mixes thc quantifiers.

108 Jon Barwise and Robin Cooper (35) (a) John and a woman and three children were invited. (b) *John but no woman but three children were invited. (c) *Few inathematicians but many linguists but no physicists have workcd on natural language conjunction. This lack of iteration might be related to the fact that monotonicity is not guaranteed for a mixed conjunction and hence that the verification procedure we have discussed might apply separately to each conjunct. It is interesting to note that similar pcculiarities are true of more c o i ~ ~ p l econjunctions s that might be considered as mixed

(38) (a) John and not Mary is invited to the party.'' nobody else (b) John and can kcep the party golng. no other man As with but these kinds of NP's cannot be further conjoined with other NY's. (39) (a) *John and not Mary and not Helen is invited to thc party. (b) *John and no other man and Helen can keep the party going. An extension of fragment 1 to include the basic cases of conjunction of simple NP's can be found in Appendix A.

4.1 1 Negation of noun phrases and duals Certain NP's in Lnglish may be prcceeded by not when they occur in suhject position, while others can't. Here are some data: Not every inan left. Not all men lcft. Not a (single) man left. Not one man left. Not many men left. *Not each man left. *Not some man left. *Not John left. *Not the man left. (*) Not fcw men lcft. *Not no man left. ?*Not most men left. Notice that this distl-ibution cannot be explained pure/), in tcrins of the semantics of quantifiers, as comparison of (40a, h) with (412) and (40c) with (51b) shows. (One might try to explain the unacceptability of ( I l a , b) as having sonlething to do with the preference of so17~cand ecrr.h for wide scope reading.) Therc are some semantic gencrilizations to be captured, ho\vcver.

Generalized Quantifiers and Natural Language 109 The tirst observation is that only mon T quantifiers can be negated in this way. Recall our universal that to every mon simple NP a denoting a quantifier Q there corresponds a nlon 7 simple NP a' denoting the mon 'f Q. Thus, to negate [ [ C I ] ~ ~ [ P ]one \ ' ~could ]~ simply use [[a1][P]Js.For example, instead of saying ( 4 1 ~ or ) (4lf) one could say rna91.y men l ~ f or j some ??le?zIrSf. T o see what is going on in (41c, d), we use the model-theol-etic notion of the dual of a quantifier.

-

-

DEFINITION. T h e ' h a / of a quantifier Q on E is the quantifier =- (Q ) = ( Q ) -. If Q = = {X EI(E - X) @ Q, i.e., called self-clual.

0

0

N

0 defined by 0 then Q is

EXAMPLES. 'The dual of' llsome man11 is llevery man11 and vice versa. On a finite set A 2 E of odd cardinality, {X C_ EIX contains more than half A ) is self-dual. For any iz E E, {_X C Elu E X ) is self-dual. Hence / the I rlI is always self-dual, when

0

-

defined For any the dual of is the original Q. Also, if Q is nlon " Q =- Q and two minuses niake a plus, so to speak). T h e following is clearly valid:

1. so is 0(since

As special cases of this we have the usual

-

-

vxcp 3X(P

-

3s

t .

VX

2 . r

cp (P.

If Q i s self-dual, then the above simplifies to

That is, wc can push negations back and forth across self-dual quantifiers. Hence there is no need to use any syntactic construction to show that negation has wide scope ovcs quantification when the quantifier is self-dual. Thcse observations lead us to proposc the following as a candidate for a languagc

U9.

Constraint on negating seIf-dual and mon 1 quantifiers. I f a l(lngr~iige has a syntnclic constrmc~ior~ll~hosrsemnntic Junc.tion is to negate a quantz/iL.v, t/z~'n this c.onstruction mill nor he usell i ~ i l h-W'se.vpressing mon 1 or s e ~ / ~ l l u ayunrzli/ Jieev.

Of the unacceptable determiners in (41), aside from (a), (h) \vhicli we haw alrclldy discussed, this constraint leaves only (g) unexplained:

(41) (g) "Not most men left.

110 Jon Barwise and Robin Cooper T h e odd thing herc is that there just isn't any way to express the intended sentence without using sentencc negation:

1, ~

1'

j

(42) It is not true that most men left. (If most meant cxaetly the same as more tllarl hid[ then (42) could be paraphrased by

(43) At least half the Inen didn't leave since the dual of ) ( More than half the q'sll is 1) ,4t least half the rl'sll.) ,If 1 Dl is a determiner interpretation, nre can define Ilbll(-d) = IlDll (-4). For example, IlsoXlell = Ileveryl and IIe~G-yll= IIsomell. We do not know exactly why the following should be true but we can find no counter-examples to it, so propose it for consideration:

UlO. Dual quantifier universal. I f n ~iatural/~inguwgrklrs u basil. i/~.teriiliircrf i r zacl~ f D liirr/ D rlwn ~ b r s 61t re .st~iz(lnti~d/y ~yuiz~~i/(v?i' 111 ' ?onlr9' NIU/ " ~ > z w ] r 'I,

,4n apparent exception to U10 as stated is the pair ~ h rI , the I. In other words, the 1 is self-dual when defined. But then this is not rcall!. an exception, since whcil fhc 1is defined it is semantically equivalent to both soine and cz'r'i-y. In connection with UlO, we ~vouldpoint out the follou-ing simple fi~ct.It may have something to do with tlic reason U10 is true (if' it is true). PROPOSITION. If Q is mvnoLvar inrreosiq thcn Q i [ g ( s ) ] n o i l ) l ( , r ) 1 implies 3.ifq4.v) r. $(s)l.(Cf. C10 in Appendix C.) An example of a pair of dual determiners from mathematics is "more than half" and "at least half". Some people consider "most" as synonymous with "more than half" but therc is no l~asicdeterminer in English synonymous with "at least 1ia.lf". Another dual pair is "more than 75%". and "at least 2jC?4o". U10 would predict that no hurnan language would have basic determiners for each eleinent of such pairs. T h c proposed universal also predicts that of the sentences below, only (#a, b) could be paraphrased as D Inen /
1

which amounts to using "quite a few" as thc dual of "many". However, faced with (46) they are not usually willing to paraphrase it by (47), which suggests that they arc not 1 consistent in treating "quite a few'' and "ma11!7" as dual.

Generalized Quantifiers and Natural Language 111

(46) Not many men left. (47) Quite a few men didn't leave. Also, faced with the fidlowing argument, which would be valid if "many" and "quite a fen-" w-ere dual, (by the above proposition) they judge it highly dubious. Many men voted for Carter. Quite a few inen voted for Ford. Therefore, some mail voted for both Ford and Carter Thus, we see that "quite a few" and ''man>" arc not consistently used as duals of each othcr. And, even if they were, it is unlikely that "quite a few" should be considered a basic determiner element.

5 Conclusion In this paper we have focused attention on the semantics of English determiners and r l o u ~phrases, ~ defined and illustrated a numbcr of semantic propertics of them and proposed a number of possible universals. Ultimately, however, we are less concerned with the fate of these proposals, or eve11 of the details of our senlantic treatment of nounphrases and determiners, than with illustrating sonlc genesal points about the analysis of natural language - points not always fully appreciated by linguists or logicians.

5.1 Semantics is part of a linguistic theory Linguists often feel that a model-theoretic semantics is an appendage to a linguistic theory and that it will not further the linguist's aim of characterizing thc class of possible h u n ~ a nlanguages. Sucll a view suggests that the relationship between Ianguages and models of the world has more to do with the world than with thc structure of language. It might even claim that facts elucidated by a model-theoretic scinantics arc logically necessary facts and thus cannot possibly serve to separate the class of natural languages from the class of logically possible languages. We believe that the t-csults of section 4 show some ways in which this is mistaken. 'The confirnlation of any of the universals presented there (or more refined versions of them) would invalidate such a view. None of the proposed universals is logically necessary, and scveral of them effect sharp reductions in the class of possible human languages. Fut.thermore, it seems that such universals could be related to a psychological theory of language. T h e drastic reduction in the available interpretations of natural language determiners suggcsted by our proposed universals hints at a theory of acquisition following Chomsky, in that children faced with the task of learning language need only consider a restricted set of possiblc determiner interpretations. Another relationship to a psychological theory is discussed in section 4.9, where it is suggested that the nature of' determiner interpretations gilarantces the availability of certain verification procedures.

112 Jon Barwise and Robin Cooper ~-~ -

We should emphasize that the psychological considerations have emerged from examination of certain fornlal set-theoretic propcrtios of the interpretations of natural language determiners. We feel that this illustrates the possibility of basing psychological theories on research in model-theoretic semantics. It is a mistakc to reject such research as irrelevant to psychological theories just because its relationship to a thcory of language learning or use is not apparent on the surfiacc. For example, it has been suggested that taking NP-denotations to be families of sets runs counter to any reasonable psyohological theory. Wc believe that our further investigations of the structure of these families suggests otherwise. Our discussion has concentrated on purely semantic distinctions among vai.ious kinds of dctcrminers and noun-phrases. While these semantic distinctions are often reflected in thc syntax of sentences, there are no syntactic correlates to these distinctions in the structure of the noun phrases thcmselves. For example, the semantic u ~ a k / ,, strong distinction is closely reflcctcd in the acceptability of the "Thcrc is construction, but it is not reflected in the syntactic structure of the associated NP's (6 many men", "most men", etc. Similarly, the fact that an NP corresponds to a rnonotonc increasing or decreasing quantifier is not reflected in rhe s j ntactic structure of "many men" or "few men" (although it is rcflccted in the arbitrar~choice of basic Icxical i tems). T h e importance of this type of semantic analysis for a linguistic theory has rarcly been emphasized - even in the literaturo which has adopted a n~odcl-theoreticapproach r has sl~owil toward semantics, such as hlontague Grammar. Previous work, f i ~ example, that the use of model-theoretic semantics allows us to capture semantic relationshil)~ between sentences bithout making the relationships explicit in the syntax. It is clcu that, in the long run, ui~lerstandingthe relationship between syntax and sclnantics will be at least as important as, say, that b e t w e n syntax and phonology. Howevel-, important as this is, we believe it is only a part of the role that semantics can play in linguistic theory, and we suggest that the study of semantics in its own right will be as important as the study of phonology or syntax. -

5.2 Semantic intuitions AThileit is seldom made explicit, it is sometimes assumed that thcre is some system of that an inf'crencc in natural axioms and rules of logic engraved on stone tablets language is valid only if it can be formalized by means of these axioms and rules. In actuality, thc situation is quite the reverse. T h e nati\.e spcalicr's judgcinents as to whether a certain inference is correct, whether the truth of'the hypothesis irnplics the truth of the conclusion, is the primary evidence for a semantic theory in just the way that gran~maticalityjudgcments are used as primary evidence for a syntactic theory. We have used such judgeri~entsconcerning inference in order to detcrniinc many aspects of the model-theoretic treatment we have provided. In particular, all o E the properties of determiners and NP's w-e have used rest on such evidence. Just as a syntactic theory must draw the boundaries around grainmaticality in some way, so too with semantic thcory and infcrcncc. For example, just which inferences -

Generalized Quantifiers and Natural Language 113 involving "most" count as "logical" depends just whcrc one draws the lines. 'l'hc raw data of speaker judgements may be represented diflcrent1)- within different theories. Nevertheless, our clues to the meaning of the string of souilds rcprescntccl by "n~ost", and the inferential uses to which it may be put, are not determined by ally logic \\;sit in stone, but come only from the intuitions of native speakers. We have built one semantic intuition about determiners (the one captured by the determiner universal) directly into the semantics. Thus, "hilost men run" is /ugj~.nllJ~ equizllllent to "Most men are ~ n c n and run" in our semantics. And, of course, just as with grammaticalit? judgements, there are some very clear cases and some for which it is difficult to get a clefinitivc answer - as we saw at the end of 4.8.

5.3 The Role of translation and complexity of fragments Like htontague in PTQ, wc have used translation into a logic to induce a scina~ltieson our formalization of n fragment of English. It has been pointed out m a n j times in the literature, initially by Montague himself, that the intermediate language is a convenience, not a necessary stage in the interpretation of English. It \vould be easy enougli to define the semantics directly on the syntactic component of the English fragment. In studying Montague's fragment in P T Q and subsequent work in thc same tradition, however, it is easy to get the in~pressionthat the model-theory per sc is essentially trivial. It often appears k o m this work thal the translation procedure must be more contentful since it is so complex. 'There are taro reasons for this imprehsion. A theory may be trivial because it says so little that it is easy to understand it completely, or because it is so complicated that there is little known to say about it. T h e model theory that goes along with Montague's logic I L is trivial for the second reason. Montague packed so much into the semantics of his logic that it is extrcmcly difficult to discover any very general facts about it. His reasons for doing this were, presumably, two-fold. In the first place, he wanted his logic to be sufficiently expressive to use ils a tool for showing that very large portions of English could be given a model-theoretic semiultics. Secondlj-, Montague had an unflinching Platonistic attitude toward set tlieorj- which is deeply imprinted on his logic. The reason Montague's translation procedure is more complex than necessary, is that the syntax of his logic 11, very directly reflects the semantic intcryrctation, Once one has mastered his symbolism, the model-theoretic interpretation can be read directly off the formulas of the logic in a straightforward manner. T h e situation can be visualized as a scale of 1 to 10, with the syntax of Montague's English fragment at 1, the model-theory at 10. One could imagine interpolating a formal language anywhere in between. Montaguc chose to put his I L at about 9.5. His decision has allowed researcl~ersextending his work to concentrate their efforts on the translation relation of larger English fragments into 11,, leaving the model theory largely untouched. This has been a fiuitful approach, but it has had the unfortunate sideeffect of diverting attention away from the properties of the model theory. A major lesson learned fro111over 60 years of work in model-theory is that there are great insights to be gained by (temporarily) limiting the cspressive power of your

114 Jon Barwise and Robin Cooper formal language (as with first-order logic) so that one has tools for studying the resultant models. By making the language less expressive one obtains a non-trivial model theory with applications to those areas which happen to lie within the rcalm of the logic. Now that we have learned that it is possible to give a model-theoretic semantics for large portions of English, the timc seems ripe to apply this lesson as a research strategy for natural language semantics. T h e strategy has guided us in the work reported 11cre. We havc deliberately restricted ourselves to a very si~lzplefragment of extensional English, concentrating on determiners and NP's. We have set up our logic so that the translation procedure is essentially trivial, concentrating our efforts on genuinely scmantic issucs. The and noun-phrascs potential contributions to the linguistic theory of dcterrnine~.~ suggested in section 4 result from this attention to model-theoretic semantics. Thcy would certainly not have been apparent had we studied translation - eithcr ours or Montague7s. I

5.4 Logic as a part of linguistics

/

If our claims in 5.1 and 5.2 are correct, then the traditional logical notions of i validi~yand inference are a part of linguistics a conclusion not likely to comfort , many logicians or linguists. T h e phenomenal succcss of first-order logic within mathematics has obscured, indeed, nearly severed, its tics with its origins in language. Except for tense and modal logic, rescarch in model theory in thc past twentv five years has taken irs problelns almost entirely from pure mathematics, becoming ever more specialized and renlotc from languagc. 1;vcn thc work in generalized quantifiers mentioned in the introduction is devoted almost cxclusively to mathematical quantifiers, going out of its way to avoid mentioning possible applications to natural language. This same success of first-ordes logic within mathematics also fostered the mistaken idca, discussed in 5.2, that the "laws of logic" are autonomous, perhaps part of mathematics, but not a property of language and language use. It is here that kIontaguc nlade his biggest contribution. I o most logicians (like thc first author) trained in model-theoretic semantics, niltural language was an aiiathema, impossibly vague and incoherent. 1'0 us, thr re\-01utio1iai.yidca in Montilgue'~ paper P T Q ( a n d earlier papers) is the claim that natural languagc is not in~possibly incoherent, as his teacher Tarski had lcd us to hclicvc, but that large portions of its semantics can be treated by combining known tools from logic, tools like functions of finite type, the A-calculus, generalized quantifiers, tensc ancl modal logic, and all the rcst. R~fontaguehad a certain job that hc wanted to do ancl used whatever tools he had at hand to do it. If the product he built looks a bit libc a Rube Goldberg machine, well, at least it works pretty well. It proved its point and should lead others to explore natural language semantics further, while at the same timc paying rigorous attention to its syntax. It is an exciting possibility, onc that could lead ro a revitalization of model theory and open up ncw domains for thc construction of linguistic theories. r-

7

Generalized Quantifiers and Natural Language 115

Appendix A. Additions to fragment 1 Fragment 2 incorporates ilzeru sentences and definite determiners following the iclcas in section

4.6. /!/'~h~re-serzt~r.rlc~>s. T h e s!-ntactic analysis we present is culled from FRAGMENT 2. I~ll.o~-pcr~atiorz Gazdar (19'79)' and Jcnkins (1975). .Add to the rules of Fragment 1:

SD1.1

SD 2.1 SD3.1

NP [there] VP [there] S-NP [thcrel

+

there

+

be NP

STP [thcre]

T o the translation rulcs we add: translates as thing

NP [therc] there VP [thcrel

translates as j'

[il\~

14;1\T

[there]

[therc]

It is important for our seman~icanalysis that only an NP follon- bc in the /here-VI' and it is llopcd that this fcature of thc analysis could be niaint.ainecl in larger fragments which includc si~chscntc~lccs as 1hei.e u o I?JLL?It n I ~ ~PL I Y I / ~ t?/ i~t ,> ~~lP-r,fi,~li, .(~ C J O P / CS ~ L I T I ( / I ~ ?/?)I R ~ / ~ ~ . / ; , L ~ N ~ The N I I I . plausibility of such an anal~sisis argued for n-ith a lilrgc nulnber of csnmples by Jenkins (1975). Even Jenkins ho\j,c\cr clocs not consider the unclerlincd strings in (1) to be NP's. (1) (a) Thcre are Inlo pcoplt ril.k/drunk (b) There are,fire i c~okieslt;/i. Indeed, the!. do not occur in all the pti~ccs~ l i e r cone ~ ~ ~ o ucxpect lcl NP's to be, as shown in the ungi.arnmilticat sentences in (2).

(2) (a) *Two pcople sick/drunh entcrecl the room (b) ?*The cookies left were mould\;. Howcvcr. they do show up in gran~rnalicalsentences after analysis 1%-ouldshow thcm to be NP's.

where tlic on14 rcasonablc

116 Jon Barwise and Robin Cooper (3) (a) “bong the people sicli/drunli, were 13ob and his wife (b) Of tlie cookies left, two were mouldy. While we do not u~iderstandtlic distribution of thcsc strings it clocs not sccni unlibcly that thcj arc NP's which are somehow restricted ill their distribution to ~lr~~rc-sen tcnces and certain othcr contexts. 011 illr r.onIcsr(often rcfcrrcd to in the Other problematic examples i~ivolvcph~ascssuch as s~~rlr~lirig transformational litcraturc as reduced relative clauses) when they occur aftcs a full rclativc clause. It is not normally possible to have such a scqucncc occurring within a single NP. This is shown b j the ungrammatical example (4a) which is contrasted with tlic grammatical example (4b) with the same string in a tlrere-sentence. -I [n~ho~ I I O I P S.you] Is/ri~irIin~o r ) 111~ c~onic*r.l~+-l;avcd to nic as I went by in the hus. (4) (a) *,girl (b) There is a girl who knows !-ou standiiig on the corner.

,iZ possible

w7i1y out of this problem is to say that s~trlrilrrrgorr ilrr r.m,aur is a scntcntial nioclificr i ~ n d hence not uithin the \'P at all. This is supported b!. the fact that sl~r~r~lit~g or/ 111(.(~1171~1.in also occur at the beginning of the sentence: Stul~(/i~rg on tlre i.or~rrrllrerc is tr grr1 i i 4 o k11/~n7s yolr. Iio\vcecr, not all such "reduced relati\ cs" may be explained away in this fi~sl~ion. (5a) suggcsts {hat 11 girl w h o Avlnr~?v,)!a~~ artr.r-~,.
( 5 ) ( I ) *I rnet a girl who knows you intcrcstcd in this proble~ii. (b) There is a girl who knows you intcrcstcd in this problem. ( c ) *Interested in this problem, there is a girl who lino\vs you. It is not clear, howc\er, whether there Ilia!. not bc otlicr special NP positions in which these strings may nevertheless occur as NP's. Consider: O[tkt, girls m)lio o ~ zA ~ r r r ~ Ii I~ Il I P ~ ~ ~ .111 < I /lrr.i C ~ proh/t111,.I/Ior:yIS /!)I /i/r //if ~ r i o ~likely */ 10 ./i~id (1 ,co/uttott. Finall!-, arc would expect that in a larger fiagment tlie feature /IIL'~LJ on the l'-P would percolate up to higher VP-nodes in thc rnaniicr suggcstcd by Gazdar (I 970) in order to account for sentences s ~ ~ as ch ~ h r r rupperrr. l o he./ji~~ m ~ i~r ~ t h p(/rk. ~

I?uorporntion of Det uf'NP Acld to the lexicon:

Xcld to the s!;ntactic rules:

SD1.2 If is a N P constructed with a ~lcfinitcdctermincr, then [of (1, is an SI>. SD1.3 N P d D c t N I"( I lof] [ofj In order to translate this cxtendetl fragment we must sliglitl~enlarge the logic (thcrcby creating L(GQ),) by adding the Sollowing syntactic and semantic 1.~11~s: Syntax: if Q i s a quantifier, then Semantics: Ir;Qll is n 11-(211.

AQ

is a set term.

Generalized Quantifiers and Natural Language 117 l'hc trailslatio~lof the syntactically special determiners in tlie lexicon is thc same as their traoslation in Fragment 1. ranslates

as A

translates as

<'


~ / ~to( .the I~O syntax ? I . oC fragment 1: FRAGMENT 3. X P - ~ ~ I ~ ! ~ I.4dd ,%-P-~.o,!/~mnc.tio~~ ilnd the ( a ) If x, {j are of the form [[lN1>and [jlNPwhere neither or cj is oF the form [qINr,bur I~%jNI,, denotations of r , fi induced by translation arc mo~iotonequantifiax of the same kind, then [ x ant1 PIYP and [ m or- flJNP arc. mcinbess US SD. (b) If x, 11 arc of the form specified and denote monotone quantifiers of dil'fcrcnt kinds, then [ a hut IjINPis ;1 rncn~bcro~ SD". 5

<

Wc specif) that tlie translation is into the bnguage L((;Q)2 defined at thc beginning 01'4.10 and acld the following translation rule:

translates as j'

translates as

A

5'

6' v 5'

Appendix B: Semantic postulates for few, most and many In the course of'section 4 wc discussed 1-ariousscniniitic properties of the non-logical clctermincrsjh, rnos/ and I I I N I I ) I , propcrtics which are not insured hy our definition oF modcl in section 1 . j . To gual-antee that thc fornial scniantics rellects the intuitions from English we must restrict the class of ;ill models to those which satisSy thesc properties. Wc refer to tlie Sornial versions :IS seman~ic

118 Jon Barwise and Robin Cooper postulatcs. Thep are not quite of the same character as thc restrictions on moclcls introduced by M o n t a ~ u ein P T Q for thcy arc not expressed as sentences in our lornlal language, but rather as scttheoretic condi~ionson the models thcrnselves. The extent to which such semantic postulates can bc capti~rcdsyntacticall! ma! be discussed in a latcr paper. Let $1 = { 1 I ) . From section 4.2 we ha\.e the follon-ing:

SP1. Most i.~n po.dizt~s/rorzg Iletzrrrzincpr. That is, for every A

C E, A E

llrnostl(-d).

From 4.3 n-c have

SP2. Most und many ore nzon [',f'cw is mot/

L. That is, for all X, Y,.4 c E:

.Yc L', X t Ilmost ll(A) implies L' E Iinust 1(?4) -YC I',A- E (Imanyll(.4) implies Y E Ilmany ll(.A) Y & X,.Y E Ilfew1(-,4) implies Y E Ifewl/(.-i).

If most people do X and most people do Y then someone does hoth. This I I I L I C ~S C C I ~ Sclcar from the meaning of "most". JVc can express this by:

If one wants to demand that ,/in)mzn bc ccluivalcnt to no/ nlnqt r~ren(or postulate one of:

7101

stzvrrll m t i i ) onc cdn

IFewll =- (manyll. 1.e. for ail!- -4, SP4. (op~~onlrl): l(17ewll(-A)=

(1\111anyIl(-i))

=

or :( 1 fewI/(.i)=

{-Ji C E ( X # Imanyl1(..4)) Iscv~raIl((~-l).

T h e persisteilcc of nrurzy and anti-persistcncc of/>n)discussed in 4.7 nas less clcir than most of'the above. many SPS. (oplio?ln/):few is pti.sasr~t~t,

1s

~1~7tipcrxrst~~11t. That is for a11 -4

c B C E,

SP6. I / ' X E llmany1((.4)thcn X f @. This guarmtees that if man^- men (lo something thcn some man docs it. These are by no mcatls all of thc semantic properties that sccm to bc cnjoj-ctl h!- the dctcmincrs iuost, nr~rtt)r,~/;'~r, but they are the ones which seem most clearll- rcilectcd in tllc scnlantic judgements of iiati\;c Ihglish speakers.

Appendix C. Some simple results about quantifiers and determiners LJntil C12, wc k t hf = (E, 11 I ) be a fixed model. A Y ~ ( ~ ~ ~Qon t ~ / :1/f ; ~is~an) r sct ofsuhscts o l ' l . Q i s a proper qnontz/ier.or .vi~.i.tif Qis nun-empty and is not the sct of ;ill subsets oi' I?. Q/izle.v nt? -4, where :i is some subsct of L, if for a e r y A- C I?, X E Q iff (X n : I ) t Q . ('Lit't"' is all abbreviation for "if and only if.")

Generalized Quantifiers and Natural Language

PROOF. Since Q lives on . i , E E Q iff (I7n A) E Q but E proof'.) A quantifier Q is called the principtrl filter gencriltcd by B if

n.4 = .-I.

119

(amarks the cnd of a

Notc that the principal filter generated by H is a sieve unless B = 1/1.

C2. PROPOSITION. PR001:.

If R

!f'Q Is the prini.~pol~fille~gcize,z~le(l /!I, B rlreir Q 1ii.t~1111 .-I ! / ] ' R C : I .

-I, thcn for ;my X' the following ilre ecluiralcnt:

?i E

B g .AB & (A- 1-1 - 4 ) (since B C '4)

. \ n . -E~Q . Thus Qli\ cs on -4. Notv supl>oseQ l i \ cs on i and Ict us show B (:I. T h u s B C_ .-I hy the definition of princip;ll filter.

C -4. Siilcc 11 cII E, /1 E Q so .-l E Q h!

.4 cletcrn~incrD is n i l e / i i ~ ideterminer /~ if tbr all . I E, D(.4) is ii such that, lor ;in! .-I f tloiiiain(D), I)(.-!) is a quantifier that liws on -4. :I clcterinincr D ispi.opc1- if D(.-1) is dcfined tor all .I C_ II and, for some .-I & E, D( -I) is proper. Uni\crsal UJ in 5 4.4 illlplics that ever! naturnl languilgc clctcrmincr is thc restriction of a proper natural language determiner. r i dctcrmincr D is ;I tlc/jn~recletcrniincr if for all -4 2 E, D ( 4 ) is ;t principi~lfiltcl,. I ) is ~ ( ~ . < i /s/rnri,:r ~i'l' if for c\ cry A, -4 t D(.-I).

1 I

I'ROOE'. Sincc D is clcfinite, D(.-I) is the filter gcncratcd by solnc R. Since D(.-I)lihcs o n . f , B b! C:2. But then .-I E D(.4) by the definition of principal filter. [7

5 :I

il determiner D is .glln~~telric if f i ~ rall -4, B. B E D(-4) iff .i E D(U). D satisfies the ~n/c~r;sc~~~/~orr rn/~rli/ronif for all . i , B, R t D(.4) iff R E D(.i n R). iVc will shon that thcsc two conclitions itrc eqitiralcnt in C5"

1 i

U E: DCi) iff E E D(/i n B). JJROOF. T h c follot+inp are cquiv;llcnt:

,

R E D(I) ( i n B ) E n(-4) (-4 n B ) E />(.i r~ (.i (-1 11)) ( 4 n R) E I>(.-1 11 B) E E 4 4 i?B )

(since D(. 1 ) lives on -4) (the i~~tersectiol~ condition) (-4 n R = ,i n (-4 n R ) ) ((11 applicd to f n B),

120 Jon Barwise and Robin Cooper PROOF. Assul-tle I) satisfies the interscctian condition. Thcn .-l E D(R) iff 1; :' lI)(il n R) by C4 hut B E D(A) iff.,!?E D(*4n R) also by C1. Thus .,.IE D(B) iff /1 E D( -1). For the converse, assume I1 is symmetric. The follo~~:ing arc then equivalent:

(by symmetry) (since D(H) lives on B) (by symmetry). [7 C6. THEOREM. 1,er D be rr: p r o p ~ rmont clrrrrnrrnc*r. Tjren D ron(/iiiotr (rrnd hewre j.< 11ofS J ~ I I I N I ~ ~ / ~ ~ ( ~ .

( ~ I ) P S rror

so/is[jl /lip irilerrc~/to~i

PROOF. T o rccall the definition of strong, D is posrrrre S I ~ U I Iif~ for it11 . I, >.I E /)(--I). D I.? I I C , ' C ( ~ ~ ~ M strorz.q if for all 4,,4 $ D(,-1). D is stro112 if D is positi\c strong or nc#ati\c strong. .lssurne that I1 satisfies tllo intersection conclition. tiye claim that if D is positive strong then Li~rcvcry -4, lJ(.i) is the set of a11 s~ibsctsof E whereas if D is negati~estrong thcn for every .4, D(.f) is empty. Thus if D is either positive or ncgati~estrong, thcn L> is not propur. To prove our claim, note thc tidlowing equivalences:

R E L)(A n B) R E D(-4) iff iff(..l n B) E D(B) iff(A ilB) E D(.4 n B)

(the n-condition) (s_vmmctr~-, C5) (the n-conclition again).

Thus if D is positive strong, R E D(.i), for all ,i, B wliercas if D is negative strong thcn B $! D(:.l),J i r ull .,.I,B. 17

,4 quantifier Q o n M is monotone I Y J ~ . ~ P I I (mon S I ~ ~ T) if for all Y, 1' C E, .Y t Q and . I C'Y implies Y E Q. determinu I> is wnrl f if for all .4, if I)(-1) is defined then D(:l) is mon T. 'I'his should not bc conf~~sed with thc notion of a persis/ewi determiner, one such that for ill1 4,11 E, if . A C B then D(A4) lJ(R). Here is an examplc of'a determiner which is persistent but not mon 1 or syn>inctric,Let E h;lw at least two elen~cntsand define I) by D(.i)

=

{.Y C E.4 n X # O and -4 X f 8). -

1

to scc that .-l C B implies 1'11at is, Dc4) mcans "some but not ill1 of the things in .-I". 11 is D(--1) C D(B) so that I) is pcrsistcnt. H o ~ ~ ~ e vDc ris, not mon 1 since I: $! /J( 4) for :ill :f. Sincc, For I 0 # 4 # E,.i E D(E), this also slio\vs that D is not symmctric. 111 our persistent drtcrminer universal (U8 in 4.0) \vc proposcd that 1111 siiuplc persistent determiners of human languages arc nion '[ and n-cak. In view of the following proposition (and C b ) , a stronger universal would he to assert that the simplc pel-sis~cntdctcr1ninel.s of' I i ~ u m ; ~ nI languiigcs arc all s!n~metric, i.c.. satisfy the intersection conclition. Our lacl, ol' clear c u ~intuitions " ahout \vhicll non-logical weak determiners satisl'!. the intcrsc.ction corldition prcvcnts us from ruiiking , this proposal. I

C7. PROPOSITION.

[/.Di . ~ptrsis/(vi/ (!11,1: ) ~ ~ I / ~ I I L //li'7/ ~ / ~ I ~ IJ , is

II~IIII

1.

PROOF. Suppose .y E D(.-1) arid .Y C I.'. b'c nccd to show I - E 13( 4). I3ut .X E D(.i) implies 4 E D ( X ) by symmetry so -4t D( I.') by pcrsistcnce and hcncc ).' E I)(--f) hv symmctr>.

Generalized Quantifiers and Natural Language 121 (1) (.-I n B) E D(a-In 4) since D is positive strong so R E I)(.-!fl 8 ) sincc .f is similar. Recall the definitions nf'Q and Q from section 4.7 and from 4.1 1.

PIi00F.

PROOF.

- -

(1) ,lZssuine Q i s mon f . First, suppose Y

( E - Y) c ( E - X) so ( E - X) E Q s o .Y t (Q then I' 4 Q so X @ Q so X E ( Q ) .

-

( 2 ) This is similar to (1). (3) This fllovis from ( I ) and ( 2 ) sincc C10.

PROPOSITION.

I f ' Q i s nrorr

r,

zN

-

n R g L3. ( 2 )

E (Q -- ) and X C_ 1'. Then ( E - I.') E Q and ). Now suppose J.- f ( -- Q )and .Y C 1'. Rut

(Q

E Q nrwl

).

O l h m -i n 4 f 0.

BE

-

PROOF. Suppose A TI B = G?. Then .4i (E - B ) so, by monotonicity, ( K - B) E Q .13ut thcn U E (Q ) SO 4 @- ( Q ), a contradiction.

A n7irnrs,( set fur a quantilier Qliving on A is any subset n ) of.2 that is an clement 01'Q. C11.

PROPOSITION.

LC/ rrrrige oT7er~ ~ i t t z zsets,fi~r a the rl~inf~ttfin. Q fhur lii.~.r011 .-I.

/ i ) ~X, X Q $jfsoii~eIP 1s (1 S U / ) S ~ J(!JAY. / (i) I1.Q i.q 1 1 1 0 ~ 1 ~ / 0 1 i1 ~t ~ o . ~ v z . ct lt '~f (t ~~ n -((?Z)I J ~ ~ ~ ~ ~rblw < ~ ./ij~. L z .LII?.)) s ~ -X, I z ~.\- E Q I[[ 3-n .-I ix ~/tttlr1?7c(l sonic (ii) r f Q Is r~~oi~ototrc

131.

PROOF. (i) Assumc that -A' E Q. Then .Y n .4 is in Q since Qlives on -4, so wc may tillic .X n .-1 lib]. 111. Conversely, if IT, ,Y, thcn since 11. E Q and since Q is monotone increasing-, Y E 4. (ii) It' E Q, then X n ,4 is suitable. Conversely, if (.Y n .I) I?), thcn sincc n? f Q ;lnd Q is monotone decreasing, X n -4 is ill Q ancl hence .X- E Q, since Q lives on -1.

.x

T o conclude this appendix we return to some af thc pointsmadc in 5 I, cspccially in 1.2 and 1.3. Wc want to prove that, in our terminology, "niost" and "more than half" must be treated as dcterniincrs, nor ;IS qu;~ntificrs.In other aiords, we u-ant to prove that there is no uay to clcfinc wlosl I tr urt. li's in tcrrns of i ~ o s it l ~ i ~ l ~,v(g .s . . La'. . . C' . . . I.. . . ). T o a ~ o i dproble~nsof vagueness, we treat "niorc ha11 hall". be convenient to first protc a weakcr result, namely, that ~trorc/htr?l ktr//'/he 1':t urc3 For the proof; i t li:r cannot be defined in first-order logic. This result is probably somewhere in the litcraturc, bui wc ha\ cn't been able to find it so present a proof. It is a routine application of t l "Vraissi: ~ letho hod". T o motivatc the cnmplcxity of tlic yrool; note that for ail!- fixed uppcr bound k' on thc sizc of tlic unikerse E, there ts a sentence c p , that "works'' Ibr models of sizc 5 K , a giant disjunction of k formulas.

C12. TIIEOREM. CIINSI(/CY 11 jiu/-or(ftr I L I I ~ ~ L I U XLP nlifh qutl1i1.1.rlrru' t n ~ oi r ~ r t r r : )predr'culc ~ s)rrrlhols L, V. Tl~erei\. 1111 xrnirnc.cJ cp ( ! f L so i h ~ l iin ei.cr:l~-/i~ri~e n~odiv'.I4 = ( E , I ', 1'),

PROOF. Wc will prove morc for thc purposcs oi'thc ncxt proof. Namely, for all n;~turalnunlbers nl and k with k > 3n1 we construct ttvo mndcls MI = ( E , 1/', If) ancl .Mz = (E, Liz, 1 -) with thc same domain E and same interpretation {'of Y, such that

.

122 Jon Barwise and Robin Cooper (1) til g Ij2 k. (2) 2 . Card (lTr)> Card(L7) = 3n1, hence, ,+Izk "hlorc than hall' the j'.'s are I:'s" (3) Card (1,;) = 2 . Card(Cil), hence, ,+I1 "More than half the C.'s are Ir's." (4)

(5)

Chrd (I?) = k For an! sentcncc cp of L \\-it11 less ihnn

HI

q ~ ~ a l ~ t i f j c.+Il rs,

y iff MZ

(p.

Ignoring condition (4), this \ d l prove thc theorem, for given a purported definition rp of "More than half the I/"s are i;'s", we apply this to some nl greater than the number of'cluantifiers in rp and some k 2 3 7n. T o construct M I and satisfying (1)-(5) we let E be anv set of 1, objects, b ' a s~thsetof /?of size 2 nr, C'? a subset ot' I/' of size nr 1 and LTl a subset of 1:? of size rr1. Only (5) needs to be proved. Notice that if n(nl then Card ( E - V ) 2 r1, Card ( L - / I I ) n, Czard ( I ' - [ I r ) 2 /I as nell as Card (I;,) n and Card (l??) n. Tliis fact allo\ts us to prove (5) b!- proving the following strongcr (6). Define for an!? formtila ip, r.(cp) = number of cluantifiers in cp+ number of free variables in (p.

+

>

>

>

) a formula with ~.(ip) < HI and if wc h a w an?;. one-one corr~.sponclcncc ( 6 ) If (p(.ri . . . . I . ~ is

hl

'71 &+

.

bctnccn clcnlents o f E satisfying ir, E lil iff b, E L.'2, and '1, E 1,- iffh, E I , l i ~ rall i = 1, . . . I,, then k tp((li . . . l r i ) iff /El2 q(bl . . . h,). ( ( 5 ) is the special case of (0) \there t = 0.)

+

.MI

Stated this explicitly, the proof of (6) is cluile eas! - by induction o n I-(cp).'I'hc point is tlint therc is always enough room to cstcnd the onc-one corrcspondenec onc more step c\licn !.OLI comc to a quantifier. (Draw a picture.)

PROOF. hlorc explicitly, \\ hat \t-c prove is the follon ing. I.ct I , be 11ie fi~.st-orctcrmonaclic langi~age of C12 and introduce a ncn quantifier symbol Q. Lcr I,(Q hc the Ii~nguagcwhich nllo\\s ;ill thc sj-ntactic constructions of' 1, plus, for each tbr~nulacp(.\.)of L(Q ), Q.\,[q~(.v)) i ~ ~ic\v i f'ornlula of L ( Q ). T h e semilntics for Q i s defined on finitc moclcls !Vf by I%f

k Q.~[rp(.v)]

iff Card

111.24

t=

cp(rl)) > $ard

(E).

(a

What w-c prove is that there is no scntencc (p of L so that :I1 cp iff more tliiln half the Ins arc Lrs. l'lie intuitil-c idea is that i f E is very large con1p;ircd to [,.and I -111cni t \till swamp out Iliitid 1.' in the language L ( D . T o mahe it prccisc Ne will dciine 1' fi~nction* fiolti for~iiulasI/! of' L(Q) to formulas (1% of L so that II/ is cclui~alentto I//" on moclcls it3 nhcrc thc gap bcl\vccn the size ol' I',~IIJ that of E is great enough. Namel!-:

(P) For an!. formula 11/(.\.~. . . .rr.)of L ( Q ) and an! lnodcl 44 (E) 2 (Card ( V ) i.(~,!!))

>

+

=

( E , I:, 1 ) uhcrc I 1 C I '

C E and Card

Generalized Quantifiers and Natural Language 123 From (P) and the proof of C12 we can easily concludu the proof of C13. For supposc tliat cp is ;I sentence of ~vhichis tl-uc in a modcl /l4just in casc illore than half the I"s and (j's. IAct ill > r(cp) and let k > 2(2 111 r.(cp)). For this rra and let .All, M2 be models sarisljing conditions (1)(5) in the proof of C12. Thus &IL /=- (p but /MI q , b\- (2) and (3). B L I ~since (lard ( E ) = k > 2(2 m r.(cp)) = 2 (Cart1 (F) r.(q)), Condition (P) implies that :Vll (cp -+ cp"), M2 ((p '-' cp"). But b) ( 5 ) , M I rp* iff ,%Ir (p", since cp" is a first-order sentence with r.(cp*) < IN. This is a cont~adiction (since All (p implics M I cp" iniplics Mi rp* implics & .. /= (p but /t12 k- q). T h u s u-e need only define I//*, show- that r.(~//)= C(I/I"),and prow (P). ?'he definition of I//* is h!. recursion on 11and only docs things to the quantifier Q. Thus:

/,(a +

+

17

+

If I// is atomic then I)* is 11. If Gi/ is 10, (01 ~ 1 1or ~ )b'.v[R] rcspectivcly, then $* is ](H"), (l17,t0;) or V.rl O"], rcspecti~.ely If i// is Q~.r(I(.v,.]1~ . . ..ill ), then ~b* is ti.v[V(.r) ,v = ,111 1, . . . , v = .),k v O*(X,.),~ . . .,yk)l. ,J

(l.c., I/I" says that ever! .Y # I - C! ( y I . . satisfies ~"(.Y,,J,~ . . .yi.).) 'I'o prorc (P) onc ;irgucs b!. induction on the length of 11).T h e onl!- nontrivial casc is \vhcrc $ is of the for111Qd)(.r.,l~~ .. So supposc that (P) holds for 0, by induction, ancl Ict M = (E, I.', I.') be ;I nioclcl t\ it11 . , ) j b )

.,)ln.).

First assume $(nl . . . i l k ) holcls in .l4, i.c., that more than half the h's in E satisf! O(h, 111 . . . u k ) . Since X, 5 r(0). and since f- C:;~rd ( E ' ) > Card ( V ) r(t1), at least one such h is not in 1 C! { o 1 . . . ( / A , } . But a trikial autoniorpliisn~ argument then shows tllat any h ' # I - U { a l . . . ak} satislics O ( / j ,r r l . . . I I ~ . ) . Il! our inductive assun~ption,O*(hl, rtl . . . irk) holds I'or an! such h'. In othcr words th'(rtl . . . (11) holds in .*I, T h e othcr half of thc equit-alcnce is easier. This proves (1') ;IIICI hc-ncc tllc thcoreni.

+

'

After finishing this papcr, n r learned that ;I tlieorcni relatcd to Thcoreni C;13 J V ; I ~pro~cclb! l.);~i;iJ Laplan in 1065 hut v-as ncvcr puhlished. Extend the yual-rtifier "\,lore than 1ii11fof all things" into thc infinite following Rcschcr (1062) by defining JM k Qa.4 to mean that the set of'n such thilr .Ill k r/)(n) !>;IS greater cardinality than its complement. Kaplan showeel tliat the rclatijizcd notion could not be defined from the unrelati\izcd. This follow-s from C13. Kaplan's proof nlahes esscnti:~lilsc ol'inlinitc structures. His proof is unpublished, but some othcr intcresti~~g results fill- this clu;lntificr ilrc contuincd in his nhstracts Kaplan (1966). 3lonotonc iluantificrs hat c been stuelied in model thcorj- ;ind gc11cr;lliz~drecursion theor! fix somc tinlt'. Sce l3ar\vise (19'79) for refcrcnccs. l ' h c notion of persistence \\as ititroduccd in Har\visc (1078). 'The othcr notions are nee hcre. b'c 1ia1.e incluclcd 3 Lin of the classic pi111e1-s on gcnercllizcd quantifiers in the rcfcrenccs: hlosto\vski (10.57); Lindstroln (1900); Lcislcr (1060). Other relkrcnccs can be lounil in I 3 a r n . i ~(1078, ~ 1970).

Appendix D

NP's containing simple Det's 1, some/a 2. every/each/all 3. no 4. (at least) 1, 2, 3, ... 5. the 1 , 2, 3, ... 6. both 7. neither 8. most 9, many/several 10. few 1 1. th~s/that Other Det's 12,a few 13. exactly 1, 2, 3, ... 14. at most 1, 2, 3, ... 15. more than half 16. at least half 17, fin~telymany 18. infinitely many 19. open Proper names and

logical?

always defined?

always sieve when defined?

Yes Yes Yes Yes Yes yes Yes no no no no

Yes Yes Yes Yes no no no Yes Yes Yes ?

no no no no Yes Yes Yes no no no Yes

no yes yes no no yes(?) yes(?) no

Yes Yes Yes Yes Yes yes yes Yes

-

Yes

no

no no no no no no no

man 1‘,

& strong

or weak (w)

w +S

w w +s s -s

+

is

w w SI

w w w

+s i s w w w

definite? no no no no Yes Yes no no no no Yes

1 or neither

simple dual?

self-dual?

pers~stent?

antipers~stent?

intersection condition (= symmetric)

1

(2) (1 no no the 1 (11 no no no no (11)

no no no no the 1 no no no no no Yes

Yes no no Yes no no no no ? no no

no Yes Yes no no no no no no yes(?) no

Yes no Yes Yes no no no no ? ? no

no no no (16) (15) no no

? no no no no no Yes

no no Yes no no Yes no

no

no no no no no no no no

(20)

Yes

-

-

T 1 I

r

i

no no no no no no no no

pronouns 20, John, he

Yes

A

s

Yes

T

-

-

-

Generalized Quantifiers and Natural Language 125

Notes 1 This is proted formally in Theorcni C13 of Appendix C. 2 'I'hroughout this paper we use "determiner" to refer to a wide class of s!-iitactic clcnlcnts which also include what are solnetinies called predetermincrs, postdctermincrs, numerals, ctc. -4 more detailed investigation may well show that some of these liner distinctions arc ncccss;uy. 3 For esample, a number theorist interested in prinlc numbcrs will usc a measure which "livcs on" the set of primes so that (4) would be false. More common ineasurcs tvliicli do not give special weight to primes will make (4) true. T h e notion of "lives on" will be clcfined below. 4 Karnp's proposal is basically to evaluate a sentence with respect to a class of nlodcls, rather than a single model. 5 For each of (19) and (20) there are alternate derivations of thc same SL) bthich d o not use the quantification rule. In thc translalion dctined bclon, these alternilre deritations \\.ill translate, respectivel\;, as: m o s t ( m e n ) ,i[ s o m e (woman),j/[kiss [ m a n y ( m e n ) .i [see (s,h ) ) ] .

-

6 7

8 9

10

II

(s..)l)]l

T h e unlikelj-hood of interpreting (6) with this particular scope relation between no/ ant1 I I I ~ I is I ~ discussed in section 4.11 below. T h e notion of simple N P is well-defincd only !$-ithi11 tlie contest of a given synt;lctic analysis. For example, not ctcry analysis s i l l treat u.f,?u~as a single determiner clement. Notc that this is different from claiming that John cuists. U'e might assuiiie that the n~otlvl includes sonic lhings whicli do not actually exist. T h e set of things that exist is a subset of tlic sel of things that there are (in the model). I11 applying this tcst, we must niakc sure that we do not violate our assuniption of t i ~ c dcontcul. za1./'1 docs not cntail I ~ I O Rrpriblil.rit~s .YI It n i i g h ~be objcctcd that I I Z O S ~ Repub/zc.llns r~rlrrellrhe rlllr~c~rl I ~ NI(.P Z since thc former is often used in contest to mciln I I I O S I R e p ~ i h l ~ ~ u I Vi/ IiO. ~ r.r~r~r.r~i/ ~ltr, rille e)l/rrerl it c a r l ~ This ~ . is an esaniplc of the violation of thc fised contcst assumption. Clcnrly the N P mosl Repub/ic.titis corresponds to different q u i ~ n t i f i ~ins diffcrcnt contests. We arc intercstcd at prescnl in isolating the properties of the quantifiers thcmsclvcs ratl-icr lhiui t l ~ c coniples relationship bctwccn NP's, quantifiers and context. Some spcakcrs scein to feel thilt not :\I1 ]nixed conjunctions with irntl eleser\,c a l'ull star, particularly if the conjuncts are not simple NP's: John hirs rlii'i~ed or /~u.\.t J;ZY I P ~ ) I I I ~ [~ II I I ~111 most f k r nwll lo r h ~~( z I - / nwn,)! y. ~fthr I ~ Z C I IZ I M I~ I ~uost ~ s i . O~/ ' I / I P I P O ? ? I I ~ ~ IIra~.c./iii/i~d 1/11. e . ~ , t ~lrv~ lici . have no explanation for why there should be variation on the juclgcments in these cases. -Ipl>arcntl>-11ot A I N I should ~ not be considered as an N P since i t cannot occur ~ l o n cin 211 NP position. "Not Mar! is invited to the parly.

13 Tllcsc rules do not meet tlic rcquircmcnts of autonomous syntax, i.e. thcy use information about the semantic intcrprctation of constituents in order to define sj~ntacticwell-for~lictl~.rcss. 7'hei.c are, of course, ccluivalcnt fol.mulations in which the category NP is subclividccl in the syntax according to tlie kind of quantifier dcnotcd (a species of autononl>-preserving tlutment often h u n d in Montaguc Grammar). Wc beliebe that it might also bc possible to allow frcc gcncl.atioii of conjoined NP's and design a semantic filter (cf. Chon~sl;!~)which would rulc ouc ccrrain of thc conjunctions as semantically unacceptable.

126 Jon Barwise and Robin Cooper

References Barwise. J ~ I I .1978. Monotone quantifiers and admissible sets. Ln J.-L. Fcnstad, R. 0. CGanJ!., and G.E. Sacks (cds), C ~ ~ n ~ r n l ~Rn.rrr-siojl zcd ir'l~eir~l 1I: Proi.rerIrrrgs (!/' 1hl8 1977 O.vlo ,5'~~111/)1~srunr, Amsterdam: Nort h-Holland, 1-38. B:~r~visc, Jon. 1079. On branching quantifiers in Fhglish. -~orrrrrtr/~~/'Plrilosophii~tII I,o~rr.8: 47-80. Barwise, Jon. 1980. Scenes and othcr situations. Jo~irrrrrlr~/'l'l~ik~soplr,)~ 5 0 : 300-90. Chon~sky,Noani. 1080. On binding. /,irigur.\./I't.Inqrlir)~1 l(1): 1-40. C:lark, I-lerbcrt 11. 1976. Ser17a~rlti.sonrl Cr~~i~pr-~/z~~tzsion. The I laguc: Aloutot~. C;ooper, Robin. 1978. .-\ Fragment of English with Qucstions and Rclativc C;l;~uscs.University of T\'isconsin, Madison. Dowty. David K. 1979. Il/>~tlMeanitr,y u t d Ml/n/ugur Grir~tirzlar:771~~ Se/!rr~rr/ic.s I!/' I >r/)srrrrrl TIIIIPS III C&r~er-ci/i;.e.9cw1onlic.~(atlil i ~ iVlon/cicyuc's i PTQ. Dordrccht: D. lieidel. Fensrad, J.-1. 1978. Models for natural languages. In Jnahko IIintilika, Ilkha Niiniluoto, and Esa Saarinen (eds), E.c.sc)ls 011 iMiirh~nrrt~r,rrlclrrd Pliilr~soplrI'r.lrl I,o<~rt~: Proiec~ilirrgs(!/'I 11i l.'orrr/l/ .St riacli17i/i'r(/r1 Lo$i(. S ~ ~ n r p ~ ~ rr~il s i r(!/'/hr~ ~ t ~ ~P ~ I . S.Eorr~~r-Finnrsh I 1,ogii. Ctr~!/bre~tii,, JyiisLyli, Finland, Junc 20-July 6 1976. Dordrecht: 13. Reidcl. C;;lzdar, Gerald. 1970. Erz~li.v/( 1 s a (;'ontr.v/-Fr~~~~ La~tg-rrugc.Univcrsitj. o f Susseu. Gricc, Paul. 1975. Logic and conversation. In Petcr (;ole and Jcrry ;\lorg;un (ctls), kYpc~r~i.l~ .-I( 1s (.S)vr/a+v trtrrl S ~ ' P I Z ~ I IYO]. I ~ ~.3), ' L .NS ,e w York: Acadcnlic I'rcss. Jenkins, Lyle. 197.5. T I I E ~ I I ~ / IL S. ~~i F t ~ ~ ~ Tiibingcn: /iirl. Nicmcycl-. l,t~.y11~~11 Op1~~(11ors 111 L'tzg-lislt. I3loonii1igton,Ind.: Horn, I .aurcncc. 1976. 011111rS t ~ ~ i ~ zPr~~prlrt~c>s n~ic Indiana University 1,inguistics Club. Kanlp, J.X.W. 1975. T n o theories about adjectives. In b;clwnrd Kceni~n(ccl.), firmer/ S'rvr1r11111i.s o/' Mrrtnral 1,trt1gurrtqr: Prrptrs ./ion1 u C~ol/oq~~i~rrn .\'l,on.vor~d h y IIIP h;rr,y's Collrgr~ Rase~trrr.lr C'errlrr, Grnibri&c, Cambridge: C:ambridpc University ['rcss. Kaplan, D. 1066. Rescher's plurality-quantificatioli and gcncralizcd plurality quan~iiication,abstracts. Journrrl c!~S)~nrholr'i L ( < ~3I1:C 1.5.34. Karttunen, Lauri. 1977. Syntax and se~nanticsof questions, l,ityii~!il.,s( I N ( / P / I I / I I . ~l(1): I ~ ~ 3-44. ~I)~ Keislcr. 11. Jerome. 1969. Logic t ~ i t hthc quantifier "thcrc cvist c~ncountabljnian~". :l~rrnr/si!/' 2 4 ~ l ~ r / h ~ ~ ~ldosqic t z i ~ /1i:~I r-93, ~/ Klccne, S.C. 1953. In/ror//irlion I I I :2/relr1111a1h~n1~11i~~s. Amstrril;lni: North-T IolI;111cl. Ladusaw, William, 1079. Polarit? Scnsititity as Inlicrent Scope lielation. Pli.11. dissertation, University of' Texas, Austin. l,indstrom, P. 1906. First-ordcr logic and gencralizcd quantificrs. 7hcwr.1'1133: 187-95. Vlilsark, Gal-!. 1977. To\+-ardand cspian,ltion of ccrtain peculiarities ol'thc. cuistcriti:ll constrcrction in 13:nglish. l,irlglrt~./icAntr/lls,\< 3(1): 1-30. hlontague, liichard. 1974. For-rrrr(lPlrilosoplr~~. Srll~c.rtJI'iipriu ~~/'Rrrlrrr~.rl ~~/1oll/~i,~/lr~, ccli~ccliind with an introduction b!- Richmond H. Thomason. Nev fla\.cn. C:crnn.: Yale Uni\crsit! Press. Zlostc;.rr.sbi, A. 1057. On a generalization of cluantilicrs. l'rrrrt/trnr~rr/ir44rr/lr~11rn/rt~cr~ 44: 12-36. l';~rtcc., H;lrb;lrll. 1953. Some structural analogies hctu ccn ~cnscsand pronouns in Lnglish. J'ojl)rr~rrtl I!/ 1'11i/osop11~)~ 1X X ( I 8 ) : 601--0. Pcacocbc, C. 1979. Game-thcoretic scrn,lntics, cluan ti liers ancl triltli: conltiiellts on ProI'Cssos Hintikha's p'ipcr. 111 Lsa Saarincn (cd.), C ~ a 1 ~ 1 r ~ - ? 7 1 c o r c.Sc'trlrri~/iis: ~/i~~ril ~ ; : s . Y N1/11 ~ ~ sJ'(JIIIIIII/II..T, 1101.drccht: 1). Reidcl, 1 19-34, Rcschcr, N. 1962. Pluralit!- qu,lntif?cstion, abstract. Jorrr-trol ~!/'.Sllrnho/ic.1,1q1e.27: 373- 4. Sgro, J. 1977. C:omplcteness tlreorerns lor topological models. ,.ltrrr~~/.s 4' /LIu/l~c~~nir/ic.rrI I,O%I(I(. 1I : 173-93.

The Logical Analysis of Plurals and Mass Terms: A Lattice-theoretical Approach Godehard Link

1 Introduction The weekl!~ Mnga.zirtc. of the Gernlan newspaper Fra~lkjiurtcrA i l l ~ e t i z ~ ~Ztirung ine rcgulasly issues R/Ial.cel Proust's famous questionnaire which is answered each t i n ~ eby a different personality of West Gcrman public life. One of those reccntly qucstioncd was Rudolf Augstcin, editor of Der Spiegel; his reply to the question: "Which property do you appreciate most with your friends?" was ( I ) "that they are fcv ." Clearly, this is not a property of any one of Augstein's fiiends; yet, cven apart from the espyit it was designed to display the answer has a straightfbrw-ard interpretation. The phrase ( I ) predicates something co/lective()~of a gro-olrp of objects, here: Augstein's friends. As it is well known, coIlcctivc predication is a rather pervasive phenomenon in natural language, as the following sanlple of sentenccs shows:

(2) (3) (4) (5) (6) (7) (8)

T h e children built the raft. T h e Romans built the bridge. Tom, Dick, and Harry carricd the piano upstairs.' T h e playing cards are scattered all over the floor. T h e members of the committee will come together today Mary and Suc are room-mates. T h e girls hated each other.

There is a striking similarity betwcen collective predication and predication involving mass nouns.

(9) (a) The.children gather around their teacher. (b) T h e water rathers in big pools.

128 Godehard Link Moreover, a characteristic feature of mass terms, their c.11112rrIirtizlr~ ~ ' ~ ; / i r ~p~rioipcec~ I y2, can be imitated by plurals. (10)

If n is water and /I is water then the sum of I/ and /I is water. (b) If the animals in this camp arc horses, and the animals in that cilnll> are horses, then the animals in both &Imps arc horses. (a)

All this has been observed and discussed in the literature although the notcd pi~rallclism has perhaps not been stressed too much.3 As it can be seen fi-om Pcllcticr's 1079 volume, l~owcver,there is much disagreement about the proper bvi1y 01' attacking the logical problems posed by plurals and inass terms. 1;rom a scn~anticpoint of view the basic question is: what do mass terms and plural expressions denote? Some havc thouglit that in order to be able to give a satisfactory anscver to this question it is necessary to givc up or at last extend the underlying set theory and to clefine new kinds of objects, for instancc ~nsc~nlhkes (Bunt 1979) or k ' o l l t . k t i o ~ ~(Blau ~ n 1079). 1 think, l ~ o ~ ~ c vthat e r , cvc can retain the usual set-theoretic metalanguage and sinlpl~lenricl~the structure of our models as to ~ ~ c c o i ih~rl tproperties like cumulative reference. On 111y view, such properties arc also not secured by ik/inirrg some plural or mass term denotations out of others through settheoretic n~anipulations;they all should be recognized as simply being thcrc. What wc rather should try to discover, then, is the nctworli of thc various relations which thcy enter and through which they are tied together. In the case of group and mass objects this picture naturally leads to the notion of lattice structi~rc,'an iclca which is, again, not new: it is inherent in mereolog-ical predicate logic and the (:aIculi~sof Individuals as developed by Leonard and Goodman ( 1940) and Goodman and (luiric (1947). Iiowcver, its possible use in the present context has perhaps been ohscured b! reductionist ontological considerations which are, in my opinion, qilitc alien to the purpose of logically analyzing the inference structures of natural language.' Our gnidc in ont~logicillmatters has ro he language itself, it seems to me. So if we havc, for instance, two expressions ir and h that refer to entitics occupying the same place at the samc time but have cliFferent sets of predicates applying t o them, then the entitics referred to arc simply not thc samc. From this it fol1ou.s that my ring-and the gold making up my ring arc different entities; they arc, however, connected by what I shall call the c.ons/itzl~ionrulrrtioi~:'I'licrc is exactly onc portion of matter making up my ring at a time. A co~~stitution 1.clilti0110' has bee11 explicitly introduced into the discussion by Parsons (1079). Sharing his intuitions on this point 1 shall provide a similar 2-place I-elation, "/,", for ~.ons/it~rtrs or nrr~krs~ l p Its . semantic counterpal*tin the theory to be presented below, the "materialization" function h, lies at the heart of my reconstruction of the ontology of plurals and Inass tc~-nls: individuals are created by linguistic expressions involving dift'ercnt structiircs cvcn if thc portion of n~attcrnlaking them L I is~ the samc. C:onsidcr thc esitmple from I3lau (1079) (imagine that there is a cleclc of playing cards on the table):

(1 1) (a) the cards (h) the deck of cards 1Vhile the portions of matter denoted by ( 1 la) ilnd ( I 1h) arc the same, I consiclcr the individuals as being distii~ct.~' ( 1 l a ) refers to thc pure collection of objects, and in many

The Logical Analysis of Plurals and Mass Terms 129 contexts (1 lb), too, refers just to this collcction. In general, however, ~ h introduction c of a collective term like (1lb) is indicative of connotations being added enough for it to refer to a different individual; for instance, a committee is not just the collection of its members, etc. Note, by the way, that the transition to an intension function would be of no help here. There might be two different committees which necessarily consist of exactiy the same members.' It might bc tllougllt, then, that collective predication is just the context in whidl pairs of expressions like ( l l a , b) refer to collcctions and thus are corefi'rential. 'I'his is not so, however, as can be seen from the following cxample. Imagine that thcrc are several decks of cards, a blue one, a green one, etc., lying on a table.' Then the two is a collective following sentences do not mean the same although number con.s~cu~iz~eIj~ predicate (the German ~ ~ is du~hnumerier~n). r d (12) (a) T h e cards on tllc table arc numbered consecuti\rcly. (b) T h e decks of cards on thc tablc are numbered consecutively.

By contrast, spntio-ten~por~ck collective predicates do refer to the pure collection, or, as 1 conceivc it, the portion of matter making u p the individual in question. Examples are bc-on-llzu-lahlu, occupy, etc. I call such predicates inz'nrinnt. So the following (a) sentences are indccd equivalent to their corresponding (b) scntcnccs.

(13) (a) T h e cards are on the tablc. (b) T h e decks of cards are on thc table. (14) (a) T h e stars that presently make up the Plciades galactic cluster occupy an area that measures 700 cubic light years. 0 (b) T h e Plciades galactic cluster occupies an area ctc. 111the following I shall distirlguish between pure plural ilzdividuals involved in (1 2) and collections in the portions-of-matter sense referred to in (13) and (14). 'I'he I'ormcr 1 call (individual) sums or plzlral ohjecrs; thcy respect levels of "linguistic cornprchcnsion" as shown by (12). Ry contsast, collections do not, they typicallj- merge those Ievcls. Sums and collections are similar, howevcr, in that they both are just individuals, as concrete as thc individuals which serve to dcfinc them, and of the same logical typc as these. T h e latter feature is important because therc is no systematic type ambiguity inherent in predicates like ( . a n y , b~ii/d,derr~o/ish,ri
130 Godehard Link to refer to the concrete "scattered individual" that you just find everywhere, hcnce Quine's analysis in terms of mereology. In this sense the sentence should be synonymous to the water (on earth) is mirJespread. Of the samc type is the use of~qcp/,lcl in ifmericn,i gold is stored in Fort Knos. Here, again, a concrete object is refcrrcd to by :lmtlua \gold, namely the material fusion of all quantities of the US gold reserve. So there can be no doubt that some notion of fusion is needed to account for definite descriptions involving predicative mass terms (the poperator dcfined below docs just this). Gcnuine stuff names, however, arc something else. Substances are abstract entitics and cannot be defined in ternls of their concrcte manifestations, Thc question, then, is of what kind the connections are that are intuitively felt between substances and their quantities. Take water, for instance. A quantity is water if it displays thc internal structure of water, that is H20. Hut this relation is not a logical one. Or elsc we might look for substance properties which carry over to the quantities of the substance in question. Water is a liquid and yet, all concrcte water might be fsozen. So we have to go over to dispositional properties, getting morc and more involved into our knowledge of the physical world . . . What I am getting at is that laominat w i ~ ~ sterms s do no1 stew to lzilve a proper logic. Be this as it may, this issue is completely independent of' the lattice structure that governs the beltaviour of predicative mass tcrms ancl plural expressions; it is only this structure that I want to address myself to in the prescnt paper." Now what I am going to propose, then, is basically thc Sollowing. First of all, lct us take seriously the morphological change in pluralization, which is present in many matural languages, and introduce an operator, """, working on 1-placc predicates P, which generates all the individual sums of members of the extensions of P. Such a starred predicate now has the same cumulative refercncc property as a mass predicate, it is closed under sum formation: any sum of parts which arc " P is again *P. This property gives rise to the introduction of a Boolean structure on the domain of discourse, E: technically, E becomes an atomic Boolean algebra which is taketi to be complete so that every subset of E possesses a sum. Now let 11. (1 be the denotation function in a model, and ( ( P (the ( extension of P. Then I"PII, the extension of "P,can be defined in terms of IlPll as the coinplete join-subsemilattice" in E generated by 11 PI(. This construction is the mathematical expression of the closure propcrty referred to above. T h e set A of atoms of E consists of the "singular objects", like this card, that deck of cards, etc. Among them are all the different portions of matter, like the water making up this ice cube. Now, let a and h denote two atoms in A. Then there are two more individuals to be called below a 6 and a @ /I, a b is still a singular object in ,4, the nzatel-kiil./i~.sionofcz and b; n $ b is the irdi~kduul.turn or pturrd objt>rtof o aod b. l ' h e theory is such that a b constitutes, but is not identical with, a .'f; b. This loohs like a wild platonistic caprice strongly calling for Occam's Razor. Language, however, seems to function that way. Take for a, b two rings recently made out of some old Egyptian gold. The1 /he N $ 6, are new, tht stutf; n + / I , is old. Sunls are partially ordered through the intrinsic ordering relation on L' which is expressed in the object language by the 2-place predicate "11". It is callcd thc in(l,'.z'id~~nl part relation (i-purt relation, for short) and satisfies thc biconditional

+

+

+

I ~ ~ I ~ J J ,

"<;"

The Logical Analysis of Plurals and Mass Terms

131

The semantic countel-part of (15 ) is the well-known Boolean rclation (wherc U, denotes the join operation on E):

Now if P is a 1-place predicate and *P the corresponding plural predicate let (,'P (the proper plural predi~'atrof P ) be true of exactly the non-atomic sums in the extension of "P. Then we can define the sum and the proper sun1 of the P's, 0sP.v and a'.rP-~:, respectively, as the supremum of all objects that are 'P and 'P, respectively ("i" is the description operator): (17) (a) oxPx : = IX("P-YA A .y(*Py -+ ~1rI.r)). (b) a3xPx : - rx("px P, Ajf(*Py -+ ~ I l x ) ) . a*xPx carries the presupposition that there arc at least two P's; in this case a.z.Px and a"sP.~*coincide. The material~fi~sion of the P's, denoted by pxPx, becomcs that object which constitutes the sum of the P's:

The poperator has the effect of merging levels of comprehension, as I called it above. Thus we M-illhave p.z.Px = /isQx, if P stands for Is a curd of v~teorzhe card decks, and Q for is r i i-nrd rrleik. cr.rP.t.and a,xQz' are not the same, however. If we have two decks of Bridge cards, for instance, axPx contains 104 atoms whereas axQv contains only 2 atoms. There is a second ordering relation, called the material part (FFZ-picrt) rCln/ion and denoted by "T". It establishes a partial order on portions of matter, but only a on , the , whole ,domain of individuals. Objects which are m-parts preorder, called I, of one another are materially ~gunlal~tlt in that they have the same portion of matter constituting them. If a is an i-part of 11 then a is an m-part of h; syn~bolicallg:

In order to explain the meaning of "T" Inore precisely let me supply the remaining concepts of the model structure to be defined below. In addition to the domain of indivictuals, E, thcre is a set D which is endowed with a join operation "U" making D into a complete, but not necessarily atomic, join-semilattice. D is partially ol-dered by its intrinsic ordering relation, defined by

<,

(20) x 5 v

iff

.r U ,v = .y

D represents the set of all individual portions of matter in the model, and as such, it is considered as a subset of A, the set of atoms of E. T h e relation (20) stands for a material part-whole relation." It can be used to order the individuals of E materially. Rlr this I postulatc for everjLmodel the existence of a scinilattice homomorphism h from E' \ (0)

132 Godehard Link to D such that h is the idcntity function on L) and conlmutes with the supremum operator. Then h is order preserving, i.e. we have (2 1)

.Y

5 ,31

+

iz(.~)5 h ( , l ~ )

for all x,y E E with x (22)

Y

,

y

iff

# 0. I can now

define the relation

h(x) 5 h(31)

<,,, mentioned

above by

( ~ x )E . ~E~ \ (0)).

I,,, is the semantic counterpart of "T".

Ob\~ioi~sIy, 5 , is coarser that1 <,,,, a Fact that is syntactically expressed by (19). In its intended interpretation, then, which is formally inlplementcd into thc nod el structure, a T b can be read as follows: "the portion of matter constituting a is m-part of the portion of mattcr constituting 6". One-place predicates are interpreted as subsets of E \ (0). (Herc, thc null clcmcnt 0 is assigned the role of a dummy object to which no predicate applies and which can take care of denotation gaps arising in our description theory; for details see 1,ink (1979, 5.2).) If P is a mass term the extension [IPII of P in a given model should be a set of portions of matter which is closed under joins. So IlPll becomes a subsemilattice of D. This completes the informal description of the Boolea??moikd simiiure @! = (E, '-1, D, h) and of the LP-M-mode/ /)/I = 1 . 1 1 ) . For precisc definitions scc bclom-. If P is a predicate we can introduce its mass term cowr.spondt?~t,called "'P; if llPll is the extension of P in a model, define

(a,

If P is already a predicative mass term we have, by this definition, IlPll term correspondents occur in natural language.14 Considcr

C IItl'l'II.Mass

(24) (a) There is apple in the salad. (b) Vx(" P.r A

ar)

(24 b) is a formalization of (24a), with P for is an applt, "'P for is uppic, and Q for is in /he s a l ~ d From . this we can infer, intuitively as well as formally:

(25)

(a) There are apple parts in the salad. (b) VXVJI("P.YA,,ITX/\@)

We have, in fiact, the following theorem (cf. (T. 14) lxlow): (26) "'Pa

-

V.y("Py~aT.11)

Returning now to the model structure consider once again the extension of a 1-place predicate P. It can contain atoms as well as proper i-sums. This general case of a ii71.vrd e.~~e?zsion is exemplified by predicates like can-)! rkepillno: think of Tom, Dick, and (together), Obelix (all by himself), ctc. Common nouns and intransitive verbs likc die, however, seem to admit on\y atoms to their cstcnsion. 1 call such predicates iIis/rihu/ive:

I

The Logical Analysis of Plurals and Mass Terms

133

(here the prcdicatc -At stands for the property of being an atom in the model). To illustrate take the intuitively valid inference from (a) to (b) in (28).

(28) (a) John, Paul, George, and Ringo are pop stars. (b) Paul is a pop star. This inference can be fornlally represented if we consider pop star as a distributive predicate P in the sense of (27). In this case the extension of "P is closed under nonzero i-parts (see theorem (T. 10) below), so every atom of an i-sum which is "P is itself "P, hence it is a P . In symbolic form the inference (28) looks likc this. (29) (a) (b) (c) (d) (e)

*P(a (3h ( 7 > c @ d ) Distr(P)

bnu@h@~.@d "Ph Ph

In a similar way we have the following valid inference with the distributive predicate Q for dip ( P stands for nninznl):

(30) (a) T h e animals dicd. So every animal died. (b) *Q(a*xPx) A.v(Px + Qx) For non-distributive predicates we have, of course, no such result, witness ravq!: n CP h might be in the extension of cnrqr while a or h alone is not. Noticc that these predicates enter formalizations unstarred. T o illustrate,

(31) (a) T h e children gather around their teacher (b) Q(c~*xP.v) (with Q for gnther. etc.). I think there is no harm in accepting this systematic difference: i.e. distributive predicates working on plural terms have to be starred, all the other predicates must not bc. For distributivity seems to be a lexical feature. If we have a formal translation procedure the predicates have to be subcategorized accordingly. There is one morc operator, "T", in the logic LPM to be presented below. ' I ' P , for a predicate P , is to be read as part~ikesin P . I introduce this operator in order to be able to distinguish betwccn the plural terms tht ~.kriWrtnand LL// the ~.hilrlren.It seems to me that in ill1 the chikdren /?uilt the rufi it is claimed that every child took part in the action whereas in tire chil~/vpnbuilt thp r.4it is only said that the children somehow managed ro build thc raft collectively without presupposing an active role in the action for cvcrjsiilglc child. This intuition enters thc fi~rmalizationof the two phrases givcil bclow. I Y ~ only bc partially characterized in want to stress, however, that the operator C ~ ~ I ' can view of the essentially pragmatic nature of its intended interpretation. So Ict me formulatc just thc following lneaning postulates for "'l'" which seem to be plausible:

134 Godehard Link

@);

(-32) (a) A.V('PX + V,y(sn)!A b)) (b) Distr(P) + A.Y("'P,Y+ PX)

I conclude the informal part of the paper with some more formalizations of natural language sentcnces involving plurals and mass terms. Most of thc principles governing thcir logic that have bccii mentioned in the literature come out valid in the system L P M below. Some of them are instantiated here, like Masse!,'s pluralitv principles of symmetry, expansion, and contraction (scc _Masscy (1976)). What I did not treat in LPIL'I, however, are any "downward" closure properties that are somel~owfelt to bc present in the behavior of mass terms ("a part of water is still watel-"). Such principles can be added when a careful linguistic analysis has succeeded in giving them a form that takes care, in particular, of the problivz (!f'nrinimal p~irts(is every m-part of lenlonade really lemonade again?). For some discussion of downward c1osul.c propcrtics scc, c.g., Hunt (1979) and Hocpclinan and Kohrcr (1980). (33) (a) (b) (34) (a) (b) ( 3 5 ) (a) (b) (-36) (a) (b) (37) (a) (b)

child built the raft Vs(Px ,Y @); Children built the raft. VX("P.~A @); T h e child built the raft. V,JI(]I= i.rP.r A QJ); The children built the raft. V.9(11 = n*vsP.v11 Q.1)); Every child saw the raft. Ax(Px

-

(38) (a) ,411 rhe children built tlze raft. (b) /\y(y = o " s P . ~+ Q.1)); (39) (a) (b)

(10) (a) (b) (41) (a) (b) (42) (a) (b) (43) (a) (b) (41) (a) (b)

P.v: .r is i~ child Q.Y:.I. built the raft P.r, Q-r: dto. J'.Y, Q-x: dto. Ps, Q v : dto. Px: dto. IQt.: s saw the raft

+

P s , Q.1, as in (33) = i"Y(QX. A A.:(."rI.V +"Qz)). Tom and Dick carried the piano upstairs. P(n @ /)); a: Tom, 6: Dicli, P.v: .x carried the piano upstairs Tom and Dick carried the piano upstairs, so Dick and Tom carried it upstairs. P(a B b) + P(h @ a) (S~~III~~IC~I;~) John and Paul are pop stars and George is a pop star, so John, Paul, and George are pop stars. ' ; ~ ( a
0:

-

i '1

@Y:

The Logical Analysis of Plurals and Mass Terms

(45) (a) This ice cube is water. (b) Pi.z(s L a);

135

a: this ice cube Px: as in (43) (46) (a) T h e gold in Smith's ring is old, but Smith's ring is not old. (b) Qis(Px .Y L a) A I@; P.Y:,v is gold .T is old : Smith's ring

2 The Logic of Plurals and Mass Terms (LPM) LP%T is a first ordcr predicate calci~luswith the usual logical constants "I", "v", "A", , H", "V", (LA",the description operator denoted by "i", and the abstraction operator "A" .1" T h e syntactic variables are, for forn~ulasof LPM, "d)", "tk", "x"; for (<+v

kL

individual terms, "a", "B", "I."; for variables, "Lv", ")I", "z"; for (1-place) predicates, "P","Q". These symbols can also appear with primes and indices. For metalinguistic (definitional) identity the s!-inbol "A", (": =") d l be used. Thc set of I-place predicate constants contains two specified subclasses: the set M T of prtdii.i~lizlr' nrass t~rmsand the set DP of 1listribz4tieltpredicates. h4'T and DP are taken to bc disjoint sets. As specialprimilii:~.\:l~nlbolsof 1,PM we have a I-place predicate symbol "E", thrcc 2place predicate constants, "II", "T", "L", and two operators on 1-placc predicates, cc*?, ~('1'" , The intended interpretations arc the following. En stands for " n e.~is~s"; all/) for "a is an in~lizli~llirzlpav~ (i-part) of h"; r ~ T hfor "11 is a ma teri~zlpr~rl (m-part) of I)", rr 1,I!. for "o ~onsti/u/esor mnkts up h"; *P for "thc pllrml prnlnutr of P";"'P for " p ~ ~ n o hinc ~ P". No\\- I introduce a number of defined e,zpri~ssion.s. Let P, Q be I-place predicates, R a 2-place 1 Gl~neralfirst o~prler i/blr~ezlin~kons. predicate, and n an individual term.

Furthermore, the usual definitions for the following formulas involving R arc assumed: R ~ f (R) l ("R is reflexive"), Trans (R) ("R is transitive"), S I ~(R) I ~ I("R is symmetric"), -Antis),vu (H) ("R is antisylnmctric"). We then have, with P r o (R) for "R is a preordering rclation", P O (R) for "R is a partial ordering relation", and Eqzr (R) for "R is an equivalence relation": (D.5 ) PrO(R) (D.6) PO(R) (D.5) Equ(R)

--

H

Kefl(R) 4 Trans(R) R
136 Godehard Link

-

2 Defined preriicate con.stnnts. With two individual ternls L I , h, let a = b stand for " a equals b", a b for "a is m-equival~nlto b", ,-l, n for " ~ is i an L L ~ O ~ I I " , and Mpa for "a is a portion o f matter". Define

3

&find prcilicate oper.rztors. Let P be a 1-place predicate and rl an individual term. T h e proper plz~rnlprrrlicale CP of P and the nlass term (.orrespond~ntto P, "'P, itrc then defined as follows.

(D.12) ' ~ r r ( D .13) "'Prr 4

t t

t-t

Defined lndicir/uu/terms. With I-place predicates P and individual terms a, b, definc the i-sum of the P's, the proper i-sum of the P's, the i-suttz of N and h, thc ~?zatericll .fusion of the P's, and the rtiateritcl JLsiun of N and 11, respectively:

( D .14) axPx : = ( D .15 ) aS.vPx : = (D.16) a i s b .. ( D.17) psP,r : = ( D .18) n b : =

+

5

"Pur,r~~$t~~ Vjl(*Pll A &Ti.+ L.y)).

ix("P.1.A Ay("Plt ia("~,nA A y(*Py abr(Ii,@ I/Jbr ix(s L crxPP~) ~ , V (3 I (I/,)&r ~

-+ +

.I)

rZ s ) ) . r[s ) ) .

Sp~cirrlabbrczliali~wfuvtn~rlrcs.Let P be a 1-place predicate.

( D .19) ( D .20) (D.21 )

--

Dlstr(P) tf A.v(P;t. A&,\') M ( P ) tt As(P.t lVpvr) Itiz!(P) t-t /'\.rA~!(x ,)I + (Ps ++ PI,)).

Dlslr ( P )is to be read as " P is ~listributiz~e" (i.e. Pis true of atomic individuals only), -44( P )as " P i s a r?tnterialpredicntc"(i.e. it is true of portions of matter only); In;r (P) means: " P is an in~lariu~~t predicate" (i.e, it is closed uncler substitution of mequivalent terms). 6

Mermirrg postulates fnr.".'"'. v,]f(xl-I]! A. PI!)). A . ~ ( ~ Pt.. YP,.) i.c. for all .r, if .v partakcs in P, thcn .t is an i-part of a -11 which is P (VIP.1); if P is distributive, then for all .r, .\- partakes in P just in case .z. is P (MP.2).

The Logical Analysis of Plurals and Mass Terms 137 'I'l1e sevnantil:~c!f LPM. I shall en~ploythe usual set-theoretic terminologj (scc, for for set iilclusion and 't/'[YJ" for the/: instance, Eberle (l970), Link (1979), with image { J'(.Y)1 .T E 1') of Y under the function J': _X + Z. Moreover, some elementary notions of lattice theory are needed (see, e.g., Griitzer (1971). Sikorski (1969) for their definition) pr~rtircladeritzg replnlion, pnrtial!j/ or(l~>r~~rl sr/ ("pos~t"), 1elemenl, 0-ele~tent,atom, sewzi-lattice, Join-semil~ittir~,lattice, ~~{blntlice, iill>al,prin~.ipnl illral, cov~pleteI~ittit.e,Boolc~znlattice (ulgrhm), irtomll. ldttice, (serizi) llittice /~orrzomo~pllism. The supremum of a subset k;of a poset X, relative to its ordering rclation if it exists, will be denoted by sup,- Y , the principal ideal generated by an clement .v E X,whcrc X is a lattice, by (x]. So we have (x] = E X Ij t 5 s). If X is a complete (semijlattice. and Y C X, then [E'] denotes the complete sub(semij1attice generated by Y. 1 now provide a model-theorctie interpretation of the formal system LPIL1.

"c"

<,

-

(D.22) 1 2

3

4

Boolenn rnodel structure [pith homogeneous kernel ("hoosk") is a quadruple @, (E,A, D, h ) such that E is a complete atomic (c.a.) Boolean algebra, with join operation U, and the intrinsic ordering relation 5,; A E is the set of atoms in E; D C is a complete join-semilattice with join U and ordering relation 5; h : E\{O) + D is a semilattice homomorphism such that (i) h2D idD, i.e. h(x) A .t. for all .r E D; (ii) / ~ ( s u= Ip B) . ~ = suphi B] for all B C E\{O).

It follows from this definition that we have, in particular, for all s,,I!

r: E\{O):

The homomorphism h induces a second ordering relation on E\{O) which will be called the material part relation on E\{O) and denoted by <_,,,: I

(D.23)

.tT

<,,,

iff

/z(x)

5 /I()!)

I,,, is only a preordering relation. It gives rise to an equivalence relation, defined I

(D.24) s N ,,,11

iff

by

xxl,,,.11 and . ) ! S m . ~ ( b ~ , . ~ ~ ~ E \ { o } ? ,

I

and thus to a partition of E\{O} into equivaleilce classes each containing all the indivicluals that are made up by the same portion of matter. In the following definition of a model for 1,PM I am going to interpret only I-placc predicates, for simplicity (except for the special 2-place predicate constants). All the other many-place predicates receive their usual first order interpretation.

I

(D.25) A moi/el.fiv LPhl is an ordered pair .MA(@, (1 - (I) such that if1 hl, 24the srt oj'nlonrs in 1 @ (E,A, D, h ) is a boosli (E is the domai~rq/'indiz~ir/~inl.s M, D the S P qf'portions ~ c!rmatter in A4, and h the "nznterir/licn /it111Ji~n(.~ior~" in Aq);

1

138 Godehard Link 2

11.II is a first order assignment of denotations to the primitive expressions of LPM such that if a is an individual constant; (i) lll~llE E if P is a I-place predicate constant; (ii) 11 Pll E\{O) if P E DP; (iii) 11 PI1 (iv) IlPll is a complete subsernilattice of D if P f MT; (v) I " ~ P I I{r t Elx # 0 & 3.~1E IlPll such that x 5;, y ) ; (vi) II"PII-IIPII ifP E DP.

T h e model is such that predicates are interpreted in the non-zero elements of E (condition (ii)). Conditions (iii), (iv) guarantee the special properties of the distributive and mass predicates, respectively. (v) and (vi) are designed to validate the meaning postulates (MP.1) and (MP.2) above, respecti\rely. Let h f= I /I) bc a model for 1,PM. The usual first order sernantical reci~rsion rules are assumed, where quantification is taken to run over the non-zero elements of the domain of individuals only. T h e truth and (/cnota/ion cortditiun.~for the special primitive symbols of 1,PM are defined as follo\irs (" 1" stands for "truc"; bivalence is assumed):

(a,

(D.26) (D.27) (D.28) (D.29) (D.30)

~ ~ P a [ ~ ~iff l 11i.sP-~l=d iff IIEa,ll 1 iff Iln.llhI=I iff IlaTbllAl iff

(D.31) (D.32)

Ila L lill -1 iff l\*pll=rllpll~,

IlaIl E IIPlI; d # 0 and 11 PI = { d ) , and 0 otherwise; IIa11 # 0 Ilnll # and llffll 5,Ilhll; Ilall, Ilbll # 0 m d h(llnll> 5 h(llbll); 1611 # 0 and IlallAh(llbI); (the complete U, -subsemilattice generated by 11 PI[);

,4 nu~nbcrof scmantical facts can now. be derived that give truth and denotation conditions for all the defined s~mbolsof LPM.

llp c QII-1 iff Ilpll l l Q I IIP = Q l l A I iff IIPIIAIIQII IIP @ QII=IPI u IIQII I I O ll={IInlI) [la = bll=l iff I l ~ l l ?Ibll # 0 and II~ll-llbll iff /Iff 11, 1611 # 0 and h(ld)-h(llhll) 110 bll-1 (IA4ta II 1 ifT EA ~ ~ M p ~ i ~ [ = l iff llal E D ll*PII A {X E E13X C lIPI & X # 0 s.t. vv-supiX} IICPII = II*PII\A IIU1PII A (suPih[llP11]]=(x E D ( x 5 sup5h[llPII])= .r E 0133' E [*PI\such that ,v 5 k ( ) l ) )

-

The Logical Analysis of Plurals and Mass Terms 139

(60) 1o.t.P.rII = sup, IIPII, with sup,@'O (61) Ia*sP.vI lon.Pxll if llPll has 2 2 elements, and 0 otherwise (62) In @I hll 11~111U, llhll (63) 11j1.~P;t.(I = sup,hlllPII]if llPll#@, andootherwise (64) /la + bll = h(llall) h(llbll) if llall # 0 # 11BIl Let the notion of ~rutlrin a given model be defined in the usual way. A formula is italirl if it is true in every model. I now give, in a loosc order, a list of theorems of L P M that come out valid undcl- the above interpretation. I may mention, in particular, the honrogenrous refi.renl,e properties (T. 1l), ( T . 12), and the eslsierice and idunlil.)~~,rilerinfor the a- and ![-terms, (T.16)(T.21). (T.1) (T.2) (T.3) (T-4) (T.5) (T.6) (T.7) (T.8) (T.9) (T. 10) (T. 11) (T. 12) (T.13) (T.14) (T.15) (T.16) (T.17) (T.18) (T.19) (T.20) (T.21) (T.22) (T.23) (T.24) (T.25) (T.26) (T.27) (T.28) ( T .29) ('r.30) (T.31) (T.32)

rt. = h

aHbr\hIIa aIIb + aTh n =B nTb~bTn Equ( = ) A Equ( ) PO(17) fi PrO(T) Dlstr (P)+ As(P.y -+ J ~ P ~ Y ) P c "P A.v (-Atx 4 (P,Y c-1 "P.1.)). Ax(*Px xlIaxPx r\V,y(P)l~ . ) l n . ~ ) ) . Distr(P) + AsA.y('Py A x l l ~ + l "Px) AxAy(" P.r r,"Py + "P.r 91,) for P E k I T A.x A-]l(P,r A P)!+ P,Y+ y) M (P) + P C "'P M P ~ ("lm4 v.)I(*P~ b, ~LT-II)). VwP*t.A P c Q 4 *Q(a.rP.v) V.vP.t. 4 EaxP.r VxP.v E~J'P,z' Ea'xP-r +t VxV.y(Px A P y A x # .I/) P = Q + a x P . ~= cr.~Qx Dislr(P) A Distr(Q) --; ((TXPX = a,rQr + P = Q ) P = Q 4 p.~P,z.= 1rxJQr jltd 4 a = a.r(.r = a ) A4pn n = p,x(,r = n ) ~ i x P x= is(Px A Ajl(l3, + yTx)) for P E M T a h p.v(x = a) = /i.r(x = b) /1xPs = ix.(.VC /lLxPAY) Mp(px.Px) a L h c-1 Mpo n (1 -. 17 /lbvPx-. CTXP.T 0xP.z. = a.vQ~+ /~xP,t^= [L~VQY A.vA.y (x"y * .Y CE = -11) A.v/ly(sTy .r +.)I = y) c-1

-

-

-

-

-

140 Godehard Link

3 Applications to Montague Grammar I.et the basic synta.r be as in PTQ'" T h e category CN of common noun phrases h a to be subcategorized into MCN (mass noun phrases), SCN (singular count noun phrases), and PCN (plural count noun phrases). 'The quantifiers disc~~ssed are a, some, ihe, a// the, roer)r, all; they are of category T / C N with suitable subcategorizations (term formation is done compositionall?;). have the obvious plural rule

a,,,

cpl=

cpl&

where [A hand becomes /lands7 5; child, c/zil(/ren, ctc. T h e logic of P T Q TITL,, is extended as follows. TIT'L', or esten(/e(l Y'ITL, contains as new symbols all the special symbols of LPM. Additional rnenni?rg/i/ c,rprts.sions are: E ME,, for t = e(t E Type, p-tt or ST/,[ E .ME,,); (i) *<, (:(, .l'< t MEi,, and (ii) aucb, ~ " u d ) , luqb E ME,, and ,urn4 E ME,. (z f Type, u E V~zr.,,gS € ME,); (iii) all/?E IZIE, ancl a % fl E ME, ( t E Type, a, E /tlET); (iv) a T P , a j, a L / 3 E ME,, and ct+p E ,441/IE, (x,B E )'llE,.). T h e sevlanlir.s for 'TI'I'L' has to specify the "boolification" of thc sets of possible denotations since the i-sum operation applies to expressions of any type (m-sums are formed on level e only). Let E be a c.a. Boolean algebra, I , 3 sets, and K = I x J. A Boolean hiererch~y?fpossib/c (knotnlions over E with respe1.t to K is a family of sets (DT,E , K ) i t l j l r defined as in P T Q , but cndo\r.cd with a c.a. Boolean structure for every D, as f o l l o ~ ~(i) s : T h e sets Dl, = E and D, = 2 are already c.a. Boolean algebras; (ii)l; g E D,,; then: (f' U,, g)(k) : = J'(k) U, g(k)(k E K), similarl!? for the other operations; (iii) J'; g E D,,; then (f U,, g-)(.r): = /'(x) U, g(x) ( s E D,), similarly for the other operations. T h e resulting structures are c.a. Boolean. An in!erpretation for TITI,' is a 7-tuple 8=(E, A, D, h, I , 3 , I l . I I ) such that (i) (E,.4, D,h) is a boosk, (ii) K = I x 3 is as in P T Q and (iii) I l . j J is the interprctation function that naturally emerges from a combination of T I T L and LPM. As rults o/' truth ntzd dtnotntion provided by an appropriate recursive definition let me mention the the characteristic function of L{x t DTlllill(x)= I}], ,,([ E MEn); following: (i) (ii) *
"'c

//'
x,,,:

<

<,

(c

The Logical Analysis of Plurals and Mass Terms 141 Most of the basic count nouns like child are taken as distributive, similarly IV phrascs like die or see. In accordance with what I did above the translation rule T4 involving distributive expressions has to be such that their translations al\v\lays entcr this rulc under the star operator. While this seems to me the correct move from a technical point of view 1 am aware that it carries the empirical prediction that d i s t r i b ~ t i ~ i is t ya lexical property. I now give transl~~tions for the quantifiers. Let U be the translation relation, and P: ) , ~ I [ P (A ~Aslxnl1 ) -'V~(X)]].

-

1 2 3 4

a),,

a, some the a// /he emry, nN

U i @ ~ r [ ~ A( Pr ()x ) ] u ~ Q P lv ~~ b A, )AX[Q(X)

u U

I~QFA.~[.,,= OYQ(+) I~QFAX[Q(X)+ P ( s ) l

--

x n y l PC?)]

P(.~?)I

a applies only to singular count noun phrases and GP1to PCN phrases. 'The quantifiers some and the, with one and the same translation, apply to both singular and plural phrases. As can be seen from 5 through 8 below it is only the incoming CN phrase which differentiates between the appropriate singular and plural readings. While this is obvious with some, a comment on the transformations under 7. is in order. T h e conjunct A s [ Q ( x ) + xIIJJ-] in the translation of the asserts maximality which is needcd for the intended sum formation in the extension of*Q. At the same time, however, it gcncralizes the usual uniqueness condition for definite dcscriptions. This comes out when /he is applied to a singular count noun like chili/: T h e i-part s of.)! in 7. cannot bc 0, and.y is an aton? because of DISTR (i,hildl);so x equals .y. 1 think this is a nice instance oC strict compositionality in times in which this principle has come under heavy fire in vicw of all sorts of recalcitrant data (see below). Finally, 9-1 1 show that universal q~lantifiuationis as in LPhl where, again, the difference in meaning between the c h i l ~ / ~ eand n 1111 thi~ a/rildrr.n is only partly characterized ( P being defined in terms of "l'").

5

a child some child some water 6 (sonze) children 7 the chill

8 the childrepi

1 may mentioil here that the incorporation of nuincrals like oue, III~O, thr'e, into the fragment is straightforward. T h e extension of t h r e ~men, for instance, is the set of 1111 isums in l/rnen'll~llcmsn'llwhich contain exactly three atoms. Sentences like rlrrut nrm went t o .mom a rnearlolz?receive a translation of the form V:z[(lhreeyylen)'(z), A Q ( z ) ] .

142 Godehard Link ?'he final topic 1 want to say something about is the vexing pl-oblem of relativc clauses with more than one head noun.'' Call those structures I!)u/~l'ilc.Let me consider restrictive relative clauses only. First of all, there is a rather fi-iendly type of hydra, like the following. (67) the German or Austrian John met yestcrda!~ (68) the cabinet-member and mafioso who was deeply involved in the scandal P T Q style relativization, i.e. C N modification, takes care of these pets yielding the obvious representations for (67) and (68), respectively:

-

( 6 7 ) the ( (German or Austrian) such that John met him yesterday) Bv.]~A.r [Gemran' @ Ar,strirrnl(.r) n @[.r] .r = ,)I]A P(y)] (68') the ((Cabinet-member and mafioso) such that he was decply in~olvcdin the scandal PV.)~[A r [Cnbinet-menrb~r~ G n~~/io.so'(.v) n i,hlsl * r. = ,)I 1 n P(y)J

-

Here, @ and rl/ are the translations of the relative clauses of (67)and (68), respectively; furthermore, i€3 q ;Is[r(.~)v rl(s)] is thc Boolean join and ( ci,~17 h[[(x) ,\ ~(.r))l.' the Boolean meet of iand 11. This case is simple because CN wnjunction does not lead I to plural structures, and there is only one determiner present.'X 1 Next, let us conjoin t\vo singular count nouns to form a plural phrase. 13san1plcs arc ! 77alin l ~ r t l n?ot?latl, l h q f crnd girl, hushand arivl )PI/;>,I~rnlllovJ( I r1(1tennllt. Such phrascs can bc ; true of a sum of two individuals one being of the first and the othcr bcing of thc sccond kind. An appropriate translation, therefore, is of the form (69) ([ and 4)

U

IL.zV.YV,)![~'(S) n )11()1)A c = s $,)I]

\%Tiththis sentences like J'oltn art(/ Mar)! nrt hu.chanrl N I I 1711/i~ ~ can hc handled in a first approximation wl~ilcthe non-symmetric features of this sentence have to be taken care of by other clues. This is because the predicate (69). by itself, is ncccssarily symmetric reflecting the fact that pluralization has the force of group formation which typically gives rise to symmetric construction^.^^) Such is the following CN phrase: (70) boy and girl who dated each other Wit11 (69), the standard P T Q r u l e yields for this:

Now term formation with one and the same determiner for both head nouns is again standard if we decide to have it distributed over the two nouns in a kind of copying process. So, for instance, n ho)! and il girl n~homecptbccon~es (72) an((buy c l t d girl) sltch tllirt the)! meet) U PVn[VsV.)~[bo~)~(,v) ~ g i r l ' ( j )A s = s B ,y A YIIPP~'(.C)] A P(.s)]

The Logical Analysis of Plurals and Mass Terms 143 In a further step we admit conjunction of plural nouns. This move doesn't really add any ncvl difficulty so I can write down an example immediately. Let (1 be the translation of thc phrase J I I I ~ C M ~ EM^ S profi~sorsm/lo IlorJ ~ I I Cin~ srrrrt:

Adding a determiner as before, say the definite article, cve get thc term

(74) the students and the professors who had met in secret u P V z [ z = fi*.I"O(x) A P(z).I h

T h e present conception of conjunction of two CN phrases [ and 17 is such that the extension of (( nntl y) contains i-sums of objects which are of kind [ and r l , respcctively. Unlike the Boolean join this carries the presupposition that both sets of objects be non-empty. I think this is as it should be. Notice that in this case the overall sum is the same as the one u-hich is formed in terms of the Boolean join, i.e. wc have a.z.(i'@ ~j')(w) = ax([ n,zd vl)'(.v). What is not captured in either approach, howcvcl-, is thc proper pair reading which is dominant in sentences like Inncllorri.~ilrrd tr~r~lnts 1~/7o l ~ n t eerrc./l other rvili ai~r~nysfifinil so~lrrhingto argzic r~lrout.I find these constructions hart1 to treat at the moment though I an1 confident that they will finally lend thcn~selvcsto an analysis which is compatible with thc present framework. What is nccclccl here is somc notion or ordered pair in the objec~language, apart horn the symmetrical sum operator."' It is only with such an additional instrument, it seems to me, that 1r.c can. in a close-to-language treatment, attack the most dangerous hydra lurking in the reillin of pair reading and hrmching quantification.21 T h e last type of hydra I want to address myself to shows up in a scntencc like thc followiing who hacl met in secret \vest (75) all of the students and some of the professo~.~ arrested after tlle coup d'ittat. From a purely syntactic point of view it might look natural to try a T-S-analysis 11erc: first conjoin the t n o unrclativized terms ( I / / the .stud~'?clsand som~.cd'the p~(!fis.sonand then modify the conjunct by the relative clause. Iiowever, I agree with Jansscn (1981) in his sceptical attitude towards the semantical soundness of this approach in gcncral, and the present case, I think, is apt to confirm these doubts. Eken il gencralizcd quantifier account along the lines of Harwise and Cooper (1981) is not cas! t o givc because the set of properties cleiloted by thc subject term of (75) is not the obvious intersection of t z ~ opropert!- sets. T h e point is that the collective predicate mrc~t-inser-vet cloes not distribute o\-er the conjuncts. Now there is no reason to lcave the approach taken so fils, it sccms to me. iVe alscadj, ha\-e a clear underslanding of the meaning of the plural CN phrase str~li~>rr/s (ill(/ p r ~ f i s s o ~1i1/1o s kaii ~ w in t s ~ c l ~\vllicl~ ~ ~ t is expressed by the i.-term O of (73). So in tcrms of this, what is the meaning of the above NP? Well, the set of propertics thilt all the students of the group of students and professors who had met in secret and solne of its professors share. This set can be fbrmally rcpresentcd in TI'l'l,l. I;rom the abovc

144 Godehard Link group of individuals we have to pick out again the students ancl the professors, respectively-, which is done by mcans of the Uooleail meet @; wc can thcn write (with a-*studentf and P=*pvofesso~*'):

(76) all the students and some of the professors who had met in secret U P [ A . y b = rr*.v(~ @ O)(x) + P(.,/)] n V,l~[(/l!-> B ) ( y ) /: P ( J I ) ] ] h

In the sqrntnx,thcn, we have to introduce thc dctcl-miners all and some simultaneouslv. 1 hope that a rule to this effect does not look too outlandish to the eye of the syntactician. Let me summarize what I consider to be the virtues of the present approach to plurals and inass terms. ( I ) T h e logic of plurals and the logic of mass tcrms share il common lattice structure the only difference being that the formcr lcads to an atomic structure while the latter does not. (2) By mcans of the star operator pluralization and tcrm formation involving plural constructions can bc treated compositionally. (3) Plural terms (the curds) and collcctive tcrms ( t l ~ (JL'k e o J ' L . ( ~ . ~are ) equivillent in that they are interchangeable in invariant contexts; this does not make then1 corcfercntial, however, in contrast to systems of the rcduetionist lot. (4) Collective prcdication becomes possible in a unified way accounting for the Fact that many p r c d i c i l t ~(e.g. ~ (.an:)!) are not marked with respect to distributivity and can, therefore, have mixed extensions.

Notes The basic idea leading to the present approach grew out o f a seminar on the semantics of mass tcrms which I held in the summer of 1980. hlean\vhile I had the opportunity to discuss various stages oSthc paper with a ilulllbcr of pcoplc whom I wish to thank here for helpful comnlcnts, hints, and criticisms as w~cllas for general support. .lmong thcsc I should like to mention in particular Ulrich Blau, Paul Ciochet, Barbara Partec, Christian Rohrer, Peter Staudacl~er,Arnim v . Stcchow, Alice tcr hlculcn, b,latthias Varga v. Kibkd, and D i c ~ m a rZaefferer.

1 $lassey's example; see X/lassej ( 1976). 2 See Quinc (1960, p. 91); Bunt (1979). 3 T h e main sourcc for mass t e r m is Pelletier (1979); furthcr~norc,see 13cnnctt (1980), I3cmt (1979), and tcr hleulen (1980, 1981). For 1l1c treatment of plurals and collective terms, see Masscy (1070), , Burgc (1977), 131au (1979), Hoepel~nanand Rohrcr (1980): and Scha (1081). 'l'hc parallelism referred to is explicitly expressed in Bunt ( 1979). 1 Rcccnll!, Keenan and raltz (1078) and Kccnan (1981) 3dv:~nceda "Roolcan approrlcli" to rhe seiniintics of natural language. I feel very s!.nlpathctic with this cntcrpl-ise ~:hicli,unli)rtunatcly, I became aware of only a !.ear ago (January 1981). It is reassuring to scc similar techniques hc success full^- applied in other areas of semantics, too. I have to d c k r a concrete cvnluation ol'thcsc ideas to another occasion. 1 I -5 011 this point I agree vvith tor h/Ieulen (15)81),1 think. Hut I d o not follon 11~1.in ~ h conclusions c she c 1 r . a ~from ~ this obscrt-ation. The inherent lattice structi~rcis indepcndc~itof the philosophical I motives t h ~ gave t rise to the construction of' mcrcolo~icalsystems. 1"or rhc rolc ol' noniinal mass noun dcno~ationsscc the remarks belo\\, also note I I. h I guess that in German, with (lieK~~lr./c~r~ vs. drrs J;nr'tpnsprl~l, the point might come oui nlorc cleilrly. 7 l'hc point 11-a~;ippareiitly made first b j David Kaplan '1s Bennett (1980) rclx)rts. 8 This is the situation originally analyzed b ~Blau - in his I079 paper. 9 This is Burge's cxamplc, scc 13urgc (lOi7).

The Logical Analysis of Plurals and Mass Terms

145

This approach is rhc traditional one. In one form or another it can be founcl, fi)r instance, in Bennett (1974). Hausscr (1973), von Stechow (1980), Hoepelman and Rohrer (1980), Sch;l(lOlil). Contributions to the problem of substance names can be found in Pellcticr (1079) (in p;lrticulur, Parsons (1979)), Bunt (1979), and ter Meulen (1980, 1981). Let mc comment on the latter work. which is formulated in a h,fontague framework. T h e few- remarks I illadc here will makc it c~iclcnt that I f ~ ~ lalgye c \vith tcr hleulcn in that nominalmass nouns cannot be rtr/~iitJto prcdicati\~cnxlss nouns. But for this very reason I fail to see any cogent argument for the kind of denotation rcr Meulcn wants to assign to these termsat a given reference point (i.c. intension functions dcnoting in each world the set ofconcrete quantities of the substance in question). As it turns out, the arguments she puts forth in ter Meulen (1981) really lend support only to the tirst, the critical, poi111(viz. that recluction is impossible). But whai she then goes on to call a nominal mass noun's "extensional reference to an intensional object" (viz. the intension fiinction referred to abovc) sccnls to me both syntactic all^ and semantically misguided. For the inevitable doubling of syntactic rulcs is ccrtninl~ un\\-clcome, to begin ~vith.But what is morc, those intension functions, cven when lifted to still another intensional level as tcr Meulcn wants to h a w it, are simplj-not well motivateti as substimcc name denotations. T h c statemcnt, for instance, that two fictional substances can be diffcrcntiiltcrl (op.cit., p. 4.38) is not compatible with rhc principle of rigid designation introduccd earlier (op. cit., p. 424). More gcncrally, rllerc arc no rules that could justify intuitivel! lalid infercnccs from contexts in\ olving nominal mass nouns to contcxts nirh their corresponding prcdicative terms - ir is my view, anyway, that such inftrenccs are not basctl on pure logic alone. I conclude from this that the problcm of nominal inass nouns is best approached in ;I spirit of logical abstinence. Nominal mass nouns denote abstract entities, to be s ~ ~ rand e , as such they are nanics of incfividuals just lilic John, Il/luntck, ancl the rest. Bcyond this minimal account things become notoriously vague. For this concept see, for instance, Gr3tzcr (1971). Let me point out that the notions o f l ~ l c r ~ ~ r i ~ l and l p a rportiotz-u/~~rta~/~~~' t arc only a paradigm casc ol' fixing intuitions for honrogenrous w/i.renr~.T h e structural propertics actuall! uscd (non-atomicity, cumulative reference) are also found ro govern the behavior of abstract entities like c\.cnts. Implications for modes of temporal reference are cliscussed in IIoepelman and Rohrer (1080). See alrcad>-Qiiinc (1060), also Bunt (1979), Hoepelinan and Rohrcr (1980). For an outline of such systems ("PLlIKA") scc Linh (1970); nnticc that, in LPM, identity of indi\-idual terms need not bc taken as primitive, but can be defined in terms of hlontague (1974a); the folio\\ ing notation is that of Link (1979) (I\-hichdiffers only slightly fiom the one uscd in P T Q except that the interpretation function F is denotcd by the "norm" symbol I . 11 here. I also ignore, for thc present purpose, the individual concept language o f P T Q 'Thanks to P. Staudachcr and A. von Stechow for bringing the severeness of the problem to niy attention. See \ on Stecho\\- ( 1980) and Janssen ( 1981) for thorough and critical discussions of' the issues involved. In Gcrman there seems to be a restriction to the effcct that thc tivo nouns have to agrcc in gcndcr for this construction to be possible. T h c same article can then bc related to both nouns. reading see the remarks belot*. For the T h e device of "multiple quantification" introduced in Thomason (1077) might be rclcvant here. Thanlts to N. Bclnap for bringing these unpublished notes to my attention. See Bwwise (1979) for a lucid account of the latter phenomenon.

"n".

References B;u\t-ise, Jon. 19'79. On branching quantifiers in English. Jo/n.nu/ c!/'Pl~i/orop/~trNILoglr- H: 47-80. Barwise, Jon and Robin Cooper. 198 1. Generalized quantifiers and natural Ianguagc. Ltt/g/~isoc.s~ifrd Philosopli-1' 4: 159-2 19. Bennett, Michael, R. 1974. Some extensions of a Montague fragment of English. PI1.I). clisscrt.ition, UCLA. Distributed by Indiana University I-inguistics Club.

146 Godehard Link Bennett, Michael, R. 1980. Mass nouns and mass terms in Montaguc granlmar. In Ilavis and hiithun 1080, 263-85. Blau, U. 1979. Distributive und kollektive Priidikation, Q~antifikation und Kcnnxcichnung. '/'lrr,orcr1cl11 J,ii~,g/~is/ I(,$ Bunt, H. C. 1979. Ensembles and the formal semantic l-rropertics of mass tcrnls. In Pcllctier 1970, 249-77. IJurge, T. 1977. A theory of aggreptes. ,Vous 11: 97-1 17. Davis, Stmen and Marianne hlithun (eds). 1980. Lzt/gut.c/ir~.s,P/lr/osop/<j),r u ~ r /I M N I I I N ~ I / C;I~IIIINIIII'. L, Austin, Tes.: Tcxas Unit-ersit? Press. Ebcrle, Rolf A. 1970. Nortrirrul~sti~~ .\:jrsiciw.s. Dordrecht: D. Reidel. Goodman, N . and Willarcl Van Orman Quine. 1947. Steps to\$-arda constructive noniinalism. Jourtrtrl (!/'Sjlrrrholir.Logic 12: 105-22. Gratzer, George. 1971. Lo/tri.t Tlrcoty: J1Ii's/ Cot~~.i>/tls lrirrl ~ i . ~ l i ' ~ / ~Lr~llrter. l l / ~ ~ r / San Francisco, Calit: W.I-I. Freeman. Groenendijli, J. A. G., T. M.Y.Jansscn, and h4. B. J. Stohhof (cds). 1981. Fo~tlr(11.4/lr/horls 111 llrt S / r r ~ l oj ~f L a r r g u ~ g c Amsterdam: . Mathematisch Centrum, Univcrsit~of' Amstcrdrlm. Hausscr, R. 1974. Q~iantificationin an Extended Montapue (3ranimcr. Ph.L). dissertation, University of Austin, Texas. IIintikka, K. J . J., J. h1. E. hloravcsili and P. Supprs (cds). 1073. :lpprnur.l~s10 Na/unrl J , I I I I ~ ~ I ( L ~ P : Proc~rdiugsy/'/hr 19711 Stai!firJ C.I.i,rX-sliop on Grilrrrmcri' r~ndSrr~rrrtr~irs. Ilordsechc: D. Rcidcl. Hocpelman, Jakob and C;hristian Rohrer. 1980. On the mass count distinction and the F'rcncli I~nparfaitand Pass6 sin~ple.In Rohrer 1080, 620-45. Janssen, Theo M. V. 1981. Conlpositional semantics and relati~cclausc formiition in Xiont;~guc grammar. In Grocnendijh ct al. 1981, part 1, 2-37-76, Kccnan, E. I,. 1981. A Boolean approach to seninntics. In Grocnendijh ct al. 1981, part 2, 313-70. Kcenan, E. I,. and L. Faltz. 1978. Logical Types for Narur;ll 1,angu;lgc. U(:I.,iZ 0cc;lsional Papcss in Linguistics, no. 3, 1-0s Rngclcs, California. L-conard, M.S . ancl N , Goodman. 1940. T h e calculus of'inclividuals and ils i~scs.Joj,urrrrrl c!/'.~)~rn/~olir. Lo,gic 5: 45-55. Link, Godehard. 1979. t M o ~ / n y ~ i t ~ - G r / r tDie ~ ~ ~Io,~tsr.lrt* ~ ~ ~ ~ /Gi ~k..t ~ i ~ r l l ~ /hlunich: , ~ r ' i i . U'.Pinh. hlasscy, G. J. 1976. Toni, Dick, and I-Iarry, and all the king's men. . Irrri,t.ir.irrr Pl~ilosophi~~olQrrtrt~/ci~Ij 13: 89-107. R,lontague, Richard. 1973. Co~nnlentson Mora\ csik's paper. In Hintihka ct al. 1073, 280 -04. %lontaguc, Richard. 1971. Forrrrrrl Phi/osop/rj~.Sc/tc./cr/ Ptlpcvl~(!/'Rii.l~(trd I / ~ ' ~ ~ I / Ic~lircd ( I , ~ ~and I P ,witl.~,113 introduction h!. Richmond I-I. Thomason. Ne\v I4a\.cn, Chnn .: Yale Uni\ ersit! Press. h,Iontague, Richard. 19743. The proper treatnlent of'cluiu~~titicatiotltioi in o~.din;lr>ll:nglish. In hlon~ag~lc 1974, 247-70. Parsons, T. 1979. An anal!-sis of' mass tcrnls and anlount tc~.ins.In Pclleticr 1070, 137-00. Pcllrticr, Francis Jeffry (ed .). /E4rrss T ~ ~ r i nSorrlc s: Plr rlosopltir.rr1 Proh/i~l/r.v.Ilordrccht: I>. Rciclcl. Quinc, Willard Van Ormarl. 1000. I.li)ril u?iil O / ! ~ P(:atnbridgc, ~I. h;l;lss.: hlIT Press. Rohrrr, Christian (cd .). 1980. Tir~rc.,Tcr?si~,(rllil Q ~ ~ ( I I I / ! / L't.or.~~~~Iir~gs ~ L * I : ~ : o/'111i~ S / I I I / < ~I ,(' Io I~~ I/ ; ~ ~ L J0I1I1~ . P [Ire J,ogir. I!/ T r n s ~lrrril ~ Q~trrrl/j/i~.rr/rorr. Tiibingcn: Nicmc! cr. Scha, I<. J. 14. 1981. llistsibutivc, collcctivc and c ~ ~ m u l a tcluaiititication. i~c In Groencnclijk et al. 1081, part 2, 483-517. Sikorshi, Roman. 1960. BOO/LJNII .*l/gch~d.r.Hcitlelbcrg: Spsinga--Tcrlag. tcr Illeulcn, Alice. 1080. Substances, Quantities and Individuals. -4 Stud!: in rhc E'orm;il Scmanrich of' hlass Terms. Ph.D. dissertation, Stanford. C:alif'ornia. ter I\/Ieulcn, Alice. 1981. An intensional logic for mass ternis. In Grocncnrlijk ct 31. 1081, 421-43. Thoinason, R. H. 1977. hlultiple Qi~antification, Questions and Bach-l'ctcrs Scntenccs. Some Pre1inlin;lr~-Notes, i~npublishedmanuscript. von Stechors, .4min1. 1980. $lodification of noun phrascs. '4 d~allcngel i ~ rcompositional semantics. TI~POIYIIL.CI/ Lingz~istii.~ 7: 5 7- 1 10.

Assertion Robert C. Stalnaker

Let me begin with some truisms about assertions. First, assertions have contcnt; an act of assertion is, ainong other things, the expression of a proposition - sometl~ingthat represents the world as bcing a certain nr\ray.Second, assertions arc made in a context a situation that includes a speaker with certain beliefs and intentions, and some people with their own beliefs and intentions to whom the assertion is addressed. Third, sometimes the content of the assertion is dependent on the context in which it is made, for examplc, on who is speaking or when the act of assertion takes place. Fourth, acts of assertion affect, and are intended to affect, tllc context, in particular the attitudes of the participailts in the situation; hou; the assertion affccts the context will depend on its eontcnt. A'iy aim in this paper is to sketch some theoretical concepts with which to develop these truisms, and to show how these concepts can be used to explain some linguistic phenomena. I want to suggest how contcnt and contest might be rcprescnted in a theory of speech, and how the interaction of content and context to which the abovc mentioned truisms point might be described. 1 will not propose an analysis of assertion, but I will make some modest claims about the way assertions act on the contexts in which they are made, and thc way contexts constrain the interpretation of assertions. In conclusion, I will look briefly at an example of a phenomenon ~ v h i c l1~think these modest claims help to explain. Tllree notions \\:ill yla! a central role in the theory l will sketch: thc notion of a proposition, the notion of a propositional concept, and the notion of speaker presupposition. Each of thesc three notions will be defined or esplained in terms of the notion of a possible world, or a possible state of the world, so one might think it important to begin with the question, what is a possible world? 'Fhis is a good cluestion, but I will not try to answer it here, and I am not sure that an abstract theory of specch should say very much in ansm-er to it. In particular inquiries, deliberations, and conversations. alternative states of the subject matter ill question are conccivcd in various rlifferent ways depending on the interests and attitudes of the participants in those activities. But one thing that is common to all such activities, and essential to them, is that the pal-ticipants do seek to distinguish among alternative n7aysthat things

148 Robert C. Stalnaker might be, or might have been. It may be that the best way to bring out the formal structure of such activities is to focus on what is done with a given relevant set of alternative states of the world, setting aside questions about the nature of the alternativcs themselves. T h e decision to treat possible worlds, or possible situations, as primitive elements in a theory of propositions and propositional attitudes docs not require an ontological con~n~itment to possible worlds as basic entities of the universe. Rather, it is a decision to theorize at a certain level of abstraction.' 'The analysis of proposition in tcrms of possible worlds \vas first proposed in the context of intuitive semantics tbr modal logic.' T h e analysis is this: A proopuosition is a f~~nctioii from possible worlds into truth valucs (true or false). More roughly and intuitively, a proposition is a rule for determining a truth value as il function of the facts - of the u-ay the world is. Or, a proposition is a w-aji - any way - OF picking out a set of possible states of affiiirs - all those for which the proposition talics the value true. T h e intuitive motivation for this analysis is something like the following-. A propusition - the content of an assertion or belief is a representation of the world as being a certain lvay. But for any given representation of the world as being a certain way, thcre will be a set of all the possible states of the world which accord with the representation - which a r e that way. So any proposition cleterinines a set of possible 1%-orlds. And, for any given set of possible worlds, to locate the actual world in that set is to represent the world as being a certain way. So evcrjTset of possible worlds determines il proposition. Furthermore, any two assertions or beliefs will represent the world ils being the same way if and only if they are true in all the same possible worlds. If we assume, as sccms reasonable, that representations which represent the ~~rorltl as being the same way have the same content (express the same proposition), thcn we can conclude that there is a one-one con-espondencc between sets of possible worlds and propositions. Given this con-espondence, it seems reasonrlble to use sets of possiblc \\-orlds or (equivalently) functions from possible worlds into truth values, to play the role of propositions in our theory. T h c analysis defines propositions in terms of their essential function - to represent the w~orld.' Supposing for convenience of exposition that there is just a small finite number of possible states of the world, we might represent a proposition by enumerating the truth values that it has in the different possible worlds, as in the following- matrix: -

'4

i

j

k

i, J, and k are the possible worlds - the different possible sets of facts that determine thc truth value of the proposition. But there is also a second way that the facts enter into the determination of the truth value of what is expressed in an utterance: It is a matter of fact that an utterance has t11c content which it has. What one savs - the proposition l ~ expresses e - is itself something that might have been diffcrent if thc facts had been different; and if one is mistaken about the truth value of itn utterance, this is sometimes to be explained as a misunderstanding of what was said rather than as a mistakc about the truth value of what was actually said. T h e difference between the two ways that truth values depend on facts is exploited in the familiar riddle, If7,1~ou call a horsc's tail a leg bun? rnan.y legs rloi~s(1 horse

1

Assertion 149 h a w ? "The answer, of course, is four, since calling a tail a leg does not make it one, but one can see a different way to take the question. 1,ct me givc a simple example: I said You arc. a fbol to O'Leary. O'Z,eary is a f'ool, so what I said was true, although 0'1-.e.dry does not think so. Now Daniels, who is no fool and who knows it, was standing nearby, and hc thought I was talking to him. So both O'Leary and Daniels thought I said something false: O'Leary understood what J said, but disagrees with me about the facts; Daniels, on the other hand, agrees with me about the fact (lie knon-s that O'Leary is a fool), but n~isunderstoodwhat I said. Just to fill out the example, let me add that O'Leary believes falsely that Daniels is a fool. how compare the possible worlds i, j, and k. i is the world as it is, the world w-e are in; j is thc world that O'Leary thinks tve are in; and k is the world Daniels thinks we arc in. Jf ufc ignore possible worlds other than i, j, and k , wc can usc matrix -4 to represent the proposition I actually expressed. But the following two-dimensional matris also rcpresents the second way that the truth value of my utterance is a function ofthc facts:

T h e vertical axis represents possible worlds in their role as context - as what dctermines what is said. T h e horizontal axis rcpresents possiblc worlds in their role as thc arguments of the functions which are the propositions expressed. Thus the different horizontal lines rcprescnt what is said in the utterance in various different possible contexts. Notice that the horizontal line following i is the same as thc onc fol1oiving.j. This represents the fact that O'Leary iind I agree about what was said. Noticc also that the vertical column under i is the same as the one under k. This reprcsents thc fact that Daniels and I agree about the truth values of both the proposition I in fi~ctcsprcsscd and the one Daniels thought I expressed. In a sense, J said something true at i and fdse at j and k, even though in none of thcsc worlds did I express the proposition that is truc in i and filse in j and k. Although not expressed in any of the contests, this proposition is represented in the matrix. I will call it the diagonal proposition sincc it is the function from possible worlds into truth values whosc values are scad along the diagonal of the matrix from uppcr left to lot\e~. right. In general, this is the proposition that is true at i for any I if and only if what is expressed in the uttcrance at i is true at i. I shall say Inore about diagonal propositions latcr . I will call what a matrix like B represents a propositional concept. A propositional concept is a function fi-om possible w-orlcls into propositions, or, cqui\~alentl!-, i2 function fiotn an ordered pair of possible worlds into a truth value. Lac11 concrctc utterance token can be associated with thc propositional concept it determines, and, I will suggest below, some of the principles constrai~~ing the interpretation and evaluation of assertions are constraints on propositional concepts determined hy- i~ssertivc utterances rather than simply on thc propositions cxprcssed. This is rn! motivation for introducing- propositional concepts, but one can study this kind of structure from an abstract point of view, independently of utterances or contests of utterance. 'I'llc

150 Robert C. Stalnaker I

I;

abstract theory of \\,hat I am calling- propositional concepts has rcccived some attention 1, from logicians recently under the name two-dimensional modal logic.' T h c thcory focusses on thc n o t i o ~of~ a two-dimensional modal operator. A two-dimensional rnodal operator is an operator which takes a propositional conccpt into a propositional concept. If o is such an operator, then the incaning of o will be a rule that givcs you the propositional concept csprcssed by oP in terms of the one expressed by P, for any P. I will describe onc such opcrator, and contrast it with nlore traditional extensional and intensional sentence operators..i T h e dagger is an operator which takes the diagonal proposition and projects it onto the horizontal. If 4 is the diagonal propositio~ldetermined by P , thcn 1-Pexpresses 4 relative to all coiztexts. So if B is the propositioni~lconcept dctel.mincd by my statcment to O'Lear?; in thc example above, the following matrix gives the psopositional concept,

1 1

-/B:

What t B says is roughly this: CZ.'/zrr/is sirid in S's ul/erarrc.e (!/'You are a fbol is lrut, whcre thc definite dcscription, Mfhtlt is sniii in S Y: i~ltrvir)rl,z(!/'You are a fool may be a nonrigid designatole a dcscription that refers to different propositions in diffcrcnt ~vorlds.Notice that the dagger always yields a constant propositional conccpt as its value. That is, \tihatever the case with P, 1-Pm-ill al\vays cvprcss the samc proposition relative to every contest. If Y itself is already a constant propositional conccpt in this sense, then tP will express the same propositional concept as P." Compare this opcrator with a more familiar modal operator, prolx~sitionalnecessity. UP expresses in any kvorld thc proposition that is true at that world if and only if the proposition espressed by P at that world is the necessary proposition - the one that is true in all possiblc ~vorlds.Propositional necessity is a one-dimensional operator in the follom~ingsense: T h e proposition espressed by 01' at any point dcpeilds only on the proposition expressed by P at that point. T o evaluate UP on an) horizontal line, one need look only at the values of P on that line. 'This distinction between one-and two-dimensional ope]-ators parallels, on the nest level up, thc distinction between extensional and intensional operators. Compare the extensional negation opcrator: to evaluate P at any point, o i ~ eneed 100li only at the \;slue of P at that point. Extensiollal operators take points (truth values) into points; one-dimensional operators take horizontal lines (propositions) into horizontal lincs; two-dimensional operators takc the whole matrix (the propositional concept) into another whole matrix. Eacl~kind of opcrator is a generalization of the kind preceding it.' I,et me mention onc complex operator, square-dagger, which says thilt thc diagonal proposition is necessary. This can bc understood ils the a priori truth opcrator, observing the distinction cnlphasized in thc \vork of Saul KripLe bct~vccna priori and necessary truth. An a priori truth is a statcment that, tvl~ilcperhaps not expressing a necessary proposition, expresses a truth in evcrj contest. This will bc thc case if i~nd only if the diagonal proposition is neccssary, wl~ichis wl~atthe coniplcx opcrator says. -

Assertion

151

I will illustrate this with a version of onc of Kripke's own examples (1071: 273-5). Suppose that in worlds i, j, and k , a certain object, a ~nctalbar, is onc, two, and thrcc mctcrs long, respectively, at a ccrtaiil time r. Now supposc an appropriate authority fixes the reference of the expression orte Inrter. by nuking thc fi)llowing statcmcilt in each of the morlds i, j, and k: T/71s h a y is or7c m t e r /077g. Matrix C below represents the proposition;il concept for this statement. Matrix t C represents the propositional concept for the claim that this statement is a priori true:

C

i i

j w

k l

.The proposition expressed hj- the authority is one that might have been fi~lse,although he couldn't havc caprcssed a false proposition in that utterance. I have said how propositions are to be understood, and what pro1x)sitional coilcepts are. T h c third notion I need is thc concept of speaker presupposition. 'J'his, 1 want to suggest, is the central concept needcd to characterize speech contcxts. lioughly speaking, the presuppositions of a speaker are the propositions whosc truth he cakcs for granted as part of the background of tlze conversation. A proposition is presupposed if the speakcr is disposed to act as if he assumes or believes that tho proposition is true, and as if he assumes or bclicvcs that his audicncc assumes or believes that it is true as well. Presuppositions arc what is taken by the speaker to be thc c o m i n o n ground of the participants in the conversation, what is treated as their c o m l n o n knowledge or m u t u a l knowledge."he propositions prcsuppnsed in thc intcndcd sense need not reall!- bc cominon or mutual Itnowledge; the speaker nccd not even belie\.e thcm. t-Ie may presuppose an!; proposition that he finds it convcnicnt to assuinc for the pilrposc of the convel-sation, pro\ ided he is prepared to assunlc that his audience ~villassume it along with him. It is propositions that are presupposed - f ~ ~ n c t i o from n s possible worlds into truth values. Hut thc more fundamental n7apof representing thc spcalicr's presuplwsitions is not as a set of propositions, but rather as a set of possible \~orlds,the possiblc \\-orlds conlpatiblc with what is presupposed. This set, wllich 1 will call the context set, is thc set of possiblc ivorlds recognized by the speaker to be thc "live options" relekant to the conversation. A proposition is presupposed if and only if it is true in all of these possiblc worlds. T h e motivation for representing the speaker's presuppositions in terms of a set of possiblc worlds in this \my is that this representation is appr.opri:ite to a description of the conversational process in ternls of its essential purposes. '1'0 cngilge in con\-crsation is, esscntially, to distinguish among alternat-ive possible \vilys that things may be. T h e purpose of expressing propositions is to make such distinctions. T h e presuppositions define the limits of the set of alternative possibilities among c~hichspeakers intend thcir expressions of propositions to distinguish. Eaeh participant in a conversati011 has his own context set, but it is part of the cviicept o f presupposition that a speaker assumes that the rncnlbcrs ot'his auclicnce presuppose ever! thing that he presupposes. \IVe may define a nondetkctive context as one in which the prcsuppositions of the val-ious participants in the convcl-sation arc all

152 Robert C . Stalnaker the same. A defective context will have a kind of instability, and will tend to adjust to the equilibrium position of a nondefective context. 13ecause hearers will interpret the purposes and content of what is said in terms of thcir own presuppositions, any unnoticed discrepancies bctween the presuppositions of speaker and addressees is likely to lead to a Fdilure of comnlunication. Since communication is the point of the cnterprisc, ewrvone nill have a motive to try to keep the presuppositions the silmc. And because in the course of a convcrsation man!- clucs are dropped about what is prcsupposed, participants will normall!; he able to tcll that divergences cxist if tlwy do. So it is not unreasonable, I think, to assume that in the normal case contexts are nondekctive, or at least close enough to bcing nondefective. A contest is close enough to being nondefective if the divergences do not afkct the issues that actually arise in the course of the conversalion. Suppose for cuamplc that you know that Joncs won the election, believe mistakenly that I know it as well, and are prepared to take the truth of this proposition for granted if tllc occasion should arise, say by using it as a suppressed premiss in an argument, or by using thc description fhc * mlln who mon t h eie(.tio~ ~ to refer to Joncs. On m! dispositional account of speaker presupposition, if you are preparcd to use the proposition in this wily, thcn you d o presuppose that Jones won the election, even if you ncver have thc opportunit! to display this disposition because the subject docs not come up. Since I do not know that Jones won the elcction, I do 11ot presuppose it, and so the contest is defcctike. But the defect may he harmless. It nill not necessaril! be harmless: If. the news is of suficiently urgent interest, your failure to raise the subject n u y count as a display of your disposition to takc its truth for granted. There u-ill not be exactly a fi1il111-eof comn~unication,but there will be il misperception of the situation if I infer from the fact that you clo not tcll nlc who won that you do not know either. A conversation is a process taking place in an ever-changing context. Think of a state of a context at any given lllonlcnt as defined by the presuppositions of thc participants as represented by their context sets. In the normal, nondefectjvc case, thc context sets d l a11 be the same, so for this case zve can talk of thc contcxt set of the convcrsation. Now how does an assertion change thc context? Thcre are two \~~a\-s, the second of which, I will suggest, should hc an essential component of the analvsis of assertion. I will mention the first just to set it apart from the second: 'The tlct tlla~a speakcr is speaking, saying the words he is saying in the way hc is sa\-ing them, is a fact that is usuaIly accessible to everyone present. Such observcd hcts ciln be expcctcd to change the presumed common background knowledge of the speakcr ancf his a ~ ~ d i c n cinc the same way that any obviousfy observable changc in the phvsical sul.~.o~lnding;c; of the conversa tion will change the presuined common know lcdge. If u goat \vt.all;ecl into the room, it would normally be presupposed, from that point, that therc was ii goat in the room. And thc fact that this was presupposed might be exploited in thc E conversation, as when someone asks, HOIDrliri t h i i ~thing gtr in lr~~re.7,assunling tllat others will know what he is talking almut. In the same n.a?, 1\11eii 1 spcali, I presuppose I that others know 1 ail1 speaking, even if I do not ilssunle that anjonc knew 1 was going to speak before I did. This fact, too, can be exploited in thc con\,crsation, ijs when Daniels says 1 crin balil', taking it for gl.alitcd that his a ~ ~ d i e n ccan e tigiirc out who is bcing said to be b;lld.

'

i

Assertion

153

I mention this commonplace way that assertions changc the contest in ordcr to make clear that the contest on which an assertion has its essential effect is not definccl by what is presupposed before the speaker begins to speak, but will includc an! infornlation which the speaker assumes his audience can infer from the performance of the speech act. Once the context is adjusted to accommodate the information that thc particular utterance was produced, how does the content of an assertion alter the context? My suggestion is a very simple one: T o nlahe an asscrtion is to reduce the context set in a particular way, provided that therc are no objections from the other participants in the conversation. T h e particular \%-a!-in which the context set is reduced is that all of the possible situatioi~sincompatible with what is said are eliminated. To put it a slightly different way, the essential effect of an assertion is to changc the presuppositions of thc participants in the conversation by adding the content of what is assertcd to what is presupposed. This effect is avoided only if the assertion is rejected. I should emphasize that I do not propose this as a definition of assertion, but only as a claim about one effect which assertions have, and arc intended to have - an effect that should be a component, or a consequence, of an adequate definition. There arc scvcral reasons why one cannot define asscrtion in terms of this effect alone. One reason is that other speech acts, like making suppositions, have and are intended to have the sanlc effect. A second reason is that there may be ~ a r i o u sindirect, even nonlinguistic, means of accomplishing the same effcct which I would not want to call assertions. A third reason is that thc proposed essential effect makes reference to another speech act - the 0 rejection of an assertion, which presumably cannot be explained indcpendcntly of assertion. Our proposed effect is clearly not a sufficient condition for asscrtion. Is it even il necessary condition? It might be objected that a person who makcs an assertion does not necessarily intend to get his audience to acccpt that what he asserts is true. T h e objector might argue as follows: Tahe one of your own examples, your statement to O'Leary that he is a fool. You knew in advance that O'Learp w-ould not acccpt the assertion, so according to your account, you knew in advance that your assertion u-ould fail to achieve its essential effect. That example should be anomalous if your account were correct, but it is not anomalous. Would it not be more plausible to charactcrizc assertion as trying to get the audience to accept that the speaker accepts thc content of the assertion?'" But this Gricean twist is not required. My suggestion about the essciltial effect of assertion does not impl? that speakers intcnd to succeed in getting the addressec to acccpt the content of the assertion, or that they believe they will, or even might succeed. A person may make an assertion knowing it will be rejectcd just as Congress inay pass a law knowing it will be vctoed, a labor negotiator may make a proposal knowing it will be met by a counterproposal, or a poker player may place a bet knowing it will cause all thc other players to fold. Such actions need not be pointless, since tliey all have secondary effects, and there is no reason why achieving the secondary effects cannot be the primary intention of thc agent performing the action. The essential effects will still be relevant evcn when it is a forcgone conclusion that the assertion, legislative act, proposal, or bet will be rcjccted, since one generally explains why the action has the secondary effects it has partly in terms of the fact that it would have had certain essential e f i c t s had i t not bccn rejected.

154 Robert C. Stalnaker One may think of a nondefective conversation as a game whcrc the common context set is the playing ficld and the moves are either attempts to reduce the size of the sct in certain ways or rejections of such moves by others. T h e participants have a common interest in reducing the size of the set, but their interests may diverge when it conics to the question of how it should be reduced. T h e overall point of the game will of course depend on what kind of conversation it is for example, whether it is an exchangc of information, an argument, or a briefing. T h e game could be expanded by introducing other kinds of moves likc making stipulations, temporary assumptions, or promises, asking questions, and giving commands and permissions." Each of these kinds of linguistic action is presumably performed against a background of presuppositions, and can bc imderstood partly in terms of the effect that it has, or is intended to have, on thc presuppositions, and on the subsequent behavior, of the other participants in the conversation. This is a very abstract, and a verq simple, sketch of what goes on when someone says something to someone else. Hut there is enough in it to motivate some principles that are useful for explaining regularities of linguistic usage. 1 will mcntion three such rules which illustrate the interaction of context and content. Given the framework of propositions, presupposition, and assertion, the principlcs arc all pretty obvious, which is as it should be. Tlicg are not intended as empirical generalizations about how particular languages or idiosyncratic social practices work. Rather, they are proposed as principles that can be defended as essential conditions of rational communication, as principles to which any rational agent would conform if he were engaged in a practice that fits the kind of very abstract and schematic sketch of comn~unicationthat I hale given. 12 I nil1 list the three principles and then discuss them in turn. -

1 ,4 proposition asserted is always true in some but not all of the possible worlds in the context set. 2 Any assertive utterance should express a proposition, rclativc to each possible \r;orld in the context set, and that proposition should have a truth value in each possible world in the context set. 3 T h c same proposition is expressed relative to each possible wol-Id in the context set. T h e first principle says that a spealies shoulcl not assert ~vhathc prcsupposcs to he true, or wl~athe presupposes to be false. Gih-en the meaning of 1>rcsupposition and the essential effect ascribed to the act of assertion, this should be clear. T o assert somcthing incompatible with what is presupposed is self-defeating; onc wants to reduce the context set, but not to eliminarc it altogether. And to assert something if-hich is already presupposed is to attempt to do somcthing that is already done. This rule, like the others, can be applied in scvcral ways. If one could fix indcpendcntly what was presupposed and what was said on a given occasion, tlieii onc could use the rule to e\-aluate the spealier's action. If he failed to confi)l+mto the rule, tl~cnhc did soinetlling that, from the point of vieif- of thc convcl-sation, was unreasonable, inefficient, clisorderly, 01- uncooperative. But one can also ~ s the c rule, or tlic presuniption that the speaker is conforming to the rule, as evidence of what \+-asprcsupposed, or of what was said, Perhaps as more than just evidence. T h e r ~ ~ l ma\; e s be takcn to

Assertion

155

define partially what is presupposed and what is said in a context by constraining the relation between them. So, if a speakcr says something that ndnlits of two interpretations, one compatible with the context set and one not, then the contcxt, through the principle, disambiguates. If the speaker says something that seems prima facie to be trivial, one may take it as a clue that the speaker's context sct is larger than was realized that the contcxt was defective - or one may look for another intcrprctation of what he said. There are thus three ways to react to an apparent violation of the rulc: First, one may conclude that the contcxt is not as it secms. Second, one ma! conclude that the speaker didn't say (or didn't mean) what he seemcd to sily (or to nzean). Third, one may conclude that the rule was indeed violated. Sincc there is usually a lot of flexibility in both the contcxt and the interpretation of what is said, the third reaction will be an unusual one, although it will not be unusual to use the rule to explain whq- some utterance would have been deviant if it had occurred in a given contcxt. T h c second principle concerns truth value gaps, i ~ l dconnects semantic presupposition with pragmatic speaker p~.esupposition.T h e principle implies that if a scntcnce .v semantically presupposes a proposition (I, (in the sense that .\. expresses il trut-11 or a falsehood only if qb is true), then c , is presupposed by- the speaker in the scnse of prcsupposition discussed above. There are tv70different ways that a truth valuc gap ma!- arise: a scntence may filil to cxpress a proposition at all in some possiblc situation, or it may succccd in expressing a proposition, but express one that is a partial function - one that is undefined for certain possiblc worlds. Both kinds of truth value gap are excluded fi.01~1the contcxt set by this rule. T h e rationale for this rule is as follows: 'The point of an assertion is to reduce thc context set in a certain determinate way. Hut if the proposition is not (rut or false at s o n ~ epossible world, then it would be unclear whether that possible world is to be included in the reduced set or not. So the intentions of thc speaker vcrill be unclear. Agnin this principle can be used in any of the three ways: to interpret what is said, as a clue to what is presupposed, or as a basis for evaluating the action of a speaker. T h e third principle, which says that an utterance must express the same proposition relative to each possible world in the context set, is closely related in its motivation to a fundainental assumption of the logical atomists and the logical empiricist tradition. In Wittgenstein's tcrminolog!; the assumption is this: CVhether a proposition (read: sentence) has sense cannot depend on whether anothcl- proposition is true ~ ~ ~ I . Y ; 2.021 1). Meaning and truth must be sharply dividcd, (cf. T T L Z I . LProposition aceording to this tradition, in order that one bc able to use language to communicate in il determinate waj-. One must be able to tell what a statement says independently of any facts that might be relevant to determining its truth. Now it has alwa!rs been clcar that this kind of principle requires qualification, since it is a matter of fact that words mean what they mean. And the phenomena of contcxt dependence are evidcncc of other ways in which what is said is a function of what is true. 'l'hc franiework of presupposition and asscrtion at once providcs a natural waJ- to ~lui~lif'~ this traditional assumption so as to makc it compatible with the phenomena, and a clear explanation of why i t must hold in thc qualified version. To sec why the -

156 Robert C. Stalnaker principle must hold, look at the matrix for the propositional concept D.Suppose thc context sct consists of i, J, and b, and tlic speaker's utterancc dctcrniines D. What n~ouldhc be asking his audience to do? Something like this: If wc arc in cvorld i, leavc

D

i

i

k

the context set the same; if we are in worldj, throw out worlds i and j, and if we arc in ~vorldk, throw out just world i. Rut of course thc audience docs not know which of those worlds we are in, and if it did the assertion \+-ouldbc pointless. So the statement, made in that context, expresses an intention that is essentially ambiguous. Notice that the problem is not that the speaker's utterance has fliled to dctcrminc a unique proposition. Assuming that one of the worlds i, J, or k is in '1ct the actual world, then that world will fix the proposition unambiguously. 'The problem is that since it is unhnown which proposition it is that is expressed, the expression of i t cannot do the job that it is supposed to do. 1-3 As with the other principles, one mag respond to apparent violations in different ways. One could take an apparent violation as evidence that tlie speaker's context set was smaller than it was thought to hc, and eliniinate possible 1%-orlds relative to which the utterancc receives a divergent interpretation. Or, one could reinterpret the uttwance so that it cxprcsses the same proposition in each possible ivorld. C:onsider an example: hearing a woman talking in tlie ncxt room, I tell !TILI,Tl~iilis ei~herZsa Zsisn Gabor ol- Elicr~beth_.in.v~-ontbe. Assunling that both dc~nonstrativcpronouns and proper names are rigid designators - terms that refer to the same individual in all possiblc worlds - this sentence comes out expressing either a necessary truth or a necessary falsehood, depending on whether it is one of the two mentioned \fromen or somconc else who is in the ncxt room. Let i be the cvorld in which it is Miss Ciabor,J thc world in which it is Professor Anscombe, and k a \I-orld in which it is somconc else, s a j . Tricia Nixon Cox. Now- if wc try to bring the initial context sct into confol-mity with tlie tllird principle by shrinlring it, say by throwing out world k, cve \vill bring it into conflict with the first principle by- making the assertion trivial. But if we look at what is actually going on in the example, if we ask what possible states of affairs the speaker \vould be trying to exclude from tlie context sct if he made that statcnicnt, \vc can work backward to the pi.oposition expressed. 14 moinent's rcflcction shows that what the speaker is saying is that the actual world is either i or.;, and not k . Whnt he means to communicate is that the diagonal proposition of tlic iiiatl-ix E exhibited below, the proposi~ion expressed by t E , is true.

Assertion

157

I suggest that a common way of bringing utterances into conformity with the thircl principle is to interpret them to express the diagonal proposition, or to perti)rin on them the operation represented by the two-dimensional operatos dagger. Thcrc ilre lots of examples. Consider: Hespe~ziszs i11'entical wirll Pl~o.sphort~s,it is i ~ o r rthrce ~ o 'l.loi.k, cln ophtlzalmologist is an eye d o r t o ~ In . each case, to construct a context which conforms to the first principle, a context in which the proposition expressed is neither trivial nor assumed fitlse, one must include possible worlds in which the scntcncc, interpreted in the standard way-, expresses diffircnt propositions. But in any plausible contest in which one of these scntcnces might reasonably be used, it is clear that thc diagonal proposition is the one that the speaker means to communicate. T h e two-dimensional opcrator dagger maj- represent a common operation used to interpret, or reinterpret, assertions and other speech acts so as to bring them into confi~rmitywith the third principle constraining acts of assertion. T o conclude, let me show how this last suggestion can help to explain a pi~zzle concerning singular negative existential statements. T h e puzzle arises in the contcxt of a causal or historical explanation theory of reference according to hvhich p ~ q names ~ r refer to their bearers, not in virtiie of the tact that the bearer has certain properties expressed in the sense of the name, but rather in virtue of certain causal or historical connections between the referent i ~ n dthe spcakcr's use of the name.'' According to this theory, the proposition expressed by a simplc singular statelnent containing a proper name, like O ' L e a q ~is afhol, is the one that is truc if and onlj- if the individual who i h in fact causally connected in the right way with the speaker's use of thc namc has the property expressed in the predicate. So the proposition is detcrmincd ils il function of the individual named rather than ils il f~lnotionof the name, or the sense of the nillnc. What does this theory say about statements like O'L~LII:)I rlors not c . r ~ s t .If thc statement is true (which this one h a p p c ~ ~tos be), then there is no individual appropriately related to the speaker's use o f t h e namc, and thus no proposition detcrmincd as a function of such an individual. So at least for t r u e negati~eexistential statements, it seems that proper names must play a different role in the determination of the proposition expressed from the role the? play in ordinary prcdicativc statements. Perhaps a negative existential statement says, simply, that there is no indiiidual standing in thc right causal relation to the spenkcr's use of the nilmc. 1 5 This cloes seem to get the truth conditions right for ncgativc cxistcntial assertions, but it elearl! gets them tvrong for some other kinds of singular negati\-e existential constructions. Consider, for example, countcrfactual suppositions, as in the antecedent of the conditional Ifi-ir~stolle11(1~/tr't c.t.~sferi,t11t l ~ i s t n ~~J'philosopl~~)~ y rno~al~l hare hc.efz z:ei:ll O~flLv-~vrl J ~ I I I 16 n ~ i ~ i/ l l rvas. Clearly the proposition expressed in the antcccdcnt of this conditional is not the proposition that our use of the name -.-Iristotit~is not appropriate\\; connected with any individual. T H A T proposition is conlpatible with Aristotle's existence. 1ci1rthermore, if Aristotle hadn't cxistcd, then our uses of his nanw probably would not have esisted either. ?'he proper name seems to function in the antecedent of the counterfi~ctualmore like the way it functions in ordinary predicative statcmcnts: 'l'l~c proposition is dctcrmined as a function of the person Aristotlc; it is truc in possible ivorlds where he does not exist, and false in possible ~vorldsL\-herehe does esist. So it seems that not only do proper naincs act differently in negative existential assertions than the>-do in singular 17rcdicati~eassertions, the? also act diffcrcntly in

158 Robert C. Stalnaker negative existential assertions than the) do in negati\-c existential suppositions. What oiic asserts when he says L4rzslo/ledoes not c,t'jst seenis to be diffcrcnt tiom what one supposes when he saj-s S14ppose -.ir.i.~totlchadn 'I c~.t.ls/rr/. Let us see how the yragniatic principle can account for these facts. I3cgin with tllc most straightform~ardscmantic account of negative cxistcntial const~.uctions:.iiri.s/orlt does not c ~ i s tlike , -4rUtori~~ I D ~ ~ntse, S is a proposition about Aristotlc. It is true in possiblc worlds whose domains contain the pcrson we call Aristotlc and in possible worlds whose domains do not contain that person. \$'l-rat if the name cloes not, in fact, rcfcr? Suppose for exa~nplcthe statement is SIZP~IOI-k J I ~ I I I Z(/o~>.s Z S lot ~.vist.Then thc proposition will be ncccssarily Glse, by the same rule, sincc the domain of no possible world contains the actual person we call Shcrlock I-~olrnes." Now lct us use this straightforward semantic account to construct a propositional concept fix an uttcrance of .Sl~evlo~~k H o l n ~ ~does s ,rot e.ri.st. 1,et the \\-orld I be the actuaI world. Let j be a world in w~hicha famous detective named Sh~r.1oi.kH/)/t?reslivcd in ninctecntll century London, and Sir Arthur Conaii Doyle wrote a series of historical accounts of his cascs. J.et \vorld X. be a possiblc ~vorldin uhich Sir Arthur Conan I-Ioyle was a fikrnous detective i~amecl Slrerlock Holines who wrote a series of autobiographical accounts of his own cascs under the the pseudonj-m S i r Arthur Conan D(!ylr. These stipulations determine the follo\ving two-dimcnsional matrix fc)r the uttcrance:

Now suppose i, j, and k are a contest set (say a person llas hei~rdthcsc tl~rccrumors about the origin of the Sherlock I-Iolmes stories and docs not know which is true). GS the matrix show-s, the uttcrance violates the third principle, and so a reinterpretation is forcecl on it. Diagonalization, or the dagger operation, brings thc utterance into line n-ith the principle, and yields the intuiti\;cl>-right rcsult:

But now contrast the case of thc counterf~ctual.To intcrprct the statemcilt !/'-.lrisint/c I ~ r i r l ~~.vi.~/e'~l, '/ ~ l r ehistoiy q f p hilosoplq! n)o~r/rlhaz-r hci.11 z.cl:)? rl![';'~.enl./;om/ / I P I J J ~ ! ) ! 11 rvas, we clo not need to diagonalizc, sincc in an! possiblc contcst appropriate to chat statement, it will be presupposed that -4ristotlc does exist. So tlic pro~~osition si~~posed is the one ohtnincd by the straightforward rule,'' Again, this is int~~irively the right result. We have not escaped the conclusion that the content of the assertion :frI.~tnl/t~ llirl no1 P ~ ~ is ~ different S I fi-om the content of the supposition s~ipposc. Irtstotl~hri~111'/ e.risrcd. But m-e 11avc cxplaiiied that consequence using a single semantic account of sitlg~li~r

Assertion 159 negative existential constructions - the account which is most natural, given thc causal theory of names - together with independently motivated pragmatic principles. T h e general strategy which this explanation illustrates is to use 1~rapniatic~hcory theory of conversatioiial contexts - to take some of thc weight off sen~anticand syntactic thcorp. Some other problcins where I think this strategy ant1 this theory will prove uscful are the explanation of presupposition phenomena,'" the explanation of the differences between subjunctive and indicative conditi~nals,'~'the analysis of definite descriptions, and the behavior of deictic and anaphoric pronouns. hly hope is that by recognizing the interaction of some relatively simple contextual factol-s with the rules for interpreting and evaluating utterances, one can defcnd simpler scmantic and granima tical analyses a n d give more natural cxplanations of many linguistic phenomena.

Notes The development of the idclis in this paper was stimulated 115 David Icaplan's lectures, somc ?c;ws ago, on the logic of dc~nonstrativcs.T h e influence of Paul Grice's ideas iibout logic ancl convcrsari~)n will also be evident. I have benctitcd from discussions of earlier ~crsionsof this p:lper ~ i t hot11 h 01. these pliilosophers and man!- others, including D;lvid Lenis, Zcno 1-encller, and Ltlmu~idGctticr. 1 am indebted to the John Simon Guggenheim Memorial Founclation for rcscarch support. (107Ga) that one ciln take possible worlds seriousl! without accepting an 1 I argued in S~~ltnaLcr ilnpli~usiblcmetaphysics. 2 Tllc possible worlds analysis of propositions \$-assuggested origin;lll> by Sa~llKriphc in thc c v l y 1900s. 3. I recognize that I am slia~ingquickly over large problems here. In particular, the identit! conditions ~vhichthe anal5sis ;\ssigns to propositions havs somc cxtl*on~eI\paracloxical conscquenccs (such as that there is only one necessary proposition) which SCCIII to makc the ani~l!sis particularly unsuited for an account of the objects of propositional attitudes. I discuss some ot' these problems, inconclusi~cl~, in Stahi;~lier(197hb). -I The most general discussion of two-dimensional modal logic I Lno~vof is in Segcrhcrg (1073). Scc also :iq\ist (1073) and Kanip (1971). T h e earliest in\.csti~ationsof two-dimensional opcrators ncrc, I beliebe, carried out in the context of tense logic by Franh Vl;lch ancl Hans kiunp at UCL-4. 5 T h e tensc logic analogue of the daggcr operator mas, according to llavid L,enis, in\c~ltccl11) Frank Vlach and is discussed in his U C L _ iPhD dissert;ition (1974). The notation is Lcwis's. Scc T,c\\-is (1073a: 6.3-(,-In). 6 Another. operator which 11'1s intuitive application is reprcscntetl by Lewis as an i~psidc-do\z;n dagger. What it docs is to project the diagonal propr)sition onto the verticaI, vhicli. in cft'cct, turns contingent trutlis into neccssar!. truths and contingent falsehoods into necessary L~lsclioods. Hilns kanip (1071) proposcil the temporal analoguc of this operator as a rcprcscntativc ol' tllc sentence ;~dverbr r i , ~ ~it. is N O I P / I . I I P f / i i l / -4 said ,it time / expresses a proposition th;~tis true ;lt ;dl times just in case . I is true at I . The operator n1;lkes a difference when now is en~heclclcdin tlic contcxt of other temporal moclificrs. Using it, one can represent scntcnces like Onc.~,e7*o:)lotr~, tion7 u l i ~ ' r11trijt1'I ,)I('/ / v ~ t ' ~/)or11 i without object language q i~antiticrsover times. Tlavid I,c\vis and I)a\ id kaplan 1131c suggcstcct tliiit this operator shov s the semantic function of crprcssions libc ~~i.tuirl/l~ ancl in,/;~i/, as in I/'ihod nron, ~norrqjl~hirrtI ill jirr.1 I i i l i ~ ,I a?olr//lhi. /rapprc,t-. 7 4lthougl1 the dagger ancl the upside-clown dagger are clcfincd ;is operators on propohitio~~;lI co~iccpts,the\: CAI he generalized to any kind of t\\-o-dimension:~lintension. For c\-:ln~plc,they

160 Robert C. Stalnaker niay be interpreted as operators on tmo-dimensional individual concepts, or on property concepts. L.et cr rcprcscnL a dcfiriitc description, say ~ h cI'/.r.qil/i~il/ / ! / ' ~ l i( :r~ r z / c , r / S~ale.v,nrirl Ict i, J , and k be three times, say 1967, 1971, and 1975. h,latrix (i) hclow represents the t\r.odimensional intension of this definite description rclati\e to thcsc times. Matrix (ii) rcprescnts the rigid description, t l r ~Frrson wlro ii i~rjurr, 01- now, l h t P~-(lsidetrl~ ! / ' I / I L , l!iri~i~d S I L ~ This I ~ J ~is . the two-dimensional intension of I N . David Kaplan, in "13'TIIAT" (107X), discilsscs this operator on singular tcrnls ant1 compares it with Keith Donncllan's account of the rcfercntial use of definite descriptions.

8 1 have discussed this concept of presupposition in two earlier papers, Stiilnakcr (197.3) and Stainaker (1974). Stephen Schiffcr (1972: 30-42) and Ila\-id I.cwis (1069: 52--60) have discussed coticcpts of mutual knowlctlge and common knowledge ~ h i c hresemble tlie notion of prcs~~pposition 1 have in mind. Paul Cirice spoke, in he IVillinm Jnmcs I,ccturcs, IJ(' prol~ositic~ns having common ground status in a conversation (pitblished in part in Gricc (1075) ). 9 It shoulcl be nude cIear that to reject an assertion is not to assert or assent to thc contradictory of the asscrtion, but only to refuse to accept the asscrtion. If an asscrtion is rcjectcd, thc context remains as it was. (Rlore exactly, rejection of an asser~ionblocks the second kind of effect that assertioils have on the context. The first k i d of crti.ct cannot bc blocked or witl~dl-awn.) 10 David Knplan, in discussion, raised this objection. 11 Llavid Lew.is (19'7313) outlined a laiiguage ganle of cotniiiantling ant1 permitting which would fir into this frame\\-ork. 12 T h e influence of Grice's theor! of conversation should bc clear ti-om my rliscussion 01' the applicntion of these principles. 13 A clarification is needcd to rcsolvc an ambiguity. T h e third pl-inciplc says t11;it thc proposition espresscd in any possible \vorld in the context sct must coincirlc within the contcxt set \tit11 the proposition expressed in any other possible \E-orldin the contcst sct. So, for example, ifthc context set is {I,./;, then an utterance determining the propositional concept rcprcscntcd bclow mill not b~iolalcthe principle. I:vcn though the proposition c\prcsscd in I divergcs from tllc proposition csprcsscd in J , the divcrgcncc is outsirle ~ h contcut c set. Ilavid I.cwis pointed out the need h r this claritication.

Tlic ca~rsalaccount of refereilcc is defended, in general, in KripLc (1971) i ~ n dDonncllan (1071) Donnellnn ( I 974) discusses tlie problem ol'singular negative csistenti:~lstatements in the contcut of this account of reference.

Assertion 161 15 Donncllan's explanation of the truth coilditions for singular ncgativc csis~c~ltial stiitcmcnts is roughly in itccord with this suggestion, hut he cautions that the rulc hc propows "cloes not provide a11 analysis of such statements; it does not tell us what such statcmcnts mean, or nhilt propositions they express. This means that in this cilse we are dikorcing truth conclitions from meaning" (1974: 2 5 ) . liccording to Donnellan, "no obvious may of representing propositions expressed hy existential statemcnts suggests itself' (1974: 30). 16 Kripkc, in talks on this subject, has made this point ahout counterf'i~ctuals ivith ncgativc existential antcccden ts. 17 I bclicve this straightforward semantic account is the one that Kripkc has dd'enclctl in the r;~ll,s nlentioned in notc 16. 18 I t is interesting to notc thal if the conditional were in the indicativc mood, the result ~vouldhil\-c been diskrent. This is because an indicative condition;ll is appropriate only in a contest u.Iicl-c it is an open question \vhctlier the antecedent is true. So to sa!- l f , - l r i s / ~ / rlil111 ~ / e 'I l~.vislis to suplmsc just what is asserted ivhcn one asserts r;lristorlz r/irl?l'/P . Y I S I . 19 Tliis is discussed in Stalnaher (1973). 20 This is rliscusscd in Stalnaher (1976~).

References :\qvist, L. 1973. Modal logic with subjuncrive conditionals and dispositional prcdiciltes. .701/rn(11I!/' P / ~ i l ~ ) s ~ ) p/ hI,ogic. t i a 2 : I -7h. Ilonnellan, K . 1971. Proper names and identifying descriptions. In D. Daliclson and G . IIarn~an (ccls), Stttznnti~sof iV~/ltrrr/lI , i i n ~ / ~ r zDordrccht: ~c, D. Reidel. Donnellan, K. 1974. Speaking of nothing. P/~ilo.~oplrrc~aI R L J ~ I83: ~ J3-31. ?~ Gricc, 11. P. 1975. Logic and conversation. In P. Colc and J. H. Morgan, (cds). . S ~ P O IAI.I.\. . / I (.xyrlrl/,v (rtlil Scwitr~~/irs vol. 3), New York: ,4carlemic Press. Iiamp, H. 1971. Formal properties of "Now;". T/ii,orW 37: 227-73. Krtplan, David. 1978. Dthat. In Petcr Colc (ed.), I),-[ignrnlics (5")~ntii.vrl~rilSrrtr~lii~il.s, ~ o l O), . New Yorli: hcadernic Prcss. n l ~Zi~~/l/rrrl ~~~ Kriphe, S. 197 1 . Ni~mingand necessity. In 11, llavidson and G. I Iarn~an,(eds), S ~ ~ n r r r I!/' 1,11~1gun,qe, r>ordrccht: D. Reidel. Lewis, 1). 1969. Couin7tion. Cambridge, Mass.: Ilarvard University Prcss. Lewis, D . 1973a. C o / / ~ ~ / ~ / : / i r rOxford: . t / ~ ~ ~ lSs .i l ~ iBlackacll. l L,cwis, D. 1973b. Problem i~boutPermission, unpublished paper, Princeton Uni\crsitq, I'rinceton, New Jersey. Schiffer, S. 1972. Il/leanii~g,Oxibrd: Clarcndon Press. Scgcrberg, K. 1973. Two-dimensional modal logic. Jor~rwwl ~~f'/'l~z/osop/iir.trl L I / ~ I2(: .77 96. Stalnakcr, R. (:. 1973. Prcsuppositions. .~oiinralc~~Philoso~)l1il111 Logii 2: 447-57. Stalnaker, R. C;. 1974. Pragmatic presuppositions. In M. K. Munitz and P. K. Lngcr, (cds), Scrr~trn~ic~s irrld Pki/osophj1, Yorli: New York University Press. Stalnaker, R. C. 19763. Possible ~vorlds.n'or/s 10: 65-75. Stalnakcr, R. C . 1976b. Propositions. In A. F. Mackii~and 1). D. hierrill (eds), lss~~esti iltt P/li/lJ.~l~p/~)J i ! / ' L ( ~ ~ ~ g / dNew l / g e , Haven, C:onn. Yale University Prcss. Stalnahcr, R. C. 1 9 7 6 ~Indicative . conditionals. In A. Kashcr, ( 4 . ) . Lrrrqrrngr 111 P o ~ . m Porrrrrln~io~u, : d!fr/hor/.r,a~tcr'S)~.vli~rirs, essays in honor of Yehoshua Bar-I Iillcl, I>ordrccht: I). Rcidcl. Vlach, F. 1974. Unpublished Doctoral dissertation, University ot'C:aliii)rni;~,Los .411gclcs,Calili)rnia. \L-ittgenstcin, I,. 1961 . Trrzi.rmlw Logi~~o-Pl~iIosop//i~.~rs (Translation). Nea Yorli: lioutlcclgc and I i c p n Paul. (Originally p~tblishcdin 1911).

Scorekeeping in a Language Game David Lewis

Example 1: Presupposition1 At any- stage in a well-run conversation, a certain amount is presupposed. 'The parties to the conversation take it for granted; or at least they purport to, whether sincerely or just "for the sake of the arg~iment".Presuppositions can be created or destroyed in the course of a conversation. This change is rulc-governed, at least up to a point. 'l'hc presuppositions at time t' depend, in a way about which at least some general principles can be laid down, 011 the presuppositions at an earlier time / and on the course of the conversation (and nearby events) between t and I'. Some things that might be said require suitable presuppositions. Thcy ilrc acceptable if the required presuppositions are present; not otherwise. "The king of Francc is bald" requircs the pl-esupposition that France has one king, and one only; "Evcn Gcorge Lakoff could win" requires the presupposition that George is not a leading candidate; and so on. We need not ask just what sort of unacceptability results whcn a required presupposition is lacking. Somc say falsehood, some sap lack of truth villue, some just say that it's the kind of unacceptability that results when a required presupposition is lacking, and some say it might vary from case to case. Be that as it may, it's not as easy as you might think to say something that will be unacceptable for lack of required presuppositions. Say somctliing that requires a missing presupposition, and stsaiglit~vaythat presupposition springs into existence, making nrhat you said acceptable aftcs all. (Or at least, that is what happcns if pour conversational partners tacitly acquiesce - if no onc says "Hut l'rancc has ~ h w ekings!" or "Whadda ya mean, 'ez?enGeorge'?") That is w-hy it is peculiar to say, out of the blue, "All Fred's children are asleep, and Fred has children." 'l.'he first part requircs and thereby creates a presupposition that Fred has children; so the second part adds nothing to what is already presupposed n-licn it is said; so the second part has no conversational point. It would not havc been peculiar to sily instead "lired has children, and all Fred's children are asleep."

Scorekeeping in a Language Game 163

I said that presupposition evolves in a more or less rule-governed way during a conversation. Now we can formulate one important governing rule: call it tlic 1r1dt I!/' n~~rowzmorZ~tion .fir prrsuppo.silzon. If at time t something is said that requires presupposition P to bc acceptable, and if P is not presupposed just before t, then - ceteri-s paribus and within certain limits presupposition P comes into existence at I. --

This rule has not yet been very well stated, nor is it the only rule governing the kinematics of presupposition. But let us bear it in mind nevertheless, and move on to other things.

Example 2: permissibility2 For some reason - coercion, deference, common purpose - tw-o people are both willing that one of them should be under the control of the other. (At lcast within certain limits, in a certain sphere of action, so long as certain conditions prevail.) Call one the sl~zve,the other the masttr. T h e control is exercised verhall!;, as fi)llows. At any stage in tlic cnslavcment, there is a boundary between some courses of action for the slave that are permissible, and otllers that are not. 'Tile range of permissible conduct may expand or contract. T h e master shifts the boundary by saying things to the s l a ~ e Since . the slave does his best to see to it that his course of action is a perniissiblo one, the master- can control the slave by controlling w h ~ is t pcrmissible. Hcrc is how tlic mastcr shifts the boundary. From time to time he says to the slaw that such-and-such courscs of action arc in~permissible.Any such statement depends for its truth value on the boundary between what is permissible and what isn't. 13ut if' the nlastcr says that something is impcrinissible, and if that would be false it'the boundary remaincd stationary, then straightway the boundary moves inward. T h e permissible range contracts so that what the master says is true after all. Thereby tlic mastcr makes courses of action ilnpermissible that used to be pern~issible.But from time to timc also the master relents, and says to the slave that such-and-such courses of action are pcrmissiblc. 01perhaps he says that some of such-and-such courses of action are permissihlc, but doesn't say just which ones. Then the boun(iary moves outward. T h e pern~issible1-angeexpands, if need be (and if possible), so that what the mastcr says is true. Thereby the master makes courses of action permissible that used to be inipermissible. T h e truth of the master's statements about permissibility - one aspect of their acceptability - depends on the location of the boundary. T h e boundary sliifts in a rule-govcrncd Fva!.. T h e rule is as follows; call it the rult qf'irc~.on?mo~Ii~~ion/i,r per~/lissihiLi/)~. If at tlme I something is said about permissibility by the mastcr to the slave that requires for its truth the pernlissibility or impertnissibilitj- of certain courscs of action, and if just before t the boundary is such as to make the master's statement tilsc, then crteris parikris and within ccrtain limits - the boundary shifts at 2 so as to nlakc the master's statement true.

164 David Lewis Again, this is not a very satisfactory formulation. I-;or onc thing, the li113its and qualifications ;ire lcft unspecified. 13ut more iniportnnt, the rulc as stiitcd does not sal exactly how the boundary is to shift. What if' the master says that some of such-and-such courses of actions arc permissihlc, when none oi'thcn1 were permissible before he spoke. Hy the rule, S(.)IIIC of thcm must str,iightway become permissiblc. Some - but \vIlich oncs? 'I'lie ones that wcr closest t o pcrn~issihilitybeforehand, perhaps. Well and good, but now we have a new problem. At every statc thcrc is not only a boundary bct\vcen tlmu permissiblc and the in~permissible,hut also a relation of comparativc near-pcmlissihility bctwccn the courses of' action on the irnpermissiblc side. Not only do we neecl rules governing the shifting hounrlary, but also we need rules to govern the changing relation of complrrativc near-permissibility. Not only must we say how this rclation evolvcs when tho master says something about absolute l~ern~issibility, but also cvc must say how it evolves when he says something - as he might - ahout comparativc ncar-permissibility. He might saj, for instance, that the most nearly pern~issiblecourses of' action in a class .-1 are those in a subclass A'; or that somc courses of action in class B are more nearly permissible than any in class C. Again the rule is a rule of acco~nmodation.'The relation of comparative near-permissibility changes, if need be, so that what the ni;lstcr siiys to the slave is true. But again, to say that is not enough. It docs not suffice to de~cmmine just what the change is. Those were Examples i and 2 Eyarnplcs of what? 1'11 say shortly; hut first; r digression.

21

Scorekeeping in a Baseball Game At any stage in a well-run baseball game, there is a septuple of numbers h, i, s, h, o ) which I shall call the scorc. of that at that stage. We recite tlie scorc as follons: the visiting team has ri,runs, the ~ O I I I Cteam has t.1, runs, ir is thc hth half ( h being 1 or 2) of the ith inning; there are s strikes, h balls, and o outs. (In anothcr terminology, the score is onl! the initial pair (r,., r,,), but I need a word for the cntirc septuple.) A possiblc codification of the rules of bascball would consist of' rules of' four djflerent sorts.

1

2

3

Spe~.$~.a/ions~ J ' l h ekine?r~niicsof .s~.or'>,Initially, thc score is ( 0 , 0 , 1, I, 0, 0, 0). Thereafter, if a t time t the seore is s, and if bctnecn timc I and timc I' the p l i ~ ~ c r s behave in manner m, then at time I' the score is s', \\jl~crcs' is dctcrmincd in il certain way by s ai-rcl n l . Sp~c~fijica~ions (,J'~~o.r-rect p l q ~ If . at time I the score is s, and if bctwccn t i ~ ~/ iand c tinlc t' the players behave in manner m, then the pla!;crs have bchar.ecl incorrcctl!;. (Correctness depends on scorc: w,hat is c o ~ ~ r c pla!. c t after t\vo strikes difi'ers from what is correct play afier thrcc.) What is not incorrect play according to thesc ~ L L I C S is correct. Dire~.ltz~~ rfqwiu'ng cot.re~*lpla.)!, All players arc to bchavc, througliout t l ~ cgame, in such a way hat play is correct.

Scorekeeping in a Language Game 165

4 L)il.c~.~izvs f.o1-1l.er~i)1~q .SCOI.C. Players are to strive to make the score evolve in certain directions. Members of the visiting tcam trj- to makc ri,largc and I.,, small, mcmbcrs of the home tcam try to do thc opposite. (Wc could dispense with rules of sorts (2) and (3) by adding an eighth component to the score which, at anv stage of the game, measures the amount of incorscct play up to that stage. Specifications of correct play are then included among the spccific;~tionsof' tlie kincmatics of score, and the directivc requiring correct play bccomcs onc of ~ h c dircctivcs concerning score.) Rulcs of sorts (I) and (2) ilre sometimes called r~olzslitzr~iz~c r/des. They arc said to be akin to definitions, though they do not havc the form of definitions. Rules of sorts (3) and (4) are called ~ I J ~ ( I ' I { / Lru1r.c. II~T~ Tliey are akin to the straightfbl*ward directives "No smoking!" or "Keep left!". Wc could cxplain this more fully, its follows. Specifications of sorts ( I ) and (2) arc not thcmsclves definitions of "score" and "corrcct play". Hut thcg arc consequences of rcasonable definitions. Further, there is a systematic way to construct the clefinitions, given the specifications. Suppose we u~ishto define the sl.ore~.fiinr./io?~: the function from game-stages to septuples of nunibcrs that gives the score at every stage. T h e spccifications of the kinematics of score, taken together, tell us that the score function cvolvcs in such-and-such way. We may then simply define the scorc function as that function which evolves in such-and-such way. If' the kinematics of score are ivcll specified, thcn there is one function, and one only, that evolves in thc proper way; and if so, then rhc score function cvolves in the propcr way if and only if the suggested definition of' it is correct. Once we liavc defined the score function, we h a w thereby dctined the seorc and all its components at any stage. 'Thcre are two outs at a certain stage of a &~rnc,for instance, if anrl only if the score fi~nctionassigns to that game-stage a scptt~yleivhosc seventh component is the number 2. Turn next to the specifications of correct play. Taken together, they tcll 11s that correct play occurs at a game-stage if and onlj- if thc players' bchavior at that stage bears such-and-such relation to score at that stage. This has the form of an csplicit definition of correct play in terms of current behavior. If current scorc has already bccn defined in terms of the history of t l ~ cplayess' behavior up to no\\', in the \vilj! just suggestcd, then vve have defined correct play in tcrms of cu~.rcl~t itnd pre~:iousbehavior. Once scorc and correct play are defi~icdin terms of tlie players' behavior, then wc ma!: eliminate rlie dcfined terms in the directive requiring corrcct plav and the directives colicerning score. Thanks to the definitions constructed from the constitutive rules, the regulative rules become simply directiws to strive to scc to it that one's present behavior bears a ccrtain rather complicated rclation to tlie history of' thc players' behavior in previous stages of the gamc. A player might attenipt to confi~rni to such a directive fol- various reasons: contractual obligation, perhaps, or a convcntional understanding with his fellow players based on their common interest in enjoying a propcr game. The rules of baseball could in principle be formulated as straightforward dirccli~cs concerning behavior, without thc aid of definable terms for scorc and its components. Or thcy could be formulated as explicit definitions of thc score f~~nction, rhc com1)onents of score, and corrcct play, fi)llowcd by directives in which the ncwly dctit~cclterms

166 David Lewis appear. It is easy to see why neither of these n~ethodsof formulation has found Gvor. T h e first method ~vouldpack the entire rulebook into each dircctivc; the second would ~ ~ a cthe l i entire rulchooli into a single preliminary explicit definition. Understandably a\-crse to very long sentences, we do better to proceed in our more dcvious way. T h e w is an alternative analysis the baseball cquivalcnt of operationalism or lcgal realism. 1nste:ld of iippe;~lingto constitutive rules, wc might instead claim that tlic score is, by definition, whatcver some scorcboard says it is. Which scoseboasd Various answers arc clefcnsible: maybe the visible scoreboard with its arrays of light bulbs, ma!,hc thc invisible scoreboxd in the head umpire's head, maybe the n1atiy scoreboards in many heads to the extent that they ng-rec. No mattcr. 0 1 1 any such view, the specifications of the kincnlatics of score have a changed status. No longcr are thcy constitutive rules akin to definitions. Rathcr, they are enipirical genel.alizations, subjcct to exceptions, about thc ways in which the players' behavior tends to cause chnngcs on tlic ai~thoritativescoreboard. Uncler this analysis, it is impossible that this scoreboard fails to givc thc score. What is possible is that the score i s in an abnornial and undesired relation to its causes, for ~vlzichsomeone may perhaps be blamed. 1do not care to say which analysis is right for baseball as it is act~~i~ll!/ played. IJcrhaps the question has no detcl-minrlte answer, or perhaps it has different answers for formal and informal bi~schall.I only wish to distingi~ishthe two altel-nativcs, noting that both ;Ire livc options. -

This ends the digression. Now 1 want to proposc some general theses about language theses that were eseniplified by Luamplcs 1 and 2, ancl that \ \ r i l l bc exemplified also by several other examples.

Conversational Score With any stage in n well-run conversation, or othcr process of linguistic interaction, there arc associated many things analogous to thc componcnts of a hascball score. I shall therefore speak of them collectively as thc s1.ol.e of that conversation at that stage. 'The points of analogy are as follo\vs.

1 Like thc components of a bascball score, the components of a conversational scorc at a given stage are abstract entities. They may not be numbers, but they are other set-theoretic constructs: sets of presupposed propositions, I~oundaricsbctwcen perniissible and inipermissible courses of action, or the like. 2 What pla!- is correct depends on the score. Sentences depend for their truth value, or for their acceptability in other respects, on the components of conversational score at the stage of conversation when they are uttered. Not only aspects of acceptabilitv of an uttel-ed sentence may depend on scorc. So ma! othcr semantic properties that play a role in dctcrmining aspects of acceptability. For instance, the constituents of an uttered sentence - subsentcnces, names, prcdicates, etc. - - nlay dcpcnd on the score for their intension or extension. . arc rules that spccify thc 3 Score cvolvcs in a more-or-less rule-govcrned ~ ; a yThere kinematics of score:

Scorekeeping in a Language Game 167

If a t time r the conversational score is s, and if between tirnc r and tiinc I' t l ~ ccoursc of conversation is i., then at time r' the scorc is s f , where st is c\cterinincd in a certain wily bg s and i.. Or at least: . . . thcn at time I' thc scorc is soinc ~llcmberof the class S of possible scores, ~vhcrc

S is determined in a ccrtain cvay by s and

I..

4 The conversationalists may confol.n~to directives, or may simpll; clcsirc, that the! strive to steer certain components of the conversational score in certain directions. Their efforts ma!. bc cooperative, as when all participants in a discussion try to incrcase the amount that all of them willingly presuppose. Or thcre may be conflict, as when each of t ~ v odebaters tries to get his opponent to grant him to join with him in presupposing - parts of his case, and to give away parts of the contrary case. To the extent that conversational score is determined, givcn thc history of thc convcrsation and the rulcs that specifj~its kinematics, rliesc rules can bc rcgasdcd as constituti\:e rules akin to definitions. Again, constitutive rulcs could be traded in fi)r explicit definitions: the conversational score function could be defined as that Function from co~lvcrsation-stages to n-tuples of suitable entitics that evolves in the specified way. -

5

Altcrnati\~cly,conversational score might be operationally defined in tcrms of mental scoreboards - some suitablc attitudes - of the parties to the conversation. T h e rulcs specif!ring the kinematics of conversational score then bccomc empirical generalizations, subject to exceptions, about the causal dependence of what the scorcboarcls registcs on the history of the conversation. In the case of baseball score, either approach to thc definition oE scorc and the status of the rules seems ~atisf~ictory. In the case of conversational score, on the other hand, both approaches seem to meet with difficulties. If, as scems likely, the rules specifying the kiilematics of conversational score are seriously incomplete, thcn often there m a - be man!. candidates for the score function, different but all evolving in the specified wily. Rut also it sccms difficult to say, without risk of circularity, what arc the nlcntal representations that con~prisethe conversationalists' scoreboards. It may be best to adopt a third approach - a middle n7aq, drawing on both the alternatives prcviouslj- considel-ed. Conversational score is, hy tlefinition, n.batcvcr the mental scoreboards say it is; but mTcrefrain fi-om trying to say just \\,hat the collvcrsiltionalists' nlc~italscoreboards are. We assume that some or other mental reprcscntations are present that play thc role of a scoreboarcl, in the Following sense: \\-hat they register depends on the history of the con1:ersation in the w q that score should according to the rulcs. T h c rules specifying the kinenlatics of score thereby specify the rolc of a scoreboard; the scoreboard is whatever best fills this rolc; and the scorc is whatever this scorcboard registers. T h e rules specifying the kinematics of scorc arc t-o some extent constitutive, but on this third approach they cnter only in a roundabout way into the definition of score. It is no harm if they undcrtletermine the evolution of score, and it is possiblc that score sometimes evolves in a way that violates tlic rules.

168 David Lewis

Rules of Accommodation Thcrc is one big difference between baseball scorc and c ~ ~ ~ v c r ~ i ~scorc. t i o ~ iSupposc al the batter walks to first base after only three balls. His behavior woulcl be correct play if there were four balls rathcr than three. 'That's just too bad his bd~aviordocs not at all , nlakc it the case that there NIX' foul- balls and his behavior IS correct. Baseball has no rule of accommodation to the effect that if a h i ~ r t hbill1 is requircd to makc correct the play that occurs, then that very fact suffices to change the score so that straightway t11a.e ilre four balls. Language games ilre different. As I hope my cxa~npleswill show, conversational , scorc does tend to evolve in such a way as is required in order to makc whatever occurs count as correct play. Granted, that is not invariable but only a tendency. Granted also, convel-si~tionalscorc changes for other reasons as well. (As when something conspicuous happens at the scene of a conversation, and straightwaj- it is presupposed that it hay yened.) Still, I suggest that many components of con\iersational scorc obey rules of accommodation, and that these rulcs figure prominently anlong the rulcs govcr~liiigthe kinenlatics of conversational scorc. Recall our cxaniplcs. Example 1: presupposition evolves according to a rulc of acconlmodation specifying that any presuppositions that ilre required by wl~iitis said straightway come into existence, proviclcd that nobody objects. Esamplc 2: permissibility evolves according to a rulc of acconlmodation specifying that thc houndarics of the permissible range of conduct shift to make true whatever is said about them, provided that what is said is said by t l ~ cmaster to the slavc, and provided that thcre does cxist some shift that would make what he says true. I-Icre is a general s d ~ e m cfor rules of accommodation for conversational score. -

If at time t something is said that requires component s,, of convcrsatiolial score to liavc a value in the range 1. if what is said is to be true, or otherwise acceptable; and if's,, does not have a value in the range r just before 1; and if such-and-such further conditions hold; then at t the score-coinponcnt J-,,takes sonlc value in the range r. Oncc we have this scheme in mind, I think \trc will find man; instances of it. In the rest of this paper I shall consider some further examples. I shall have little that is new to silv about the individual examples. My interest is in the common pattern that they exhibit.

Example 3: Definite ~escriptions~ It is not true that a definite description "the F" denotes .r if ;ind only if .I' is the one and only F i n existence. Neither is it true that "the F" dcnotcs .v if and only if .r is the one and only F in somc contestui~llydetermined domain o f discourse. For consider tliis sentence: "The pig is grunting, but the pig with floppy ears is not grunting" (1,cwis). And this: "l'he dog got in a fight with anothcr dog" (McCawley). T11cy could he true. But for them to be true, "the pig" or "the dog'' must denote one o f t\vo pigs or dogs, both of which belong to the domain of discourse.

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Scorekeeping in a Language Game 169

The proper treatment of descriptions must be more like this: "the P" dcnotcs .v if and only if .v is the most salient I: in the domain of discourse, according to sonic contextually determined salience ranking. The first of our two sentences means that the most salient pig is grunting but the most salient pig with floppy ears is not. l'lic second means that the niost salient dog got in a fight with some less salient dog. (I shall pass over some con~plications.Never mind what happens if two 1"s are tied for maximum saliencc, or if no /: is at all salient. h#loreimportant, I shall ignorc the possibility that something nliglit he liighly salient in one of its guises, but lcss salient in another. Possibly we really necd to appeal to a salience ranking not of individuals but rather of individuals-in-guises - that is, of individual concepts.) There are various w-ays for something to gain salience. Somc have to do with thc course of conversation, othel+sdo not. Imagine yourself with me as I write these ~ ~ o r c l s . In the room is a cat, Bruce, who has been making himself very salient by dashing madly about. He is thc only cat in the room, or in sight, or in earshot. I start to sycab to you: Tlic cat is in the carton. 'l'he cat will never meet our other cat, because our othcr cat lives in New Zealand. Our New Zealand cat lives with the Cresswells. And tlierc hc'll stay. because -Miriam would be sad if the cat went away.

,41 first, "the cat" denotes Bruce, he being the most salient cat for reasons having nothing to do with the course of conversation. If I want to talk ahout Albert, our New Zealand cat, 1 have to say "our other cat" or "our New Zealand cat". Ilut as 1 talk morc and more about Albert, and not any more about Bruce, 1 raise Albert's salience by uonversationnl means. Finally, in the last sentence of nly monologue, I am in a position to say "tlie cat" and thereby denote not Bruce but rather tlie ncwly-most-salient cat Albcrt. , 1 he ranking of comparative salience, I take it, is another component of conversational score. Denotation of definite descriptions is score-dependent. Hence so is the truth of sentences containing such descriptions, which is one aspect of the acceptability of those scntcnces. Other aspects of acceptability in turn are score-depcndent: 11011triviality, for one, and possibility of warranted assertion, for anothcr. One rule, among others, that governs the kinematics of salience is a rule of accommodation. Suppose my monologue has left Albcrt more salient than Brucc; but thc nest thing I say is "The cat is going to pounce on you!" If Albert remains niost sillicnt ancl '&thecat" denotes the most salient cat, then what 1 say is patently false: Albcrt cannot pounce all the way from New Zealand to Princeton. What 1 have said requires for its acceptability that "tlic cat" denote Bruce, and hence that Bruce be once again more salient than Albert. If what 1 say requires that, then straightway it is so. By saying whi-lt 1 did, I have made Bruce more salient than Albcrt. If nest 1 say "T11e cat prefers moist food", that is true if Bruce prcfcrs moist food, even if Albcrt doesn't. T h e same thing would havc happened if instead I had said "The cat is out o f t h e carton" or "'l'he cat has gone upstairs". Again what I say is unacccytablc unless thc salience ranking shifts so that Bruce riscs above Albert, and hence so that "tlie cat" again denotes Bruce. T h e differencc is in the type of unacceptability that would cnsuc without the shift. It is trivially true, hence not worth saying, that Albcrt is out of the carton. ("The carton" dcnotes the same carton as before; nothing has bccn done to

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170 David Lewis raise the saliencc of any carton in New Zealand.) It may be truc or it may he Ealse t l ~ a t Albert has gone upstairs in the Cresswells' house in New Zealand. Hut I havc no way of knowing, so 1 have no business saying that hc has. We can formulate a rule qf accomnzo~i?~ition .fir c-ot?zprir~~tizl~ si~licnremore or lcss as follows. It is best to speak simply of unacceptability, since it may well be that thc three sorts of unacceptability I have mentioned are not the only sorts that can give risc to a shift in salience. If at time t something is said that requires, if it is to be acceptable, that ,z. bc morc salient thanjl; and if, just hefore t, x is no more salient thail.)~;than - - reteri.~parihus and within certain limits - at r, ,r becomes more salient than .)I. Although a rule of accommodation, such as this one, states that shifts of score take placc when they arc needed to preserve acceptability, we may note that the preservation is imperfect. It is not good conversational practice to rely too heavily on rules of accommodation. T h e monologue just cot~sidercdillustrates this. Because "the cat" denotes first Bruce, then Albert, then Bruce again, what 1 say is to some extent confusing and hard to follow. But even if my nlonologue is not perfectly acccptable, its flaws arc much less serious than the flaws that are averted by shifts of saliencc in accordance with our rule of accommodation. Confusing shifts of salicnce and reference are not as bad as falsity, trivial truth, or unwarranted assertion. (It is worth mcntioning another way to shift comparative salience by eonve~.sational means. 1 may say "A cat is on the lawn" under circumstailces in whieh it is apparent to all parties to the convcrsation that there is some one particular cat that is responsible for the truth of what I say, and for my saying it. Perhaps I am looking out the window, and you rightly presume that I said what 1 did because I saw a cat; and furthcr (since I spoke in the singular) tllat I saw only one. What 1 said was an existential quiuntification; hence, strictly speaking, it involves no reference to any particular cat. Nevcrtheless it raiscs the salience of the cat that n u d e me say it. Hence this newly-most-salient cat may be denoted by brief definite descriptions, or h p pronouns, in subsecluent dialogue: "No, it's on the sidewalk." "Has Bruce noticed the cat?" As illustrated, this may happen cven if the spealier contradicts my initial existential statcmcnt. Thus although indefinite descriptions - that is, idioms of existential quantification - arc not thcmselvcs referring expressions, they may raise the salience of particular individuals in such a way as to pave the way for referring- expressions that folloiv.)

Example 4: Coming and ~ o i n g ~ Coming is a movement toward a point of reference. Going is moveillent away from it. Sometimes the point of reference is fixed bj- thc location of speaker and hearer, at thc time of conversation or the time under discussion. Rut soinetimcs not. In third-person narrative, whether fi~ctor fiction, the chosen point of refercncc may have nothing to do with the speaker's or the hearer's location. One way to fix the point of reference at the beginning of a narrative, or to shift it later, is by means of a sentence that describes the direction of somc movement both

Scorekeeping in a Language Game 171

I

wit11 respect to the point of referencc and in some othcr waj . "The beggars arc coming to town" requires for its acceptability, and perhaps even for its truth, that the point of retkrence be in town. Else the beggars' townward movement is not properly called "coming". This sentence can be used to fix or to shift the point of reference. W hcn it is said, straightway the point of reference is in town where it is required to he. 'Thereafter, unless something is done to shift it elsewhere, coming is movement toward town and going is movement away. If later we are told that when the soldiers came the bcggars went, we know who ended up in town and who did not. T h u s the point of reference in narrative is a component of conversational scorc, governed by a rule of accommodation. Note that the rule must provide for two sorts of changes. T h e point of reference may simply go from one place to another, as is recluired by the following text: When the beggars came to town, the rich folk went to the shore. But soon the bcggars canlc after them, so they went home. But also the point of referencc is usually not fully determinate in its location. It may become more or less determinate, as is required by the following:

1

After the beggars came to town, they held a meeting. All of them came to the square. Afterwards t l ~ c ywent to another part of town.

II

T h e first sentence puts the point of reference in town, but not in any determinate part of town. T h e second sentence increases its deterininacy by putting it in the square. T h e initial fixing of the point of reference is likewise an increase in determinacy .- the point of reference starts out completely indeterminate and becomes at least somewhat more definitely located.

,

I I I

Example 5: vagueness5 If Fred is a borderline case of baldness, the sentence "Fred is bald" may have 110 determinate truth value. Whether it is true depends on where you draw the line. Rclativc to some perfectly reasonable ways of dratving a precise boundary between bald and notbald, the sentence is true. Relative to other delineations, no less reasonable, it is fl~lse. Nothing in our use of language makes one of these delineations right and all the others wrong. We cannot pick a delineation once and for all (not if ure are interested in ordinary language), but must consider the entire range of reasonable delineations. If a sentence is true over the entire range, true no matter how we the line, surely we are entitled to treat it simply as true. But also we treat a sentence more or less as if it is simply true, if it is true over a large enough part of the range of delineations of its vagueness. (For short: if it is true ~nolcgk.)If a sentence is true enough (according to our beliefs) we are willing to assert it, assent to it without qualification, file it away among our stocks of beliefs, and so forth. Mostly we do not get into any troublc this way. (But sometimes we do, as witness the paradoxes that arise hccausc r-l-11111preserving reasoning does not always preserve the property of being true cnougli.)

172 David Lewis When is a sentence true enough? Which are the "large enough" parts of thc range of delineations of its vagueness? This is itself a vague matter. More important for our present purposes, it is something that depends on context. What is true cnougl~on one occasion is not true enough on another. 'The standards of precision in fbrcc are different from one conversation to another, and may change in the course of a single conversation. Austin's "France is hexagonal" is a good example of a sentence that is true enough for many contexts, but not truc enough for many others. Under low standards of precision it is acceptable. Raise the standards and it loses its acceptability. Taking standards of precision as a component of con\-crsational score, we once more find a rule of accommodation at work. One way to change the standards is to say something that would be unacceptable if the standards remained unchanged. If yo^^ say "Italy is boot-shaped" and get anrag with it, low standards arc rcquircd and the standards fall if need be; thereafter "France is hexagonal" is true enough. nut if you deny that ltaly is boot-shaped, pointing out the differences, cvhat you have said rcq~~ircs high standards under which "France is hexagonal" is fils fro111 truc enough. I take it that the rule of accommodation can go both ways. Hut for some reason raising of standards goes more smoothly than lowering. If the standards have heell high, and son~ethingis said that is true enough only under lowered standards, and nobody objects, then indeed the standards arc shifted down. Hut what is said, although true enough under the lowered standards, may still seem imperfectly acceptable. Raising of standards, on the other hand, manages to seem commendable cvcn when we know that it interferes with our conversational purpose. Because of this asymmetry, a playcr of language games who is so inclined may get amray with it if he tries to raisc thc standards of precision as high as possible so high, perhaps, that no inaterial object whatever is hexagoi~al. Peter Unger has argued that hardly anything is flat. Take something you claim is flat; he will find something else and gct you to agree that it is even flattcr. You think the pavcment is flat - but how can you deny that your dcsk is flatter? 13ut "flat'' is iln n/?so/l,lte term: it is inconsistent to say that something is flatter than something that is flat. Having a g ~ e e dthat your desk is flatter than the pavement, you must concede that the pavement is not flat after all. Perhaps you now claim that your dcsk is flat; but doubtless Unger can think of something that you will agree is even flattcr than your desk. And so it goes. Some might dispute Ungcr's premise that "flat" is an absolute term; but 011 that score it seems to me that Unger is right. What he says is inconsistent docs indeed sound that wa!. 1 take this to ~ n c a nthat on no delineation of the correlative vagueness of "flattcr" and "flat" is it true that something is flattcr than soinething that is flat. l'he right response to Unger, I suggest, is t l ~ a the is changing the score o11 you. When he savs that the desk is flatter than the pavement, what he says is acceptable only under raised standards of precision. Under the original standards the bumps on the pavement were too small to be relevant either to the question \vhethel- the pavclncnt is flat or to the question whether the pavement is flatter than the desk. Since what he silys requires raised standards, the standards accommodatingl!~ rise. T h e n it is no longcr true enough that the p;l\Iement is flat. That docs not alter tllc f3ct that it I))(IS true enough in its nrigitlnl corrtc.a/. "The desk is flatter than the pavement" said undcr raisecl standards does not contradict "Thc pavement is flat" said under unraised standards, -

Scorekeeping in a Language Game 173 any more than "It is morning" said in the morning contradicts "lt is afternoon" said in the afternoon. Nor has Ungcr shown in any way that the new context is morc Icgitilnatc than the old one. H e can indccd create an unusual context in which hardly anjthing can acceptably be called "flat", but hc has not thereby cast any discredit on the morc usual contexts in which lou7er standards of precision are in force. In parallel fashion C'nger observes, I think correctly, that "certain" is an absolute term; from this he argues that hardly el7er is anyone cestain of anything. A parillld response is in order. Indeed thc rulc of accon~modationpermits Lnger to crcatc a context in which all that he says is true, but that does not show that there is anything w-hate\rcr wrong with the claims to certainty that we make in more ordinary contexts. It is no fault in a context that wc can move out of it.

Example 6: Relative ~ o d a l i t y ~ The "can" and "must" of ordinary languagc do not often express absolute ("logical" 01"metaphysical") possibility. Usually thcy cxpress various relative modalities. Not 1111 the possibilities there arc cnter into considcration. If we ignore thosc possibilities tliat violate laws of nature, we get the physical modalities; if nrc ignore those that are known not to obtain, wc get the episteniic niodali~ies;if wc ignore those that ought not to obtain doubtless including actuality we get the dcontic modalities; and so on. That suggests that "can" and "must" are ambiguous. Rut on that hypothesis, as Kratzcr has convincingly argued, thc alleged senses arc altogether too numerous. We do better to think of our modal verbs as unanlbiguous but relative. Sometimes thc relativity is nladc explicit. Modifying phrases likc "in view of what is known0 or "in view of \\;hat custonl requries" may be present to indicate just which possibilities should be ignored. But sometimes no such phrasc is present. Then contcxt must be our guide. 'l'he boundary between the rclevant possibilitics and the ignored oiics (formally, the acccssibility relation) is a component of conversational score, u-hich cntcrs into the tr~lth contlitions of sentences with "can" or "must" or other n~odalverbs. It niay change in the coursc of conversation. A modifying phrase "in view of such-and-such" docs not only affcct the sentence in which it appears, but also rcmains in force until filrthcr notice to govcrn the interpretation of modal verbs in suhscqucnt sentences. This boundary may also shift in aceordancc with a rule of accon~niodation.Suppose I am talking \11ith sonlc elected official about the ways he might dcal with an embarrassment. So far, \vc have been ignoring thosc possibilities that \\rould bc political suicide for him. He says: "You see, I must eithcr destroy the evidence or else claim that I did it to stop Communism. What else can I do?" I rudely reply: "'l'l~ere is one other possibility - you can put the public interest first f'or once!" That would bc fillsc if the boundary betwccn relevant and ignored possibilities remained stationary. h.11 it is not kilse in its contcxt, for hitherto ignored possibilities come into considcration and make it true. And the boundary, once shiftcd outward, stays shifted. If lie protests "1 can't do that", he is mistaken. 'T'akc another example. T h c conimonscnsical epistemologist says: "I ~ N O I I Ithc cat is in the carton there he is before my cyes - I just r.al1'1 be wrong about that!" 'I'lic sceptic replies: "You might be the victini of a dccciving demon". Thereby hc brings -

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174 David Lewis into consideration possibilities hitherto ignored, clse what he says would bc hlsc. The boundary shifts o~ltwardso that what he says is true. Once the boundary is shifted, the conlrnonsensical epistemologist must concede defeat. And yet he was not in any way wrong when he laid claim to infillible knowledge. Millat he said was truc with respect to the scorc as it then was. We get the impression that the sceptic, or the rude critic of the elected official, has the last word. Again this is because the rule of accommodation is not f'~111yreversible. For some reason, I know not what, the boundar?. readily shifts outward if' what is said requires it, but does not so readily shift inward if what is said requircs that. 13ccause of this asymmetry, we may think that what is true with respect to the out~\ritrd-shiftcd boundary must be somehow more true than what is true with respect to thc original boundary. I see no reason to respect this impression. I .ct us hope, by all nicitns, that thc advance toward truth is irreversible. That is no reason to think that just any change that rcsists rc\~ersalis an advance toward truth.

Example 7: performatives7 Suppose we are unpersuaded by Austin's conten tion that cliplicit perfi~rmativeshave no truth ~ a l u e Suppose . also that we wish to respect the seeming parallelism of form between a performative like "I I~ereb?name this ship the Grwt~r.alis.~inro St(~/ill" and such non-performative statements as "E'rcd thereby named that ship the Pirs.i~/(vitNison". Then we shall find it natural to treat the ~erformative,like the non-performativc, as a sentence with truth conditions. It is truc, on a givcn occasion of its utterance, if and on14- if the speaker brings it about, by means of that verv utterance, that the i~~dicated ship begins to bear the name "Generalissimo Stalin". If the circumstances arc felicitous, then the speaker does indeed bring it about, by means of his utterance, that the ship begins to bear the name. T h e performativc sentence is therefore truc on any occasion of its felicitous utterance. In Lemmon's phrase, it is a sentence verifiable by its (felicitous) use. When the ship gets its name and the performative is vcrificd b~ its use, mhat happens may be described as a change in conversational scorc governed h y a rule of accommodation. T h e relevant coinponcnt of score is the rcli~tionthat pairs ships with their names. T h e rule of accommodation is roughly as follon~s. If at time t something is said that requires for its truth that ship s bear name 11; and if s does not bear 11 just beforc r ; and if the form and circi~mstailcesof what is said salisf) certain conditions of felicity; then s begins at / to b a r rr. Our performative sentence does indeed require for its truth that the indicated ship bear the name "Gene]-alissimo Stalin" at the time of utterance. Thercforc, when the sentence is felicitously uttered, straightway the ship bears the name. T h e scntencc has other necessary conditions of trutl~:the ship must not h a w bornc the name beforehand, the speaker must bring it ahout that the ship beings to bcar the name, and lie must bring it about by uttering thc sentence. 011 any felicitous occasion of utterance, these further conditions take care of theniselvcs. Our rule of accommodation

Scorekeeping in a Language Game 175

is enough to explain why the sentence is verified by its felicitous use, despite the fact that the rule deals only with part of what it takes to make thc sentencc true. A similar treatment could be given of many other l~erhrmatives.In some cases tlic proposal may seem surprising. "VC'ith this ring T. thee u-ed" is vcrifjed by its fclici~.ous use, since the marriage relation is a con~ponentof convc~.sationalscore govcl.necl h!. ;I rulc of acconimodation. Is nrarriage then a Iiirgzlistil. phenomenon? Of course not, birt that was not implied. T h e lesson of performativcs, on an! theory, is thi~tuse of language blends into other social practices. We should not assume that a change of conversational score lras its impact o n l j within, or by way of; the rcalm of language. Indeed, we havc already seen another counterexample: the cilsc of' 1~er111issibilit!., considered as Example 2.

Example 8: Planning

I

S u p ~ o s cthat !;OU iind T. are making a plan let us sa!., a plan to steal sonic plutoni~~nr from a reprocessing plant and make a bomb of it. As I\-c talk, our plan cvolves. I~lostl?;it grows more and more complete. Sometimes, however, parts that had been definite are revised, or at least opelrcd for reconsideration. hfuc11 as some things said in ordinar! conversation require suitablc presuppositions, so some things wc say in the course of our planning requisc, fbl-their acoeptabili~y,that the plan contain suitable provisions. If I sag "'l'lren you drive the getaway car up to lhc side gate", that is acccptable only if the plan includes provision fix a getaway car. 'I'hat might or might not havc been part of the plan already. If not, it may beconrc part of thc plan just because it is required by what I said. (-4s usual the process is rlefeasihlc. Yo11 can liecp the getaaay car out of the plan, fbr thc time being at least, by saying "Woilldn't we do better with mopeds?") 'I'he plan is :I c o n ~ y o n e of ~ ~conkcrsational t score. T h e rules governing its evol~~rion parallel thc rules governing the kincnriltics of' psesupposition, and they include a rulc of accon~modation. So good is the ~>arallelbetween plan a n d presuyrposition that we might well ask if our plan simply is part of what we presuppose. Call it tlrat if you like, but there is a distinction to he made. We might take for granted, or purport to take for granted, that our plan tvill be carried out. Tlren we would both plan and presuppose that wc are going to stcal tllc plutonium, Hut we might not. UTemight be malting our plan not in order to casr! it o u ~ , but rather in order to show that the plant needs better security. Then plan and prcsupposition might well conflict. W e plan to steal the plutonium, all the while presupposing that wc will not. And indeed our planning ma!: be intel-spersed wit11 comnrentnr! that requires presi~ppositionscoirtradicting the plan. "Then 1'11 shoot the guard (l'm glad 1 won't reall! do that) while you sn~nshthe Iloodlights." U n less we distinguislr plan Li.om presupposition (or distinguish two levels of presuppositio~~) \vc 111ust tlrink of presuppositions as constantly disappearing and reappearing throughout si~cha convcrs;ltion, T11c distinction betit-een plan and presupposition is not the distinction between wl~at we pu~aportto take fbr granted and what \ye really do. While planning that wc \vill stcal the plutoniun~urd presupposing that we will not, tve might take for granted 11cithc.1. that we ~ v i l lnor that \\re won't. Each of us might sccretly hope to recruit the other to 1hc terrorist cause and carr! out the plan after all.

176 David Lewis One and the same scntencc may require, and if need bc creatc, both provisions of he plan and presuppositions. "Then you drive thc getaway car up to the side gate" requires both a getaway car and a side gate. Thc car is planned for. l'hc gatc is more li kcly presupposed.

Notes I am doubly gateful to Robert Stalnakcr: first, for his treatment of presupposition, here sumiiiarizcd as lixamplc 1, n~hicllI have taken as the prototype for pari~lleltreatments of other topics; anel second, for valunblc conlmcnts on a previous version of this paper. I an) ~ l s much o inclcbtcd to Stephen Imrd, who discusses many ol'thc plienomenit that I consider here in his "(:hanging the C'ontcxt" in Erlrvard I,. Kcennn, ed., J'or1~1irlS r t t ~ i ~ r ~c!f!\'crtnral tils L ~ I Z , ~ I (C:;unbriclgc I(/SP Univcrsit! I'rcss, 1974). Proposals along sonien~hatthe same lines as ]nine are to be found in 'Thomas T. Hallmcr. "Iinfulirung uncl Kontrolle yon Diskursu~clten", in Dieter Wunderlich, etl., L~i~q~risrI.~t~/rr~ Pru,q~trc~/rX~ (Atl~cnai~mVerlag, 1972), and Hallnier, Log.I"~i/ C > I . L I ~ I I~P ~I /I/ I~SI~~L:' I . IC( IoIt ~ s I ( / ~ ~ r ~1!/'TofiII:~ / / i o t ~ iil Corl/e'~'/(J/ilnge (North-I Iollancl, 1978). ,411 early vcrsioii ol'this paper was presented to the Vacation School in L,ogic ,lt Victoria Uni~,crsity of b'cllington in ,August 1976; I thank the New Zealand-United States I
I

2 3

1

S

6

This trcatiilent of presupposition is taken from two papers of Rohe1.t Stalnahcr: "Prcsupp~aitions", .$t~rrntrlof Plrilnsopl~i~~al Logic 2 (1973), 447-457, and "I'ragma~ic Presuppositions", in Milton K, nlul~itzand Peter K. Ungw, cds., .S~?rratl/rtstint/ Plrilosoplr,)~(Nett York University Prcss, 1974). This treatment of pcrinissibility is discussed more fully in rn) paper " 9 I'roblcm abour Pcmission", in Esa Saarincn L'I ril., cds., ESS(I,)~S 111 I ~ O I I ~c!/'.7(1akX.11 ) I I I ~ I - I I I I I I X ~(licidcl). ~~I Definite descriptions govcrilcd hy salience are discusseel in ni!- C O I I I I / ~ I : / ~(I3lacl\xvcll, / ~ ~ I I I ~ I 1973), /S 1'1). 11 1-117; and in Jalncs McC;awlcy, "Prcsuppositinn uncl r)iscoursc Structure", in Ilnvitl Dinncen and Choon-K!-u Oh, eds., Syizlu.\. trncl .S'c.ltziln/irs, Vol. I I (12a1tlcmic Prcss, 1979). A similar treatment of clcmonstratives is Lhund in Isard, op. c i / . blatifrecl Pinkal, "How to Rcfcr r~it1-1 Vague Descriptions" (prcscntcd i1r the Konst:lnz cellocluiu~non semantics, September 1958) notes a Fiirthcr co~nplication:if some Iiighl! si~licntthings are borderline cases of F-hood, Jcgree of F-hood ancl sulicncc ma! t ~ d off. c Inclctinitc cicsc~.iptionsthat pave the wa! for referring csprcssions arc diccusscd in Charlcs (:liastaiii, "Rcfercncc ancl Context", .&finneso~u. S I ~ I ~111/ ~I L~~Plr~/osr~pl~,j~ PS ?/'Srrisrrr.c7 (1975), 104269, and in Saul Kripkc, "Spcakcr's Rcfercnce and Scmantic Rcfcrcncc", .113101/1~~.v/. S / I I L / inI ~ ~ S /'lrilosoph)l 2 (1077), 255-276. Sec Charles Fillmore, "I Ion- to Know i'1'herllcr You're C:on~ingor Going", in I;;lrl I I!lclg;urdJcnsen, ctl., Lrtrgr~is/iX,1971 (Atheniiuni-Vcrliq, 1072), ancl "Pragmatics ; ~ n dthe 1)cscription of Discourse", in Siegfried J. Schmiclt, cd., P ~ - ~ ~ , ~ / r z ~ / i k / / ' t ./~I / (\l'ilhclni ~ ~ ~ / c / / / Finh i . . v \'crl,lg, 1070). Scc the trcatmcnt ol' vagueness in m! "Cicncral Scm:lntics", . S ) ~ n ~ l r ~22~ s(15)70), c IS 07. For arguments that hardly anything is flat or certain, scc Pctcl- Ungcr, ~ / / o r o ~ (0xIi)rcl / c . ~ ~ L~~~\'crsity Prcsl;, 10'7.5). pp. 6-5-68. For another es;lmplc of acconiniodatinp shifts in rccolution of vagilcncss, sec the cliscussion of bi~ch-trilcking counterfi~ctu;llsin m!. " C : ~ u ~ ~ t e r f ' a c Jt ~~~~ip~cl ~ i ~ I cdn(I ncc 'Time's .4rron~", ,Yois 13 (1975)). Scc :Zngcliha Kratzer, "R'hnt 'Must' and 'Can' \;lust ;uid C:;III hiean", / , ~ I I , S I ~ IiS/ i ./ I( /~I'l~I/osctpl~~~ (:V 1 ( 1977), 337-355. T h c accessibility semantics consiclcrecl here is cqui\.alcnl to a slightl? restrictcd form of Kratzer's semantics Tor relati\-c modalit!.

Scorekeeping in a Language Game 177 Knowledge and irrelevant possibilities of error are discussed in .Alvin 1. Goldman, "I )iscrimination and I'erccptual Knowledge", Jorinlnl q/'Pliiiosopl~,)~ 73 (1970), 771-701. 7 Sce J. L. Austin, "P~rforn~ativc Utterances", in his PI~iloso~hic.uI I'rip~rs (Ouforcl L~~ivcrsit! I'rcss, 1961) for thc original discussion of perfi~rmatives.For treatments along thc lincs hcrc prclkrrcd, sce E. J. I,emmon, "On Sentences Vcrifiablc by Thcir Use", .inli/)~srs22 (1902), 80-80; Ingcmar Hedcnius, "Perlh-mati\:es", T/?~wrj~/ 29 (1963), 1-22; and Lcnnart Acl\.ist, I)r.i$/ri~rr~li~les clnr/ I >rz/iabilitj, 191 //re C.'sr I!f ' Lrr~igita~ye (Filosofiskil Studier, Uypsala Univcrsit! , 1072). Isard (up. r.il.) S L I ~ ~ C Sas~ IS do that pcrform:ltive utterailccs are akin to otlicr uttcritnces that "ch;uigc thc context".

Adverbs of Quantification David Lewis

Cast of Characters T h e ad\.-erbs I wish to consider fall into six groups of near-synonyms, as follows.

(1) Always, inbariably, universally, without exception (2) Sometimes, occasionally, [once] (3) Never (4) Usually, mostly, generally, almost alwal-s, with few eeccptions, lol-dinarilyl, [normally] ( 5 ) Often, fi-cclucntly, commonly (6) Seldom, infrequently, rarely, almost never Bracketed items differ semantically from their list-mates in here; onlit them if ~ ~ prefer. o u

WLI.;~ J

shall not consider

First Guess: Quantifiers over Times?

It may scem plausible, especially if we stop if,ith the first w'or.cl oil each list, that thcse adverbs functioli as quaiitificrs over times. That is to say that illl~r~)ls, for instancc, is a tnodificr that combines with a sentence F to malie a sentence . - l l ~ , ~ i /: ~ l that s is tl.ue iff the modificd sciitcncc P is true at 2111 timcs. I,ikcnise, wc might gucss that S~IIIIJIIIIIP F, ~VLJZ?CI, I;', C ~ s ~ / a lP, I y Qfirr~? F, and Seldolrr F arc true, respectively, iff /: is true at some times, none, most, many, 01- fell;. But it is easy l o fincl various rcasons w h j this first guess is too simple. First, we may note that the times quantified o\-cr neccl not bc inomcnts of timc. The)- can be suitable stretches of tinle instead. For instance,

( 7 ) T h e fog usually lifts before noon here

Adverbs of Quantification 179 means that the sentence inodified by itsz~ul!)lis true on most days, not at most moments. Indeed, what is it for that sentence to be true at a moment? Second, we may note that thc range of quantification is often restricted. For instance,

(8) Caesar seldom awoke before dawn is not made true by the mere fact that few of all times (past, present, or fi~turc) are timcs when Caesar was even alive, n-llerefore fewer still are times when he awoke before dawn. Rather it means that few of all the times when Caesar aivoke are times before dawn; or perhaps that on few of all the days of his life did hc awake bcforc dawn, Third, we may note that the entitics we are quantifying over, unlike times,' may be distinct although simultaneous. For instance,

(9) Riders on the Thirteenth Avenue line scldom find seats may be true w e n though for 22 hours out of every 24 - all but thc two peak hours when 8604) of the daily riders show up - there are plenty of scats for all.

Second Guess: Quantifiers over Events? It ma!; seem a t this poii~tthat our adverbs arc quantifiers, suitably restricted, over events; and that tiincs enter thc picture only because events occur at times. 'Thus (7) could mean that most of the daily fog-liftings occurred before noon; (8) could mean that few of Caesar's an-akcnings occurred before darvn; ancl (9) could nlean that most riders on thc Thirteenth Avenue line arc seatless. So far, so good; but further clifficulties work both against our first guess and against this alternative. Sornctimes it seeills that mie quantifv not over single events but over enduring states of affairs. For instance,

(10) -4 man who onns a donkey always beats it now and then means that evcry continuing relationship between a man and his donkey is punctuated by beatings; but these continuing relationships, unlike the beatings, are not events in any commonplace sense. Note also that if u ~ J I ~ ~were . ) ~ . sa quantifier orcr times, thc sentence would be inconsistent: it would say that the donliey-beatings are incessant and that they only happen now and then. (This sentence poses other problcms that tvc shall consider later.) We come last to a sweeping objection to both of our first two guesses: the advcrbs of quantification maj- bc used in speaking of abstract cntities that have no lociition in linlc and do not participate in events. For instance,

( I 1) A quadratic equation never has more than two solutions ( 12) A cluaclratic equation usually has two different solutions

180 David Lewis mean, respecti~ely,that no quadratic equation has morc than two solutions and that most - more precisely, all but a set of measure zero under the natural Illcilsure on the set of triples of coefficients - have tm-o diffcrent solutions. These sentences have nothing at all to do with times or events. O r do they? This imagery comes to mind: someone is contcnlplating quadratic equations, one after another, clrawing at random from all the qi~adraticequations there are. Each one takes one unit of time. In no unit of time does he contcillplatc a quadratic equation with more than tnro solutions. In most units of time he contemplates quadratic equations with two different solutions. For all I know, such imagcry nlay sustain the usage illustrated by (1 1) and (12), hut it offers no hope of a serious analysis. Thcre can be no such contemplator. T o be more realistic, call a quadratic equation .si)rzpll* iff each of its coefficients could be specified somchow in lcss than 10,000 pages; then we may be cli~itesure that the only cluaclrntic equations that arc ever contemplated arc sinlplc ones. Yet

(13) Quadratic equations are always simple is fillsc, and in fact they are almost never simple.

Third Guess: Quantifiers over Cases What we can say, safely and with full generality, is that our adverbs of quantification are quantifiers over cases. What holds always, sonietimes, ncvcr, ilsually, often, or seldom is \vhat holds in, respectively, all somc, no, most, many, or few cases. Hut we have gaincd safety by saying next to nothing. What is a case? It seems that somerimes n7ehave a case corresponding to each moment or stretch of time, or to each in some restricted class. But sometimes we have a case for each cvcnt of some sort; or for each continuing relationship between a man and his donkey; or for cach cluadratic equation; or as in the case of this ver} sentence - for cach sentence that contains one of our adverbs of quantification. -

Unselective Quantifiers It will help if we attend to our adverhs of quantification as they can appear in a special dialect: the dialect of mathematicians, linguists, philosophers, and lawyers, in which variables arc used roiltinely to overcome the limitations of more colloquial means of pronon~inalization.Taking m, 12, p as variables over natul-al numbers, and .I+,, ) I , : as variables over persons, consider: (14) (15) (16) (17)

Alwavs, p divides the product of m and 17 only if somc F~ctol-o f p divides 111 and the quotient of p by that factor divides tl S o m e t h c s , p divides the product of m and t~ although p divides neither tn nor w Sometimes it happens that .I+sclls stolen goods to .)I, \vho sclls thcm to 2, who sells them back to .r Usually, .v reminds me of.)! if and only if ~1 reminds me of .x.

Adverbs of Quantification 181 Here it seems that if we ixre quantifying over cases, then \ye must haw a case corresponding to cach admissible assignmcnt of valucs to thc variablcs tllat occur free in the nzodified sentence. T h u s ( I 4) is true iff evcry assignment of natural nurnhcrs i1s valucs of m, w , and p makcs the open sentcnce aftcr LIIII~OIS truc - in other tvo~.ds,iff all triples of natural numbers satisfy that open sentence. Likewise ( 1 -5) is truc iff some triple of natural numbers satisfies the open sentence after som~/jmcs;(10) is truc iff some triple of persons satisfies the open sentence after somrtirrrrs; and (17) is tsue iff most pairs of persons satisfy the open sentence after ~ r . ~ l r u l I y . The ordinary logicians' quantifiers arc selcctivc: 'v'sor 3.v binds thc variablc .s and stops there. Any other variables y, .c, . . . that ma! occur frce in its scope arc left frce, waiting to be bound by other quantifiers. We have the truth conditions: (IS) b'.t-F is true, undcr any admissible assignment J'of values to all variablcs frce in li' except .v, iff for cvery admissible value of .Y, P is true under the assignment of that value to ,v together with the assignment J'of values to the other variablcs free in P; (19) 3,rF is true, undcr any ad~nissibleassignment/'of 1-aluesto all variablcs hce in /: exccpt .I+,iff for some admissible valuc of .r, is true under the assignment of that value to x together with the assignmcntJ'of values to the other 17ariables free in F;

r

and likewise for lhe quantifiers that selcct other variables. It is an entirelj- routine matter to introduce unsc/i.c*tiz~i~ qriartt!fi~i~~:s b' and 3 that bind all the variables in their scope iildiscriminately. Without sclectivit!,, thc truth conditions are much simplel.; with no variablcs left frce, we need not relativizc the truth of thc quantified sentence to an assignment of values to the re~nainingfrcc variables.

(20) V F is true iff F is truc under cvery admissible assig~zmcntof valucs t o all variables fsee in I=; (21) 31: is true iff r is true under some admissible assignment of values to all variables free in F

~,

'These unselcctive quantifiers have not deserved the attention of logicians, 1mrtly because they arc unproblematic and partly bccausc strings of ordinary, sclcctivc quantifiers can do all that they ciln do, and more besides. They ham o n l ~thc adviuitagc of brevity. Still, brevity I:\. an advantage, and it should he no surprise if unsclective quantifiers are used in natural language to p i n that ildvi~ntage.That is ivhat I claim; tllc unselective V and 3 can show up as the adverbs n/nli~ll.s,and soi~/r/irIr~~s.' T,ilic~viscI/t'ilt\., IISULI//~, o f j 1 7 1 2 , and sc/~/ol,m can serve as the unselectil-e analogs of the selective q~iancitiers j i r no .v, fi)r ~ O S .v, I jiv I T I L ~ ?.v,~ ~and ./i)r./i~~l 1 o summarize, what we have it1 the variable-using dialect is roughly as follows. Our adverbs arc quantificrs over cases; a case may be regarded as the 'tuple of its yarticipants; and tlzesc participants are valucs of the variables that occur fiee in the open sentence rnodificd by tlze adverb. In other words, we arc taking the cases to bc thc admissible assignments of' \values to these i*ariables. ~

r

7

3

.

~

182 David Lewis But matters are not quite that simple. In the first place, ive may wish to quantify past our adverbs, as in (22) There is a number y such that, without csccption, the product ot'rlt and rr divitlcs (I only if IJI and 11 both di\-ide q So our ;-ldverbs of quantification are not entire11 unselcctive: they can bind indefinitely many Cree variables in the modified sentence, but some variables the ones used to quantify past the adverbs - remain unbound. In (22), nl and n arc hound by ~ l ~ i l h o ~ l rsl-eprinn; but g is immune, and survives to be houi~dby ~ l l e ~ is e 71ti1~zbrr q S I I L . IIINI, ~ a selective quantifier of larger scope. In the second place, we cannot ignore time altogether in (1 6)-(17) as we can in tlie abstract cases (11)-(15); (16)-(17) are not confined to the present moment, but are gcncral ovcr timc as ivcll as over 'tuples of persons. So \v-c must treat thc moditicd sentence as iC it contained a free time-variable: the truth of the sentence depends on a time-coordinate just as it depends on the \alucs of the pcrson-variables, and ive must takc thc cases to include this time coordim~tteas well as a 'tuple of persons. (Indeed, we could go so far as to posit an explicit time-variablc in underlying structure, in orclcr to subsurne time-dcyendc.ncc under dependence on values of variahlcs.) Our first gucss about the adverbs is revived as a special casc: if the modified scntcncc has no frcc variables, the cases quantified ovcr will i~icludenothing but the timc coorclinatc. As noted before, the appropriate time-coordinates (accompanied by 'tuplcs or not, 21s the case may be) could cithcr be moments of timc or certain stretches of tinic, for insl-ancc days. So~nctinlcsivc might prefer to treat the modified sentence ;IS if it contained an eventvariable (or even posit such a \-ariable in underlying structure) and include an e\-ent-coordinate in thc cases. T h e event-coordinate coulil rcplace the time-coordii~atc, since an event cletermines the time of its occurrence. If so, thcn our sccond guess also is revived as a special case: if tliere are no free variables, the cases might simply be c\eilts. In the tliircl place, not just an? 'tuple of values of tlic frcc variahlcs, plus perhaps a time- or e\ent-coordinate, will be admissible as one of the cases cluantitied over. Various restrictions ma!; be in force, either permancntl!- or temporarily. Sonic standing restrictions in\olve the choice of varial>lcs: it is tlic C L I S ~ ~ I IinI mntliematics that i, is a variable that can takc o1i1\;li~ilit01-dinalsas values (at least in a suitable context). I set up senii-permanent rcstrictions of this Iiind a few paragraphs ago bq writing -

p as variables over natural numbers, and .v, .)I, and z as variables over (2.3) 'Taking ~r-l,~i, persons . . . Other standing rcstrictions rcquir-c the participants in a case t-o be suitabl! related. It'a case is a 'tuple of persons plus a time-coordinate, we n ~ a ytake i t g-cncl-ally that the peiesons niust be alivc at tlie timc to make the case admissible. 01. i f a casc is il "tuplc of persons plus an event-coordinate, it may bc that the persons must take part in the event to malie the case admissible. It may also be requircd that the participants in the 'tuple are all different, so that no two variables receive tlie same 1-alue.(I am no[ sure ivhethcr these restrictions arc always ill force, hut I believe that they often are.)

Adverbs of Quantification 183

Restriction by IfClauses There arc various ways to restrict thc admissible cases tempora~.ily- pcrhal~sonly fillthe duration of a single sentcnce, or perhaps through s e ~ e r a lsentences connected bk anaphoric chains. If-clauses seem to be the most versatile device fbr imposing temporary restrictions. Consider: (24) Always, if .T is a Inan, if.)] is a donkey, and if -x owns ,)I,,T beats , ) I not\- and thcii

A case is hcrc a triple: a value for x, a \raluc fur y,and a time-coordinatc (longish stretches seem called for, perhaps ycars). T h e admissible cascs are tl~osethat satisfy the threc if-clauses. 'That is, the? arc triples of a man, a donkey, and a time such that the man otms the donkey at the time. (Our proposed standing restrictions arc rcdundant. If the man (I\\-ns the donkey at the time, the11 both are alive at the time; if thc participants are a man and a donkc\-, the!- are different.) Then (24) is true iff' thc modified sentcnce (25) ..r. beats

+)I

now and then

is true in all admissible cascs. Liltewise for

(26) Sometimes (27) Usuall! (28) Often (29)

Nca-or (30) Seldom

if .v is a man, if.], is a donliey, and if , ) I now and then a man, if.)! is a donkey, ancl if now and then

.T

owns .)I,,r heats

owns .jf, docs .r

The admissible cascs are the triples that satisf- the if-clauses, and thc sctltcncc: is true iff' the modified sentence (25) - slightly transformed in the negative u s e s (29) ( 3 0 ) - is true in some, most, many, none, or fern7 of the adnlissible cases. It may happen that every free v:~riablcof the modified scntellcc is restricted b y an ifclausc of its own, as in

(31) Lrsually, if -T is a man, i f j , is a donkeq,, and if z is a dog, weighs less than .xbut ,)I

morc than :: But in gencral, it is best to think of the ifrclauscs as restricting whole cases, not particular participants therein. \Vc may have a n y number of if-clauses - including zero, as in (14)-(17). A frce variable of the modified sentence ma? appear in morc than one if-clause. Morc than one 17ariable may appear in the same if-clause. 0 1 - it niay be that no ~ a r i a b l eappears in an if-clause; such if-clauses restrict the admissible cases I>! restricting their time-coordinates (or ycrhaps their event-coordinates), as it1 (32) Oftcn if it is raining nly roof leaks

184 David Lewis (in which thc time-coordinate is all therc is to the case) or (33) Ordinarily if it is raining, if ,r is driving and sees , ) I walking, ancl if.)fis x's fricnd, s offers y a ridc It makes no difference if n-e compress several if-clauses into one by means of conjunction or rclative clauses. T h e three if-clauses in (24) or in (26)-(30) could be replaced by any of:

(34) (35) (36) (37)

if x is a man, is a donkey, and .r owns . ) I . . . if .r is a man and ,y is a donkey owned by "v . . . if s is a mail who owns y , and ,]I is a donkey . . . if x and .y are a man and his donkey . ..

Such compression is always possible, so wrc would not have gone '~r wrong to confine our attention, for simplicity, to the case of restriction by a siilglc if-clause. We have a three-part construction: the adverb of' quantification, the if-clauscs (.~crc~ or morc of them), and the modified sentence. Schematically, for thc case of a single ifclausc:

But could we get the same effect by first combining C and F ~ n t o3 conditional sentence, and then taking this conditional sentence to be the sentence n~oditiedby tllc adverb.? On this suggestion (38) is to bc regrouped as Always Sometjn~es

Scntence (39) is true iff the conditional I/' C, F is true in all, somc, none, most, many, or few of the admissible cases - thnt is, of the cascs that satisfy any permanent rcstrictions, disregarding the tcinpol-ary restrictions imposed by the if-clause. 13111is there any way to interpret thc conditional I/' C, F that nlakcs (30) ecluivalent to (38) for all six groups of our adverbs? No; if the adverl? is U / I I ~ ( L . J I Swe get tllc proper cquivalcnce by interpreting it as the truth-functional conditional (; 3 F , whereas i f the advel-b is somethles or I ~ P S ' C T , that does not w-ork, and we nus st instead intcrprct it as the conjunction F & C. In thc remaining cascs, there is no ndtur'll interlj~-e~ltio~l that wwrks. I conclude that the f o f our restrictive if-clauses should not bc regarded as il sentcntial connectivc. It has no meaning apart ti-om thc adverb i t restricts. T h c f i n

Adverbs of Quantification 185

iflr. . . , . .. ,S O I ? I C E Z ' ~ ~ I L ' S if '. . . , . . . , and the rest is on a par with the non-conncctivc

N/II)~)~s

(lnd in / J P ~ I P P C ~..I . ~ l n d ..., with the non-connecti\:c or in z ~ ~ k e .~..kor~ .r. . , or wi t11 the non-connective (f'in [he prob~chilit)?thaz ... if.. . It serves merely to n ~ r an k ilrgumentplace in a polyadic construction.'

Stylistic Variation Sentences made with the adverbs of quantification need not have the form

liaic considered so far: adverb if-clauses modified sentence. We will tincl it convenient, however, to take that form - somewhat arbitrarily - as canonical, and to regard othcr forms as if they were derived from that canonical fi)rm. Then we are donc with semantics: the intcrpretation of a sentence in canonical fornl carries over to its derivatives. T h e constituents of the sentence may be rearranged:

+

+

we

(40) If s and)! are a man and a donkey and if r owns,)!, x usually beats.)! now and then (41) If .v and JI are a man and a donkey, usually x beats now and then if'.x. owns ,)I (42) If .T and .y arc a Inan and a donkey, usually if r owns y, .r bents .y now and then (43) Usually .v beats-)!now and then, if s and are a man and a donkey and .v o w ~ ~ s , ) ~

1

All of (40)-(43), though clumsy, arc intelligible and well-formed. Our canonical restrictive if-clauses may, in suitable contexts, be rcplacocl by whcnclauses: (44)

When I ~ Iand N are positive integers, thc powcr successive multiplications

nl"

can alhwys 1,c computed by

Indeed, a url~en-clause may sound right when the corresponding if-clause would bc questionable, as in a close relativc of (8): (45) Seldom was it befill-e dawn

{;pen)

Caesal- awoke

Or we may have a where-clause or a participle construction, especially if the scstrictive clause does not come at the beginning of the sentence:

(46) T h e power m",where m and ?I are positive integers, can always be con~yutcdby successive multiplications (47) T h e power m" (m ancl n being posit-ivc integers) can always be computed by successive multiplications il/~alr)lsif - or i s i t L ~ / I PIPI?PFI? ~ ~ S - may bc contracted to nr/zenez*er, a eornplcs ~~nsclective quantifies that cornbil~estwo sentences: (48) Whenever m and n are positive integers, the power successive multiplications

111"

can bc computed by

186 David Lewis

(49) Whenever x is a man, is a donkey, and .z. ou7ns,I!, .r beats (50) Whenescr it rains it pours iihuir)~s

now and then

simpl!; be omitted:

(Always) When it rains, it pours ( 5 2 ) (Always) If .r is a man, 1)is a donkey, and .r owns y, s beats ,I! now and then (-5.3) When WJ and 1.1 are positive integers, the power ltzN can (always) be coniputed by successi~lemultiplications

(51)

Thus ivc reconstruct the so-called "generality interpretation" of free variables: the variables are bound by the omitted clin?l!j~s. Our stylistic variations have so far been rather superficial. We turn ncxt to a much more radical transformation of sentence structure - a transformation that can bring us back from the variable-using- dialect to everyday language.

Displaced restrictive terms Suppose that one of our canonical sentences has a restrictive if-clause of the form

where a is a variable and z is an ii~dcfinitcsingular term formed from a coinmon noun (perhaps plus modifiers) by prefixing thc indefinite article 01- S O N I P . Exaniples: (55) if s is a donkey . . . (56) if s is an old, grcy donkey . .. (57) if x is a donkey owncd by y . . . (58) if s is somc donkcy that ,)I owns. (59) if ,r is something of J'S . .. (60) if .v is someone foolish .. . (Call 7 , \\-hen so used, a ~r.srrii*tkletrnn.) Thcn we can dclcte the if-clause and place the restrictive term .r in apposition to an occurrence of the val-iablc r~ elsewhere in the sentence. This occurrence of may bc in thc lnodified sentence, or in anothcr if-dausc of the form (53),or in an if-clause of sonie other fihrn~.Often, hut not always, the first occurrence ofa outside the deleted if-clause is fiavoured. If z is short, it may go before a; if long, it may be split and go partl! bcfill-e and partly after; and sometimes it may follow a parenthetically. T h e process of displacing restricti~ctcrms may -- but nccd not - be repeated until no if-clauses of the form (54) are left. For instance: (61)

Sometimes, if ,x is some man, if,])is a donlie!, then

+

and if ,s owns,)),.r heats,), now and

Adverbs of Quantification 187 Sometimes if .y is a donkey, and if somc mall .s owns . ) I , .s bcats , ) I not\ and then

*

Sometimes, if somc man .s owns a donkey 51,s beats 3, now and then

(62) Often, if .z. is someone who owns ,y, and i f y is a donkey, ,t. beats,))now and then =+

Often, if's is someone who owns .,I, a donkey, x beats y nowr and then =3

Often, someonc ,r who owns ,,I, a donkey, beats

now and then

Instead of just going into apposition with an occurrence of the ~ariablcr , the restrictive tcrm t maj- replace an occurrence of cx altogether. T h e n all other occurrences of .A. must bc replaced as well, either by pronouns of the appropriate case and gender or b ? terms /hll/ 11 or t k 11, ~ where v is the principal noun in the term t. 170s instance,

(63)

Always, if

is a donkey and if .v is a man who olvns .y, ,r beats

now and then

=+ Alwavs, if .v is a man who owns il donkey, .z. beats i t now and then =+ Aljvays, a man m-ho owns a donkev bcats it now and then NOWit is a small matter to m o w a11~~ct)rs and thereby derive the sentence (10) that \vc considered earlier. Sure enough, the canonical sentence with which the deri~ation( 6 3 ) began has the proper mcaning for (10). It is in this way that we return from thc ~ariable-usingdialect to an abundance of everyday sentences. I concluclc with some further examples.

(64) ,4lways, if gives

.Y

.t. is sonleone foolish, if .y is some good idea, and if ,r has .)I,nobody credit for

=3

rllways, if,)! is some good idea, and if someone foolish has .]I,nobody gives him credit for ,y

=+ Always, if somcone foolish has some good idea, nobody gives him credit for that idea

(65) Often, if 31 is a donkey, if .v is a illail who owns ,)I,and if

kicks .v,

.c'

beats

,)I

=+ Often, if.)! is a donkcy, and if,))kicks a n u n who owns , ) I , he beats =+ Often, if a ctonkcy kicks a man \\rho owns it, l ~ beats e it

(06) Often, if .)I is a donkev. if .v is a man who owns y , and if

kicks ,v, .v bests , ) I

=+ Often, if .t. is a inan who owns a donkc?, and if it kicks .r, .x bcats it =+ Often, if it kicks him, a man who owns a donkey beats it

188 David Lewis

(67) Usually, if x is a man who owns .y and if .y is a donkey that kicks x, .v beats y =+

Usually, if s is a man who owns a donkey that kicks s, .\, bcats it =+ Usually, a man who owns a donkey that kicks him bears it

(68) Usually, if a-is a man who owns

and if31 is a donkey that kicks .v, x beats 11

=+

Usually, if ,)I is a donkey that kicks him, a niaii who owns -11beats

+-

Usually, a inan who owns it beats a donkey that kicks him

Notes 1 Unlike genuine moments or stretches of time, that is. But we may truly say that Miles thc mr hero has been 1t7ounJcd 100 times if he has suffered 100 woundings, cvcn if he has been ~vountled at only 90 distinct niomcnts (or stretches) of time because two of his wo~lndingsucrc simultaneous. c by using 2 It is pleasing to find that liussell often explained thc nou-standard s ~ l e c t i \ ~cluantiliers i o*O, an unselective adwrb of quantification to modify an o p a l sentence. For instance in P r i ~ r i . ~ p 1, \Ire find the first introduction of quantifiers in the formal clevclopn~cnt:"U'c shall denote 'F,:.v . . . We shall dcnotc 'F.Y sornellnrcs' by rhc nokltion (3.t). F.Y." i l l ~ ~ ~ r , )by l . \ .the ' notation ("1,). It is customary to work $5-it11 assignments of valucs ro all ~ariablesin thc language; the part of the 3 assignment that assigns values to uneinploycd variables is idle but harmless. 13ut for us chis otherivise convenicnt practice \\-oulcl he more bother than it is worth. In dcaling with rrsrroll)~, ,!/tea, ancl srldonl we must consider the fraction of value-assignments that satisfy the motlified sentence. Given infinitel!. man!- variables, these fi-actions will be ~ / x(unless ; thcl ;we 0 or 1). We would ileecl to fbctor out differences involving o n l ~thc idle parts of assigr~rncnts. 4 What is the pricc of forcing the restriction-marking !/'to bc a sentential connective after all? Exorbitant: it can be done if(1) we use a third truth I-alue, (2) tve adopt a [;IS-Petcliccl inter~)rctation of the conncctivc j/; and (3) wc impose an additional permanent restriction on the ilcllnissiblc cases. Let I/' C, F have the same t r ~ ~ value t h as F if c' is true, and Ict it bc third-tal~rcdif C is fdse or third-valued. I,et a case be admissible only if it makes the modilictl scntcncc cid~ertrue or flllsc, rathcr than third-~tllued.Then (39) is ctluivalcnt to (38) for all our ;ld~~crhs, 3s dcsircd, at lcast iC we assuinc that C and I: themselves arc not third-ii~lucdin any case. .S, trcatnicnt along sinlilar lines of if-clauses used to rcstrict ortlinary, sclcctivc cluantifiers ma! bc found in nel~lilp(1070).

References Rclnap, N. 1970. C:onditional assertion and restrictcd quantification. 1 1 ; u ~4: s I - 12. Russell, B. and A. N. Whitehead. 1912. Prirri.ipii~/i.Clulhcnlalil.n, vol. 1 . 1,ondon: C;ambridgc University Press.

A Theory of Truth and Semantic Representation Hans Kamp

1 Introduction Two conceptions of meaning have dominated formal semantics of natul-al 1itnguag.c. The first of these sees meaning principally as that which determines conditions of' truth. This notion, whose advocates are found mostly among philosophers and logicians, has inspired the disciplines of truth-theoretic and model-theoretic semantics. According to the second conception meaning is, first and foremost, that which a language user grasps when he understands rhe words l ~ ehcars or reads. This second coi~ccptionis implicit in man\; studies by computer scientists (especially those involvcd with artificial intelligence), psychologists and linguists - studies ~vhichhaw been concerned to articulate the structure of the reprcsentations which spca$1k ers construct in response to verbal inputs. It appears that these two conceptions, and with them the theoretical conccrns that deri\-e from them, hat-e remained largely separated for a considerable period of time. This separation has become an obstacle to the developn~entof semantic theor!, impeding progress on either side of tlic line of division it has created. T h e theory presented here is an attempt to removc this obstacle. It combines a definition of truth with a systematic account of semantic representations. 'l'hesc two components arc linked in the following manner. 'l'he representations postulated lzerc are (like those proposed by others; cf. c . ~Hendrix . (1975) or Karttunen (1976)) similar in structure to the nlodels familiar from model-theoretic semantics. In fiict, formall). they are nothing other than partial models, typicallj. witlz small finite domains. Such similarity should not surprise; for the representation of; sav, an indicative sentence ought to embody tlzosc conditions which the world must satisfy in order that thc sentcnce be truc; and a particularly natural representation of' those conditions is provided bj- a partial model with which the (model describing thc) real \vorld will bc con~patiblejust in case the conditions are fulfilled. interpreting the truth-conditional signiticance of reyrcsentations in this wa! ure arc led to the follo\ving cl~aracterizationof truth: A sentence S, or discourse I), with representation m is truc in a model hq if and only if M is compatible with m; and

190 Hans Kamp compatibility of h t with tn,we shall see, can be defined as thc existence of a propcr embedding of m into kf, where a pvopcl- enrBc~/~iing is a map fiom the universe of rn into that of R.4 which, roughly speaking, preserves all thc propertics and relations which m specifies of thc elements of its domain. A theory of this form differs fundamentally from thosc fainiliar from thc trutlltheoretical and model-theoretical literature, and thus a substantial argument will hc wanted that such a radical departure from existing frameworks is rc;~llynecessary. 'l'he particular analysis carried out in the main part of this paper should be seen as a first attempt to provide such an argument. T h e analysis dcals with onl!- a small nurllher of linguistic problems, but careful reflection upon just those problclns already revcals, 1 suggest, that 21 inajor revision of semantic theory is called tbr. T h e English fragment with 11-hich the analysis deals contains sentcnccs built up fiom thcse constituents: common nouns, certain transitive and intransitive verbs (all in the third pcrson singular present tense), personal and relative pronouns, proper names, and the particles a, r w q I , and if.. . (tl~en).Thesc can be cornlined to J-icld the following sorts oC con~pounds:

1 complex singular ternis such as u Inan, er.cry I I > O I I I L I I ~ , a l r z i i n n)ho /o?+c.s r~rt3~ iPi)wrLuz, czlery 117oma11 mhom il nli~n~alzo011111s n donkey /oc~?s, ctc. (M'e can embed relative clauscs inside others and there is no upper bound to the depth ofemhcclding!); 2 singular tcrms i.e. complcx terms oC the kind just excmplificd, proper names and personal pronouns - can be combined with verbs to yield sentences; 3 sentences may be joined u-ith the help of ifto form largcr sentences of conditional form; sentences scrve moreover as the sources of relative clauses. -

T h e choice of this fragmcnt is motivated by two ccntral concerns: (a) to study the anaphoric behaviour of personal pronouns; and (b) to f o r m ~ ~ l aat cplausible account of the truth conditions of the so-called "donkey-sentences" (which owe their nanic to thc particular examples in Geacll ( 1 962), the M ork that kindled contemporary interest in sentences of this type). -4s these donkey-sentences will pl~iya prominent role in the theory developed below, let me briefly review the problcni that they have been taken to present. 1Ve shall concentrate on thc following two instances: If Pedro owns a donkey he bcats it ( 2 ) Every Carmer who owns a dol~kc!; beats it. (I)

For what needs to be said at this point it will suffice to focus on (1). For inany speakers, including the author of this paper, the truth conditions of ( I ) arc those tlctcnnincd by the first ordcr formula

(As a matter oC Pact not all English speakers sccin to agree that (3) correctly states the truth conditions of ( l ). Unfortunately an adequate discussion of di\-crging intuitions is not possible within the confines of the present contribution.)

A Theory of Truth and Semantic Representation 191 T h e problcm with ( I ) and (3) is that the indefinite description rr d o n k ~ ;of ) ~ (1) reemerges in (3) as a universal quantifier. How does an expression of a tgpc which standardly (or so it always seemed) coiivcys existence manage to express universality in a sentence such as (I)? One way in which one might hope to explain this is b y referring to the familiar equivalence between universal quantifiers with wide and existential quantifiers with narrow scope. Sentence (4), for instance, can be symbolizecl not only as ( 5 ) but also as (6). (4) If Pedro owns a donkey he is rich ( 5 ) (b'x) (Doilkey(x) A Owns(Pedso,x) (6) (3x) (Donkey(x) A Owns(Pedro,x))

Rich(Pedr0)) + Rich(Pedro).

--t

Out of these two (6) would appear to be the "natural" symbolization of(4) as it renders the indefinite a dorzkqy as an existential quantifier. (.i), \ve might be inclined to is adequate only for indirect reasons, viz. in virtue of its logical equivalcnce to (6). Notc, how-ever, that ( 1) callnot bc captured by an analogue of (6). For in such a formula the scope of the existential quantifier would have to be restricted, just as it is in (6), to the antecedent alone; but then the quantifier would be incapable of binding the position corresponding t o that occupied hy it in the main clause of (1). No one of the solutions to this problem that can be found in thc existing literatiu-e strikes me as fully satisfactory. As I see the problem a proper solution should provide: (i) a general account of the conditional; (ii) a general account of' the meaning of indefinite descriptions; and (iii) a general account of pronominal anaphora; which when jointly applied to (1) assign to it those truth conditions which our intuitions attribute to it. These requirements are met, I wish to claim, by thc theory stated in thc next two sections. As earlier reillarks implied, there are three main parts to that theory:

1 A generative syntax lor the inentionecl fragrncnt of English (I have cast thc syntax in a form reminiscent of the syntactic descriptions which are used by Montague; the reader map verify, holyever, that many other syntactic descriptions would he equally compatible with thc remaining components of the theory); 2 a set of rules whicl~from the syntactic analysis of a sentence, or sequence of sentences, derives one of a small finite set of possible non-equivalent representations; and 3 a definition of what it is for a inap from thc universe of a representation into that of a model to be a proper embedding, and, with that definition, a definition of ti'utli. T h e analysis thus obtained not only yields an account of the truth conditions of the donkey sentences (as well as of certain other notoriously problematic sentences which the fragment admits, such as e.g. some t ~ p e sof Bach-Peters sentences), it also reveals two more general insights concerning, respectively, personal pronouns and indetinite descriptions. 1 Personal pronouns, it has been pointed out, have a nurnbcr of apparently distinct functions. Sometimes they seem to behave as genuinely referential terms, as e.g. the he

192 Hans Kamp in PL>~I,o on?ns N donkc)). H t Oeats it. Sometimes, as the him of Ez~erynaun tvho lo~lesa moman who lows him is h~zpfi)~, they appear to do precisely what is done by the bound variables of formal logic. Yet another occurrence, noted in particular by Evans (1977, 1980), who coined the term "E-type pronoun" for it, cannot be understood, or so it has been claimed, either on the model of a simple referential expression or on that of a bound variable. An example is the occurrence of it in IfPedro omf2.s (i .~lul/kyyhe be(~tsit. The present theory brings out what these three different types have in common in that it offers, at the level of representation-formation a single rule \vhich equally applies to each of them. This rule may interact in various ways with other rules, which are associated with different syntactic constructions, and this gives rise to the seeming multiplicity of functions which the recent philosophical and linguistic literature has noted. ( T l ~ e r eare several pronoun uses, such as "pronouns of laziness" and deictic pronouns, ~vllichhave no instances within the fragment of English studied in this paper and which, therefore, cannot he discussed here. Such occurrences, however, can also be accommodated along the lines sketched in this paper.) 2 Indefinite descriptions are, on the account given here, referential terms, not existential quantifiers. When an indefinite has existential force it has that force in virtue of the pal-ticular role played by the clause containing it within the sentence or discourse of which it is part. It is true that the clausal roles which impose an existential, rather than a universal, reading upon indefinites are the more prominent; and this, I take it, has been responsible for the familiar identification of the indefinite article as a device of existential quantification. But they are not the only roles. 'l'he antecedent of'a conditional, for instance, plays a role which is not of this kind; a simple cliluse which occurs in this role confers a universal interpretation on the indefinite descriptions it contains. There is much that ought to be said about the conceptual implications of the present theory and about the range of its possible applications. Hut, as space is limited, I shall confine myself to a couple of brief remarks.

1 It should be stressed that truth as it is defined here applies not only to single sentences but also to multi-sentence discourse. This is of special importance cvhcrc intersentential relations within the discourse (such as intersentential anaphoric links) contribute to its meaning. As will bc seen below the links between anaphoric pronouns and their antecedents invariably have their impact on the discourse representation (irrespective of whether pronoun and antecedent occur in the same, or in different sentences) and thus on the truth conditions of the discourse, which the discourse representation embodies. Other intersentential relations, such ils the relation which obtains between the sentences of past tense narratives on account of their secluentiat order - which is typically understood to convey the temporal relations between thc events \vhich the sentences report - can be encoded into the discoi~rscrepresentation with equal ease. 2 T h e role representations are made to play within the theory developed in this paper places substantial constraints on their internal structure. (Careful reading of the subsequent sections will, I hope, confirm this asscssmcnt.) This is of particular significance if, as 1 have already more or less implied, discoursc representations can be regarded as the mental representations which speakers form in response to the verbal

A Theory of Truth and Semantic Representation 193 inputs they receive. I should point out that the specific theory that is presenred bclow docs not render such identification essential. Even if the representations it posits are thought of as purcly theorctical devices whose raison d'etre is to bc found solely in the contribution they make to an effective account of certain scrnantic propcrtics of sentences and sentence complexes, the theory may merit con~parisonwith orhcs schemes of linguistic description which have been applied to the same phenomena. Uut this is not how I would like ro see the proposal of this paper myself. I conjecture that the structures which speakers of a language can be non-trivially described as forming to represent verbal contents are, if not formally identical, then at least verj- similar to the representations here defined.

If this identification is legitimate then a theory of the sort I have tried to develop brings to bear on the nature of mcntal representation and thc structure of thought, a large and intricate array of data relating to our (comparatively firm and consistent) intuitions about the truth-conditions of thc sentences and sentence sequences we employ. I very much hopc that along these lines it may prove possible to gain insights into the objects of cognitive operations, as well as into thesc operations thcmselves, which are unattainable if these data are ignored, and which have thus far becn inaccessible to psychology and the philosophy of mind precisely because those disciplines were in no position to exploit the wealth of linguistic evidence in any systematic fashion.

2 The Theory: Informal Preliminaries 2.1 Anaphoric pronouns The analysis of p~-onominalanaphora I shall slietch is informed by the conviction that thc meclianisms which govern deictjc and anaphoric occurrcnccs of pronouns are basically the same. This is an intuition that has guided many recent theories of pronominal reference; inevitably the account given here will resemble some of these in various respects. 1 Our point of departure will be the hypothesis that both deictic and anaphoric pronouns select their referents from certain sets of antecedently available entities. The two pronoun uses differ with regard to the nature of thesc sets. In the cilse of' a dcictic pronoun the set contains entities that belong to the real world, whereas the selection set for an anaphoric pronoun is inade up of constituents of the representation that has been constructed in rcsponse to antecedcnt discoursc. About deixis I shall have no more to say in this paper. But a little inore needs to be said about anaphoric pronouns before me can proceed to the detailed analysis of s o ~ n c particular pieces of discourse. T h e strategies used in selecting the referents of anaphoric pronouns arc notoriously complex; they usually employ background assumptions about thc real world, "grammatical" clues, such as the requircnlcnt of number and gendcr agrcernent between thc anaphor and its antecedent, and the order ill which the potcntial referents were introduced bl- the preceding discoursc.2

194 Hans Kamp T h e integration of these various factors often in\~olves,moreover, what sccm to bc quite intricate patterns of inference. Efforts to understand these strategies have claimed much thought and hard work, but, in its general f o r n ~at least, the problem appears to be far too complex to permit solution with the limited analytic tools that are available at the present time.3 About the strategies I shall have nothing more to say. Our concern will be, rather, with the sets of referential candidates from which they select. These entities will constitute the universes of the representatio~lsof which I spoke in Scction 1. I have already said that these discourse represcntations, or DR's as I will call them for short, are formed in response to the discourses they represent and that their formation is governed by certain rules. These rulcs - and this is a new, and crucial, assumption of the theory opesate on the syntactic structures of the sentences of the discourse, and it is via them that syntactic form determines what the resulting DR will bc like. This determination is not complete however. T h e syntactic structure does not, for instance, determine the anaphoric links between pronouns and their antecedents, which the DR makes explicit. Most of the real work that the present theory will require us to do concerns the exact forn~ulationof the rules of DR-formation. T h c exact formulation of these rules will be rather compact, and will betray, I suspect, little of either motivation or en~pirical implications to any but the initiated. I have decided therefore to first present a numbcr of applications of the theory. I hope that if we proceed in this manner its formal features will reveal themselves more naturally and that the subscqucnt reading of the exact definitions in Section 3 will thus be less disagreeable than it would bc without such preparation. Let us begin by considering the two sentence discourse: -

(7) Pedro owns Chiquita. I4e beats her. T h e DR for the first sciltence of (7) will contain two elements, call them u and v, wl~ich represent, respectively, Pedro and Chiquita, and furthermore the information that the first of thcse, u, owns the second, v . Schematically we shall represent this information as follom-s: n1,(7)

u

V

Pedro owns Chiquita u = Pedro v = Chiquita u ow11s v 'To incorporate the informatioil contained in the second sentence of (7) wc must extend structure m1(7).But to do that we il~ustmake two decisions, regarding thc r e f rencc of, respectively, he and her. It is natural to understand he as referring back to l'ecllro and hipr as referring back to (,'/~iqz/ila.Let us agree to interpret the pronouns in this way and to expand n11(7) accordingly. What we get is:

A Theory of Truth and Semantic Representation 195

Pedro owns Chiquita u = Pedro v = Chiqui ta u owns v H e beats her u beats her u beats v

I said that linking he with Pedro and h~.rwith Chiqziita yields what seems the most natural reading of (7). "But", you might ask, "what other readings could (7) have?". The answer to that question depends on the setting, or context, in which (7) is supposed to be used. If (7) were uttered by a speaker who points at some individual othcr than Pedro while saying he, or at some being distinct from Chiquita when he says her, the gesture would recruit this demonstrated individual as referent for the pronoun. Similarly, if (7) were part of a larger discourse he or her could conceivably refer back to some other individual introduced bq- an earlier part of that discourse; and this could result in a genuine refcrential ambiguity. Iiowever, if (7) is used by itself, i.e., ~+-ithout preceding verbal introduction, and also in the abscnce of any act of demonstration, then - and this is another important hypothesis of our theory - there arc no other potential referents for he and her than the discourse referents which have becn introduced in response to Petlro and Chirjuita. Let us agree that hcnceforth (esccpt where thc contrary is indicated explicitly) all our examples of simple and multi-sentence discourses shall be understood in the last of these three w.';iys,i.c., as used without accompanying deictic gestures and not preceded by any related discourse. Even when we understand (7) in this third way its anaphoric links arc not fully determined by what we have said. For why cannot he and her both I-efkrto I , , say, or he to v and her to u? T h e reason is of course obvious: lie must refer to a male individual, and her to a female one. Rut, obvious as the determining prii~ciplemay be, it is not quite so easy to state it in a form that is both general and accurate. For what is it that determines an antecedently introduced discourse referent as male, rather than female, 01. neither male nor female? ('7) allows us to infer that 14 is male because we know that Ptd~o, typically, refers to male individuals. But often the antecedent term which led to the introduction of a discourse item is not quite so explicit about the gender of its referent. Consider for example such terms as: Robin, Hil~i1:11,tlzlle sztrgilon, t l l ~PI-eszrlen/, an q[{icer in the -Air Fwcc, t h ~~O ~ ~ S S tO hY ~~'ofis.wr'S ,~ sec.retaq!, ti~e,fjntitzizt~h~ta~~t ol'this C ~ I Z Y . Often wc can do no better than guess wl~etherthe referent is male or fcmale, or human or non-human. Some of these guesses are more educated than others. And not infrequently where the anaphoric link between the antecedent and some particular pronoun is clear on independent grounds it is in fact the gender of the pronoun which resolves the uncertainty.t Applying the principle of gender agrecinent will thus often involve drawing various inferences from the information that is givcn explicitly; and as in all other processes

196 Hans Kamp \\;here inference can be involved, there appears to be no clcar upper bound to its potential complexity. There is a further con~plicationthat an cxact statenlent of the principle must takc into account. T h e gender of the pronoun that is used to refer to a certain object is not exclusively determined bj- the nature of that object, but, to some extent, also by the actualJ~rm of the anaphoric antecedent which made it available as a referent. Thus let us suppose that the name Chiqui~a in (7) actually refers to a donkey. In most situations we refer, or at any rate may refer, to a donkey by means of it. Hut in a discourse such as (7) this would be inappropriate. T h e name Cjziquilu highlights, one might wish to say, the fact that its referent is female, and this makes she the corrcct resumptive pronoun. Hut nonetheless thc task of giving even an approximate forinulation of the principle appears to be well beyond our present means. In what follows wc shall ignore the principle of gender agreement, just as we ignorc all other that help to disambiguate the reference of anaphoric pronouns. But whcre, in subsequent examples, the need for gender agreement clearly excludes certain anaphoric links I shall not bother to mention those without referring to the principle explici tly. Clearly (7) is truc, on the reading of it that is given by m(7) if and only if the rcal Pedro stands to the real Chiquita in a relation of ownership and also in the relation expressed by the verb bent. Put differently, if M is a model, representing the world consisting of a domain Ubl and an interpretation function Fh,, which assigns to the names Pecl~oand Chiqzritn members of Uhl and to the transitive verbs o l ~ nand berit sets of pairs of such members - then (7) is true in A4 iff the pair (l+'hl(Pedro), F,,, ((3iqlri1a) ) belongs both to Tw (ozmr) and to FhT(bent). Moreover, the right hand side of this last biconditional is fulfilled if there is a map f of thc universe of m(7), i.c. the set {u, v}, into UhISO that all specifications of m(7) are satisfied in hl - i.e., f(u) is the individual denoted in h1 by Pedro, f(v) is the individual FJv1 (Ci7iqrdita), and it is truc in M that f(u) both owns and beats f(v), in other words, that (f(u), f(1-)) belongs to both FR,, (own) and FA,(beat). Let us now consider

(8) Pedro owns a donkcy. He beats it. T h e first sentence of (8) induces a DK that can he represented thus: u

v

Pcdro owns a donkcy u = Pedro u owns a donkey donkey u owns V (17)

Once again there is no choice for the anaphoric antecedent of citlier /re or i~ in the second sentence of (8). So the complete DR of (8) becomes:

A Theory of Truth and Semantic Representation 197 U

1'

Pedro owns a donke!; u = Pedro u owns a donkey donkey (v) u owns v H e beats it u beats it u beats v

(8) is true in the model M provided there is an element d of Uht such that (Ftt4(Ptc/ro), d) belongs to both F3{ ( o ~ ~ and n ) FAT(bear); a i d furthermore d is a tlonliey in M formally cf E Fhl (donkyy), if we assume that common nouns are interpreted in the model by their extensions. This condition is fulfilled if there is a map g from = {u, v ) ) into UhIwhich preserves a11 conditions specified in m(8). Note that g(v) is not required to bc the bearer in M of some particular name, but only to belong to the extension of the noun donkey. Heforc turning to the donkey sentences (1) and (2) of Section 1.2 let us take stock of some principles applied in the construction of the DR's which we 11ak-e encountel-ed so far:

1 Certain singular terms, among them proper nouns and indefinite descriptions, provoke the introduction of items into the DR that function as thc "rel'erents" of these terms. We shall later address the question which singular terins give rise to such introcluctions and whether these introductions are obligatory or optional. 2 Othcr singular terms, viz. personal pronouns, do not introduce elements into the DR; instead they can only refer to items which the L)R already contains:'

2.2 Conditionals Our next aim is to construct a representation for the "donkey sentence" (I), which for convei~iencewe repeat herc:

(1)

If Pedro owns a donkey he bcats it.

Before we can deal uith ( 1 ) however, uie must say something about conditionals in general. 'The semantic analysis of natural language conditionals is a notoriously complicated matter, and it seems unlikely that any formiilly precise theory will do justice to our intuitions about all possible uses of sentences of this form. T h e literature on conditionals now comprises a number of sophisticared formal theories, each of which capti~res some of the factors that determine the meaning of conditionals in actual use." Although these theories differ considerably from each other they all seen1 to agrce on one principle, namely that a conditional

198 Hans Kamp

is truc if and onlj- if (10) Every one of a number of ways in which A can be true constitutes, or carries with it, a w-ax of B's being true.

Up to now this principle has generally been interpreted as meaning that H is true in, or is iniplied by, ewry one of a certain set of velecnntpossihl~.sitr~nrio?zsin which A is truc. (This is true in particular of each of the theories mentioned in the last footnote.) The analysis of truth in terms of DR-embeddability, however, creates room for a slightly different implementation of (lo). Where M is a model and m a DR for the antecedent A there ma>-be various proper embeddings of m into M, various ways, we might say, of showing that A is true in 111. This suggests another interpretation of (lo), viz. that each such way of verifying A carries with it a verification of H. In u-hat sense, however, could such a may of verifying X - i.e. such a proper embedding of m cntail a verification of B? T o vcrify 13, in that sense of the term in which we have just been using it, we nced a representation of R; but as a rule the content o f B will not be represented in thc DR n~of A. T o verify B in a manner consistent with some particular verification of A we must thcrefbre extent1 thc DR m involvcd in that verification to a DR m' in which l3 is represented as well. Thus we are led to an implementation of (10) according to which the conditional (9) is true, gizlerr a pair (m,rnf), consisting of a DR m of A and an extension m' of m which rcprcsents H as well, iff -

(1 I)

every proper embedding of m cin be extended to a proper cnihedding of m'.'

This is not yet an explicit statement of the truth conditions of (9), for it fails to tell us anything about the target structures of the verifying embeddings, and about their relation to the situation, or model, tvith respect to which (9) is c~aluated.Here we hcc all the options that lrave confronted earlier investigators. Lie may elaborate (I 1) by stipulating that (9) is true in a modcl 34 iff every propcr embedding of 111 into M is, or is extendable to, a propcr embedding of m' on M. Or we may insist that (0) is time in the possible worlcl w iff every proper embedding of m into any of the (n~odelsreprcscnting the) nearest A-worlds induces some proper embedding n ~ into ' that \vorld. Indeed, any one of the existing theories could be combined with the principle conveyed by (11). Here we shall, primarily for expositor>- simplicity, adopt the first of the options mentioned:

(12)

Let n~be a DR of A ancl m' an extension of n~ which incorporates the content of B. Let M be a modcl. Then $A theft B is true in ha, given (m,mr), iff every proper embedding of m into M can be extended to a propcr embedding of m' into M.

For conditionals in which there are no anaphoric links between antecedent and consequent, (12) boils clown to the truth conditio~lsfor the material conditional. But where

A Theory of Truth and Semantic Representation 199

(

, 1

I

1

such a link exists its implications are somewhat different. T o see this let us applq thc condition to (1). We have already construcrcd DR's of the kind ncedcd in thc application of (12) to ( I ) , namely, n11(8), and m(8). Accordillg to (12), (1) is true in & givcn I (m1(8), m(8)), iff every function f from Un1,(,C4) ( = {u, v)) into Ublsuch that (1) f(u) = FkI (Pedro). (ii) f(v) E I?,\,, ( d o ~ z k e ) ~and ) , (iii) (f(u),f(v)) E FvI (on?it),can be extended to a function g from into U5,\such that (g(u),g(v)) E FIr (beiit). Of coursc, in the present case U,,(,C~, = Um,(,3) and consequently there is no question of ~ . ~ t ~ n J ifnto , q g. So the above condition reduces to the stipulation that every f as describecl 112s thc additional property that (f(u),f(v)) E F41(bmt).Clearly this condition is eclui\lalent to the truth in M of the formula (3) which we adopted in Section 1.2 as giving the (ruth conditions of (1). It is easy enough, however, to come up with examples which do involvc thc extension of cmbeddings, e.g.: (13) If Pedro owns a donkey hc lent it to a merchant.

If we extend m r (8) to a DR which incorporates the content of the consequent of (13) we I

get something like: u

lT

W

Pedro owns a donkey u = Pedro u owns a donkey donkey (v) u owns v hc lent it to a merchant u lent it to a merchant u lent v to a merchant mcrchant (w)

In relation to in~(X) and in(13), (12) requires that evcry mapping f of the kind described in thc preccding analysis of ( I ) can bc extended to a function g from { u , v , w ) into Lhl such that - if we assume for simplicity that lent to is interpreted in k1 as a set of ordered triples of members of Unl (i) g(w) E F,\, (ii~~vchunt); and (ii) (g(u),g(v),g(w)) E lTYl (Imt to). -

2.3 Universals

'

Onc of the important insights that went into Frcgc's discovery of the predicate calculus was that the restricted quantification typical of natural language is expressible in terms of unrestricted quantifiers and truth fuunctions. Our handling of indefinite descriptions, which formal logic treats as expressions of existential quantification, harmonizes with this insight. For, as can be seen for instance fiom m1(8),the introduction of a discoul-se referent u for an indefinite term is accompanied by two conditions, one to the effect

200 Hans Kamp that u has the property cxpressed by the common noun phrase of the term, and the other resulting- from substituting u for the term in the sentence in which it occurs. I wish to propose a treatment of terms of the form ezlrqt 3 that is in similar accol.d with Frege's analysis of restricted universal quantification. ,%gain it will be easier to illustrate the proposal before I state it. Consider: (14) Every widow admires Pedro.

A representation for (14), like those for conditional sentences, involves a pair of DR's. T h e first of these states that some "arbitrary-" item x satisfies the common noun ~rlii/on); the second extends this DR by incorporating the content of thc condition .z. admiws Pedro. Thus we obtain:

LI

widow (x) x admires Pedro LI = Pedro s admires u

widow (x)

T h e truth value of (14) in h/l is to be determined by (m1(14),m 2 ( l 4 ) ) in precisely the same way as that of (1) is determined by (m1(8),n1(8)).T h u s (14) is true iff cvcry correlation of x with an element a of UhIsuch that a E FXl( I I J ~ ~ ~ O Ican I ) ) be extended to a proper ernbedding of m2(14), i.e., to a f'unclion g such that g(u) = l:cl (P~r/ro) and (g(x),g(u)) (a,g(u)) E Fh (izdn~i~t~s). Clearly this confers upon (14) the intuilivcly correct truth conditions. In the same way

-

(15) Every n-idow admires a farmer licenses the construction of the following pair of DR's:

x widow (x)

X

U

widow (x) x adnlires a farmer farmer ( u ) x adn~ircsu

Again the condition that evcrjr associatio~lof x with an objcct a that is a widow in thc sense of M can be extended to a proper embedding of mz(l.i) gives the correct truth conditioils of (1 5 ) ; or, to he precise, the truth conditions it has on what is generally considered its most natural reading.

A Theory of Truth and Semantic Representation 201 Consider now the second donkey sentence of Section 1.2:

(2) E\.ery farmer who owns a donkey beats it. Sentence (2) gives rise to the following pair of DR's:

m, ( 2 ) X

v

firmer (x) x owns a donkey donkey (v) x owns v

(

I

farmer (x) I x owns a donkey donkey- (v) x owns v x beats it x beats v

So (2) is true in M iff every f such that f(x) E (.fi~t)ter),f(v) E F4.1( ~ / o ? f k q l )and , (f(x),f(v)) E FX1( U J I J T I ) has the additional property that (f(x),f(v)) E FA,,(heot). This is esactlp as it should be. Our treatment of conditionals and universal sentences gives - for the cases, at any rate, that we have thus far considered - intuitively correct conditions of truth. Hut it seems at odds m-it11 the generul definition of truth which I put forward earlier, according to which a cliscourse is true in M, givcn some rcprescntation m of it, iff there zs some proper embedding of m into Ad. T h e semantic analyses of the sentences wc have considered in this section refer to pairs of DR's rather than single DR's and involve conditions on aN propcr embeddings of a certain kind, instead of demanding the existence of at least one proper embedding. T o resolve this apparent conflict I must say a little more about the intuitive ideas behind the DR constructions of which we have no\v seen a few instances. Essential to the analysis of the majority of our examples was the nay in which we have treated indefinite descriptions. It would be quite unsatisfactory if there were no other justification for that treatment than the observation that, combined with additional principles for DR-construction thcy give thc truth conditions that speakers in fact associate with the sentences we have sampled. Tllere is, however, a reason why we should e,vprl.t a construction principle for indefinites such as we have applied, but no dil-cct analogue of it for phrases of the form r z Y P q / a. Let us go back to the tirst sentcnce of (8). What justifies us in adding to the partial DR of (8) the elcment \- as a "rcferent" for a d o n k ~ y is this: as I, already argued, the DR of a sentence functions as a partial description of how the world ought to be if the sentence is true. T o fulfill that role the DR must represent whatever information has been encoded into it in such a way that the significance of that representation is unaffected when one extends it to incorporate further information -- or, what eolnes in this connection to much the same, when the D R is identified as a certain substructure of a larger "real urorld" nlodet via SOIIIC proper embedding. T h e conditions u = Ped~u,d o ~ l k q ) ~ ( zand ? ) u o)v)~.v 11which makc up ml(8) clearly satisfq- this requirement. They convey precisely the same information in any extension of m1(8)as they do in n11(8)itself,"he content of an existential sentcnce

202 Hans Kamp has been exhausted once an inditridiial has been established which satisfies the conditions expressed by the indefinite description's common noun phrase and by the rcrnainder of the sentence. Rut a universal sentence cannot be dcalt with in such a once-and-fbr-all manner. It acts, rather, as a standing instruction: of each individual check whether it satisfies the conditions expl-essed by the common noun phrase of the universal term; if it docs, you may infer that the individual also satisfies the conditions expressed by thc remainder of the sentence. This is a message that simply cnnnot be expressed in a form more primitive than the universal sentence itself. The universal is thus, at the level of the DR to which it belongs, irredt~csible.T h e same is true of conditionals. I/" t h ~ Bf ~ functions as an instruction to check, and keep checking, whcthcr the antcccdent A has been satisfied, and to infer, when this is found to bc so, that the consequent 13 must also hold. This too is a piece of information that cannot be represented in any more elementary form. This means that when we form the DR of a universal sentence, suc11 as (14), or of a conditional, such as (I), we cannot decompose the sentence in some such fashion as we were able to decompose, say, the first sentence of (8) when constructing m1(8).So the DR for (14) cannot itself be elaborated beyond the trivial initial stagc:

Every widow admires Pedro in which the sentence (14) occurs as a condition, but nothing else does. There is however, another way in uthicl~we can represent the internal structure of (14), namelv by constructing separate DR's for its components, and by integrating these DR's into a structure in which their connection reflects the syntactic construction by means of which these different components are amalgamated into the complex sentence. This is, in Oct, essentially, what I did when constructing the DR-pairs 1 earlier presented for ( l ) , (14), (IS), and (2). Rut thesc pairs do not provide, by themselves, the structural rcpresen~ationsto which we can apply our general definition of truth. To obtain such a representation for, say, (14) w-e must combine the pair (m1(14),mz(14)) with the DR mo(14). 'This gives us the following structure:

K(14) m,,(14) Every widow admires Pedro

r;l \+?idow(x)

~ridoiv(x) x admires Pedro x adrnircs u

A Theory of Truth and Semantic Representation 203

Similarly the complete representation for ( I ) will now look thus:

If Pedro owns a donkey, he beats it

U

V

Pedro owns a donkey u = Pedro donlicy (v) U ow11s v

u

V

Pedro owns a donkcy u = Pedro donkcy (v) u owns v u beats it u beats v

It may appear as if something is still missing from these structures. For what tclls us that the subordinate DR's ml(1) and m r ( l )rcpresent the antecedent and consequent of a conditional, while m1(14) and mz(14) rcpresent the components of a universal? Thc answer to this is simple: the necessary information is provided by the sentences in mo(l) and mo(14) whose componcnts are represented by the subordinate DR's ml(l), m,(l), and m1(14), rn2(14). In fact we shall assume that with each syntactically well-formed sentence is given a particular syntactic analysis of it, which specifies unambiguously its immediate components and the construction which forms the sentence out of theso, (For the fragments we shall study in Section 3, this condition will be automatically fulfilled as each of its wellformed expressions has a unique syntactic analysis.) T h e role which, say, ml(1) and mz(l) plaj- in the representation of (1) can thus be recognized by comparing their relevant entries, viz., Pedro owns n ilonkyy and he heats it, with the syntactic nnalvsis ofthe sentence ( I ) to be found in mo(l). 1411this will be discussed in dctail in Section 3. A representation of the sort just displayed, which involves structured families of DR's, will be called a Discourse R~>presen/atinnStmr.fzire or, for short, DRS. Each sentence or discourse induces the construction of such a DRS, and only wl-lere the selltcnce or discourse is comparatively simple will the DRS consist of a singlc DR only. Among the DR's that constit~~te a DRS there will always be one which represents the discourse as a whole. (In the two DRS's we displayed these are, respectively, mo(14) and mo(l).)'J'his DK will be called the principal DR of the DRS. Once we assign to (1) the DRS K ( l ) the earlier conflict between the general definition of truth and our particular account of the truth value of a conditional call be resolved. We slightly moditj the truth definition to read: (16) A discourse D is trzrr In M , g i z m a DRS K of D iff there is a proper e~nbcdding into M of the principal D R of K. Let us try to apply (16) to (1) and its DRS K(1). (1) is true given K(1) iff thcrc is a proper embedding of mo(l) in to M. Since the universe of mo(l) is the empty set, thcrc

204 Hans Kamp is only one embedding from m o ( l ) into M, viz, the einpty function, /\. What is it fbr A to be proper? A is proper iff the conditions of mo(l) are true in A 1 ofthe corresponding elements of Ukl.In the present case however there are no elements in U,,,,(,1, thus no corresponding elemcnts of Uh,I;and there is only one coi~ditionin mo(l), namely (1) itself. Thus A is proper iff (1) is true in h4. It might seem at this point that we are trapped in a circle. Hut in fact we arc not. T o see that we are not it is necessary to appreciate the difference between (i) asking for the truth value in M of (I), given K(1); and (ii) asking for the truth value in hl of some condition that belongs to somc member of K(1). This second question has, as we saw earlier, a straightforward answer when the condition has thc form of an atomic sentence. For in that case it is directly decided by the embedding and the function FhI.But when the condition is a complex sentence, e.g., a conditional or a universal, which permits no further analysis iailhin the cer:y DR l o rvhirsh it he/or~g.s,the answer involves an appeal to certain members of the DRS that are suOordiwate to that DR. T h u s the condition (1) of m l ( l ) is to bc taken as true in hI iff it is true, in the sense delined earlier, ginen the pair ( m r ( l ) , m r ( l ) ) of DK's subordinate to m(,(l); and in that sense ( I ) is true in M, we sawr already, iff M verifics the first order formula (3). T o see more clearly how the various components of our theory are to be fitted together, we should look at a few more examples. T h e next example shows why it is that certain anaphoric connections are impossible. In (17) If Pedro owns every donkey then he beats it. it caniiot have Lpi?erydnnke)~for its antecedent. T h e reason for this becomes transparcnt wheil we try to construct a DRS which gives such a reading to (17):

If Pedro owns every donkey he beats it.

U

U

Pcdro owns every donItey u = Pedro u owns ever? donkey

Pcdro owns every donkey u = Pedro u owns every donkey he beats it u beats it

1 donkey (x)

A Theory of Truth and Semantic Representation 205 We cannot conlplete this DRS as intendcd, fbr the discourse referent x, which we want to assign to the pronoun it of m2(17), is not available, as it occurs only at thc Ickel of m3(17), which is betow that of mz(17). A similar explanation shows why il cannot bc anaphoricall!~linked to evevy donkey in ( 18) Every farn~erwho onms every donlie; beats it

/

and also rvhy in

I

(19)

If Pedro likes every woman who owns a donkey he feeds it

1

it cannot be co-referential with a donkey, whereas such a link docs seem possible in

1

(20) If' Pedro likes a woman who owns a donkey he feeds it."

I I

'

These last examples give, I hope, an inkling of the predictive powers of what in particuli~r linguists might think constitutes the most unusual feature of the theory 1 have so far sketched: the Gct that it handles singular terms of the forms n/J and CZ>EI:E) /J in entirely different ways. I hope that these and subsequent illustrations will help to pcrsuadc rhcm that the conception of a perfect rule-by-rulc parallelism between syntax and semantics is one that must be proved rather than taben for granted.1" In fact, the data here presented point towards the conclusion that this conceptioil is ultimately untenable. Anotllcr fcature that distinguislles the present account fiom many, albeit not all, existing theories of reference and quantification is its entircly uniform treatmcnt of third person personal pronouns. This has already been apparent from the examples at which rye have looked. I t is further illustrated hy such sentences as: (21) Every fi~rmercourts a widow who admires him.

I

I

I

1

I

I

Occurrences such as that of him in (21) have been put forward as paradigms of the use of pronouns as bound variables - an identification that is natural, and in fact well-nigh inescapable, when one believes that the logical forms of natural language sentences are expressions of thc predicate calculus. Indeed several earlier theorists have perceived n real chasm separating these pronoun uses from those which cvc find cxemplitied by, say, her in (7) and Ile in (7) and (8); and, looking at pronouns fieom this perspective, they have oftcn felt helpless vis-a-vis the pronoun occurrences that h a w becn of particular concern to us in this section, viz. those exemplified b?- (1) and (2). Forcing these either into the mold that had been designed (or uses such as that in (7)) or into that measured to fit occurenccs such as that of h i ~ ~inz (21) turned out to be hopeless enterprises. IIvans (1977, 1980) gives conclusive evidence against the latter of these two; but his ow11 suggestions, which go some way towards assimilating the problematic pronouns to definite descriptions, do not appear to be full>-satisfactory either. I I Note that the more unified treatmcnt of these pronoun i~sesgiven here is possible r operates both at the lcvel of the partly because the same construction rule f i ~ pronouns principal DK's and at subordinate levels. T h u s the DRS for (21) is constructed as follorrs (the numbers in parcnthcscs which prcccde discourse referents and conditions indicate the order in which the operations are carried out; we shall oftell use lhis notational device):

206 Hans Kamp n1,,(21) (0) Every Farmer courts a widow who aclnlires him.

r (1) farmer (x)

(1)

(2) v

(1) farmer (s) (1) x courts a widow who adn~ires him (2) w ido tv (7) (2) 1; admires h i n ~ (2) x courts v (3) v admires x

T h e rule for pronouns applies here in just the same way to the Iri~riof z. irr/rrrircs 111111 in m2(21) as it does for example to the l?e and i / in the DRS construction of (8) or thc i~ of (1) in the construction of the D R of (1).

3 The Formal Theory

3.1 Syntax T h e time has comc for a more f o r i ~ ~and a l systematic presentation. We shall consider a fragment of English for which 1 shall g i ~ an e explicit syntax and cxplicit formal rules for DRS construction. Our fragment will be exceedingly simplc to start with, much simpler even than that of Montague (1073).12 T h c syntax adoptcd resernblcs Montague's, but the resemblat~ccis rather superficial; for thc syntactic analysis of il sentence \rill play a much more modest role in the cletermination of its interpretation than it does in Montngue grammar. In presenting the syntax 1 shall presume somc f:c~nliliiirity w~itl.1I~/roi~tague grammar, specifically with hlontague (1970a) and (197.1). Our fragment, to which 1 shall refer as I,(),contains expressions of the following catcgories with the following basic members: : P t d r o , C'lriqrri/~r,John, Mnry, Bill. . . . ;hip, shr, it 1 T (Term) 2 CN (Common Noun phrase) : ,/h~-~?ri>r, ~/otrk~;]l, J P ~ ~ / O ~11?(1t1, IJ, J?lot?z(fn,. . . 3 1V (Intransitive Verb phrase) : l I ~ r i v ~ .>. s . o l ~ ~ n shear.\., , Io'I~L~s,N ~ I I I ~ ~ C~.oi~r/.v, S , likes, /i~l.ds, 4 T V (Transitive Verb) /,a/ hes, . . . 5 S (Sentence) 6 RC (Relative Clause)

YR1.

If a E T V and /i E T then all' E IV where 11' /? = she and 11' = /? otherwise.

=

/rim if

fi

= lie,

P'

=

lrer il

A Theory of Truth and Semantic Representation 207 FR2. I f x E I V a n d fl E T t h e n p ~E S. FR3. If z E CN then (i) (1 (1.1) x, and (ii) evrry x are in T. F'R4.k If b(, E S and the k-th word of (1) is a pronoun then Pd,' E R<:, whcre (/I' is the rcsult of eliminaling the k-th word from cf, and P is v h o , n?/zorrr, n)ki~,h, according as the pronoun is he or slzt., him or her, or it, respectively. FKS. If a is a basic CN and E RC then ap E CN. F116. If cf,, $ E 5 then f/'(j, $ and if 4 then rC/ E S.

P

our of 1 The rule schcrna FR4.L is defective inasmuch as it allows for wh-~~lovcrncnt

forbidden positions. Within thc prcsent fragment therc are only tivo sorts of 1101111 phrase positions to which wh-movement may not apply, those inside relativc clauses and those inside the antecedents of conditionals. It is not difficult to modify tllc syntav in such a way that these restrictions are observed. For instance tvc could stipulate that cach time a relative clause is formed all pronouns it contains are marked, and that the same is done to those occuring in the antecedent of a conditional at the time wllcil antecedent and consequent arc joined together. The rule of relative clausc formation can the11 bc altered so that it applies to unmuked pronouns only. Such a solution is rathcr ad hoc, so as it would moreover complicate the syntax 3s a whole, I llavc refrained from incorporating it. I must beg the reader to keep in mind that the syntax of this section is intended as no inorc than a convenient basis for the dcfinition of I3KSconstruction rules, and that it has no pretentions of capturing important syntactic generalizations. 13 2 T h e present fragmcnt differs from most fiamiliar versions of htontague grammar in that ir ajntains neither variables nor indexed pronouns.14 G)nseqiiently thc syntactic analysis of a sentence of the present fragment tells us nothing about annpl~oricI-elations. 3 EL-cry ndl-formcd expression of Lo has a unique syntaclic anal!.sis. 'I'his is a fraturc that is bound to be lost at somc point as we extend thc present fragnlent. It allou-s us, howevcr, to omit, while uniqueness of syntactic analysis obtains, all explicit reference to sj-ntactic analyses in discussions and, pal-titularly, in definitions whcrlsuch r e h e n c c becomes essenrial as soon as well-formed strings do 11ot un~ln~bigiio~isly determine their analyses. 4 When defining the process of DRS construction we shall have to specify the orcler in ivhich various parts of a given sentence are to be treated. What we necd hcre is, in essence, a specification of scope order. I shall assunle in this paper that the scope relations within a scntence arc dircctlj- determined by its syntactic construction. 'Th~ls the subject term of a simple clause will always have wide scope over the object term; the $of a conditional sentence will always have wide scope over the terms occurring in antecedent and consequent, etc. Idet us call the forlnation rule which is applied last in the construction of an expression ;I* the ontcnnost rule of;!. iYhe1.e l1 is a sentence and thc outermost I-ule is FK6, 1' is called a r-onditiona/ cspn/~jnl.t).If the outcl-most sulc of 1' is FK1 or FK2 and this rule forms bx combining some IV or T V with thc 1-CSIII a, a is said to ha.s:c,or to Fc the term ~ m t hrnn.rinmlscopr , in :I.If the outermost rule is FR1 nncl a begins with rccJ
208 Hans Kamp By eliminating ~Montague'srule of substitution and quantification we have dispcnscd n-ith one natural way of distinguishing between alternative scope relations - such as, for instance, the two possible relations between n n7ido11;land cve~:l~/ii~.mer in (22)

-4 widow adinires every firmer.

Sentence (22) can be generated in only one way and according to that generation the subject has wide scope over the direct object as it enters the construction of thc sentence at a later stage. No syntactic analysis iciould thus appcar to convey upoll (22) the reading given by

It might be thought that the construction of a L)RS which imposes this lattcr rcading upon (22) involves an order of application of the construction rules which contravenes the scope relations implied by the syntax. This problem too must be left for another paper. .5 We shall refcr to the basic terms Pcdro, C h i y ~ i t nJohn, , ,Vf/lat:y, . . . as thc prop^^. rmzes p will bc called of Lo and to he, she, it as the pronorrns of Lo. Terms of the form uniccl-su/ terms. 6 I have admitted only c o ~ l ~ p o u ncommon d noun phrases consisting of a common noun and eve relative clause. It would of course be possible to relax 1:KO so that it can attach several relative c l a ~ ~ s etos the same llead noun. Many of thc resulting expressions, hoivcver, seem marginal at best. I have decided to cut the knot and keep such complex common nouns out of the fragment altogether.

3.2 Models and discourse representation a r~odc/~fi,lLo we shall understand a structure of thc form (U, 1;) where (i) U is a non-empty set and (ii) F is an interpretation function ivhieh assigns an clcmcnt of U LO each of the proper names of I., a subset of U to each of its l3asic CN's and basic IV's, and a set of pairs of clclnents of U to each of thc basic TV's. We nl~lstno\\. address ourselves to the main tasks ofthis section, the formulation of the rulcs of DRS-construction and of the definition of truth for 14,.T o state the rules wc shall have to decide on a format for DR1s and DRS's. In choosing such a format I have been partly guided by considerations of notational convenience. In partic~~lar it is just a matter of con~;enienccto specify (as I have already done in the examples discussed in the prcceding section) that one or inore discourse referents satisfy il certain predicate by adding to the relevant D R a scntcilce which is obtained by colnhiiling that predicate with, in the appropriate positions, these rcf'crents themselvcs; using thcm, that is, autonymousl!; (a policj- against which there can be no objection, given thc syinbolic naturc which must be attributed to the discourse rcfercnts in any case). L41~nost all otl~erfeatures, however, of the DR-format I have choscn arc detcrmincd by empiricallj significant aspects of the rules of DRS-construction. Let V be a denumerable set of entities none of M-hichis a bi~sicexpression of Lo or it string of such expressions. 'V is the set froin which the clcn~cntsare clra~t-nthat nuke up lr3jr

A Theory of Truth and Semantic Representation 209 the universes of the DR's. We shall often refcr to the members of V as tli.sc.o~rr-sc r~;/erents.For anj- subsct X of V let I,o(X) be thc result of adding the n~ernhcrsof X to the set of basic terms of Lo. As all our earlier examples showed, the introduction of a discourse referent is always accompanied eithcr by a condition which identifies it as the referent o f a proper name or elsc by one which stipulates that it satisfies some common noun. Thcse conditions be expressed in Lo@); so we nus st slightly extend the notation which that language provides. We shall allow in addition to what Lo(X)contains already, sentences of the form u = o! where LX is a proper name and 11 E X, to exprcss thc former, and sentences of the forni P(u) where, again, u E X and p E CN, to express the latter t!.pc of condition. We shall refcr to the language obtained from I,o(X) through tllcse additions as L;,(X). We shall limit ourselves here to the simplest type of discourse, that of a discourse constituted by a finite sequence of declarative statements, made by one and the same speaker. Formally we shall identify - as in fact we already did implicitlq in Section 1.2 such a discourse with the sequence of the uttered sentences. So let us, wherc 1, is any language, define an L-discourse to be any finite string of sentences of I,. T h e examples we considered in the preceding section were carefully chosen so that the same singular term would ncver occur more than once. This made it unneccssnry to distinguish between different occurrences of the same expression. In general, howevel., different occurrences must be kept apart. T h e need for this is most obvious in connection with pronouns - it is only too common a phenomenon that the very same pronoun occurs twicc in a bit of discourse, but each time refers to a different individual, as c.g. might be intentled by someone using the sentence -

(24) If Bill courts a widow who adinires him then Pedro courts a widow who admires him. Rut in longer stretches of discourse otl~erexpressions are liable to recur ns well. Although the DRS construction rules defined bclo\v only require 11s to kccp track of the individual occurrences of certain expressions, little if anything would be gained hy introducing a mechanism for distinguishing just tltose individual occurrences. In E ~ u t probably the simplest way to distinguish the indi\-idual exprcssion occurrenccs is this: Let 11 = . . . ,4n)be an Lo-discourse and let ( T , , . . . ,z,) bc the scquencc of the (uniquely determined) syntactic analyses of the sentences of D. It is easy to formulate an algorithm which assigns a unique index, - sap, a positive integer - to each of the nodcs of thesc analyses, and, by proxj-, also to the expressions formed at any such node. For instancc we enumerate first all the nodes of T I , in somc order fixed by its structure, then those of TZ, etc., until we have dealt with the entire discourse. Thcre is no point to go into greater detail here. we shall simply assumc that one such illgorithnl has been fixed. By an o~.c-urretir.c.of an expression a in D me shall understand n pair (a, n) u-herc n is thc index of a node of the syntactic analysis of one of the sentences of D to which a is attachccl. T h e relation \vhich holds between two cxpressions o! and /3 if is a subexpression of [j has an obirious counterpart betwccn exprcssion occurrences: (2,n) is a " s i ~ b ~ c c i ~ r rci~ce"of (p, m ) i f (a, n) occurs as part of the syntactic analysis of (p, m ) . I shall of'ton lx

210 Hans Kamp speak, by a minor sleight of lzand, of one espression occurrence being a subespri~.ssion (SM~/UYII~U/L~, etc.) c-,/'some other occurrencc. No confusion should arise from this. 'I'he construction of a DRS for D does not only require the separate identification of particular occurrences of expressions of Lo; ure must also be able to keep track of different occurrences of the same expressions of Lb(X). However, as our examples llave already indicated (and we shall soon make this fully explicit) the expressions from Li,(X)\Lo which enter into DR's arc always derived from corresponding expression of Lo. T o be specific, they result either (i) through one or more substitutions of'memhers of X for singular terms in some sentcnce of Lo; or (ii) fi-om placing a member of X in parentheses behind a CN of Lo; or (iii) from combining a inember of X with = and a proper name of Lo. In the first case .cvc can labcl the L.I,(X)-scntencc occurrence unambiguously with the index of the occurrencc of the LO-sentence from which it is obtained through successi\-e substitutions; in the second case we assign the indes of the relevant occurrence of the common noun; and in the third the indes of the relevant occurrenee of the proper name. In each of the cases (i), (ii), and (iii), wc shall say that the sentence of Lb(X) is a ~ t e s r - u ~ d u of n t the relevant expression of 1.0, and similarly that the occurrence of the L:,(X)-sentence is a clesl-enJfint/$the corresponding occurrencc of an expression of I,(). Formally we shall represent any c~ccurrenceof such an expression also as a pair consisting of the expl-cssion togcthcr with the appropl-iatc index. There is one other notion which we ha\-e already defitlecl thr LObut which must also he extended to cover certain expressions of IJ{,(X)21s well. 'I'his is thc notion of die outemlost rrrlt ?/'an expression. We shill1 need to refer to thc outermost rulc only of those sentences of L6(X)\Lo which result from n-laliing in scntenccs of Lo one or more substitutions of mcinbers of V for occurrences of singular terms of Lo(X). An?; such substitution leaves the syntactic structure of the sentence in which it takes place cssentiallj- inviolate: it can only lead to some "pruning" of' the syntactic tree, viz. cvl~erethe replaced singular term occurrence is itself' complex. In that casc the subtree domiluted by the node to which the singular term ( Y ) is attached is delctcd and replaced by a single node to which is attached the inserted (basic) tern] (11). 'The outcrmost rule FKi of the resulting sentence should not count 1-1s outermost rule of the syntactic analysis of the substitution result. For FRi is the rulc which combines u with the remainder 21 of thc sentence, and this is a syntactic operation which, unlike the analogous operation that combines the replaced singular tc~-111with :,', should give rise to no further step in the DRS construction (the singular term 2 has nitcr all just hecn dealr with!). Thus we should identify as the o r ~ ~ r r r t ~ o s ~c-,/'thesubstitution result, rather the outermost rule of 7 . Since, as ttle already ohser.\,ed, each of the I ,{,(X)-sentences in question results from a finite scquence of such substitutions the above stipulation defines the outermost rule of each sue11 sentence. Having exteilded the concept of the outermost rule of an expression to certain sentences of Loo() we can now also apply the notions ~.ow~liiinnn/ and ri~riz~i~l-sul snl/elrlr to those sentences. Moreover, we shall call ato~nicthose sentences of L,:,(X) which consist eitl~er(i) of a discourse referent followed by an IV; 01-(ii) a 'I'V flanked b y two discourse referents; or (iii) a CN follou-ed by a discourse I-cfcrentin parentheses; or (iv) a discourse referent followed by = and a proper name of Lo. Here is the definition of the "format" of Discourse Representations 1 have choseo, as well as of some related notions which are shall need in later definitions:

A Theory of Truth and Semantic Representation 211 DEFINITION 1. Let D be an Lo-discourse. 1 A possddtj D R (Dis~.oz,~rsu Represe~.ztntion)of'D is a pair (U, Con), where (i) U is a subset of V; and (ii) Con is a set of occurrences in D of sentences of Lb(U). 2 Where rn and m' arc possible DR's for D we say that m' e,vteil~ism n if L,,,

3

U,,,~and Con, 5 Con,,,, . Let nl be a possible D R for D . A sentence 4 E Con,,, is called uizrc.ritrier/i r ~m iff Con,,, contains no descendant of 4. m is called m~n.rfizalif each unreduced member of Con,,, is either (i) an atomic sentence, (ii) a conditional, or (iii) a universal sentence.

We have seen in Scction 2 that in general we must associate with a givcn rliscoursc a Discourse Representation Strur-tzivr, i.e. a partially ordered of llli's, rather than n single DR. As it turns out the partial orders of thosc DRS's which our rules cn:~blcus to construct can alu-ays bo defined in terms of the internal structure of their niembers. This makcs it possible to define a DRS simply as a sct of DR's. T o show how the partial order can be defined in terms of the structure of the I>K7s that make LIPthe DKS we have to make explicit the structural relationship that hc~)lds between a D R m which contains a conditional or universal sentence (p and the pair of DR's which must be constructed to represent the content of But before we can d o that we must first discuss, and introduce, a slight n~oclification of the schema fix representing conditionals and universals that we have used in our cxamples. So fir cvc have reprcsentecl conilitional $A ( ~ h mB) bq- a DR ml of A together with an extension nil of r n ~which incorporates into it the information contained in B. 'There can bc no objection to this schema as long as the information contained in A can be fully processed in ml beforc onc extends it by processing B. It is not always possible, honever, to proceed in this way, as is illustrated by (25). (25) If a woman lovcs him Pedro courts her. 'Thc order in which the construction rilles must be appliecl to 1-ield a DKS ~vhichlinks /rim with Pedro and her with a n7onra12, is indicated in the following cliagram: n1,,(25)

(0) if a woman loves him Pedro courts her m,(25)

( I ) a woman loves him (2) woman (u) (2) LI loves him (5) u loves v

n1,(2.i)

( I ) a woman loves him (1) Pedro courts her (2) woman (LI) (2) u loves him (3) v = Pedro (3) 1: courts her (4) \- courts u (5) u loves v

212 Hans Kamp Not only is there duplication here of the conditions which occur both in m1(25) and m2(25)but some of the operations have to be performed simultaneously ~rrrrli w I ~ L sarnc J I I I ~ z . ) ~ 011 , the identical entries of these two DR's. It would be possible to characterize DRS-construction so that such entries are treated simuitaneously in all the DR's in which they occur, and give rise in each of these DR's to the same descendants. But tlis is a\vl,tvard, particularly where the treatment produces new subordinate DR's. It is easier to introduce into the second DR of the pair representing a conditional only the information conveyed by the consequent. In the case of (25) this will lead to a DRS of thc form:

I if a woman loves him Pedro courts her I

I a woman loves him /

woman (u) ( u loves him u loves \;

Pedro courts her v = Pedro v courts hcr

Similarly, we shall represent a universal sentence by a pair of DR's into the second of which w-e enter the information that the remainder of thc sentence is true of the discourse referent ~vhiclistands in for the singular term ct*ery P in question. For example the DRS K(15) for ( 15) Ei-ery-nidow admires a farmer

now becomes

( Every \vidow admires a fiirmer (

x admires a firmerfiarmer (u) s admires 11

Evidently the second nlembers of the representing pairs about which we have bccn speaking up to now can be reconstructed from these ncw pairs: where ( m l ,mr) is the old pair and ( m l ,in;) the pair which replaces it according to the prescnt stipulation, rnl

A Theory of Truth and Semantic Representation 213 is thc union of ml and 114, wherc the lmion of two DR's (U1,Con,), (Uz,Conr) is the DR ( U 1 U L2,Coill U Con?) - thus, in particular, m1(15) is the union of ml(l 5) and d,(15), and m2(25) that of m1(25) and mi(25). Note that the truth clausc (12) for conditiorials and its al~aloguefbr universal sentences arc not affected bv this change. Let us now describc how we can recogilize two DR's ml and n12 as rcyrcscnting conditional or universal sentence that occurs among the conditions of'thc T>R m. We first assume that m contains the occurrence (4,k) that 4 is a conditional ai~dthat its antecedent and consequent are, respectively, (I/!, r) and (x,s).li We say thi~tthe pair of' DR's {m ,inz) represcvr~s(4,k) iff:

(i)

($, r) E ConIllland every member of Con,,, is a descendant of a subexprcssion of r); (x,s j E Con,,,, and every membel- of Con,,, is a descendant ofa subcxl>ressionof' ( $ 7

(ii)

I

Now suppose (4, k) is a universal sentcnce. Here it is conveniei~tto distinguish between the casc where the term with maximal scope is of the form czqer)f11, where /j is a basic C N and that where it has the forin ere[-! /1j1 wiih /i a CN and 11a RC. I,CI us begin by considering the fjrst of tllese. We say the pair (mr,n12) r~yrc*si?r~rs (4,k) iff for some x E V (i) x ; ( i ) C o n , = { ( ( x ) i } ; ( i ) (9'.k) E G)n,, and cach member of Con,,,, is a descendant of a subexpl-ession of (d', k ) , where i is thc index of the oceurrence of /? in the term (occurrence) tz;e?y fi in question and 4' is the rcsult of replacing that term occurrence in 4 by x. N O Mconsider thc case wherc the term with maxinial scope has the form rz.e1:)~/I;), where /i is common noun and y a relative clause. In this case ( m l , mr) ~ ~ ~ I ' L ~ S P(I dI I ,Sh) iff fui- suine x E V (i) x E U,,,,; (ii) (/I(x), i), (6, r) E Con:,,, and every member of Con,,,, other than (P(x), i) is a descendant of an occurrence of a subexpression of (3, r); and ( i ) { I , k E Con,, and every member of is a descendant of an occurrence of a subexpression of ((If,k) - hcse i and 4' arc as above, r is the index of the occurrence of 1' in the relerant occurrence of fcc~-yP;? and (S is determined as follows: lct be thc sentence from which the relative clause has been formed through "wh-movement"; (5 is obtaii~erlby substituting x in for the pronoun occurrence which was eliminated in tlic transition from i to ;I. Nest we must gi\:c the definition of-pariialD~.s~.ozrrsr R~p1.t7senlrr/ion Slr~lc,~icrrs.

<

<

DEFINl\iIT/ON2. Apat.tic~lDRS (Dkrolrrsr Rrpl-c.se?r~aiiorl Stnlirr~re).firi-D is 3 set I< of possible DR's for U such that whenever m is a member of K and Con,,, contains a conditional or universal seilteizce ( ( / I , k) then therc is at most one pair of me111bcl.s and m, of K which represents (q!!,k).

1111

\Ve s:ly that a meinbcr m' of K is i~linlet/iclte/)r srr/?orl/iuateto tn iff cither (i) there is a conditional or universal sentence occurrence (4,L) E Con,,, such that 111' is thc fii.st member of a pair which represents (4, k); or (ii) nl is itself the first inenlber of such a pair and n ~ is ' the second member of that pair. m' is alborrlincrte to m iff there cxists 11 iinitc chain of iinmcdiatc subordinates conilecting m and m'.

214 Hans Kamp T h e rules fbr constructing DKS's will guarantee that they ~ v i l l always have a principal mcmber. If the partial DRS I< contains such a n~emhcrit will be denoted as I ~ , ~ ( E 1Vhere ;). I(. and Kt are partial DRS's m-e say that Kt ~~rt~nt1.s k iff there is a 1-1 map f from K into K' such that for each m E K f(m) extends m. For m € K we denote as K' (m) the set consisting of'm and all the members of K that are superordinate to m. \ye shall also mrrit.e "Uh"for "Umth Urn7' and "u; (m)" for "UIl U(LnI/: m' t K and n ~ is ' superordinate to m }". We sal- that a partial DKS K is ~,on~pli'te iff (i) every mcmber of K is maximal; and (ii) \vhencver m is a membcr of K and Con,,, contains an occurrence of ((/,, k) of a conditional or universal sentence K contains a pair w~hich represents (4,li) . \JTe can now proceed to give a precise statement of the rules for DKS-construction. It is they, I must repeat here, that carry virtually all the empirical import of the theory. 'Their exact formulation is therefore of the greatest importance. Instead of trying to do justice to all relevant linguistic F ~ t at s once, I shall begin stating the rules in a fairly simple manner. This will then scrvc as a hasis fi)r further exploration. ]!or thc fragment ldothcre we five rules, one for proper names, one for indetinire descriptions, one for pronouns, one for conditionals and one for universal terms. The effect of applying a rulc to a particular condition in some mcmber of a IIRS is always an extension of that DRS. Only the rules for conditionals and universals lead to the introdi~ctionof ne1v L)R1s. But this does not mean that the effect of each of the othcr rilles is confined to ~ h c particular DR m which contains the condition to kv11ich the rule is applied. Thus, for instance and this is a point we have so far ncglccted in our ertamplcs - the appliciltion of tlle rule for proper names \\rill always result in the introduction of a new discourse rcfcrent into the principal DK of the DKS, even if the condition to which the rulc is being applied belongs itself' to some othci- men~berof the structure. (I shall argue bclow that the rule for proper names 77zust operate in this f~shion.)Directl! conncctcd with this is the need to refer, in the statement of the rulc for pronouns, not just to the unii-ersc of the D R m that contains the rclcvai~tcondition, but also to the univcrscs of certain other members of the DRS - in fact, as it turns out, of all ihose mcmhers 1~11ich are superordinate to m. T o state the first three rules let us assume that K is a partial IJRS, that nl E EL, that (4,k) E Con, is an unreduced member of m, and that (31, i) is an occurrence of a term in ($, k ) which has nlaximal scope in (4,k) . -

CK1.

CR2.

Suppose a is il proper name. We add to U,,,,,(h) an elemcnt 11 from V\'UL. Furthermore, me add to Con,,>,,(~, the occurrence (u = x, i} ancl to Con,,, the occurreIlce (4')10, where 4'is the result of replacing tho occurrence of ;x in ((I),k) with index i hj- u. x is an indefinite singular term. (a) z is of the f i ~ rr(w)/j, ~ n n-her-c/j is a common noun. 1Ve add to U, an clement u from \i\U1, and to Con,,, the occurrences (/j(u), r} (where r is the intlex of the occurrcncc of 1) in (a, i ) ) ancl ((b', k), where 4' is as under CRI. T h c other members of K remain i~nchanged.(b) a is of the form a(n)P;l, wl-rerc p is a basic common noun and 11a relative clause. Wc add u E \i\UF; to L;, and expand Con,,, with ((j(u), r), ((/)', k) and the pair ((S, s)

A Theory of Truth and Semantic Representation 215 wherc 5 is determined as in the definition of I - C ~ I ~ ' S Z I Igivc11 ~S above, and s is thc indcx of the occurrence of ;l in ( a ,i). CR.3. Assume a is a pronoun. Choose a "suital~le" n~cmbesu fi-om UI, (111). Adct (#', li) to Con,,, is as under CR1.

NB. I have given a deliberately "fudgey" formulation of this rule by inserting the urord "suitable". T o state what, in any particular application of the rulc, the sct of suitable referents is, we would have to nuke explicit what the strategies are that speakers fbllow wllen they select the antecedents of anaphoric pronouns. In the applications we shall consider below thc restriction to "suitable" referents that I h a w built into CR3 will never play an overt role (although I \vill occasionally ignore, ~vithoutcomment, readings of the sampled sentences which would impose anaphoric links that arc rulccl out by various fiactors that enter into these stratcgics, such as e.g. the ~ r i i ~ c i p lof' e gender agreement). Noncthcless, I have included "suitable" in thc fi)smulation of C X . 3 , as a rcminder that the rulc is incomplete as it stands. 7'0 statc thc last two rules let us assume that K and m arc as above, that ((I,, k ) is an unreduced member of Con,, and thar q5 is either a universal sentence or a conditional. CR4.

CR5.

(x,

Assumc ((b, k ) is a conditional with antecedent (ti/, r) and consequent s). \Vc add to I i the member {((I, r) ) ) and { (x,s) )) . Assume ( 4 , k) is a universal sentence and the term with maximal scope is /j,i) with p il basic CN. We add, for some u E v\Dk ( { u), { (/I(LI),I-))), and (0, {((b', k))), wherc r and 4' are as 2 pages above. Similarly, where thc term with maximal scope is (~z:el:)l r) whesc p E CN ant1 .,I E RC: the IlR's that must be added are ({u), {(/J(u),r), (S, s ) ) ) and (O), {((I,', k ) ) ) , where, again, u E V\VIc and s, 6, 4' are as in the statement of CR2.

(a,

(a,

(tzle.~:)~

p;.j,

Note that if K is a finite DRS, i.e. a finite set of finite UR's, then a finite number of applications of the rulcs CRl-CRS will convert it into a coinplete DRS. Any completc DRS obtaincd from K by a series of' rulc applications is called a c.nn~pl~tion (!/'K. Clearly, if K has a principal member, then so does evcrj- completion of' K. \ICre ciln at last define the notion of a ronzplcrp DRS./i)r a discourse B. T h e definition proceeds by rccursioi~on the length of D.

L)EFf,VlT/OrV 3. (i) Suppose D is a discourse consisting of one sentence (1). I,et k be the indcx of 4 in 1).'4 c-on/plt.r~DRS (D~.SL'OL/UP Reprre~.el~t[/iior7 . C ; I I ' ~ I ~ / I I T ( ' )/Or 13 is any completion of the DKS { (0, { (4,k)})). (ii) Supposc that D has thc fi)r-m ((/I,, . . . , (/I,, @,+,) and that the set of complete DRS's for thc discourse D' = (cbI, . . . ,4,,) has alreadj- been defined. Let k be the indcx of the occurrence of d),, as last scntencc of D. Thcn K is a c.o,nplctr DRS Jilr D iff K is a complction of a IIRS of the fixm (K' - { ~ I ~ ( K ' )U) ){m), where K' is somc complete DliS for 13' and nl is the DK ( ~ , l l ( , ( k fc)o?l ~ , , , , , u ( ~{~(4% ) k) 1). ;

NR. It fbllons ti-om this definition together with earlier renlarks that e\cry scc of possible DR's which is a complete DRY for some discourse D contains a principal

DR.

216 Hans Kamp

3.3 Truth Our ncxt task is to define truth. 1 . . . ) There is just one feature of the definition that might he puzzling \nrithout a brief preliminary discussion. T h e evaluation of conditionals and universals as a rule involves only embeddings that respect certain previously assigned values to some of the discourse referents in superordinate positions. In other words we keep, in the course of such evaluations, certain functions fixed and consider oilly embeddings compatible with these functions. This means that the recursive definition underlying the characterization of the truth in M must be of a concept which is sensiti\.c not only to the information encoded in the D R S but also to some partial function fiorn the discourse rcfcrcnts of that DRS into Us,. If a sentence contains several nested embeddings of conditionals or universals, the maps considel-ed in the evaluation of deeply cn~hcddcd constructions may have to agree with several functions that have been stored, so to speak, along the way down to the conditional or universal concerned. However, as these stored functions must also be compatible with each other \nrc need consider only single functions in this connection; intuitively these arc thc unions of the scts of different fi~nctionsaccumulated along the path towards the embedded construction. Let I< be a complete LIRS for D and .M a model of L). We shall give the definition of the truth ~:rrllrrof'D in M give?? K in two steps. 'l'hc first stagc will give 3 charactuization, by sin~ultaneousrecursion, of two rclations: (i) T h e relation which holds bctwccn a member m of K, a function f from U,, into UM and a partial function g from Lkinto UL.riff, as we shall express it, f zlrr?fifirsnl in M gizlen k,~ t l i ~ ~10i g; z ~and t (ii) the relation which holds bctwcen rn, an unreduced member ((b, k) of Con,,,, il function f from U,], into U31 and a function g- from Uk into UMiff, as we shall say, ((b,k ) is /rut iii ~r,wler f, gizrrr K, relr~tiz'elo g. T h e second stage uses thc first of these two rclations to define truth:

DEFlNIT102V 21. 1,et L) be an J,o-discoursc, K a complete IIIRS of D and M a model for ITdo.D is trur in M on K iff therc is a function f from U,,l,,cr,l into Up,[ which verifies ml,(K) in hl, given k,relative to A. ( A is the empty function!). T h e recursive part of the definition is inevitably somcivhat more invol\ied.

DEFllV17'10AT 5. Let D, k,R/I be as in Definition 4; let n1 E K a11d let g be il partial function from UK into U-4r. (i) f crv(fir.s m in M gizvn k,re/ntiz*rto g iff each unreduced n~ember{{l,,k) of (:on, is true in _M under f, given K, relative to I$. (ii) Suppose (4,k) is an occurrence of an atomic sentcncc in Con,,,. 'I'hcn (I, has onc of the following four forms: (a) ua, where u E V and IX E IV; (b) uav, where u, v E V kind a E TV; (c) u = u, where u E V and a is a propcr namc; (d) ~ ( u ) where , u E V and a is a basic common noun.

A Theory of Truth and Semantic Representation 217 The question whether (4,k) i\. lrrlc in M un&r f g l ~ l t ~K, n r.rllr/icr io g splits u p into the corresponding four clauses below (we omit the qualification "in M under f, givcn K relative to g"): (a) (q!!,k) is 11.u~iff f(u) € FsI(a); (b) (4,k) is true iff (f(u), f(v)) E Fzl(a); (c) (9, h) is /rue iff f(u) = FAr(y); (d) (4,k) iv true iff f(u) E Fnl(a). (iii) Suppose (rh, k) is an occurrence of a conditional or universal sentence in (:on,,,. Then K will contain a unique pair (ml, m2) which represents ( 4 ,k). ((/I, k) is trzw it? M under f givrn K, rel~lti~ie to g iff every map h from U,,,, into UMwhicll is compatible with g U f and which verifies ml in M given K relative to p U f can bc extended to a function k from U,,, inlo Ukt and verifies rns in h4 given K relative to $ U f. Wc shall call a function which verifies mo (K) in M, given K, relative to A a rel-~[jtin'q, or tvt.it~fill,embedding oj'K illto M. We shill1 also say of such a map that it ctwfifirs L)111 M oil (the re~z~Iing proz~ihdby) K. Adany of the DRS's 11-e have earlier displayed fail to be in complete agreement with the construction procedure as we have now fornx~llpdescribed it. This is truc, in particular, of the second representation I gave in Section 2.3 for (14). T h e DRS K(1.4) violatcs the rule CRl in that the item u, which is introduced as the referent of the proper name Pudm should have been entered into the universe of nlo(14) rather than into that of m(14). Let us give the DRS for (14) once more, this time in its proper fosm .

Everv widow admires Pedro

m;( 14) s admires Pedro

T h c need to place the discourse referent introduced by a proper name into the principal DR is illustrated by (25) for which I gave a DRS in Section 3.2. 'This 1.IRS is unacceptable by our rules as the rcferent u in m2(25) is not acccssiblc horn the position of him in m1(2.5), to which, at step ( 5 ) it was nonetheless assigned. This difficulty would not have arisen had CR1 been properly applied in the first place. The correct DRS for (25) looks as follows:

218 Hans Kamp

(3) (0) if a n-oman loves him, Pedro courts her (3) v = Pedro

( 2 ) 11 (1) a woman loves him (2) woman (u) (2) u loves him

( 5 ) u loves v

(1) Pcdro courts her (3) v courts her (4) v courts u

Let us, for good measure, also give a corrected version of the DRS for (I), as the analysis of that sentence motivated so much of what 1 haic been saying, a i d yet its earlier representation also contains a violation of' CR1:

(2) u

(0) if Pedro owns a donkey hc beats it (2) u = Pedro

V

(1) Pedro owns a donkey (2) u owns a doi~kcy (3) donkey (v) (3) u owns v

(1) he beats (4) u beats it ( 5 ) u beats v

We alreadq- saw in Section 2 how important it is that the discourse refcrcnts available to a given pronoun must all occur in the same, or else in some superorclinate, DR. This, 17'~saw, accounts for the fact that it cannot hare ezvql itonkey as its antcccdcnt in a sentence such as (17) or ( I 8), or be anaphorically linked to il i l o t ~ k i yin (19). 1'he reader will inevitably ask, however, whv subordination is defiled in thc preeisc way it has been. Why, for instance is, where (ml, m2) represents a conditional or universal, mz subordinate to m, but not ml subordinate to m2; or, to put it more dircctlj-, wl~ymay the elemcnts of mz not ser\-c as referents for pronouns in sentences belonging to Con,,, jt-l~ilethe members of C,,, arc admitted as referents for pronouns occurring in mr?

A Theory of Truth and Semantic Representation 219 That the elcments of 11-11 must bc available for the pronouns of rnz is too central an assumption of our theory to permit tampering: our analysis of the crucial scntcnccs ( I ) and (2) depcnded essentially on that hypothesis. But what about rcftrents in niz for pronouns in m l ? Here is an example which shows that the sets of possible rcfcrcnts must bc ;is we have specified them: (26) Every fim-rler who admires her courts a widow. It is my intuitive judgement that in (24) lzer can be coreferential with N ~uiilo~??, but only if o mi(lon~has wide scope over ezler:y,fkmzer. Such "nridc scope" readiiigs for indefinites that occupy positions which correspond to narrow scope according to our syntax arc not ctiscussed in this paper. A reading which (21,) can plot have is, according to rn! intuitions, the one given by (27)

(Vx) (fari~ier(x)+ (37) (widow(y) A admires(x, y) A courts(x, y))) -

'To block this reading we must stipirlate that thc element v ofm2(26)is not a\:ailablc to the pronoun in ml(26):

/(0) evcry farmer who admires her, courts a widowl

(1) farmer (x) (1) s admires her

(1) x courts a widow (2) widow (v) (2) x courts i7

Our theory secnls to rule out a parallel reading for thc conditional (28) If a farmel- adinires hes, he courts a \vido~v. It predicts, that is, that (28) cannot mean what is expressed by (27). Again, h ~ in r (28) can be understood as corefercntial with a u~z(lo~?~ if the latter is taken to have wide scope as it normally would in, say, -

(29) If a farmer admires her he courts a certain widow I have dated and therefore know quitc well. (28) appears to have still another reading, in N-hich a widor?? is taken as gcneric, a reading that is approximated by (30) Vxb'j I farmcr(x) A widow(j7) A admires(x, y) - courts(x, 7.;) 1.

220 Hans Kamp Generics, however, arc among the most recalcitrant constructions know to me. T h c j will not be treated in this paper. Note also that (31) If Pedro admires hes he courts a widow, though understandable, on the assumption that her refers to a ~r~iill)n>, docs not sound natural - basely, more natural in fact than do (26) and (28) on their wide scope reading, given by

T h e rcason is that in order to get a reading of (31) in which her and ri 1~?ihr17 are corcferential we have to suppose - just as we must in connection with (26) and (28) that n miclom has \vide scope over the subject Pedro. In another paper nTeshall have more to say about why such readings tend to be somewhat unnatural.

Notes This paper wasrvritten w-hiie I hcld a Post-Doctoral Fcllonshir, at the Center for C;ognitivc Science of the Uniwrsity of Texas at Austin. Anybod!- who has the faintest acquaintance with n ~ qpersonality &-illrealize that it \vould not havc heen written had the Directors of tlic C:cntcr nut giwn me this opportunity, and thus understand the depth of my indebtedness to then^. I would ;11s0 like to thank, among the many who lidped me {luring my stay in Austin, Kate Lhrlich, Ali111 Garnhani, 1,auri Kartuncn and Stai~lcyPeters for their comments and suggestions.

I

Thcorics that to a greater or lesser dcgree accord with this intuition havc emerged within -12rtilicial Intelligence and Computes Science, as well as within 1,inguistics. A signilicant wntrihution of this kind that comes froni the first field is Wcbber (1978). l<xamplcs ol'such theories that havc bccn proposed by linguists arc: the theories outlined in Bartsch (1976, 1079), Cooper (1975, 1079), Hausser ( 1 974, 1979), Karttunen (1976). B!. no mcans cvcry reccnt account of pronouns is predicated on the assumption that all cases of pronon~i~lal reference can be brought under one unifying- principle. Cf, for instance l':\ans (1977, 1980), Lasnik (1976), Partee (1978). 2 Thcrc seems to be il rough preference for referents introduced b j terms that appear in thc discourse b e b w the anaphoric p o n o u n occr those that art. introduced by subsequent terms, as well as a prcference for referents that are introducecl by terms that occur n ~ ~ rthe ~ r . anaphor. (Thus the refercnt introduced by the last rcferenrial term preccdil~gthc anaphoric pronoun is, other Factors permitting, a strong referential candidatc.) 3 ,4 large part of the rcsearch that has been donc on anaphora by computer scientists and pcoplc working in Artificial Intelli~cncehas been concerned with this pn)bleni - undcrstantlably enough, ;IS the lackofcffectii-e routines for the detection of anaphoric antecedents has li)r many !cars bccn one of the main obstacles to producing satisfilctory computer systclns for cluestion answering and translation. However useful some of this work may have been, I havc the in~pressionthat its ~heoretial significance is rather limited. Tntleed J much incline to the opinion expressed, for exan~ple,in Parrce (1978, p. 80) that all we can reasonably expect to achieve in this area is to articulate orders of preference among the potential referents of an annphoric pronoun, without implying that the iten1 that receives the highcst rating is in cach and every case the referent of the anaphor. 4 UTeare much assisted in our making of such guesscs by the spectrum of our social prejudices. Sometimes, however, these ma\- lead us astray, and embarrassingly so, 11s in the tbllowing riddlc

A Theory of Truth and Semantic Representation 221 which ad\ocates of Women's Lib have on occasion usccl to expose mmll~crsof tllc chau\-inistic rearguard: In a hcad-on collision both fathcr and son are criticillly \voundcd. The! arc r ~ ~ s h c ~ l into hospi~alwhere the chicfsurgeoll perforn~csan emergency operation on the son. 13ut it is too latc and the boy dies on the operating table. When all assistant asks tlic surgeon, "C:ould o u lxl\-c a look at thc other victim?", the surgeon replies "1 could not hear it. I hnvc alrcacl!. lost niy son." Someone who has tlie built-in conccption that chief surgeons arc men \\.ill lincl it substantially more difiicult to make sense or this stor! that those who hold no such lien. 4s \Ye ha\e alreadv obser~ed,this is not quite correct, since a pronoun can be used deietically, in \vhich case the referenr need not belong to the 1lR; we shall, lioivever, ignore the dcictic use oi' pronouns in the coursc of this paper. See for exa~nplcLewis (1973), Turner (1981), i'elu~~ian (1976). Kratzer (1970). ( I I) is akin in spirit to the game theoretical analysis of if.. . t h e n . . . sentences proposccl in Hintikka and Carlson (1978), according to which a \\inning strategy for the dcfcndcr of t / ' A /hr?l I3 is a lilnction which maps evu; vc-inning strategy for thc del'cndcr of .4 onto ;I n~innirlg stratcgx for tlie dcfender of H. T h e t:act that iic~istential"quantifier phrases can he represented in this manner is closclj- rclatccl to the familiar nlodel theoretic proposition that purclj- existential scntenccs arc prescncd untlcr ~nodclextensions. 1 have found at least one speaker lor whom (20) is distinctly less acccytahlc than for instiincc (1). Scr for example C:arlson (1076, Chapter I), which warns against this prejudice in similar terms. Proposals siniilar to that of E\-ans can be found e.g. in C:ooper (1970) and IIausser (1974). Thcsc suffcr in my vicw from similar shortcomings. T h c t\vo fi-aginen~shave roughly the same quantilicational powers. Rut the prescnc fi-agnient lacks adjectives, prepositional phrascs and intensional contests. One might ]lave hoped that a theory of semantic proccssing such as the one attempted here could provide an explanation of why island-constraints exist and n.hy lie!. operite in yrcciscl!- those linguistic contests that are subject to then]. 1 h a w not succecdetl, however, in iinding such ;In explanation. See c . g hlontague (19703,b; 1973), Partee (1975), Thomason (1076), C:ooper and Parsons (10'76). Cooper (1079). With the O C I . Z ~ I . T E N L ~ ((I), P k) are associated, of course, particular ol.i./irrenc-c>soS antccedcllt and consequent.

References Biwtsch. R. 1076. Syntas and scnlantics of relative clauses. In Groenendijk and Stolihof 1076, 1 24. Bartsch, R. 197% T h e s! ntax iuld se~nanticsof subordinate clause constructions and pronominal rcfcrencc. In Hen? and Schnellc 1979, 23-59. I
222 Hans Kamp Groenendijk, J. and hl. Stokhof (eds). 1976. Proc,eedilrgs I!/' /Ire .-f~trs/err/rrnrCalkqr~iu~rt on Morr/agnc Gr/rrr!~narrrnd Rrltr/etl 'li)pic-s, -41nsterdani Papers in Formal Gramtnar 1. C:cntralc Intwl~~cultcit, University of .4rnstcrclanl. Hausscr, R. R., 1974. Q~~nntification in Extended Montagi~cGran~nlal..Ph.11. Ilisscrtation, Univcrsity of Texas. IIaussel., R. R. 1079. I low clo pronouns denote? I11 Hen? and Sclincllc 1079. 93-1 30. Hcndrix, G. 197.5. Partitioned Networks for the k~athcmatic~~l R/Iodclling of Natulxl I.;lnguagc Scmantics. Ph.D. Disscrtation, University of Texas. Hcny, F. and H. S. Scli~lellc(cds). 1979. Se/ei/iom,/ianr /he Tlrir-(l C~.oniiryr'i~ IZorriri/ 'I;rblt.( S ) I I I / ~tird ~.V S P I / I O ~ ~ vo1. I I L S10). , New York: :lcadernic IJrcss. I-Iintikka, J. and I.. Carlsson. 1958. Conditionals, generic qiiantifcrs and suhg;~mcs.In: 1.: Saarincn (cJ .), Gmrtze Tl~roveti~.al S z n l ~ ~ r i cDordrccli s, t: D. Rcidel. K;l~.rtuncn,1,. 1076. Discourse referents. In McCawlc! 1976. Kratzer, A. 1979. C:onditional neccssit~and possibility. In Haucrlc cr al. 1979, 1 17-147. I,asnili, H. 1970. Rcmarbs r)n corcfcrencc. L,i~/gtlrs/i~. . ~ I I ( I / ) I S I S , 3. Lewis, L). 1973. Colr~l/ei;lir~~/z~~i/s. Oxford: Blackwell. RlcCawlc?, J. D. (ed.). 19'76. 12'o/csJi.ort7 / k t I , / ~ ~ g u i s /I:nrlel;clr*o/lnr/ /i. (S)lrr/rr.v lrntl St~i~rrin/l(.s, vol. 7). New York: Acadcmic Prcss. hlontaguc, K. 197Oa. English as n fornlal languapc. In B. 1,-iscntinict i l l . (ccls), Z.i~/g~/irg,c~ nc'llrr sor.ir/rr(, rrc~llrr/ec.lric.rr, hlilan: Edizionc cli Communita, 180-224. Rep. in Thomason 1971, 188-22 1 . h/lont;lgue, R. 1970b. Universal grammar. Tlreoritr 36, 373--308. Rcpr. in 'Thonixon 1974, 222-46. 1\4ontague, R. 197.3. T h e propcr treatment of quantification in ordinary I
File Change Semantics and the Familiarity Theory of Definiteness Irene Heim

1 Introduction What is the difference in meaning between definite noun phrases and indefinitc ones? Traditional grammarians, in particular Christophersen and Jespersen, worked on this question and came up with an answer that nowadays finds little favor with semanticists trained in twentieth century logic. It amounts to the following, in a nutshell: (1) A definite is used to refer to something that is already/irnliliar at the currcnt stage of the conversation. An indefinite is used to introduce a nrn7 referent. This has been labeled the "familiarity theory of definiteness."' When confronted with (I), the logically minded semanticist will notice immediately that it presumes something very objectionable: that dcfinites and indcfinitcs arc referring expressions. For only if there is a referent at all can there he any qucstion of its familiarity or novelty. Advocates of (1) cannot happily admit that there arc nonreferring uses of definites or indefinites (or both), because that would be tantamount to admitting that their theory leaves the definite-indefinite-contrast in a significant subset of NP uses unaccounted for. But the existence of nonrefcl-ential uses of dcfinitc and indefinite NPs can hardly bc Just denied, and I will take it for granted without repeating the familiar argi~ments.~ think of examples like (2) and (3).

( 2 ) Every cat ate its food. (3) John didn't see a cat. (2) has a reading where "its", a personal pronoun, i.e. a typc of dcfinitc NP, functions as a so-called "bound variable pronoun" and doesn't refer to an! particular cat. Under thc preferred reading of (3), with negation taking widest scope, the indefinitc "a cat" fils to refer.

224 Irene Heim So the cards appear to be stacked against tlie Cnmiliarity theory of dclinitcness. Nevcrtheless, I will trv to revive and defend it, or a tlieory vesy much like it. 'l'he version I will defend is just different enough from (1) to avoicl the problematic presuniption of reftrentiality. Otherwise it agrees with ( 1 ) - and accordingly deviates Li-om standart1 assumptions in logical semantics - in ftindanicntal respects: It involvcs familiarity and novelt~-as il central pair of notions, ancl it takes neither cletinitcs nor incleli~~itcs to be quantifiers. What is the point of rehabilitating- a problem-ridden traditional approach \vlicn much more sophisticated alternatives have become a~iailablcthrough the work of logical semanticists from Russell to thc present? - I would like to ilrgLlc that a familiarit!. theory of definiteness, if construed along the lines of' this article, enables us to makc hcttcr predictions than competing theories about the behavior of definites and indefinites in natural languages, in particular about their p;~rticipation in anaphora relationships. I return to this point in section 7 below, but first I niust lay out the tlicory 1 a m proposing.

2 Karttunen's "Discourse Referents" Mine is not the first attenipt to rehabilitntc tlic fC~niiliarity theory of dcfinitcncss by dissociating it tiom the problematic presumption that dcfinitcs and indefinites are referrins crprcssions. In the late 1960s, Karttunen wrote sonic directed at the same goal. In order to ac'oid untenable claims i~boutref'crenee, Karttunen refi)r~nulates the familiarity theory by using a new notion, that of "discourse I-efcrcncc", in place of "refcrence". So instcad of principle (I), he lli~sa rccli~i~-cn~cnt that a tletinite NI' has to pick out itn all-cady familiar ~/iscollr.s~referent, whereas an indefinite N P always introcluces 3 new ~ / ~ ~ ~ ~ O ~rcfercnt. ~ Y . V . S P Since discourse refcrence is distinct from retirrcnce, and since, in particular, an NP may Iia\-e il discourse rcfercnt even c\-hen it has no re fercnt, this reformulation makes the fi~niiliaritythcory inim une to the objections encountel-ed by its traditional version (1 ). Let me illustrate with two c~i111iple~ how tlie distinction bctwccn discourse rcfcrcnce and genuine rcl'ercnce can be csploited in evading z.lilemmata that the tlxclitional fhmiliaritj. theorist must find f:;ital. C:orisider the tcst under (4).

(4) John came, and so did &far!,. Otre c!J'l/i~ntbl-ought a cake. Tlic underlined NP L'onc of them" is indclinitc, therefore (1) ~z'oulclseen1 to predict that it niust rcfer to an as yet L'unfii~iiilii~r" person, i.e. n ~ e r s o niiot already introduced in the prc\-ious discourse. Now t l ~ cfirst sentence of (4) mentions both John and Mary, hencc both of them arc fL~11~ilii~r when "one of tliem" gets uttered ant1 should conscqucntly be excluded as potential referents fi)s "one of tliem". 13ut that is countcrintuiti\ c, since (4) is naturally rcad as s:lying that one ol'John and Rilarl, not some third pwson, brought a calie. "Onc of thcni" if' ~c ilre t o ; ~ ~ l l i iti lt i ; ~il~rcI'Ct-s t o anything at all - clearly can rcfer to John or hfarj. here, in apparcnt 1,iolation o f thc Limiliarity theor>-. - Uut noif- suppose we 11a1.e rcplaced ( I ) 13) Kat.ttunen's version in tci.111~of discoursc ret'crcnrs. T h e n the prediction aboui "one of thcni" will be thilt, since it is inclcfinitc, its discol~rscreferent ~iiiistbc n e ~ and . milst be distinct from tlic ~liscoursc: -

File Change Semantics 225

/ I

referents of "John" and "klary" in particular. There is no prediction about the seferents of these three NPs, and we may consistently hold any assumption we please about those. In particular. we may assume that NPs with distinct disa)ursc rcfcreiice sometimes happen to coincide in reference, and that (4), being a case of this kind, involves three discourse referents, but only two referents. Next, consider (5).

( 5 ) (a) Everybody found a cat and kept il. (b) It ran away. Thc relevant facts here are that the "it" in (Sa), but not the "it" in (jb), can \ ~ c interpreted as anaphoric to '
226 Irene Heim theoretical construct which mediates in a way to be made precise between language and the world.

3 Conversation and File-keeping A listener's task of understanding what is being said in the course of'a convc~.sation bears relevant similarities to a file clerk's task. Speaking metaphorically, let me say that to understand an utterance is to keep a file which, at every time in the course of the utterance, contains the information that has so far been conveyed by the utterance.' Supposc, for instance, someone is listening to an utterance of the followii~gthreesentence-text .

(6) (a) A woman was bitten by a dog. (b) She hit it. (c) It jumped over a fcncc. Before the utterance starts, the listener has an empty file, i.e. 3 collection of zero file cards. Call that empty file "FoV.As soon as (ha) has been uttered, thc listener puts two cards into the file, gives each card a number - say " 1" and "2", and writes the following entries on them: on card 1, he writes "is a woman" and "wi~sbitten by 2", and on card 2, "is a dog" and "bit 1". H e now has a two card file, call it "FI",which looks iilic this:

-

is a woman was bitten

1

- is a dog

(-

bit 1

Next, (6b) gets uttered, which prompts the listener to update card 1 by adding the entry "lzit 2", and to update card 2 by adding "was hit by 1". H e now has V r ,still a two card file, but a different one:

- is a dog - bit 1

- is a woman - was bitten

by 2

L- hit 2

I

-

was hit by 1

u

Now comes the utterance of ( 6 ~ )T. h e listener takes a new- card, numbers it "3", writes on it "is a fence" and "was jumped over by 2", and also updates card 2 by adding on it "jumped over 3". This leaves him with F;, a thrce card file:

1

11

I - is a moman ( - ;:iten - hit 2

(

- is a dog - bit 1

- was hit by 1 - jumped over 3

1 1 w:rjurtrl;d 1 ( (

- is a fence -

I

File Change Semantics 227 With this illustration in mind, let us repeat our initial qaestion: How do rlcfinites differ from indefinites? We may now answer: They diffcr in the way they intluciice thc clevelopment of the file; the listener treats them differently, appaseiltly fbllowing an instruction like (7) in his file keeping.

(7) For every indefinite, start a new card. For every- definite, update an old card. For instance, cards 1 and 2 were newly introduced in response to t-he indefinites "a woman" and "a dog" that occurred in (6a). Only definites, namely "she" and "it", occurred in (hb), therefore F2 only contailled the same cards that were already in albeit updated. (hc) had both an indefinite ("a fence") and a definitc ("it") iii it, I~cncc it prompted both introduction of a new card (card 3) and updating of an old onc (card 2). All of this conformed to (7). Instruction (7) is reminiscent of principle (1) above and can in fact bc sccn as incorporating a version of the familiarity theory of definiteness: Like (I), (7) links definiteness to fimiliarity (= "oldness") and indefiniteness to tinvelt!i. Thc only difference of (7) from (1) is that not referents are supposed to bc old or new, but rather file cards. By substituting file cards for referents in the formulation or tlic familiarity theory of definiteness, I have made basically the same move as Karttunen, who substituted discourse referents for referents, and like in Karttunen's case, this move enables me to avoid the presumption of referentiality which caused si~chproblems tin the traditional version (1) of the fi~miliarit!; theory. Examples like (4) and (-5) are easily acoonimodated, once we think of file cards instead of refercnts, sincc it is quite conceivable for there to be a file card that fails to describe a referent, or for two different filc cards to happen to describe the same thing, or for file cards to bc introduced into and be removed from the file, depending on what is getting uttered. In short, just the properties we have found it necessary to attribute to Karttunen's discourse referents are properties that fit right into the file card metaphor. "This is why I would like to suggest that Karttunen's talk about "discourse referents" bc rephrased by substituting "file card" for "discourse referent": once we realize that discourse referents arc essentially like file cards, their identity critcria and their r-clation to referents come to look much less mysterious. In this section, I have introduced the file metaphor and have applied it informally to examples. Now it remains to give a more precise account of the theoretically relcvant properties of files and of the role thej- play in the semantic interpretation of natural language. Roughly, the model of seniantics that I am going to present will embody the following assuniptions. T h e grammar of a laiiguage generates sentences with representations on various levels of analysis, among thorn a level of "logical form". Each logical form is assigned a "file change potential", i.e. a function from files into files. Given an utterance with a certain logical form, this function will determine how you get fro111 the file that obtains prior to the utterance to the file that conies to obtain as a result of the utterance. T h e system moreover includes an assignment of truth conditions to files. Notc that logical forms themselves arc not assigned truth conditions, only files are. Only in an indirect way, i.e. via thc files they affect, will logical forms be associatcd with truth conditions. T h e diagram under (8) shows how this lnodcl of seniantic interpretation is organized, I will elaborate on its various

228 Irene Heim components in the next few sections, starting with the association of files with their truth conditions.

syntactic representations

grammar

logical forms

files

.

.

1 .

1

file change potentials

. . .

truth conditions

.

.

files

.

.

.

.

4 Files and the World ,4 file can be evaluated as to whether it corresponds to the actual facts or misrepresents them. Takc e.g. the file F1 of our example above. If it so happens that among all the women and clogs that there are there is not a woman-and-dog-pair such that the dog bit the woman, then F1 obviously misrepresents the facts. I will speak of a "ihlse" filc in such a case, and corrcspondingly will call a filc "truc" if it fits t l ~ c what does it take for a file to be true? T o establish the truth of a filc, we have to, so to speak, line up the sequence of cards in the file with a scqucncc of actual individuals, such that each individual fits the description on the corresponditlg card. Or, as I will put it, wc have to find a sequence of individuals that silli.$cs the filc. For tile I.'], for instance, we have to find a two-membered sequence, i.e. a pair, that consists of a 1st member a , and a 2nd member a2 such that a1 fits card 1, and a2 fits card 2 of F1.Any such pair will satisfy F I , i.c. we have: (al,a2) satisfies Fl iff a1 is a woman,

a1

is a dog, and a? hit a,

Depending on how many cards a file contains, it will take pairs, triples, quadruples, or what not to satisfy it, therefore I speak generally of "scquences". Technically, a sequence is a function from some subset of N (the natural numbers) into A (the domain of all individuals). T h e pair (al, az), for instance, is the function which maps 1 to a1 and 2 to az. (Notice that 1 also admit sequences whose domains are not initial segments of N. E.g. a function that assigns an individual each to thc numbers 2 and 7, but is not defined for any other numbers, also qualifies as a sequence. This would be the sort of scquence to satisfy a filc whose only two cards arc numbered "2" and "7".) A degenerate sort of sequence is the onc whosc domain is the empty set 4 and which is therefore 4 itself. 4 is the only sequence that satisfies file Fo, the file o f zcro cards in our example above.

File Change Semantics 229

I will often want to refer to the set of all sequences that satisfy a given file, thercftbrc 1 introduce a piece of notation, "Sat(F)" (read: "the satisfaction set of I;").

(9) Sat@) =,l,f

{aN:a~ satisfies F}.

(Hcre and elsewhere, "aK", "bxl", and the like range ovcr sequences, wherc the subscripts "N", "M", elc. stand for each sequence's domain.) I also need a short way of referring to all the card-numbers that are used in a given file, so 1 usc the notation "Dom(F)" (read: "the domain of F"). (10) Dom(F)

=d,f

{n E N: F contains a card with number n}.

As I said before, a filc is to count as true if some satisbring scqucnce for it can bt. Cound. Definition (11) expresses this. (1 1) F is true iff Sat(F) #

6 (and

Fdse otherwise).

In the remainder of this article, I will often describe a filc solcly in terms of its domain and satisfaction set. It should bc clear that that does not suffice to pick out a unique file. There are always many distinct files that happen to have the same domain and satisfaction sct. T o give an extreme example, any two false filcs which happen to employ the same set of card numbers are indistinguishable if you look only a t donlains and satisfaction sets, the satisfaction scts being empty for all files. Yet, t\vo such files may have completely different entries on their cards. So by specifying only the domains and satisfaction sets, I am leal-ing the files I am talking about grossllunderspecified. Nevertheless, for certain selected purposes, such as those of the present article, it is possible to abstract aw;Iy from all the ways in which files with identical domains and satisfaction sets map differ, and to still formulatc thc rele\~ant principles.

5 Semantic Categories and Logical Forms I will now turn to the upper part of diagram (8) and highlight some of the assumptions about logical fi)rms that I need to rcly on. Following stantlard practice, I assume that logical forms differ from surhce structures and other syntactic l c ~ e l sof representation in that the!? are disambiguated in two respects: scope, and anaphoric relations. Scopc i s marked configurationally, with a n element c-commanding its scope, and anaphoric relatedness is marked by coindcxing, with two anaphorically related clen~cntshearing iclentical numerical subscripts. T h e relation between sentcnccs and thcir logical forms, generally a one-to-many relation, is defined by a set of transfijrniarionnl ri11es that derive logical forms from syntactic representations and by wcllformcdncss constraints on the output of those ~ u l e s . ~ Both the rules that derivc logical forms and the rulcs that interpret them 13y assigning them file change potentials appear to discriminate between elcmentb of different semantic categories, s11ch as variables, operators, and the like. Here I will

230 Irene Heim not go into such questions as how many and n-hich senlantic categosics there arc, and to what extent the syntactic category of an element dctcrmines its semantic category. I just assume that thcrc are at least the following semantic categories and they includc at least the kinds of things listed, u-hether as a matter of stipulation or of principle. t.aviab/[~:pronouns, empty NPs, indices on NPs with predicate heads (see hclow

for

illustration of the latter); pw(/ic(ltes:verbs, nouns; ~l)eriztorx: " c v c ~ ~ "negation. , As for the rules and constraints that define the rclation hctwcen the syntactic representation of a sentence and its logical forms, I will be very informal and incomplcte here. Consider the structures in (12), each of which represents one of the logicat forills that the English sentence below it can have.

she, LC

it2

hit

She hit it."

a cat

el

arrived

",A cat arrived."

- cat <<

e,

died

Every cat died."

("e" nlarks an cmpty NP-position; the blank beforc "cat" in (12c) indicates an cmpty determiner-position.) These three examples ma!; scrve to illustrate a few general assumptions about logical forms: Every N P in logical forin carries a numerical index. Only variables occur in the argument positions of predicates." NPs that are not variables, i.e. those headed by predicates, arc adjoined to their scopcs and coindexed with the argument position they originate from.' Operators are adjoined as sisters to their argument(s). (hlost operators are 2-placc operators, in particular the quantifiers; some nzay be 1-place, e.g. negation.)

File Change Semantics 231 There is more to be said about how these assumptions follow from the way in which rules of logical-form-construction, wellformedness constraints on logical forms, and limitations on semantic interpretability interact with each other. Note the contrast between structures (12b) and ( 1 2 ~ )which ) is duc to an assurnptio~~ whosc significance I will have more to silv about, viz. the assumptioil that the articles (L, 7 7 a and "the" are not operators, whereas certain othcr determiners, e.g. "every", are. What then is the semantic category of articles? None at all. They arc treated as though they weren't there at all when it comcs to semantic interpretation. bVhat I ha\-c so f ~ si~id r about semantic categorization applies on]! to lexical itcnls and othcr basic units, but fails to specify a se~llanticcategory for the complcx building blocks of logical forms, such as S-constituents and predicate-headed NP-constituents. With some simplification, we may assume that all complex constituents that are of any semantic category at all are propositions. l'hese subdivide into atomic propositions, which consist of a predicate and its arguments, and nlolecular propositions, which are made up of other propositio~lsand may or may not involve an operator. One kind of atomic proposition is dominated by S and made up of a verb and its subject and complements (if an!;), where the verb is the predicate and the variables in the subject and complement positions are its argumcnts. In (12), [,shel hit it2], [,elarrivcdJ, and [,eldiedl exemplify this kind of atomic proposition. T h e other option for an atomic proposition is to liave a noun as the predicatc, in which case thc dominating node i s NP. (12) contains the cxamples [Np, a cat] and [Nr,- cat]. Nominal predicates always have one of their arguments realized as a mere numerical indcx livhich appears on the clominating NP-node. "Cat", for instance, is a 1-place predicate, and its argument in the cxamplcs just cited is the index 1. This is why I included "indices on NPs with predicate heads" in the above list of variables.

6 Logical Forms and their File Change Potentials We can now proceed to the heart of the system diagrammed in (8), the assignment of file change potentials to logical forms. It mill be useful to have another piece of which stands for the file change operation. Suppose ure notation, the symbol have a logical form y that determines a file change from F to F'. W-c express this by writing:

"+",

(read: "the result of updating F on account of p is 12'"). T h e task of assigning tile change potentials to logical forms can now be seen as amounting to the task of defining "F p" for files F and logical forms p of arbitrary composition and complexity. Actually, I will limit my efforts to a more modest task than that: Instead of comnlitting myself to a full specification of thc formal properties of files and the changes they undergo, I will characterize only one aspect of file change, namely how thc satisfiaction set is affected. As I noted earlier, this means that I am leaving a lot about the files I am talking about wide open. What I will define, thus, is not actually "F p", but rather "Sat (F p)".

+

+

+

232 Irene Heim A standard way of assigning interpretations to a language with expressions of unlimited complexity is by means of a recursive definition. Following this format, I will begin by specifying the file changes induced by atomic propositions and then characterize the file changes that molecular propositions bring about in terms of the file change potentials of their parts. Consider (12a), repeated below, one of the logical fi)rms of thc simple sentence "Shc hit it."

shel

hit

it2

In the informal introduction of the file metaphor in section 3, I had the file clerk react to this sentence by changing a certain file F 1 into a certain file Fz. Recall what F1 and Fz were supposed to look lihc. Using the terminology I have since made available, thcy can now be described as follows: Dotn(F1) = Dom(F2) = { l , 2 ) Sat(F1) = {(a,, ar): a] is a woman, a2 is a dog, and ar bit a l ) Sat(F2) = {(a],a*): a1 is a woman, a? is a dog, a2 bit a], and a1 hit a * } It is apparent that the transition from Sat to Sat (Fr) consists in eliminating from Sat (F1)all those pairs which fail to satisfy the sentence being processed, i.e, those pairs which fail to stand in the relation that the predicate of the sentence denotes, in this case the relation of hitting. Put formally: Sat(FL)= {(a],a2): (al, a2) E Sat(FI) and (al,a2) E Ext("hit")} (I write "Ext" for "the extension o f '.) T h e general rule under which this transition falls may be given as follows (subject to later revision): (13) lAetF be a file, and let p be an atomic proposition illat consists of an n-placc predicate R and an n-tuple of variables \vhose indices are i l , . . . , and in respectively. Then: Sat(F

+ p) = {aN:a\

E Sat(F) and (ai,, . . . ,a,,,) E Ext(R)}.

,4pplicd to the file F1 and the logical form (12a), (13) gives us:

as intended. W-e just focussed on a particular logical form that grammar provides tbr the sentence "She hit it", namely (12a). But there are infinitely many others, since the choicc of indices is supposed to be free. So (l2a) represents really only one of many readings that the sentence may be uttered with, and we have yet to talk about the others. We also

File Change Semantics 233 have to say something to explain the puzzling fact that despite the infinity of distinct logical forms assigned to each sentence by the grammar, most real-life utterances can be immediately understood in an unambiguous way. T o appreciate the problem, put yourself once more into the imaginary file clerk's shoes. You have so far constructed the file FI, and now you hear the speaker say: "She hit it". How do you guess that the intended reading is "Shel hit it2", and not, say, one of the following? (14) (a) Shel hit itl. (b) She3 hit it;,. (c) Shez hit itl. (14a) is pretty easy to exclude: there is a well-known constraint, called "Disjoint Refercncc", which we may think of as a wellformedness condition on some levcl of representation in the grammar (logical form or one of the levels it is derived from). By this constraint, coindcxings like the one in (14a) are ruled out, so (l4a) doesn't count as a welformed logical form and thus doesn't represent an available reading for any utterance of the sentence "She hit it" whatsoever. With (14b), it's a rather different matter. No known constraint on indexing applies here, and it would quite clearly be wrong-headed to expect that anything would rule (14b) an ill-formed logical form. It can't be ill-formed, because we can imagine utterailccs of "She hit it" where (14b) would be precisely the logical form that represents the intended reading. Suppose, for instance, the preceding conversation had taken its course in such a way that you, the file clerk, had come up with a file Ft, ~vllich,unlike Fl, is characterized b!; the domain Dom (F4)= {3,7) and the satisfiaction set Sat (F4) = {(a3, a,): a3 is a woman, a;, is a dog, and a;, bit a3). If at this point you were confronted with an utterance of "She hit it", (14b) rather than (12a) would be the reading to construe it with. - What this shows is that in order to disambiguale the uttered sentcncc as (12a) as opposed to (14b). the file clerk must take into account what his current file looks like. What is at work here is thus not a constraint on logical forms considered in isolation, but rather a principle that constrains the choice of logical form ~ e l i ~ r i to z ~ (1e gir~njilu.I iv;lnt to propose that a principle of this sort, and in fact just the right principle to help us rule out (14b) \vhcn givcn FI, is suggested to us by the familiarity theory of definiteness. The principle, which I call the "Novelty/l+'amiliaritj Condition", is this: (15) Let F be a file, p an atomic proposition. Thcn p is appropriate ~vithrespect to I? only if, for every noun phrase NP; with index i that p contains: if NPi is definite, then i E Dom(F), and if NP; is indefinite, thcn i @ Dom(F). LVith respect to the filc F I , for instance, (14b) is inappropriate because it contains two definite NPs, "she3" and "it,", whose indices fail to be in Don1 (FI). (12a), 011 the other hand, with the definitcs "shel" and "it2", meets (15)'s requirement for appropriatencss w.r.t. F 1 . Note that for (15) to be applicable in the in~endedway, we must generally assume that NPs in logical form are marked for the fcaturc (fdefinite).

234 Irene Heim

(15) is presumably only one among other conditions on when a logical form is appropriate w.r.t. a file. hf uch of what has been discussed undcr the name of "prcsupposition" seems to be a matter of conditions of this sort.' From the point of view of the task of assigning file change potentials to logical forms, we may take appropriateness conditions as delimiting the range of pairs (F, p) for which the tile change operation F p is at all defined. Unless p is appropriate w.r.t. F, there is no file change result 1.' p determined. -4s you will come to see shortly (once I have discussed indefinites), (15) interacts with the rules for file change in such a wa? that files will in effect always develop in aceordance with instruction (7), which I fi)rmulatcd in section 3 as a first informal way of incorporating the familiarity theory of definiteness into a file-based semantics. Returning to the file clerk's problem of eliminating all but the intended one among the infinity of logical forms for a given sentence, the Novelty /Familiarity Condition (15) will certainly help to rule out a lot of unwanted options, but it will still let through some. (14c) above is a case in point: Given the file F1,the indexing "shez"/"itl" violates (IS) no more than "shel"/"it2" (and (14c) is of course not ill-formed as a logical from either). In order to predict the inappropriateness of (14c) w.r.t. F1, we need some account of gender, which I will not provide here. Another problem whose solution I must leave fbr another occasiony is the Fact that diffcrcnt kinds of dcfinites, e.g. personal pronouns in conlparison with definite descriptions, differ in their appropriateness conditions in a way that the Novelty/Familiarity Condition, which is sensitive only to the distinction between definites and indefinites, is incapable of predicting. IAetus now turn to an example with an il-ldefinite, such as the scntcnce "A cat arrived", one of whose logical forms is (12b), repeated from above, this time \itit11 the definiteness features tilled in.

+

+

-

a cat

[+ def]

To determine the file change that (12b) induces, we will have to consider two questions: First, since (12b) is a molecular proposition, we have to ask ourselses how its ovcrall effect on the file may be calculated on the basis of the file changes that each of its two parts would induce. Second, which rules of file change pertain to each of those parts? T h e answer to the first question is as simple as it could bc: We compute the filc change of (12b) as a whole by subjecting the filc first to the change that the left constituent dictates, and subsequently to the tile change that the right constituent dictates. T h e general rule for this successive left-to-right mode of file change is this:

,

File Change Semantics 235

(16) Let F be il file, and let p be a molecular proposition whose immediate constituents are the propositions q and r (in that order). Then: Sat(F p) = Sat((F q) r).

+

+ +

Applied to (12b), this means that we get from a given file F with satisfaction set Sat(l;') to Sat(F (12b) ) by first calculating Sat(F [NPIa cat]) and then, from that, Sat((F [,) a cat]) isel arrived]). UnPl a cat] is an atomic proposition. Before we try to determine S a t ( r a cat]), we have to make sure that it is even welldefined, i.e. that LNpl a cat] is appropriate w.r.t. F in the sense of' the Novelty/Familiarity Condition (15). Sincc (N1)l a cat1 contains (in this case, exhaustively contains) an indefinite with indes I, (15) rcquircs that 1 @ Dom(F). Let's assume F meets that requirement. Then Sat(F a cat]) is defined and should, by rule (13) above, equal the set:

+

I

I

+

+

+

++

(N13,

+ rNpl

(17) {aN:a~ E Sat(F) and ai E Ext("cat")) That doesn't seen1 right, howe\-er. T h e problem is that if, as wc are assuming, 1 4 Dom(F), then no element a~ E Sat(F) will have a first member a, at all, let alonc one that is in the extension of "cat". So the set described in (17) would of necessity be empty. This is not consistent with our intuition that "A cat arrivcd" is a contingent statement and should, at least sometimes, lead to a non-empty, i.c. true, file. We have to fix up rule (13) accordingly. T h e revised version under (18) is more adequately equipped to handle the example under consideration, while it still ~vorks just like (13) in cases of the sort that made us first rlesign ( 13).

I

I I

'

j I

(18)

Let F be a file, and Ict p bc an atomic proposition that consists of an n-place predicate R and an n-tuple of variables wllose indices are i l , . . . ,i,, respectively. Then: Sat(F p) = {aN u bzl E A""": a~ E Sat(F), M = {il, . . . , i n ) , and (b;,, . . . ,hi,,) E Ext(R)).

+

+

In contrast with (13), (18) allom~sfor cases where r p has a larger domain than F, i.e. where the sequences in Sat(F + p) havc to bc longer than those in Sat(F). Put informally, (18) says that every sequence in Sat(F p) has to include as subsequences a sequence a~ satisfying F and a sequence bhl satisfying the proposition p. Whenever you can find an a~ satisfying F and a bRI satisfj~ingp, where a~ and bsl agree on the intersection of their domains, link them together and the result, a~ n bnl, will be a member of Sat(!? p). (That a~ and bl,l havc to agree on the common part of their donlains is expressed in (18) by requiring "ah U bbl E AN\ICJ\IW AKU" denotes the set of functions from N U M into A, and the union of two sequences is itself a sequence (i.e. a function) just in case they coincide on their cornmoll domain.) (18) reduces to (13) whenever { i t , . . . , i n ) happens to be a subset of Dom(F). Returning to our example, assume fol- concreteness that we start out with the enlpty file FO, i.e. the one which has L)om(Fu) = f and Sat(Fe)= Fe is of course among

+

'

+

/ I

v}.

236 Irene Heim those filcs w.r.t. which [KP1 a cat J is appropriate in thc sense of (1 5). What, then, docs (18) tell us about the lile-change result Fr,+ LNp, a cat).? We calculate: (19)

Sat(F,,

+ LNl,

a cat]) = {(b,): b l E Ext("catw)).

It is now easy to compute Sat(Fo+ (12b)) by applying (16) and, once more, (18). (20)

+ (12b)) = = Sat((Fo + IIhL,, a cat]) + [,el arrived]) =

Sat(Fo

= {(b,): b l E E ~ t ( ~ ' c a t "and ) b l E Ext("arrived")}.

This result is in line with our earlier, metaphorical, characterization of the change: Starting from a zero-card file, the sentence "A cat arrived" has brought us to a onecard file which is satisfied by any one-membered sequence whose one mcmber is a cat and arrived. Before I conclude this section, let me substantiate a remark that I made at thc cnd of section 3. 'Thcrc 1 said that, although logical forms are not directly mapped onto truth conditions in a semantics that is organized along the lines of diagram (8), they still receive truth conditions indirectly, via the tiles they affect. 1 had in mind thc following truth criterion for logical forms: (21)

I x t F be a true file and p a logical form. Then p is truc w.r.t. I; if 1' truc, false \\-.r.t. I; if F p is false, and truth-valuc-less w.r.t. 1; if is undefined.

+

+ p is +p

17

(21) makes i-eference to the notion of truth that I defined for files in (1 1) above, and it basically equates the truth conditions of what is being said with thc truth conditions of the resulting file. However, the applicability of this truth criterion is limited to cascs where we can assume the truth of the file we start out with. If we have a false file to begin with, then we will always end up with another false tile, however "true", in an intuitive sense, the utterance under consideration may be.

7 The Non-quantificational Analysis of Indefinites I an1 only half way through with my recursive sct of rules for assigning tile changc potentials to logical forms. But this is a good point to take a brcak and have a critical look at the present analysis of indefinite NPs and how it compares with t l ~ cwidely accepted Russellian analysis. Russell 10 argued that intuitively correct truth-conditions for sentences with indefinites result when the indefinite article is trcated as an existential quantifier ant1 sentences of the form (22) are assigned logical analyses of roughly the form (23). (22) [,Xl,pa YlZ1 (23) 3x (Y(x) & (X x Z)).

File Change Semantics

1

237

"A cat arrived", for instance, would be logically analyzed as: "3x (cat(x) & x arrived)". This "q~~antificaional analysis of indefinites", as I will call it, is nowadays accepted in one variant or another by the vast majority of philosophers and linguists. 1 his paper contains what I will call, by contrast, a "non-c1uantification;ll analysis of inclefinites". T h e logical analysis of an indefinite, as presented above, is just a proposition with a variable free in it. E.g. "a cat" corresponds to something like "cat(x)". When an indefinite occurs in a sentence, as in schema (22), the logical analysis of that sentence is again a proposition with a variable free in it:

(

r

7

I

(24) Y(x) &- (X I

Y

Z)

The free variable in the indefinite remains free in the sentence as a whole. An existential quantifier is not part of the indefinite or of the sentence that contains it, neither is a quantifier of some other force than existential." This section is intended to bring to bear some linguistic evidence on the choice between a quantificational and a nun-quantificational analysis of indefinites. Rut first let me clarify to what extent the two analyses agree in their empirical predictions. Despite the absence of an existential quantifier in the logical forms of sentences with indefinites, my thcory predicts what are, in effect, esistential truth-conditions for such sentences. Consider again "A cat arrived" with the logical form (12b). By the truth criterion (21) for logical forms, we know that (12b) is true w.r.t. a true file F if and only if F (12b) is true. For F + (12b) to be true, in turn, means two things: First, (12b) must be appropriate w.r.t. I!;*, in particular, Dom(F) must not contain 1, for F (121,) to be defined. Second, Sat(F (12b)) must be non-cmpty. Rules (16) and (18) determine that Sat(F (12b)) = {aN U b i l \ E A " ~ I ' I : a, €Sat(F), bl is a cat, and bl arrived). Given that Sat(F) is non-empty (since F is true), tliis set is non-empty just in case there is at least one cat that arrived. What we have just shown is that (12b) is true w.r.t. F if and only if at least one cat arrived. Since the proof did not depend on any particular properties of F other than that it be true and that (12b) be appropriate w.r.t. it, we may suppress relativization to F and simply say that (12b) is true if and only if at least one cat arrivcd. Moreover, since an analogous proof would havc gone through for any other wellformed logical form of the sentence that ( 12b) represents, we can say that we have shown that the sentence "/I cat arrivcd" is true if and only if at least one cat arrived. This prediction coincides of course with the familiar existential truth-condition that a quantificational analysis would have predicted as well. At first sight, one might have thought it impossible that an existential truthcondition can be predicted while assuming a quantifier-free logical fol-111 like (12b) 01. (24). Rut there was of course 110 magic involved in the proof I just gave. 'I'hc truthcondition came out existential because the notion of truth of a filc has, so to speak, existential quantification built into it: truth of' a file was defined as t11el.r h'itlg. rrf lcrlst orle satisfying sequence. So my disagreement with the quantificational analysis of indefinites is not a disagreement about whether or not we understand statements with indefinites in then1 as existentially quantified. It is rather a disagreement as to what is to be held responsible for the existential force of such stateillents: the indefinite artide itself, or rather the way in which files generally relate to the facts that verify them? If we are to find any empirical evidence that will discriminate

+

+

+

+

238 Irene Heim between these two points of view, it won't help to simply examine our illtuitions about what sei~tenccslike "A cat arrived" mean. We will havc to rcsort to considerations based on relati\rely indirect evidence like the following. It is well-known of certain undebatable cases of quantifying NPs in natural language that they are subject to tighter restrictions on anaphora thail certain other NPs. 1 have in mind contrasts like this one: (25) Every soldier is armed. H e will shoot. (26) H e is armed. He will shoot. T h c tw-o "he'"s can be anaphorically related in (26), but no anaphoric t.elation is possible between "e\;erj~soldier" and "he" in (25). why should this be so? - An explanation suggests itself if wc assume that "evcry" is a quantifier, pronouns are variables, and (25) and (26) have logical analyses of essentially these forms: (25') (26')

Vx;(soldier (xi) -+ armed (xi))& (xi will shoot) armed (xi) Sr (xi will shoot)

Is i = j or i # j? T,et us try to get away with the simplest possible assumption, i.e. that both texts pernlit readings with any ;~rbitrarychoice of i and j, and in pasticular readings with i = j as u ~ las l readings with i # j. Now look at the ~ a t i s ~ l c t i oconditions n that forniulas like (25') and (26') receive under standard intcrprctations of predicate calculus. If (26') has two different variables xi # x,, then a sequence satisfying it will have t o contain an armed person and a (possibly distinct) person that ~ v i l lshoot. If the variables are the same in (26'), then a satisfying scquence has to include il pcrson that is both armed and will shoot. So in the casc of i = j, we have a substantially different satisfiction condition than in the case of i # j. Now take (2-5') and compare the satisfaction conditions that wc get with i = j to tl~ose we gct with i # j. It turns out that it makes no difference: seclucnce t h a ~satisfies (25') must contain a person that will shoot, and provided it does, will satisfy (25') only if every soldier is asmed. This same satisfaction condition applies regardless of whethcs xi and x, arc differcilt variables or the same. This seems to be what is behind our judgment that (25) has no reading where "every soldicr" and "he" ilrc "anaphorically related": Evcn if we make a point of coindexing "evcry soldier" with "he", i.e. of picking identical variables in the logical analysis of (25), the coindexing is of necessity a semantically "~racuous" coindexing. " What nie have just observed about (25') Ldls under a general law, so to speak a design feature of cluantificational logic:

(27)

If xi is bound by a quanfif~crtvhose swpc does not include x,, then cci\nc\cx'~ng between xi and xi can only be vacuous.

(27) m~ilcescxplicit what it is about the logical analysis of (25) that makes it dif'fcrcnt from the logical analysis of (26) in such a way t l ~ (25) t will pernlit only vacuous coindexing whcre (26) permits the sort of non-vacuous coindexing that we perccivc as an anaphoric reading. T h c crucial point is that "every soldicr" was analyzed as a

File Change Semantics 239 cluantifjing NP, whercas there ~vasno quantifier assumed to occur in the corrcsponding position in (26). What does all this have to do with the choice between a quantificational and a nonquantificational analysis of Indefinites? Well, since (27) makes reference to quantifiers, we might try to exploit it as a diagnostic test for quantifyingness: If indefinites turn out to bear non-vacuous coindexing relations to variables outside their scope, then that ought to slio\v they are not quantifiers. Unfortunately, this test is not as foolproof in application as one might hope. But let's try it first. Consider (28).

/

(28) A soldier will accompany us. Hc will shoot. Prcsuniabl!:, (28) would be analyzed as (28') under a quantificational treatment of indefinites, but as (28") ~rndera non-qurultificiltioni-11treatment.

I

3xi(soldier (xi) & (xi will accompany us)) & (xi will shoat) (28") (soldier (xi) & (xi will accompany us)) & (xi will shoot)

(28')

I

By (27), thc coindexing i = j in (28') is bound to be ~ a c u o u s w~hile , (28") contains no obstacle to non-vacuous coindexing. Our intuitive judgnlent is that anapliora is possiblc in (28), just like in (26), and unlike in (25). We can straightforwardly predict thc anaphoric reading by assuming a logical form along the lines of (28''), with i = j, il nonvacuous coindexing. (28'), on the other hand, ~vouldseem to preclude an anaphosie reading. This is prima fiicie evidence in favor of the non-quantificationiil analysis of indefinites. There arc various ways in which thc conclusion just drawn can be, and has been, challenged. First, one might call into question a tacit assumption I have been making about tllc scope-options for quantifiing NPs. With both (25) and (28), 1 took it for granted that a quantifying N P that occurred in the first sentence of each text eould take scope at most over that sentence, not over the entire biscntential text. Had I permitted the quantifyit~gNP "ever!- soldier" in (25) and thc putativdg quantifying NP "a soldier'' in (28) to take wider scope than the sentence, then the variable xi in (25') and (28') could have come under the scopc of 'd or 3, in which case i = j would have been a non-vacuous coindexing. (Cf. ( 2 7 ) . ) 'This suggests that the quantificatioilal analysis of idefinitcs could be saved if one were to maintain that indefinites, unlike certain other quantifying NPs, can take scopc across several sentences. A second way of undcrrnining 1i1y use of (28) as evidence against a quantificational analysis of indefinites goes like this: What we customarily describe as "anaphoric relations" may not be one and the same liind of logical relation in all cases, and in particular, need not always be non-vacuous identity nf variablcs. So even if the logical analysis of (28) is (28') (with either i = j or i # j, it doesn't matter), we may still ~1st(28) with the intention that xi I-ekr to whatever individual is responsible for the truth of "3x;(soldier(x;) & (xi mill accompany LIS))".Viewed in this way, the so-called "anaphoric" use of the pronoun in (28) has really a lot more in common with deictic pronoun uses than with bound-variable anaphora: T h e pronoun is here taken to refer to

'

A

240 Irene Heim a contextually salient individual, just like deictic pronouns do, except that in this case the crucial factor in illaking thc intended referent saIicnt is the fi~ctthat it verifies a piece of immediately preceding d i s ~ o u r s e . ' ~ Both of'thcse objections deserve serious consideration before we can bc sure that the ability of indefinites to serve as antecedents for anaphoric pronouns beyond thcir scope is indeed a symptom of the non-quantificational nature of indefinites. I will have to be brief answer to both objections is that the alternativc i~ccountsthey give of the anaphoric relatioil between "a soldier" and "he" in (28) do not carry over to ccrtain other exan~plcsof an analogous nature. Consider (29).

here.'"^^

( 2 Every time a soldier accompanies us he shoots. Under a clu;tntificationaI analysis of indefinites, (29) ought to get the following logical analysis:

(29')

Vt (3; (soldiel.(xi) gi (xi accompanies us i t t))

+

(x,{shoots at t)).

Unlike in the case of (28), the truth-conditions of (29) arc clearly inconsistent with an alternative analysis under which "a soldier" takes wide enough scope to include xi.16 'This shows that if a quantificational analysis of indefinites is to be reconciled with their behavior w.r.t. anaphora, it will not sufficc to appeal to their i~nconstrainedscope options. But (29) also doesn't lend itself to an account in terms of the sort ofcluasi-dcictic use of "he" that had some plausibility for examples like (28). 'l'he problem is that thc "he" in (29) fails to refer, and that deixis without reference is a contradiction in terms by a11 available explications of thc concept. So (29), inorc compellingly than (28), sho\vs that indefinites entcr into anaphoric relations where this is not to be expected fi-om the point of view of a quantificational analysis. I have yet to show that the non-quantificational alternative that 1 ilm dcvcloping in this article covers examples like (29) in a natural ax;. This lcads us to the topic of quantification.

8 File Change Rules for Quantified Sentences Before I give the file change potentials for operator-l~caded logical fi~sms,in particular universally quanrified ailcl ncgated ones, I should say somcthing ahout "closed" propositions (i.e. propositions without fi-ee variables) in general. Take a simple sentence with a 0-placc predicate:

(30) It is raining. In the context of the file metaphor, one doesn't quitc know how to dcal with (30): As an informative scntence, it ought to call for an updating of thc file somehow; but what exactly is the filc clerk supposed to do? T h c information that it is raining docs not helong 011 any particular file card, it seems, since each file card is a description of m

File Change Semantics 241

individual, but (30) is not about any individual, Should the tile clerk perhaps writc on sollie arbitrary card: "is such that it is raining"? 01.should he write that 011 all cards? And what if thc file so far doesn't contain any cards yct? - Fortunately, \ic can lcavc thesc questions unanswered here. Recall that urc have already resigncd ourselves to characterizing file change only as far as the domain and satisfaction sct arc concerned. So we need not specify anything else about the file change potential of (30) than its impact on domain and satisfi~ctionset. And that is already taken care of by rule (18) abovc. We only need to assume that the extension of a 0-place predicate is cnipty if'thc corrcsponding state of affairs fails to obtain, and is the unit set of the empty sequence if it does obtain. E.g. we have Ext (L'rain") = ( 4 ) if ir rains, Ext ("rain") = (/) otherwise. This way we can apply (18) to give us:

I

I

This amounts to the correct truth conditions for such sentences. The reason why I dwelled on this point is that quantified and negated propositions are similarly puzzling if we are so ambitious as to want to say what exactly thc file clerk docs in response to them. Under thc modest aspect of domain and satisfaction set change, however, they pose no problem. An example of a universallq- quantified logical form is ( 1 2 ~ repeated )~ from above.

-

cat

Note that I have here marked the determinerless NP - cat] as indefinite. I assume that NPs tvhich have had their determiners moved out generally qualify as I - definite]. Unlike in the case of operator-fi-ec molecular propositions, the file clx~ngeincluced by (12c) cannot be broken down into a simple, so to speak "linear", succession of smaller steps that correspond to cach of the sub-propositions. T h e pl-csence of an operator makes considerably higher demands on the file clerli's memory and computational abilities. We may think of the evaluation of (l2c) as proceeding in thrce steps ils folloivs:

Step 1: Teiltatively update the original file F by incorporating [INrl - cat] into it. This gels you to F' -- F [NPI - cat] with the follo~vingsatisfaction set, as detern~inedby rule (1 8):

+

sat(^') = {aN U h ( l l t A " ~ { ' ) :

t Sar(F) and b l is a a t .

242 Irene Heim T h e change ti-om F to F' is only "tentative" insofi~ras the file clcrk retains F in his memory and is prepared to make his next actions depend not only on F', but also on F. Stc~p2: Tentatively update F' by incorporating [,el died] into it. This results in F", determined by rule (18) as follows:

sat(^")

=

{aN U b j l i E A ~ " { ' ) a~ : E S a t ) , and hl is a cat, and bl died}.

Again, F' is retained in memory, which now contains both F and F'. Srep 3: For each sequence ah in Snt(F), do the following: 13etcrmine whether all continuations" of ax that arc in Sat(F1)arc also in Sat(Fi'). (By a "continuation" of aN I mean a scquencc that includes ah as a subscqucnce.) If yes, carry a~ along into the satisfaction set of the new file F (12c); if no, eliminate ah. Afkcr you have done this for each as E Sat(F), you will thus have: LL

+

Sat(F

+ (12c)) = {an- E Sat(F):

for every 2 a\, if bkl E ~at(l:')then bAlE Sat(F1')).

You may now clear the memory of F , I;", and 1:". Step 3 is obviousl>-the one which takes into account the specific force of'thc operator involved, here universal quantification. T h e preceding two steps serve only to set up thc auxiliary filcs on which the calculation in step 3 is basctl. 'I'hcse two steps are the same for all tn-o-place operators. Lct us figure out the rcsult of this three-step procedure for a concrete choice of initial file, the empt!- file Fo Starting from Fo, the outcomes of steps 1 and 2 will look like this:

+

-

Sat(F0 [ N P ,cat]) = { b { ,1: bl is a cat. Sat((Fo 4-[NpI- cat]) [,el died]) (b;, \ : 131 is a cat

+

311~1bl

died}

T h e rcsult of step 3 is then the following:

Sat(Fo

+ (12c)) =

Sat(Fo), if every- cat died; (11, othcrwisc.

In view of the truth crirerion (21) ilbove, this implics that (12c) is true \v.r.t. just in ease ever>-eat died, an intuitively adequate prediction. I-iowcvcr, we still have to show that equally adequate predictions are generated with ehoiees other than for thc initial tile. At first glance, there seems to he a problem with initial files F that already contain a card number 1. For instance, if wc assun~ctlUom(P) = {1) and Sat(F) = {a(,]: a, is a pet), then each sequence in Sat(F) could have at most onc continuation in Sat(F [Np,- cat]), namely the trivial continuation, which is itself. T h e result of step 3 w-ould then be this:

+

File Change Semantics 243 -

Sat(F

/I I

+ (12c)) = {aili:a1 is a pet, and if a1 is a cat,

then a, died}.

This conflicts with the intuitive truth conditions of (12c) and in particular with its universal force. However, we have no reason to worry about this result, because it only arises if we neglect the constraii~tswhich the Nor.elty/Familiarity Condition imposes on the choice of F. Recall that the Novelty/Familiarity Condition (= (1 5 ) above) has to be met each time an atomic proposition is incorporated into the file, or else there won't bc a file clzangc result defined at all. Applied to the evaluation of (12 c), this means in particular that step 1 cannot be carried out unless lN1-',- cat] is appropriate w.r.t, the initial file F. According to (I j), F is therefore not permitted to contain the number I in its domain, "-catl" being indefinite. In particular, the choice of E' which in the example above seemed to lead to inadequate predictions about the truth conditions of (12c) was inconsistent with the Novelty/Familiarit>- Condition, and eve should have realized that neither F+ (12c) nor, consequently, the truth of (l2c) 1v.r.t. F is at all defined for such choices of F. Turning to examples of greater complexity than (12c), we find that the three step procedure that 1 have proposed applies analogously, and that it interacts with thc Novelty/Familiarity Condition in such a way as to predict the contrast betcveen definitos and indefinites when they appear inside a uni~rcrsallgquantifying NP. Coniparc (31) and (32). (31) Every man who likes a donkey buys it. (82) Lverq- man who likcs it buys it. (31) expresses a generalization about man-donkey-pairs; it is as though the universal quantifier "every" Lvas here binding the donkey-variablc along N-iththe man-variable. (32), by contrast, is read as generalizing over all men that like a fixed object. The variable corresponding to the "it" in "every man who likes it" may refer to a contcxtuall\ supplied object, or may be anaphoric to an antecedent in the larger text in which (32) appears. Either way, it is not understood as hound to "el-ery" in the may that "a donkey" in (01) is. Let me briefly sho~vhoe\- this contrast is derived from the assumptions I have introduced. (31) is represented on the logical form level rough1~-as follo\vs. Starting from an initial file F, steps 1 and 2, in analogy to the specifications given aboke, provide us with ;~uailiaryfiles 17' = F p and F" = F' q. These liavc the following satisfaction sets, according to rules (16) and (18).

+

+

Sat(Ff)= {ar, U bl I,?):ah E Set(F), bl is a man, h2 is a donkey, and b l likes b ? ) . Sat(F1') = {au U b{1, 1: ah E Snt(F), bl is a man, b2 is a donkey, bl likcs b?, and b l buys bz). Concerning F , we must assume that Dom (F) contains neither 1 nor 2, because otherwise the Novelty/Familia~-it?Condition would not let F' be defined. We now

244 Irene Heirn

- man

A

[-dcf]

r,

likes

it2

a donkey

proceed to step 3, in which wc considcr one by one thc mcmbcrs ax of Sat(F). For each such a s , w-eform evesy continuation of aN that is in Sat(Ff)and dcterminc whethcr it is also in Sat(F"). T o satisfy F', iI continuation of aw has to contain two mcmbers, number 1 and number 2, which are a man and a donkey hc likes, respectively. Every man/ donkey-pair of this sort will figure in some continuation of a ~ hccause , i l ~itself does not contain any members number 1 and number 2. Thcrcfore thc requircmcnt that e\ery continuation of a,- that satisfies F' must also satisfv k"' amounts to the rcquirement that every man-donkey pair in which thc man likes thc donkey is also si~chthat the man buys the donkey. T h e result of step 3 is therefore: Sat(F -t(31')) =

Sat (F), if every man who likes a donkey buys it, 4, otherwise

T h e logical form of (32) differs from that of (31) in that i t has the dcfinitc "it" instead of the indcfinitc "a donkey":

------?\-\

every

A

NP,

A'-----. NP I [- clef,

A - man

yS\

who,

el

A el

likes

it2

[+ dcf]

buys

I'

it,

File Change Semantics 245 -

This time, steps 1 and 2 will produce the auxiliary files F' = F (where F statlds again for the initial file):

-

+ p' and F" = 1;' + ~ 1 %

Sat (17') = {aN U bl 1, z} E A ~ ~ I ' , ' } : a~ E Sat(F), bl is a man, and b l likes hz} Snt(F)" = {aN U bIl,,}: ah t Sat(F), bl is a man, bl likes b?, and bl buys h2}

1 1

Unlike in the previous example, the Novelty/Fainiliarity Condition this time requires that Dom(F) doesn't contain 1, but does contain 2. This has important consequences fol- how step 3 applies. In step 3, \vc look at each ah E Sat(F) and fi)nn all continuations of aN that satisfj. F'. Because 2 E Llon~(F),a~ il~cludesn member az, and every continuation of a~ lias that same a2 as its member number 2 as well. Tllerefore, not every pais of a inan and an individual he likes will necessarily be part of a continuation of a ~ hut , rather, only those pairs a-here the individual the man likes is none other than az. The predicted result of step 3 is a lile with the folloiving satisfi~ction set: Sat (F

+ (32') ) = { a~ E Sat(F): for every b l , if b l is a man and bl likes i12, then bl buys a? ).

+

The difference bctwecn this and Sat(F (31')) above reflects the intuition that (31) involves universal quantification 01-er pairs, wl~ereas(32) quantifies ovcr men which like a "fixed" indi\.idual. It remains to write up explicitly tlie file change rule which dictates the thl-ee step procedure 1 have described. We want this rule to bc general enough to work not only for examples like (12c), (3 l ) , m d (32), but also for examples like (33):"

(33) Every man who owns a dunkcy sclls it to a merchant. (33) contains an indefinitc ("a merchant") in thc right-hand argument of the qunntificr,

I

I

and this creates complications for step 3 as 1 have specified it so far. T h e prol>lcm is that in a case like this, F" will contain more cards than F', ;und it uill thcreforc bc impossible in principle fix any sequence that satisfies F' to also satisfy F". T h e following brmulation of the file change rulc h r universally quantified propositions is designed to deal with this additional complication. This is why it cloesn't simply require that every continuation o f a given a h that satisfies F' also satisfj. I.;", but 1.at11cr that a further continuation of the continuation satisfy F". (34) Let F bc a file, and let p be a molecular proposition \vl~oseimmediate constituents are a universal cluantifier and the pl-opositions q and r (in that ordcr). Then: Sat(F p) = {ay E Sat(F): fbr every bAI2 ax such that bhr E Sat(F q), thcre is s c,, b$! such that CL E Sat ((F q) r)}.

+

>

+ +

+

I leave it to the reader to verify that (34) applies satisfactorily to eraniplc (3.1). I complete this section by for~nulatingthc file change rule for ncgatcd propositions, can come up with his or her own illustrations. trusting that the ~-eadct*

246 Irene Heim

( 3 5 ) Let F be a file, and let p be a molecular proposition whoso immediate constitucnts are a ncgation operator and the proposition q. Then: Sat(F p) = {aN E Sat(F): there is no bAl a~ such that bxl E Sat(F

+

>

+ q)).

Notes T h e ideas contained in this article arc elaborated more fully in 111!: Pli. 11. thesis (1-Icim 1082). All tllc pcoplc whose llclp I acknowledge thcre should also be mentioned hcrc, in particular Angelilia liratzer and my thesis advisor Barbara Partee. 1 T h e label is due to Hawkins (1978).

3 See in particular KusscH (1919, Ch. 16), Quine (1960), Kaplan (1072), and Cicach (1002). 3 Karttunen (1968a, b, 1976). 4

5

0 7 8 9 10 11

12

13 14 15

T h e file metaphor was first suggested to mc by .Anpelil\a I<mtzcr, in rcsponsc lo a n earlier attempt of mine to modif?- Grice's and Stalnnher's notion of "common ground" (cf. especially Stalnaker 1979) in such a wa! as to i~npcrseon common grounds an csscnti;llly lilc-lihc struclurc. I subscqucntl~found uses 01' the file nlctaplior for- rnorc or less similiir I)urposcs elsen hcrc in tllc litttraturc, c.g. in Knrttuncn (1976). II'ith respect to their role in a moclcl of scnlantics, m! files arc closcl~related not only to Stxlnabcr's "common gro~~ntls", but p~vtiuularlyto the "discourse represcntntion structures" of ICamp (1981 ). These ;~ssumptionsabout logical form arc taken over from C:Iiolnsky's n-orli and other work in the fi.anic\vork of the "Revised Extended Standard Theory", see in ~>ilrtic~~l;lr Mil!. (1977) ant1 Rcinhar-t (1'976). This is similar to thc "predication condition" of Ma!- (1077). h l a y (2977) ~llakcsthis assun~ptiononly for quantifying NPs, nlicrcus I cstcnd it to all prcclicatcheaded NPs, quantif! in,w or not. Heim (1983) argues that this view of n-hat presuppositions arc throihs light 011 tlic hcha\.ior of presuppositions with respect to tllc so-callccl "projection problem". See Hcim (1'382). Russell (1910, Ch. 6). II~hcnI say (hcrc and elsewhere in this article) that the intldinitc is no^ a cluanlilicr, 1 a111 of' course not using "quantiticr" in the scnse oE 13arwise ;ll~clCloopcr (1981). In thcii. scnse of "quantifier", an!-thing that dcnotes a function lion1 predicate-~~icaning!, to proposition-nica11i1igs is a quantifier, and every hind of NP, cl-cn proper names and pronouns, can therefore be construed as quantiliers. 7'hc rclcvant notion of "v~tcuity" could he dcfincd as follo\vs: DP/.': Let p be a li)rmuln, s ;i \miable, and !I the set orall occurrences o f s in 11.Suppose B a i ~ c Care l two disjoint subsets of A, with :I = 13 U C:. Thcn the mcinhcrs of I3 ;u-c i v r ~ . c l o l ~ n~irrr/~,,v~~d sl)~ nit11 the members uf C iff for some ~ariable! = 7i, 1) and p' ha\c idct~ticalsatisfaction conditions; whcrc p' results Li-on1I:, by substituting y Li~rcr-cry occurrence ofx that is in C:. Note that the "laa" under (27) in the tcrt is not a clcfinition of \acuity, bill rather a thcorcm lhar follows from the definition above, gii-en the stantlarcl intcrprctation 01' cluantilicrs. 'This is \vhy one could not sinlply choose to replace (27) by a stipulation tl1;it pcsnlits certain quantiticrs to IN coinclcxecl non-\acuouslp c\ith variables hcyond tlicir scopc - i~t~lcss one \\,ere to use logic ;is an uninterpretcd formalism ;~ltogetlier. This is basicall! what Geach (1962) suggests. This linc is taken b!- Ksipke (107'7). Leu is (1979), and clscwhcrc. For more carcf~ilargumentation, see I-lcim (10X3, Clh. I), nlicrc I also atldrcss 3 third way of undermining the use of (28) as evidence against the cli~nntificationd ;inalysis of inclclinitcs, ad\-ocutcd b!- llvans ( 1975) and (;noper ( 1 979), among others.

File Change Semantics 247 10 Unless one ijssunles, moreover, that the wide-scope taking indefinite s\vi~chcsits quat~titicational force from existential to uni\crsal. That assumption has been pursued in Egli (1979) and Smaby (1979), whose proposals are discussed in depth in Heim (1982, Ch. 1). 17 ?'he example is from Kamp (198 I), whose treatment of' quantilicaticrn (designed to go with his version of the non-quantificational analysis of'indcfinites) milde nlc an-are that I had o\crloohed cases like (33) in a earlier version of ni! theor-\-.

References l3;irwise, Jon and Robin Coopcr. I98 1 . Gencralizcd qualltificrs and natural language. L i ~ ~ . q l ~ j stin[/ tli:~ Philosophy 4: I 59--2 1 9. C:hristophel-sen, Paul. 1939. TIIP.-lriic.lr~s:-1 S i t i ~ / )i!/'//~(>I'r t T11ccti:yrr11d I.:\.? 1'11 Engliih. Copcnhagcn: M unksg~ard. C:oopcr, Robin. 1070. T h e intcrl~retationof pronouns. In 1'. 1 Icny arld 11. Sclinellc (cds), .Y\'cli~~.~ions Ji.oln /Irr, 7X1ril C I . I ) I I Round ~ I I ~ Tah/t~ ~ (Syrrttr.~trr~rl S ~ . n ~ l w ~ ivol. t . s , 10). N ~ \ TYorb: ,lci~dcnlic Prcss. Egli, L. 1979. TIlc Sloic concept of anaphora. In Rainer Biuerlc, Lrs Egli, ant1 hrnim vrjn Stcchou (eds), Sei~irlir~li.s,/i.onl J>[;'ITIII I'oin~s (!/' T'ienl, I3crlin: Springer-Verlag. L\-ans, Gnreth. 1977. Pronouns, quantifiers, and relative clauses. Cr~iarilitr~i Jorirrlnl r!/ Pli11rrsopi1)l 7: 407-5 3 6. Geilc11, Peter. 1962. Rcli,ri.n~,eirvrii Getrcraliil~;.;lit E.vu1nrna1io1rI!~.YOIN(* .I i l ~ l / ~ ~t~ilJ r i i /.21oi/i~r117'1/(,0i.iri. Ithaca. N.Y.: Cornell Univcrsit!. Press. I Ia\vl;ins, John -4. 1978. L>c;/initer~cxsL111d I n ~ l i ~ / i r 7 i / ~ ~-4 ~ r ~S .IvI.::( ! J111~ R L : / ; ~ I Yi111i1 I I ~ .(~; I~. ~ ~ I I I ~ I I)I~ I / ~ ( . ( I / I / P r ~ l l t ( ~ i o London: tl. Croon1 Helm. I-leinl, Irene. 1982. T h e Scmiintics of Definite and lncleijnire Ncurn Phrases. l>octor;~lclisscrt:~tion, Univcrsit!, of I\lass~~chusetts, Amhers~. IIcim, Irene. 1083. 0 1 1 the projection prohleni for prcsuppositioi~s.In 5.1.B.ulon, 1.). l;licl\inpcr, nnrl A!. \J,'cscoat (cds), M,%'CE% 2: .Sct.onil .Airr!iiul il'i,si Coils/ C ~ I ! / ; ~ I . Loi7, IFI O ~ ,I~. IJI ILLI~I/ I ~ I ~ .St;~nlijrd, ~/~~.Z, Calif.: Stanf'orcl Univcrsit!-. Jespersen, Otto. 1949. :I ,440d~t-u/??7g/ish Grilnlnrc~i.oil rIisrorir.a/ Prinl.ipks, part YII, completetl and l>ublishcd by N. Haislund. Copenhagen: I\,Iunksgaard. Lamp, I4ans. 1981. A theor!; of truth and semantic rcprcsentation. In J. 14.G. Groenendijk, 'IT. hI.1:. Jansscn, and kt. 13. J . Stokhof ( 4 s ) . Forn~izl:%fe!hnils ill t l ~ eSlirr/~l(!/' Lr~llglii~~r,, Amsterdam: A4athcmatisch Centrum, Univcrsitj: of .-2mstcrdam. Kaplan, Ilavid. 1972. What is Russell's theor! of dcfinice descriptions?. Tn D. Jlavidson and G. tlarman (cds), f i 7 ~Lo
248 Irene Heim Russell, Rcrtl-and. 19 19. Inrvodl,r.zion to Il.lntkevwnlir.rrl Phi/osop/i,y. 1,ondon. Sniaby, R . 1979. L4mbiguouscoreference with quantiticrs. In F. Gunthncr and S . J . Schmidt (cds), Pomlcrl Sctnnntics ~lnliPmgnzrrti~.sJ;,r&l~r(z/ Lrrn,~raages,Dordrecht: 13. lieidel. Stalnalcer, Robert C. 1978. Assertion. In Pctcr Cole (ed.), Prtrgi.nritics (S)ln~a.vlint/ SCVIIIPIII(.S, vol. 1)), New York: Academic Press, 315-22.

On the Projection Problem for Presuppositions Irene Heim

'I'he projection problem is the problem of predicting the presuppositions of complex sentences in a compositional fashion from the presuppositions of their parts. A simple illustration is providcd by the following three sentences. (1) T h e king has a son. ( 2 ) T h c king's son is bald. (3) If the king has a son, the king's son is bald. Restricting our attention to existence presuppositions resulting from dcfinite descriptions, we observe that (3) inherits the presupposition that thcre is a king, which \wth of its constituents carry, but does11't inherit the presupposition that thc king has a son, which its right constitucilt carries. T h e solution I will advocate was in some sense already arrived at by Karttunen (1974), but its full potcntial was not realized ilt the time, perhaps because an appropriately sophisticated view of contexl change and its rclation to truth-conditional meaning was not available then.

1 Complementary Strengths and Weaknesses of Two Recent Theories I start with a bricf comparison between two well-k~zown recent treatments of the problems, one due to Gazdar (henceforth G.), the othcr to Karttunen and Peters (K.&P.).

1.1 Explanation vs. mere description G.'s strongest objection to K.&P.'s theory is that it mcrely describes the projection facts instead of explaiiling thcrn. Recall what wc just observed ahout (3). T o predict this observation, K.8iP. appeal to the assumption that the grammar of English supplies three pieces of information for each lexical item: T h e first piece pertains to the item's

250 Irene Heim purely truth-conditional content. For the word "if", let's say this is the information that "if" is material implication.' T h e second piece specifies what the item a)ntrihutes in the way of presuppositioi~s.E.g. for thc word "the", this includes at least the information that "tlie" contributes the prcsupposition that the noun it coinbiilcs with has a non-empty extension. (For "if", K C presumably have the information that it contributes nothing.) T h e thircl piece of information becomes relevant only for itcms that are fiitlctors rather than arguments, and it concerns thc itern's permeability fi)r the presuppositions of its arguments. E.g. for "if" (a fi~~zctor talcing two propositional argunicnts), this is the information that "if" lets through the full presupposition of its left argument, as well as as much of the presupposition of its right argument as docsn't follow from the lcft argument. In other words:

(4) If A has p as its truth-conditional contcnt and as its pl-esupposition, and B has contcnt q and presupposition q', then the prcsupposition of "If 11,B" is p' 8.(p qf).

-

Let's refer to these three pieces of information 3s the "content prop~rty","pres11pposition property", and "heritage propert!-" of the item in cluestion. G.'s point of criticism is that the K.&P.-theory treats these three propcrtics as mutually indcpendent. None of thein is del-ived fi-on1the other two. T h e thcoi*!. thus implies - it~~plnusibly - that somconc who learns thc word "if" has to learn not only \ ~ l ~ i ctl.uth l i function it dcnorcs and that it contributes no presupposition, but moreover that it has the heritage propcrt!. spccilied in (4). It also implics that there could n-ellbc a lexical item - pr-esurni~blynot attestccl as yet whose content and presupposition properties are identical to those of "if", ivhilc its heritage property is different.' We have to agrec with G. that n more explanatory theory would not simply stipulate (4)as a lexical idios~ncracyof "if", but \vould sonichow derivc it oil the basis of gcneral principles and the other semantic properties of "if". G. further claims that his own theory is explanatory in just this respect. Whilc he, too, takes every basic expression to be lexici~llyspcciticd for a content and a pt.csupposition propert>-,he manages to get away without heritage propcrtics. In their stcatl, he invokes a gcneral and quite simple theory of 11ow utterances cllangc thc contest in which the!. occur. In the case of (3), for instance, G. assunzes that onc of tile existence presuppositions of the consequent gets cancelled by a conflicting con\ crsational iinplicature of (3): (3) implicates that, for a11 the speaker knows, the king may not Izavc a son, which is not consistent with a prcsupposition to the effect that the king must have a son. T h e callcellation that ensues is dicratecl by a conipletclj gcneral strategy of lnaintaining consistency during context change; it docs not depend upon a hcritagc property or other idiosyncratic property of "if". -

1.2 Differing predictions It has been obscrved" that G. sq.stematicalIy niakes inadccluatc predic~ionsfor cx;lmples of the f o l l o ~ i n gtwo typcs.

(3) If John has children, then Mary &ill not like his twins. (6) If John has twins, then Mary will not like his children.

On the Projection Problem for Presuppositions 251

Intuitively, (6) as a whole presupposes nothing, in particular not that John has cl~ildrcn. ( j ) ,bq- contrast,

is slightly strange, at least out of context. It somehow suggests that it is a matter of course that someone with chilclren will have twins among them. K.&P. predict just these judgments. But G. unfortunately predicts the opposite, i.e, that ( 5 ) presupposes nothing while (6) carries a substantial presupposition, viz. 'That John has children. Thcse examples suggest to me that there is something fiu~~damentally wrong mith G.'s idea that presupposition projection in conditionals is a matter of cancellation. T h e Iiterature also contains a battery of examples designed to show that G.'s predictions arc superior to those of K.&P. One group of such czamplcs is supposcd to discredit K.&P.'s assumption that conditionals prcsupposc the conditional p + q' (cf', (4) abovc) rather than q' simpliciter. I agree with Soames (1982) that nonc of thcsc examples are convincing. 'The remaining groups of genuine countcrcsaniples to K.&P. are disjunctions whose clisjuncts carry cnntradictorj- presuppositions (c.g. "He either just stoppcd or just started smoking.") and conditionals in xvhiclr a prcsupposition of the antucedent Fails to survive (e.g. "If I later realize I haven't told thc truth, 1 \+Tillt d l you.").

1.3 Subsentential constituents and quantification In c o n ~ p ~ ~ tthe i n gpresuppositions of sentences from the ~~rcsuppositions of thcir parts, onc must eventuallj- attcnd to parts that are not completc sentences ti~cmsclvcs.?'his presents no difficult!; to K.&P., since their theory assigns prcsuppositions t o c'il7rcssions of an?- syntactic category and semantic tqpe and employs projectiol~rules aboke and below the scntelrce level that arc not different in liiird. G. remains silent about presupposition projection below the sentence level, and it is not ubvious how he ~vould l~andleit. Presumably, nonsentcntial phrases don't haw pl-esuppositions that arc propositions; in the extended sense that they have any presuppositions at all, those are of other semantic t!-pes. Hut then G.'s mechanism of contest change is not applieablc to them: prcsuppositions that are not propositions arc not the sort of thing that can gct nddcd to a context, at least not with contexts construed ils sets of propositions. Given that G.'s main point is that prcsupposition projection is an cpiphenomcnon of the la\\-s governing context change, his solution to the projection prohlem rcn~aiils incomplete until this issue is addressed. Quantified sentences provide il particularly interesting illustration of thc task that G. faces here. Consider (7).

( 7 ) Every nation, cherisllcs itsi king. The parts of (7), at the relevant level of analysis (logical form), arc something like the following three:

(8) every xi, xi (is a) nation, x; cherisl~esxi's liing 'The third part of (8) contains the definite description "aj7s liing", ~vliicllone might want to say carries the existence presupposition crprussed in (9).

252 Irene Heim I

(9) x; has a king

I

I

But whatever (9) expresses is not a proposition: thc free variable in it makes it incomplete. Would G. say that (9) expresses a potential presupposition of a part of (7) and hence of (7) as a whole? If so, what would it mean for this presupposition to get added to the context?

2 The Conceptual Priority of Context Change T h e following is an attempt to combine the descriptive coverage of the IS.&P.-theory with t11c explanatory adequacy demanded by G.

2.1 Admittance conditions We start by reformulating the heritage property of "if", currently stated as in (4). As Karttunen (1974) has shown, a stipulation like (4) is reducible to a stipulation like (10) combined with a general principle along the lines of (1 1).

+

If "If A, B" is uttered in context e, then c is the local context for A, and c A (read: "e incremented by A") is the local context for B. (1 1) A context c admits a sentencc S just in case each of'the constituent sentences of S is admitted by the corresponcling local contcxt.

(10)

A context is here construed more or less like in G.'s theory, i.e. as a set of propositions, 01' more simply, as a proposition, namely that proposition which is the conjunction of all the elemcnts of the set. (See e.g. Stalnaker (1079).) (1 1) appeals to a relation of "admittance" which is to hold between contexts and sentences. This relation is taken to be intcrdefinablo with the relation "presuppose" that relates sentences to the propositions the!- presuppose, under the following equivalence: (12)

S presupposes p iff all contexts that admit S entail p.

Givcn their intcrdefinability, either relation can be used in the fi>rmulationand treatment of the projection problem. Following Karttunen (1974)' wc approach the problcm in terms of the "admit" relation: How do the admittance conditions of a complex sentencc derive from the admittance conditions of its parts? E.g. we want to predict that for a context c to adn~it(3), c has to entail that thcre is a king, but needn't entail that the king has a son. (10) in conjunction with (1 1) tells us that c will admit (3) just in case (i) c admits (1). and (ii) c -I- (1) admits (2). Given that we already know the admittance conditions for (1) and ( 2 ) , this amounts to the following: (i) c has to entail that thcrc is a king, and (ii) c conjoined with the proposition that the king has a son has to entail that there is a king and he has a son. Requisement (ii) will hold automatically whcnever (i) does, so the admittance condition for sentencc (3) is mcrelv (i). We have now shown that (10) together with (1 1) can do the job of the previous stipulation (4).

!I I'

On the Projection Problem for Presuppositions 253

2.2 Context change potentials The gcncral principle (1 1) need not worry- us any further, but (10) is still a stipulation specifically about "if' and is apparentlj- independcnt of that item's content and prcsupposition properties. G.'s objection, as reported in 1.1 above, therefore still applies. Next I wiIl show that (10) is actually nothing but an incomplete specification of what I cill thc "contcxt change potential" (henceforth CCP) of "if'. I will suggest that, while the CCP of "if' cannot be derivcd from its other properties, one ~.rr?zderive thc content property from the CCP. More generally, the truth-conditional aspect of the meaning of any expression is predictable on t l ~ cbasis of its CCP. Since the CCP also determines the heritage property, I can then answer G.'s objection: A two-fold lexical specification of each item, in terms of CCP and prcsupposition property, can rcplace thc threc-fold specification that appeared to be needcd in the K.&P.-theory. What are CCPs? Intuitivelj-, they arc instructions specifying certain operations of context change. T h e C C P of "It is raining", for instance, is the instruction to conjoin the current context with thc proposition that it is raining. (If we construe propositions as sets of possil->lclt-orlds, as we will here, "conjoin" nleans "intersect".) 'l'he CCPs of complex sentences can be given compositionally on thc basis of the (:CPs of their constituents. We lvill illustrate this shortly. We will always write "c+S" to dcsignatc the rcsult of executing the CCP of sentence S on context c. Therc is an intimate connection hetwecn the C;CP of a sentence and its truthcondition;il content: (13) Suppose c is true (in IV) and c admits S. Then S is true (in w) if-it171 respect to c iff c+S is truc (in w). (Informally: T o be a true sentence is to kecp the context true.) Something like (13) has occasionally been uscd to define CCP in terms of truth-conditional content (see c.g. Stalnakcr (1979)). 1 want to cxploit it for the opposite purpose: to give an - albeit onl!~ partial .- definition of truth of a sentence in terms of the CCP of that sentenuc. T h e partiality results from the fiict that (13) says nothing about the truth of S when c is false. I bclievc, without offwing justification here: that (13) is nevertheless good enough as a truth definition for scntences. If this is so, then a compositional ~issignmcnt of CCPs to the sentences of a language can fully replace a compositional assignment of truth conditions of the sort normally envisaged by semanticists, without any loss of empirical coverage. 1 indicated that, by specifying the CCP of an expression, the nccd for a separate specification of its heritage property is obviated. Suppose, e.g,, the CCP of "if" is as described in (14).

("hI\N" stands for thc intersection of M with thc con~plementof N, as usual.) Supposc further, as seems natural, that admittance conditions are conditions on the dcfinedness of the CCP, i.e. that c+S is defined iff c admits S. It is apparent from (14)

254 Irene Heim

+

that c If A, H is only defined when both c+A and c+Ai-13 arc. Under our assumptions, this means that c admits "1C A, H" only if c admits A ilnd c+,4 admits B. In this way, the heritagc property of "if" Falls out from its CCP (14). To give another example: If (15) describes the CCP of "not", we can scad off immediately that c will admit "Not S" only if it admits S.

In other words, (1-5) determines that negation is il "hole" in the scnsc of Karttuncn (1073). Of course, (14) and (15) are motivated independcntl!. of the heritagc propertics of "if)' and "not". The!; are just the CCPs that one would be Icd to assunlc if one's only and "notvgoal were to arrive via (13) at the standard truth conditions for "if" sentences. ( T h e reader should convince hersclf of this.) So it is fiztir to say that cvc haw reduced two seemingly independent semantic properties, 111e content and the heritagc property, to just one, the CCP. T h c cussent theory no longcr implies that content and heritage properties tvill j-ar!- indepcndently across lexical items, or that they need hc learned separately, and it is hence no less explanatory than G.'s. -

2.3 Accommodation Suppose S is uttered in a context c which doesn't admit it. LVc h a ~ , said c that this ~vakcs c+S undefined. What does that mean in practice? Iloes it mean that context changc simplq- comes to a halt at this point and communication hrcaks clown? That ~vouldhc an unrealistic assumption. In real-life conversations, people deal with this kind of situation effortlessly: They simply amend the context c to a slightly richer context c', onc which admits S and is otherwise like c, and then proceed to compute cJ+S instead of c+S. Following 1,cwis (1979), 1 call this adjustment "acconln~odation". Accon~modation accounts for the commnil observation that utterances can convey their presuppositions as new information. 'The inibrnlal characterization of accommodation that I just gave contains ;I hidden ambiguity, 13 hich comes to light when we looh a t an esample: Supposc S presupposes p, and "Not S" is uttered in a contest c which Liils to cntail 11, hence docsn't adinit "Not S". Some sort of accommodation is callcd for. One can imaginc two quite different ways in ~ ~ h i itc might h occur: (A) T h e "global" option: Amend c to c&p and, instead of c 4-Not 5,calculate c&p Not S. Follo~ving(IS), you will end up with cgip \ c & ~ S. (13) The "local" option: ,+inend c to cgip so that yo11 can calculate c&11 S instcad of c S. l'llcn substitute thc result of this calculation in the place of "c -tS" in (15))so that j 011clld u p with c \ c&p + S. A is more like pretending that cgip obtained instead of c all along (hence thc word "global"). R is rather like adjusting the context only (or thc immediate purposc of evaluating the constituent sentencc S (hence "local"). 'l'hc results ilrc obviousl~rdifferent, so which waJ- do people proceed in real life? 1 suggest that the global option is strongly preferred, hut the local option is also available in cerlain circumstances that make it una~~oidablc. Consider a concrete cxainple,

+

(16)

T h e king of France didn't come.

+

+

+

On the Projection Problem for Presuppositions 255 uttered in a context which is compatible with France having no king. Bv the global option, we end up with a contcxt that entails that France has a king; this is prcsuinablj how we tend to read (16) in isolation. Undcr the local option, thc resulting context will only entail that either France has no king or he didn't come. We will read (16) this way if me are for some reason discouraged from assuming France to have a king, e.g. if the speaker continues (16) with "because France doesn't have a king". Note that b7! stipulating a cctcris paribus preference for global over local accommodation, we recapture thc effect of G.'s assumptioi~that presupposition cancellation occurs only under the threat of inconsistency.' I am lierc stopping far short of il general and precisc formulation of thc laws governing accon~modationand their interaction wit11 the instructions contained in the CCPs.

3 The Interpretation of Variables While the theory I have sketched builds in man!- ways 011 that of K.&P., it also shares a problematic feature wit11 G.'s: It treats presupposition projection as a side-cffcct of thc rules governing context change. It is therefore not straightforwardly applicable bclow the lcvcl of complete sentences (cf. 1.3). Like G., I am faccd with the diffic~ultof assigning CCPs to constituent sentences with variables free in theni, i.c. to expressions that don't express propositions.

3.1 Contexts as sets of sequence-world-pairs We can solve our problem if we abandon the identification ol' contexts with propositions. 'The information accumulated in a context need not all be propositional; much of it is rather like information as one finds it represented in a card file, i.c. a collection of cards with a (more or less informative) description on each card. Depending on the facts, such a file may be true or true if there is at least one collection of individuals that can bc lined up wit11 the cards so that each indih-idual fits the description on the corresponding card; False otherwise. If contexts arc like files, then conrcxt changes in responsc to utterances are likc updating operations: additions of further cards and/or additions of further entries on already established cards. This metaphor is naturally applicable to utterances containing variables: 'The contcxt change induced by, say, "s7 is a nation" consists of writing the entry "is a nation" onto card number 7, where this card is either created 011the occasion or found among thc already established cards, ils the case mag be." 'I'cchnically, files and, I suggest, contexts can be identified, with properties of sequences of individuals, i.e. with sets of pairs (g,w), where g is a sequence of individuals (a function from the set of natural numbers into the domain of individuals), and w is a world. Since each such set of pairs determines i~niqucly a proposition: (17) Let c be a set of sequcnce-world-pairs. Then the proposition determined by c is ( w : for some g, (g, w) E c).

256 Irene Heim we don't give up any of the advantages of identif>-ingcontexts with propositions when w;e identify them with properties of sequences instead. In particular, we can still evaluate contexts in terms of truth and falsity, as shown in (18), and can retain the trutli definition for sentence (13) which relies on that. (18) c is true in w iff for some g, (g,w) E c. We can now assign CCPs to sentences with free variables, e.g. to sentence (9): (19)

c

+ (9) = c n {(g,w): g(i) has a king in w)

(As for the CCPs for "if" and "not" that I formulated earlier, (14) and (15) carry over just as they stand into the new framework.) We can also formulate admittance conditions for sentences with free ~ariables.E.g. in order to admit (20):

(20) xi cherishes xi's king, a context must, informally speaking, "entail that xi has a king". By this I mean that it has to be a contest c such that, for every (g,w) E c, g(i) has a king in w .

3.2 Presuppositions of quantified sentences So how are we going to predict the presuppositions of a sentcncc like ( 7 ) We have alniost everything we need, except for the CCP of "ever.". Considering the truth conditions to be captured, the following formulation suggests itself. (21) c

+ Every xi, ,4,

l3 - {(g, w) E c : for ever\- a,

("g:" stands for the sequence that is like g, except that g! (i) = a.) We need a further stipulation to ensure that (21) always yields adequate truth conditions: x, must somehow bc required to be a "nc~v"variable at the tinze when "every xi" is uttcrcd. In terms of the file metaphor, we want to require that the file which obtains prior to the uttcrance doesn't j-et contain a card nuniber i, so that a fresh card will be set up when xi is ellcoilnterecl in the evaluation of A. More technically, the stipulation wc need is this:

( 2 2 ) For any two sequences g and g' that differ at most in their i-th member, and for any world cf-: (g, u-)E c iff (g', w) E c. Given (22), (21) will derive the intendecl truth conditions for a sentence like (7), but not without (22). (Thc reacler should verify this for himself by compilting c (8) fi)r a choice of c that violates (221, e.g. c = {(g,w): g(i) = France).) For our present purposes, Fve take (22) to be a lexical property of "every", i.e. part of its presupposition property. In other words, we stipulate that no context that violates (22) will admit a sentence of the form "Every xi, A, B".:

+

On the Projection Problem for Presuppositions 257 Back to the issue of presupposition projection in "everyM-scntcnces, (21) dctermines that c "Every xi, A, B" can only be defined if c+A and c+A+B are. Applied to (8), this means that c will not admit (8) unless (i) c admits "xi is a nation", and (ii) c "xi is a nation" admits (20). We suppose (i) to be trivially satisfied. As for (ii), wc determined in the previous section that c "x, is a nation" = c f l ((g, w): g(i) is a nation in w }, and furthermore that this will admit (20) just in case the following entailment holds:

+

+

+

(ii) For e \ ~ e r y (M-) ~ , E c n {(g, w) : g(i) is n nation in w), g(i) has a king In w. Now suppose that in every world in which c is true, every nation has a king. This is clearly a sufficient condition for (ii) to hold. It turns out that it is also a necessary condition; one can prove this by exploiting (22). We therefore conclude that a context that is to admit (8) must entail that every nation has a king. In other words: (7) presupposes that every nation has a king. T h e reasoning by which we arrived at this prediction may strike you as somewhat complicated. Hut bear in mind that all the macl~inerywe had to in\.oke (in particular (21) and (22)) was needed independently to predict the truth conditions. For the type of example discussed so far, i.e. universally quantified sentences with the presupposition-inducing element (here: a definite description) in the "consequent" (i.e. in the 13-part of " E ~ e r yxi, A, B"), our predictions coincide with those of K.&P. (1979): If B presupposes X, "Every xi, A, R" presupposes "Every xi, A, X". Hut when the presupposition-inducing element is in the "anteccdent", i.e. in A, as in (23), niy clailns differ from thcirs. (23) Everyone who serves his king will bc rewarded. According to K.&P. (1979), (23) presupposes nothing. I am committed, by the assumptions I havc introduced so far, to the claim that (23) -- norn~ally,at any rate presupposes thal everyone has a king. I say "normally", because the prcdiction stands onl!; to thc extent that there is no local accommodation. As we observed in connection with (16), local accon~modationmay produce what looks like presupposition canccllation. I.,imitations of space prevent me from exploring the implications this might have for cases like (23). I can only hope the reader will agrec with m y iinprcssion that a theory which assigns a universal presupposition to (23) as the unmarked case is toIerabI!r close to the actual facts, or at least as closc as K.&P.'s analysis or any other simple generalization that comes to mind. What about yi~antifiersother than universal? Concerning "no", we find conflicting factual claims in the literature, According to Cooper (1983). (24) should presuppose that every nation (in the relevant domain of discourse) has a king; for 1,crner and Zin~mern~ann (1981), it presupposes merely that somc nation does. (24) No nation cherishes its king. Herc as elsewhere, the theory I am advocating gives me no choice: Once I have iissigned "no" a CCP that will take care of its truth-conditional content, it turns our that I have

258 Irene Heim to side with Cooper. But again, this applies only for the "ordinary" cases which don't il~volveany local accommodation. When the latter is brought into play, the univcrsal presupposition will appear to be weakened in various ways or even canccllcd.

3.3 Indefinites K.&P. (1979) point out a difficulty with sentences like (25).

(25) A fat man was pushing his bicycle. Their rules assign to (25) a presupposition that they admit is too weak: that somc fat man had a bicycle. On the other hand, a universal presupposition that ever!. fat man had a bicycle would be too strong. What one would like to predict is, vaguely spcaking, a presupposition to the effect that the same fat man that verifies the content of (25) had a bicycle. But it is neither clear what exactly that means nor how it could bc worked into K.&P.'s t h e ~ r y . ~ I have argued elsewher:' that indefinites are not quantifying. T h e logical form of (25) thus lacks the part corresponding to "every xi" in (8):

(26) xi (was a) fat man, x, was pushing xls bicycle (26) is just a sequence of two open sentences with free occiirrences of xi, which arc interpreted as though conjoined by "and". T h e CCP of (26) is simply: (27) c + (26) = (c f xi was a Fat man) f xi was pushing x,'s bike

'l'his gives adequate truth conditions - provided that xi is a new variable. We thercforc stipulate that a context must conform to (22) if it is to admit a sentence conlaining an indefinite indexed i. Now what about presupposition projection? (27) shows that for t: to admit (26), c "xi was a fat man" must entail that xi had a bicycle. It turns nut that, due to (22), this entailrncnt will I~oldjust in case every fat man in any world compatible with c had a bicycle. So we are prima fiacie committed to an unintuitively strong universal presupposition for (25). I suggest that our actual intuitions are accounted for by the ready availability of a certain kind of accommodation in the evaluation of indefinite sentences. In the case of (25), when c fails to entail that every fat man had a bicyclc, the following appears to happen: First, c "xi is a fat man" is computed, call the result of rhis c'. l h e n c' is found not to admit "xi was pushing xi's bicycle". So it is amended to c", which presumably is c' & xi has a bicycle. From there, c" + "xi was pushing xi's bicycle" is calculated. T h e net result is a context which entails that x; was a fat man, had a bicycle, and was pushing it, but entails nothing about fit men having I>icyclosin general. This sort of accommodation seems to happen with thc case typical of global, rather than local, accomn~odation.In fict, it IS global accommodation if we take the defining feature of globalit!; to be that the accommodated piece of information (hcrc that xi l~ada bicycle) I-emains in the context ,fhr good. (Notice that chis criterion distinguishes

+

+

On the Projection Problem for Presuppositions 259 appropriately between the global and local accommodatiol~options as exemplified above for example (16).)In othcr words, I speculate that the relative easc uith which a missing presupposition is accom~nodatedin thc midst of evaluating an indefinite sentence can be subsumed under the general observation that global accommodation is more common than local accommodation. Incidentally, this speculation relies crucially on the nonquantificational analysis of indefinites: only because xi remains free in (26) does the information that xi had a bicycle end up being cntailcd by thc contcxt evcr after.

4 Final Remark Many non-trivial aspects of presupposition projcction could not evcn be alludcd in this paper, e.g. the heritage properties of "or", modal operators, and propositional attitude verbs. As for the latter two, I expect that the present approach will inakc reasonable predictions when ct)mbined with a treatment of modality in terms of quailtifieation over possible worlds."' But I don't expect my readers to take this on faith.

Notes This work is supported by the Ccnter for Cognitive Science ofM.1.T. under a grant from the Sloan Foundation's particular program in Cognitive Science. I thank Stanlcy Peters, Lauri Karttuncn, Rob~nCooper, and Thomas "Edc" Zimmermann for illun~inatingconversations on the material. 1 I don't bclici-e that, but it doesn't matter here. 2 G.'s point is not affected by the fact that K.&P. (1979) use a "heritage function" cvhicl~assigns ha-itage properties to pairs consisting of the content and presupposition properrics. For not-ice that this function is defined point by point, not as a general procedure. 3 Peters, personal communication. G.'s yrohlcm with (6) is also pointed out hy Soan~es(1082), whose proposal, however, continues to be affected by the prohlem with (5). -I I discuss this point somewhat further in Hcim (1982). at thc end of section 1.2 may also be amenable to a treatment in terms 5 The examples ~ncntio~lcd of local accommodation. 6 For a more explicit motivation of the file metaphor and the correspondi~lgtechnical concepts, see I-Ieim (1983) [This volume]. 7 This stipulation is derived from the indcfinitencss of quantif!ing NPs in Hcim (1982) and (1983). 8 A solution very different from the one sketched below is developed in Coopcr ( 1 98.3). 9 See Hcim (1982) and (1983) L'or details. 10 E.g. along the lines of7Kratzer (1981).

References Coopcr, R. 1983. Q t ~ a r l r ( f i c ~ ~Ll Z~IoI nSjlntac.ri~ ~ T/zeoy~l.Dordrecht: D . Reidel. Gazctar, Gcrnld. 1979. Prngvtzatics: I n ? p / i c ~ ~ u rPr~slrpposi~ion c, (z~(/ Logic.vl I:ot,nr. Ncw York: Acadc~nic Press. Heim, Ircne. (1982). The Semantics of Definite and Indefinite Noun P h ~ s c s Ph.L). . dissertation, University of h4assachusetts, i4mherst.

260 Irene Heim I-Ieim, Irene. 1983. On the projection problem for presuppositions. In M. 1%1rlow,I>. I:licAingcr, and M. U'escoat (cds), II'CCFI. 2: S ~ c o n d;ltir11~'11 West C O N X( ,I' O ~ I ~ ~ ~ ~ P0 N1 1LF01~11ril .L~ I,i~l~~:'ui.cl if..$,Stanlid, Calif.: Stanford Unircrsity. Karttuncn, Lauri. 1973. Presuppositions of conlpound scntcnccs. Lln~uisllc.Itfqrril:)~ 32):l h 0 - 9 3 Karttunen, Lausi. 1974. Presupposition and linguistic context. T/7c~owltcrrlI , i ~ r g r ~ u /1: i c ~181 -93 Karttunen, Lauri and Stanley Peters. 1979. Conventional implicature. In C:. K. Oh and D. Dineen (eds), Pr~nlpposition( S j ~ n l uclnd . ~ S~.mliznti~.s, vol. 1 I), New York: Aoaclemic Press. Kratzer, Angclika. 1981. T h e notional category of'modality. In Hans-Jeitrgcn LiAmcycr and 1-Ianncs Riescr (cds), Wi~rds,PVorl~fs,~ r ~ iCr lu n t r ~ l s:hT~lz~ ..ilppru(tr.h~rin I,t'ord .Sci?rrrntir:v, N L'W Y orh: Walter de Gruytcr. Lewis, David. 1979. Scorekceping in a language game. In Rainer Biuerle, Urs Kgli, ant1 ,4rnini von Stcchocv (eds), Sen~a~~ri~..sJi.o~iz Djflire-enl Poinls I!/' I.i'e7)?,Berlin: Springer-Vcrlag. Lerner, J, and Thomas Zimmermann. 1981. Mehrdimensionalc Semantik: 13)ic Prasupposition und die Kontcxtabhingigkeit von "nur", working paper no. 50, SF13 99, Konstanz. Soamcs, Scott. 1082. How presuppositions are inherited: a solution to the projection problcn~. Linguistic Illqurq! 13: 483-545. Stalnakcr. Robert C. 1978. Assertion. In Peter Cole (cd.), Prugnruiics (S:)fi?/lr.t.ilnrf Se?nrrr~rir.s,vol. Y), Nen York: Academic Press, 315-22.

I

I

Toward a Semantic Analysis of Verb Aspect and the English "Imperfective" Progressive David R. Dowty

1 The Problem For somc time I have been concerned with a problem in English syntax and semantics that I wilI call the "imperfective paradox". This paper will sketch a ncw appn~achto this problem based on previous treatments I have given (Dowty 1972) and similar to treatments in Hennett (1974), Bennett and Partec (1978) and Hoepelman (1974). hly present proposal differs in important respects from all of these, however. T h e problem in~olvesa class of verbs (actually, of verb phrases) variously called nc.~.o~i~~lzsh~zcnt z!erbs (Vcndler 1967; Dowty 1972), mholislzz z1et.h.s (Rescher and Urquhart 1971), nor~suhinter.valilerbs (Bennett 1974; Bennett and Partec 1978) and by other names. Accomplishment verb phrases are distinguished by (among other tests) the fict that the entailment from thc progressive tenses (also known as contiwzions tenses) to thc simple tenses fails. Thus druiz? n circle is an accomylishmei~tverb phrase, since thc inference from (1) to (2) fails, 117hcreas prrsb a curt is not, since the inference from (3) to (4) is intuitively valid:

'

(1) John (2) John (3) John (4) John

was drawing a circle. drew a circle. was pushing a cart. pushcd a cart.

'The meaning of an accon~plishmentverb phrase invariably involves the conling about of a particular state of affairs. For example, dral~i~zg ti ~ i r l . 1 involves ~ the coming into existence of a circlc (or perl~aysmore corrcetly a vrprese~rtntiorzof a circle), kicking I / I ~ tloov o p m involves the door's coming to be open, and dririrzg the crtr into t/7c xarnse involvcs the car's coming to be in the garage. I maintain that it is inlpossible to give an adequate semantic analysis of accomplishment verb phrases without providing for the entailment that such a result-state comes about. Yet it is just this entailment that such a

262 David R. Dowty result-state comes about which fails when the accomplishment verb phrase appears in a progressive tense.' In other words, the problem is to give w account of how ( I ) entails that John was engaged in bringing-a-circle-into-existence acti~itybut clocs not cntail that he brought a circle into existence. This is thc "imperfective paradox". Notice, furthermore, that to say that John was drawing a circle is not the same as saying that John itas drawing a triangle, the difference between the two activities obviously having to do with the difference between a ciscle and a triangle. Yet if neither activity neccssasily involves the eristeilce of such a figuse, just 1low arc the two distinguished? An immediate answer to these questions is that accomplishments must bc defined in terms of the intention of an agent to bring about a particular rcsult statc. But this condition fails in two ways. Consider the ninety-year-old conlposer \v ho undertakes the composition of a symphony. He may not believe that he n,iH live to complete the symphony nor scriously intend to try to complete it, but hc still correctly dcscsibes his (and not merelj- as n?r.itingpal-t oJ'a q~rriphony).Moreover, activity as ruritilzg. LE .~j~~rlphutiy these al-e instances of accomplishments that have no sentient agent who can havc such an intention. Consider The rains fire ~/e,stri).)~ing the ~.rofis,hut pr~lllzpsrhe)~~ v i /slop / htfirc 11ze .crops n1.e destry)ted, or The I.ZT'L'I' I I ? C ~ S~.i/tiii~g ii I?C/P i./znnnel l o ~ h sea, r brri f l z ~I I ~ P ~11,ith I the snndbags sstoppctl ii .fionz doing so. I \+-ill;lssume that the logical form of ( I ) is (l'), whcrc.?ohn J n i i ~ ~a sl.irr.1~represents a tenseless sentence and PAST and YROG are scntcncc operators, ancl that the logical form of (2) is (2'):

(1') [PAST[PKOG[-rohrr ~lra~ar u c.irc/t.]]] (2') [PAST (John d m IPS a circle]] (See the caveat below about my use of the term "lo~ical form".) Sincc thcrc i s absolutelj; no evidence from English syntax that the progressive tense of ( 1 ) is distinct from that of (3), 1 assume that an adequate analysis n ~ u s temploy exactly the same operator "PROG" for both sentences. Thus the solution to this problern ties not only in finding the correct truth conditions for [PKOG 41, but also in dctcrmining how thcse truth coizditions interact differently with the semantic analyscs given to accomplishments vcrsus non-accomplishments. My carlicr approach to this problem (Dowty 1972) relied on tllc intuitive plausibility of Gilbcl-t Kyle's suggestion (Ryle 1949) tllat a scntcncc with an accomplishment verb ( I ~ L . ~ Z P E ~ ? IZZ~ EP ~T ~Iin ~I Ryle's termino1op)-) makes il "double assertion": not only docs it entail that some act or event takes place, but also that sonle particular state of aff~irs comes about "above and beyond" the act or event as a ~xsult.In (2) thc act is drawing and the state of affairs is that a circle (or the image of il circle) exists. In view ofthis 1 analyzed (tenseless) accomplishrncnt sentences as hacing the logical form ( 5 ) :

(5)

14 CAUSE [BEC:OhlE tb11

Here q5 and t,b arc sentences, CAUSE is a two-place sentcntial connective, and BECOME a one-place tense operator. A sentence 113ECOMI.: rbJwas to be givcn the value ~ T L L Pat timc I if and only if $I is true at t and False at the moment of time just

The English "Imperfective" Progressive 263

before 1. T h e operator CAUSE was to be g i ~ e na kind of counterfactual modcltheoretic interpretation, such as that discussecl by Lewis (1973a). I sug-gcstcd that the truth conditions for the progressive tense operator be given in such a way that from (6) (representing an accomplishment sentence in the progressive tense),

(6) [PROCi[4 CAUSE [BECOME

rk]]]

one could infcr cb but not infer [BECOME $1 (whereas from (5) both (b and [BECOME $1 could be inferred). Rather, one should only bc able to draw from (6) the wcaker inference that [BLCOME $1 is possible. Thus from example (1) one should be able to conclude that some activity of drawing took place and that the existence of a circle was a possible but pcrhaps not actual outcome of this activit). l n my earlicr trcatmcnt I assumed a theory of Generative Semantics such as that proposed in LJakoff (1970). Thus what I here call the "logical forms" of accomplishment sentences, such as (5) and (6), m-cre there regarded as the logical deep structures of English sentences, these deep structures being sentences of a model-thcorctically interpreted "Natural 1,ogic". In this paper I implicitly assume a theol-2- such as that founcl in NIontague's "Proper Treatment of Quantification in Ordinary English" (Montague 1973, henceforth PTQ), though my proposals arc cqually compatible with a theory of the Generative Semantics type. In the P'T'Q theory mol-eover, it makes no difference for the purposes of this paper whether my "logical forms)' are taken to be the translatiolls of English sentences into intensional logic which result directly from the translation rules, or merely sentences which are cntailcd by the translations of English scntences by virtue of aclded meaning postulates for accomplishment verbs. See Dowty (1976) for more coninlent on this point. The question whether an operator CAUSE should be postulated to correctly account \:erbs remains, of course, a controversial one, as for the entailments of acco~llplishn~ent 1 think it should. O n the other hand, 1 think the necessity of capturing the state-change entailments for which I have postulated the operator BECOME cannot seriously bc denied. T h e operator CAUSE, however, is not directly involved in my present proposal for the semantics of the progressivc. Those who find it objectionable to postulate such an operator need only accept the weaker claim that an acconiplishment sentence entails a scntencc of the form (5')) rather than (5), u;herc (b is a sentcnce specifying that an act or event took place, and $ is a scntencc specifying tlie result state.

2 Inadequacies of the Earlier Analysis I now believe there are several things wrol~g\vith my earlier analysis. First, though I did not attempt to formalize the requircd truth conditions for [PKOG (b1 this task was tahen up in Tedeschi (1973), and it is clear from that article that truth conditions for [PROG d)II in line with my suggestions are impossible to give in terms of an arbitrary 6, but only for the special case of formulas of the form of (6). 'To see this, recall that

264 David R. Dowty PROG[$CAUSE [BECOMEth']] must entail $ but not BECOMEII/', even though [I// CAUSE [BECOME$']] entails both I,!! and HECOMEI~'.l'he only obvious way to satisfy both these requirements simultaneously is to write a semantic rule for [PROG[I~CAUSE[BECOME$']]] wl~ichexplicitly makcs reference to both I/! and BECOME$', and this is what Tedeschi does. Thus the rule (which I simplify hcrc) states roughly that [PROG [$CAUSk, [BECOMEGI,'I]] is true if and only if !,I is true and [I~CAWSE (BECOME$']] is possible. This rule, however, violates the dictum that a semantic theory must specifj- the meaning of a sentence as a function of the meaning of its immediate parts and the syntactic rule used to form it, for we have now stated the meaning of a sentence [PROG 41 not strictly in terms of the meaning of (I, (which woulcl be identified with the set of possible worlds in which cj, is true, under our semantic theory), but rather in terms of the meaning of certain syntactic subparts of cb. And even if this violation of compositional semantics were admitted, it would bc necessary to supply a further truth condition fol- I~PROGg]for those cases where c j does not have the form [$CAUSE [HECOME$']], i.e., for cases where 4 is an activity sentence. But it would then be quite unclear how we would have captured the intuition (mentioned above) that the progressive tense of an accomplishment sentence such as ( I ) is the sanze as the progressive tense of an activity sentence such as (3). A more serious difficulty is the assumption implicit in this analysis that the resultstate of an acconlplishment comes to be true at a single moment rather than over an interval of time. For example, it seems a doubtful claim at best that no matter how long the activity of drawing- referred to in (2) lasted, there is a single Inonlent at which a circle came to exist. Postulating an instantaneous change of state is even more counterintuitive for accomplishments such as br~ilila'rzgLL Izousc or c.ros.sitrg the rlesel-l. T h e case of what Vendler called al-kiezje~ttentrerl~sis worse still. 'These are verb phrases which, like accomplishments, involve a particular change of stale, but ~u~likc accomplishments, do not assert that the changc of state was brought about by any evcnt or action. Examples are die ("come to he dead"), ./i,rgtl ("come to not know"), ./ill1 oljr .. the table ("come to be not on the table"), etc. I earlier analyzcci achievements as having thc simpler logical form [BECOME 41, and still wish to maintain that they have this form (or at least entail sentences of this form), but the truth conditions I gave for [BECOME (b] wo~lldagain require that the change of state occur at a point in time. This may be plausible for "mental" changcs of state such as notic.e, recognize, r ~ u l k t , etc., but is not so plausible for cxan~plessuch as The ilool. opcnc~ls l o n ~ / l ~ . Moreover, achievements that occur in the progrcssivc (which are rare and which 1 mistakenly claimed not to exist) exhibit the same fc~i:,lilurc of inference as illustrated for accomplishments in (1)-(2). Consider (7) -(8)and (9)-(10):

(7) John was fillling asleep. (8) John fell asleep.

(9) John was dying. (10) John died. T o see that the inferences in qucstion do not hold, considerclfohli iws./i~llirlgus/cep rvhen M n r y sl~onkizi~n.or 3o17n rvc~s(/yirrg mhen thc opcrrrlion r~>ns pe1:fi)rrncd n~hirhsilzlzll his /i/i.

The English "Imperfective" Progressive 265 T h c parallel between these cases and t l ~ eaccomplishme~ltcases suggests that the solution to the "imperfective paradox" lies in correctly formulating the truth conditions for [PROG c , ] and [BECOME $1 and does not, as Tcdeschi and I had supposed, directly involve the truth conditions for 16 CAUSE $1. (Hence the irrelevance of thc operator CAUSE for what follows.) I will suggest in this paper two modifications of my original proposals. I will attempt to show not only that these modifications together result in eorrcct entailments for accornplishmcnts and achievemcnts in both simple and progressive tenses, but also that each nlodification is motivated independently of accomplishment and achievenlent verbs. Finally, I will consider hour to extend this analysis to so-called "futurate progressive" sentences such as John i.v /c.aviz?gtomowom.

3 Truth Conditions Relative to Intervals, Not Moments The first modification is to assign truth values to sentences relative to intervals of time, rather than to moments of time. (In this I follow Bennett and Partee (ms.) exactly.) Such a change would be fairly trivial if it were always the case that a scntencc is true for an interval of time if and only if it is true at every moment in that interval. But of course this equivalence does not always hold, the most obvious case of failure being accomplishment sentences. From the fact that John built a hduse in exactly the interval of time I it does not follow that John built a house at every (or even at any) moment of time within I, nor that he built a house in any subinterval of I (hence the terms "wholistic~' and "nonsi~binterval" for accomplishment verbs). But the equivalence apparentlj- also fails to hold in ordinary language for many verbs which are not accomplishlllent verbs, e.g., for verbs which are r r r ' ~ i r l i ~ , lrcrhs l in Vendler's ternlinology like p ~ l s h(I car/ ill (3) and (4). As has often been observed (cf., e.g., Rescher and Urquhart 1971, p. 160), one can truthfully be said to 11ave spent an hour at activities such as reading, working on a mathematical problem, or playing thc piano, even though one did not engage in the activity at literally every moment within that hour." There are two positions one could take with respect to this discrepancy. One could maintain that ordinary language is simplp inaccurate at this point; that it is, strictly speaking, false to assert that one spent an hour at an activity if there were really "pauses" during the hour. Hence for purposes of the formal theory of semantics, the above-mentioned equivale~lccshould hold for all non-accomplisl~ment 1-erb phrases. Though there may be advantages to such a position, it seems to depart dangerously from our intuitions about how ure use ordinary language. Alternatively, one could accept the situation at face value and allow an interpretation of English to assign a truth value to an activity sentence at times ivithin an interval quite independently of the truth value assigncd to the sentence fi)r the whole interv;~l. Of course one might want to add certain requirements to this assignment; c.g., that if an activity sentence is true at all times during an interval I, then it must be true for I (though not conversely), and perhaps we would require that if an activity sentence is true for an interval I, then it must be true for at least some subintcsval of I. (1 will have more to say about such requirements in the section on the progressive below.) If this

266 David R. Dowty second position is adopted, then there is motivation independent of accon~plishment and achievement verbs for interpreting sentences relative to intervals.

3.1 Revised truth conditions for BECOME In order to give the revised truth conditions f'or BECOME, I will have to introduce definitons for intervals and related notions. I adopt them in the form Ibund in Bennett and Partee (ms.), which I believe is a fairly standard form. Let T,which we will intuitively regard as the set of moments of time, bc the set of real numbers. Let 5 be the standard dense linear ordering of T: I is an interz~nliff I c T and for all moments tl, 12, tx, if t l , t j E I , and tl 5 tz 5 t3, then t 2 f I. (Intervals have no internal gaps.) T h e following notation will be used for intervals: [tl, t 2 ](a closed interz~al)abbreviates ( t : ti 5 t 5 t z j (i.e., end points are included). ( t I ,t 2 ) (a Bounded inlerval) abbreviates f t: tl (t(tz) (i.e., end points are excluded). [t] (a moment) abbreviates [t, t], which is ( t j .

I is a subi~ztervalof J iff I & 3 , where I and 3are intervals. I is a proper subinterra1 ofJ iff I c 3. I is an initial szkbinte~valof 3 iff I is a subintel-val of g and therc is no t E ( 3 - I ) for whic11 there is t' E I such that 1 5 t'. Final subinterval is defined similarly. t is an initial bound for I iff t $! I and [I] is an initial subinterval for { t ) U I (i.e., t is the latest moment just before I).Final hound is defined similarly. T o Bennett and Partee's definitions I will add two more: I is an initial bounl(4tq1irttevcal for 3 iff I and -7 are disjoint, I u 3 is an interval, and I is an initial subinterval for the interval I uJ (i.e., I is an interval immediately preceding9. I is aJinal bom~zdaryinterz~nlfor -7 iff I and 3 are disjoint, J U I is an interval and I is a final subintel.va1 for the interval 3 U I (i.e., I is an interval immediately fbllowing 3. T h e truth conditions for [BECOME 41 relative to an interval I are now as foilows: (1 1)

[BECOME 41 is true at I iff there is an initial boundary interval J for I such that n 4 is true at J and there is a final boundary interval K for 1 such that cb is true at K.

In terms of the usual linear diagram for time, [HECO-ME following s i t ~ a t i o n : ~

74

is true

41 will

be true in thc

@ is true

Notice that (1 1) does not put any requirements on the truth valuc of c j at I itself, nor at times within I. This will have thc following undesirable consequence: Suppose that I / ( / ) is the casc throughout a large interval, and that this is followed by a large interval throughout which 4 is the casc. According to ( 1 I), [BEC;OME $1 would be the case in

The English i'lmperfective" Progressive 267

such a situation at a number of successively larger intervals 1, I f , I", etc., as in rhc following: i $J is

true

$J

is true

A

But this is surely counterintuitive. If a door is closed for a long period, then suddenl!~ conles 10 be open and remains so for anorher long period, it would be very odd to claim that the sentence /he chor nptns is truc of any interval whatsoever within this whole period, as long as the interval contains the first moment that the door was open. Rather, we would want the truth of The door oppens to be limited to the smallest interval over which the change of state has clearly taken place. One way to remedy this problem would be to add to (1 1) a third clause to givc (11'):

(1 1')

[BECOME 41 is true at I iff(1) there is an initial boundary intervalJfor I such that n 4 is true at -7, (2) therc is a final boundary interval K for I such that E/ I is truc at K, and (3) there is no non-empty interval I' such that I' C 1 i ~ n d conditions (1) and (2) hold for I' as well as 1.

This is a very strong requirement: As long as 4 is bivalent, then [BECOME 4 1 can only be true at an interval no larger than a nlolnent under ( 1 1'). (Perhaps we will want to allow for truth value gaps in this situation, of course. Jt does not seem totally implausible to maintain that during the building of a house there is a period of time when it is no longer false that a house exists on the building site but when it is not yet true either. However, I don't want to commit myself on this issue.) A different way to attack the problcm would bc to claim that the third clause of (1 1') is not a part of the truth conditions for [BECOME 41 but is rather to be intcrpretcd as a felicity condition on assertions which follows from some Gricean conversational maxim. If we take this position, then we do not have to appcal to a truth value gap to justify every sentence which asserts that a change of state took place over an interval longer than a moment. Rather, it ma?; be that because of the limits of our knowledge we cannot narrow down precisely the interval or moment at which the change actually took place (or it may be that it would be irrelevant to our interlocutor to know this). But there is another inatter which bears even more dircctly on thc status of ( I 1'). Up to this point I have been considering- only changes of statc in whicl.1 the initial statc is specified by a proposition wliich is the negation of the proposition specifying thc final state; e.g., opening is a transition from "not opcn" to "open," dyztrg is a transition from 'Lnotdead" to "dead." Rut there are accomplisl~mentand achievement sentences which do not fit this pattern, thc most obvious examples being those involving changes

268 David R. Dowty of location. Tmvcling from place -A to place B is not merely changing from bcing at .A to not being a t A, nor is it changing from not being at B to being at B, but is apparently the conjunction of thcse two state changes. Imaginc that (12) is true of a (past) interval I:

;

(12) John walked from the Post Office to the Bank.

I

If we let P represent Johrz is a t the Post @rice and B represent 3ohw is al lhe Bnrzk. then the state-changes of (12) will be representable as follows:

-,

P andiB

T P and B

i Pa n d ~ B A

1 -

i

Obviously, during the interval I itself both w P and n B are the casc; no truth-value gaps are involved. But what form of change-of-state sentence does (I2) entail? It cannot, under my analysis, be (13):

since the truth conditions for BECOME (according to ( I I ) ) would make (13) true for any interval containing the last moment of I. (It would bc immediately follo\~-edby an interval in which n P & B is true and immediately preceded by an interval in ivhich a [ P I P8r B] is true.) According to the stronger condition (1 l'), ( 1 3) would be true only at the very I U Smoment ~ of I and at thc.flrst moment o f 3 . But this is intuitively wrong for (12). (12) must rather entail a sentcnce of the form (14):

There is clearly no interval smaller than I in this situation at which (14) can be true. (I am assuming that the truth conditions for "&" and the other truth functional connections are temporally "straightforward"; that is, that 1-45 & ~,b]is truc at an interval I iff.$ i s truc at I and $ is true at I, etc.) If the requirement in the third clause of (1 1') is interpreted as a felicity condition on whole sentences, it would seem to give the right results for (14). But if we takc ( 1 1') as the truth conditions for BEC:OR/IE, we are in serious trouble. If John took more than one moment to move between the Post Office and the Bank, there would be no interval m-hatsoever at which (14) would be true according to (1 l'), since each of the conjuncts could only be true at diffcrcnt, nonoverlapping intervals (actually, moments). This seems to be a persuasi~creason for demoting the third clause of (1 1') to the status of a conversational principle, at lcast if we want to retain the operator BECOME in the analysis of (12). This brings me to one additional alternative which I will mcntion briefly. Instead of the one-placc operator BECOME we might analyze (12) in terms of a twtrplace

,

j

,

,

I

The English "Imperfective" Progressive 269 temporal connective much like von Wright's "And Next" operator N (won Wright 1968). In an interval-based semailtics such an operator would be defined as in (15): (15) [q$N$]is truc at an intcrval I iff (1) there is an initial boundary interval J for I such that 4 is true at J and $ is false at -7, (2) thcre is a final boundary intcrval K for I such that (I/ is true at K and 4 is hlse at K, and (3) there is no nonempty interval I' such that 1' C I and such that (1) and (2) hold for .I' as well as for I . The BECOhIL operator is definable in terms of

Rr:

(16) [BECOME 41 = def 1~4N$l Although the strong condition corresponding to (11') is included in (15), thc problem with (12) disappears since it can be represented as LPNB] rather than a conjunction [PNftP] 82 [n BNB]. Nonetheless, I am less than entl~usiasticabout (15), since I am still intercstcd in investigating Lalioff's proposal of a "Natural L,ogic," (Lakoff, 1970) a formal language in which the set of' logical constants is empirically motivated from natural languages and is perhaps language universal, no matter whether this "Natural Logic" is construed as the language of the underlying structures in a Generative Semantics theory or thc translation language of a Montague Grammar.) There seems to me to be abundant linguistic evidence for a one-place operator BECOME: as such a universal "atomic predicate" but little ur no evidence for giving the two-place operator N such status.' If one believes, however, that N can be linguistically motivated, or if one is not interested in the empirical linguistic significance of such operators but regards them as mcrely a technical convenience for stating truth conditions for "surface" English, then there is of coursc no objection to replacing BE:COR/IE with N,or to using both operators for that matter. (Rules for producing and interpreting sentences such as (12) in a P T Q grammar are given in an appendix.)

4 Truth Conditions for the Progressive Rily sen~anticanalysis of the progressive tense will be similar to that of l3ennctt and Partee (ms.), which in turn is similar to earlier analyses by Scott (1970) and by Montague (1970). However, there will be an important difference in the present analysis. Bennett and Yartee's truth condition for the progressive stipulatcs that [PROG (/I 1 is true at I iff there exists an interval I' such that I c I', I is not a final subinterval of 1', and ( j is true at I'."l-re difficulty with this analysis is that it licences the infercncc from an accomplishment sentence in a progressive tense to the same sentence in some simple tense. Actually, the inference from the past progressive to the sinlplc past does fail in the Bennett and Partec analysis, but for an irrelc.\.ant reason. It c o ~ ~ turn l d out that (1) is true and (2) false because the only interval for which John dr~firv,vLJ circle. is true is onc beginning in the past but including the prescnt.

270 David R. Dowty

( I ) John was drawing 11 circle. (2) John drew i1 circle. Nevcrtheless, the inference from (1) to (17) would be valid (given a stanrlartl tcnselogical analysis of the future perfect), as would the inference from -7oh11 is rluiln~iaf( I l~'r-c/c to (17) and the inference from 30hn n~illb p ilrni77it1~-N cirz.1~to (17).

(17) John will have tlrawn a circle. But intuitively, all these inferences should fail and they should fail for the same reason: to sa\- that John was, is, or will be drawing a circle is not to conunit onesclf to thc coming into existence of (a representation of) a circle at any time. On the othcr hand, to assert that John dren, draws, or will draw a circle is to postulate the existence of a circle at some time or other. As I pointed out earlier, however, one should be able to conclude fi-om ( 1 ) no more than that the existence of a circle was (or will be) a possihiil outcoinc of John's activity. This observation suggests that the progressive is not simply a temporal operator, but a kind of mixed modal-temporal operator. A natural proposal lvould be the following truth condition, in which a ruth value is assigned to a sentence relative to both an i n t e n d 1 and to one possible ivorld m out of a given set of possible vvorlds 1F (18) [PKOG cb] is true at I and iff there is an interval I' such that I C I' and therc is a world r~' for w-11ich 4 is true at I' and IIJ',i ~ n d is exactly like n?' nt all times preceding and inclining I. /I)

(The idea of one possible world being exactly like another up to a certain time is of course the crucial notion here. I take it that it is intuitively clear enoi~ghto the reader what this ought to mean. I will return to the problem of formalizing this notion short1j-.) Consider now the special case of [PROG (b 1 in which qh has the form (BECOME I// 1, i.e., [PROG[BECO_ME tb] 1. According to (1 1) and (18), this kind of scntence will bc true in the following situation: -I

I'

ry is true

-L

ty is true

1

PKOG [BECOME ry1 is true In this diagram the two lines labeled n7 and nl' represent, respectively, the acti~al world and some possible world perhaps distinct from it, and the dotted line indicates the point up to which 171 and are exactly alike. Note that this analysis does not require that $ be true at any time in the actual world sl (though it docs not cxcluclc this possibility), but it does require that some initial subintorval of the coming

The English "Imperfective" Progressive 271

I

'

I

I

about of (/, namely, that part of I' up to and including I, is "actualized". It also requires that there be ;1 time in the past in the actual world at which 11th was the case. l t might be feared that this analjsis will he too weak in allotving 111 to hc just ;lii!. possible world esactlv like n7 up through I, since this might seem to allow il morc generous number of progressive sentences to be true of each interiral than our intuitions will allow. Consider, for example, a situation in which John is crossing the street. l'hcrc are no doubt many possible outcomes of such situations, including, say, ones in whidl John is knocked down b? a truck before he reaches the other side of the street. Does thc analysis thercforc rccluire thatJohn is bciizp knocked clon~n41, cr tl.us.t is true automaticall\.whenever John i.s c,ros.~it7,y tErc strret is true? It does not, I believe, if we strict]!. o h s e r ~ c the recluirement that a BEC:OhlE-sentence is true only of the sr~lall~~st intcrvnl ovcr which the appropriate change-of-state takes place (regardless of whether this requirement is to be a truth condition, as in (1 l'), or a felicity condition). 'The progressi1.e truth conditions, in turn, will require that we have a/rc.ad'~ entered this sm;~llcstinterval if the progressive of ;l BLCOME-sentence is true now. In thc case of the e\ent7 (an accomplishment) ofJohn's being linoclted down by a truck, the defining change of statc ~vouldbe, approximately, the transition from John's standing or walking crcct to John's lying 011 the ground (where this change of state is caused by the collision with the truck). Thus the progressive sentence 3011~ is bfi??g knor.krd ( 1 0 1 ~ 1 7 b.11 LI 1r11c.kshoitld 0 1 1 1 ~ be true if this transition has already begun, i.e., if we have alread!. passed the first iuoment at which john's position is displaced by the truck. In a simili11. ~ ~ i a n n eitr should be possible to show that other such "estrancous" progressive sentences will be cxcluded fioin counting as true except in just those situntions where they ought to count as true by our intuitions." For those accon~plishmentsin which the intention of an agent is relevant in detinins the nature of the accomplishment the analj~siswill also be adequate, since iln agent n ~ r ~ s t normallq- have the intention of producing a cel.ti~itlresult when hc begins his action, if' not even earlier than that, and the beginning of the action n ~ u s be t "actuill" under in!analysis. Though this analysis gives u-hat 1 believe is a fairly adequate account of our judgments about sentences in the progressive, further refinements ma- be ncedecl. 'l'hc observation in the p r e ~ i o u sparagraph, for example, leads o11e to consider the rarc case ivherc an agent may be undecided as to just what purposehl activit~hc is engaged in. Suppose John has begun inaking a draw..ingbut has not j-ct decided tvhethcr it is ultimately to be a drawing of a horse or a drawing of a unicorn. Xly anal!-sis aypcars to g are truc sentences predict that both.?ohw is i l r - a r n i ~ ~Irorsr andJo/?n is r i r a ~ ~ ~ i(1l lzrnii-om in this situation, and this seems counterintuitive. (On the other hand, the sentcnce .?o/zn 1s dran7ing e i l / w ~a Irnl-st 0 1 .a tinicon/ is intuitivcl!. true here.) I aln not sure what the linguistic facts are in this case, and thus 1 do not know what will bc the bcst approach to treating it. Perhaps what we need here are meaning postulates for intentional accomplishment verbs requiring that the agent intend from the beginning of thc activity to produce certain results, or perhaps some stronger limitation is neeciccl on which possible worlds may satisfy the truth conditions in (18). It has been suggested LO mc by David Lewis that perhaps [PROCi 4 I should be defined as truc in case q5 will bc true in th.11 possible world sinlilar u, the actual one in which the "natural course of even~s"

272 David R. Dowty obtains. This may indeed be correct, but I presently see no way of making "natural course of evcnts" precise in model-theoretic terms.

4.1 Motivating the progressive analysis independently of accomplishment sentences As I indicated earlier, I believe this modal treatment of the progressive (as opposed to the non-modal analysis) can be motivated from non-accomplishment uses. On the fice of it, this urould not seem to be so. Sentence (19) certainly seems to cntail that the time of John's watching television (which is an irresultativc activity) actually extended at least a few moments beyond the time that Bill entered the room: (19) John was watching television when Bill entered the room. However, I think it is only an "invited inference" (due to conversational rules) that the activitj- continued. To see this, compare (19) with (20) (where Jolln is the antecedent of he): (20) John was watching television when he fcll asleep. (20) clearly does not rccluire us to suppose that the period of John's watching tclcvision extended beyond the time of his fialling asleep, but Bennett and Partcc's analysis of the progressive, like Scott's and Montague's, would require that it did (if n~hrnis given a straightfoswal*d analysis as "at thc time at which"). T h e real entailment that I believe both (19) and (20) share is that it was possible that John's activity continued beyond the time specified by the i~hen-clause.These filcts about (19) and (20) would follow exactly from the truth conditions in (18), hence (20) providcs independent motivation for (18). (I suspect that it is because of convet~sationalprinciples that we take (20) to suggest also the counter-hctual "if John had not fiillen asleep at that particulal. time, he \vould have continued watching television at least a few nionients longer.")

4.2 Inferences from activity sentences in the progressive I have not yet directly discussed the inference from (3) (-7ohn 1 ~ 7 r prl.~hir~g ~s ( I cart) to (4) (John pusheii n (.art). If we follow the first alternative mentioned in connection with activity sentences earlier and treat them semantically as temporally homogeneous, then the entailment from (3) to (4) follows automatically, since my progressive analysis requires of (3) that a least some initial subinterval of thc activity was actual. If howcver we follow the second alternative - that is, if we have only the weakcr rcquirement that if an activity took place at an interval I then it took place at some subinterval of I -. then thc inference from (3) to (4) fails, since tlie only subinterval of I at which the activity took place might be one in the later, "possible" part of I. One way of remedying the situation without making actitities fully homogeneous is to add the requirement (2 1 ):

The English "Imperfective" Progressive 273 (21) If (! is an (atomic) activity sentence, then if 4is true at interval I, thcn there is some non-empty initial subinterval of I at which 4is truc and sonlc non-cmyt? final subinterval of I at which 4 is true. (21) allows for both the case where the activity is completely homogeneous ovcs the interval and the case where initial and final subintervals for the activity are separated by one or more "pauses", thesc initial and final subintervals likewise being either homogeneous or having their own proper subintervals of activity, and so on. (21) admittedly strikes me as somewhat artificial, but it makes the inference from (3) to (4) a logical one. In favor of (21) it can be argued that it is natural to measure the time we spend at activities from the first moment of "actual" activity to the last, ignoring pauses in between. But against this, one coultl claim that it is hardly more truthful to assert that John spent two hours at a certain activity if he began precisely at 9 and ended at 11 and took a five minute break in the middle, than it is to make the same assertion if he began at 9:05 and ended at 1 I but took no break. Thus at thc moment I have no conclusive reason for choosing one of these analyscs of activity sentences over another.

5 Some Problems with "Likeness" of Worlds I return now to the matter of formalizing the notion of identity of possible viral-Ids up to a givcn timo. At first the criterion might seen1 trivial: two worlds should be alike up to a time t if and only if everything truc in the tirst world at any time up to t is truc in tlze second world at the corresponding time. But this is too strong, since we must cxclude propositions about the future or clse we will end up wit11 a criterion ti>r two worlds being alike at all times, not just up to t. How is the appropriate sct of propositions to bc defined? Montague solved this problem in one n-a!- in his "Pragmatics" (hlontaguc 1968, p. 112 in Thornason edition) for a formal language which combincd tenses ivith "temporally dependent necessity". Hc defined first a tcnsecl formal language and its interprctation, then an auxiliarp formal language exactly like the original formal language except that tense operators were omitted, and finally an intcrpretation of the auxiliary language which was to be exactly like the interpretation of the original language ercccpt for the relevant omissions. H possible lvorld 177 was then to be exactly like a \vorld 171 up to a time t "in all features represented b ~ tlie - language" iff the intcrpretation of any expression of the auxiliary language in 127 at a time t' is thc same as tlie interpretation of that expression in r ~ ' at t', for all times r' prcceeding t. (hlontaguc used this clcfinition in giving truth conditions for in such a way that could be read as "it is necessary on tlze basis of the past that 4.") This same method could, in principle, be used in giving the interpretation of the progressive tense for English, but in contrast to the simplc formal language Montaguc used, the auxiliary Litensoless" language corresponding to English would have to excludc not only tenses proper but also quite a number of other basic expressions, e.g., adjectives likc .future and moriburrrl, adverbs such as /omovron>, verbs such as postpone, etc. It could turn out to be a quite complicated matter to decidc just which basic expressions of English depend for their denotation on times fbllowing the time of

"a"

"n$"

274 David R. Dowty valuation and which do not. If our goal is to define a class of possiblc interpretations of English for which the interpretation of non-logical constants is not fully specifiecl, thcn \vc may feel quite uncomhrtable in having to make such a decision for every nonlogical constant. Is therc not another way of formalizing the notion of worlds being alike up to a time that does not require us to refer to a particular Ii~nguageand to its interpretation? Could the appropriate set of "tenseless" propositions perhaps be defined directly in terms of a model? Rescher and Urquhart (197 1, pp. 147, 148) offer a semantic criterion for a "chronologically pure proposition" that might appear to bc adequate h r this purpose. (If I underst-and thcir criterion correctly, it works only if time has il first and a last moment, but I will ignore this point.) This notion, however, does not allow tivo worlds to be alike up to a certain time as long as our theoretical framework takes points of reference (here, world-time pairs) as primitive and defines a proposition as m y set of points of rcfereiice whatsoever. (This is the framework I havc bccn assuming.) C:onsidcr corrcsponding tcinporal segments of any tivo worlds, i.e., a set of' pairs (n,,, I ) fbr all t earlier than a given t; and a second set of pairs (117,~ t ) for all t earlier than that sillne I , . Then there is alwa!s sotlle set containing the one hut not the other. In other words, from thc point of view of our present inodel thcorj- alone, there is no such tliing as two 11:orlds being exactly alike at certain times. T h u s we nlust either define likcncss of worlcls in terms of a particular interpretation of some language, or else takc it ils a new, additional condition specified in giving the definition of a model. That is, the sccond alternative ivould mean taliing a model structure to include not onlv a sct of worlds bt', set of tinles T, and a relation < on T, but also a three-place relation R on pairs of worlds and tirncs; R(n,,,nJ,, t ; ) would assert that I P , is exactly lilic 117, at all tinles up to and including f,.

Perhaps this latter alternative would not sccnl objectio~iablci f one acccpts (as I do) the proposal in Idc\vis' C ' o ~ l r t ~ ~ f i ~ . t r l(Idem-is rils 197.311) that a cornparati\-e oicl.al1 similarity relation anlong possible worlds is to be taken as antecetlently given in the definition of ,I model. 1,ewvis' discussion of deterministic laivs on pp. 75 -76 presupposes that it nukes sense to talk of one woisld being exactly lilic anothcr up to a ccrtiiin timc, and rnoreoi;er that discussion seems to me to suggcst tlli~ta world exactly likc il second world up to a time t \+-ouldbe more similar to the seconcl ~vorld(on 1,cu.i~'account) than would any mrorld mrhicl~diverged Dom the sccond world earlier thiln I . Thus illy desired criterion for likeness of worlds might somehon~be mildc to follo\v horn il similarity assignment, but I do not yct see hoiv to construct t11c apl>rol~riatc definition. (Idenis docs not actually construct "mixed" temporal-modal systems in his book.)

5.1 Semantics of the progressive in branching time There is however an altogethcr tliffcrent ivil!- of approaching the sort of progi.cssivc analysis I am advocating. This is to talie time not as lineal- but rather. as "branching". That is, for an! given time there may be not merely a single future course of time, but multiple possible futures. Rather than alternativc possible worlds, we can now deal with alternative possible futures in stating the conditions for the progressive, and this will t u r i ~out to simplif'y the problem drastically. T h e idea is that (PROG $1 is to be true at I iff here is an interval 1' including I i ~ n dthus cxtcnding into some possible

I I

i

The English "lmperfective" Progressive 275 fiiture(s) of I such that y3 is true at I t . In terms of the usual branching trce diagram for this nlodel of time, [PROG (b] xvould be true at I in the following case:

d~is true

Hcrc it is easy to see how soine initial subinterval of the interval of 4's trutll is automatically "actual", ivhile in the special case where $ is a BECOME-sentence it mily or ma!; not be the case that the result-state will be the case, since thc final bound of' I' may or may not lie in the possible future of I that turns out to be the actual one. In order to formalize the truth conditions of [PROG ( / I ] I \vill rnakc usc of the semantics for branching time proposed by Richmond Thon~asonin Thomason (1970). Thonlason here uscs branching time to construct a theory which cmbodics the "traditionallq. popular" 1-ieu that future contingent statements ("sea battles tomosrow" and the like) may be neither true nor false. He t ~ k e [FUTURE s Ij,] to bc true if (b is true at some time in ever]. possible future and f;~lseif 4) is false at all times in every possible future; if (b is truc in some futures but never in others, thcn [IW'I'URE 41 lacks a truth value. 'The disadvantage of such a treatmen1 is that certain formulas, such as [ F U T U R E 4 v F U T U R E 1 7 4 1 , which are valid for linear time (and rightl!. so, according to o u r intuitions) arc invalid in thc usual formulation of branching tcnse logic. Thomason avoids this consequence bq- employing van Fraasscn's iclca of a supervaluation. the suycl.\-aluation method as applicd to tense logic, the definition of truth at a morncilt of time is given through the interll~cdiatcnotion of truth a t a time relative to a possible historj- containing- that time (a "linear pathway" through the time structure, on which pathway that time is located). T h e definition of possiblc history is as follotvs: Assume, as before, that I ' i s the set of times, but < is not a total lincar ordering of T as before, but merely a transitive rclation on T which is "treclike", having the property of "back\vards 1inearit~-"(i.e., for all 1 1 , 1 7 , t3 E T), then if tl < t j and tz < I:,, then cither t , < tr or 12 < 11 or 11 = tz.) A hisior:y (or ina.t.imcll c.lraii~)on T is a subsct h of 7' such that (1) for all tl, tl ~ h if ,ti # 12 then 11 < tr or 11 < rl, and (2) if g is any subsct of T such that for all / , , I * ~ g if, tl # t:, thcn 1 1 < rz or tz < r , , then g = h if h Cg. t is a membcr of T, let Ijl denote the set of lzistories containing I. No\\. we define thc truth value of il for~nula4)at the timc t rclativc to a histor! h containing t (denoted 17j'(())) as follows for thc case of the future tense: (22)

V:(FUTURL 4) = truc if ~ ; ( 4 )= true for some t' E h such that t V:(FUTURE 0 ) = fi~lseotherwise.

< 1'.

T h c past tense is defined similarly, and the truth values for non-tensed fbr~nulasarc the same as in classical logic. Note that the valuation at a t i ~ n crelative to a history is always bivalent.

276 David R. Dowty T h e actual definition of truth relative to a time (denoted V,(q!!)) is now as follows: (23)

V,(4) = true iff v:(+)

H,. iff vF(q5)= False for all 11 E H,. = true for all h E

V,(g) = V,(g) is undefined otherwise.

Thoinason shows that the definition of validity that emerges from these definitions is the same as the definition of validity for linear time, but on the other hand, that this system can distinguish between what was truly going- to be the casc and what was ine\ritably going to be the case. See Tl~omason(1970) for further discussion. In order to accommodate my analyses for accomplishinents and progressives only a few small changes are needed in Thomason's systcm. First, we must redefine an interval for branching- time:

(24) '4n interval 1 is a subset of Tsuch that (1) J is a proper subset of some history 1 in T, and (2) for all t l , t ~i 3 , E h, if t l , i 3 E I and 11 < 12 < 1 3 , then t E I. All of Thoinason's truth definitions can no.cIr be reconstructed relative to intel.vals, rather than moments, and to possihlc histories. T h e truth conditions for \BECOME $1 are the same as before cxcept for being rclativized to a history. T h e truth conditions for [PROG 41 relatiye to an interval and to a history can now be stated very simply:

(25) V! (PROG cb)

= true iff, for some g E = true.

HI, there is an interval I' C g such that I

c 1' and V:,(qb)

(It is the introduction of the second history I$ in this definition which makes [PROG $1 depend only on the truth of in some possible history containing I , even though the definition of' truth is ultimately stated in terms of (ill possible histories.) Tl~ougha branching time structure certainly appears to be a simpler and more elegant framework for ni!; progressive analqsis than a world-time iildex system with thc "likeness" relation R addcd, it would probably be a mistake to place too much e~nphiisis on the advantages of the former system, bccause the following problem will crop up sooner or later. Notice that in the branching time model structure as g-i\-en, instants u-hich lic on different "branches" arc not temporally ordered wit11 rcspcct to each other. Thus if wc arere to attempt to make possible histories do the same work as possiblc worlds, we would run into difficulties in treating certain inodal and counterfactual statenleilts such ~ i arvieled as I [ / n7cre in New York rlgkt rzorv, I nloulrl [lo .suc.lr- nil-sui.11, or Jolrrr ~ n i g l l~nzlc~ or1 Thrd~-sdi~,y, hut l?e also rni'ht arrive tovtlorro,a. Such statements seem to require that we be able to determine whether an instant in some possiblc history comes before, after, or at the same time as an instant in another possible history which has already "split away" from the first. Thomason, in fact, encounters just this problem in an unpublished paper "Deontic I,ogic as Founded on Tense lJogic", where he applies branching time in analyzing- certain problems in deontic logic involving "conditional oblig~tion".

!

I

The English "Imperfective" Progressive 277 His solution appears in the following quote (p. 13), where he is considering a variety of alternative LLsccnarios"that stretch ahead of some past instant and thus represent counterfactual alternatives to the situation he now finds hiinself in: Along each of these scenarios, then, I choose a particular inst;unt to serve as an alternative for the one in which I unhappily tind myself: The most natural way of' doing this in our example is to use the metric properties of time and take instants along the othw scenarios in which clocks show the same time they do at the instant in which I find

mj self. Of course the effect of Thomason's clock, which will run at the same ratc in each possible future, is to partition thc entire set of moments of tinle in the branching structure into equivalence classes, each of which contains the moments of various possible histories that are co-temporal from a "mcta-historical" point of view. Since these ecluivalence classes will, in effect, be ordered with respect to one another, by adding thc "clock" we have actually in~poseda linear timc structure upon the branching time structure. T h e branching time structure expanded to iilclude the clock is now exactly equivalent to the bvorld-time index structure expanded to include the likeness relation R in the "information" ropresented by the model. For each time in the branching structure (respectively, for each index ( m , t ) in the morld-time structure) we know (1) what the future and past of a time is relati\-e to n given history including it (respectively, we knou the past and futurc of an index ( n ~I), relative to its possible ~ ~ o r w), l d (2) we know which times in other histories are earlier than, later than, or the saint as that tiinc by means of the clock (respectively, we know this information ahout an index from its time coordinate), and (3) we knou- the various possiblc fiitures of a time because R'C know which possible histories contain it (respectively, we know thc various possible futures of each index (a,, t ) by looking at the futures of ; ~ l lother wol-Ids \vhich are like r~ up to t according to R). It is ;i straightforward exercise in ten~poral model theory to reconstruct equivalent definitions of the tense operators proposed in Thomason's systeix (including the supervaluations and future contingencies) rclati\e to an index system with likeness relation, or to reconstruct equivalent truth conditions for the tense and modal operators in Montague (1973) relative to a branching time model with clock. ( T h e two systenls would of course cease to be ecluivalci~tif we substractcd either the clock from tho branching structure or the likeness relation R fi-om the world-time coordinate structure.) Despite this equivalencc, there may nevertheless be significant conceptual advantages in studying linguistic problems such as the progressivc, the seinaiztics of various modals, or "conditional obligation" with a branching timc structure.

6 Extending the Analysis to the "Futurate Progressive" T h e present progressive tense of English, in addition to its use in describing an action currently in progress, can be used as a special kind of' futurc tense, as in (26): (26) John is leal ing town tomorrow,

278 David R. Dowty For (26) to be true it is apparently not required that we have already entered the smallcst interval of time of \vl~iehit may later bc true that Johr~ keazlc~stown, so the analysis proposed so car ~ s ~ inot l l accommodate it. How-c~-cr,there may appear to be a certain intuitive but 1.ag-uc connection betulccn thc imperfective progressive and the so-called "futuratc progressive" of (26). Consider a ~.ii.i./tmil!: be truly uttered first that an imperkctive sentence such as John is 111'[111ling on ccrtain occasions u hen no portion of a circle exists yet on paper, hut when John is illcrelv obscrvcd to be malccs anlong (29a-f), argues that the notion of p l ~ i ~ ~ ~ cl-ucially in,g distinguishes the tenseless fi~tureand futurate progrcssi~efrom the rcgulal- futurc (and not Jncrc certaintj-, as 1,akoff had claimed.) (29)

(a) Ton~orrow,the Yankccs will play the Red Soclts. v , Yankees play the Red Socks. (b) T o n ~ o r r o ~ the ( c ) Tonlorrow, the Yailltees are playing the Red Socks. (d) Tomorrow, the Yankees will play well. (e) ?'I'on~orrow,the Yankees play well. (f) ?Tomorroiv, the Yankees are playing well.

The English "Imperfective" Progressive 279 (29e-f) are quite odd, except in the unlikely event that the speaker knows that thc game has been rigged. T h e subject of the sentence necd not bc the agcnt kvho does the planning, as can be observed in (30). Note that the event in (30) is naturally understood as planned, thoi~ghno agent is immediately involved, whereas the event in (31) cannot be naturally construed as planned or scheduled: (30) (a) (b) (c) (31) (a) (h) (c)

T h e bomb will go off at 2 PM. T h e bomb goes off at 2 PM, T h e bomb is going ofT at 2 Phi. T h e telephone in my officc will (uncloubtedly) ring tomorsou-. ? T h e telephone in my office (undoubtedly) rings tomorrow. ?'The telephone in my office is (undoubteclly) ringing tomorrow.

Goodman (1973) observes that the notion of "planning" is not quite general enough, but should be replaced by a notion something like "predetermined on the basis of past cvcnts" because of'exal~lpleslike The sun sr/s /omorrom at 6:.77, in which planning by a human agent cannot be involved. (Scc Goodman (1973) for discussions of t\vo hlrther selnantic entailments of the tenselcss future which I will not mention hcrc nor attempt to incorporate in my analysis, though they in fact present no problem for it.) Though Vettcr had assumed that the futurate progressive had the same semantic properties as the tenseless future, Princc notes that this is not so. T h e tcnselcss iuturc implies a greater degree of certainty than the futurate pi-ogressi\~e,as can be seen ti-oln the contrast in acceptability between (33.3) and (33b), despite the Gct that hoth sentences in (32) are acceptable. (Examples are taken from Prince (1973), whcrc they arc attributed to Jcff Kaplan.) (32) (a) T h e Kosenbergs die tomorrow;. (b) T h e Kosenbergs arc dying tomorrokv. (33) (a) "The Kosenbergs die tomorrow, although thc President ma! grant them i1 l-xtl-don. (b) T h e Rosenbcrgs are d ~ - i n gtomorrow, although the Presicleilt may grant thcm a pardon. Consider also the contrast between (34) and (35):

(34) (a) I am leaving next Thursday at 4:30 PNI. (b) I am tentatively leaving next Thursday at 4:30 Phf. (35) (a) I l a v e next Thul-sday at 4:30 P-M. (b) ?"I tentatively leave next T l ~ u r s d aat~ 4:30 Ph1. ('I'l~oughPrince marks (393) with "7%" . , I think (35b) is in fact acceptable, but only in a situation where a plan or schedule of some sort has been arranged. What is tentative is whether the plan 1%ill be carried out or changed. With (34b), the speaker's leaving need not depend 011 any arrangements which have a l r e a d ~been ~ madc. Iiis departure may dcpend only upon his making up his mind when to go.)

280 David R. Dowty Lauri Karttuncn has suggestcd (personal communication) that the futuratc progrcssive might be handled by the strmt? tense operator as the imperfective progrcssivc if an analysis such as mine were n~odiliedto allow I PROG $1 to be true at an interval I if and only if 4 is truc at some interval I' which includes I or else is l u r ~ rthan I (in some ayyropriatc possible history containing I). However, this move would not allow us to account for the semantic differences between the imperfectivc progressive and the futurate progressive that Prince observcs. These differences can be clcarly seen in (36), which, as Princc points out, is ambiguous betwecn an imperfectivc progrcssivc reading and a futurate progressivc reading:

(36) Lee was going to Radcliffe until she was acccpted by I'arsons. T h e imperfective reading, which Prince paraphrases as "Lee's going to Radcliffe was in progress until she %-asacccpted by Parsons", entails that 1,cc did go to Radcliffe (since go to KndclzfI2 in the sense of ultenll Rarlclifi, the only scnse relevant hcrc - is naturally interpreted as an activity). T h e futi~ratcprogressivc reading, paraphrased as "Lee's going to Radcliffe (at some future date) was thc plan until she was acccpted 134' Parsons", does not have that same entailment, but on the contrary, conversationally implicates that Lee did not go to Radcliffk. Oiie should bear in mind that the futuntc progressive consistently involves the notion of' plan or prcdetcnnination, though the imperfective progressivc does not. Compare, for example, (3 1 c) with Thp rrl~~phrnnc in m)~ O [ / ~ C E zs ~ i ~ q i (l ~~u g ID). 1 wish to suggest that if we give the tenscless futurc the semantic analysis suggested by Prince, Vettcr and Goodman, the facts about thc futurate progrcssivc will follow automatically from the analysis of the "irnpcrfective" progressive I havc already proposed. -411 we need to do is treat the "futuratc progrcssivc" as an impcrfkctivc progrcssivc operator combined in a purelv conlpositional way with a sentence in thc tenseless future. This will enable us to treat "futurate progressives" cvithout ilny syntactic and semantic rules except thosc needed independently for other kinds of scntences. Henceforth, I will not attempt t o give rigorous modcl-thcorctic dcfinitions but rather indicate truth conditions informally. T o avoid having to develop thc sj~ntaxand semantics for a full range of time adverbials, I will simply illustrate the semantic rule for the tenseless future b j a truth condition for a sentence with future tilnc adverbial -

'

tonZf)TrO 127:

(37) [/orno~rujn$1 is true at I iff ( 1 ) (I! is true (in all histories containing I ) at some interval I' such that I' is includcd within the day following the day that i~~cludes I, and (2) the truth of C1, at I' is planned or pre-determined by facts or evcnts truc at some time I I."

<

T h e vague notion in this definition is of course "planned or predetermined bj- facts or events", and at present I have no idea how to make this notion more precise in modcltheorctic terms. Nonethcless, the interaction of (37) with rnv more cxact analysis of thc irnpcrfective progressivc should be sufticieiltly clear for present purposes.

The English "lrnperfective" Progressive 281 Schematically, 1 tontorro~~~ 411 will be true at I in the following situation:

I

time of plan or p-edetermination I

1

I I I

-

r

I

t

1 I I I I I I

1

I

I

day 0

I

A futurate progressive will thus have the logical form [PROCi[lorvrorrow~(/)I], and such a sentence would be true at an interval I0 according to (25) if thcre is an interval 1, 3 losuch that [tornorrolj? (I'l is true at I I in solnc history contiairling 10.And by (37), Itorvrorror~41 would thcn be true at I , if 4 is truc at a futurc interval f2 in all histories containing I , , and 4 is planned or predetermined at somc time at or preceding the lower bound of 1,.Such a situation would be rcprcsented as follo\vs: time of plan or predetermination

I

day 0

I

I

I1

I I

I

I I I

+

truc

day 1

Note that 4 will not have to he true in all futures containing 10, but only in all futurcs containing I,. This will account for Prince's observation that the futurate progressive is L less ccrtain" than the tenselcss futurc, and it will also distinguish the futurate progressive from the "regular" progressive, since thc planning or predetermination of 4 must have actually occurred with the futurate progressive. If a straightforward analysis of the regular future is given (such as Thomason's analysis, mentioned earlier), then we can distinguish among the threc English futures neatly and, according to the literature, accuratcly: The regular future will imply (a greater or lesser degree of) certainty but not planning; the tenseless futurc will imply both plannillg and certainty; and the futurate progressive will inlply planning but not certaintj-. (I here ignore the important problem of whethcr "certainty" should be associated with epistemic necessity or logical necessity or perhaps some othcr notion, and the problem of just what degree of certainty is required h r regular future and tenselcss future.) 6

282 David R. Dowty Of course, futurate progressives do not always have an cxplicit future time adverbial: recall that sentences likc (36) or John i.~ Ieavi?zg ronw have futurate as well as regular progressive intcryrctations. It is thus of interest to inquire whcthcr there are also sentences which are intcrprcted semantically as "tenseless futurcs" but havc no explicit future time adverb (i.e., sentences having present tense and no time adverb which are interpreted as describing a future event planned or predetermined by past events). For if such sentences exist, then the analysis of the futurate progressive that I havc proposed already predicts that sentences such asJolzn i.s Ieazliug toran can bc interpreted as futurate progressivcs, since it should be possible to dcrive a futurate progressive sentence from any tenseless future scntence whatsoever, includi~lga teizseless fi~turc with no adverb. And in fact, tenselcss futures with no explicit advcrb can be found, though thcy may not be too common. Consider the dialog in (38): (38)

A: Which of the contestants do you suppose you will ultinzately selcct as the winner? B: Oh, number five wins the competition. 'Iis perforinancc was unclucstionably bettcr than the others.

Notice how the tenseless future of H's response (as opposed to He r~illn1i11 he conzpetition or fi ix minning [he r.orrzpetitiorr) suggests that the outcome of the nzattcr has already been determined and does not really depcnd on any activc deliberation by the judge or judges. I also think that a special use of past tcnsc sentences ~11ichwas obscrvcd by Charles Fillmore (in his unpublished "L,ectures on Dcixis") and which might bc called the restaurant-order past tcnsc" also involves a tcnsclcss future without any cxplicit future adverbial, the difference being that thc scntcnce is here further e~zlbeddcdin a past tense operator. Such a sentence would be (39), u-hen addrcsscd to il waitress contemplating a table full of customers and a tray full of orders, trying to tigurc out which ordcr gocs with which customer: CC

(39) I had the checscburger with onions. In contrast to the normal use of (39), this spccial ilsc does not entail that the speaker has ever bee11 in possession of thc cheeseburger in question, but rather conversationally implicates that he has not yct acquired it. If (39) is analyzccl as thc past of a tcnsclcss future (with an indefinite future tiilzc adverbial that is not pho~zologicallyrealizcd but scmaiztically plays the same role as tonrorron) in (37) ), then (39) mrould be intcrprctcd as entailing- that at some time in the past (namely, after tlzc custonicr had placed his ordcr with the waitress) it was planned or predetermined that at some indefinite fut-111-etiilzc the scntence I ha114 t11e ~*heesrhuvger rvith onio~ls\'oulcl bc true. 'This scenls to me to be a correct account of this special use of (39). T h u s there seems to be no objection to treating futuratc progressives - . with or without future adverbials - as "in~pcrfcctivc" progressives of tensclcss futures. We can now account for the curious cornhination of past and future advcrbials that Princc observes in some of these sentences. T h e e-uarnple from the titlc of Prince's papcr ("Yesterday morning I was leaving tomorro\t7 on thc Midnight Special") would have

The English "Imperfective" Progressive 283 the logical form (40), where a tenseless future is crnbedded in a progressive cmbeddcd in a past: Ly~7stm morwirrgl' l~ [PROCi [ton~urron~[I/r.ir~ron i bc MNInigl11 Spr(HI) [PAST iliflfl]]]

Finally, we can associate Prince's ambiguous example (36) with the two logical forms (41) and (42). T h c imperfective reading is (41), and the futuratc reading is (42), in which "indef. fut." is the phonologically unrealized future time adverbial corresponding to tomor~on?ill (37): (4 1 ) (12)

[PAST -I- until shc was . . . [PROG[Lee go to Rndc/?[Ti-l J] [PAST zlnlif she lnas . . . [PROGl (indef. fut.) [Lee go to Raricliffi~] (I]

+

I leave it to the reader to confirm that ( 2 5 ) and (37) when applied to (41) and (42) do account for Prince's observations.

Appendix This appendix gives rulcs (stinted as cutensions of the PlXLgran~mar)fix gcncrating and transhlting the type of scntence mentioned in Section 3.1 and f i relatctl ~ sentcllccs \tit11 transiti\,c vcrhs. 'The rulcs lor the latter scnrenccs presuppose to some extent the discussion of' causativcs and ~ r ~ ~ n s i t i ~ e verbs in Dowt!. (1976). In addition to ( I ) , M.C havc sentences (2) ;und (3): ( 1 ) John walked fi-on1 Boston to Detroit. (2) John walked to Detroit. (3) J o l ~ nwalked from Boston. Syntactically, it is thus best to treat ~11cphr3scs to Detroit and Con1 lJoston as indcpcnclcnt modiliers, both of category PI \ \ . Semantically, hohl-etcr, (2) ancl (.3) are "elliptical", (hilt is, (2) implies an ~lnlnentionedpoint of clepartul-c and (3) implies ;In unrncn~ioncddestination. T l ~ c s et\vo observations suggest the follu~ving:1,cc to, from E BI,,\rl.. Lct their translations hc:

to lranslalcs into:

iL.3iPix3{ f[P {x } \. Vz HECOhlI1:[natl',('s, "x)1 :, Bb~COhI1~[atfl,("x, ' y ) j] } from translates into:

In these translations, atrf"is ro bc the constan1 of type (c, (e, t)) which "corrcsponds" to l
284 David R. Dowty

(On the question of whether the connective "CAUSE" should appear in place oT the conncc~ivc" n " in the above, cf. footnote 12 of Dowty (1976), but note the problem bclo\v.) T h c corresponding transitive causative sentences lihenisc exhibit all thrcc li)rms: (4) John drove a c a r f r o m Boston t o Detroit. ( 5 ) John drove a car t o Detroit. (6) John drove a c a r f r o m Boston. In these sentences, I believe the prepositional phrases must be treated as TV-niodilicrs, not as 11'modifiers (lor reasons discussed in detail in Dowty (1976)). Momever, if we attempt to treat both these prepositional phrases as members of PTv/.I?- and capture the causative rc1;ttionship bctjvecn activity and result slate at the same time, ~c will arrive at a girblcd translation for (4), roughlj (7): (7) MVx[carl(x) A [drivel,(j, 'x)CAUSE BECOME I.natf',('x, b) I]CAUSI' 13KCOhfl<;atu,(-x, cl) 1 ) I An alterilative urhich avoids this problem is to treat the phrase f r o m B o s t o t ~as moclif'ying the phrasc t o Detroit. Thar is, the verb phrase in (4) W O L I I ~be built up as in (8):

drive a c a r f r o m Boston t o Detroit. IV

f-1 car, '1'

drive f r o m Boston t o Detroit, 'l'Y

il

f r o m ~ o s t k nt o Detroit. 'l'V/'I'17 drive. '1-V f r o m Boston, (T\r/TV)/(TV/T\')

t o Detroit, T\/'/'I'V

from, ((TV/TV)/(TV/TV))/T Boston to, (I'V/'fV)/T Detroit, T Titking 3 and 4 as variables of type (s,f(T)), 5 as a variable of type (s, q T V ) ), and 6 as il variablc of type(s, f(TV/T\:)), the rans slat ions for thc t i o m and t o which occur here arc as follo~rs: t o (E B[,rLj.~.\ );.I.)translates into: ?,3iSi.4~.~.3(f4{i ['5 (P ~ { z }(x) ) CAUSEIVvl HE:C:OMI[,latll,('z, 'XI )1 BECOhlK[at",('z, '!-)]]]}} f r o m (E B(rr.1 /~I.\')/(T\:,,Ti~) )IT) translates into: 3.3iv6;,jA43,x3{ f4{2 ['G (5) (P P{z))(x) r ["S(PP(Z})(X)C;~~USI; HI;C:OME [natl',('z,

'?)I 11))

Despite thcse rather complicated translations, (4) and (5) will havc translations equivalent to (4') vld (5') respectivel!. As bcforc, vacuous parts ha\-e been deletcd from (4'):

The English "Imperfective" Progressive 285 b)] ( 4 I IVx[cart(x)n 1-drivcl,(jl "x) CAUSE B13COME[~at1t~('xl \I I drivel,(j, "2;) CAUSE BECOME(natU,(-x, b)] \: [drivet,(j, 'x) CAUSE BECOME[at",('x, d)] J]]I HVx[cart(x) n ] drivet,(;, -x) C-%USE Vy BECOME[nat"('x, 'y))] (5') n [drivel*(j, -x) CAUSE BECOME[atl',('x, d)]]]

Of course, sentence (6) could not be generated directly in this analysis, but m+ouldhave to be PI-oduced by a deletion transfornma~ionfrom some longer sentence. Indeed, (6) sounds distinctly n ~ o r eelliptical to my ear than (j),as (3) sounds more elliptical than (2); it is for this reason that 1 chose to set up tlic ,/ion/-phrase as the ad-modifier rather than the to-phrase. But it may be that the only significance of this judgment is that it is more common in conversation to assun~c~11caddressee's hnowledge of the origin than of the destination. Note illso that (6) sounds no more elliptical than (3).

Notes In M-ritingthis papcr I havc bcnefrttcil greatly from discussions with Stanlc! Peters, 1l);tvid l,cwis, Lkluri Karttunen, Michael Bennett and Richmond Thomason. None of these people will agrcc w i ~ h everything I havc to say in this paper, and I alone am responsible for errors remaining in it. Work on this papcr was supported in part by grants from the American C:c)uncil of 1,carnccl Societies ;~ndthe Institute for ,%dvanced Study. 1 Though Hoepelman concerns himself only with \-crb aspect in liussian and not will1 tcnscs in English, the basic semantic problems he Gees arc quite simili~rt o those I ;1n1concerned with. Our analyses agree in regarding tlic notion of a change of state as essential, hut his ;ipprollch to lcnsc operators is entirely axiomatic, not model-theoretic. My main objection to his treatment ol' the proble~iiof inipcrfcctivc aspect is that is that i t tlcpcnds cruciall> on Timoth!. Putts's operator "1)" (lLiscoming to he"). T h e xiom oms cited for this operator by 1-Iocpclnian d o not in thcmscl~ca account for n hat 1 call ~ h "impcrfcctive c paradox," and in yic\\- of the lack of an! rnoclel-thcorctic interpretation for this operator, its usefulness, if any, for the analysis of verb aspcct remains obscure to me. o~~t 2 Though I havc used the term "progressive ~rnse" rather than "progressive rrspti.~"t h r o ~ ~ g h this papcr, I do not thereby wish to deny that in terms of the linguist's traditional sc~nanticrlistinction between liJrlse and tispur the English progressi~cis more clearly a cast. of aspect than tense. 'l'hc tcrniinolog!- in the literature on the English progressive is of course inconsistent; those who h a ~ c approached the problem from the point of' view of tense logic - as 1 do here - havc tended to use the term "progressive (or continuous) tense". :4s I mentioned in foottlotc 1, I suspecl that the problem of' giving a sclnantic analysis of tlic inipcrkctivc aspect of verbs in the slavic languages is essentially the same as that cvitlcnccd in tlle English sentences I discuss in tl~ispalm. I-Iowctcr, semantic as well as syntactic details of the analyses bill no doubt clil'fer for English and tlicsc liinguagcs. .3 Rescl~crand Urquhart claim that actil-itics can he f'urthcr subdivided into 17on10~yr11rorrsacti~itics those that must go on literally e \ a y moment of the intcrval one spends at them, mr/jol-//r~/ii~i~ actit-itics those that go on at nos^ tinlcs in the interval, and oi.r.osionrrlactivities those that go on at only some times during the interval. Ho\ve\rcr, I find their suhclassiii~~ition quite dubious, since I can im;lginc situations \nherc the examples tllcy gi\-e in cach category could belong in the other catcgorics. In particular, I doubt that thcrc arc an!. necessarily homogeneous activities. I u.ln -

286 David R. Dowty certsinly i~nagincsituations \!here bo~hiiigo ~ t e s e i / ~ o r , / ? )a~ i/)l/rrr~ ~ t g or ~ . I L / I I I !:I~ I I O ~ S C(Rcsclicr's and Urq~lhart'scxa~iiplesof I i ~ m o g e ~ i e oiicti\~ities) ~~s need not be homogenco~~s. 4 4lthough I have draun this di;igram such that thc intel.val I is a closccl interval, thc. dclinition ill (1 1 ) would equally apply to the case where I is hounded, rather t1i:ui closed, :it its upper or loner end, or both (i.e., lacks a first and a last moment). I know of no linguistic reasons Ibr distinpuisliing bouncied from closctl intcrvills in such cases. If tinic were discrete rather r1i;ln dcnsc, all intervals would of course be closed. 5 For cxamplc, most i l not all natural languages have proccsscs of \vord fi)rmation cvliich derive change-of-state verbs from stativc ~ c r b sor adjcctives. (English has, among othcr such processes, the suffix-r111which forms (inrkrn from drrk, s7irlc.n from r~liiic,etc.) slnd PI-acticall?all Ii~nguagcs have a common verb (such as English herome or ~ e t uliich j combines syntacticiilly uitli srntivc verbs, adjectives or participles to form change-of-state verb plirnses. 'l'lic one-place operator "BllCOME" captures thc semantics of S L I C ~~ ~ e r band s dcriviltionnl ilflixcs in ;t tlircct \ l a j - . klo\+cver, 1 know of no process of word Sorn~~tion which combines /njo stativc roots X and I' to form a word meaning i l z a ~ t g,/i,onr ~ D e i ~ ~Xg to h~in,qY. Though tlicrc arc certain "two-place" cliangc-of-state vcrh phr;lscs such as l
The English "Imperfective" Progressive 287 perfectly prcdic~ablccon~binationof a future tcnsc (with future time atlscrb) and a scntcncc in the (in~pcrftctivc)progressite, i.c. [FUTURE ftor~rorron,[PROC; IJoi~n /i~uz~c]J. (See footnotc 12 for explanation of the "+" here.) 10 Since I fear it may be objected that Prince's trample could in\.olvc merely a lexical ambiguity in go to Rar/r,/t(ji,1 \vill supply an ambiguous cxample of niy own which does not have this problem: (i) Rob was working on the research project until he got the job offcr lioln U. of hI. T h c fururatc progressive reading, ~vhichconversationally impliciitcs that Rob cvill not ant1 puhaps never clid work on the project, would be a na~uralreply to the qucstion "I4 hat is Rob planning to tio next Fall?" T h c itnperfective progressive reading, which entails that he did ctork on the project ancl in~plicatesthat he no longer does, would be an answcr to the question "What has Koh been doing for the past >ear?" I 1 It is natural to ask whether part of this condition should be relegated to c o ~ l ~ e n t i o nin~plic;lturc. i~l X scntcnce like Ir :r possi1)le lh~rtJohn leaz~estc~rnol-l~o~~~ does seem to n ~ cto commit the speaker to the view that the question whether john will leave and whcn is subject to soine already arranged plan or scliedulc. I Iorrcver, it doesn't implicate that John detinitclj- n ~ i / Icate / (at somc t i n ~ cor other), since the plan might require that John not leave at all. Note that it will not do to test for imp1ic;iture with an i/~clausehere, since rvill is routinely absent from i/Lclauscs inuolving future time; llencc what I am calling the tenseless future construction cannot be syntactically tlistinguished in an !fljlclilusc from a statement about future time that neither entails nor implicates anything at all about plmning-. Strangely, the use of n7ill in an ~flclauscsccrns to be rcstrictcd to the "willing-to" scnsc of lnili: c t . vJo11n mzcts Rill at llri>pi7r-(1)~c/trrol.t.o~~ .. . vs. I/:J'olllr a~illrtriliJ/ Bill a t the przr'[)i Ionrorror)7. . . and also *I/'tl?e tel~pphoncwill rirrg ~orr~orro~r~. .. . 12 The "+" in the formula (#I) is nieant to informally indicate that this "norn~ill" combinalion of time advwl-, and tense (i.c., past tense with past adverb and future tcnsc vith future ;icl\crb, but not the h t u r e aclverh of thc tenseless future nor the "internal" ad\erbs of 1I)onty 1076) is not compositional in nieaning bur sync~tcgorcn~atic. 'That is, the tense ancl tinlc ;ldvcrb arc not independent sentence operators semantically, one within the scope of the other, but ratlicr the tense is redundant. For csamplc, Jo/~n I ~ / i , ~ ~ e . ~ is r nnot . ~ lrealized ~ j ~ ~ ~ semantic all^ as ( r o ~ ~ g h lL'It y) was true at some timc I in the past rhat John left on the da!. beforc 1" nor as "It c\;ls true ycstcrda!. that John left at sotnc tinic beforc that," for both thcse parnphrases inconectl! represent the meaning of the example. It is more correct to sa! that Johrr Ilfi ,jt~>s/c~ri/i!y entails that "At some timc r on the day preceding the time of utterance it \+as true that John left" and, rcdundantlj, that "At some indciinitc time 1 eiirlier than the time of utterance it was true that John left." In a generative seman~icstheory these "normal" tenses should probably not be represented in Logical Deep Structure but (as has freclucntly bcen suggcstcd) be introduced b!. a transfimnation sensitive to the kind of time adverbial present. In a Rlontnguc grammar, tcnsc and time adverb should prohabl? be introduced simultaneously by a sjntactic rulc. Ungran~~natical combinations such as *.IJllhrl inill Ii~u7~e~1rster-r1(1,)1 and thc ungammatical reading of (*)JoIln IL:/~ /oir~on.on)would be ~cneratedbut could bc given a contradictory intclp-ct;~tion. ('I'his last sentence, as has bcen pointed out in the liter-aturc, also has a g~.arnn~atical reading, hut this is of course the past of a tenscless future and implies a plan.)

References Rcnnctt, Michael, R. 1074. Some Extensions of a Montague Fragn~entof'1:nglish. Ph.1). dissertation, UCJ,A. Distributed by Indiana Universitj. I,inguistics Club. Benncrt, Michael K. and Barbara Partec. 1978. Tol~ardthe Log~r.qf' Ti~nseaud ..lspc~.tit/ Kt~glisll. Bloomington, IN: Indiana University Linguistics Club.

288 David R. Dowty Dowty, David. 1972. Studies in the Logic of Verb Aspect and Time Rcfercnce in English. 1'11.T_). dissertation, University of Texas, Austin. Dowty, Ilavid. 1976. Montague grammar and lexical decomposition of causative vwbs. In Barbara Partcc (ed.), Montcrgrte G m m n ~ a rNew . York: Academic Press. Goodman, Fred. 1973. On thc Sen~anticsof Futurate Sentences. Ohio State University Working Papers in Linguistics, no. 16. Hocpelman, J. Ph. 1974. Tcnse logic and the scnlantirs of the Russian aspects. 7%ture/~culJ,znau~.r/jr:r l(1): 158-80. Lakoff, Georgc. 1970. Linguistics and natural logic. S'IZIIIPSL~ 22: 151-271. Lewis. David. 1973a. Causation. Journal of'Philosop/~,y80: 557-67. Lewis, Dabid. 197%. Courr~erfuc-lua/s.Cambridge, Mass.: Harvard University Press. Rilontague, Richard. 1960. On the nature of' certain philosophical entitics. The Monirt 53: 159-04. Repr. in Montague 1974. Montague, Richard. 1968. Pragmatics. In Raymond Klibansky (ed.), (,'or~rt~?t~por~~ril Philt,lr,sopJ~)l:.A S z t r ~ e y Florence: , La nuova Italia. Rcpr. in Montague 1971. Montaguc, Richard. 1970. Pragmatics and inteilsional logic. Synlhase 22: h8-94. Repr. in Montaguc 1974. Montague, Richard. 1973. The proper treatment of quantification in ordinary 1;nglish. In K. J. J. Hintikka, J. M. E. Moravcsik, and P. Suppes (eds), -4pprrnacl7es to IV(r~urillLun,yuapc: ProieeJl'3tg.t (!/' the 1970 .Slatz/urd kl/orl?.rhopon Grummrar and Sernanlir:~,Dordrecht: D. Rcidel. Repr. in Montag~ic 1974, 247-70. hlontaguc, Richard. 1974. Formal Philosoplq~.Selecl~ilP n p c ~ ~:v!/'Richarrd s hlnrrti~~rre, edited and viith an introduction by Richmond H. Thomason. New Haven, Conn.: Yale Univct.sity Press. Prince, Illen. 1973. Futurate Be -irrp, or Why Yestrrdg)~nrorninp, I illas /(~i/i;i?~g ~nrt~orrtra~ otr ~ h p Ililid~7iglriSpeeiirl is OK, unpublished paper, read a t the 1973 Summer Meeting of the Linguistic Society of America. Rescher, Nicholas and Alisdair Urquhart. 1971. Te~rtponrlLogic. New York: Springer-Vcrlag. Rylc, Gilbert. 194'9. Thp C'oncrpl qf'MinJ. New York: Barnes and Noble. Scott, Dana. 1970. Advice on modal logic. In K. Lamhert (ed.), Phrlosophical ProPl~~nrs in I,ogi~, Dordrecht: D. Reidel. Tedcschi, Philip J. 1973. Some suggestions for a semantic anal!.sis of progrcssivcs. li~l/zur-s~/)i I,J' 12.1ichigrrn P a p ~ r sin I,inpuisiics l(2): 157-68. Thomason, Richmond. 1970. Indeterministic time and truth value gaps. Theoria 18(3): 261-81. Thomason. Richmond. 1974. Deontic Logic as Founded on Tense I.ogjc, unpublished paper, presented at the Temple University Conference on Devianl Semantics, December. Vendler, Zcno. 1967. Verbs and times. In Li?zgui.stil.s in Philosoph.jl, Ithaca, N.Y.: Corncll University Press. Vettcr, David. 1973. Someone solves this problcin tomorrow.. Li?zguislil Iirqrriry 4(1): 104-8. von Wright, G . M. 1968. An essay in rlco~~tic logic and the general theory of action. .lll.ra Phi/osoph~'ca Ft'rinj~.~ 1 8.

The Notional Category of Modality Angelika Kratzer

I t I P O U / ~be considered rrni.11~to&)! lo uttelrrpt, ns did Wegener (IcYNS), to c/esc.vibc tht serlziotic. strat&-ntion oj'human language with examples vestricted to Gtr.m(ir~,Creek und Larin. Bur tt is rcnzarkrzblt. lloia mell P?'e,gent.u v: theory s/an~/.vup w o ~ vl k n ~ rarigcJo f our ezkdence lzas been ~?nst!ybrnariened. I t ~ n k r solzly a s/ight/)l more/lt.xiA/c calculus. I believe, to acco?rarnodote ( I / / lhe zjarieties qf'semioti~.S I T L I C ~ U ez)idtw/ ~.~ in oriiinary discourse. Uric1 M'einrrich.

Introduction In this study, I want to explore the notional category of modality ils reflected in certaln expressions of German. I chose German since this is the language I know best. Thcrc is a number of very detailed investigations of the German modal system.' I profited fi.orn all of them. In dealing with the semantics of n~odals,the main danger one is facing is to get utterly lost in the variety of interpretations one and the same expressioil can receive in different utterance situations. As a result, one may bc tempted to develop sophisticated classifications and to study the characteristics of major types like aletl~ic,cpistcmic or deontic uses of a tnodal expression. I am not primarily interested in such classifications. My main concern is to answer three questions: What is the logical nature of these intcrpretations? What is their variety due to? How is this variety restricted by the vocabulary of German itself? These questions are w r y much in the spirit of Gunnar Bcch. I think, however, that I am in a better position today than he u-as: In rnodal logic, a scnlantic fi-amcwork has beell developed, which is more suitable fol- describing semantic relations bctwecn modal expressions than the tools available thirty years ago.

290 Angelika Kratzer Traditionally, investigations of n~odalityhave concentrated on expressions like neressarily, possibly, urzust, can, should or wzaj~.Little attention has been paid to the fi~ctthat natural language have means of grading and comparing possibilities. Furthermore, conditionals are usually not considered in connection with modality. Yet, &clauses very often serve to rustrict modals in an explicit or implicit way. In what follows, 1 am trying to present a unified analysis of modality, which incorporates these facts. Many insights gained in separate examinations of some of these phenomena will then come out as special cases of a few very general principles.

1. Expressing Modality in German Modality has to do with necessity and possibility. In German, as in other languages, there are many ways of expressing these notions. Here is a selection:

1.1 Inherent modality ( I ) Niemand lauft in Nobody runs in (2) Dieses Auto fahrt This car goes

zehn h l i n u ~ e nvon Andechs nach Aufhauscn. ten minutes from Andechs to Aufhauscn. zwanzig Meilen pro Stunde. twenty miles per hour.

(1) and (2) have a lnodalizecl reading: Nobody is able to run from Arldechs to Aufhausen in ten minutes. (2') This car can go twenty miles an hour. (1')

Sentences (1') and (2') make explicit the modal element which scums to be inherent in the verb in the two original sentences.

1.2 Suffixes on adjectives There are two suffixes in Gcrman which often have a modal meaning: -1ich and -bar. Consider the following lists, parts of which I borrowed from Hermann Paul.

-1~~b erblich umganglicl~ zugiinglich kiiuflich zerbrechlich sterblich unsterblich vergeBlich

hereditary sociable accessible, approachable saleable, purchasable fragile mortal immortal tbrgetful

The Notional Category of Modality 291 untriistlich unvergel3lich liislich

inconsolable unforgettable soluble

-bar zahlbar unfehlbar brauchbar brennbar dehnbar denkbar enbar tragbar waschbar

payable infallible useful, practicable combustible, inflammable flexible, extensible conceivable eatable, edible portable, bearable washable

In general, the suffixes -1ich and -bar express possibility. There are exceptions like

xnhlbar:

(3) Die Miete fur das Haus auf dem Leoni-Acker betrigt T h e rent

for the l~ouseon the

Leoni-Field

amounts to

zwanzig Gulden, zahlbar am ersten Januar. twenty guilders, payable on the first of January. Here, it is not that the twenty guilders can be paid, they definitively have to be paid on thc first of January.

1.3 Modal auxiliaries The following auxiliaries are directly connected with the notions of necessity and possibility: must can may shall will may

mu13 kann darf sol1 wird mag

miiBte kiinnte diirfte sollte wiirde mochte

The English translations are very rough approximations. The exact meaning of most of these auxiliaries will be discussed in detail as we go along. 1 included rvird, as I was convinced by the arguments Heinz Vater gives in his article "Wcr~Jenals ~odalverb".' MiiJi'te, kci'nnte, diirfte, sollte, wiirde and mci'chte are subjunctive forms of the corresponding verb on their left. They often have an independeilt meaning.

292 Angelika Kratzer

1.4 Sentence adverbs and impersonal constructions moglicherweise notwrendigern~eise wahrscheinlich

possibly necessarily probably

Phrases like: es ist miiglich da13 es ist notwendig daR es ist ivahrscheinlich daR

it is possible that it is necessary that it is probable that

are used in a similar function.

1.5 Adjectival phrases imstandc sein in der Lage sein

to be able to be in the position

What becomes obvious from this selection is that therc is no syntactic category corresponding to the notional category of modality. What then is modality? T h c following sections are meant to shed some light on this question.

2 Basic Notions Most of what I have to saj- in this section is found in mo~-cdetail in my dissertation or in related articles listed in the bibliography. Anyone who is already familial- with my pre\ious w-ork on modals can skip whatever docs not sound new to hinl or her. In order to see what is involvcd in modality, lct us look at the following exnmplc:

The mzrru'pr Much-Girgl has been murdered on his way hon~e.T h e police start invcstigations. Certain conclusions may be drawn from w-hat is known about the ci~.cumstanccsof the crime. Utterances of the following sentences are likely to have occurred in such a situation:

(4) Der Icastenjakl kann der Mijrder T h e Kastenjakl can

sein. thc n~urdcrcrbe.

Kastenjakl may be the murderer.

( 5 ) Der Gauzner-$ficlzl n1ul3 der h/lorder sein. T h e Gauzner-Michl must the murderer be. Gauzner-Michl m 11sr be the murderer.

The Notional Category of Modality 293 In uttering (4), a poIice inspector claims that it is possible in vicw of what is known about the murder, that KastenjakI is the murderer. Some time Iater, when better evidence is available, the same inspector cIaims in uttering (S), that it is necessary in view of what is known about the murder, that Ganzner-Michl is the murderer. The example shows that there are at least two ingredients involved in the interpretation of modals like knnn or muJ: A con7!e~sationalbackground which contributes the premises from which conclusions are drawn. And a m o h l rflntiorl which determines the "force" of the concIusion. In his secoild utterance, the inspector drew a stronger conclusion than in his first. In the example above, the conversational background was obvious from the context of the story. Modals are context-dependent expressions since their interpretation depends on a conversational background which usually has to be provided by the utterance situation. Only occasionally do nre use phrases like in view of what is known . . . for referring to conversational backgrounds in an explicit manner. T o make all this more precise, I have to introduce a few notions of what has been called "possible-worlds semantics".

When Lenz uttered thc sentence

(6) Bis jetzt

hab' ich dir genug Bier weggesoffen. U p to now have I you enough beer boozed away.

he thereby expressed a proposition. In possible-worlds semantics, a proposition is idcntificd with thc set of possiblc worlds in which it is truc. T h c proposition cxprcsscd by Lenz's uttcrance of (6) would be the set of all those possiblc worlds whcrc Lcnz has drunk enough beer in Fink's pub up to thc day of the uttcrancc (roughly). T h e meaning of a sentence is then described in specifying which proposition is expressed if the sentence is uttered in a situation. Let W- be the set of all possible worlds. A proposition is a subset of \I:.

Truth of'u Proposition: h proposition p is true in a world w E W if, and only if, w E p. Otl~crwisc,p is false in w. Logical (,'unscquence: A proposition p follows from a set of propositions A if, and only if, p is true in a11 worlds of W where a11 propositions of A are true. Co~rsistc'ni:y: A set of propositions A is consistent if, and only if, there is a ~vorldin i,' wl~ereall propositions of A arc true. Logical Conzpatibility: A proposition p is compatible with a set of propositions A if; and onlj- if, A ~ { p is) a consistent set of propositions.

294 Angelika Kratzer

We know already that a conversational background is the kind of entity which might be referrcd to by the utterance of a phrase like u7hrr.l is known (wc might ignorc the in z k m of-bit). What is hnown is different from one possible world to anothcr. And what is known in a possible world is a set of propositions. In our semantics, a conversational background will therefore be construed as a function which assigns sets of propositions to possible ~vorlds.In particular, the meaning of whrrt is known will be that function from W into the power set of W, which assigns to any world w of W the set of ;dl those propositions which arc known in w. This is an example of an epistenlic conversational background. We will consider other hinds of conversational backgroi~ndsInter. First, I want to sag' something about modal relations. T h e most familiar of thcsc relations are simple ncccssity and possibilitl. Assume for the following that f is an arbitrary conversationill background, that is il function tison1 possible worlds into sets of propositions.

Sinzplr hie~,c.ssitli: A proposition is a simple necessity in a world w with respect to the conversational background f if, and only if, it follows from f(\\-). Si~uplePossibkli{)l: A proposition is a simple possibility in a world

ii7with

respect to the conversational

background f if, and only if, it is compatible with f(w). Tlic obvious thing to do now, is to link the meaning of thc German llloclals corrcsponding to mzrst, necessaril'~, it is necessary that, can, possiblj~or i t is possible tlzccl to the notions I have defined above. We might want to say - for example - that a certain modal e;vpresses simple necessity. I am going to spell out fix one example what this woilld incan.

The meaning of Notmen~/zgt.rmeisc C:onsider an uttel-ance of a sentence Y. of the form notruendigermuise /) such that the proposition q is expressed by the utterance of the constituent sentencc /j. We have then:' (i) A proposition is expressed by rlle utterance of a only if there is one, and only onc, conversational background for this uttcrancc. (ii) If a proposition p is expressed by the utterance of sc, and i f f is the convcrsntional backgrouncl for this utterance, then p is that proposition which is true in exactly those worlds w of \$I, such that q is n simple necessity in w with respect to E Let us take this as a first approximation for a meaning rule for tnodals rclatcd to necessity. One may wonder why there should bc a unique conversational background t o l a a modalized sentence to express a proposition. We'd better assume that in the case of several conversational backgrounds, there are scvcral propositions exprcsscd, one

The Notional Category of Modality 295

relative to each background. It would then be part of the vagueness of modal expressions that sometimes, it remains unclear which proposition was intended. 'These considerations lead directly to the work Manfrcd Pinhal has done about definite descriptions.' There is also a problem if the constituent sentence contains further modals, each requiring a conversational background of its om-11. T o account for this, we \vould have to split up thc utterance situation of a further and consider those parts whcrc cach 111oda1is uttered. I elaborated this in Kratzer (1978) and I don't want to spencl any more time on these kinds of refinements. T h e analysis as it is, allows for one parameter to be fixed by the contcxt of use. It implies that it is this parameter which is responsible for the variety of intcrprctations many modals can 1.cceivc. In the murderer example, we had an epistemic conversational background. An epistemic conversational background leads to an epistemic interpretation of modal expressions. Othcr kinds of conversational backgrounds could lead to different interpretations. For further refcrcnce, I would like to draw attention to thc following kinds of conversational backgrounds:

Re~lliszilConz:ei-sationriE Ruckgroun~ls: In vie127 of facts qf such and such k i n d . . . A realistic conversational background is a function f which assigns s c ~ of s propositions to members of W, such that for any w E W: iv E n f(w-). That is, f assigns t o every possiblc world a set of propositions which arc true in it. 7bt~1lIyReirlisti~.Conrer.ssational Backgrounds: In view oj'mhat is the case . . . A totally realistic conversational background is a function f which assigns scts o E propositions to members of LV such that for all w E W: n f(w) = (w). That is, f assigns to any world a set of propositions which characterizc it in a unique way. For each world, thcrc arc many ways of characterizing it uniquely. This is the source of the vagueness of counterfactuals as we'll see in a later section.

E'i.ste~aU

Con~~ers~llional Bi~ckgrovtrtls: In view of mhat is known . . .

A11 epistemic conversational background is a function f which assigns scts of propositions to members of W such that for all w E W: f(w) contains all those propositions which are established Irno\vledge in w - for a group of people, a community etc. Since only true propositions can be known, epistemic conversational backgrouncls arc special cases of realistic ones. Of particular interest are:

S t e r ~ ~ o ~ l p Couversationi~l i~.nl Barkgrounds: In view of the nomzal course oj'evenls ... A stereotypical conversational background is a function f which assigns sets of propositions to members of \i sucll that for airy w E W: f(w) contains all those propositions p such that it is the normal course of events in w that p

-

for someone, for a community etc.

296 Angelika Kratzer

A deontic conversational backgl-ound is a function f which assigns sets of propositions to members of LV such that for any w E W-: f(w) contains all those propositions p such that it is commanded in w that p -- by someone, by the Law ctc. teleologic.^,! c.nnver.sniiona/ ba~,kgroundsare related to aims and /)u/~>ticconvenationla1 bacX7grounils have to do with wishes. An extreme case is the c v ~ p t )con~lersi~/iunul ~ bnckgrtlund:

The Enzpty Conversarional Background: T h e empty conversational background is that fi~nctionwhich assigns to any w E W the empty set. We might think nowT that the "semantic field" of modal expressions could he described along two axes: One specifying a modal relation and the othcr one specifying ~.estrictionsfor admissible convers;ltional bachgrounds. For example:

1.14 Modal I-elation: Silnple necessity Conversational backgrounds: No restrictions ~lllI:/' Modal relation: Simple possibility Conversational backgrounds: Only deontic, buletic or teleological backgrounds are admitted. T h e follobving sections will show that this view is too simple.

3 Grades of Possibility J would like to take up the murderer example again. Instcad of (4) or (S), the police inspector might have uttered one or sei7eral of'thc following sentences:

(7) Es kann gut sein, da13 der Gauzner-Michl dcr hliirder It can

well be

war.

that the Gauzner-Michl the rnurdcl-er was.

There is a good possibility, that Gauzner-Michl was the murderer.

(8) Es bestcht aber immer noch cine geringc -Miiglichkeit, There is however still a slight possibility da13 der Kastenjakl der Miirder war. that thc K'istenjakl thc rnurdcrer was. Thcrc is, however, still a slight possibility that Kastenjitkl was the murderer.

;I 1 a\

1

The Notional Category of Modality 297

(9) Der Gauzner-Michl kann eher der Morder sein als der T h e Gauzncr-Michl can rather the murderer be than the Kastenjakl. Kastenjakl. Gauzner-Michl is more likely to be the murderer than Kastenjakl. (10) Es ist wahrscheinlich, dall der Gauzner-Michl dcr Miirder war. It is probable that the Gauzner-Michl the murderer was. It is probable that Gauzner-blichl was the murderer. T h e police inspector does not know what the real world is like. Hut hc call draw conclusions from the growing evidence available to him. At any time, this evidence is compatible with a set of worlds which "co~~ld" be the real world. These are the epistemicalil~acr-essihle worlds. There is a straightforward connection between conversational backgrounds and accessibility relations as used in modal logic: If f is a con\rersational backgn~und,then the set of worlds which are accessible in a world w with respect to f is simply n f(w). That is, the set of worlds where all propositions of f(w) are true. There are certain worlds among the accessible m-orlds which are more f~r-fetched than othcrs. A world where Kastenjakl is the murderer is more far-fetched than a world where Gauzner-Michl has killed Girg-1. Gauzner-Michl couldn't stand Girgl, but Kastenjakl got along very well with him. Even more far-fetched are worlds where someone from the other end of the world committed the crime. Far-fetched in respect to what? In respect to what is the case in the real world? This can't bc truc, since it seems quite natural to say that something which was almost impossible, turned out to be the case. Actually, it is things like this which usually happen in detcctive stories. T h e most unlikely candidate is the murderer. What is far-fetched about someone from the other end of the world having killed Girgl, is that things like that do not correspond to the normal course of events. Normally, you don't meet people from the antipodes in that village. And should someone show up who docs not actually live in the neighbourhood, he wouldn't just go and kill Girgl. Normally people need a motive for killing someone. It couldn't have been for money since Girgl \vasn't robbed: all his money was found on him. In view of the normal course of cvents, it is far-fetched that someone from the othcr end of the world has killed Girgl. And in view of the normal course of cvents it is more far-fetched for Kastenjakl to be the murderer than for GauznerMichl. Worlds in which the normal course of events is realized are a complete bore, there arc no adventures or surprises. T h c concept of a normal course of events is analogous to the concept of "frame" which plays an important role in psychology and artificial intelligence. In our example, the epistemic conversational background determines for cvery world the set of worlds which arc accessible from it. It fornls thc modill hnse. There is a second conversational background involved in the above uses of modnls, a stereotypical background. It induces an ordering on the set of accessible worlds, thereby functioning as ort/cri,zg source."

298 Angelika Kratzer on the set of all Quite generalljr, a set of propositions A can induce an ordering possible worlds in the following way: (The idea is taken from David Lewis' work on ordering senlantics, personal comnlunication.) T h e Ordering SLq: For all worlds w and z E W: ~ < . ~ z i f a n d o n l y i f ( p : p ~ A a n d& z ~{ pp ): p f A a n d w ~ p ) T h e intuitive idea is this: A world w is ar least as close to the ideal A as a world z if, ant1 only if, all propositions of A which are true in z, are true in w as well. is reflexive and transitive. It can be shown that the relation We are now in the position to define some additional modal relations:

Human Nc.cessitL)/: A proposition p is a human necessity in a world w with respect to a modal base f and an ordering source g if, and only if, the following condition is fulfilled: For all u E n f(w) there is a v E n f(w) such that (i)
L

1

ci

Roughly speaking, a proposition is a human necessity in view of a modal base and an ordering source if, and only if, it is true in all those accessible worlds which come closest to the ideal. T h e accessible worlds are determined by the modal base and the ideal is provided by the ordering source. As we can't assume that there have to be such things as closest worlds, the definition is rather complicated. It resembles the one David Lewis givcs for counterfactuals." Hulnlcn Pussibilit)~: A proposition is a human possibility in a world \?I wit11 respect to a modal base f and an ordering source g if, and only if, its negation (that is its complement) is not a human necessity in w with respect to f and g.

Sligh r Possibility: A proposition p is a slight possibility in a world w with respect ro a modal base f and an ordering source g if, and only if, (i) p is compatible with f(w) (ii) the negation of p is a human necessity in w with respect to f and g. Human possibility is just the dual of human necessity. If a proposition is a human necessity in a world with respect to a modal base and an ordering source, there may still be accessible worlds in which it is not true. In this casc, its negation will be a slight possibility in the same world with respect to the same parameters.

The Notional Category of Modality 299

1

Conrprrrrrtiur Possibili~,i: A proposition p is more possible than a proposition q in a world nrin view of a modal base f and an ordering source g if, and only if, the following conditions are satisfied:

For all u E n f(w): If u E q, then there is a world v E n f(w) such that v <,(,b) u and v E p. (ii) There is a world u E n f(w) such that: u E p and there is no world v E n f(w) such that v E q and v Sg(..)u. (i)

In simple words, these conditions say roughly this: For every accessible q-world there is an accessible p-world which is at least as close to the ideal. (ii) There is an accessible p-world for which there is no accessible q-world which is at least as close to the ideal. (i)

It can be shown that the relation of comparative possibility is transitive and a s p metric. T h e proof is left to the reader. I think that these four modal relations can be linked to the four modal expressions in the sentences (7) to (10) in the following way: Es Es Es Es

kann gut sein daJ3 . . . besteht eine geringe Moglichkeit dal3 . . kann eher sein dal3 ... als da13 . . . ist wahrscheinlich daB . . .

Human Possibilitjl Slight Possibility Comparative Possibility Human Necessity

T h e English equivalents would be roughly: There is a good possibility that .. . There is a slight possibility that . . . It is more likely that . . . than that . . . It is probable that . . .

Human Possibility Slight Possibility Con1parative Possibility Human Necessity

I think it is clear enough how these linkages are to be understood: 'The four nlodals require a pair of parameters to be fixed by the context of use. T h e rest of the corresponding meaning definitions would be as for n o t w e n d z e w e e with the neccssary adjustments made. T o check the correctness of this analysis, imagine utterances of sentences of the following form, wherc modal base, ordering source and the propositions expressed by x stay the same for all examples: Es It (12) Es It (13) Cs It (14) Es It

(I I)

ist wahrsclieinlich, daJ3 a is probable that a ist wahrscheinlich, da13 nicht a is probable that not a kann gut sein, daB x can well be that a kann gut sein, dal3, nicht a can well be that not a

300 Angelika Kratzer (15) Es kann ilicht gut sein, daR cr It can not well be that a (16) Es kann nicht gut sein, dafi nicht a It can not well be that not x (17) Es besteht eine geringe h/loglichkeit, da13 fa There is a slight possibility that cr (18) Es ist eher miiglich, dalj nicht x , als daR a It is more likely that not sl than that ,x We may suppose further that the modal base for these utterances is normal. A conversational background f is normal if, and only if, for all w of W, f(w) is a consistent sct of propositions. 14ny realistic conversational background is norn~al.The above analysis of the four modal expressions gives us now for example thc following predictions: T h c psopositions expressed by the utterances of (1 1) and (12) arc not con~patible with each other.7 T h e propositions expressed by the utterances of (13) and (14) art: compatible with each other. T h e proposition expressed by the utterances of ( 1 3) follows from thc proposition expressed by the utterance of ( I 1). T h e proposition expressed by the utterance of (14) follo\~sfrom the proposition expressed by the utterance of (12). T h e propositions expressed by the utterances of ( I I) and (14) are not compatible with each other. T h e propositions expressed by the utterances of (12) and (13) are not compatible with each other. T h e propositions expressed by the utterances (12) and (15) follow from each other. The propositions expressed by the utterances of (1 1) and (16) follow from each other. T h e proposition expressed by the utterance of (18) follows from the propositions expressed by the uttcrances of (12), ( 1 5 ) and (17). T h e interpretations of the four modal expressions in sentences (7) to (10) depend on a pair of conversatioilal backgrounds. In our example, it nras an epistenlic nlodal base and a stereotypical ordering sourcc. Does this mean that for different types of modals, n different number of parameters has to be fixed by the utterance context? Would it be one parameter for modals like mup, faun, es is1 tzotmendig duP ctc. and a pair of parameters for exl~ressionsof the kind we haw discussed in this chapter? We shall see in chapters yet to come that moclals of the first kind may express gradcd notions of nlodality too. And grading involves an ordering source as well as a modal base. So a bcttcr view would be to assume that the interpretation of modals in general depends on a modal base and an ordering sousce ~ ~ h ceither r c parameter may be fillcd by the empt? con\lersational background. 1:urther support for chis view will come froin the analysis of practical inferences and conditionals. Simplc ncccssity and possibility might now be seen as special cases of human necessity and possibility rcspectivcly. The

The Notional Category of Modality 301

1 I

reader may convince him- or herself that the following equivalences arc true for any modal base f and the empty ordering source g:

Simple and Hurnajz Nel-cssity: A proposition is a simple necessity in a world w with respect to f if, and only if, it is a human necessity in w with respect to f and g. I

1

Simple nrrd Human Possibilzty: ,4 proposition is a simple possibility in a world w with respect to f if, and only if, it is a human possibility in w with respect to f and g. As a new start, we may try now to describe the semantic field of modal expressions along three axes specifying: (i) a modal relation (ii) conditions for the modal base (iii) conditions for the ordering source. In the following section I will bcgin with a discussion of thc two major types of modal bases which are realized in German.

4 Two Basic Kinds-of Modal Reasoning We have seen that in modal reasoning, a con\~ersationalbackground may play the role of a modal base or an ordering source. T h e modal base determines the set of accessible worlds and the ordering source determines an ordering on it. In this chapter, I want to investigate the two major types of modal bases which are relevant for German. Soinc examples ill be useful:

Root or Circumstantial +&lod~il Bases: (19) Sie uollte schreieil und konilte nicht, gewann abcr S11c wanted to scream and could

not,

regained hoivev-er

endlich die Herrschaft iiber ihre erlahmten Glieder. over her paralyzed limbs. finally the control Genovev was so terrified that shc was unable to move. (20)

Dcr Jani-Hans schimpfte nie, fluchen konnte er gar nicht. T h e Jani-Hans scolded never, curse could he at all not.

Jani-Mans had such a mild character that he just wasn't capable of getting angry. (21) Hier kijnnen die Tomntcn gedeihen. Here can the tomatoes prosper.

302 Angelika Kratzer (22)

Wer nichts hat, den1 kann man auch nichts nchmen. MTho nothing has, fi-om whoin can one also nothing take awal-.

Ep isterni~.,2lorlrz / Bnses: (23) Es kann nus cincr It can

gewesen sein, der sich im I Iaus only someone been have, who (refl.) in the house

auskennt hat'. been at honlc has. T h e Heimrath's have been burgled and Girgl tries to find out who might have been the thief. It must have beell someone \\rho was fitmiliar with the house.

I

(24) Sie hatten den Befehl, den jungcn Kiinig zu suchen, dcr sich The>-had order the young king to look for, who (ref.) in einer sciner Jagdhiittcn aufhalten imuflte. in one of his hunting huts stay must (past). T h e young king has disappeared and in view of n-hat is Lnown, hc must be hiding in one of his hunting huts. Unlike the English nlust, the German nrup has a past teilsc form I I ~ I I [ ~ L C . (25)

Soweit wir wissen, muR es fiir sic nie etw-ns As fAr as we know, must thcre for them never an)-thing

1

I 1

1

I

anderes gegeben haben als Gcborenn-erden, Aufivachsen, else beell have but being born, growing up, unermiidliche Arbeit und Sterbcn. tireless work and dying. Oskar Maria Graf draws this conclusion from the h i s t o r i ~ sources ~~l ahnut the life of thc Hei~nrathfanlily some centuries ago. T h e term "cpisten~ic~nodality"is fan~iliarin linguistics and philosophy. T h e term "root modality" is usual in the tradition of generative grammar. "Circumstantial modalit?" is in the spirit of Terence Horgan (1977). There is a clear intuitive difference between the two kinds of occurrences of modals which I grouped under the two headings. Kt is a differencc in thc kind of premises from which we reason. If we use an epistemic modal, we are interested in what else may or must be the case in our world, given ez1~qrlhir1gn)e k n o a ~~ r l r r a ~ l ]Znd y. if we use a circumstantial modal, we are interested in what call or must happen, givcn i-il-i~i~ii~s~i~ni.e.u , (,l'n r.erjain kirzL Circumstances of a certain kind are hcts of a certain kind. I':~cts 1 concaning the outside world, our bodies or our mind, fbr cxample. Usually, circumstances permit or exclude that certain things happen. Only sometimes do thry ncccssitare an event or an action: We hare to die, to cough, to vomit, to laugh, to cry or to realize that we are lost. I Epistemic modality and circumstantial modality involve a different categorization of I the facts. T h e problem is now to find out some more details ahout this partition.

I

I 1

i

i Ii

The Notional Category of Modality 303

1

I

I

/

I

I I

I

I shall present a few observations towards this goal. Consider the follocving pairs of scntenccs: (2h) ( i ~ ) Aus dicscr Kannc Milch kann die Kathl ein Pfund From this can of milk can the kathl one pound of Auarli n~achen. cottagc chccsc make.

(26) (b) Es kann sein, dill3 die Kathl aus dieser Kannc Milch It may be that the katlrl from this can of milk

I

ein Pfund Quark macht. one pound cottage cheese makes.

I I

; I I

1

'

I!

/

1

I

(27) (a)

I n dieser Gegend lionnen Z\vetschgenbaunre \vaclrsen. In this area can plum trees grow. (27) (b) Es kann sein, da13 in dieser Gegend Zrr-etschgenbiiume \\-achsen. It may be

that in this

area

plum trees

groll-.

Sentences (26) (a) and (27) (a) have a circumstantial reading besides an episte~niconc. For sentcirces (26) (b) and (27) (b), the epistemic reading- is prominent. Gi\,en a circumstantial reading for the (a)-sentences and an epistenric reading fos the (b)sentences, \fie can imagine situations where I sap sonrething true in uttering an (a)scntcncc, but something fi~lscin uttering the corresponding (b)-sentcncc. 'I'ake the first two sentences: I11 view of quite general conclitions concerning the pl.oduction of cottage cheese, it is possible that Kathl is going to product: a pound of cottage cheese from thc milh in the can. We know, however, that Kathl never uses the zvhole can of milk for thc production of cheese. She uses a bit for her coffee, a bit for her porridge, a bit for the cat and the rest for her cheese. This means, that in view of everything rve k110\5, it is not possible that Kathl is going to produce a pound of cottage cl~eeesfronr the milk in the can. 111 using a circumstantial modal, we iicglect certain ltiiids of hcts. In our case, it is Gcts ahout what Kathl always actually docs. T h c situation is sin~ilarwith thc scntcilces (27) (a) and (27) (b). Suplmsc I iain travelling in an exotic countrj and discover that soil and climate are \;el-!. much like that in nry own country, where plum trees prosper cvery~z~here. In such a situation, ill1 utterance of' (27) (a) in its circunrstantial sense would probablj be true. Rut (27) (b) could very well be false, given that this country had no contacts \vhatsocvcr with wcstcrn ci\iilization and the vegetation is nlltogcthcr different from ours. Since M-c kilow this, it is iinpossiblc in view of what we know that pluin trces grow ill this a1x3. Again, we h a w to neglect certaiir facts fils (27) (a), although we might be aware of' them. T h e kind of Facts we take into account for circumstantial modality are a ratheld slippery nratter. This nlay give rise to nrisunderstandings and jokes.x I once 11enrcl a philosopher say that one of the defining properties of a cup is, that yo11 can pour things like coffee in it. A student objected to this in pointing out that - if this were true a cup ~11ic11has coffee in it already, \vould not be a cup anymore.

304 Angelika Kratzer When we talk to each other, we hardly ever make explicit in view of which circumstances something should be necessary or possible. We may give hints. Usually people undersrand. And they all understand in pretty 111uch the same way. Consider the following sentence:

(28) Ich kann nicht Posaune I

can

not

spielen. trombone play.

Depending on the situation in which I utter this sentence, I may say quite different things. I may mean rhat I don'r know how ro play the tl-ombonc. 1 am sure that there is something in a person's mind which becomes different when he or she starts learning how to plav the trombone. A programme is filled in. And it is in view of this programme that it may be possible that I play thc trombone. O r supposc that I suffcr fi-on1 asthma. I can hardly breathe. In view of my physical condition I am not able to play the trombone, although I know how to do it. I may express this by uttering (28). O r else imagine that I arn travelling by sea. 'I'he ship sinks and so does my trombone. I manage to get to a loncly island and sadly muinble (28). 1 could play rhe trombone in view of my head and my lungs, but the trombone is out of reach. There are more conceivable interpretations for an utterance of' (28), but most of them in\-olve other conditions in addition to the facts. That is, most of them involve a non-empty ordering source. A distinction between circumstances concerning mainly the outside world, the body or the mind of a person, plays a role in rhe semantic dcvclopmcnt of kiittpletz. According to Gustav Deggau, a student of Otto Hehaghel's, the Old High Gcrnlan equivalent of this modal was first used for intcllcctual capacities. Then, it could csprcss possibilities in view of the outside situation. Onll- considerably later was it used for talking about physical a b i l i t i c ~ . ~ tnadc in Iiungitrian. In Fercnc Kiefer (1980) has shown thar similar distinctions Hungarian, the verbal suffix -hat/-het expresses possibility. In its circumstantial reading, it can only be used for possibilities in vicu- of the outside situation. In Kicfcr's oivn rerms: "Modal senrcnces with -hat/-het can only express outer dispositions". 'Taking up some of Kicfcr's further obse1-1-ations, I would likc to present some analogous fi~ctsabout modern Gcrman. Co~lsidera phrasc likc inrstanill~stin (to hc ablr). I could say (29) Ich bin nicht inlstande, Posaune zu spielen. I am nor able trombone to play. if I have asthma or weak ncrves or if I am just too stupid. I doubt whether I would say it in a situation whcrc I haven't learnt how to play the tron~bonc.,\nd I coilld never say it on the island with my tron~bonelost at sea. T h e prominent circi~mstances for irnstande sein are concerned with the strength of our body, charactcr or intellect. For karfn, there is a f ~ ~ r r h type c r of restrictions.

The Notional Category of Modality 305 Consider: (30) Dieses This Dieser (31) This (32) Dieser This

Messer kann nicht schnciden. knife can not cut. Hut kann den Kopf warmhalten. hat can the head keep warm. Ofen kann nicht richtig heizen. stove can not properly hcat.

These sentences sound funny. They suggest that the knife, the hat or the stove are agents which take an actib-epart in the cutting, the warming of the head or the heating. T o avoid this effect, we would have to say: (33) Dieses This (34) Dieser This (35) Dieser This

Messer schneidet nicht. knife cuts not. Hut halt den Kopf warm. hat kccps the head warm. Ofen heizt nicht richtig. stove heats not properly.

1 think that sentences (30) to (32) havc some features in common whose co-occurrence might be responsible for the fact that they sound bizarre. One of thesc properties is concerned wit11 agency: The knife is not an agent, but an instrument for cutting something. The hat is not an agent, but an instrument for warming the head. And the stove is not an agcnt, but an instrument for heating a room. After all, it's.)!ou who cuts the bread, keeps the head warm and heats the house. Somc machines, like music boxes, can do things all by themselves, thus functioiling as true agents. I can't find anything peculiar about (30):

(36) Diese Spieluhr kann This music

"La Paloma" spiclcn. box can "La Paloma" play.

Hcre, the music box is an agent and thc use of kann is appropriate. Another feature is concerned with the kinds of actions which are said to be possible or impossible for a knife, hat or stove to be involved in. That a knife cuts, a hat keeps the head warm or a stove heats a room, is fairly well colnpatible with our stereotypical notions about knives, hats or stoves. Consider in contrast:

(37) Dieses This (38) Diescr This (39) Dicscr This

Messer kann cincn Fclsetl zerschneiden. knifc can a rock cut into pieces. I-Iut kann epileptische Anfalle verhindcrl~. hat can epileptic attacks prevent. Often kann wahlweise mit Kohle oder 01 hcizen. stove can at choice with coal or oil hcat.

Knives which cut rocks into pieces, hats which prevent epileptic attacks and stoves which work with coal or oil at choice come as a surprisc. I think this is the reason why sentences (37) to (39) sound all right although the knife, the hat and the stove remain

306 Angelika Kratzer instruments for the actions under consideration."' Further rcsearch has to be done in this area. e s u~ellas Kicfer's examples) show, however, is that il is still a What these e ~ a ~ n p l(as simplification to describe the meaning of modal expressions by specifying nothing more hut a modal relation and some restrictions for possible modal bascs or ordering sources. Some constraints seen1 to involve agency or stereotypes associated with natural kind tel+ms.'' I shall nevertheless stick to this simplification. I think it is still rewarding to examine the modal system of a language with respect to these three parameters, even if this is not the whole story. In this chapter, I have examined the two major kinds of modal bascs which arc relevant for German (and all other languages I know): C:ircurnstantiill and epistemic modality are both based on realistic conversational backgrounds, but involve a different catcgorization of the facts. T h e distinction is clearly marked in the vocabulary. Verbs with inherent n~odality, modal adjectij-es on -1ich and -bar and phrases like iurzstande scin or in [lev Luge sein never express epistemic modality. and auxiliaries like rvird Sentence adverbs like muhrsc/zeinltc/z or n~ci'glic/zc~rmeke always express opistemic modalit! if they express modality at all. Some of thcse expressions involve a grading. In the examples discussed in this chapter, I avoided grading as far as possible. In the follo\ving sections, I will show how different niodal bascs interact with different kinds of ordering sources to yield thc variety of the German modal system. -

5. The Quest for Certainty In section three, I gave an example of the grading of' an cpistemic modal hasc. As a result, sfre obtained some new modal relations tt~hichwcrc linked to expressions like there is a good possibililj~ hat or it is probable that. In this section, I want to discuss some further issues concerning the grading: of epistemic tnodal bascs. It has often been observed that I make stronger claim in uttering (40) than in uttcring (4l):I2 (40)

Das This (41) Das I'his

ist die Biirgermcister-Wein-Stral3e. is the Burgermcister Lt7eifi Street. mu13 die Biii.genneister-MTei13-StraI3e sein. must the Hiirgermeister LVein Street be.

These utterances present a psoblem if we assunle that MJUJ~'gets a "pure" epistomic interpretation. In this case, the yropositio~lcsprcssed by thc utterance of (40) \vould fbllow from the proposition expressed by the utterance of (41) but not vice versa. 'l'l~us, uttering (41) should lead to a stronger claim than uttering (40). Since this is not the way things are, we have good reasons to assume that the utterai~ceof mt$I in (41) docs not express "pure" eyistemio necessity. In our framenrork, this means that the ordering source is not empty.

The Notional Category of Modality 307

In uttering (41) instead of (40), 1 signalize that I don't reason from established facts alone. I use other sources of information which may be more or less reliable. 'Takc for example the route description of a friend, a tourist guide or my own vague memories from years ago. Thcse other sources of information may form ordering sources for episten~icmodal bases. set of facts is :~lwaysconsistent. Other sources of information may themselves bc inconsistent or else be inconsistent with the established fL1cts.If these other sources function as orderir~gsources and are not part of the modal base, it can be explained why they can still be usefirl, even if there are inconsistencies. And why they never ovcrridc the facts: In the case of a conflict, established facts have priority over route descriptions, tourist guides and memories. I shall give an illustl-ation of' the treatment of inconsistencies in section seven. So 1 needn't go into details here. T h c next point I want to discuss, was brought up by John Lyons (1977): In principle, two kinds of epistemic modality can be distinguished, objective and subjective. This is not a distinction that can be drawn sharply in the ever?-day use of language; and its epistemological justification is, to say the least, uncertain. . . . It is iionethelcss of some theoretical interest 10 dlxw the distinction betmeen objective and subjective episte~nicnloclality .

T h e distinction is manifest in the vocabulary of German. Imagine that Lenz, who often has bad luck, is going to Icave the Old W70rldby boat, today, on Friday thirteenth. On 13 hcaring about this, someone might utter one of the following sentences:

(42) MTahrscheinlich sinkt das Schiff. Probably

sinks thc boat.

Probably, the boat will sink.

(43) Es ist wahrscheinlich, dalJ das Schiff sinkt. It is probable

that the boat

sinks.

It is probable that the boat will sink. (44) Das The (45) Das Tlle

Schiff wird (bestimmt) sinhen. boat will (certainly) sink. Schiff diirfte sinken. boat sink.

It is probable that the boat will sink. In German, thc aoniliar) mird has a temporal and a modal use.'' 1 intended the modal reading for (44). I couldn't find an appropriate glossc for diirftte, so 1 lcf't a gap. In uttering (42) or (44), I make a more subjective claim than in uttering (43) or (45). I may be rather superstitious. I couldn't dcfend my claim on objective grounds. But I would ha\.-e to do so if 1 uttered (43) or (45). There are established facts about the boat, the tcchnical equipment nowadays or the weather. And there are commonlj held conccplions about the normal course of events. In a world reigncd hy scie~lcc and technology, these conceptions don't include superstitions. Es is1 mrchrscheinlicl~ dajJ and diirJie seem to require an "objective" stereotypical bachground as their

308 Angelika Kratzer ordering source. Wabzrsrlzeitzliclz and wird prefer "subjcctivc" stereotypical backgrounds. John TJyons believes that in its subjective reading, iln cpistcmic modal doesn'i contribute to the propositional content of an utterance at all. This is a vcry debated issue on the border of semantics and pragmatics. I don't want to go into it, as I won't bc able to examine the different positions here. In the following section, I want to discuss ways of grading circumstantial modal bases.

6 Approaching Ideals Tn this section, I am going to examine how different ordering sources interact with a circ~u~l~stantial modal base and how this is reflected in German. Circumst-antial conversational backgrounds are special kinds of realistic oncs. They involve the sort of categorization oiE~ctswhich we have discussed in section four. Wc can include the empty conversational background as a special case of il circurnsta~~tial one. Circumstances create possibilities, the set of possible worlds which are compatiblc with them. These \vorlds, which are accessible in the circumstances under consideration, ma!- be closer or further away from The Lam-, What my fither provided in his last will, What is good, What you think is good, Our plans, Our aims, Our hopes, Our wishes, Our conception of a good life, NJhat Ferdl recon~mendsto his wife, What is rational

T o all of these ideals correspond conversational backgrounds. In the terms of possible worlds semantics, these would be functions g from possible worlds into sets of pr.opositions, such that for every world w, g(w) is the set of all those propositions p such that The Law provides that p in w, My-father provided that p in his last will, p is good in w In w, you think that p is good, Our plans in w provide that p, It is our aim in w that p,

The Notional Category of Modality 309 We hope in w that p, We \vish in w that y , It is in w our conception of a good life that p, Ferdl recomnlends y to his wife in w, In w, it is rational that p,

All of these "normative" conversational backgrounds could bc propcr ordering sources for a circumstantial modal base. Just as in section two, they would inducc an ordering on thc set of accessible worlds. From this, we get corresponding notions of human necessity, human possibility, slight possibility and comparative possibility. Somc modal expressions of German tolerate a wide range of ordering sources. Others have to obey more restrictions. l e t us look at some examples:

(46) Du

kannst doch nicht nus HCuser bauen oder Seml~lelnhacken You can not only houses build or rolls bake und wenn du dann gestorbcn bist, ist nllcs aus, and when you then dead arc is everything finished, allcs weggewischt. everything wipcd out.

Shortly before his death, the old Graf realizes that in view of some conception of an ideal life, you sllould do more thail just care for your property or do yoiu dailj work.

(47) Sagen kannst Say

geuiB nicht, dafl ich dir einmal schlecht can you certainly not that I you once bad

hab'. geraten advice given haw. Jani Hans always advisecl the Heimrath widow- well. Given this fact, it is iinpossible in view of an ideal of truthfulness and trust, that she says anything to the contrary.

(18) Dicscs Brot kann man ja This

bread can

direkt seiner one indeed straight a\vil? to his

Majestat empfehlen. Majesty recommend. This bread is good. If you recommend him something good, his htlajcstj- will hc plcascd. If you recommend him something bad, ho\vever, his Majest!. niill hatc you. Given these fi~cts,it is possible in view of an ideal where his h4ajest~loves \:ou, that you recommend this bread to his Majesty.

310 Angelika Kratzer (49)

Kann ich jetzt gehen? Can I nouT leave?

Imagine a pupil who says (49) to his teacher. T h e teacher is the source of law and order for him. What she wants is commanded and nothing is con~mandedunless shc wants it. Tlic boy wants to know whether it is possible in vicw of what is commanded that hc leaves. In this case, the kann in (49) is deontic. Welbe (1965) and Buschn et al. (1977) think that this purely deontic use of XIlrrlw is 1 colloquial. Klaus Welke quotes from "Muttersprache" ("Mother Tongue"), whcrc teachers of German are adviscd to correct pupils cvho use kann fr expressing ( permission. They should say ~hrf (muk)/).For me, klrm may express permission and I , don't feel that there is anything colloquial about it. For doff; a deontic ordering source is common but not ob1igatol.y. Suppost two burglars arc trq-ing to enter a firm house and cvhispe~to each other:

1

I

(50) Jctzt diirfen cvir keinen Liirm machcn Now may

we no

noise make.

It is not that they arc not i~llowedto make a noise. They can't niakc a noisc in ~ric~v of their aim to burglc the farmers without getting caught. KLINPI und dnr/.havc sin~ilarmeanings. Both express hunian possibility. I3ut there are differences. " Dart' requires an ideal in vicw of which possibilities are assessed. / h n n is morc ncutral in this respect. Here, possibilities may dcpcnd o n brutc facts onlj, that is, thc ordering sourcc may be empty. O n the other hand, (/i/ij'docsn't admit crrzy "normative" conversational background as ordering source. Suppose I have il 11ot.ribIe headache and say wit11 a dcep sigh:

'

(51) lch kann das n i c h ~aushalten. 1 can this not bcar. This use of karzn invol~esstandards concerning normal tolerancc thrcsholds for pain. 1 couldn't cxyrcss thc same thing in uttering. (52)

Ich darf das nicht aushalten. may this not bear. I

Dilt:J'does not tolerate a "normal standards" ordcring sourcc. O n the other hand, karw may have difficulties with buletic ordering sources: 'I'oinorrow is thc coronation of thc King and I utter darf es nicht regnen. (53) NIorgcn Tomorrow may it not rain. What I say hcrc is roughly, that in view of what wc all want, it shouldn't rain tomorrow. I couldn't get this intcrl~retationin uttering:

The Notional Category of Modality 31 1

(54) Morgen

kann es nicht regncn. Tomon.ow can it not rain.

We can conclude that there arc certain restrictions for knn~gand cl~rrfwhichconcern the acimissible ordering sources. Again, inorc derailed investigations have to reveal the exact nature of these restrictions. That an expression requires a coniplemcnt of a ccrtain kind to he provided by the context of use, l ~ a si~ilportantconsequences for the wa>- we understand these expressions. These rules of use ciin influence certain features of thc utterance context itself by means of what David 1,ewis has called "rules of accomn~odation".'" In our case, a rule of iiccommodation in the style of David Lewis \vould loolc as follows:

RuIc ~!fiii~~~ommu~kc~tioir: If the utterance of an expression requires a complement of a certain kind to bc corrcct, and the context just before the utterance docs not provide it, then ceteris paribus and within ccrtain limits, a complement of the required kind conlcs into existence. This is black magic, but it works in many cases. Suppose, I have a bsc-)lien leg and say:

( 5 5 ) Ich dasf nicht laufen. I

may not

\vl.alh.

So far, I have been talking about how I fell dorvn the ladder, how they plastered my Icg ... just &~ctsand nothing else. With the utterance of (5-i), suddenly ideals start ciitcring the picture: ideals where people don't have crookcd legs, where they don't fccl pain or where they just listen to their physician. As Dayid 1,ew.i~shows, rules of accommodation play an important role in our conversations. So this is an example of how the w-ay w-c unclcrstand a particular occurrence of a modal can bc at least partly explained by an interaction of independently motivated semantic and pragmatic principles.

(56) Wegcn der I,ola Montez hat er den1

Tliron cntsagcn miissen. Because of' Lola -Montez has be the (dat.) throne abdicate must (inf.).

Ludu-ig I of Bavaria loved Lola Rlontez. People became angrj-. Revolution hrokc our. In view of the publit: interest, it was necessary in this situation that he resignecl. (Note the use of the infinitive nziissen hcrc. You would expect the participle perfect ~ a s s i v c gtmtflt. This peculiarity of German is discussed in Edniondson (1079).)

(-57) Es mu13 mir gehoren, es inul3. It must to me belong, it must. klastenjakl is desperate to buy a piccc of land from the 13eimrath's. In view of what hc wants, it must belong to him.

312 Angelika Kratzer (58) Lump mu13 man sein, ilur als Lumyztvingt Crook must one be,

man die luinyige Wolt. only as crook conquers one thc crooky world

Lcnz presents his aim in the secoi~dpart of tlie sentence. Given our world as it is, it is necessary in view of the aim to conquer thc world, to be a crook.

(59) Arbeiten haben wir bis jetzt iniissen, arbeitcn w~crdeii Work have we up to now must (inf.), work will iniissen. wir auch weiter we also in future must (iiif.). T h e Heimrath's are peasants. Given their social status, thcy have to work in vicn of an ideal of a decent and honest life. They don't want to be beggars or burglars. Like kan?~,r~zz!Ji' accepts a wide range of ordcring sources. 'I'he ordering sourcc inay be empty too, This is suggested by sentcnccs lilic:

(60) Er niuljtc

hustei~. I-Ie must (past) cough.

Like riarf; .sol1 requires a non-empty ordering source. I x t us considel*sonic examples: (61) Ein Richard Vl'agnel. k'estspielllaus sollte nach dcii A Richard Wagner festival hall shall (past) after tlie Architektcn Scnipcr gebaut werden. Entwurfen des designs of the architect Seinper built be.

In view of the plans of King Ludwig I1 of Bavaria, a Richard Wagner festival hall was to be built after the designs of the architect Semper. (62) Ich bitt' euch gar schdn, der bochwurdige I-Icrr Pfi~rsersoll koninicn. I ask you very nicely, the reverend Sir curatc sliall coinc. Gauzncr h4ichl is dying. I11 view of what he wants, a priest must come. In Luther's translation. God uses sollen a lot when hc talks to bloscs.

(63) Sechs Tage soltu erbciten und allc deiile Werck thuii. Six clays shalt tl~oulabour and all thy work do. In view of \+-hat God wants, it is necessary that 5-ou work six days a week. In sonic societies, what God wants is commancled. In other societies, M hat God wants is good and recommended, but not commanded. If I lived in a society of the first kind, I would most naturally say: (64) Ich muR seclis Tagc arbeiten und allc mcine lVerlic tun. 1 must six days work and all mjdo.

The Notional Category of Modality 313 If I lived in a socicty of the second kind, however, I would prefer to say: (65)

Ich soll sechs l'age arbeiten und alle meine Wcrke tun. I shall six days worli and all my work do. I am supposed to worli for six days and to do all my work.

SollCn expresses necessity. It requires an ordering source which is crcatecl by what is good, planned or recommended, or by what a particular someone wants, plans or recon~mcncls.Act~~ally, it is not just what nn)lone wants, plans or recommends. ?'hc onc who does so cannot be identical with the individual referred to by thc subjcct of thc sentence in which sollen occurs. I can't say (66) Ich soll cin H3cker werden. I shall a baker become.

I arn supposed to become a baker. if it is inine but no-onc else's wish that I become a baker. Compare this with Gunnar Rech's (1949) characterization "sullen . . . bezeichnet einen nicht dem Subjckt innetvohnenclen Willen" ("sollerz refers to a will which is not inhcrcnt in the subject"). If tvc assume that in a passive sentence likc (67), er is not the logical subject, (67) is not a counterexample to this principle: (67) Lr sol1 in Ruhc gelassen ulerden. Hc shall in peace left be.

I think that I could use (67) for expressing that it is in view of what hc wants himself that he shouldn't be bothered. -Mz{Ji'is neutral with respect to who wants me to becomc a baker.

(68) Ich mu13 ein Bickcr werden. I

must a

bakcr

become.

y ~visl~es that I have to bcco~nea may be uscd if I want to say that it is in view of n ~ own baker . T h e suffixes -(lui. and -lzch allow all kinds or ordcring sources, depending on the adjective they arc attached to.

Consider:

(69) Dieses Eintrittsbillet ist nicht iibertragbar. This admission ticket is not transferable. In view of the regulations, it is not possible to give this ticket to somconc else.

314 Angelika Kratzer (70) Diese Tasse ist zerbrechlich. This cup

is fragile.

1 think that this is a case of "pure" circumstantial modality. It is in view of certain properties inhelent in the cup, that it is possible that it breaks. T h e ortlering source seeins to be empty.

(7 1) Dieses Vorschlag ist annchmbas. This

proposal

is acceptable.

In view of our common aims, it is possible to accept this proposal.

(72) Diese Lage

ist unertraglich. This situation is intolerable.

Every night, Marie-1,ouise's living room bccomcs the n~cctingplacc for all thc cats in the neighbourhood. This is intolerable in view of quite normal standards concerning property, noise and smell. We may add a phrase like-fi)r NI(irie-Louise to indicate that the standards involved are more subjecti~e.

(73) Fiir Marie-Louise ist diese Lage For Marie-Louise is this

unertr3glich. situation intolerable.

Ordering sources permit thc grading of possibilities:

(74) Ich h n n ehcr Backer als Stelln~ilcherwcrdcn. I call rather bakcr than cartwright becoinc. I'd rather become a baker than a cartwright. Vlaxl was wounded during thc w~aragainst the Prussians. Ciivcn this, he comes closer to an idcal where everyone is good in whatevcr his craft m a y be, if hc becomes a baker and not a cartnrright. Kann chrr . . . rlr expresses comparative possibility. In section two, the main motivation for introducing a clear-cut distinction bctwecn conversational backgrounds functioning as modal bases or as ordering sources, Ivas thc necessity to obtain notions of graded possibility. In the hllocving section, 1 want to discuss further arguments in favour of this bipartition.

7 Practical Inference There is an obvious connectio~~ between m? wa? of analj.zing modals and what has bcen called "practical infcrences"." A practical inference may hnrc the following form:

'

The Notional Category of Modality 315 I want to becoille mayor. I will becomc mayor only if I go to the pub reguIarly. Therefore: I must go to the pub regularly. Let us adapt this infereilce to the present framework. Tf w is any possible world, we nlould hake: In w, all I want is to become mayor. In w, thc relevant circumstances are such that I will become mayor only if T go to the pub regularly. Therefore: Considering the relevant circun~stancesand what I want, it is necessary in w that I go to the pub regulal-ly. T h e reader can easily check that this inference should be valid. ' l o do this, \ye have to interpret some expressions in a certain way, namely: Necesstcry expresses human ~~cccssitj-. T h e phrase lire r - t ~ 1 ~ z l l r l r~-ir.~-ct)tls/arl~-es / contl-ilrutes a nrodal basc f. f is that fitnction from possible worlds into sets of propositions which assigns to any world the set of propositions which constitute the relevant circunlstances in it. T h e phrase mlzat I mnnt contributes the ordering source g. g is that function from possible \vorlds into sets of propositions which assigns to any possible world the set of those propositions which constitute what I want in it. For the particular world w mentioned in the inference, f(m) contains just one proposition, nan~elythat T will become mayor only if I go to the pub regularly. And g(n) contains nothing but tlze proposition that I will becolne mayor. T h e union of f(w) and g(w-) is a consistent set of propositions. It can be proved that if this is so, then it is a human necessity in \lTwith rcspect to f and g that I go to thc pub regularly if, and only if, it f'ollo\vs from the union of f(w) and g(w) that I do so. It does indeed follow. Thus the inference is valid according to our definitions. I should like to look at a more intricate cxamplc: In FV, all I want is t ~ v othings, namely to beconle mayor and not to go to the pub regularly. In \v the relevant circun~stancesare such that I will becomc mayor only if T go to the pilb regularly. Therefore: Conclusion one: Conclusion ti\-o: Conclusion three: Conclusion four: Conclusion five:

Considering the relevant circumstances and what I want, it is necessary in vi that I go to the pub regularly. it is necessarjpin kv that I don't go to the pub regularly. it is possible in w that I don't go to the pub regularly and still will become mayor. it is possible in w-that I go to the pub regularly. it is possible in w that I don't go to the pub regularly.

316 Angelika Kratzer This is the horrible story of someone who wants something but rejects the necessary means leading to the fulfillment of her desires. Which conclusion can we draw in such a case? 1 think that the first three conclusions are f'aulty, but thc last t\vo are correct. T h e above analysis predicts this. Let us see why. 'l'hc expressions necessary, ihe circz~mstlcr~ces and what I want ase interpreted as above. Possible expresses human possibility. This time, g(w) contains exactly two l>rolx)sitions: That 1 will become mayor and that I don't. go to the pub regularly. I i c may now- reason as follo~vs:

n f(w) is the set of worlds which are accessible from w. For all worlds v E n f(w), we have: If I don't go to the pub regularly in v, 1 won't become mayor in v. Given the definition of human possibility, it follows immediately that conclusion three is false. Let us now consider the set g(w). It induces a tripartition of the set n f(w) of accessible worlds as follows: A is the set of all those possible worlds v of n f(w) such that I will hccomc mayor in v. B is rhe set of all those possible worlds v of n f(w) such that I don't go to thc pub regularly in v. C is the set of all those possible worlds v of n f(w) such that 1 \von't beco~ncnlilyor but yet do go to the puh rcgularl!i in v. T h e reader may vcrify that (a)

(b) A, U and C: are not empty, they are pairwise disjoint and A u B u c = n f(w). It is easy to check now that all of the following statements concerning the orclcl*ing rclation qg(\\) are true:

<

(c) For all v and z E n f(w): If \- E A and z E B, then neither i:
It follows from (b), (c), (d) and (f), that there is a world 1. in n f(w) such that for any world z in n f(w) such that z < g ( a ) V , 1 will bccomc mayor in z . Given (a), it follows that there is a world v in n f(w) such that for any world z of n f(w) such that z <,(,.I 1-,1 go to the pub regularly in z. This meiins that it is a human possibility in \v with respect to f and g that 1 go to the pub regularly. Thus, conclusion two is false and eonelusion four is correct. An analogous argument would show that conclusion one is false and conclusion five is correct. In a practical inference, facts have priorities over ideals. You can't give up f ~ c t in s favour of an ideal. That's why conclusion thrcc is false.

The Notional Category of Modality 317 T h e analysis I proposed (1977, 1978) cannot cope with these more conlplicated examples in a straightforward way. 1 did not distinguish facts and idcals.'"or tthc second example, therc would be false predictions since we would proceed as follows: VlTe would not h a w two conversational backgrounds f and g, but just one, h. For any world w, h(w) = f(w) U g(w). h (w) is an inconsistent set of propositions. We would try to inakc the best out of this inconsistent set by looking at all its maximal consistent subsets. If a proposition f o l l o ~ ~from s all of them, it would be necessary in \v with respect to h. If it is compatible with one of them, it would be possible in w with respect to h. Unfortunately, there is a tllaximal consistent subset of h(w) which contains all I want in w, namely that 1 will become nlayor and that I don't go to the pub regularly. Thus, conclusion three should be correct under this interpretation of possibility. As it isn't, we have good reasons to prefer my new analysis to the old one. l'herc is another reason. T h e new analysis offers a very natural way fbr treating certain kinds of conditionals. In Kratzer (1978, 1979) I was not able to say what happens, if an iJ1 clause modifies an arbitrary modal. I had to gi\-c meaning rules for each modal separately. Doing this, I nlissed an obvious gcneri~lization. In t11c following section, I will sketch how conditional modalities fit into the present framework.

8 Conditionals I argued in Ksntzer (1978, 1979) that many conditionals seen1 to in\:olvc modals in an explicit or implicit waj-. I want to talk about these conditionals in this scction. 'The! may have the ibllo\4-ing form: (If. ....... ), (then necessarily ......) (If........), (then possibly ......) (If. .......), (then probably ......) etc. T h e second part of these coi~structionsis 3 ilorn~almodalized sentence of the kind we have discussed so far. (Let us forget about the then in what follows). 'I'hc first part is an zficlause. Its job is tlery easy: It makes sure that a hypothesis is added to the modal base requircci by the modal expression to follo~t-.I would like to make this more precise:

Conditional modality Consides an utterance of a sentencc of thc following form: (ifa), (then modal. . . . .) This utterance has two parts: the first part consists of the utterance of the (/lt.lausc, and the second part consists of the utterance of thc then-clause. Suppose that tllc proposition p is exprcssotl by the utterance of a. 'l'hc rule is nou-:

318 Angelika Kratzer (i) T h e first part of the utterance requires one, and only one, modal basc and onc, and only one, ortlering source to be correct. 1 ') (ii) I f f is the modal base and g the ordering source for the first part of the utterance, then f + is the modal base and g the ordering source for the second part of the utterance, f' is that function from possible worlds to sets of propositions, such that for any world w, f+(w) = f(w) U { p f. We obtain different kinds of conditionals by fixing the parameters f'aild g in different ways. I want to demonstrate this with a few examples. For the following, consider utterances of sentcnces which have the Sollowing form: (if a), (then necessarily j) Suppose that p and q are the propositions expressed by a and /j respectively, and that nelesuzri/y expresses human necessity. As our first example, let us look at material implication:

A4a terirr 1 I~~?p/ic.u 1iarr : A material implication is characterized by a tora//y rralzstic mollrrl hrrsr f and an (lttzptlf orrlrrinLgsourccr g. We have to prove that thcse reiluircments for f and g indeed give us material implication. Skutc.h of u Proqf.' 1x1 \jT be any possible wol'ld. Vic must show that q is a hunlan necessity in w with respect to f-'- and g if, and only if, q is true or p is fialse in w . Ctrsr one:

Suppose that p is truc in w . Then f(w) U (17) = f'(w) is a consistent set of propositions. Since ? f ( ~ - = ) {w) and f'(1v) is a consistent suycrset of f(w), nf+(w) = {w) as well. It follows immediately, that in t-his case, q is a lluman necessity in R with respect to f and g if, and only if, q is truc in wr.

''

that p is false in w. Then f(w) ~ { p = } f+(w) is an inconsistent see ( h s e t l ~ o : SUPPOSC of propositions and nf+(\v) is the empty set. Thcn it is \~acuouslj,truc tl~al q is a human necessity in w with respect to fi and p. Our next e ~ a n ~ pisl estrict implication:

S~rzl-tit~zp/il.cition: A strict implication is characterized bj- an e~tzpt,))mor/[rl h~rscf and an cmp[]/ or.rl1~1.in~ sollrce g. Again, 14-e have to prove that these rcquiremcnts for f and g l~icldstrict implication. Shetch qf a Pro?/.; I,et w be any possible world. We must show that q is a human necessity in w with respect to f i and g if, and only if, q is true in all worlds in which p is true. Since g(w) is the cmpt! set, w'c liavc:

The Notional Category of Modality 319 For all worlds 11 and v e nf'. (w): u v. Since f + ( n ) = f(w) U {p) = {p), this mcans that y is a human necessity in \v with respect to f + and g if, and only if, q is truc in all worlds of n{p) = p. T h e most interesting kinds of conditionals are counterFactuals. Thcy arc thc exact mirror images of material in~plications.

A counterfactual is characterized by an empty modal base f and a totally rcalisric ordering source g. It follows from David 1,ewis' work mentioned above, that this analysis of countcrihctuals is equivalent to the one I give in Kratzer (1981). I don't want to discuss counterfactuals in detail here. I do this in Kratzer (1981). T h e idea is this: All possible worlds in which the antecedent p is true, are ordcrcd with respect to their beingI more or less near to what is actually the case in the world under consitleration. "IVhat is actually the case" is a vague concept. There are many ways of uniquely clzaractcrizing a world. In formal ternis: There arc many fi~nctionsg from W which assign to any world w of i\' a subset of the power set of W such that f~g(w) = {w). Let us consider an exampic: T w o totally realistic conversational backgrounds g, and g2 may differ in thc f'ollowing way: for some world w

g, assigns to w a set which contains two propositions, the propositions r and s. g, assigns to u- a set which contains one proposition, thc conjunction (that is the

intersection) of r and s. If gl and g7 filnction as ordering sources, such a difference may becomc important. gl (w) and g, (I!-) induce different orderings on the set of all possible worlds. Consider two worlds u and v such that r is true and s is false in u, and r and s are both false in v. \Vc have now: Y <,,(,,, u, but not v<,,(,,)u. I think that this \T;lgucncssabout "what is the case" is responsible for the vagueness of counterfactuals. It is tvorth noticing that no such vagueness can arise for material implications where totally realistic conversational backgrounds function as modal bases. As a last example, I ~ ~ ~ o like u l dto discuss a kind of conditional which has led to paradoxes in the past."'

Dcorztic' parnilox Consider utterances of the following sentences:

(75) Jedem

Menschen mu13 Gerechtigkeit widerfahren. must justice bc given.

'To every pcrson

320 Angelika Kratzer

(76) Wcnn jcmand If

ungerecht behandelt wurde, mull das Unrecht someone unjustly treated was, must the injusticc

wieder gutgemacht u-erden. amended for bc.

(77) Wcnn je~nand ungerecht behandelt wurde, mull er mundtot gcmacht If someone unjustly treated was, must be reduced to silence wcrdcn. be. In traditional modal logic, sentences like this lead to problems. I think that thesc problems arise because of two reasons: O n the one hand, conditional sentences like (76) or (77) are analyzecl as modalised rnatcrial implications. They would have the following logical form:

O n the other hand, the interpretation of the modal is based on nothing else but a simple accessibility relation. In our case, the traditional analysis would look as follows: T h c proposition I express by my utterance of (75) would be true in a world w if, and only if, it is true in all worlds which are mova//y rrccessihle from w, that justice is given to everyone. A world is morallv accessible from a world w if, and only if, the moral ideals prevailing in \I; are aH realized in it. T h c proposition I express by my utterance of (76) miould be truc in a world iv if, and only if, for all worlds w' which are morally accessible from w, the following holds: If sonleone has been treated unjustly in w+,the injustice is an~cndcdfor in w + . And the proposition I express by my utterance of (77) would be true in a world w if, and only if, h r all worlds w+ which are morally accessible fsom w, the following is true: If someonc has been treated unjustly in,'w he is reduced to siIence in n'. What is paradoxical about all this is that, supposing that the proposition I expressed in littering (75) is true in a world, the propositions I expressed in uttcring (76) and (77) would both be vacuouslq- true in this world. If there is no injustice in any nlorally acccssible world, anything you like is true in all those morally accessible worlds where sonlcone has been treated unjustly. T h e analysis of conditionals which I proposed above, avoids this paradox: Assume that for my utterance of (75) and the first part of (76) and (77), the modal base f was cmpty 2 1 and the ordering source g was determined b\: what is morally conln~anded.If f + is the modal base for the sccond part of (76) and (57), then for any world w, fi (w) contains nothing but the proposition that someonc has been treated i~njustly.Roughly speaking, the three propositions which I expressed in uttering (75), (76) and (77) ivould be true under the following conditions: T h e first proposition would be true in il world iv if, and only if, justice is given to everyone in all those possible worlds which arc closest to what is morally commanded in u-.T h e second proposition would be true in a ~vorld\v if, and only if, thc injustice is amended for in all those possil~leworlds of nf+ (w)which are closest to what is morally com~nandcdin w. And the third proposition would be truc in a world \I- if, and only if, the one who has been treated unjustly is

The Notional Category of Modality 321 reduced to silence in all those worlds of nfs(w) which are closest to what is morally commanded in w-. Under this analysis, it is not excluded, for example, that thc first two propositions are true, but the third is false in a world. For us, a world where injustice is amended for, is not idcal, since there is no injustice in an idcal world. But it inay still be closer to what is ideal than any world where people who suffered injustice are reduced to silence. Whether an analysis of conditionals is appropriate is usually assessed by examining their predicted bel~aviourin certain kinds of inferences like "transitivity", "strengthening the antecedent" or " ~ o n t m ~ o s i t i o n "T. ~ h c~ analysis I am proposing here predicts that these three inference patterns can't be expected to be valid for all those typcs of conditionals which involve a non-empty ordering source. In the literature, the failure of thcse inference patterns is often discussed in connection with deontic conditionals, probability conditionals and countcrfactuals. If we analyse thcse conditionals in the way outlined abovc, their specific bchaviour in inferences is an automatic consequence of the analysis.

Conclusion A person who has a complete grasp of the modal system of' German has certain abilities. It was the aim of this paper to say exactly what these abilities are. As a result wc havc (i) T h e ability of categorizing conversational backgrounds according to thc rcquircinents imposed by the vocabulary. T h e ability of drawing infercnccs of various strength involving two conversational (ii) backgrounds: a modal base and an ordering source. Actually, it is a simplification to assume that there is never more than one 01-dering sourcc involvcd in inodal reasoning. Suppose I draw conclusions ~vhic11involve establishcd facts, the Encyclopedia Britannica, the local newspaper and the gossip I picked up at the corner. And suppose further that thc established facts have priority over thc Encyclopedia Britannica, the Encjiclopcdia Britannica has priority over the local newspaper and the local ncwspapcr has priority over the gossip I pickcd u p at thc corner. I-Iow do we reason in such a case? I think that thc sclnantics of nlodals which I have presented so Gir can be cxtended in u-ay to handle thesc cases. T h e interpretation of a modal cxprcssion a straightfor\~~ard would have to depend on a modal base f and a finite sequence of ordcring soi~rccs g,, . . . g,,. FOI-any world w, g, (w)would induce an ordering on n f(w) in thc usual way. g,- (w)~vould- if necessary - refine this ordering in undoing the "tics" lefi by its predecessor and so on for every successive member in the sequence. Probably, we can't assume that thc diffesent ordering sources form a nati~ral sequence with respect to having priority over each other. Therc may be ordering sourccs which h a w equal priority. This all sounds as if it mere the beginning of my next paper.

322 Angelika Kratzer

Notes I ail1 very much indebted to David Lewis u h o informcd me about his work on ordering seinantics before publication. T h e research for this paper was carried out as part of my collaboration wit11 the L>Ij(;-projccr on modals in Ilusseldorf. I'd like to thank Gisela Briinner, ,411g-elikaRedder and Dieter Wunderlich for discussions, hospitalit) and patience. I am also grateful for the opportunity to talk to hllanfred Ricr\visch, Gerald Gazdar and Ewaltl 1,ang about the topic of this paper. An earlier version was presented at the D F G conference on the semantics of context ant1 vagueness in Rochuin, March 1980. Special thanks go to Colin Brown and Lorraine Tyler for chccking my English and to Edith Sjoertlsma and Marion Iclaver for typing the manuscript.

18 19 20 21 22

Bcch ( 1949), Calbert (1 979), Debrunner (195 I), Grabshi (I '974)) Raynaud (1074), Reinwein (1977)) Welhe (196.5). Vatcr (1975). Strictly speaking, rules like this would have to applj- on a level of 1ogic:il form, whcrc all nlodal operators are scntential operators. See Pinkal (1977, 1979). 'The term is inspired bv what Fr'inzisha R a p a u d calls "source" in French. Lewis, personal communication. See also Burgess (1979). A proposition p is compatible with a proposition q if, and only if, p is compatible with i q i . Likewise: proposition p follou~sTrom a proposition q if, and only if, p follows from ( q ). See Horgan (1977), Kratzer (1977) or Lewis (1979) for a further illustration of this point. Ciustav Deggau ( 1907). Ewald Lang proposed an explanation along these lincs (personal communic;ltion). See Putnam (1975). Sce Tor exarnple Karttunen (1972) or Rrunner and Redder (1979). T h e inspiration for these examples came from Gerald Gazdnr. See Vatcr (1975). I neglect the epistcmic usc of "knt~n" in what follows, which is, ol~coursc.another cliffcrcncc. "Dnrf" can neker have an epistemic intcrpreration. See Lewis (1979). Sce Anscombe (1957), Rrunncr (1979) or von LVright (1963, 1972). Franziska Raynaud raised an objection of this kind, personal comn~unication. Instead of the uniqueness contlition, a Pinkal solution would he preferable hcre as well. Thcrc is quite a bit of vagueness around conditionals. I4i1nsson (1969), van Praassen (1972). I.ewis (1973) give a tlctailed rliscussion of the problem. This assumption is not essential. See for example Lewis (l973), Kratzer (1979).

References Anscombe, Gertrude E. M. 1957. /nlerr/ion. Oxford: Basil Hlackw-ell. Bech, Gunnar. 1949. Das seinantische System der deutschcn Modalverba. ?i*az'cir~s 1/11 C'~.c./l> 1,iryrrisliqr4e I/. Cop~uhnga~e 4. Rrunner, Gisela. 1979. Strulitur und Funlition motlalisierter Schliissc in gcsprochencr S~~';ichc, unpublished manuscript, Dusseldorf.

The Notional Category of Modality 323 Brunncr, Gisela, and Reddcr, Angelika. 1979. Einige Tests zum Modalvcrbgcbrauch, unpublished manuscript, D~isseldorf. Burgess, J. 1979. Quick Completeness Proofs for Some Logics of Conditionals, unpublished manuscript, Princeton. . VEH Verlag Ruscha, Joachim, Gertraud Heinrich and Irenc Zoch. 1977. . 4 ~ o h l z ~ c r h e n1,cipzig: Enzyklop'ddie. Calbert, Joscph and Heinz Vater. 1975. -dspekte t k r iblodalitdt. Tuhingen: M . Niemcyer. Debrunner, Albert. 1951. Von den modalen Hilfsrerben im Deutschen. Sf)r~t~.h.tpie,ycI, Mi//eil~rrr~c~n (les D r u t ~ ~ ~ h ~ - S c h i ~ e i z ~Sprrrchcereins ~ r i s ~ ~ h e n 7(6-10). Deggau, Gustaw. 1907. Uber den Gebrach und die Hedeutungscntwichlung dcr Hilfsverbcn "k611nen" und "mcigen". Dissertation, GicRen/Wiesbadcn. Edrnondson, J. 1979. Gradienz und die doppelte Infinitiv Kons~ruktion,unpublished manuscript, Rcrlin. van Fraassen, B. 1972. The logic of conditional obligation. 3ournnl i!/'Plrilosop/~i~Irl L o ~ i i I. . Grabski, h.1. 1971. Slntax und Scmantik der h4odalverben in Aussagesarzc dcs Deutschcn. Dissertation, Stuttgart. Graf, Osliar Maria. 1917. Das LrBeti rrrerner i2lulte~.Xlunich: K . Dcsch. Hansson, B. 1969. An analysis of some deontic logics. Nous 3. Horgan, Terence. 1977. "Could", Possible Worlds and Moral Responsibility, unpul~lishcdrnanuscript, D e Pauw University. Karttuncn, Lauri. 1972. "Possible" and "must". In John P. Kimball (ed.), .Syt~turrtnd Scnrrintrc:~,vol. 1, Neb York: Academic Press. Kicfer, Fercnc. 1980. What is Possible in Hungarian, unpublished manuscript, Stockholm. Kratzer, Angclika. 1977. Wllat "must" and "can" must and can mean. J,ingui.q/irj iirld Pkrlo.vop/i,~~ I: 337-55. Kratzer, Angelika. 1978. Sevnnntik der R ~ ( i eI S e ~ n ~ z r i ~(!f-speer,k]. ic.~ Khnigstcin: Scriptor. kratzcr, ,9ngelika. 1959. Conditional necessity and possibility. In Railrcr 13auerle, Urs 14;gli,and Arnim von Stechow- (cds), S e m a n / i c s f j . o D ~ ~ ~ ~ YPoitzt.~ L ' I I I l/'ien?, Berlin: Springer-I'erlag. Iiratzcr, AngeliLn. 198 1. Partition and revision. T h c semantics of counterfactuals. j'otirnnl ~!/'Phi/osop/~li(rlLog~rli~. 10: 201-16. Lewis, David. 1973. Courz~cf:firrtuil/.t. Oxford: l3lnckwell. Lewis, David. 1979. Scorekceping in a language game. 111Rainer Biiucrlc, Urs Egli, and Arnim von Stechow (eds), Semantic.s~fiomD!rererlt Poinls of L'iclv, Bcrlin: Springer-ITerlag. Lyons, John. 1977. Setnaiztir:s, vol. 2. Cambridgc: Cambridgc University Prcss. Pinkal, Manfred. 1977. k-orite.~twnd Bedtwung. Tubingen: TBL-Vcrlag Narr. Pinkal, hlanfred. 1979. How to refer with vague descriptions. In Rainer Bkuerlc, Urs Egli, and Arnim yon Slcchon (eds), .Senia~ilic.s./rol~~ Dijfirrir~Poinrs of T.%JP, Berlin: Springer-Verlag. Putnam, I-Iilary. 1975. T h e meaning of "meaning". In ,Ziirzd, Lungltuge i~ririReali~.y:Plrilosophrc~al Prcpers, vol. 2, Cambridge: Cambridge University Press, 21 5-71. Raynaud, Frnnziska. 1971. Lcs verhes de modalite en allcmand contemporain. T'hkse prkscntkc dcvant I'Universiti: dc Paris. Reinwein, Joachim. 1077. Mo~lulz~erh-Syntax. Tiib~ugen:TBL-Verlag Narr. I'ater, Heinz. 1975. "MTerdcl~" als Mndalvcrb. Sprfichspie'gei. Mitteilrdng~nJcs Drutsrh-.Sr-hn~eizerischr?~ Spra i.h-rvreins 7(6-10). Wclke, Klaus. 1965. Untersuchungen zum Systcm der Modalverben in dcr cleutscl~enSprache dcr Gegenwart: ein Bcitrag zur Erforschung funktionaler und syntalitischer Bczichungen. .S'rkr!fien z ~ r Phonrrik, Spt.urhlrissensrlrr!fi zrnd Ko?t~nau~~ikntio~~/(IrscI~~~ng 10. Wright, Georg Henrili von. 1963. Practical infercncc. Ph11osophic.ul R t z ~ i r n72. ~ \Vright, Gcorg Henrili von. 1972. On so-called practiciil inferencc. Ar.///Sor.ic~/ogir.a15.

The Algebra of Events Emmon Bach

0 Introduction A number of writers have commented on the close parallels between the mass-count distinction in nominal systems and the aspectual classification of' verbal expressions (Allen 1966; Mourelatos 1978; 1,. Carlson 1981; Hoepclman and Rohrer 1980) that Iias heen the subject of much attention in recent years in linguistics and philosophy. To take just one class of examples for now, there is a parallel between the two scts of distinctions in their cooccurrence patterns with expressions dcnoting- numbers or amounts, as in Examples (la)-(%): Much mud was in evidence. *h4uch dog was in evidence. John slept a lot last night. *John foui~da unicorn a lot last night. Many dogs were in the yard. *Many muds werc on the floor. John fell asleep three times during the night. *John slept three times last night.

(By the use of "*" 1 intend to indicate two things: that we have to do a certain amount of work to impose a special interpretation on the sentence and that the intcrprctation is i shaped by the presence of the number or quantity expression.) i T h e basic aim of this papcr is to try to clucidalc this propo1-tion: cvcnts: processes:: things: stuff. T h e account draws heavily on a recent paper by Godchard link ' on the count-mass-plural domain (Link 1983) as well as on the work of a, nuinbcr of writers who have contributed a great deal to our understanding of "verbclassification".' In Section 1, I review briefly the classification and in Section 2 idink's analysis for the nominal domain. In Section 3, I set forth our proposals ahout cvcnts and processes and in Section 4 take up a ilumbcr of problems, somc with, somc without, solutions.

The Algebra of Events 325

1 Events, Processes, States Here's a schenle of the kinds of distinctions we want to doal with (based on L. Carlson (1981), but using our terminology in part): eventualities states

A static (b)

dynamic (a)

non-states

/", events

processes (c)

A A

protracted (d)

momentaneous

happenings (e)

culminations (f)

Typical examplcs are:

1

(a)

(b) (c) (d) (e) (f)

+

sit, stand, lie TOT be drunk, be in New York, own x, love s, resemble s walk, push a cart, be mean (Agentive) build x, walk to Boston rccognize, notice, flash once die, reach the top

1 will take it as givcn that it is necessary to have at least this much of a classification if we are to deal adecluatcly with the syntax and semantics of English. A great deal of evidence for this point has been given in the last several years, for example in connection with attempts to understand the English progressive and similar construc7 tions in other languages.- Most recently, Hans Kamp (1981) and E. Hinrichs (1981) have shown the necessity for these distinctions for in~erprctingnarrative structures.

2 Mass, Count, and Plural in the Nominal System In the work :dludcd to above, G. Link (1983) argues for the adoption of a somewhat more richly structured model than those made available, for example, in h4ontague's work,"n this scction, I will briefly sketch the outlines of Link's system. The main idea in Link's semantics is to give more structure to the domain of individuals. Along with ordinary individuals like John and Mary as in standard interpretations of the predicate calculus or in Montague's work we arc to have pli~ral individuals like those denoted by the ~.bzi/Jvenor j'ollrz and ~Ilat:)tas well as quantities of "stuff" or matter that correspol~dsto individuals of both kinds, such as the gold in Terry's ring or the stuff that makes up thc plural individual John m d ~ a r y . ~ Moreover, ccrvain relations among these various subdomains and the elements making

326 Emmon Bach them up are proposed. I present thc essentials in an informal way (fbr precise details the reader is referred to Link, 1983). Start with a set A, of individuals of the more familiar sort, for example, John, Mary, this tahle, Terry's ring. We extend this domain by mcans of a join operation to clcfinc a superset E ns follow-s: (i) AI E, (ii) If a, p E El tllen the i-join (individual join:

XU,

P) of a and P E E,.

So the i-join of John and Mary is in E, if each of John and Mar) is. We establish a partial orclering on the members of E,( 5, ) by saying that a is "less than or equal to" (or "is an individual part (1'-part) of ") just in case thc I-join of cx and /I is just /I itself. Thus the individual John is an i-part of the plural individuals John and Mary or Terry's ring and John. 'I'he individuals from which we started are atoms in thc big structure that we are building. ,4n1ong the elements of 14, (and hence E,) there is a subset which forms a special subsystem of its own. These are the portions of matter or stuff, for example, the gold of which Terry's ring is composed. This subsystem has its own join and partial ordering (m-join: U,,,; m-part: Call this set Dl. Finally, we nccd to specify the reli~tionship between the system of D, and the rest of the domain. We do this by assuming a mapping h, from indi~riduals(atomic and plural) to the stuff' out of which they are composed. This mapping should satisfq- the requirement that the ordering 5, among the individuals be preserved in the ordering F,,, among the quantities of m a t t c ~nlakiilg them up (it is a homomorphism). Moreover, h,(x) = s just in case x E D;. For example, if John is an i-part of the plural individual Terry's ring and John, then the stuf'fn~aliing up John had better be an m-part of t l ~ cstuff making up Terry's ring and John. Notc that we have two different part-whole relations. John is an i-part of the individual John and Mary, but John's arm is not an individual part of John, both arc atoms. On the other hand, the stuff making up John's arm is an nz-part of the stuff making up John. Note further that the same quantity of stuff can correspond to many different individuals. For example, there may he an individual falling into the extension of the singular count noun man, say John, but there is also a plural inclividual filling under the extension of thc plural noun cells such that the values for h, given the two arg~lments are identical. T h e two individuals are members of the equivalence class induced by fhc relation of material identity. Link calls a system of this sort a "Boolean modcl structure wit11 homogeneous kernel" (boosk). Some consequences of Link's construction that T find interestirlg and appositc for the present context arc these (I haven't given enough details to sho~t.that these consequences follow):

s,,,).

Suppose Eiengsta is a horse and Wcngist is a horse. Then the plural individual 'T (contrast Inass Hengsta and Hengist is not a horse, but is in the extension of I~orxc. terms). (6) Suppose the plural individual A and B is in the extension of hon\.es and likewise C and D. Then the plural individual A, B, C, and D is also in the extension of horses (cf. mass terms).

(5)

The Algebra of Events 327

(7) Even if the individual that is the quantity of gold co~nposingTcrry's ring is old, Terry's ring need not be. (8) T h e two meanings of sentences like John and Mercy Iified the h o . ~(each vs. together) can be nicely represented in Link's semantics by adding the interpretation provided for the plural individual to the interpretation provided, say, in Montap~e'sP T Q

3 The Algebra of Events and Processes We now want to try out Link's ideas in the domain of eventualities, that is, to characterize the structure of the model when we extend it to the donlain of events and processes, which for the moment I will consider just as new kinds of elements in the (sorted) domain. I will start by considering cvcnts to bc analogous to the singular and plural individuals and bounded process ("bits of process") analogous to thc portions of matter that make up the "material extensions" of those individuals. Our new system will then include the following: (1) El,:the set of events with join operations U,, and partial ordering 5, (a complete atomic Boolean algebra); atoinic events; (2) ,4, C 4,: (a complete join (3) Dl, C A,: bits of process with join Up and partial ordering scmila~tice); (4) In addition, we will need two temporal relations on El,x E,. : r x : "strictly prccedes" (tr., irr., a s ~ m m . ) , ': "overlaps" (nontr., refl., synlm.) (cf. Bach 1981; Kaillp 1980); K , ") to (D,, U,,, I p , cx, ") such that ( 5 ) a honlomorphism h , from (E,, U,., I,, ) r iff x E D,,, (i) h , ( ~= (ii) hl,(aU,/3) = IZ,(Y)U~~,(P), and xRP + h,.(ct)R'h,(P) for R , x ," and R' =
=<,.

For purposes of illustration, I will assume that tenseless clauses of 1.7nglish arc to be interpreted as denoting sets of eventualities, i.e. members of the domain El, (for some discussion of the general kind of model structure I assume, see Hach, 1986). So here are some examples of the kinds of eventualities that correspond to the above distinctions: John kiss Mar?;: atoinic event mar^ stunlble and Mary twist her ankle: plural event Mary stumble: atomic evcnt People discover the hiddcn cove: plural event Sally build a cabin: atomic event Sally pound in a nail: atomic event Jones poison the populace: atomic event Jones pour poison into the water main: atomic event

328 Emmon Bach Our homomorphism /I (henceforth I will drop si~bscriptson all symbols where it is clear from context which domain we are considering) will deliver up for us the bounded bits of process corresponding to instances of each of these event types. Just as in the case of the nominal domain it is esceedingly difficult to find English expressions which corresyond to these "pure processes" (cf. our remarks 011 """ after our first examples). Somc intuitions I want to capture with regard to the above examples are these: i l l 1 (10) and ( I 1): a plural event of type (10) has (necessalily) a singular cvent of type (1 1) as an t-part, and the processes associated by h with the latter is a p-part of the process ilssociated with the former. ,4d (13) and (14): an event of type (14) might very well be such that its proccss is a p-part of the process associated with an event of type (13). Ad ( I S ) and (16): Events of these two types might be materially (processually) equivalent while the events themselves are different. Thus, Jones might very well intentionally your poison into the water main (in order to rid waterbeds of bedfish) and not intentionally poison the populace (cf. Davidson 1980, pnssinz). Just as in the nominal domain (Link 1983), I will assume that our interpretation assigns various predicates to different classes according as they fall under the sort of classification outlined above. (HOW we decide or do this will not be my uonccrn in this paper.) So Dying names an atomic kind of event, Running docsn't, and so on. Familiar properties of these various kinds of eventualities will follow, such as indivisibility and additivity (cf. L. Carlson 198 1; Bach 198 1): no proper p-part of a dying is a dying; the filsion of two runnings is a running, but no two dyings are a clqsing. I will return bclow to some interesting probleims connected with such facts.

4 Some Parallels and Puzzles We have found it quite instructive to think about parallels and differences obtaining between the two domains. In a number of places questions and observations about one of the donlains has led us to consider problems in the othcr domain in a new light.

4.1 Packaging and grinding It has frequently been observed that practically any count noun or name' can be used ils a mass term: Therr was [Jog .splait~rer/(l/l oaer the r o d ; il/lucl~~nissiorzaq)n7as ca~ewa! I ~ ~ L J .fisriz!nl (David Lc-cvis's Universal Grinder, cf. Pellctier 1979). Moreover, the opposite switch occurs as bvcll: tuu~/.v= "kinds of mud", ic~-trc~crnl= L L portions of ice-cream" (Universal Packager). In each case, we have a change of meaning with no overt masking in the forin of thc word. In the verbal domain, we find the same sort of phenomenon. Dowty (1972) observed that practically any process verb can be uscd "evcntuallq-", given the right context. One of his examples was the process verb look Jar. One of the characteristics of process verbs is that they don't occur comfortably in the context NI-' ,fitrisl~rd bring: ?I jit~ish /oukti2g ji)r ( E t [ l ~ i ~ . oYet ~ r ~ .in the context of a library with a welldefined search procedure, a sentence like Isfit/iskrd /ooking.fi~r(1 hook seems perfectly ordinary.

The Algebra of Events 329 In English, the way of switching back and forth between count and mass, cvcnt and process typically iiivolves no change in the forms involved. T h e difference is rather induced by the context. In other languages, overt nlorphological processes or relationships are available or obligatory, for example, in the perfective-imperf'ectivc contrasts in Slavic languages. This raises important qirestions of principle for the analysis of English, D o we want to invoke formation rules with zero-morphology (identity opcrations in the syntax of words), as in Link's rule for forming the mass-term counterpart to a count noun like apple? O r do we want to somehow give meanings for words that are unspecified along this dimension? It seems to me that there is an asymmetry in these relations between count and noncount meanings that runs in the same direction in the turo domains. That is, if we start with a count meaning and derive the non-count meaning (as in Link's rule) there seems to be a regular and predictable meaning. T h e mass-term upplC seems to mcan the stuff such that tl~ereis at least one apple such that that stuff stands in the constitutionrelation to the apple (but see below, Section 4.3 for some remaining problems with this account). On the other hand, going in the other direction, the connection seems much less systematic, as already- noted. A beer may be a serving of bccr or a kind of beer. Similarlj-, in the verbal domain, when wc put a process expression into a count context, we must come up with some kind of corresponding- event, but just what it is is relatively frcc, perhaps the beginning of the process in question, or some bounded portion of it. This asymmetry is predicted by our formal set-up: there is a fbnction (homotnorphism) from the count elements to the non-count ones, but it is a many-to-one mapping so that we can't in general expect a unique answer hen we ask what count element this portion of non-count stuff n i g h t correspond to. Count elements come as alread! bounded and discrete items. Therefore we can count them. Non-count elcments don't and therefore need, some additional specification in order to be used as countable expressions with plurals or nun~bers.Furthe]., expressions which carve out measures or quantities of stuff, - pounds of, portions of, etc. - cannot go with pure count-items in the singular, but demand interpretation of the count-itern as mass-term or process counterpart. Moreover, for plurals size and measure are relcvant to determining naturalness and usefulness of the particular expressions; t l ~ otolzs of horses is odd for practical reasons in a way that tn?o t o l ~ s(!/' benns or.f$y toils (![horses are not (cf. L. Carlson 1981, on these and many other details). Thcrc are interesting puzzles about counting that we will return to below (Section 4.4).

4.2 The partitive puzzle Uowty (1977) and others have discussed the socalled "imperfective paraclox" (1 prefer to call it a puzzle). Briefly, the puzzle is this: how can we characterize the meaning of a progressive sentence like (17) on the basis of the meaning of a simple sentence like (18) when (17) can be true of a history without (18) ever being true? (17) John uras crossing the street. (1 8) John crossed the street. (See Vlach 1981; Dowt!; 1979.)

330 Emmon Bach Naturally, we want to use the apparatus we have set up to provide an account of the English progressive, perhaps along the lines of Vlach (198 1). Thinking about how to do this has led us to see that there is a perfectly parallel problem in thc nominal domain, which we call the "partitive puzzle". Consider Link's account of the following sentence: (19) There is apple in the salad. Link's interpretation amounts to this: there are some apples, such that some of the stuff making them up is present in the salad. Note the existential quantification over apples; the sentence could not be true of a history whicl~never had any apples in it. This seems reasonable enough for this sentence, but consider the following: (20) This is part of a paper on natural language metaphysics. (2 1) We found part of a Roman aqueduct. It seems as if (20) could be true even though (alas!) the paper in question nevcr reached fulfilment, and (21) true when there no longer is an aqucduct or cven if progress on the construction was interrupted forever by hordes of barbarians from the north. Let us look more closely at Link's account. T h e denotation of thc mass term correspondent ml,of a predicate P is given as this (p. 309):

(Here, sup stands for supremum.) That is, the denotation of upple (uscd as a predicative mass term) is the set of quantities of matter that are rn-parts of the valuc o f applied to thc set of apples in the world. Thus, no apples, no apple. 13ut these could surely be a world in which it was possible to artificially manufiacture apple without there being any apples, or for less farfetched examples, considcr again Exan~plcs(4) and (5). Such examples show that we need to allow for a more indirect rclation between the denotation of a mass predicative mass term and the corresponding count predicate. Basically, we need to be able to say when certain stuff is of the right kind to qualify as falling under the extension of the mass term, or better we need to assiime that we can say m~he1.1this is the case. T o actually givc criteria is no part of linguistics (cf. Putnam 1975, passim). Further, although we have assumed that the two domains of things and stuff are separate, it seems to me to be reasonable to assume that our knowledge of what qualifies as a quantity of apple or mud or gold is based on our understanding of what is meant by the term phrases apples, murl, or gold, understood as names for kinds (G. Carlson 1977) or properties (Chierchia 1982). Both Carlson and Chierchia argue that such terms are more intensional than the properties of Montague, which are functions from worldtime pairs to individuals. We may say that a property or kind determines such a function, which then may hc used to get thc denotations of the corresponding prcdicativcs apple, go/(/ and mud. So to say that therc is apple in the salad is to say that there is some stuff in the salad of the right sort as to qualify as apple and the latter involves

The Algebra of Events 331 appealing to our knowledge of the kind of apples or the property of being an applc. It should thcn f ~ l out l of our theory that particular apples are made of applc and so on.

4.3 How old is the gold? Link provides a nice analysis of the puzzle presented by a sentence like this: (22) The gold making up Terry's ring is old but the ring itself is new- (not old). Puzzles like this one are among the best evidence for not identifying things with theis material counterparts. But there is still a problem. The interpretation of (22) is this: The x such that .v makes up Terry's ring and is gold is old but Terry's ring is not old. No contradiction, sincc s and 'Terry's ring asc not the same thing, ,z. is just the value of 67 with Terry's ring as ~rgument.But now consider a sentence like (23):

I; I

1; I

/

(23) The snow making up this snowman is quite new but the H 2 0 making it up is very old (and the H and 0 even older!). The interpretation of this sentence comes out like this: The ,r such that ,t. constitutcs the snowman and x is snow is new but they such that 31 constitutes the snowman and )I is water is very old (not new). This is contradictory according to Link's account since x and j/must be identical (since h is a function). If we follow Link's sage advicc - "our guide in ontological matters has to be language itself" (Link 1983, pp. 303f.) -then it seeins to me that we have to set things up in such a way that we can refer to individuals under a description, somehow. This puzzle is closely connected to the ncxt one. If we follow Link's advice, then we must acknowledge that two things with contradictory properties cannot be identical. Thus the snow making up the snon7manand the HrO making it up must be different, and neither can be equated with the undiffercntiated quantity of matter given by Link's homomorphism. What to do? The first possibility is to ackno~vledgethat our language allows us to talk ahout chains of composition, so to speak. T h e snow in the snowman is itself made up of the water in the snowman (plus air) and so on. What the example shows, then, is that we cannot use the constitution relation directly in an interpretation of a phrase like rhr snon? maki~fgrkp rhe snom?ma?z.Our interpretation of such phrases must be such that it does not hold that if x makes up LZ and y makes up a then x = , ) I . We can essentially keep 1111 of Link's apparatus including the hon~omorphismand the equivalence classes generated by it but merely amend the way in which English words like rnrrk~. up, constitute or phrases like the gnlci in the ring are interpreted. A second way would be to remove altogether the entities in L) from the domain of individuals. I explore one way of doing this based on Cresswell's (1973) metaphysics of possible worlds and individuals in Bach (1980). This n-ould amount to saying something like this: Slqlf'an sich (just like the Dirv crn sich) can have no proyer~ies,at least as far as our language is concerned.

,

332 Emmon Bach

4.4 How many things are there in the room? In both domains inany writers haye pointed to characteristic properties like additivity, subdivisibility, antiadditivity and atltisubdivisibility which play clear roles in giving an account of entailment relations among sentences: I-Iengist's ear can't be a horsc, mud plus mud is mud, a horse plus a horse isn't a horse, and so on. But in both domains there are clear and ordinary examples of count items that don't follow thesc restrictions. These are words like thing, r.z:ent, happerr, and so on. Suppose it is true that something happened, then in the normal case there are smaller subevents that make up thc big thing that happened that are also happenings. Similarly for things. In both domains we are at something of a loss to try to answer questions like these:

(24) How many things are there in the room? ( 2 5 ) How many events took place in the last hour? Gupta (1980) has stressed the importance of criteria of rcidet~tificationand individuation in the logic of common nouns. Our disc~issionhere shows chat principles of illclividuation arc: crucial for expressions and conccpts in the verbal domain as well. We follow Link in not requiring that the subdomains D; and D, be atomic Boolcan algebras. This is as it should be. It is not part of linguistics to dccide whether all matter is atolllic or all happenings are reducible to little granules or process. Indeed, if contcinporary physical theories arc to be believed, such ultimate questions are basically incoherent. Events and processes are disjoint, and this seems to be more an artihlct of our language or conceptualizations of the world than something ilbot~tthe world itsclf, so that probably here too our strictly semantic theories should remain silent.

Notes A large part of the substance of this paper derives from joint work \.I ith Barharii I'artcc, first presented bx us at a cdloquium at Stanford University, hencc the frequent "ne". I taltc full responsibility for errors or infelicities. Grateful ackno\sledgment is tendered to the Max Planck Institut fiir Psycholinguistik in Nijrnegen, which supported part of'the work reported on herc. Besides the writcl-s mentioned in the first paragraph, see for cxnn~plc,thc excellent survey in Dowt!; (1979) and the rcfercnccs cited thc1.c. T h e classic mndcrn works dealing with vcrbclassification are Kenn! (1963). and Vendler (1957). T o n ~ !knonledgc, Vcrltuyl (1072) was the first extensive work which recognized the import;~nce of these distinctions for linguistic theory. 2 Do~vty(1077), TTlach( I 98 I), for cxamplc. 3 It is important to noticc that Link's proposals differ cruciall!- from prcvious attempts to deal with plurals w htch constructed interpretations for plurals in purely set-tha~reticways. as for cxumple in Bennett's (1971) classic trcatmcnt. 4 Strictl!' speaking, w-c will hate the corresponding NP ctcnotations, that is, propert! scts fi)r thc individuals mentioned. I ignore this complication throughout thc pilpcr. 5 T.ink does not deal with rhc usc ofnamcs in nlass contexts: 7 ' / 1 q ) 1 p u / , / i z ~porriit/.r c//'Pork)l ir,/o 111c

I

slcrl'.

The Algebra of Events 333

References

'

Allen, Robert Livingston. 1966. T h e l 4 - l , Systcrn c!f'Prt*sen/-Drql .-lmeri~lrn E1iglisli. T h c Hague: Mouton. Bach, Ilmnion. 1981. On time, tense, and aspect: an cssay in English rnetaphj-sics. In Peter Colc (cd.), Rr~rlir.(ilPragrnrltii.~.New York: Academic Prcss, 62-8 1. Bach, Emmon. 1986. T h e metaphysics of natural language. In Ruth Barcan Marcus, Gcorg J. W. Dorn, and Paul Weingartner (eds), Logz~,,Metlrodolo.g)l a~lrlPlzilosophy of Sr.i~nr.e:PI-occ.e~/ingz(!/'/Ire Sezlcn/h I n t e r n n ~ ~ o n ~Congress rl I!/' Logi~,n/lethuclo/ogy ilnJ P/ziZos~pl~y of' Sclrrzcr, Salzburg, 1983, Amstcrdani: North-Elolland. Bcnnett, hlichael, R. 1974. S o ~ n cExtensions of a Rilontaguc Fragment of English. Ph.D. dissertation, UCLA. Distributed by Incliana Uni\~ersityLinguistics Club. Carlson, Gregory. 1977. Reference to Kinds in English. Ph.D. dissertation, University of Massach~isctts, rlmhcrst. C;arlsnn, Lauri. 1981. Aspect and quantification. S y n t a s lirid S e ~ r r ~ t ~ 14. ~ics Cliierchia, Gcnnaro. 1982. Nominalizations and hlontague grammar: n semantics without tjpcs fi)r nr~turallanguage. Lzngzlistlr.s rrnd Pl~i/i)sop/~j~ 5 : 303-54. Crcsswell, May. 1973. Logics iltzd Lamgr1lige.t. London: Mcthucn. Davidson, Donald. 1980. Eis(iys nn Ac.liol~s( z ~ I Ezlrnts. / Oxford: Clarendon Prcss. Dowty, David R. 1972. Studies in the Logic of Verb Aspect and Timc Refcrcncc in English. Pli.11. dissertation, Uni~crsityof Texas, Austin. Dowty, David R. 1977. Toward a semantic analysis of verb aspect and the Lnglish "imperfcctitc" progressiw. LznLquisril.s and Philosophj~ 1 : 45-77. Dowty, David R. 1979. C.170rd /l.le(rrzing uniE Monr~lgusGrclmnzi~r.Dordrecht: D. Reidcl. Gupta, Anil. 1980. T l ~ Logic e r!f'Cummon LVuuns. New I-lavcn, C:onn.: Yale Lnivcrsit!. Press. Minrichs, Erhhard. 1981. Temporale Anaphora in1 Englischcn, Magisterarheit, University oi'Ti~l)ingen. Hoepelman, Jakob and Christian Rohrer. l(1XO. On the rnass count distinction and the Frcnuh Imparfdit and Passe simple. In Christian R o h r a (ed.), Tz'lr~e, Ttnst., t r d Q ~ i i z n t ~ f i r P~oci~~t1111gs .~: of /he Sluttjyrt Cor!/iren~.eon lire Logic o f Tense is?irl Quiint!fii.a/Ln. Tiibingen: Nicmcyer, 029-45. kan~p,IIans. 1980. Some remarks on thc logic of changc, part I. In Christian Iiohrcr (ed.), Tlrrr~, Tensr, tinrl Qziantifiets: Proceecdings o f t h r Sluttg~~trr~ Co~!fi.rrnc.e0 ) r 11ze 1 , o ~ l cr!f T l ~ t s z( ~ i r Qz~rrnltficvt //on. Tiibingen: Nicrneyer. Kamp, I-lans, 1981. Evcnements, rcprescntations discursives ct refkrencc temporellc. La~igrdr~~gr 04: 39-64. Kenny, Anthony. 1963. Ac/ion, Einc~rlorz,ar~rlRfiEl. New York: 14umanitics Press. ],ink, Godehard. 1983. ?'he logical analysis of plurals and mass terms. In Rainer Bauerlc, Christoph Schwarze, and Arnim von Stechow (cds), :tlenning, Use, iznd Int~~rprc/ri/ioi~ (!/'I,rir~,y~r~pc, Hcrli11: Walter dc Ciruytcr, 302-23. Alourclatos, 8lexandes. P. D. 1978. Events, processes and states. L i r ~ g ~ ~ M ~t iiltzl lP1111o.~opI~)~ i 2: 41 5-34, Pclleticr, F. J. 1975. Non-singular reference. In J?. J. Pelleticr (ecl.),cL1tlss Ter.rrrs: So?iw Pl~ilosopbrci~/ Proble~ns.Dordrccht: D. Rcidel, 1-14. Putnam, Hilar!-. 1975. Phil/).soph~irllPapzrs, vol. 2, ,2/linr/, Lungrl(ipc utitl R~tilitll.Cambridge: C:ambridge Univcrsity Press. Yendler, Zeno. 1957. Verbs and tinics. I~lrilosophii.alR t r i e n ~-56: 113-60. Yurliuyl, I~lcnh.1972. On I/IPC o n ~ p o s i ~ j o n'-ufui.e n ~ ~ I o f //re ,4sptrr.<. Dordrecht: D. Reiclcl. Vlach, Frank. 1981. T h e semantics of the progrcssivc. Sl/n/a.v r r ~ r .Sernurrtics ~l 14: 271-92.

Generalized Conjunction and Type Ambiguity Barbara H. Partee and Mats Rooth

1 Conjoinable Categories It is well-known that in English and in inany other languages, virtually c\rerli major category can be conjoined with nnd and or. T h e question we address here is whether we can give a singlc meaning for m d and a single meaning for or that co\.ers their uses across the full range of categories. In order to make the question more precise and forestall a qi~icknegative answer, we need to distinguish the central usc of and from a number of special uses. Informally characterized, what we mean by the central use of (inn' with conjuncts of' ilny category is related to the sentential conjunction nr~d with thc meaning of ordinary logical conjunction (although becausc of interaction with othcr logical elcmcnts in the scntence, there may not always exist a natural paraphrase in terms of conjoincd English sentences.) Examplcs of the central use of nnd with various categories arc given in (1); some special uses which we will not treat are givcn in (2). (l'here do not appcar to be any special uses of or which need to be excluded; if there arc, we rtrc not treating them.)

(1) (a) John and Mary are in Chicago. (b) Bacon and eggs are (both) high in cholesterol. (c) Susan will retire and buy a Farm. (d) She was wearing a ncw and expensive dress.

(2) (a) (b) (c) (d)

John and Mary arc ;I happy couple.' Bacon and cggs is my favorite breakfast. Susan will try and sell her house. She was wearing a blue and white dress.

We assume a franicwork in which all kinds of conjoined constituents arc directly generated syntactically, not derived via conjunction-reduction from conjoincd sentences. In order to be able to say that it is nevcrthelcss thc same ar~rlant1 the same or

Generalized Conjunction and Type Ambiguity 335 that appear in all the constituent conjunction rules, we want to be able to give a single meaning for (normal) and, and a single meaning for or. Wc bcgin by reviewing the type thcory of Montague (1973) (PTCI), and his treatment of phrasal conjunction. Then in section 3 we present a generalized conjunction schema that is a natural generalization of that presented in Gazdar (1980). In section 4 we show some repercussions that the conjunction schema has on h,!lontague's type theory and propose changes (in p~~rticular, that extensional verbs bc assigned simpler types than intensional ones, plus predictable homonyms of higher type.) In section 5 we compare this approach with that of Kecnan and Faltz (1978), and ill the final section urc discuss some difficulties and summarize our conclusions.

2 Montague's Type Theory We assume familiarity with P T Q , but review thc type theory here for future reference. The basic types are u and t , the types of entities and ti-uth-values (sentence extensions) respectively. Tllerc arc two recursive rules:

If a, b are t?pes, then (a, b) is a type (the type of functions fson~a-type things to b-type things) (ii) If a is a type, then (s, a) is a type (the type of functions from world-time pairs to atypc things) (i)

In the rest of the paper, we will simplify t11e discussion by omitting all the s's from types that should contain them. This is purely for espository purposes and docs not affect the substance of the discussion or the proposals; wherever it could make a difference, wc provide the "correct" tseatment in a footnote; intensional types are also discussed in Appendix A. Omitting s's, then, Pl'Q has the follo~vin%correspondence hetween syntactic categories and scmantic types (not a complete list):

(I) t (scntence)

-

t

e (empty) - c CN, IV - (c, t) rI' (term, or NP) ((e, t), t) TV - (type (T), type (IV)) -

In particular, intral~sitivcverbs (and verb phrases) are treated as denoting scts of entities, term phrases as denoting higher-ordcr scts, and transiti\,e \;erbs as denoting functions from term-phrase interpretations to sets of entities.2 Montaguc introduces linrl and or syncategoren~aticallyfor three catcgorics in PTQ t, IV, and T.' T h e rules produce pieces of derivation trees of the f'ollon~ingfonns:

(2)

(a)

(Dl lifld

44'1, t

A

(b)

6, a~rcl6?,IV

A

(c)

a1llnd a ? , T

A

336 Barbara H. Partee and Mats Rooth His translation rules provide the following translations for the thrce cascs (where IP', is the translation of 1 1 7 1 , ctc.)

(3) (a)

(~'lw;

(b) 3,x[Si(x) A 6/2(x)], x a variable of type c (c) AP[ix{(P) nai(P)],P a variable of type (e, t)

By linguists' usual standards, therc is clearly a generalization bcing missed here. It is no accident that the same words llnd and ur are introduecd in cach rule, and the translations fbr IV and T conjunction are clearly predictable from thc translation of corresponding sentential conjunction plus the type assigned to the category: provide each conjunct with the type of variables they necd as arguments to make a sentencc (identical variables fbr each conjunct), conjoin the resulting sentences, then lambdaabstract on those variables to get back to the original phri~saltypc. We could clearly do thc same thing for higher types such as 'I'V, just by adding on morc variable arguments and then abstracting on them in the corresponding order. Wc cspress this more precisely in the ncxt- section.

3 Generalized Conjunction Gazdar (1980), \:on Stechow (1974), and Kecnan and Faltz (1978) (in their "Lifting Theorem") describe how conjunction in D(,,,I,) (the possible denotations for a phrase with type (a, b)) can be defined in terms of conjunction in Dl,. This allows the recursive extension of operations defined in D,, the truth values, to D,, where a is any conjoinable type.

(4) DrJl)iilition: Conjoinahlc Type (i) t is a conjoinable type (ii) if b is a conjoinable type, then for all a, (a, b) is a conjoinablc type. T h e basic idca is this. Eleme~ltsf, g of D(,,,I,),which arc functions from D , to D,,, are vicwed as sequences of elements of the set Dl, indexed by the set IJ,, f and g are combined by performing an operation defined in Dl, indcx by index, in thc manner that vectors arc added." (5) defines the operators n and U ("meet" and "join") a)rmsponding to rrr?J and or. T h e s!imbols A and v are reserved for D, = {0,1}; they arc defined by their finite truth-tables.'

( 5 ) Pointwise definition of n and U X n Y = X r, Y if X and Y are truth values = ( ( 6x n y): (z, x) E X and ( z , y) E Y} if X ;and Y are filnctions (which X

are representetl as scts of ordered pairs) Y if X and Y are truth values {(z, x U y) : (z, X) E X and (z,y) E Y) if X and Y arc functions.

UY =X v =

Generalized Conjunct~onand Type Ambiguity 337 T h e definition (5) is given in tcrms of f~lnctions,which are objects in the n~odcl.It is convenient to have some rules for computing with meet and join in intensional logic (11,). Where # and $ are 3 (single) functional type, and (6) FLZCIS: (a) # n ~,b= i,z[#(z) n lk(z)] z is a variable of appropriate type not occuring (/I u 41/ = ?bz[4(2)u 41/(z)] free in 4 or I//. This is an immediate coilsequence of (5). (b) [4 n $I(@ = 4 ( a ) r l l k ( 9 ; r4 U $](a> = (l)(~) u V>r$icution: [q5 n $ ] ( a ) = [ilz[&z) n ~l/(z)]](crl) (by (6 a) ) (by lambda conversion) = #(a) n $ ( a ) (c) n Av$ = LV[# n $1 ?,vc;ll U iv$ = iv[# U $1 firzfic(dtinn: by fact a, [%v#) n [iv$] = ?.u[[ivd) l(u) n [ILv$](u)I where u is a variable not occuring free in # or $ - lwu[#~l/\ n ,j~l/'] by lambda conversian (&"I' is with u siibstituted for all free occurrences of v) by a change of variables IL\r#

$J

Because Montague's 11. substitutes thc operatorsAand' for explicit referencc to possiblc worlds, a special statement is needed for them. Corresponding to (4) we have (7).

(7) (a) (b) (c)

n $ = ^I "4 n '(/I 4 U 4, = ^rv(bU "$1 "[# n 1k1 = -4 r $ 74u (/I - -4 u "$ "(j)nA$ = ^[cbn(/II ^(f~LI *$ = ^.[#U $1

if 4 , t,b have type (s, b) for some b, and modally closed."

d>, cl/

are

Thcse identities allow us to r2late the definition ( 5 ) to Montague's PTQdefinitions, which were discussed in section 2. Take for instance his T13, governing terms:

(8) If a,

13 E Pr

translate into

d, 1)'

respectively, then a or

1) translates

into

iP(rxl(P)v P f ( P ) ) . This follows from the identities: a' U P' = ?.P(at(P) U 13'(~))(by (Ga)), which is iP(at(P)v P'(P)) since at(P) and /jt(p) have type t.

4 Repercussions on the Type Theory In this section u7eshow how the generalized conjunction schema makes somc correct predictions and some wrong ones, and propose some alterations in the types assigned to lexical items, alterations that we believe are desirable from the psycholinguistic perspectives of sentence processing and language acquisition as well. Similar suggestions can also be found in Don-ty ( 1981) and Cooper ( 1979).

338 Barbara H. Partee and Mats Rooth

Transitive verbs If as in P T Q , thc type of all transitive verbs is (type (T), type (IV)), then the ge~leralizedconjuilction schema predicts (by two applications of fact (ha) of scction 3) that the int-erpretation of [TVPl and T V P I ] should be

(9) % ~ ~ x [ T v P(3)(x) ', A TVP;(~)(~)] with 3 a variable over term-phrase interpretations and x an individual variable. In other words, a sentence of the form (10) should have a paraphrase of the form (1 1)( 10) John T V I and TV2 T(ern1 pl~rasc)

(1 1) John T V I T and John TV7 T When we conjoin two extensional transitive verbs, this gives thc wrong result, 2s seen in (12) and (13). (12) John caught and ate a fish. (13) John hugged and kissed three women. Unlcss the sentences are given a very marlicd intonation or the context is heavily loadcd, u7e inust interpret (12) as involving just one fish, and (13) as saying that the same three m70menwere hugged and kissed.' O n the other hand, when w-e conjoin two intensional verbs as in (14) 01. an intensional and an cxtcnsional vcrb as in (IS),' the reading predicted by the generalized conjunction schema is indeed the primary rcading of the sentence. (14) John ~vantsand needs two secretaries. (15)- John needed and bought a new coat.

(A "quantified-in" rending, "thcrc are two secsetarics such t h a t . . . ", map also be available in these cases, with about as much ease or dif'ficulty as with a single intensional verb; the mechanism that accounts for quantified-in readings, whether generative or interpretive, would presumably operate in the same way whether the T V was complex or simple.) Now supposc the type of T V were (e, type (IV)); then thc generalized conjullction schema would predict that [TVPl and TVP2] would be interpreted as (16): (16) IyiLs[TVP{(v)(u) A TVP;(?)(x)] In that case, sentenccs of the form (10) above should have (stilted) paraphrases of the form (17): (17)

NP is/are such that John T V l it/them and John TV2 it/them.

General~zedConjunction and Type Ambiguity

339

In this case the matching of prediction to judgments on sentences (12)-(15) above is exactIy reversed: now v7eget the right result for (l2) and (13)) and the wrong result for (14) and ( l ~ ) . ~ Note that the cases where the simpler type assignment makes the right predictions are just those cases where both verbs are subject to -Montague's meaning postulate 4, wllich says that such verbs do indeed have counterparts of type (e, typc (IV)), catch:, eat',, etc. These results suggest that we should depart from Montague's strategy of assigning to oll members of a given syntactic category the "highest" type nccdcd for any of them. Montague had reason to let intcnsiona1 verbs Iike seek denote functions taking termphrase intensions as arguments, and because he wanted a uniform category-type correspondence he assigned the samc typc to the "simpler" extensional transitive verbs, ancl then providcd meaning postuIates to guarantee that the extensionaI verbs would behave semantically as if they were of the simpler type (e, type (IV)). Suppose we give up this uniformity and enter each verb Iexically in its minimal typc, where the minimal type for verbs like seek is Montague's TV-type but the minimal type for the extensional verbs is (e, (e, t ) ) . Then in order to account for the conjoinabiIity of intensional and extensional vcrbs and the Fdct that the result patterns with the intensional verbs, vTeadd a "redundancv rule" to insure that each "lo\v-type" verb has predictable homonyms of higher type. For example, given buyl of type (e, (e, t)), we predict the availability of hu.y2 of type ( type (T), (e, t)), where: 10

A fuller specification of these redundancy rules is given in '4ppendix .4. As a third part of our proposal, we suggest as a processing strategy that all expressions be interpreted at the lowest tj-pe possible, and in particular that conjoined expressions be interpreted at the lowest type they both share. L4bbrcviatingthe minimal type of eat, bz~!,etc. as T V 1 ancl the type of seek, need, etc. as TVr, we woutcl I l i ~ ~the e follolving patterns:

'

T V I llnd TV,

I

larch

I

eat

TV2 and

I

need

TV2

I

TV,

Note that extensional transitive verbs in their basic forms arc now of a type that takes e-type things as argument. blontague assimilated proper names and pronouns to the higher type needed for quantified noun phrases, but it vlould be consonant with our alternative schema to assign proper nouns and pronouns to type e (with their PTQtypc interpretations available as predictable hoinonq-ms so that they can conjoin with quantified noun phrases and serve as objects of intensional verbs). If pronouns are

340 Barbara H. Partee and Mats Rooth assigned to tjrpe e, the quantifying-in rule (which would not have to bc changed at all) would permit quantified noun phrases to occur as objects of extensional vcrbs. Only with intensional vcrbs would quantified noun phrases be directly generated ils direct objects. In sum, wc have a three-part proposal: (i) Enter each 17ei.b lexically in its minimal type. (ii) Provide lexical rules furnishing "higherv-typc homonyms for "lowerv-type elements. (iii) Posit as a processing strategy that all expressions arc interpreted at the lowest type possible, invoking higher-type homonyms only when needed for typc coherence. BJith these proposals, all of the judgments about conjoined verbs in sentences (12)-(15) agree with the predictions of the generalized conjunclion schcn~a.As an additional benefit, sentences which are intuitively simpler now have simpler translations involving lower- types than sentences which are intuitively more complex.

Parallel issues with intransitive verbs I

In P T Q a n d in much of the subsequent litclxturc in the Montague tradition, the type of intransitive verbs, and of verb phrases in general, is ((s. e), t ) . Bennett ( I 974) proposed that IV (and CN) be assigned the type (e, t), and llowty, Wall, and Pcters (I 980) follow Bennett's type system in their presentation of P T Q Since we are ignoring thc "s" parts of types in this presentation, we will regard Bennett's IV-type and the Y'TQIV-typc as equivalent, representing both as (e, t ) . ' I n either case, subjects take verb phrases a arguments to form an espression of type t. T h e alternative, that verb phrases should bc of type (typo (I'),t) and tahc the subject as argument, had been emploj-ed by Montague in Montague (1950) (UG), and has been argued for by Kcenan and Faltz (1978) and I3ach (1980a); it is also employed by Hocpeln~ai~ (1978), Gaxdar and Sag (1981), and Bach and Partec (1980). Flynn (1981) considers the possibility that languages might differ fi-om each other with respect to which of the subject and the verb phi-asc takes thc other as argument. Hach (1980a) also discusses the possibility of assigning untensed IV's to the type {e, t) but tensed IV's to the type (type (T),t). Let 11s see what predictions the generalized conjunction schema makes about the types of IV's. Given a sentence of the form (20), if IV

is of type (e, t), then (regardless of whether the subject is of type e or typc ((e, t), t)) the I schema predicts that there will be a paraphrase of the form (21): I (21) T is such that he/it IVI

{zcl}

h e / i ~IV2.

Generalized Conjunction and Type Ambiguity 341 If, on the other hand, IV is of type (type (T),t) and takes the subject as argument, the schema predicts that there will be a paraphrase of the form (22):

Examining sentences (23)-(26), we observe that the lower type gives the right result for (23) and (24), the higher type the right result for (25) and (26).12

(23) A fish walked and talked. (24) Every participant sent in an abstract or apologized. (25) An easj7model theory textbook is badly needed and will surcly be written within this decade. (26) A tropical storm was expected to form off the coast of Florida and did form there within a few days of the forecast. 'I'his pattern of results is parallel to those with the extensional and intensional transitive verbs; the \.erb phrases in (25) are both intensional with respect to subject position, and (26) represents a conjunction of an intensional and an extensional verb So in this case as well, thc observed judgnlcnts accord with the hj-pothcsis that each itcm is listed lexically with its ininimal type, that there is a rule for generating higher type IV's from lower type ones, and that there is a processing strategy of tr!ing to use the lowest types possible. Note that in this case we are proposing that there is no fixed directionality to the function-argument structure of subject and predicate. If the verb phrase is a sinlplc one of type (e, t), it will be the firnction if the subject is of type e (as we suggested above for proper names and pronouns), but the argument if the subjec~is a quantified noun phrase. If the verb phrase is of typc (((e, t), t), t), it will always he the function, assuming hat we never find reason to posit term phrases of still higher type taking such IV's as argument. Having argued that there are two IV t!-pes, we have to reconsider our T V typcs a summary of all the newly proposed types is given in Appendix 14.

Psycholinguistic advantages As remarked above, an added advantagc of our revision of hlontague's ilnifo~.m category-typc correspondence is that tllc intuitivel!~ simpler cases no\*; have sirr~plcr intcrprctations. T h c potential disadvantage of having nlultiplc intcrprctations availablc for extensional verbs (via the lexical rule introducing higher-type hoinonj-n~s)is ofcsct b>-the processing strategj. of trying the simplest tjpe first. A4ore m-orli needs to be done to explore the workings of this strategj-, particularl! to see if extending the type-n~ultiplicity to more categories leads to cases in nhich the minimal lexical types don't cohere but thcre is more than one alternative availablc to tr! next. 111 any case, the revised system seems like a step in the right direction for making Montague grammar more plausibly connectable to a performance model of langu:ige

342 Barbara H. Partee and Mats Rooth Therc is an additional potential advantage fronl the perspective of languagc acquisition. If, for example, children learn proper names and pr.onouns before they lei1r11 quantifiers, it would be natural to suppose they tvould assign them to type e. On the original PTQrnodel, they would have to revise their interpretation of proper names and proilouils when they learn the higher term-phrase type. Under our reviscd principles, thcy would keep the original interpretation as tllc basic one, and add a higher-type interpretation via a general rule. Sinlilar considerations apply to estcnsional and intensional verbs.14 In general under our assumptions more of the child's learning of semantics could take place by accretion, and there would be less nced for restructuring. On the assuir~ptionthat accretion is easier than restructuring, this also seems a welcome result.

5 Keenan and Faltz In their "J,og-ical Types for Natural 1,anguag.e" ("L'T"), Keenail and 1:altz ("K CZi F") describe a different M-ayof endowing the types with Woolean structure. In this section, K & Fs construction is summarized and related to our analysis. At some points, references to L T arc substituted for proofs. For K & F (as for Montaguc) term denotations (elements of are (in extensional models) sets of sets. T h e Hoolean operations in this type arc set union, intersection and complementation. (This is equivalent to the pointwise definition, for il'Xr\ and Xn are the characteristic functions of A and B respectively, X:\ n X13-- Xaqrrll) k & !I givc a special status to the term denotations corresponding to individuals. If h is an elcment of the domain D, the corresponding term denotation I,, is {x C Dlb E X). (Thcsc ill-e sonletin~escalled individual sublimitations; scc Dowty, Wall and Peters (1980).) The set {Il,(b E I) of tcrnl denotations corresponding to individuals is denoted 11). ID has a useful property: it is a set of free generators (cf. Haln~os1963, p. 40) for the Boolean alpebri, f~ , U ,', U) (the set 2'")' with operations intersection, union, complementation, and constants fl (the identity for U) and D (the identity for n).) l h i s means that L)vl\)

( L ) V r ,

a,

( 2 7 ) (a) IF) generates DT: each element of D.1. can bc represented as a combination of Il,'s via the operations fl, U and '. (Sec T h m 8 of I,T, pilge 91 .) (b) Any function g from ID to a Boolean algebra H can bc estendcd uniqucly to a hoinomorphism 1 from to H. (This is the Justification Theoreln of LT, page 120.) Pictorially, (27b) can be represented as (28), where id is the identity iI-rap.

Generalized Conjunction and Type Ambiguity 343 We can now describe the Boolean structure which K & I; assign to thc space of extensional VP's, which they take to be Hom (D,l-,2), the set of homon~orphismsfrom DT to the set 2 = (0, 1) of truth values. 15 Wc do this in the following way. First, a bijection between Horn (Dcl.,2) and 2" is assertcd to exist. Then this bijection is used to transfer the Boolean structure which 2" has as an algebra of sets to I-Iom (Drl.,2). Suppose f is a charncteristic function for a set of individuals, and let I be the function mapping an element of D to the corresponding T denotation:

By thct (27b) f I-' extends uniqucl!- to a homomorphism h : D l i 2. So we can define map M w1;hich maps a characteristic function f to thc corresponding homomorphism:

I i ~ r n ( D .2) ~, (b) h4 : 2" f J7h (in the example above) ---\

is a [unction, hecause the extension licensed by (27) is uniquc. M is an injection (one to one), because if f l # f2, f l a I-' # f 2 1 ' and M ( f r ) and M(f2) cxtend f l and f 2 o I-' respcctivcly. M is a surjcction (onto) hecause if k is in f I o m ( l l ~ 2l ~) ,, M(1%? zr/ k) = k, again bccause the extension is unique. T h u s M is a bijection between 2l' and Hom(Del-, 2). h4 can be used to define operations on Horn(DT,2): t 5 ~ - '

(3 1)

h A g def =. M(M-' (h) n ~ ' ( g ) )

'

11v g dct =. h l ( ~(h)' v M - (g)) hc

= M ( L M -(]I)]') ~

def

It is easy to verify that l I o n ~ ( D ~2)~ with - , operations so defined is a Hoolcan algebra. The Boolean identities are verified by appealing to the corresponding identities in thc set algebra 2". As an instance, take the distributive law:

(32) h A (g v I,) = M ( M - - ' ( ~A) M-'M(Mv~ ' ( k ) ) ) = M(M- (h) fis M-I (g) \,h ~ - (k))) I = M ( ( M ' ( ~A )~ ' ( g )v)( ~ ' ( 1 1i?)M 1 ( k ) ) ) using the distributive law in 2l' = M ( M - ~ M ( ~ I(h) - A M - ' ( ~ ) v) M- l ~ ( 5 q - (h) l ,\ M. (k))) =( h ~ g ) v ( l ~ ~ k )

344 Barbara H. Partee and Mats Rooth This completes our exposition of K & F's construction. Obviously, it is impossible to do justice to L T in a few pages. As partial motivation for the homomorphism construction, note that hecause an extensional verb like sing is a homomorphism, sing/ (a - man' v a - woman') = singY(a- man1)v singl(a - woman'), so that LC a man or a v\roillan sings" is equivalent to "a man sings or a womiln sings", as desired. In section 4, we suggested that the basic type for extensional VP's was (e, t), with Boolean structure given by the pointwise definition. (As noted above, since elements of tliis type arc characteristic functions, this is the structure of' an algebra of sets.) The function M reveals the relation between this approach and K & 1;'s homomorphism construction. Notice that M is an isomorphism between 2" and H o n ~ ( l I , 2): ~,,

(33)

MI^', A f2) = M ( M - ' M ( ~ , )A M - ' M ( ~ ~ )= ) ~ ( ) A f~ (~ f ~ ) M ( f l v fr) = M ( h l ' ~ ( f lv)l V 1 M ( f 2 ) )= M ( f l ) v iVI(fl) M(E;) = M ( [ ~ ' M ( F ~ ) ]=~ )1M(fI)IC

Since thc algebra I( & F use in translating- extensional IV's is isomorphic to the one we use, we are in agreement here. T h e advantage of our approach, we would claim, is revealed when we consider conjunction of intensioiial 1Vs. As was shown ahovc, the pointwise definition gives the right rcsult 11e1.e. Whilc thcy clo not include conjunction of intensiorlal 1Vs (or il~tensionalTVs) in their fragment, K & F agree with us on this point (see footnote 30, page 328 of LT). Hence in an appropriate extension of I,T, crrrd and or. conjoining IVs arc translated in two distinct ways: when thcy conjoin intensional IVs, they are interpreted via the pointwise deiinition; when thcy conjoin extcn~iol~itl IVs, they are interpreted as operations in I4om(DT, 2). On the other hand, in section 4 it was shown that by translating intensional and extensional IVs by objects of different type, a sirlglc cross-catcgorial deiinition for n and U can be employed. While we consider this an advantage, wc do not believe that there is an empirical difference bctween a11 extended LT semantics employiiig features to differentiate the two conjunction modes and the analysis of section 4. In a re\-iew of LT, Ballnler offcrs the following propositions (propositions (4) 2nd (6) of Hallnzer 1980): (34)

(a) "Especially, I disagree with what could be called the function-argumcn~ ideology, namely the assumption that the role of a grammatical cntcgory of being a function or an argument is invariiibly fixed." (b) "My most serious criticism is tliis. K & F base their algebraic scmantics of i NL [natural language RHP and MR] on some mathenlatical assumptions which are mistaken. They assume wrongly the existence of certain homo- ' nlorphisins to link the Boolean algebras of certain gl-ammntical categories and arrive therefore at false conclusions and results." -

We agree with proposition a. In section 4, we suggested that an cxtensional I\' like sing has type ( e , t) and thus combines as an argument with L ' Z Y I : ~ ??itl~/) (type ((e, t)), while an intensional IV like is hpliez!ed lo h m r 169 has thc type ((s, ((e, t), t)), t) and so

I

Generalized Conjunction and Type Ambiguity 345 combines as a function with t i 7 t q ) j tnavl which is liftcd to type (s, ((c, t), t ) ) hy o11c of the rules of Appendix A,) LVc do not agrce with proposition b. Ballmer claims that in the I,T system "cvcry man sings or dances" means the same as "every man sings or every mall dances". T o draw this undesirable conclusion, he assumes that K & 1..' usc the pointwisc definition, (Ballmer's (18), our (5)) to assign a Boolean structure to extensional IVs. If this were so, Ballmer's conclusion would indeed follow. But this assumption, and the replacenienl it sanctions are in error: " .. . the definition of v [which is the hon~onlorphismdetinition, not the pointwise definition - BHP and MRI for thc VP algebra only sanctions by the corresponding replacing a join of VP fi~nctionsapplied to a member of is an I,,. We 1.unno1do this join (union) in the formula algebra if that member of TLlNI> in general for arbitrary members of TDNP." (LT, pages 131-132; K & F's is our Drr). Sincc e r w y irnlfin is not an Ib, [sing1v dance'] ( every-man') cannot be converted into singf(cvery-man)' v dance'(every-man'). Thus, while we agree with proposition a (as well as with somc of Ballmel-'s other points), we believe that his attempt to criticise J,T based on the claim that K & F made "serious mathenlatical errors" is misguided; we arc aware of no such errors.

6 Problem Cases and Conclusions Cooper (1979) discusses a reading for terms containing conjoined CNs (common nouns) not predicted by the generalized conjunction definition (5). 'The reading predicted fix (35a) is (35b), which can bc paraphrased "most hermaphrodites swim" (because man' and woman' dcnotc characteristic functions, n amounts to set intersection here.)

I swim most

CN

l

I

and

CN

I

women

(b) most'(menf n won~cn')(s~viin') Such readings are possible for CN-conjunction ("my friend and colleague", "evcry wife and mother"), but a more natural reading is "most men swim and most women swim". Cooper notes that this reading can be obtaincd by reversing the functionargument order in the construction [Det CN]. (36a) defines new translations for I ~ I ~ J I I and lvomun which map determiner mcdnings to term meanings

(36) (a) man" (b)

= ?,$$(man1) woman" = i$$(womanl) man" n woman'' = IgS$(man1)n = ;l$$(woman') = A$($(man1) n ,$(womanf) by fact (6c)

346 Barbara H. Partee and Mats Rooth

1 man'' n \voman"](most')

= L,$($(manl) fl ,$(woman'))(mosti) = mostf(man') n most (woman') = iP(mostf(man' )(P) I7 nlos tl(woman')(P))

I

1 I

bj, fact (6a) \vhere P is a variable of typeje, t) 1 [man" n woman"](most')(swim') = I.P(most'(manl)(P) n mostl(woman') (P))(swiml) = nlost'(man')(swiml) n most'(womanl) : (swim') by lambda conversion) I I

As the equalities in (36b) indicate, enlploying this elevatcd type for CNs while i reraining the pointwise definition for conjunction j-ields the desired rcading. We will now discuss a similar ambiguity in intensional contexts and examine the possibility of extending Cooper's mechanism to cover it. T h e ambiguity is illustrated in i I (37), cvhich has a t least three readings. I

I I

(37) T h e department is looking fix a phonologist or a phonetician. I

In the i/t 1-t~reading, the departmcnt is looking for a specific person, and that person is a phonologist or a phonetician. In the normal de rlicro rcading, the department would be satisfied if they found a phonologist, and they would also be satisfietl if they found ! a phonetician. T h e cfr rc reading is obtained b!- quantifying the csprcssion , [a-phonologist' U a-phonetician'] into the expression thc-department1 (f look-for' ( Q Q ( ~ ) ) (abstracting ~)), orcr the variable x. T h e nor~nali/e rlil~oreading is obtained by combinii~glook-for' with [a-phonologist' U a-phonetician'l directly to yield thedepartment' (f look-for' (A(a-phonologistlU a-phoncticia~~'J)(y)). Tcrms such as he drpart?t~uiltand a phot~ologist have type ((e. t)), and look-fin' has type ((s, ((e, tj, t,)), (e, t)). Q i s a variablc of type (e, t) and u and y are variables of type e. T h e reading we arc interested in, a second ilc i11c.10reading, is suggested by the continuation " . .. but I don't know which". In this case, thc departrncilt has a particular hind of person ill mind, but the speaker doesn't know which kind of puson this is. This reading is equihalcnt to "the department is looking for a phonologist o r looking for a phonetician" ~vittlthe object lie (/i1.1oin both conjuncts. T h e generalized form (382) of (36a) allo~vsus to derive this reading. 'This is indicated by the identities in (3813).

'

(38) (a) .filrzc./ion-urgclrn~~~f -fli'_flop Let the phrase cx have type a, and Ict b bc any trpc. Then r has a translation x" of type ((a, b), b) in addition to its translation x' of typc a: a" = i.FF (a'), where F is a variable of type(a, b) (i) a-pl~onologist" = iF1~(a-phonologist'),where F is a variable of type ((s, ((e, t ) , t ) ) , (el t)) (\vhich is the type of' l ~ o k ~ f i r ' . ) (ii) a-phoneticiai~" = iLFF(a-pilonctician') (iii) a-phonologis t" U a-pl~onet-ician'l = AFF(a-phonologist') U i)l'l:(a-phonetician') = i , ~ ( F ( a - ~ h o n o l o ~ i sUt 'F(a-phonetician')), ) using F~ct(hc)

Generalized Conjunction and Type Ambiguity 347 (iv)

[a-phonologist" U a-phoneticianl'](look-for') = lo~k-fos'(a-~honolo~ist~) U look-for'(a-phonetician') by lambda conversion for F

Note that in (iv), [a-phonologist1' U a-phoneticianf'] is the function and the T V translation kook:Ji/r' is the argument. As desired, (iv) is also the translation of the phrase "look for a phonologist or look fbr a phonetician". Unfortunately, the flip-flop rule generates many undesired readings also. In section 4, u7e noted that a sentence with conjoined extensional IVs, such as (Ma), is not equivalent to the corresponding conjoined sentence.

(39) (a) Every student fiailed or got a D. (b) Every student hiled or every student got a D. We captured this by proposing that extensional IVs primitively have type (c, t) and conjoin at this level, whcnever possible. But the derivations (36b) and (38b) are inconsistent with the principle of performing conjunction at the lowest possible level; they csscntiall~involve conjunction at the I~ighcrtype level generated by the flip-flop rule. Consicleration of other examplcs reveals il second inadequac! in the flip-flop appl-oach. (40) is ambiguous in the same way as (37). (40) John believes that a phonologist or a phonetician won. However, the embcddcd subject a phonologi.st or (7 p b o ~ ~ ~ t i c lis u /already z thc function with respect to illon, so flip-flop docs not apply. While it is possible to pursuc this approach further (cf Lan~bek(1961)) we will not do so. An alternative to the flip-flop rule \T hich deals with (40) is a rule cluantifying in tcrms of a higher type. This would yield a representation like (4 1) (ignoring tctzse).

(4 1) [i,@@(*a-phonologistf)U lu@@(^a-phonetician')I (A3[believet("['3(win')I)(j)J) where type(_?)= (s, ((e, t), t) and type(@) = (type(3), t) Since i@@ (^a-phonologist1)U A@@ (^a-pl~oncticianf) = i@ [(d)(^i~-phonologist') U #(^a-phonetician') I, lambcla conversion yields the right results, namely:

c Mihile this solves the second problem, the tirst problem remains. It can l ~ summarized as follows. While intuitions are f ~ from r clear, w-cbelieve that (42a) has a rei~ding ecluivalcnt to (42c), but no reading equivalent to (42b).

(42) (a) Mary indicated that every stuclcnt failed or got a D. (b) Mary indicated that cvery student fiiiled or ever! student got u D. (c) Mary indicated that cvery student failed or indicated that every studcnt go1 a D.

348 Barbara H. Partee and Mats Rooth In this case, the clement which is taking scope is a higher order translation of tllc IV jtlile.d or got w D. Our intuitions can be described by stating that it can take scope over the intensional operator indicute, but not simply ovcr the tcrm eve^^ rnrw (cf. (39)). We can sce no non-ad hoc way of capturing this divergence between scope with respect to intensional operators and scope with respect to quantifiers. T h e additional readings of sentences (37) and (40) that are not predicted by our generalized conjunction rules correspond to possible mcanings of "conjunction-rcduction" sources with two full sentences connected by or. ,4s noted earlier, howevcr, syntactic conjunction-reduction is notoriously non-meaning-preserving and would let in even more unwanted readings than eithcr the function-argument flip-flop rule or the higher-type qtlantifying-in rule; nor do we see any way of restricting its application to allow the mcaning-preserving cases. An added difficulty facing any invcstigation of thesc problcm cases is the unclarity of the data. As noted by Dowtj- (1981) and Bach (1980a), intuitions arc not always sharp and not always shared in cases whcre therc is a phrasal conjunction and s c ~ e r a other l scope-bearing elements in the same sentence. T h e problems discussed in this section are cascs where there seem to bc additional readings not predicted by the generalized conjunction schema. Wc believe that the generalized conjunction schema itself is not called into question by these cases, since it predicts all and only the right readings over il w r y wide range of clear cases, and predicts only good readings (hut not quite all of them) in the problematical cases just discussed. It is simple and general, and leads to an argument for revising thc association between syntactic categories and semantic types in a way which has the addctl atlvantagc of making intuitively simpler sentences simpler in their type structure, and plausibly simpler to process and easier for children to acquire. We have given up hlontague's requirement that each syntactic category have a singlc semantic type associated with it, but the set of types associated with each category is still predictablc from its specified simplest type together with the "type-lifting" rules given in ilppcndix A. Similarly, there is no longer a single semantic interpretation rule associated u-it11 cnch syntactic rule, but an instruction such as "do fi~nction-argument application", which may require the application of "type-lifting" rules to one or both expressions to find the lowest types that fit thc pattern (cr, h ) , o required for functionargument application to apply. T h e processing constraint, "use the lowest types possible", is essential to our account; without it, the rype-lifting rules allow for additional ilnwanted readings in many cases. Insocar as the overall account is convineing, it provides an exanlple of the importance of considering processing or "pcrforn~ancc" issues in seeking explanatory accounts of the relation between form and meaning.

Appendix A: Redundancy Rules for Predicting Higher-type Interpretations ,

-

1he second part of our three-part proposal discussed in section 4 was t o provide rcduntlancy 1.u1csfor predicting the interpretation of the "higher-typc" counterparts of'exprcssion whose si~ilplcstiiitcrpretation is at a lower type. Although we illustrated the process with lexical examplcs, thc rules can

Generalized Conjunction and Type Ambiguity 349 apply to arbitrary expressions, and it is probably desirable to allow tliein to do so. Suppose, for exan~ple,we are conjoining an intensio~~al ancl an cxtensional IV phrase, so \ve need to "liCt" the cxtensional IV phrase to its corresponding higher t>-pc,and suppose thc extensional IV consists of an extensional transiti\re verb plus an object. T h e processing will hc simpler if we clo the l'V-objcctcombination at tlie extensional lcvel to build up the extensional IV interyrctntion and only thcn apply the rcdunclancy rule to the IV-interpretation to get the corresponding higher-order 1V-interpretation, rather than forcing the "type-lifting" to be done on the lexical verb (particularly since an 1V pl~lasc can contain so many different hinds of lexical verbs, 21s well as verb-phrase advcrhs).'" In this appendix wc provide the formal rules for the three cascs oS type-lifting dcsa-ibcd in the paper: for tcrni phrases, for 11'-phrases, and for Ti-'s. Then we offer a tcntativc characterization of what might be the full range of cascs of type-lifting to be expected for natural languages.

Tern?pl/rases. T h e sin~plesttcrln trhrascs (proper nouns and singular pronouns I"') arc no\\: of t!.pc L~. h!Iontagi~c's original type for term phrases is {(s,((s,c), t)), t). In the Bennett t!-pc-system en~ployedin Don-ty, Wall, and Peters (19HO), the type for T phrases is ((s, (e, t)), t). Ilowty, Wall and Peters suggest (footnote 14, p. 250) that there is no reason other than that ol' preserving hlontapue's uniform category-to-type nlapping rules not to take the type of term phrases to be ((e, t), t): thc intcnsionalit); of verbs like seek could be adequately captured b y assigni~~g the rylx ( ( s , ((e, t), t)), (e, t ) ) . . % S S L I I I I ~that ~ ~ this is correct, thcn since we are giving up the unifijrm categoryto-t!.pe nlapping anyway, we will take the higher tam-phrase type to be simply ({c, t), t). The type-lifting rule fbr term phrases can be stated as follows: If x E P7. and a translates as r1E MI;,, then a also tl-anslatcs as xl' in l"lE;:,, ,), ,), where "A" = iPIP((3') I. (P is a variable of type (c. t).) 2 I l ~ i p l z r ~ ~ sTt sh.e type f i ~ rfirst-order extensional 11' phrases is (c, t). T h c t!pe for in~cnsionalTI' phrases like nppr7ar~IO he approac.hi~igis (is, (higher t!pc(T)), t), ~vhichb? the line of reasoning followed above is ((s, ({e, t), t)), t ) . If thcrc were no s is this type, ~ v c~vouldhil\.c nn arrily of typcs for terms and I\'-phrases that Sorn~sa sort of "t!pc-ladder" from 0-order predicates (entities) 10 third-order prcdicatcs, as shown in Tablc 1. The lines connecting tj-pes in Table 1 show cornpatiblc fiinction-argument t!.pcs; in two of the cilscs, tlie I\? is the filnction and the subject term phrase the iirgument, while in thc ~nidcllecase, thc subject tcrm phrase is the function (as in PT(&.'"~ tvc .cvantetl to combinc a 3rd order IV nith ;I 0 order tern], we would have to first apply the term-phrase type-lifting rulc to the term phrase, then use function-argun~cntapplication. In this purely extensional version, using IP as a variable of typc ((c, t), t), the third-ortler translation iSf' corrcsponding to a given first-order IY translation (5' would simpl!. be j.lP~~P(fi')j, exactly analogous to the term-phrase lifting rulc given above. T o reach the intensional typc we actually want, the rulc would instead he: 6" = A3["3(d1)](3 is of type (s, ( ( e ,t ) , t)) .)

I

s t ~ ~ X 7 '

Table 1 3rd order

1st order

0 order

Terms

IV-phrases

350 Barbara H. Partee and Mats Rooth scc 3 TIr Pl~rrrses.'I'ransiti\c verbs (or T V phrases, sucll as perwrrrtir. 10 It>rrzv,r.oiraricr INI~~III~CMI; Hach (108Ob)) are of synti~cticcatcgory IV/T; we now have two s c l ~ ~ i l ~tj~pcs ~ t i c for T i ~ n dtwo for IV, so potentiall!- we have at least four types for T V (eight if we allow as an inclcpendent variahlc whcthcr functions talte extensions or intensions as their arguments.) By the gcncralizations \ye present later in this Appenclis, we could predict \\-hat all of the readings would he; here for simplicity we just concern our.sclres with two: the fully extensional first-order tj-pe (c, (c, t)), and it typc n hwc the argument is the intension of a second-ordcr Lcrm phrase, i.e. (s, ((e, t), t)), and the result is a simple IV, type (c, t), so the T?' type is ((s, ((c, t ) , t)), (e, t)). Then tlie rule for giving the higher-type T V translation 6'' from the lower-tvpe one 6' is this: 6" = iSiu["3(1v~~S'(v)(u) 1) 1, wlicrc 3 is of type (s, ((c, t), t ) ) , u, Y of t>-yee. It appears to us that the actual array of kinds of type-liftings needed for 'IV's is limited in that ~hcrc are no cases ahere T V takes an intension of a full term-phrase object to girc an intcnsion:ll IV. This reflects thc apparent fact that there are no basic lexical verbs that arc intcnsionnl with respect to both subject dnd object. We can passivizc an intensional TV to get an intensional IV, but the result of passivization is no longer a T V (see Bach (1980b) ); othcr nicans of producing intensional IV's involvc the addition of mod:ll ausiliaries or perhaps advurbs to extensional IV's. 'Thcrc seem to be ;1 few simple intensional 1V's such as "be missing", as ill "one pencil is ~ilissingfrom this (nea) box of pencils" hut these do not include TV's. The only known candidates arc what Postal (1 970) called thc Psych-movemcnt" verbs like .cu?pr-ise.worry, N I I ~ ~ K U Pctc.; . whctllcr or 1101 the! ilrc really intctision~l with respect to suhjcct position (and we are inclined to believe they are not), they arc certainly extcnsio~ialwith respect to object position. So it appcars that the only cases of type-lifting actuitlly needed for T1,"s are versions ofthc case discussed in section IV, going from an argument of t ~ p t.c ton full term-phmse argument, with the r e s ~ ~ l t i alm-ays ~ n t an IV of type (c, t ) (how 113iIlly such cases thcre arc then depends on the distribu~ionof s's in the higher term-phrase type(s). It may be that the rule givcn abovc is the only one needed.) 1 Geni~nllr:atio,,ns. 1\11 of rhc rules stated abovc ancl more can bc gotten hy working from four basic "type-lifting" principles which r+e tcntativcl! hypothesize as a complctc set. The lirsc three are l>erfcctl!- general and follow fi-om the interpretation of tlie typc systcn~;the fourth is a special one fbr term phrases. 6'

~~ a' of any type I / , we can prcdict an interpretation r" of type TLl: ~ x l e n . z i o n - t o - i l 7 t c .Given (s, a) : cx" = *a' T1,2: E.rterzsiot~r1ilrgwment lo jr~te?mot7/1/ c/rgr~mcnt.Given x' of type (a, b) for any a anil b, we can prcdict x" of type ((s, a), h): cx'' = ixlx'(-x)], where x is ol' typc (s, a). /JjpT/lop. For any t q c s ii and k , given u' of type (1, wc cnn predict an TIJ: ,~frgtlt~?e~~-to~/iit~~.~i~~~~ interpretation a" of type ((a, bj, h): Y' = E.P[P(a')]. where P is of typc (a, b). plzl~rsra?:cume?rt: This rule is somewhat morc con~plcxand morc TL1: E~~lit)~-n,;rlumenf-lo-l~~r~~z closely tied to thc type structure instantiated in P T Q t h a n the first thrce. T h e r ~ ~colicems le expressions of syntactic cfitegory iZ/'T fhr any : I ((e.g. transitive vcrbs, double object vcrbs, prepositions), ant1 is designed to lift thcir translations ti-on1 type (c, t ~ ~ ~ > e (to A )typc ) (((e, t), t), type(,\)). (Rule (ii) can the11 apply ~o make tlie argument intensional.) We rcly crucially on the f ~ c that t e\,cr!- function category in P'TQ and in most extensions of P'I'Q "ends in I"; that is, for every c~pressionof r' of a catcgory othcr than c, (s, c), or t that clui arisc as the translation of an English expression, thcrc is sonic scclucnce of atpunlcnts /itl, . . . ,/(,, such that x'(fli) . . . (PI) is of typc t. For such typcs, we can stntc thc rule as follons: (TL-I).1:or any typc a t l ~ a "ends t in I", gi[en a' of type {r,a), \ye can prcdict all interpretation Y" of type (((e, t ) , t ) , a): x" iIPi.vI . . . i.v,[IP(E.u[rl(u)(\ 1 ) . . . (v,)])] irhcrc 1P is of tppc ((c, t), t). LI is of typc P and vl . . . v,, are of types such that c'(u)(vl) . . . (v,,) is of type I .

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Building on a gcncralization of "quiintifying-in" rules dcvelopcd in Kooth (19Xl), zrc call dcli~ic ttiis ri11c more formally by way of a recursive definition of n "quantif-ing-in" schcma. Llcfinc Q (11, sc, i) as follows: where 1, is of tvpe ((e, t), t ) , x is any expression, and i is an index:-)(I

Generalized Conjunction and Type Amb~guity 351

(I(;$, X . i) =

j-(Rxi3) if type (m) = t j.vc x(~,), i) il' type Q(:l,

(2) =

(c, d)

Then wt-c can restate the type-lifting rule as follows: (TL4')a" = AIP[Q(IP, xl(x,),i)]. The T V rule given earlier was an instance of this schema; one can vie\\ Montagilc's meaning postulates for extensional first-order prepositions ancl for transitive verbs as instances ofthc intel-se of' the same schema. One upsllot of those rules is that in place of Montapue's uniform translation for basic grammatical rclariol~sas xl(^lj'). we probably want to have just thc instruction "combine a' and lj' h! functionargu~ncntapplication." This is to be intcrpretcd in accordance with o ~ l rprocessing strategy as an instruction to clo thc combination at the lowest t! pcs possible; if neither x' nor /jl can take the other as ~lrgurncnt directly, the mini~num n~unberof type-lifting- rules should bc applied to get types comptible for functio11-argument application.

Appendix B: Extensions Based on Link's Algebra Godehard Link (1983) proposes a Boolean algebra structure for the donlain of entities I;:(D, in h/lontagiic's terms). T h e sct of atoms A of the Boolean algebra corrcsponcl to tho ordinary "singular" individuals, and joins of these under the join operation U, correspond to "plural individuals". ('l'hcrc is a distinguished subset D .A, corresponding to "bits of matter", which has its own scmila~ticc structure with a join opcl-ation corresponding to "lnatcrial fusion"; t l ~ cmanncr in which this "mnss term" substructurc i s intcgsated with the larger Boolean algehra proviclcs the basis for an elegant unified treatment of singxlars, plurals, and mass nouns, but we ignore the mass term subsystem here.) If (1 and b denote elclnents of E, t l ~ c"plural individual" denoted b!- a 1. b, namcl? J J JaJ IJ, J J bJ/is again an clement of L, i.c. still corresponds ro t!.pe e. Suppose then that we say that there is a second basic Icnglish owr/ tihich combines csprcssions of type tp to give a new expression of t!pc t, interpreted as Link's 1-1-1 operator. Intuitit ell-, \\;c call think of this i r r ~ r las tho "group-reading" L r r l ( l as oj)l)oscd to the "distributive-readi~~g"~ l l r r l t ~ chate been concerned with in the rest of the paper. 1f we now think of our earlier recursive definition of conjoinable types as a definition of "t-conjoinahlc" types, we can give i l p;~rallel definition of cconjoinable t j pes:

c

D

o

:

(i) e is an e-conjoinable type (ii) if b is an e-conjoinable type, (a, b) is an e-conjoinable type, for any type a.

Mo\\;cver, thc only c-conjoinable types that occur in PTQa1.e e and (s, c}, so ;llthough (11is in principle jusr as gencl.aIizable ;IS I,, it does not in fact generalize very far in 1~;nglish. \\ie can now provide a natural account of the ambiguous sentence (iii):

(iii) John and hlarp lifted the piano. Let us suppose that proper names arc basically of t>pc t: and \\c notv have two gcncralized u ~ ~ J ' s , which we can abbreviate as u ~ z i l , and [I~IL/, . Syntactically, the conjoined term phrase has two analyses, (iv) and (v) (iv)

John and, R.lar!-, T

John, 7' and, Mary, 7'

352 Barbara H. Partee and Mats Rooth (v)

john and, %,Iaq,,T

John, T and, Mary, 1' Semantically, \IT first interpret Jolzn and /2/lay)1as being of typc c, sa! 1 anci m; in (ib) they arc of the right tj.pes to combine immediately with aiarl, to give j $13 nl as the translation of the result, giving thc "group" reading, in which the lifting of the piano is predicated of the "plural individual" consisting of John and Mary. In (v), since e is not a t-conjoinable type, cve cannot combine.; and m dil-cctly with ond,; but we can l i f t j and m to the corresponding second-order term phrase intcrysctations j.P[P(j)l and i.P[P(m)] of t!-ye ((e, t), t), xhich is a t-conjoinable type. This gives the distributive reading (vi), which is logically equivalent to (bii). (vi) iuQ[jvP[P(j)](Q) iP[P(m)](Q)] (lift-thc-piano1) (vii) lift-the-piano1 (j) I\ lift-the-piano' (m) Note that we do not want the processing stratcgy of' "trying the Io~vcstpossible types first" to prevent the second tlerivation, since the sentencc is genuinely ambiguous. Jlut i l will not prevent it if we make the assumption that whenever w-c have h o m o n ~ m swith genuinely different meanings, as in the case of urz4 and and,, we can try either onc; and for atid,, the lull term-phrase type is the lowest t!pc at which the nlca~lingscan comhine.

Notes We have drawn heavily on thc work of Gazdar (1080) and Keenan and Faltz (107S), and have been influcnceci as ~vcllby discussions with Robin Cooper. A number of the ideas developed here were intlcpendcntly arrived at by Dowty (1981). We arc p t c f u l for discussions with collcagucs Ilerc, in Konstanz, and in Prague, particularly E m ~ n o nBach, Wynn Chao, Lyn Prazicr, Roger Iliggins, Kva HajiEova, Goclchard Link. Petr Sgall, Steven Weisler. T h e first author is grateful to the 1,inguistics Department for a partial teaching release this !.ear and to the Graduatc School for a Faculty Fello\vship; the second author was supported in part by N S F grant HNS 80-14326 and in part by a University Fellowship.

1 MTewill have sonlcthinp to sa\- about the "group-reading" a ~ uu-ith l IIOLLII phrases in Appuidis H. 2 T h e corrccl types, with s's, are: t-t e-c CN, 1V - ((s, c), t) T us, I)), t) TI' - ((s, rl;pc(T)j, type(1'C')) 3 .Actually he introciuces on]\- or for category T in order to avoid hal-ing to treat plurals. We ignore that and include the nnd rulc for T as well (with the "tlistributive", not thc "group" rearling). 4 Somenhat more gcnerallj-, if {13i)lE,,is a famil!- of Boolean algebras, than its product is the Cartesian product II Bi uith operations ( f ~, v and ') dcfined coordiaate by coortlinate. One way 15.1 of'dcfining the Cartesian product of' {Bi),; is as the set of all fi~nctionsfrom to .Ull l3,wU' that for each i, f(i) EB,. En the present case, all the Bilsare simply Dl,,iincl Il Dl, is simply LII,~), . For a 11 I ) , more substantiye presentation, see for instancc Halnlos (1963). 5 Gazdar gets the recursion started in a sljgl-ltly differcnt waj-. H e rcprcscnts thc truth valuts as sets, 0 = { > and 1 = {{)I and notes that the operations A and $J coinciclc with set intersection and set union, respectively. T h e denovations of type (a, t) arc also consiclcrcd sets (rather than -

4,

,

Generalized Conjunction and Type Ambiguity 353 characteristic functions); the denotations of type (a, b) with b dcfines

X UY

6

5

8 9

10

11

12

# t are fiinctions as usual. l l c then

Y if X and Y are sets = {(z, x U y}: (z, xcX and (z, ~ ) E Y if ) X and Y arc functions =X U

'

Similarly for fl. This way of formulating the definition obscures the fact that D,,,,) inherits its operations from 11; in the same wag that Dia,h)inherits its operations from Ill,, where b # t. T h e restriction requiring that 4 and IJ be rnodall!l closed (i.e. that they not vary in their denotation from world to u-orld) corresponds to the requirement in (ha) that (/) and ~bcontain no free occurrences of z. For in a sense, an expression nhich is not modally closed contciins a fi-cc variable over tvorlds. We have been assured by native speakers that the same judgen~entsin these ancl the following cases hold good for at least Gcrman, Czech, Hungarian, Portuguese, and Mehrcw as well as English. In languages like Japanese with free "Pronoun-drop", the sentences arc morc likely to bc judged ambiguous, but we m-ould be very surprised to find a languag in nhich the "wrong result" - "right result" j~~dgements were the reverse of thosc for English. We owe the observation that the conjunction of an intensional and an extensional verb fits thc predictions of the scherna to Wynn Chao. T h e reading predicted by (8) for (6) and (7) may be an available reading, but as nicntioneti abovc, we should presumably get that reading (if at all) by quantifying in (or an equivalent interpretive procedure). T h e new type assignment would incorrectly predict the unavailability of what is surcly the more natural reading for these exa~nples. With the fuIl intensional type system, b u , ~wi~uld ~ still be entered Icxically iis type ( c , ( ( , , I ) ) . If we want bzq~: to be of Montague's T V type, ((s, type(T)), ((s, c), t)), then 6101; 3u.7j.x [ S { L , ) ~ [ h u . j ~ ~ ( ' ~ ) ( ' xNote ) ] ) ] . that this corresponcls exactly to the relation between ctrr' and t a l k in PTQ but we are reversing which one is to be taken as basic. ('l'he v;iriables in this Lijotnotc correspontl to Montague's notational conventions; those in thc test are of corresponding s-less types.) In conjoining an intensional with an extensional ierb, it seems much morc nat~lralto havc thc intensional onc first, and vcry difficult to interpret a conjunction mith thc extcnsional terh lirst. L,yn Fraxier has suggested that this fiacl might have a natural processing explanation in o u r system: if the intensional verb is cncounterecl first, the hearer knows immediately that the conjunctior~must be i~ltensionaIand can applj- type-lifting rules to thc eutensional verb inmetliately; the otlier orda- would produce a temporary garden path and require backtracking. I'ctr Sgall has suggested that extensional-first is possible with sufficient prior context. His examplc, slightly modified, is this: "I often got gifts from my husband, but scldon~did I get anything u s e f ~ ~Il .rememher piles of handkerchiefs that I got and didn't need. But I got and dicl nced a new coat at thc beginning oC winter." T h e tlifficulty of construcring such examples may also be partly a reflection of the tict that in most cases t11c intensional verb clenotes an attitude toward "any old such-and-such" (such as wanting or needing) which generally is understood to precctlc the action tlclrotcd by the extensional verb, and [here is a strong preference for preserving temporal order in the order of conjuncts. Again the data appears to be the same for tlic other languages nlcntioncd in Note 7, and again we must add some caveats about thc data. MThercan intensional, or subject-ils-argu~ne~~t, reading is prcclicted (paraphrase (22) above), an cxtcnsional or subject-as-f~~nctio~ reading %illgenesall bc available as well via quantifying in. Where only an extensional reading is predicted (pi~mplirase (21) abovc), the other rcatling is predicted to bc impossible, but sometimes the other reading secms possible if the intonation is highl! marketl and/or the context strongly sul~l'ortstthat reading. For the examples given, assuming normal intonation ancl no syccial context, the

-

354 Barbara H. Partee and Mats Rooth

13

judgements seem quite clear. For discussion of conflicting judgcmcnts about somc othcr examples, see Bach (193Oa), Note 2. T h e niovc an-ay from (e, t) as thc type for IV's to a type which takcs the intension of the subjcct term phrase as argument has been motilated in part b j a move toward generating surhce structure directly without using transformations such as Passive and Subject Kaising. hlontague noted the apparent intensionalit!. of subject position in sentences such as (i), but assunled that such sentences uould be accounted for indirectly. (i) -4 unicorn appears to be approaching.

It is still an open question whether there are ;my basic verbs which are intensional with respect to subject position in si~nplcactive sentences; our examples of intensional IV's are built up by forming passives of intensional TV's (need, expect) or. b~ :idding modal operators (nil/, sr~rd)l)to extei~sionalIV's. 14 Soine intensional verbs like wnnt appear very early, before quantifier phlxses are mastered. Wc believe (without detailed investigation) that the earliest uses of w ~ l n l35 nn intcnsional transitive verb has just indefinite noun phrases or bare common nouns as object ("want a cookie", "want cookie"), suggesting that at least at thc outset, it nlay be that the objcct of intensional verbs is just a property-denoting expression. Whether this survives into the adult system is an in~erestiiigopen question; if it does, it might help to explain wliy P Z ~ C ~ ~ J - ~S ~ C~I I~I to ~ SbeC S harder than u-phrases to interpret i~~tensionally when they occur as objects of verbs like /ook.fi,i' and mlmr. 15 A lionlomorphism h between t\tfo Boolean algebras R 1 and R2 is a function "consistcnt with" the operations A , v and c and the constants O and 1; it is required to satisfj the following identities: (for all x, y E B1) : h(x) n (5.) = h(x) A h(y) h(x v y) = h(x) v h(y) h(xL) = h(x)' h(O) =O h(1) =1 T h e operations (and constants) on the left are in R,, thosc on the right in B2. T h e fact that type-lifting rules can be applied as casil\.. to phrases as to lexical itenis nlay be iln added advantage for these rules over Montague's meaning postulates. In the case ol'lcxical itcms, our rules arc in effect inverses of the meaning postulates that "Lower" the types of various words. Rut mcaning postulates. because they are constraints on possible interpretations cannot refer to arbitrary expressions of a given semantic type, and it seems to be ;In open question whether they can refer to "any expression (of 1L) which is a translation of an expression (of 1';nglish) of svntactic category A". A serious discussion of the proper characterization of mcaning postulates is w-ell beyond the scope of this paper, herb-ever. ~ , would also want singular 17 If we f'ollon- hilontague's treatment of' pricc~ and t e n l p e n ~ ~ u rwe pronouns of type (s, e); this could be acconlmodated in the generalizations cvc propose towa1.d thc end of this appendix. 18 If it turns out to be preferablc to require that the IV-phrase always cakes the subject as argument, A-ecould ctisallow the middle case; then for a first-order IV to conibine with a tnd-order turn, the IV would first haw to he lifted to the 3rd-order type. bc 19 We have not exploited this rule directly in any of our examples, One natural ~ l s cof i t ~vo~tld to eliminate ktontague's uniform assignment of intensions in translation rules of functional application, and allow fl~nctorcategories B/A to be intcrpretcd cither as of'type {a, b) or of type ({s,a), b); then if a functor ((s, a), b) is trying lo combillc with an argument of type a, this rulc

I6

Generalized Conjunction and Type Ambiguity 355

20

will lift the argument to typc (s, a). If on the other hand we llavc n f~inctorof type {a, b) and an argument of type (s, a), the next rule bclow will lif't the type ofthc functor to ((s, a), h). The intensional version oi'this rule is if type(%)= 1 if type(a) = (c, d) ,c if type(%)= (s, d) \\here

;I

#s

has type ((s, (e, t}), t}

References Bach, Emmon . 1980a. Tenses and aspects as functions on verb phrases. In Christian Rohrer (cd.), Time,TLVSL..and Qu(~nl!/kn, Tiibingcn: Niemeyer, 19-37. Bach, Emmon 1980b. In defense of passive. Lingrri.
vr

356 Barbara H. Partee and Mats Rooth Parsons, 'Terence. 1979. 'Type theory and ordinary language. In S. Ilavis and M . Mithun (cds), Monlrbgzc~Grunmclr, Austin, Tcs.: Univcrsit! of Texas Press, 127--51. Liriguisticv, Philostrpl~y, Postal, Paul. 1970. On the surfice verb "remind". Lin,yuislir I?rylriry l ( 1 ) : 37-120. Rooth, Mats. 1981. X cornparison of three theories of verb phrase ellipsis. In U'ynn C;hao and Deirdre Wheeler (eds), CT~lizler.~i/y o/'Mijssnc.husr~s O~r~rrsinni~l Pnpcrs I V I J , ~ I ~ , ~ ~ I ~ I . Svo1. / I ' I . SVII, , jjmhcrst, Mass.: University of Massachuscutts. von Stechow, L4rnim. 1974. c-/ kontcxtfrcic Sprachen: Ein Beitrag zu cincr naturlichen Sorn~alcn Scmantik. Lin~lris~i.
Noun Phrase Interpretation and Type-shifting Principles Barbara H. Partee

0 Introduction The goal of this paper is to attempt a resolution of the apparent conflict bctwccn two approaches to noun phrase (NP) interpretation, one being Montague's uniform treatmcnt of NP's as generalized quantifiers and the other, argued for by a variety of authors both before and after Montague, distinguishing among referring, predicativc, and quantificational NP's (or uses of NP's). I believe that the most important insights of both sides are basically correct and mutually compatible. 'I'o try to show this, 1 will draw on and extend the idea of general typc-shifting principles, argued for in Partee and Rooth (1983), together with thc idea of ty-pc-driven translation developed by Klcin and Sag (1985). I will draw heavily throughout on the many recent studies of modeltheoretic properties of various generalized quantifiers and determiners, especially the work of Barwise and Cooper and of sail Benthem. I believe that these tools can take us a good way toward explaining the diversity of NP interprctations on the basis of gei~eral principles relating syntax to semantics plus particular semantic properties of individual determiners, nouns, and NP-taking predicates. I will rctain from Montague's approach the requirement of a systenlatic category-tot4-pc correspondence, but allow each category to correspond to a family of types rather than just a single type.' For an extensional sublanguage I propose basic NP types e ("rckrential"), (e, t ) ("predicativc"), and ((e, t), t) ("cluantificational"). While this last, the type of generalized quantifiers, is the most complex, it is also the most gcncral; wc can argue that a11 NP's have meanings of this type, while only somc have ineanings of types P and/or (c., t ) . Part of our task will be to see to what extent we can find general principles for predicting from the gencralized quantifier interpretation of a gi\,en NP what possiblc e-type and/or ( r , t)-type interpretations it will have. This en terprisc turns out to slled nen- light on some old puzzles, such as the semantics of singt~lar definite NP's like t l ~ rX ' I ~ ~ ~ which SJ, turn out to be interpretable in all three types but with slishtly different presuppositional requirements in each. Opening up the issue of type-shifting principles and attempting to investigate them systematically also turns out to suggest a new perspective on thc copula br and on the

358 Barbara H. Partee cleterrniners (1 and ~ l w I; will suggest that this perspective ]nay offer sonic help in explaining why certain semantic "functors" may be cncoclcd either lexically or grammatically or not explicitly marked at all in different naturtll l a n g ~ ~ i ~ g e s . In sections I ancl 2 below I review a variety of proposals fol- interpreting various kinds of NP's ilnd some of the evidence for the clilini tlliit rhcre iIrc Nl' interpretations of all three types nicntionccl ubovc. T h e maill proposals for type-shifting principles are the subject of section 3. Section 4 deals with the "\Villiains puzzle" introduced the end of section 2; the proposed solution exemplities the possihiliry o f highly Ii~~iguiige specific type-shifting rules in contrast to the morc general pi-inciplcs descrihcd in scction 3. T h e paper concludcs with a brief sketch of sonic possiblc implications of the perspective advanced here for tlic trcatmcnt of English Iw in section -5.

1 Alternative Treatments of NP's: Some Examples I hegin bli reviewing altcrnativc interpretations for a ni~nibcrof diff'ereiit liinds of NP's, contrasting 12ilontague1s rrealmcnt \4,itli otl~ersthat can be foi~ndin thc litcrnture. These arc suiii~n:lrizcd in ?'able 1; coinmcnts follo\v. Considcr first the first three NP's in the table, Johrr, / I ( , , , , and i 2 z 3 c i : l frrrirn. One of Montague's best-known contrib~~tions to semantics was to show lioiv these ;IIIJothcr NP's could be given a uniform selnantic type, hy taking thc tl-pc of all NP's to he ( ( c , I ) , 1 ) .' T h e fi-uitf~~lncss of this idea is \ f . ~ l l - i ~ t t c b! ~ t ~now, d and there arc indel~endent reasons thr wanting to analyze at least some occurrcnces of proper n;llncs 11s generalized quantifiers, fbr instance ivhcn they occur in conjunctions lihc 'j"j'11t11~ u i l c~?cI:)' I P O N I N H nnd perhaps when they occur as antecedents of' "bountl L-ariablcpro~ ~ o u n s " Hut . ' otherwise it \voilld IJC iilorc natural to Iscat proper uaiiics and singular pronouns as individual constants ancl variat7les respectively; this is indeecl tlic nlore traditional view. Pastee lind Kooth (1083), in a disc~rssion~:Iiichfocuses mainly on type assignments to extensional and intcnsioilal verbs, argue for a modification of hIoiitaguc1s Table 1 MG Treatment of NP's and alternat~ves

NP

Translation

(1) John

MG: ;P[P(j)] I MG: ;P[P(x, jl xr~ MG: ,iP[Vx[man'(x) -- P(x)ll MG: iP[3x[Vy[man'(y) y = x] & P(x)]] (i) rx[manf(x)1 ( ~ i )ix[man'(x) & Vy[manf(y) - y XI] MG: ;.P[3x[manf(xj & P(xj]] (i) man' (ii) Kamp-Heirn: x, cond: manl(x,), x, "new" (i) Chierchia: ' dog' (ii) Carlson, in effect: iP[P( dog')] (iii) dog'

( 2 ) he,,

(3) every man (4) the man

(5) a man

(6) dogs

Type

-

Noun Phrase Interpretation 359 strategy of assigning to all members of a give11 syntactic catcgory the Lbl~igl~est" type needed for any of them. We proposed there that (i) each basic cxprcssion is lexically assigned the sinzplest type adequate to capture its meaning; (ii) therc arc general typelifting rules that provide additional higher-type meanings h r expressions, so that the uniform higher-type meanings Montague posited for a given syntactic category will indced be amorlg tlie available meanings for all expressions of that category; and (iii) there is a general processing strategy of trying lowest types first, using higher types only wlicn thej; are required in order to combine meanings by available compositional rulcs. (For examplc,.$hn would have to be "lifted" from j to ), PIP( j)l to interpret the conjunction John am/ e c q y n~u?rzn~r.) According to that proposal, Jolfrr ancl hr,, woi~ldhavc basic interpretations of type r, and the interpretations Montague assigned to then1 woi~ldbe predictably available by way of a general "lifting" rule. Ezlc>?:y7 ~ ~ 1 ho~vever, 7 , would havc only the gcneralizcd quantifier-type interpretation. This dual treatment of proper names and pronouns is one piece of the Inore general picture we \$-illdcvclop here. In the case of definite descriptions like the nznn, thcrc are of course millly issues of' pragmatics to worry about that affect the question of what belongs to the scn~antic content of such expressions. LVhilt I want to do is consider se\;cral possi\jle intcrprctations of diff'erent types and sec whether they can bc related by means of general tppcshifting prineiplcs; if so, that might relieve us of tlie burden of trying to decidc ~vhichis the "right" interpretation - perhaps they all are. One alternativc to Montague's generalized quantifier interpretation of thr min is thc iotn-operator analysis given in (4).of tvye r. T h e iota-operator combines with an open sentence to give an entitydenoting expression, denoting the ~ ~ n i q usatisficr e of that open sentence if there is just one, and L~iliilgto denote otherwise. (This interpretation coulcl also be "lifted" to a gcnel.alized quantifier interprctation different from h4ontaguc's, agreei~igwith that given by Bar~isiseand Cooper (1981).) Lcss familiar but at least inlplicit in some discussions is the possibility of a predicativc reading for definities, as givcn in (-Cii), which picks out the singleton set of (or the propertj of bcing) tlie uniclue man if thcrc is just one and the empty set (or empty propcrtv) otherwise. For indefinites, there again seem to he plausible interpretations of all thrce t!pcs: Montague's generalized cluantifier interprctation incorporating an existential cluilntifier; an (c, t ) interpretation equivalent to the barc common noun interpretation (the traditional translation of indefinites in pscdiGltc positions); and thc treatment suggcsted in recent work of Kamp and Hcim, which is not arlequatcly represented by the rough translation into intensional logic given in (5ii) but which can, I think, filirly be said to treat indefinites as e-type variables accompanied by conditions on assignnlcnts to those variables. 4 Barc plurals like llogs, in ( h ) , were not treated at all by h;fontaguc; C:arlson (1980) proposed that they be treated as proper names of hinds, and Chierchia (1982n, b, 1084) provides an enrichment of intensional logic including a nominalizacion operator n1;ipping properties onto property-correlates in the domain of entities, treating the barc plural as one such nominalization.' Carlson's ( ( J I , ) interpretation can then be reanalyzed in retrospect as in (6ii), as bearing the same relation to Chierchia's nominalixcd property '-'dog.' as A4ontague's translation of ordinary proper names bears t o their translation as individual constants. T h e simple (e, j) translation in (6iii) remains il plausible interpretation for bare plurills in predicate positions.

360 Barbara H. Partee

2 Evidence for Multiple Types for NP's So far I have just enumerated a number of cases where interpretations of differing types have been proposed for various NP's, without giving many arguments that a single NP may in h t have multiple interpretations. And indeed I do not intend to try to settle thc question of how many distinct interpretations any given NP has itnd just what they arc, although I will make some suggestions. In this section I will review some evidence for the plausibility of the claim that there are N P interpretations of at lcast types P and (e, t ) as well as ((P, I ) , t), and in what follows I will try to show how interpretations of thesc types can be systematically related to one another.

2.1 Evidence for type e T h e claim that proper names are basically of type e and only derivatively of type ((e, t), r ) hardly needs defense, and there is almost as much tradition (though more controversy) behind the treatment of singular definite descriptions as entity-dcnoting expressions. I-Iowever, there scemed to be no harm and considerable gain in uniformity in folloiving Montague's practice of treating these NP's always as ( ( 6 , t ) , i ) , until attention was turned to the relation between formal semantics and diseourse anaphora by the work of Kamp (1981) and Heim (1982). As illustrated in examples (7) and (8), not only proper names and definitcs license discourse anaphora, but indefinites as well; other more clearly "quantificational" NP's do not.

(7) John/the man/a man walked in. He looked tired. (8) Every man/no man/more thaii one man nialked in. "He looked tired. T h e generalization seeins to be that while any singular N P can bind a singular pronoun only an '>-type NP can liccnsc a singular in its (c-command or f-cornmand)"ornain, discourse pronoun. T h e analysis of indefinites is particularly crucial to the nced for invoking type e in the generalization, since if it were only proper naines and definite descriptions which licensed discourse aii;iphora, one could couch the generalization in terms of the retrievability of a unique individual from the standard Molltagovii~n generalized quantifier interpretation (an ultrafilter in those cases).

2.2 Evidence for type (e, t) Certain verbs appear to take ( c , r ) arguments; some allow only adjectivc phrase eomylcments (iuvn introcertcd, *fur11 an introvert), while others, like h ~ c o ~ nand e ~.on.sir/cr,allow both 14P and NP complements. Particularly strong evidcnce for tl~cseNP's being of type ( t ~I, ) comes from their conjoinability with AP's in such positions, sincc I assume that true constituent conjunction requires identical types and I have seen no evidencc for treating adjectivc phrases as either type e or ((e, t ) , t ) . (9) Mary considers John competent in semantics and an authority on unicorns.

Noun Phrase Interpretation 361 Although not all verbs that seem to take (e, t) complements allow exactly the same range of NP's in such complement positions (see Reed (1982))) I will for simplicity take occurrence with ronsi~fcras diagnostic for "predicative NP's", i.e. NP's that can have an (e, t) interpretation.

(10) Mary considers that an island / two islands / many islands / the prettiest island / the harbor / "every island / "most islands / *this island / "?Schiermonnikoog / 'Utopia. In general, the possibility of an N P having a predicative interpretation appears to be predictable from the model-theoretic properties of its interpretation as a generalized quantifier; in Gct we will argue below that all NP's in principle have an ( r , t ) interpretation, but some of them (like ezjery island, n~ost islunds) yield unsatisfiable or otherwise degenerate predicates. Williams (1983) notes that sentences lihe ( 1 1) provide counterexamples to the above claim. (11) This house has been eaery color. We will take up such examples in section 4, arguing that in these cases the possibility of an (e, t ) reading results from a language-specific and quite idiosyncratic property of the head noun of the construction, which affects the syntactic as well as the semantic properties of the resultiilg phrase.

3 Type-Shifting: General Principles and Particular Rules 3.1 A general picture While I aim to uncover considerable sj-stematicity in the phenomenon of type-shifting, 1 do not want to suggest that there is a singlb uniform and universal set of typc-shifting principles. There are some very general principles which are derivable directly from thc type theory, others which are quite general but which depend on the algebraic structure of particular domains (such as the ((c, t ) ,t) domain), others which require the imposition ofadditional structure on the domain of entities or other domains, and still others which seem to be language-particular rules. (Note that lexical rules of the sort discussed by Dowty (1978, 1979) usually involve a change of type; those which employ zero inorphology may be tllought of as a species of language-particular tj-pe-shifting rules.) 'Even the most general type-shifting principles, such as the "lifting" operation that maps j (type a) onto?. P[P( j)] (type ((el t ) , t)), nced not be universal, but I would expect such a principle to be universally available at "lou~cost" or "no cost" for any language that has NP's of type ((r't), t ) at dl.' Conversely, there might be typeshifting rules which are not of m y formal generality but which are universal or at least very commonly employcd hecause their substantive content has some high cognitive naturalness (such as perhaps the rule which turns proper names into common nouns denotinga salicnt characteristic, as in "He's areal Einstein"). T h e general picture I will sketch below will focus on formally definablc

362 Barbara H. Partee type-shifting princil~leswhich I believe are linguistically exploited in English and at least potentially universal; I believe this perspective might be helpful for studying semantic universals and typology, but I have not carried out any serious cross-linguistic study. In Figurc I, the circles represent the three model-theoretic domains DG,,),and D((,,,,I,,),labelled by their types, and the arrows represent mappings between them, operations which map objects in one domain onto corresponding objects in another domain.I will say more about some of them below; others will be discussed in subsequent sections. I should note here that while my fbcus in this paper is on type-shifting operations that can map NP-meanings onto other meanings for those same NY's, the same operations can of course be involved in rules which relate expressions in distinct syntactic categories as well. In particular, I eonsider (e, t ) a "marked" type for full NP's in English (as opposed to the "unmarked types" c and ((e, t ) , I ) ) ; it is the "unmarl<ed" type for common noun phrases and verb phrases, and one of'the possible types for adjective phrases and prepositional phrases, so we should not be surprised if the type-shifting operations mapping to or from type (e, t ) show up even more in rules relating NP's to expressions of other categories than in rules providing multiple meanings for single NP's. On the other hand, not all languages make as clear a syntactic distinction between NP's and CN's as English does, and the naturalness of some of these type-shifting operations may help to account for that fact.

Figure 1

lift : j -t AP[P(j)] lower : maps a principal ultrafilter onto its generator; lower(lift(j)) = j ident : j 4 R x [ x = j] iota : Y i rx[P(x)j iota(ident(j)) = j nom : P +"P (Chierchia) pred : x +"I( (Chiercl-lia) pred(nom(P)) = P

total; injective partial; surjective total; injective partial; surjective almost total; injective partial; surjective

Noun Phrase Interpretation 363 Many of the mappings comc it] pairs which are inverses, For examplc, the operation I$, which has been mentioned before, has an inverse /on)el-. Ll/i maps illly entity a onto the principal ultrafilter generated by a; in IL terms, it maps (the denotation of) j onto (the denotation of) ;1 P[P(j)]; in set-theoretic terms, it maps a onto LX [a E XI. L$ is total and injective ("into"). Its inverse, Inr~er, is partial and surjective ("onto"), = L r , and if mapping any principal ultrafilter onto its generator. So /oil~er(l(fi(~a)) hr,ler (3) is defined, /?fi(/un,er(3)) = 3.' T h e pair iden2 and iota are similarly inverses. Ident is the total, injective operation mapping any element onto its singleton set; in I L terms, it maps j onto Ax[x = j]. lola is its partial surjective inverse, mapping any singleton set onto its member; in IL, augmented by the iota operator, it maps P onto rx[P(x)]. (In an intensional system, we would want in addition or instead a version of inletlt mapping an entity onto the property of being that entity, and a version of iota mapping a property onto the uniquc individual having that property, if there is indeed just one, and undefined otherwise. In either case we would have iota(ident(a)) = n and, when defined, ident(tota(P)) = P.) T h e other pair of mappings between E and (e, t), now and pred, are extensional misrepresentations of the operators """ and from Chierchia ( 1 9 ~ 1 )Now, . ~ rw maps properties onto their entity-correlates if these exist (the Russell property, for instance, will be acceptable as a predicate but will not have any entity-correlate); this is the operation which on Chierchia's analysis is involved in nominalizing the common noun dog to form the bare plural dogs and the adjective blue to the proper noun blue, and in the formation of infinitives and gerunds from verb phrases. It is "almost" total, applying to all "ordinary" properties at least, and injective. Its inverse, pl-rd, applies to those entities which are entity-correlates of properties, and rcturns the corrcsponding property. Prrd is partial and "almost" surjective. Where defined, no?^^ and prerl are inverses. We will make use of these operators in our analysis of the Williams counterexample. These three pairs of operators illustrate the heterogeneity of tj-pe-shifting principles I alluded to at the beginning of this section: I ( f i is a matler of simple combinatorics that falls directly out of the type thcol-y, and would have an analogue between types a and ((a, b ) , O ) for any (1 and b. Lnmer is not independently definable in combinatoric terms since it does not apply to the whole of the higher domain, but is definable as the inverse of lifi or independently in terms of generators of ultrafilters. Ident and zuta ilre not merely combinatorial but are still "formal" insofar as they do not depend on ally particular assun~ptionsabout the domain D,.. Nurn and pwd are more "substanti~e" in that they depend on the inclusion of properties or propert?-correlates among the entities. There is also room for considerable diversity in how natural languages make use of such type-shifting principles, encoding them with lexical items (iola might be a candidate meaning for the definite article), via lexical rules (rrom or pred for the rule relating blue as adjective to blue as proper noun, depending on which one takes as hasic), syntactic rules ( n o w for the formation of bare plurals), or not encoding them at all (e.g. if l!fi is universal for proper nouns.) I will rcturn to these linguistic issues at various points below. 1 should note here that lamer is not necessarily part of the grammar of English at all, but is useful in the metathcory for predicting which NP's have e-type readings from their generalized quantifier interpretations.

"'"

1

i I

364 Barbara H. Partee

3.2 Sample application: the king in all three types By the criteria presented in section 2, singular definitc descriptions like tlze king can occur in all three types."' Figure 2 below shows mappings that could provide a possible account of'this distribution and of the slight differences in mcanitlg and presupposition that accompany the three uses. (The reader can fill in the caveats necded here ahout the wealth of research these suggestions need to be tested against and integratcd with, etc.) Solid lines indicate total functions, dotted lines partial ones.

Figure 2

Four of these mappings iwre described in the previous section: I$, lo~uel-,idmi, and iota. THE is the total f ~ ~ n c t i owhieh n maps any set Q o n t o the generalized quailtifier given by R/lontaguc's syncategorematic interpretation rule for the introduction of the (sec entry (4) in Tablc 1). In subsequent work in Montague grammar, this operation is usually assigned as the meaning of the determiner /he itselc it is cxprcssed in IL, as iQ1P[3 x ['v''{[Q(y) t.y = x) 8i P(x)J; in languages lacking an overt dcfinite article, onc would have to look for grounds for choosing between a syncategorematic treatment and the positing of a zero definite article. Sincc THE is a total function, there arc no presuppositions required for the use of definite descriptions as generalized quantificrs." If thcre is a unique king, TfIE(kinyl) denotes the set of all his pmperties; otherwise it denotes the empty set of properties, so that any sentence in which TIIE(kingl)has inaxinla1 scope comes out simply falsc. Io/a(X.ing'), on thc other hand, is defined iff thcre is one and only one king; if ivc assume that c is thc unnlarked type for subject position, 12 and the preferred type for arguments of extensional verbs genci-ally, this would help to explain the strong but not absolutc prcfercncc for taking existence and uniqucness as prcsuppositions ratheld than as part of the content in subject and other argument positions. So we have a contrast between an t2-type meaning iota(btngl) and an ((el t ) ,t ) meaning, THE(king'), traceable to two alternative meanings for the, namely iolu and

Noun Phrase Interpretation 365

1

(

THE. These are related to each other by the fiact that whenever ioirr is defined, i.e. whenever there is one and only one king, liJi(iota(kingt)) = THE(kingt) and lon7er (1HE(kinKf))= rsta(ki~b),and furthermore whenever iota is not defined, TIIE(kin'g') is vacuous in that it denotes the empty set of properties. (ir'HE(king') will generally have a non-vacuous intension, of course, which is presumably why it is useful to have a presuppositionless version of definite descriptions.) Now what about a possible predicative ((e, t ) ) reading for t/ze king? Suppose we start with the ((6, t), t) reading THE(kin,?'). We know that onc way of getting- from a denotation of type ((e, t ) , t) to one of type (e, t) is to apply the function de~lotcdby Montagi~e's PTQtranslation of English he, ?L31bx[3(;ly[y = x])]. This is the f ~ ~ n c t i o called n HE in the diagram; I will say more to argue for its "naturalness" in the next section. For now let me just present the suggestion that we treat this operator not as the meaning of the word hc but as a type-shifting functor that we apply to the generalized quantifier meaning- of an NP whenever we find the N P in an (8, t) position.'" T h e English he itself, I will suggest (following Williams (1983)), subcategorizes semantically for an e argument and an (6, t ) argument, and has as its meaning "apply predicate", i.e. ).PAx[P(x)]. This pair of proposals gives the same result as Montague's for phrases like be the king, be a man, hc John, but distributes the meaning among the parts differently, in such a way that we now have a predicative reading for NP's in positions other than after hc (which hlontague's treatment did not provide), and we can now have the same be occurring with NP's and with predicates of other syntactic catcgories. I thinh this is an important advantage and will say more about it in later sections; let's return now to the implications of this proposal for the predicative reading of lie king, which can be defined as BE(THE(king')). In IL terms, BE(THE(king')) tliorhs out to be ?"x[king'(x) & Vy[kingt(y) y = x11, or equivalently, lLx[3y[king'(x) x = yll. This gives the singleton set of the unique Ling if there is one, the empty set otherwise. Since both BE and THE are total functions, this is always available as a possible (e, t) reading of the king; no presuppositions are required. Note that if there is at most one king, king' = BE(THE(kingf)), i.e. this predicative reading of the king is the same as the common noun king in that case, since both pick out the empty set if there is no king- and a singleton set if there is exactly one king. T h e fact that the conlmon noun and the predicative definite description agree modulo this "at most one" presupposition may help explain why in English the definite article is sometimes but not always optional in predicative constructions, as illustrated in (1 2).

-

(12) (a) John is {the president / president) (b) John is (the teacher / "teacher 1 It appears that the definite article is optional in such constructions just in case the presupposition that there is at most onc such-and-such in any context is virtually built into the language, so that the conditions for thc equivalence of predicative the presiri~wt and presirlent can generally be tahen for granted. IVhile this somewhat ti~nctioni~l account may help to explain the contrast between (12a) and (12b), it cannot be taken as a predictive explanation, sincc as we will see in the next section, predicative indefinites like (1 ?nun are always fully equivi~lentto the common noun, so it would seem even more narural for a language to omit redundant indefinite articles, as in French, than redundant definite articles.

366 Barbara H. Partee T h e double-headed arrow on the 1l/c111 mapping- reflects the f ~ c that t for iolll to be clcfined there must be one and only one king, hence ki~z~c' = BE(THE(kingl)) = ident(iot~~(kil~~'j). In f:~ct,when io~nis defined, tlle diagram is fully commutative: kiugl= BE(THE(kingf)) = ident(iotn(king1)) = ii/fwt(loi~~er(THL(king'))) = BE(/zft(iotn(king'))),etc. This property of the mappings lends some formal support to the idca that there is a unity among the three meanings of the kiug in spite of the diffcrence in typc. There are of course alternatives that should be considcrcd; the diagram would also be commutati\-e if we rcplace the total function THE by a partial function identical to the con~positionliJi . iotn, so that therc would be the same presuppositions for the meanings in cvcry type, and no reading of the king lackillg those presuppositions. I tend to believe there is a presuppositionless reading, but I doubt that clear arguments can be found within a purely extensional sublanguage.

3.3 A and BE as "natural" type-shifting functors Whcn we consider possible functirrns mapping from (el t ) to ((t,I ) , t ) , the obvious candidates are all the determiners, since that is exactly their type. Natural language data suggest that a (and plural some) and the are particularly natural, siilce they are often not expressed by a scparatc wold or morpheme but by constructional features, or not expressed at all. Sometimes definites are inarked but indefinites unmarkccl. Determiners like every, nzavy, most, and numerals are always expressed by a word or morphun~e,as f i ~ r as I know. Sometinles iln indefinite article is ovcrt in referential positions, unexpressed in predicative positions. Can we find fornlal backing for the intuition that what LL and thr denote in English are particularly "natural" type-shifting functors? We havc already done this to some extent for tlte; here m-e will consider a, and also strengthen thc case for the naturalness of'the functor BE introduced in the previous section. Let A be the categorenlatic version of Montague's treatment of d u n : in IL terms, IbQ[AP[3x[Q(x)& P (x]]]. We will focus first on the naturalness of RE,'^ then argue that il is natural in part by virtue of being an inverse of BE.

Fur I:

Fact 2:

BE is a homomorphism from ( ( c , t ) , I ) to (e, I) viewed as Boolean structures, i.e.: AE(31 n 32) = BE(31) n BE(32) BE(31 U S2) = BE(31) U BE(n2) BE(n.3,) = U B C ( ~ ~ ) BE is the uniclue homomorphism that makes Figure 3 commute. (Therc are other homomorphisms, and other functors that make the diagram commute, but no othcrs that do both.)15

What exactly does BE do? Perhaps more perspicuous than Montague's IL formulation is its cspression in set-theoretical terms: A.?[Lx[{x) € 311. That is, i t applies to a generalized quantifier, finds all the singletons therein, and collccts their elements into a sct. T11e commutativity of Figure 3 is then straightfor~vard,since a generalized quantifier obtained b y applying llfi to an entity n will contain just one singleton, ILL}. And as Keenan and Faltz (1978, 1985) showed, the full ( ( e , r), I) domain can be generated by applying Boolean operations to generalized quantifiers of that special sort (the

Noun Phrase Interpretation 367

I

Figure 3

1

"individual sul~liinations",in the terms of Dotvty, Wall and Pcters (1981)). So BE does indeed secm to be a particularly nice, structure-preserving mapping fiom ( ( c , I), /) to ( P , f). The semantic naturalness of the BE operator is of course independent of whether we take it to be the meaning of English he, analyzed as a transitive verb taking ( ( P , t), /) objects as in PTQ, or, as I proposed above, treat it as a (potelltially universal) operator that is always available to turn an ( ( e ,t), t) meaning into an (r, t) meaning. T h e choice betwccn the analyses will depend heavily on syntactic considcrations. In either casc, BE is a total function, so we still have to explain why sornc NP's don't occur naturall!; aftcr be or in other predicative positions. T h e explanation is that althoupl~BE is total, and preserves important structure of the ((e, t), t) domain, it also ignores a lot of structure by looking only at the singletons in any generalizcd quantifier. A/Iosr rncn, for insrance, will never contain any singletons, so he Itlost 9~e?7will always be empty; similarly fix distributive rcadings of plurals likc cn7o men, srz~crnlrnen, etc. (Group readings of suc1-1 plurals yield good predicative readings, which is predicted if groups or plural individuals are treated as entities, ils in Link (1983).) L ' z w ) ~t?rlzrr contains a singleton only if there is just one man; although it is probably too strong (certainly among logicians!) to claim that ezltr-y presupposes "more than one", one and zero are degenerate cases, usually includcd only for the sake of generality, and to use every mczn prcdicatively you would have to krror~)you were dealing with a degenerate case, in N-hichcase the or t h ~ on!]! tvould be appropriate and more straightforward. Note that RE(no mani) = not(BE(a mani)); English seems to prefer thc latter construction, Dutch the former, although I don't think either would be declared ungrammatical in either language. In general it seems that thc NP's that yield sensible predicative readings fall illto two categories: those fosincd with "weak" determiners (Nlilsark 1077; Rarwise and C:ooper 1981), which are intui~ivelythe indefinites, and definite singular NP's. In the forn~cr case the predicative reading is tantamount to stripping -,i off tllc gcneralizcd quantifier reading and leaving the common noun meaning (since BE and .-l arc inverses); in the of defjnitc singulars, thc extensionality of the systcm discussed here u-ould make the prcdicative reading tantamount to applying iclent to the corresponding entity, Ih probdAy an unsatisfiactory analysis. Having established the naturalness of BE as a type-shifting functor from ((e, t ) , t ) to (c, t ) , one question that springs to mind is: For what possible D E l ' n ~ e a n i i ~ giss it true that BE(DET(P)) = P?" One answcr is -4, as is from the fact that in PTQ, (he a marz)' comes out equivalent to man'; hence meets one rcasonablc condition for

368 Barbara H. Partee naturalness by virtue of being an inverse of RE. (But exclctl)~one is also an inverse for BE; the general requireinent is that the singleton sets contained in DET(P) inust be all and only the singletoils of elerncilts of P.) Two other potentially significant properties of A arc that it is syinmctric and is monotonically increasing in both arguments; I coiljecture that these are both "nice" properties. That's a viigue claim, but I would expect to see it borne out in order of acquisition and in cross-linguistic distribution of determiners and of' any other functor categories for which those properties are definable. T h e properties certainly distinguish ,-I from e~vic.t/yonr, which has neither of them. I would conjecture, in Fact, that among all possiblc DET-type f~lnctoi-s.,-l (which coinbines English LE and s o ~ n p )and THE are the most "natural" and hence the mast likely to operate syncategoreii~aticallyin natural languages, or not to be expressed overtly at all, and that BE is the most "natural" functor f r o n ~( ( r , t ) , I ) n~eaniilgsto (I., t ) meanir~gs.011the t'ornial side, this rcquires finding and arguing for further formal criteria for what makes a functor "natural", and showing that 11, THE, and BE score high under such criteria. On the linguistic side, I would expect to see f'urthcr evidence that the semantic force of A, THE and R E is often carried by constr uclional ralher than lexical meaning. 18

3.4 Mappings to and from type e In AJontague's PTQ no English er;pl.essions were analyzed as type e; on our approach, there is still no syntactic category uniformly interpreted as type e, but many NP's have typc r interpretations as one of their possible interpretations. Lexical NP's, proper nouns and singular pronouns may be basically of type e alld acquire (e, I ) and ((f, t ) ,f } meanings by idmt and Izfi respectively. Non-lexical NY's with e-type interpretations are probably most easily accounted for as resulting from type-shifting operations applied to initially higher type interpretations, although it is possible that type-lowering has become grammaticized so that, for instance, the may have an interpretation as iota as well as (or instead of) an interpretation 3s THE. (It may not be eilsi to find argu~r~eirts to decide whether the e)-type iilterpretation of the king is best analyzed as iotct(Xrirtg1)or as Eome~+(THE(kin,g') ).) U7e have alrcady mentioned several mappings to and from type e: l$t and lon~er,iden/ and iofa, nom and prert. In this section we will sap n bit more about Iortler, and particularly about the Kamp-Heini treatment of indefinites as type P . Thcn we will suggest that the type-shifting perspective fits ~vellwith recent proposals by 1,ink and others for the treatment of mass and plural noun phrases using 111odel structures which inipose additional structure on various subdo~nainsof the donxiin of entities.

As described in section 3.1, louler applies to any gencl-alized quantifier which is a principal ultrafilter and maps it onto its generating clement in tho e domain. This accounts for E-type readings of' definite s i ~ ~ g u lNP's a r like ~ h kc i q , this doIq, Bill's erbr (andJohn and Ize, if these arc not directly generated as typc c.) It does not directly give e-type readings for definite plurals like t//osc tlfrre men, a principal filter whose generator is a set, nor to indefinite singulars like rr man, which on their standard

Noun Phrase Interpretation 369 treatment are not principal filters at all. T h e former case will be taken LIP whci~we discuss 1,ink's treatment of plurals, the latter right now. While Kamp's and Heim's proposals for the treatment of various kinds of noun phrases and anaphora suggest rather far-reaching changes in the semantic frameworli, Zeevat (1981) has recast central parts of thcir proposals in terms that help to localize the major innovations around the treatment of free variables and the mechanisms of variable-binding. Using Zeevat's notation, an "indexed indefinite" like [a rnrrnl,, can bc translated as in (13),

where the asterisk is a diacritic that plays a role in thc non-standard rules for variablcbinding. Alternativelq-, it could bc translated as RP(P(xE)]plus the condition manl(x,,), if the condition is treated as a scparate clause as in Hcim (1982). Tn cither case, ils Hcim has emphasized, the removal of the existential quantifier from the interpretation of indefinites makes thcir meanings much more like pronoun meanings, and apart horn the complication that u-e are here dealing with variables, the meanings arc similar to proper noun meanings like 3, P [P (j)], and loper call apply to g i ~ ea nlcllr an c-type reading x z (together with the condition rnnn'(~,,)).~"

Link (1983) proposcd additional structure within the domain of entities, including the rccognition of a subdomain of "plul-al individuals" and a subdomain of quantities of matter, each with a ccrtain amount of Boolean structure and with a mapping from the formcr to the latter; in terms of this structure Idink is able to solve a number of puzzlcs in the semantics of plurals and mass nouns. T o integrate his structure with the perspective suggested kere, u7ecan see that there is a natural pair of mappings relating 1,ink's plural individuals in the e domain to sets of ordinary individuals, in the (e, I ) domain; let us call these mappings link and ~lelink,as in Figure 4 below. 'fhen link({(4, h } ) = a B; rleliuk ( a @ b) = {a, b ) . Linh is total (singleton scts map onto the single individuals u-hich are the atoms of the plural-individual structure) and injective; ~lelinkis partial iind surjective. With this possibility of easy shifting between the group (indi\ridual) perspective and the set perspective, we can readily generate e-type readings of definite pl~ualslike tlzr three mrn, in fact via scve~xlequivalent routes. If we start with a distributive rending

+

Figure 4

370 Barbara H. Partee like Barwise and C:ooper's, taking the generator sct of the principal filter (a new operation we call gense~)would get us a sct of (the) three men, whencc /ink would get us a plural individual. Starting with the kind of group reading provided by Link, we could apply l o ~ ~ directly n. to get the same plural individual. T h e behavior of the cardinals /PO, t h e e , . .. can probably also be illun~inatcdon this perspective; briefly, I would suggest that the primar>- interpretation of three is as an ( e , i) ndjectivc applying to plural individuals (here it means "exactly three"), which can be promoted to an ( ( e , t ) , (e, t ) ) prenominal (intersective) adjective by standard treatment of techniques. Then either by composition with .i or 19- the Kan~p-Hei~n indefinites it can bccome 1.1 determiner (group reading), picking up the explicit or implicit existential quantifier which would account for thc "at least" reading normally associated with cardinal dcterrniners. Lastly, the llelink operation could naturally be extended to a corresponding operation on a11 "group" deter~ninerst o yield corresponding distributive determiners; an analogous operation was proposed in Michael Rcnnett's dissertation (Bennett 1974). Pelletier and Schubert (1989) discuss a uidc range of problems in the sy~ltaxand se~nanticsof mass expressions and provide an excellent critical survey of suggested solutions, offering some new proposals of their own. Drawing in part on the work of Link and of Cl~icrchiadiscussed here, as well as earlier work by Parsons, t'elleticr, tcr Rileulen and others, thcy sketch several alternative ayproachcs which make use of implicit semantic operations. Some of thcse operators ~ c r f i ) r ~type-shifting n OPCI.ations, others have ivhat we might call "sort-shifting" effects within a singlc ape; as noted earlier, the distinction is a very theory-dependent one that wc don't wish 10 lily any enlphasis on herc. _Much of the hcaviest dcbate in tllc mass noun literature concerns the semantics of predicative mass expressions and the question of what they are true ot': ordinarj- objects, quantities of matter, and/or substances or kinds. Pclicticr and Schubert show lloit- one can talte various positions both OII thc number and nature of the ontological distinctions inadc in the model and on thc ni~mberand naturc of discrete senses of mass prccticates relative to a given ontological bachground. A number of thc proposals tlley ctescribe involve sort-shifting operators which convert, for example, a inass prcdicate true of kinds (as in "Red wine is n,ir/c") illto one true of objects or quantities of matter (as in "'I'he puddle on the floor is ~ ~ ? i l i cor " ) vice vcrsa. 'Their own proposals suggest the desirability of letting the "unmarked" or default case for inass predicates be that a given mass predicate such as /?err can appljl indif'fcrentlyto entities of a nunlber of different sorts: quantitics oi' bcer, kinds of bccr, conventional servings or kinds of servings of' beer; objects coincident with or constituted by quantities of beer, and involving what we might call "sort-restricting- operators" as part of the sclnantics of constructions 11-hich limit thc applicability of the predicate to some propel- subset of these cases; thcse can be 1-icwcdas a special kind of sort-shiftcrs 1vhic11 talte a inore general sort onto a subsort. Such a possibilit! does not exist fi~rtypcshifting operators in a type theory like Montague's but would in some more gcneral theories of types and is ~hcreforcan interesting potential addition to the inventory of natural type-shifting operations. Chierchia, ;11so propose typc-shifting operators Pelletier and Schubert, fi)llowi~~g converting mass predicates (typically expressed as common noun phrases) ofthese various sorts to mass terms dcnoting substances (typically exprcsscd as tletern~inerlcssfull NP's)

Noun Phrase Interpretation 371 and vice versa. As in Chierchia, these are basically the same nonz and pred operators that apply in the semantics of bare plurals and other nominalization phenomena. And of course the ease of shifting between mass and count senses of the same common noun phrase has long been noted and illustrates the existence of other apparently very natural short-shifting operations that may or ma!; not bc grammaticized in different languages: count to mass via the Pelletier/Lewis "universal prindcr" (put in a chair and you end up with chair all over the floor); mass to count with either a "conventional portion of" or "kind of" interpretation.

3.4.3 Stvuclure iin the e domain All of the opcratioi~snow and pred, link and delink, and analogs for mass terms depend on the existence of richly structured subdomains in the donlain of' entities; thcse structures can bc seen to be taliing or7cr soinc of the ~ v a r kprevious1~-done by the type theory. More of the same sort of shift can be seen in proposals fin- the scmantics of comparatives which treat "degrees" as entities, and in prol>osals h r an event-based ontology in n-hich cvents are also cntities. First-ordei- thcories put \-irtually /I// of thc burden on structure internal to the entity domain; Chierchia (1984) argues thilt linguistic evidence favors a semantics which is at lcast second-ordcr but not a fully rccursivc type system like Nlontague's. This kind of investigation of trade-offs betnccn strongly typed systems and less strongly typed systems with multiple subsorts of entities is also being carried out in the domain of programming languages; see Gogucn and 12.leseguer (1984). i\lcscguer and Gogi~en(1984) and Futasugi et nl. (1985)."' i t is partly because this kind of study opens up so m;mv possibilities that have not becn explored that I feel in no position to argue for a "best" way of analyzing particular constructions. In closing this section, let n1e note that there remain NP's for which none of OUI. operations provide e-type readings; these, not surprising-lj-, are the ones traditionallj~ thought of as most clearly "quantificational": no rrlnn, wo men, a1 lrlnst o ~ wnrlrn, . / i ~ nmen, ~ sol rwyy , ~ u 1 1 ,~no.s/t l ~ c n . ~ E' P ~ nlnn T ~ could get an e-type reading via lon7cr in case t l ~ r r c is on]!- one man; but linguistically it never seems to act as a singular "referential" term, suggesting again (cf. section 3.3) that it is at least pragn~aticalljanomalous to use iJz3cr)r in a way that constrains it to just one. Such NP's can occur in e-type positions only by "qumtiifvng in", which tvould account for the tr.aditioni11 distinction between thcnl and "refcrring expressions". On the pcrspectivc advanced here, we can capture such traditional distinctions without giving up the unification achieved bk Montaguc's worli, which we still need in order to account for the possibility of conjunctions like "King John and ever?- peasant", which would be inexplicable on an analysis LI hich captured only thc differences and not thc common ((e, I ) , t ) structure.

The Williams Puzzle Anticipating the kind of proposal put form-ard in section 3.3, MTillian~s (1983) argued that the possibilit~of (e, t) readings for NP's cannor be predicted from the determiner, citing exainples like (14), where virtually any detern~iilcrcan occur.

372 Barbara H. Partee (14)

This house has been every color.

I believe this apparent counterexample and others like it can be explained in terms of the idiosyncratic and language-particular behavior of the head noun. In English (but not e.g. in Dutch) many "attribute" nouns allow this kind of construction: I-alov, size, lur~gth,weight, agt, p).ize. A relatively "tolerant" context which accepts such nouns rather casil!; is "This dress is the wrong - , a more restrictive one is in thc use of thcse "attribute NP's" as postnominal modifiers, as in (1S), where grammaticality judgments arc my own - there appears to be considerable individual variation on judgments about particular- words, reinforcing thc idea that this is 1.1 quitc idiosl-ncratic lcxical property. 9,

(15) a dress that size / that color / that length / that pricc / "that material / *that design / ?that pattern / *that origin. In this construction ure have a predicative ((r,1 ) ) use of an N P that does not correspond to the result of any of the type-shifting operations we have seen so fir. T o see what's going on semantically, consider the following pattern: (16)

(a) This shirt is blue. (b) Blue is a nice color. (c) This shirt is a nice color.

In (lha), blue is an adjectival predicate ((e, t)), predicated of the shirt. In (Ihb), we have the nominalized property blue, type e, and the expected ( c , t ) predicative use of o nile color; tlic cntitics in the extension of l.olor are colors: blue, red, green, etc. not shirts. Semantically, (16c) is quitc different from (lhb), and aniounts to something like a combination of (16a) and (I6b) with the color unspecified. Man): languages do not allow this kind of predication to be expressed with a simple noun phase but require the equi\-alent of (17a) or (17b) below, construction types which also occur with some attribute nouns in English. -

(17) (a) This shirt is of a nice color. (b) This shirt has a nice color. T h e possibilit) of using bare NP's as predicates in this way in English is rcnlinisccnt of the adverbial usc of NP's studied by Idarson (1985), which is also quite idiosyncratic: thnl ik)~, thllt nlqy, "tltnt n~anneu. T h e crucial formal tool that allows a straightforward account of this special predicative use of attribute NP's is Chierchia's nominalization theory, which relates prcdicative properties like Dlz~pas in (16a) to their type e nominalizations as in (16b). Although Chierchia's theory tahes properties as (intensional) primitives, I don't think it does any harm here to misrepresent the predicative property as type ( c , t ) for ease of exposition. If we take adjectival hlue, ( t , t ) , as basic, thc e-type proper noun hlue can be translated in Chierchia's system as "1)lue'; if we tahe the u-typc noun as basic, the adjective is "blur'; in either case the two are related by those inverse operators, the ones

Noun Phrase Interpretation 373 we called prom and prerl in section 3.1. Recall that prerl, or """, is defined only for entities which are the "entificd" counterparts of properties. Color is a colnlnorl noun, its type (r, t); entities in its extension are, as noted itbove, properties (bl~ie,red, etc.). This is the semantic content of what I mean by "attributc noun": these nouns express properties of properties. In addition to knowing this scmantic tact about the noun color, we must encode with a diacritic syntactic featlire sity, +ii - the syntactic difference between "adjectival" attribute nouns like r.olor, size, n)r>ighr ~ n dltge which clo fit into constructions like those in (14), (15), and (lbc) and otl~cr attribute nouns like propert)!, zv'rtue, and o e i n which do not. T h e combining stem -t/lir~g can function as a A attribute noun, as in the freclucntly puzzled-over construction in (18). -

+

(18) H e is everything I hoped he would be (intelligent, non-sexist, vcgctarian, etc.)

1 all1 not sure ~vllatto call the syntactic category of this special predicative use of attribute NP's; here I will assume that they belong to a syntactic catepor! Prtil (semantic type (e, 1)) which includes predicative adjective uses of NP1s, since tl~csc special attribute NP's can occur in constructions here othcr prrtdicativc NP's cannot, such as postnominal position as in (15) and in t/lCrc-constructions as in (10) bclow (on some analy-ses these arc the sarne Pact): (19) (a) (b) (c) (d)

Tl~ere'snothing hcrc a good color. 'There's no one herc the right age. "There's no one here a good teacher. 'There's nothing here the rigllt ansu-er.

To complete the anal>-sis,I need just one syntactic and senlantic rule and a couplc of uncontroversial assumptions. 'l'he first assumption is that any NP whose head noun has the feature +A also has the featurc +A; this follows from most theories of featurc 77 inheritance.-- T h e second is that the rule of quantifJ-ing-in23 quantifies generalized quantifiers into r-tlpe positions onlyl not into ( 0 , t) positions. I will also assume il proform tlzal, as an r-type +.A variable over (entified) properties; this corresponds to tlle use of thni discussed by Ross (1969), illustrated in (20).

(20) They said shc was beautiful and {that she was / she was that 1 The svntactic and semantic rule for attribute predicates can be formulated as follows: .ittriBu/e Prrw'icnte Rule Sj/ntlll.iic.RN/L>: If' a] is +A, then Semlrr-l~icRule: If IKp a] tl.anslatcs as

[Pred Y',

then

a ] ] is a Pred.

LPrecllhy X I \ translates as U,!.

Note that the senlalltic rule is defined only for NP's of type r and turns them into (e, I ) predicates; so this rule applies to attribute NP's like tlrut i.olor, I ~ i.olo~* P A4a1:)tIiX~~rl bcsr, a ~.olnrI onc-c saw ilz u .siinsel, IJIW c-olon (group reading), and the pro-form thrrl;, \vhich all l~~ive '.-type readings via the general principles discussed earlier, but not C ' L ~ P I1.oIor. :~

374 Barbara H. Partee T h e generalized quantifier reading of +A NP's is just like that of any other NP, and no special rules apply to them; we only need assume that only a +A N P can be quantified into a +A position. We can now illustrate the s!-ntactic derivation and semantic interpretation of Williams' example (14).

(10) This housc has been every color

A

(9) [every ~ o l o r ] p j ~ (8) this house has been (p,,d[n;l~that

/'\

(7) this house

(6) has been

[ P r c d [ ~that ~

i]]

( 5 ) has

(1)

[NP that

;I

xi (type c ) "xi (type(c, t ) ) ?,Pix[P(x)] ?~P~xLP(x)]("x~) 3 ?.x['-'x;(x)](typc(e, I ) ) i Q i y [ H ( Q ( y ) ) ] (here 14 is a past operator) ~ Q ~ - ~ [ I ~ ( Q ( ~ ) ) ] ( ~ - X [ ~ X ~ ( X3 )~!(H("x;(!)) ]) 1 (type(e, I ) ) hl (tvpe e; I ignore the internal structure of this NP here) ?by[~('xi(y))](hl) 3 H('~i(h1)) iPIV?r[colorl(x)+P(x) l] iP[Vx[ colorf(x)+ P ( x ) ] ] ( ; ~ x ~ [ I - ~ ())I) ~ ' x3 ~~( x~colorf(x)+l-I(!-'x(~I~ ,1 ))I T h e last line givcs the desirctl interpretation: for all x, if x is a eolol-, at some time in the past this housc has had the propertj 'ri, the predicative version of the property x. Semantically, this analysis depends heavil! on Chicrchia's treatment of nominalization; syntactically, it depends on having a syntactic derivation in which the ~ y p NP c position contained within the derived Pred senlains accessible to quantifj-ing in, sincc I assume one cannot generally quantify into (P,t ) positions. 1 belieye that thc salne principles account for the exceptional rclativization out of predicate position cxcmplified in (18). A similar approach might account for another kind of casc of quantified NP's appearing in predicate position, as in (22).

Noun Phrase Interpretation 375 (22) Olivier has been every Shakespearean king. Here we have an ordinary noun as head, and various treatments are possible, depending on what one considcrs the hest analysis of sentences like ( 2 3 ) .

(23) Oliver is Richard 111. If one analyzes both NP's as +type, either treating this is as "is playing" or by admitting a be of identity, then this isn't really a predicative position and quantifying in is to be expected. I would suggest that we have the same he here as elsewhere, and that Richard 111 as a role is a non-rigid individual concept of (t!pe (e, t)) (see Janssen (1084) for related discussion), which ean bc turned into a predicate nominal, in this case [PN034 IISP Richard III]], interpreted as E,x[x = "r]. However, unless v7e inap "roles" as individual concepts back into the entity domain in a move analogous to Chierchia's, we would still need to give a non-standard type analysis to es-cJyj!Shakespealvan king.

5 English be In section 3.2 above we suggested that the semantic operation we called HE should be treated not as the meaning of English be but as a type-shifting functor fi-culy applical~le to generalized quantifier meanings of NP's to yield predicative readings for those NP's. We suggested further, following Williams (1983), that English be subcatcgorizcs semantically for an e argument and an (e, t ) argument, with a meaning paraphrasable as "apply predicate". (This treatment of he was adopted in the derivation (21) of example sentcncc (14).) We may want to say further that bc imposes no sortal rcstrietions of its own, requising that its (e, t) argument be preclicahle of its c argument. Depending on how inclusive the e domain is, one may want to go furtl~crand c;lll be genuinely polymorphic, taking one X-type and one (X, t)-t!:pe argument, for any type X. If we accept Williams's argument that the arguments of hr may oecur in either order, we get the added benefit of aut-omatically generating both readings of an~biguous pseudoclefts; this is discussed filrther in Partee (1986). An appropriate treatment of this "semantic transparency" of he should also be able to account for eases of control phenomena and other instances of "syntactic conncctedness" (Higgins 107.3) across he, provided the control phenomena are treated semantically; but this is z; suggestion in nccd of' considerable work before it becomes a serious proposal. It may bc going too far to think of he as making no semantic contribution of its own, although this is a Girly traditional view. On the proposals just sketched, therc would be no difference in meaning at all between cllt and be n cul, askrep and be askrep, ctc. While this is also true of Montague's treatment and of most proposals that are expressible in first-order logic, it seems questionable. One should consider in this regard the insightful work of Stump (1985), mho assigns to be a kind of sort-shifting meaning, turning predicates of stages (G. Carlson ontology) into predicates of individuals but otherwise still semantically transparent.

376 Barbara H. Partee T h e syntax and senlantics of the copula in English and other languages is of course a vast subject which I can't hope to do justice to in a few paragi-aphs. But it docs seem promising that the present approach allows a treatment of bc that accords well with traditional views suggested by the word ~.opz~la, pt-escrving thc positive aspects of Montague's treatment of the br ArP construction while unifying that construction with other kinds of be Pwd construction.

+

+

6 Conclusions Much work remains to be done to determine the appropriate way to incorporate the kinds of operators studied here into a theory of grammar. I have said very little about syntax or about constraints on the mapping of syntax to semantics in this paper. Most of the emphasis has been on the exploration of certain kinds of operations which I belieye are at work somewhere in the semantics of English and many of them probably universally. Some of them may be built into the operation of specific rules, e.g. the norn opcrator in the semantics of' rilles of nominalization: some may appl!. frecly wherlever there is a mismatcl~between the simplest type of a given cxprcssion and the type nceded for a particular occurrence of it to be well-formed, c.g. /!itprovides a simple ctype N P like John with a generalized quantifier meaning so that it can occur in conjunctions like John ~ l n de z l ~ q / other st.ul/cnt. Some may be language-specific, like the +A-rule ciiscussed in connection with the Kiilliams puzzle in section 4; others, like the free applicability of lift to provide generalized quantifier meaning to +type NP's, map well be universal, at least among languages which havc NP's with generalized quantifier n~eanillgsat all. Finding which arc which, and undoubtedly uncovering new type-shifting and sort-shifting principles in the process, would appear to l3e an important and promising venture which will require close study of a wide range of languages. Another general direction of sesearch suggested by these beginnings that may be of interest beyond the study of scmalltics is the search for "cognitively natural" opcrations. As I suggested at various points above, I believe an interesting case can be made for regarding certain semantic operations or fi~nctionsof a given typc as more "natural" than others on various plausible criteria, vague as such a notion must be. I will closc by reiterating the need for interdisciplinar? collabol-ative efforts oil this issue, empirical studies to help determine what kinds of operations and functions arc particularly widespread in the world's languages, frequently occur sy11catego1-ematically, are acquired early, etc.; and fornlal studies to help us gain a better understanding of the possible structures of semantic domains and possihle formal criteria of natur.a 1ncss to apply to mappings between them. One can imagine such studies of "natural niappings" extending well beyond the sorts of cases studied here, and relating to such disparate issues as the role of symmetry in perception, the problem of projectiblc predicates ("grue" vs. "grecn"), the interpretation of metaphors, and the development of mathematical intuition. W-herever one call uncover richly structured domains and evidence of an important role being played by mappings between them, it should be possible to investigate the relatiye cognitive "naturalness" of various such mappings, and such studies should in principle help to advancc our understanding of the contribution our

Noun Phrase Interpretation 377

I

I

"hardwired" predilections make to the wag we make sense of the world we find ourselves in.

Notes I am gratefill to many sources of aid and encouragement in the development of this paper. T h e initiirl inlpctus came from Edwin M'illiani's persuasive arguments against a uniform category-type correspondcncc for NP's, ijs set out in Williams (1983); my first attempts to find a way to accept Willian~s's arguments without throwing out the indisputably fruitful uniform interpretation of NP's as gencralizcd quantifiers were out in a seminar jointly taught in the Spring of 1984 by Emmon I3acl1, Hans Lamp, and me, and I am grateful to all its participants for valuable comlnents and suggestions, particularly Nina Dabek, Roger Higgins, Hans Kamp, and Edwin Williams. T h c idea of looking for "natural functions" between a domain and range of gilen sorts or types had been earlier suggcstcd by work of David Lebeaux on unifjing the interprctation of the progrcssi~cin a seminar on tensc and aspect \vhich hmmon Bach and I had taught in the Spring of 1982. Furthcr clcvclopn~cntscame during a six-weck period in the Suminer of 1984 as visiting scholar nt Stanford's Centcr for the S t ~ ~ c l y of Languagc and Information, where I presentcd a prelinlinary version of tliis paper. My resc;irch during the summer was supported in part by CSLI and in part by a grant from thc System Development Foundation, the latter of which has also supported my subsecluent research and writing up of the paper. I received invaluable help and encouragement from collcagucs and srt~dcntswho accompanied me to CSLI, especially Gennaro Chierchia, Raymond Turner, Nina Ilabck, Craigc Roberts, and Karina Wilkinson, and from other local and visiting researchers at CISLI, including Ivan Sag, I.:wan Iilein. Paul Kiparshq, Ton Uiasow, Joan Brcsnan, h,lark Johnson, and especially Jose Mesegucr and Joseph Goguen, who introduced me to the literature on polynlorphic typcs and to the algebraic pcrspcctive on tj-pe- (or sort-) shifting opcrations that I have onl! just bcgun to learn to csploit. Further important help came fromJohan van Ben~hen-ibefore and during the .ill1 -41nstcrdam Collocluium where the nlain prcscntation of this paper was made. Other i-aluable suggestions and cncouragcmcnt came from participants in the Amsterdam Colloquium, from participants in a ~ o r k s h o pon mathematical linguistics at thc University of Michigan, especially Richmond Thomason and Hans Kamp, from thc audience at a subsequent colloquium prcscntation at the University of Connecticut, cspecially Howard I,asnik, and from participants in fall 1984 and spring 108.5 semini~rs at the Unircrsity of Massachusetts, cspecially Fred Landman, Emmon Baeh, Ray Turner, Nirit Kadmon, and Frank Wattenberg, to whom I am also gratefill for inviting mc to present this worL to '1 New England Set 'Theory meeting in December, n stimulating challenge in interdisciplinary communication which turned out to be a most enjoyable and productive experience. I hope I hatcn't misused any of the help I got along thc way; I'm sure it will take more help from collcagucs in sc\cral disciplines to overcome remaining inadequacies, fill in gaps, and extend this approach if possible to a cornprchensive theory of synlactic categories and semantic types. 1 Since he requirement of' a homomorphism from syntactic categories to s c m ~ n t i ctypes is fundamental to R'lontague's approach, one cannot literally allow a single s!-ntactic category to may onto more than one semantic type wi~hin that approach. There ;ire various wa!-s of reformulating my proposal to conform to the hon~on~orphism roquiremcnt, c.g. by csploitinp the common l-iew of syntactic ciitegorics as feature bundles. Flynn (1981) ilrgucs l i ~ r the inclusion of both X-bar and categorial identification in syntactic categories, and thcrc is considerable independent motivation for such a move, e.g. in the cross-classification ol' X-bar categories such as "PP", and "AdjP1' and catcgorial grammar categories such as "predicate", "prcdicate modifier", ctc. Incidentally, nothing I say in this paper is meant to decide bctwcen thc use of type theor> and the use of sorted domains in a type-free or less strongly typed thcorj-. I use type thcory because it

378 Barbara H. Partee is more familiar to me; I don't really know- how much diffcrcncc it makes. Chierchia and Turner (1988) discuss this question. sublanguage unless explicitly 2 Here and throughout I am simplifying to a purely cxte~~sional stated otherwise. That is one of the big gaps in this nork that needs to be fillcd. 3 See. Cor instance, Partee and Rooth (1983) on conjunction, Reinhart (1983) on bound-variable anaphorn. 1 See Chicrchia and Rooth (1081), Zcevat (1984). 5 This of course goes beyond the hounds of a purely extensional fragment; what I clo in h i s paper is systematically niisrcpresent properties as sets, hoping that the differences bctwccn them will not affect the main ideas. k See Bach and Partee (19XO), Reillhart (1983). 7 So I would predict that any language which has cspressiorls like "every man" as a syntactic NP of semantic type ( ( r ,r ) , I ) will also allow proper names likc "John" to bc ( ( c , I ) , L), hence will allow conjunctions like "John and every man". Similarly, while children acquiring English may start out with only e-type NP's, once they acquire quantificational NP's they should soon show signs of promoting simpler NP's to the higher typc as well. 8 I am using expressions of Montaguc's intensional logic, with his conventions as to the t!.pcs of variables, to clenotc corresponding model-theoretic: objects, occasionally recasting things in settheoretical vocabulary where it may add perspicuity. 'The typc-shifting operations are clcfined on model-theoretic objects; u-c might find it usefi~lto acld their namcs as logical constants to thc intensional logic or other intermediate representation language. 0 See note 5 . 10 In a fuller treatment, thc same should apply to definite plural nncl mass terms as wcll, likc /he men and the watcr. I1 There could be (and would be unlcss somethii~grules it o u ~ a) sccond generalized quanrificr reading of r h krng. ~ / ~ f t ( l o ~ r ! ( ~ i n g 'I'm ) ) . not sure hon one kvould get evidence for or against such an anihiguity. 12 I believe one can interpret Frege (1892) as inaking such a claim i~houtsubject NP's. 1.3 I assume that the grammar specifies various positions as P , (el I ) , etc., via subcatcgorizatio~land othcr rules. I helieve that positions are not suhcatcgorized as ((c, l ) , I ) unlcss they arc also intensional, like thc object oC SL'C'X~. hencc outside the scope of this discussion. In cascs of ambiguity, I w-ould predict that if any NP call be either e or ( r , i) in a certain position, e \I-ould be the preferred choicc not only because i t is a simplcr type, but also hccausc and ((E, i}, I ) are (1 believe) uninarkcd types for NP's, while ( c , l ) , the unmarkcd typc for VI"s, ,4djP's, and many PP's, is a marked type for NP's. I don't know what to cxpect in cascs of ambiguity between (e, 1 ) typc and {(e, t ) , I ) type for a giben N P in a given position, since there is then a conflict between simplicity of typc and markedness as an N1'-type. I4 h4! thanks to Johan Kin Rcnthcln for showing me that Monrsgue's 131: functor is indeed "natural", both intuitively and b!; various formal criteria, somethins 1 had never appreciated in spite of years of fdiniiiarit!. This section was nluch \veahcr hcforc he helped with it. I S Thanks to Johan van Rcnthcm for the fiact, which he knows hen to provc but I don't, and to Hans Kanip u-ho gave me further help in understancling it. 16 This is yet another place where it seems evident that we want properties and not sets to play a basic role in what we are the ( t ,1 ) domain. 'I'hc prtdir.ate reading of "the owner of this land" should ncither presuppose that the land has an owner nor depend on who the oivncr is if there is one. Although intensionality will probably complicate the type-shifting picture, I helieve it is indispensable for a satisfiictory anillysis. 17 Thal is, we arc asking what determiner-type mcai~ingsare inverses o f RE in one direction. We cannot expect any determiner meaning to be an inversc in the other clircction, i.e. to satisfy DET(BE(r)) = a for all a, since RE loscs information: BE(a) = RE(/i) for any r and 1,' that contain the same singletons.

Noun Phrase Interpretation 379 18 Moortgat (1985) gives evidence of //?a, a, ant1 Carlson-type bare-plural readings in first elements of noun-noun compounds in English, Dutch, and German, wherc semanric NP-type re;lclings arc carried by syntactic CN's. T h e formation of bare plurals should also count as "natural", I would hope, but I all1 following Chierchia in viewing it as basically a nominalization operation ((z, t ) to e) rather than a DET-type filnctor; its composition with lrJi would then be a DET-type functor. 19 Johan van Renthem has urarned me that the kinds of' type-shifting functors I have been employing cannot be assumed to apply straightforwardlj to variables, since we arc not thcn dealing Jircctlj- with model-theoretic objects in the samc way. But I believe that the samc principles ought to apply, and it would at least be siraightfor\tard if kvc includcd logical constants like /UIDCYand /{/i in an intermediate representation language such as Zeevat's reconstruction of Kam p's I)RS language. 20 My thanhs to Jose Mcseguer, Joseph Gogucn, and Ray Turner for making me aware of re1;lted work in the se~ilanticsof propra~nminglanguages. I'm not able to understand and appreciate niuch of the technical work in that field, but it seems clear to nlc that this is anotller problem area where interdiscil-rlinary. collaboration could have considerable payoff. 21 Sometimes "most men" seems to have an e-type reading paraphrasable as "a group containing most men"; this seenis even easier to get with "most of the men". See Doron (1983) fur discussion of some of these issues and of differential availability of predicati\.e (a, I ) readings for partitive and non-partitive plural NP's. Plurals and mass terms rnisc lilany more semantic issues than c~inbe touched on here; it would take at least anothcr paper to examine a significant fraction of current work on mass tcrrns and plur:lls in the light of'the type shifting pcrspccti\-e suggested here. Sce, for instance, Scha (198I), I-Iochsema (1983); van Lijeli (1983). Westcrsthhl (1989), Pellcticr and Schubert (1089). Lnnning (1984). 22 NP's hrnied with the bound CN-stem -rkilrg rnust also be able to be miirked A, per1i;lps optional]! as illustrated in (18); there should probabl? bc some gcncral way of indicating that l h ~ r ~has g nuxin~allypermissive selcctiona\ ieaturcs and corresponds to a 111axirnall> i~lclusivc "sortal rangc" of entities. h 23 T h e sanlc restrictioncould be applied to a i h c ~proposcc\ mechanisms for dcnling ~ i t clunntiticr scope, such as Cooper-sttrrage, quantifier-lo~verinp,or Q K (quantificl--laisilIg)

+

References 13,ich, Emmon and Barbara H. Partec. 1980. hnaphorn and semantic structure. In J. Krci~n~tn and A . Ojed;~(eds), Plrpr.r.\./i.otu /he Prrrtisc,aio~011 Pro~ozlrtsO J I- ~~ I I N J ~ OChicago, ~ O , Ill.: Chicago 1,inguistics Society, 1-28. ljarwise, Jon and Robin (l:ooper. 1981. Gcncralized quantifiers and natural language. Lirt,~i~i.v/i~s NII~/ P / ~ i / o s o p l ~4(2): , ) ~ 159-2 1 0 . 13cnnett, h4ichac1, R. 1974. Somc Extensions of a Montague Fragment of English. Ph.D. dissertation, UCI._4. Distributed by Indiana University Lingi~isticsClub. Girlson, Greg N. 1980. Reji.r.ent.e l o K i r ~ d sirl firlglisl~.New York: Garland. Chierchia, Gennaro. 1982n. Bare plurals, mass nouns, and nominalization. In Ilanicl P. Flichingcl., &larlys Maclicn, and N a n c ~Wicgand (eds), Prol.ect/ir~gsf ! [ r h ~Firs1 I h s / C o u s ~Co~!/>rt.nl-e 1111 170rttrll Lirz,e/ri~~rcs, Stanford, Calif.: 1,inguistics Department, Stanford Universit!., 243 -55. Chicrchia, Gcnnal-o. 1982b. Nominalizntion and Montague grammar: a scniantics without types li)r natural languages. L ~ t ~ ~ q i r i sc/wd / t r - ~Pl~ilosop,pl!ll5 : 30.1-54. Chierchia, Gcnnaro. 1984. Topics in the Syntax. and Semantics of Jnfiniti~csand Gcruntls. 1'h.l). dissertation. University of Massadlusetts, Amherst.

380 Barbara H. Partee Chierchia, Cicnnaro and Mats Rooth. 1981. C:onfigurational notions in discourse representation t h c o r ~In . Charles Jones and Peter Sells (eds), Proc.er~/ii~ps ofNEL,S 14, Amherst, hlass.: University of Massachusetts. Chierchia, Gennaro and Raymond Turner. 1988. Semantics and property thcorv. L,i?rgrdis~~cs nwil Plzilosoph)~11 : 26 1-302. Doron, Edit. 1983. Verbless Prcdicatcs in Hebrew. Ph.D, dissertiltion, Univcrsit!. of Texas, Austin. Dowty, David R. 1978. Govcrncd transformations as lexical rules in a Montaguc grammar. 1,inglrlstii. Inquiry 9(3): 393-426. Dowtv, David R. 1979. Word Mr~lningand Montaguc G!nt?irwur. Uordrecht: D. licidcl. D o ~ t y ,David R., Robert Wall, and Stanley Peters. 1981. Itz~ro(lucrion 10 Moiililg14c Srnraurrl~s, Dordrecht: D. Reidel. Flynn, Michael. 1981. A Categorial Theory of thc Base. Ph.D. dissertation, University of Massachusetts, Anilicrst. Fregc, Gottlob. 1892. Uber Sinn und Bedcutung. Zeitsrkr$ l i / u Philosoplri~~ ~ und plrilosoplilsclrr Krrlik 100, 22-50. Trans. as Gottlob, On sense and reference, in P. Cieach and h1. Hlack (eds), Tratrslltions.fi,on~thr Philosophirul I.Vrt/ntingsof'C;ottloh Frege, Blackwell, Oxford. 1960, 56-78. Futasugi, K.. J. Goguen, J.-P. Jouannaud, and J. Meseguer. 198.5. Principles of 013J2, Rcport no. CSLI-85-22, CSLI, Stanford University, Stanford, California. Goguen, Joscph and Jose hlesegucr. 1984. Equality, typcs, modules and (whj- not?) scncrics for logic Z I I I ~ Also Report CSLI-84-5, CSLI, Stanfbrd programming. .?ournicl (lf'Logic P Y ~ ~ I . I L ) I Z1 :W179-201. Lnivcrsity, Stanford, Caiifornia. Groenendijk, J. A. G., T. hl. 5'. Janssen, and R4. B. J . Stokhof. (eds). 1'981. Fornicrl /~lc~/zorls i17 llir S/u11),q/'Latrgarrge. Amsterdam: 12;lathemiitisch C:entrunl, Univcrsit) of Amsterdam. Heim, Ircnc. 1982. T h e Scniantics of Definite and Indcfinitc Noun Phrases. Ph.D. disscrtation, Ilnicersit!. of Massachusctts, Amherst. I-Iiggins, F. R. 1973. T h c Pscudo-cleft Construction in English. 1)octoral dissertation, MIT, Cambridge, Massachusctts. Hoeksema, Jack. 1983. Plurality and conjunction. In Alice G. 13. tcr h,lculcn (ed.), S~tidic.\.tn '24orleltkroretic Semnnlirs, Groningen-Amsterdam Studies in Sen~antics,1, Dordrecht: Foris, 63-83. Jansscn, Theo M. V. 1984. Individual concepts arc uscfill. In Fred L,andnian and Flank Veltman (cds). b'arietits of' F'orm~ISett~lln~atics:Proi.~~edl/zgs of' 111e I'our~li .-1r/nto.dunr Collo yurutri, Scptelnbcr 1982. Dordrecht: Foris. Kamp, IIans. 1981. A theory of truth and senlantic representation. In Groencndijk ct al. 1981, 277322. kecnan, Ldward L. and Leonard hl. Faltz. 1978. 1,ogical Types for Natural I,ilnguagr, UC1.A Occasional Papers in Linguistics, 3. Keenan, Edward L. and Leonard M. Faltz. 1985. Rooll~unSe/tiirnti~.s,/ilr ,Y-(~~l/ua/ / , ( I ~ R / Dordrecht: I~~P D. Rcidel. Klein, Ewan and Ivan Sag. 1985. Type-clri\.cn translation. L,irrauist~c:cirnil IJhilosoph,)r 8: 163-201. L a s o n , Richard. 1985. Base-NP adverbs. Linguislic L?.rqtiir:,~16: 595-621. Link, Godehard. 1983. T h e logical analysis 01' plurals and mass tcrms: a lattice-theorcticaI approach. In Rainer Raucrle, Christoph Schwal-zc, and Arniln von Stcchon (eds), M i ~ ~ n i t t gList, , (rrrll Irzterpre~(r~ion qf Ldngrri~~ct., Berlin: Waltcr de Gruyter, 302-23. L~nning,JanTore. 1084. i'blass tcrms and quantification. In Jens Erik Fcnstad (cd.), Report r!f'cbnOslo Selninirr if/ Lo,yic onil Lin~~rdistics, prcprint series, no. 9, hlatcmatisk Institutt, University of Oslo. hlcscguer, Jose and Joseph Goguen. 1984. Initiality, induction and computability. In M. Nivatt and J. Reynolds (eds), Algebicric .Me~hoil'sit/ Sen?lltzti~.s,Cambridge: Clambridge University Press. Milsark, Gary. 1977. Toward an explanation of ccl-tain peculiarities of the csistcntinl construction in 3(l): 1-30. English. Lirzguistil- 14~~alj/si-s hlontague, Richard. 1970. Uni\ersal grammar. Tlzeorztr 36: 373-98. Rcpr. in hlontaguc 1074, 22246. hlontague, Richard. 1973. The proper trcatnlent of quantification in ordinary English. In K. J. J. Hintikka, J. M. C. Moravcsik, and P. Suppes (eds), Approni.hes to ;\rl~trrrn/ Lrrngulrge: I-'ror.c~diit~s (!I'

Noun Phrase Interpretation 381 1970 Stlrrt/GrlJ Worksliop on Gvummlur un(/ Sc~ira~rtics, Dordrccht: D. Rcidel. Rcpr, in hlontaguc 1974, 247-70. Montaguc, Richard. 1974. Forttral Philosop/~)l.Sclcr~erlPr~pcr-.F cfRirhtrril Morriaglre, edited and with ;m introduction by Richlnond H. Thomason. New Ilaven, Conn.: Yalc Univcrsit!~Press, Moortsat, M. 1985. T h e mathematics of word structure. In Proceedings of thc C:onfcrencc o n Catcgorial Gl.ammars and Natural Language, Tucson, Arizona, Spring 1985. Partec, Barbara. 1980. Ambiguous pseudoc[efts with unambiguous be. In S. Bwrnan, J.-W. Choc, and J, McDonough (eds), Proccedir~gs(qf'NELS16, Amherst, Mass.: University of hlassachusctts. Pilrtee. Barbara and Mats Rooth. 1983. Generalized conjunction and type an~higuit!. In Raincr Bauerle, Christoph Schwarze, and Arnim von Stecho\\- (ecls), ;l/lrantt1g, l h r , nnil I i z [ ~ ~ r ] ) r r ~ (q/' ~~ioti Langurrgi~,Berlin: Walter de Gruyter, .361-83. Pellcticr, F. J. and L. K. Schubcrt. 1989. Mass expressions. In 11. Gabhay and 12. Gucnthncr (ells), H(lwd/)ouX~of Phrlo~sopiziroiL o g ~ r vol. , 4, Toptr..~nz tile Plri/osophy ~ J L n r ~ g r u l gDerlin: ~, Walter dc Gruyter. Reed, Ann. 1982. Predicatives and eontextual rcferencc. Linguistic. A~u/)~.vi.v 10(4), 327-50. Reinhart, Tanya. 198.3. Coreferencc and hound anaphora: a restiltenlent of thc ana]>hor;~ cluestion. Lijzg uislii:~ond Pl1ilosopl7j~6 : 45-88. Ross, J. R. 1969. Adjectives as noun phrases. In D. ReibeI and S. Schanc (cds), rMollt~.?rStuJri,s iri E~tgllslt:Rearlings in Trran$/it~~~lal t o l d Griltrirtz~i7..Englewood Cliffs, N . J. : P~venticeI la1I. Scha. R. J . 13. 1081. llistributivc, collective and cumulative quantification. In Cirocnendijk ct al. 1081, part 2, 483-17. Stump, Gregory. 1985. Tllr Sernnn~ic J;ilricthilit)~o[,4bso/ule Cowstlwl./iorrs. Dordrceht: D. 12cidcl. Van Bcnthcni, Johan. 19832. Iletermincrs and logic. Linguislri.~unti Philo.copl~16: 447-78. Van Benthem, Johan. 1983b. T'hc logic of semantics. In Fred Landman and Fmnk Veltman (eds), I4zri~rir.sof Fu?.mu/ Sc~t~an/ic.s: Aac.rerlings c! f lhr Forrrth .f llts/e~iInrnColloyr~rurii,September I 982. Dordrecht: Foris. Van Eijch, Jan, 1983. Discourse reprcscntatiori theory and plurality. Tn Alice G . B. ter bIculcn (cd.), Studie.~in Moci~~l/ht~oretit. Stn~a~ztic-s, Gro1iingcn-~4msteriIamStudies in Scniantics, 1, 1)ordrccht: Foris, 85-106. Wcstcrstihl, Dag. 1989. Qwantifiers in formal and natural language. in U. Gabba! ant1 E'. Gucnthncr (eds), Hnnlll,ook c!f Pl~ilmsopI~~ri~l Log~c.,vol. 4 , Topi~:vin /he Pkilnsopl~,)~ q / ' L r ~ 7 y l ~ Berlin: t i ~ ~ ~ ,Waltcr tlc Gruyter. Willianis, EJwin. 1983. Semantic vs, syntactic categories. Ling/ils/rl:v ~ i z dPlzilo.voph,~0: 42.140. Zccvat, I-Ienli. 1984. A Compositional Appronch to Iliscoursc Ilepresentation. Manuscript, Erasmus Unil-crsity, Ro~tcrdam. I ~ L J

,

Syntax and Semantics of Questions Lauri Karttunen

This paper presents a novel account of the syntax and semantics of questions, making use of thc framework for linguistic description developed by Ricllard hlontague (1974). Certain features of the proposal are based on work by N. Belnap (1963). L. Aclvist (1965), C. L. Baker (1968, 1950), S. Kuno and J, liohinson (1972), C. 1,. Ha~nhlin (1973), E. Keenan and R. Hull (1973), J. Hintikka (1971), I.ewis and 1,ewis (1975), and D. Wunderlich (1975), but it differs from all of its predecessors in one way or another. I will start with a number of observations which provide thc basis for the treatment of questions presented in the sccond part of the paper and conclude with a summary and a brief discussion of how the proposed descl-iption compares with recent transformational analyscs.

1 Introduction

I

I

I . 1 Direct and indirect questions There are two kinds of interrogative clauses: direct (Is it rlzi?~ing.?lil'hirh hook ilirl !l/laqt read.?) and indirect (whether it is vnining, n)lzU,h hook ,442lilq1read). Any reasonable analysis of questions should relate questions of one sort to the corresponding questions of the other tqpe. Proposals to this effect have been presented by Relnap, Aqvist, Hintikka, and others. T h e basic idea in their analvscs is to assirnilale direct questions to indircct questions. A direct question can be treated as semantically equivnlcnt to a certain kind of declarative sentencc containing the corresponding indisect qucstion embcddecl under a suitable "performative" verb. For examplc, the indirect questions in

(1)

(a) Is it raining? (b) Which book did Mary read?

1

I

Syntax and Semantics of Questions 383 (2)

(a)

I ask you (to tell me) whether it is raining.

(b)

I ask you (to tell me) which book Mary read.

This reduces the problem of thc semantics of direct questions to the problem of how indirect questions arc interpreted. There are two alternative ways of making this reduction. One way is to do it as part of the syntax by deriving the questions in (1) fi-om the sentences in (2) by a meaning preserving transformation. Alternatively, one could gcnerate the quesr-ions in ( I ) directly and set up a suitable ii~tcrpretivcrule which makes rhem semantically equivalent to the corresponding sentences in (2). I will not take a stand on 1%-hichalternative should be chosen. In the following I will concentrate exclusively on indirect questions. I assume that an\- adequate solution for thcm can, in one way or another, be extended to coITel-direct questions as well. This approach has a consequence which at first seems very cou~iterintuitive.If direct questions are semantically equivalent to declarative sentences of a certain kind, thcn direct questions, too, will have a truth value. How can this be reconciled wit11 the fact that it is pointless, even nonsensical, to inquire about the truth of Is it rnitting? One way to counter this objection is this. T h e conventions of our language are such that any felicitous utterance of (la) is a rcquest to tell whether it is raining. On any occasion ivhcrc (la) is uttered, (2a) expresses a true proposition. Consequently, the fact that it is nonsensical to inquire about the truth value of (la) can bc explained by the filct that (la) is, so to speak, pragmatically self-verifying. Whenever it is uttered, it is true. (See 1,ewis 1972, Lewis and Lewis 1975, Cresswell 1973 for further discussion of the matter.)

1.2 Alternative questions and wh-questions 'There is another distinction to be made. We have two kinds of questions: alternative cluestions (e.g. Does i2lccr)l like John or does .War:)! like Bill?), which in thcir indirect form are prefixed with mhetht~r(or if), and so-called wh-questions, which begin with an interrorative noun phrase or adverb such as lnhich girl, 177110, )?+)!, ho111, ctc, 1 So-called yes/no questions (e.g. ~zlwther~Miz<)tlikes Bill) can be considered as syntactically "degenerate" alternative questions (whether iZ/lnqj likes Bill or Mlrry rloem 'r /ikt ill).' These two types of questions have virtually the same syntactic distribution. Ncarly a11 verbs which take indirect wh-questions as cornplcments also take embedded alternative questions. A verb which doesn't allow embedded wh-questions in general doesn't complement with whether-questions either. This is illustrated in (3) and (4).

(3) (a) John knows what they serve for breakfast. (b) John knows whether they serve breakfast. (4) (a) *John assumcs what they serve for breakfast. (b) *John assumes whether they serve breakcast. There arc two classes of exceptions to this generalization, both of which scem marginal to me. So-called "emotive factives", such as br u~?~a.rir~g, he surprising, and botkcr take wh-questions but do not allow whether-questions. Dubitative verbs, such as

384 Lauri Karttunen doubt, yuestior~,and he dubious, have the opposite characteristic. This is shown in ( 5 ) and (6).

( 5 ) (a) It is amazing what they serve for breakfast.' (b) "It is amazing whether they serve breakfast. (6) (a) 'I doubt what they serve for breakfast. (b) I doubt whether they serve breakf'ast. The ungrarnmaticality of ( j b ) and the grammaticality of (6b) pose problen~sfor me ancl require some special treatment. Nevertheless, it seems correct to assume, in the light of the great majority of cases of overlapping distribution, that wh-questions and whetherquestions should be assigned to the same syntactic category. (In this respect my proposal differs from those offered by Cresswell 1973 and Wunderlich 1975.) Adopting a different policy on this malter results in an undesirable duplication of syntactic categories and rules. For instance, unless wh-questions and whether-questions constitute one syntactic category, the verb depend on must be assigned to four different syntactic categories to generate the examples in (7).

(7) (a) Whether Mary comes deycnds on who invites her. (b) Whether Mary comes dcpends on whether Max invites her. (c) Who is elected depends on who is running. (d) Who is elected dcpends on whether Connally is running. Iiaving a single syntactic category for both kinds of embedded questions entails that they should also have the same kind of meaning. This conclusion is particularly relevant in a framework such as Montague Grammar, where semantic interpretation is accomplished via translation of syntactic analysis trees to expressions of intensional logic. If wh-questions and whether-questions belong to the same syntactic category, they translate to expressions of intensional logic which are of the same logical typc. From this it follows that they should denote things of the same sort.

1.3 Question embedding verbs Our next problem is to decide what kind of denotation would be appropriate for expressing the nleaning of embedded questions. For this purpose, it is usefill to take a look at verbs which embcd indirect questions. Whatever meanings we assign to questions, it is clear that they have to combine with meanings of such verbs in an appropriate way to yield interpretations for larger phrases, such as to know ~vhethcris is r~lilining,to /let on r ~ h ornins the election. T h e following list gives an overview of question embedding verbs.

(8) (a) verbs of retaining knowledge: knom, he amare, recnll, remember, Jyyet (b) (c) (d) (e)

verbs of acquiring knowledge: lerrrn, nolice, Jind out, ilisrorcr verbs of communication: tell, shoa?, indir-atr, infkrm, disckosc decision verbs: det,ide, determine, sjec~[j!,rzgrLJe on, lontrol verbs of conjecture: guess, predict, bet on, estimale

Syntax and Semantics of Questions 385 ( f ) opinion verbs: be certain about, lzazle an idea about, be convinced ahout (g) inquisitive verbs: ask, monrler, inve.stz'gate, br interested in (h) verbs of relevance: nzatter, be re/evant, be important, care, he signzfifirrc~zt (i) verbs of dependancy: depend on, be wlirted to, hnzle an influciice on, he a fi4nc.tion qL ~ n a k ea doflirence to This is not an exhaustive classification of question embedding verbs. T h e purpose of it is to give us some criteria for evaluating proposals that have been made with rcgard to the meaning of embedded questions. An analysis which seems attractive for some of these classes inay be inappropriate for others.

1.4 Hintikka semantics for questions A case in point is Hintikka's (1976) game-theoretical analysis of indirect questions. Under his interpretation the sentences in (9) are equivalent, and so are those in (9) (a) John remembers whether it is raining. (b) If it is raining then John remembers that it is raining, and if it is not raining then John remembers that it is not raining. (10) (a) John remembers who came. (b) Any person is such that if he came then John remembers that he came.

I

I

Hintikka's game-theoretical technique of interpreting indirect questions involves, in essence, replacing the interrogative clause with the corresponding that-clause. In the context of Montague grammar, the same effect could be achieved by representing embedded questions in Illontague's intensional logic in thc way illustratecl in ( 1 1). (I will use "cc" to designate the formula which results from translating a to intensional logic.)

I

1!

(1 1) (a) whether-it-is-raining' ?"r/tr,G[[it-is-raining' + "Mr f x, it-is-raining ) I A [ it-is-raining' i t W( x, hi it-is-raining' ) ~ II (b) who-came' 2Wi l\.y[came'(y) 4 W {.r, ^came'(.j~)}] (Here W is a variable (of type (s, ((s,t), ((s, e), 1 ) ) ) ) ranging over possible intensions of question embedding verbs.)

-

e.

If so analyzed, an embedded question denotes a certain kind of function which takes as arguments intensions of question embedding verbs, such as renzeniber, and yiclds as its valuc denotations of intransitive verb phrases. One of the attractive features of Hintikka's approach is that it entails that the meaning remember has in (9a), where it syntactically combines with an embedded question, is the same it has in (9b), where it occurs with a that-clause. (As a matter of fact, it is slightly misleading to talk about question embedding vcrbs in this connection; as the translations in ( I 1) show, when rei~ierizzbercombines with mhtlher ir is raining, the indirect question is treated as the functor expression and the verb as its argument.) However, this aspect of Hintikka's analysis is also its weakness. It turns

386 Lauri Karttunen out that not all verbs listed in (8) take that-clauses as complements, and for some of them, the supposed paraphrase means something different. Consider the verb ~~~oriiicr. T h e examples in (12) do not have the same meaning as the corresponding sentences in (13). (12) (a) John w-onders whether it is raining. (b) John wonders who came. (13) (a) If it is raining then John wonders that it is raining, and if it is not raining then John wonders that it is not raining. (b) Any person is such that if he camc then John wonders that hc camc. There are two senses of wonder involved here. In (12)' n?on~levmeans "wish to know", in (13) "be atnazed at". In the first sense ~vondevembeds only questions, in the second sense only that-clauses. T o make I-Iintikka's program work, we must "lexically decomin (12) to a phrase like wish to knon,. Ny employing a similnr method of pose" 117ondt~c.r lexical decomposition, we can also make verbs such as risk, inre.sligalc, perhaps even k intewsteli in, lit into Hintikka's paradigm. T h e sentences in (14) cannot as such be paraphrased with that clauses by Hintikka's principles, but if trsk is replaced by ~ssk someone to !eM and investigrrte by atteuript to jind out, we get marginally satistictory results, as shown in (15). (14)

(15)

(a) John asked whether it was raining. (b) 13ill investigated what crimes l ~ a dbeen committed. (a) If it was raining then John asked someone to tell him that it was raining, and if it was not raining thcn John asked someone to tell him that it was not raining. (b) Any crime is such that if it was committed thcn Bill attempted to find out that it was committed.

It is clear that this necessary complication detracts considerably from thc initial attractiveness of the proposal. But this is not all. As far as I can tell, the verbs in (8i) do not lend themsclvcs to this kind of treatment. I cannot conceive of any lexical decomposition of iltpmrl on which would enable us to account for the meaning of (16) along the lines Hintikka suggests. (16) Whether Mary comes to thc party depends on who invites her. T h e crucial point hcre is that Hintikka does not assign any meaning to indirect questions as such. Instcad, they are interpreted "contestually", that is, as a part of'a larger construction which in addition contains a verb. Some r:~dically different technique must be adopted h r sentences like (16) which feature two indirect questions with only onc verb. I conclude from this that, although IJintilikn's solution works reasonably well for the cases he considers, it is not general enough to enable us LO dcal with all indirect questions in a uniform waJ1.120r this scason, 1 will not try to pursue it further.

Syntax and Semantics of Questions 387

1.5 Hamblin semantics for questions In the following, I will adopt, with some modifications, Hamblin's (1973) scniantics for questions. T h e main difference is that I will regard indircct questions as having the sort of denotation I-Iamblin proposed for direct questions. (Me did not discuss indirect questions at all.) Hamblin's idea was to let every direct question denotc il sct of propositions, namely, the set of propositions expressed by possible answers to it. Under his analysis, a direct wh-question such as Who came? denotes the set of propositions expressed by sentences like "John came," "Bill came," "Mary came," and so on. Similarly, Is ;it niining? under Hamblin's account denotes the set containing the two contrddictory propositions expressed by "It is raining" and "It is not raining." I think that Hamblin's suggestion is not the best one for explicating thc meaning oC direct questions, since it does not provide any straightforn~ardsemantic account of the intuitive paraphrase relations discussed earlier in connection with the exanlples in (1) and (2). Howcver, I believe that his idea of what questions mean can be developed to yield the right kind of model-theoretic interpretation for indirect questions. In ordcr to implement Hamblin's original idea in the framework of Montague (1974), we could translate these indirect questions in the manner shown in ( 1 7 ) . ~

-

(17) (a) whether-it-is-raining' j [ p = it-is-raining' v p = ^lit-is-raining'] (b) w-ho-came' = j V .r [ p = ^came'(.r)] A.

I will not adopt the Hamblin trcatrnent in quite this form. I clloose to make questions denotc the set of propositions expressed by their trur answers instead of thc set of propositions expressed by- their possible answers. I do not have a knock-down argument against Hamblin's original proposal; as far as I can see, it could be made to work just as well as my own. However, under my analysis the meaning of verbs like ~iependon can be explicated in a more straightforward way than under his. For examplc, a sentcncc like (18) Who is elected depends on y h o is running. obviously says that the true answer to the qucstion in the subject position depends on the true answer to the question in the object position. If indirect questions denote sets of propositions that jointly constitute a true and complete answer to the qucstion, it is n relatively simple matter to assign the appropriate interpretation to the vcrb dcpend en." Rut if we make depeyzd on express a relation between possible answers, as we would have to do on I-Iamblin's original account, the task of defining this relation in the appropriate way becomes unnecessarily cumbersome. Another point in favor of letting questions denote a set of true propositions is provided by verbs such as tell, indicate, etc. in (8c). T h e verb 1'1 with a thatconlpleinent does not entail that what is told is true; with an indircct question it docs. Consider the examples in (19). (19)

John told Mary that Rill and Susan passed the test. (b) John told Mary who passed the test.

(a)

388 Lauri Karttunen Unlike (1%)) (19b) definitely says that John told the truth. Letting- the embedded o the test in (19b) denote a set of true propositions makes it possible question ~ l z pussed to explicate the meaning of tell in (19b) in a straightforward way. That is, we can say that (19b) is true just in case John told Mary every proposition in the set denoted by the indircct question. Having the denotation of n~hoprtsscd [ h t rest contain all the false answers as well is of no use to us; on the contrary, it introduces a complication in relating the question embedding verb tell to its that-complement taking counterpart. T11e same point can be made with regard to other question embedding verbs such as be intereslc'i' in, inzlestigate, mondtrr, etc. In all of these cases, it appears that thc meaning of the verb can bc satisfactorily explicated on the basis of the more restrictive hypothesis adopted here that indirect questions denote sets that only contain the propositions that jointly constitute a true and complete answer.

1.6 More on wh-questions I will conclude this introduction with a couple of observations on wh-questions. First, there is the problem of multiple wh-questions. As illustrated in (20), there is no upper liinit on the number of interrogative noun phrases that can occur in the same question. (20)

(a) Which boys date Mary? (b) Which boys date which girls? (c) Which boys date which girls for what reasons?

T h e syntactic distribution of lnultiplc wh-questions is thc same as that of singlc whquestions. T11ere is no justification for creating a special syntactic category fr thcm. Having only one syntactic category for all indirect questions rulcs out any semantic interpretation of multiple wh-questions that assigns to thcm some different tjpe of denotation than what is assigned to single wh- and whether-questions. For instance, it is not feasible-to adopt the suggestion that has sometimes been made (e.g. II; SIC .*howicz 1974) according to which (20a) should denote a set of boys while (20b) should denote a set of boy-girl pairs. One of the advantages of Hamblin-stylc semantics for questions letting questions stand for sets of propositions - is that it accommodates n~ultiplcwhquestions just as casily as questions wit11 a single wh-phrase. Under the analysis adopted here, (20b), for example, denotes a sct which contains, for each boy who loves a girl, the proposition that hc loves her. T h e only difficulty we face is a technical one: how sliould w-e set up the syntax and the meanings of intel-rogativc noun phrases so that the desired semantic result is obtained? Since the method has to work irrcspcctive of the number of such noun phrases, a certain amount of ingenuity is required here. (I will rcturn to this in section 2.8.) T h e last observation in this section has to do with the relation of wh-questions and whether-questions. If they belong, as we assume here, to the same syntactic category, one might expect to find questions such as those in (21), whcre a wh-phrase occurs in a yes/no question. *Mary isn't sure about whether to read which book. (b) *Did Mary read which book?

(21) (a)

Syntax and Semantics of Questions 389 I-Iowever, all sentcilces of this kind are manifestly anomalous, unless taken as echoquestions, as questions about what was just said.7 ( ( 2 1 n ) could also be n quiz-show m courtroom type of "leading question".) In the light of this, it seems that we s11r)uld not permit any wh-phrases to occur in a whether-question. Yet there are well-formed questioils which are exactly like (21a) except that the wh-phrase is preposed, as illustrated in (22).

(22) Which book isn't Mary sure about whether to read? I will sl~owlater how this apparent p~izzleis resolved (section 2.9).

2 A Montague Analysis of Questions After these preliminaries I will now proceed to the substantive part of this paper. 'The syntactic rules that I will present and the corresponding translation rules to intensional logic arc: intended to augment the grammatical sketch presented by Montague in his paper. "The Proper Treatment of Quantification in Ordinary English" (henceforth, "PTQ'). By choosing the PTQ fragment as the basis, I do not mean to endorse Montague's original work over the alternative Montague-style descriptions of' English worked out bj- R. Partee, R. Thomason, M. Bennett, and others. I choose the original as my frame of reference only because it is, at this time, more widcly known than any of the later versions of 14ontague grammar. In the following, I will presuppose some familiarity with the syntactic categories, rules, and translations of the P T ' . grammar. As a first step, we need to add a new syntactic category to those discussed in P'I'Q. This category, let us call it "Q', is the category of indirect questions. We define it as t i t , in order to get indirect questions to translate to expressions of intensional logic that denote sets of propositions (that is, to expressions of type ((s, t ) ,t)). This syntactic definition of the category Q does not mean that there is some syntactic rule which combines questions with sentences to make sentences. Instead, indirect questions cnter into larger constructions by combining with question embedding verbs, such as ktionj, re~n~rnber, tell, ~uonllcr,etc. T h e resulting phrases are intransitive verb phrases. Correspondingly, the category of question embedding verbs is I v/Q.'

As one might cxpect, 1 propose to derivc each indirect qucstion froin a declarative sentence. T h e first step in generating an indirect qucstion of whatever kind is to apply a rule which I call the Proto-Question Rule. This rule is given in (23) together with the corresponding translation rule which translates the resulting phrases to expressions of intensional logic. If 4 E PI (that is, if 4 is a phrase of ( 2 3 ) PROTO-QUESTION R U L E (PQ): category t ) , then 5'4' E PQ (that is, "?$' is a phrase of category V). If cb translates to 4', then '?(bl translates to j["p ~p = ^d'].

390 Lauri Karttunen Examples: /tlary cooks and John rats out are t-phrases (declarative sentences) which translate to cook; (m) and eat-out; (g), respectively. Consequently, ?Ma,:]/cooks is an indirect questioil with the translation j [ " t , ~ p= ^cook~(m)], and ?John eats out is an indirect question with the translation j l " p AP = "eat-out$(.j)l. Obviously the indirect cluestions generated by the above rule (let us call them protoquestions) are not proper expressio~lsof English. They are just embryonic structures which exist in order to be developed into genuine indirect questions by rules that are yet to follow (the Alternative Question Rule, the Yes/No Question rule, and the R'HQuantification Rule). For reasons that will become apparent later (see section 2.7), setting up this abstract level makes it easier to generate and to assign correct meanings to indirect questions that actually do occur in English. Before going on I will comment briefly on the translation part of (23). The translation it assigns to the proto-question ? Mary cooks, j['p A P = ^cook;(m)~J(?-Mary-cooks' for short), is an expression of Montague's intensional logic which denotes a function from propositions to truth values, or equivalently, a set of propositions. If Mary cooks, then the denotation of ?-Mary-cooks' is the unit set whose only member is the proposition that Mary cooks, but in case Mary doesn't cook, ?-Mary-cooks' denotes the empty set. T h e purpose of translating proto-questions to intensional logic in this manner is to provide a suitable semantic basis for the derivation of the various kinds of "real" indirect questions.

2.2 Alternative questions Indirect alternative questions such as nlhethcv illa,:y cooks or J o l ~ nrllts out ant1 I I ~ ~ I P ~ I Z I ) Y May))IikesJuhu ov hlilg/likes Bill are formed from sequences of psoto-questions by the rule given in (24).

(24) ALTERNATIVE QUESTION RULE (14Q): If "!4,1,r'!(b21, ,.., r'!d),,l E Po , then 'mhrtlzer 41 or b2. . . or rb,,' f PQ . respectively, then If ? ! , . . . , "?~,,' translate to $',, I,!&, . . . , 'n~heiher qbl or qh? . . o r (DJI1 translates to j [ l , b ; ( p f vi j @ ) . . v $:,{P)[. Examplc: ?hlnqlrooks and ? Jijlrn eats out are indirect proto-questions. Consequently, by the AQ rule i u h c ~ h ~Mr a r j ! cooks or John cars nu( is an indirect question. The translation of this alternative question, whether-Mary-cooks-or-John-eats-outJ, is obtained from the translations of its constituents, that is, from ?-hlary-cooks1 and ?John-eats-outJ, by combining them in the manner specified by the translation part of the AQ rule. It follows from this that whether-Mary-cooks-or-John-eats-out' = jI?Mary-cooks1 (p) v ?-John-eats-out' (p)l. In its non-abbreviated hrni, the latter is jl~j['p~p = 'cookk(n~)l(p)v j [ ' p A p = ^eat-outk(j)J(p)], which in turn is equivalent to j [ ' p r, Ip = ^cookk(nz)L//) = eat-out/,(,/)[ ~ j .(The proof of this equivalence is trivial; I omit it here.) 7 What does this say about the meaning of alternative questions? The translation assigned by the AQrule to the phrase n,he~hcr(Lllcry cooks uvJohn ea/s out turns out to be equivalent to the formula I['/, v [t, = ',cookk(nz) v p = ^eat-outk(.j)ll. This expression, and hence the English phrase it is a translation of, denotes a sct of propositions '

Syntax and Semantics of Questions

391

which may have zcro, one, or two members depending on what the worlcl is like. There are four possible cases: (i) if Mary doesn't cooh and John doesn't eat out, then this alternative question denotes the empty set; (ii) if Mary cooks and John doesn't eat out, then it denotes the unit set containing only thc proposition that Mary cooks; (iii) if Mary doesn't cook and John eats out, it denotes the unit set containing the proposition that John eats out, and (iv) if Mary cooks and John eats out it denotcs the set containing both of these propositions. In one respect this is not a completelq- satisfactory account of the meaning of'i?~hc~/le~,Ma<)/cook.^ uov John cuts out. In the intuitive sense of the term "prcsupposc", sentences such as those in (25) presuppose that one and only one of the presented alternatives is actually true. I

(25) (a) It doesn't matter whethcr Mary cooks or John eats out. (b)

1

I

I

Does Mary cook or docs John eat out?

That is, (25a) and (25b) both seem to express thc speaker's belief that cases (i) and (iv) above have already been excluded from consideration and that the actual state of affairs corresponds to either (ii) or (iii). This is an important aspect of the meaning of alternative questions hut it does not sccm possible to account for it within the present framework of model-theoretic interpretation. In a sequel to this paper (Karttunen and Peters 1976), an extended analysis of questions is presented which is designed, among other things, to correct this shortcoming. (See section 3.3 for further discussion.)

2.3 Yes/no questions

('

1

1

As we pointed out earlier, yes/no questions can be considered as a suhclnss of alternative qucstions. T o generate and ii~tel-pretthem, we need a rulc similar to (24) which can apply to a single proto-question. This rule is given in (26).

(26) YES/NO QUESTION RU1.E (yh'Q):

If

"!d'

E P-Q then '1~7/1clher c j l ,

'~~hetheror not $I,and '~uhether 4 or not1 E PQ. If '?(jl translates to dl', then '1.~7hethcov 4 l , 'l~/z~?thtror 1101 (bl, and 'n~hethet. 4 or not' translate to j[$'(p) v [ i V qt//l(q)~p = Ai V 4tl/'(y)]].

Example: ? L Y ~ rooks ~ J is a proto-question. Consequently, ~z~hetho. itlar)! l,ooks, i ~ h r ~ h ~ r . or no1 /Mar)) cooks and z?>ht.therMury c-ooks or not are indirect questions. T h e translation part of the T'X'Qrule assigns to all of these three yes/no questions the same trai~slation, that is, it makes them semantically equivalent. T h e resulting translation, $['!-Marycooksl(p) v [ i V q?-Mary-coohs'(y) r,p = ^i V q'?-Mary-cooksl(q)ll is rather complicated; however, it can be shown that this formula is equivalent to j [ ' p ~lp = ^cooli:(m) v p = ^icook:(m)]]. It designates the unit set containing either the proposition that Mary cooks or the proposition that Mary doesn't cook, whichever happens to be the true one. (This is not obvious but I omit the proof here.) This result is precisely what we were ain~ingfor. Note that one o f t h e consequences of the above analysis is that the ycs/no question ~vhetherMnql cooks comes to be semantically equivalent to the alternative question

392 Lauri Karttunen 1~1zetCrrril/lnry woks or -Mrnly i h s n 't COO^, although they are syntactically generated by different rules. Another point worth mentioning is that alternative questions such as (27) have, under this analysis, two sjntactic derivations which result in nonequivalent translations. (27) whether

smokes or Bill drinks

First of all, (27) can be derived by the AQrule from the two proto-questions ?Mary smokes and ?Bill d ~ i n k .in ~ , which casc (27) translates to intensional logic in the manner shown in (28a). (27) can also be generated from the proto-question ? ; t l u q ~smokes or Bill ilrirrks by the YNQ-rule. This latter derivation results in the translation given in (28b). whether-Mary-smokes-or-Bill-drinks' (AQ) = j["p A [ p = ^smokeS(m)v p = *drjnkk(b)]] (b) whether-Mary-smokes-or-Bill-drinks' ( YNQ) = j [ - p A [ p = -[srnoke/,(n~)v drinkL(6)l v p = "[isrnolie$(rrr) n idrinkk(b)]ll

(28) (a)

Under the AQ-analysis, (27) denotes the set containing either the proposition that Mary smokes or the proposition that Bill drinks or neither or both of these depending on what the world is like. Under the YIVQ-analysis, (27) denotes the sct containing either the proposition that Mary smokes or Bill drinks or the proposition that Mary doesn't smoke and Bill doesn't drink depending on which of thcse is thc truc one. This is exactly as it should be. Note that the request in (29) requires a different kind of response depending on which of the two readings is assigned to the embedded question.!I

(29) Tell me whether Mary smokes or Bill drinks. If the addressee interprets thc embedded interrogative as an alternative question, he might respond with "Bill drinks". Under the other interpretation, a plain "Yes" or "No" mould be an appropriate response. 10

2.4 Question embedding T h e rule for embedding "real" indirect questions (excluding proto-questions) under appropriate verbs is given in (30) together arith the corresponding translation rule.

(30) QUESTION EMBEDDING RULE (QE): If (3 E P I , 19 and ct, does not begin with "?", then '64' E PI,. If 6 translates to 6'and to 4','c5qj1 translates to 8'(^d11).

€

PII and $

Example: knom is a question embedding (a IP'/Q-phrase) and 1111rethrr-3i,hur 1~c~1k.s is an indirect question (a Q-phrase). Consequently, know n?hci/zcr. John malks is an

Syntax and Semantics of Questions 393

1

intransitive verb phrasc (a11 IV-phrase). It translates to know' ( j [ " pA nJ p = ^walk:(.j) v I, = " i w a l k k ( j ) ] ~ . 'By excluding proto-questions, the rule ensures that tlicse never occur in any English sentence. Given the rule in (30) and Montague's rules for forming sentences fi-om subject noun phrases and intransitive verb phrases, ure can derive sentences such as (3 la). (3 1b) is the corresponding translation.

,

(31) (a) Bill knows whether John walks.

If we simplify matters a bit by ignoring intensions, what (31b) says is that a certain relation, expressed by know', holds between Bill and the set containing either the proposition that John u-alks or the proposition that he doesn't walk, whichever is the true onc." T h e sentence is true just in case Bill knows that proposition.

/

In order to generate wh-questions in this franieworL, one must make a number of

I

1

decisions. First there is the question of what the syntactic category of intcrrugative noun phrases is: how should one characterize the class that contains phrases like ~ l ~ l z o , lahat, rvhirh man, ctc.? In Montague's system, this decision is based in part on semantic considerations. One 111ust have an idea of how to assign appropriate meanings to whquestions before one can decide on thc syntactic classification of interrogative noun phrases. Secondly, there is the problem of setting up a suitable syntactic rule that accounts for the form of mli-questions. What I propose to do is to treat interrogative noun phrases in a way which is similar to Montague's treatment of ordinary noun phrases. Wh-questions are to be derived by "quantifying" an interrogative noun phrase into a proto-qucstion or a question that already contains an initial HfH-phrase. Questions wit11 a single interrogative noun phrase are thus derived from proto-questions which contain a subscripted pronoun (a free variable). Instead of being a simple replacement rule, as Montague's quantification rules, the new rule will in this case have an effect similar to the effect of WIT-Movement in transformational analyses. T h e semantic effect of quantifying into a question with an interrogative noun phrase pasallels the effect of Montague's quantification rule for conrmon nouns in PTQ, 'l'his solution has a number of advantages which will become apparent as I spell out the details of the proposal. The syntactic category of interrogative noun phrases, let us call it "bV"'", is defined as t//IV. One immediate consequence of this definition is that PVH-phrases come to have the same type of denotation as ordinary noun phrases (hlontague's T-phrases). Furtliermore, for semantic reasons, we make CYH-phrases equivalent ro existentially quantified noun phrases. For example, who and rahat, which are basic WH-phrases, will have the same translation as someoue and something, which are basic noun ,4ssuming that the anirnate/non-animate distinction is ignored, they all translate to P V r P { r ) . For non-basic WH-phrases, we need a rule such as (32).

394 Lauri Karttunen (32)

c'

WH-PHRASE RULE (WHP): If [ E Pcv then 'nv5il.h i' and '7uhrct E PlvHa If( translates to then 'which and 'mhat translate to I; V x[il(x) n P{r}].

c',

<'

c1

Example: Since mrcn nis a common noun (CN-phrase), 117hick man is a WH-phrase whose translation is P V x[man1(-v)A P{,Y}]. (This is identical to the translation of a man).

2.6 WH-quantification rule Having decided on the syntactic and semantic characteristics of WH-phrases, let us now turn to the rule that makes use of then1 in forming wh-questions. A preliminary formulation of this rule is given in (33). (33)

pVH-QUANTIFICATION RULE (T4lIYQ n): If ct E Pkr.lr and 4 E PQcontaining an occurrence of PRO, (i.e. either he,,, him,,, or hk,,) and 4 does not begin with rohcther, then FfVflQ,,,(a, 4 ) E PQ, where FrrFIQ, ,,(a, 4) is defined in the following way. A. If 4 begins with "i", then FkvHQ,,,(a,4)is derived by performing the following operations: (i) substitute x for the initial "?" in 4; (ii) delete the first occurrence of PRO,, in 4. If ct translates to ctl and 4 translates to 4', then F I I - H Q , n ( ~ , translates @) to ~[~'(~n[~bl@)l)l.

Examples: FC.yHQ, I (who, ? hel dates Mary) = who dates Mnyy; FHHQ, 11 (iol~i~h girl, ? he,, slerps) = which girl sleeps; FrrvHQ,2 (mhat, ? John reads /rimz) = u2hut John reads. T h e syntactic part of the rule in (33) is trivial. It replaces the initial "?" with an interrogative noun phrase and deletes the first occurrence of a pronoun which has the specified subscript. This formulation of the rule is obviously nlilch too simplistic, but let us not worry about that for the moment. T h e translation part of the rule is less : transparent. But if you are familiar with Montague's work, you will notice a close family resemblance to the rule T15, which gives the translation resulting from quanti- ' fying into a common noun. A sample of translations resulting fi-om the application of WH-Quantification is given in (34).

- - --

v

(34) (a) who' (i.e. the translation of who) r~{r}, ?-hel-dates-lMaryt p^["p ~p = ^datc$('xl, m)], who-dates-Mary' $[wh0'(2~ '?-hel-dates-Maryl(p))] $ V s["p A p = "datc$('x, m)]; P V x[girll(.r)A P(xj-1, (b) which-girl' which-girl-sleeps' $ [ which-girlt(io '!-heo-sleepst(p))] e p^ V ,x[girl'(x) A "p ,\p = ^sleepl(.z.)]; (c) what-John-reads' =- 3 V r["p np = ^read;(j, 'x)]. h

I will comment briefly on the last two translations in (34). Just as in the casc of whether-questions, a wh-question translates to an expression which denotes a set of

Syntax and Semantics of Questions 395

propositions. Roughly speaking, the propositions in this set jointly constitute a true and complete answer to the question. Thus the translation of what John rea~is, Vs["p~p = "read',(j,'.v)], denotes a set which contains, for each thing that John reads, the proposition that he reads it. If John happens to read only the New York Times and Playboy, then the indirect question Inhat John reods denotes a set containing only the two pl-opositions expressed by "John reads the New York Times" and "John reads Playboy". Correspondingly, the translation of mhich girl sleeps denotes a set which contains, for each sleeping girl, the proposition that she sleeps. In case there arc no sleeping girls at all, this indirect question denotes the empty set.'" The formulation of the CVH-Quantification rule in (33) is not intended as final. Several improvements and restrictions are needed to make the syntax of wh-questions to come out right. For example, Ross' (1967) Pied Piping conventions should be built into the rule to generate sentences such as the examples in (35). (35) (a) Bill remembers to whom John gave the book. (b) Mary asked which child's cat John rescued.

1 will not elaborate on such syntactic refinements here. (For an example of how that could be done, see Thomason's (1976) relative clause rule.) I will mention only one additional specification which is required for sentences where the inserted WH-phrase binds a pronoun somewhere else in the sentence. An example of this type is given in (36).

(36) Which girl dislikes her mother?

4) given in (33) must be augmented with For such cases, the specification of FII.FIQ,,,(~, a third clause, spelled out in (37). (37)

amendment to (33) (iii) replace each subsequent occurrence of PRO,, in 4 with a11 unsubscripted pronoun whose case matches that of the replaced pronoun and whose gender matches the gender of a.

-

Example: FwHQ,O (mhich girl, ? heo dislikes hisfso mother) = lal1ic.h girl ciislikes her mother. The translation rule in (33) is not affected by this modification.

2.7 Comments on the semantics of Wh- and whether-questions

I ,

I

The central idea in the preceding sections is that nh-questions are to be derived from proto-questions by a quantification rule. This rule, (33), is especially formulated in such a way that it does not apply to whether-questions. This restriction deserves an explanation. Syntactically it would be just as easy to derive who dudes Mary from whtlher heo ~i~ztes Aleqy as it is to derive it from? heo diztc.s M121a1:~. Ilowever, the nicaning of the wh-question would come out wrong. Let us first recall that these questions translate into intensional logic in the manner shown in (38).

396 Lauri Karttunen (38)

--

(a) ?-heo-dates-Mary' p^[-p/\p = *datek("x(),m)] (b) 11rhet11er-heo-dates Mary $["p A [ p = "dateL('xo, m) v p = -idate; ('.YO, m)]]

By applying the CV-HO-rule as it is stated in (33) to 1~110and? heo dales Mn/la?)lwe obtain for who dntes Mayy the translation in (39a). If we were to quantify ml~o into m l ~ ~ t h eheo r dates Mnq:l,, the resulting translation would be equivalent to (3%).

V .v["p ,A p = *date:("x, m)] i; V . ~ [ */\p p = "datek(".r,m) p

(39) (a) p^

(b)

;\

= ^idatek('x, m)11

As we have said, (39a) denotes the set containing all true propositions expressed by sentences of the form "x clates Mary". (39h), on the other hand, picks out the set containing all true propositions expressed by sentences of the form ''x dates Mary" and ' L . ~ doesn't date Mary". In other words, (3%) denotes a set which contains, for each person who dates Mary, the proposition that he dates I\iIary, and, for each person who doesn't date hlary, the proposition that he doesn't date Mary. This is not a suitable denotation for who h t e s ~Mnyyfor the following two reasons. i ~ n M a y had the same denotation ils (39b), i t \vould have to be First of all, if z ~ ~ tlrxtes semantically equivalent to vho doesn't date Mary, which also would come to denote the set which contains, for each person, either the proposition that he dates h4ary or thc proposition that he doesn't date Mary, whicl~etreris the true one. This is not a desirable result, considering the fact that (40a) and (10b) intuitively do appear to be synonymous.

(40) (a) Rill wonders who dates Mary. (b) Rill wonders who doesn't date Mary-. Secondly, having t ~ i l oh t e s iV1rnyy translate to (39b) would h a w the consequence that (11) would be true just in case John knows of every person whether or not this pcrson dates ~ a rl 4 ~ . (11) John knows M-hodates Mary. But this would lead to the unacceptable conclusion that, in order to know who dates Mary, John must have some knowledge about all the individuals including those hc has never heard of and whose vet-) existence is unknown to him. On the basis of such considerations, it secms best to sct up the rulcs, as we have donc, in such a way that wh-questions have the sort of denotation illustrated in (39a). This assures that the meanings of pairs like mko da,tes Maq! and ~ ~ ~lorsn't h o dote A4rcry do not collapse to the same and we avoid the difficulties pointcd out in connection with (41). A natural uraj7to achieve this result is to restrict the WH-Quantification rule to apply only to proto-questions and not the whether-questions. (The Fact that protoquestions provide us with a suitable syntactic and semantic base for the generation of alternative questions, yes/no questions, and wh-questions is precisely the reason for setting up this abstract level in the first placc.)

Syntax and Semantics of Questions 397

2.8 Multiple Wh-questions Let us now turn to cases where there are several interrogative noun phrases occurring in the same question. It turns out that only trivial modifications are needed to make (33) generate questions like the one in (42). (42) Who dates which girl? As it is stated in (33), the wH-Quantification rule only applies to questions w-hich begin with an initial "i". T h e rule is undefined for questions which begin with a CVHphrase, such as (43).

(43) who dates himl The required modification is a simple one. In case the question we want to quantify into already contains a WH-phrase, that is, begins with something other than "?", there is 11o movement. The new incoming WII-phrase simply replaces the specified pronoun in its original place. What we need to add to (33) for multiple wh-cluestions is the clausc in (44). (44)

a m e n d m e n t to (331, as amended in (37): B. If 4 does not begin with "?" then Frf/HQ,,,(~, 4) is derived from performing the following operations: (iv) substitute M fix the first occurrence of he,,, hint,,,of his,, in 4); (v) do as told in (iii) (given in (37)).

(11

by

Example: FltHO - l(u)hich girl,n?hu dates hirra]) = nlhu ~1a1e.swhich girl. What about the meaning? It turns out that the translation rule originally given in (33) can be left as it is. It assigns appropriate translations to all wh-questions irrespective of how many times the GTH-Quantification rule is iterated. This is illustrated in (45) in some detail. %

(4.5) (a) Syntactic analysis tree: who dates which girl, W H Q , 1

-----',

which girl, WHP

which dates him,, W H Q , 0

/ '

girl

?he,, dates him,, PQ I hel, dates h i h , , 4 ( P T Q )

who

A dates him,, 5 ( P T Q )

he,,

A

dates (b)

he,

Some of the corresponding translations: hell-dates-him', z date;('x.o, 'xl )

398 Lauri Karttunen

-

?-hee-dates-him', = $["p A P = Adate:("se, -.rl) J who' = B V .rP{s} who-dates-him', j[whof(.il,?-heo-dates-him, I@)) 1 = .r[p ~p = 'date',('.t-, '.el)l which-girl' G P V.)l[girl'(y) n P(1,)1 who-dates-which-girl' = j? [ whi~h-girl'(.i.~who-dates-him, '(p))] . ~ [ ~ i r l ~A("p , ~np ! ) = "date:('.v, : ) I ) ] 1

-

A

3v

a[ v.)!v

a[

As wc see in (45), mho Antes ~uhic/zpi?-/ translates to V.1' V .cl girll(sl~) A "p ~p = ^di~t~L ('s, ".y)l]. Just as it should, according to our previously stated goal, this expression denotes the set of all true propositions expressed by scntenccs of the form "x dates y" where "y" picks out a girl. Increasing the number of M/H-phrases creates no difficidties at all. For example, it is ens! to see that (46a), which is derived by fi~urapplications of the 147H-(luantification rule, translates to (46b). (46) (a) which farmer sells which horse to which customer for what price .r[price'(i~)r customer'(.z) A llorse'(.)~)A f'~rmer'(.r)n (b) $ 117 z "p ~p = ^sell~("x, :I/, " z ,"m)]

v v v j v~

This concludes the first part of our discussion of the syntax of WH-Quantification. In the following sections we will look at some further consequences of this rule, For easier reference, the rule in (33), including the a~nendmentsin (37) ancl (44), is restated in (47). This new formulation also incorporates one additional principle, namely, that the inserted R'H-phrase assumes the case of thc replaced pronoun.

(47)

IVH-QUANTIFICATION RULE (FVHQ, n): If x E PI, and (1) E PQcontaining an occurrence of PRO,, (i.e., either he,,, kitn,,, or his,,) and 4 docs not begin with vhether, then ,,(a, 4) E PQ, wherc Fllfk{Q, ,,(a, 4 ) is defii~cdin the following way. A. If q!) begins with "?" then FclFill, ,,(r,4)is derived fi-om 4 by performing the following operations in the given order: (i) substitute ii for the initial "?" in 4, where 8 comcs from n by adjusting the case of ci to match the case of the first occurrence of PRO,, in 4 ; (ii) delete the first occurrence of PRO,, in 4; (iii) rcplaec cach subsequent occurrence of PRO,, in q!! by an unsubscripted pronoun whose case matches that of the replaced pronoun and whose gender matches the gender of x . B. If 4 does not begin with "?" then Fll.FIO , ,,(a,4) is derived tkom (j by performing the following operations: (iv) substitute ti for the first occurrence of PRO,, in c j , where a is defined as in (i); do as told in (iii). (Y) If a translates to a' and $I translates to 4' then fifll,Q,.(a, 4 ) translates to [ U ' ( . ; . ~ ~P)I)I. II~)~(

-

a

Syntax and Semantics of Questions 399

2.9 Excluding whether from Wh-questions It is a direct consequence of the proposed syntactic derivation of English wh-questions

that a simple wh-question cannot begin w-ith nlhtrhev. Conseqi~ently,neither one of the examples in (48) is derivable within the system. (Echo-clucstions and "leading qucstions" are not considered here. Cf. Note 7.) (48) (a) "Bill knows whether Mary read which book. (b) "Did Mary rcad which book? However, the CVH-Quantification rule in (47) allo~vsthe derivation of questions such ils (49), where the preposed interrogative noun phrase extracts a pronoun from an embedded whether-question. (49) Which book does _Mary wonder w-hether she should read? The derij-ation of the corresponding indircct question is pictul-ed b j the analj~sistree in (SO). which book Mary wonders whethcr she should read, W H Q , 0

Q

which book, W I P

I

hook

? Mary wonders whether she should read him,,, P Q

Mary wonders nhcther she sho?ld read him,,, 10,l ( P T Q )

A

hiary

he, wonders whether hc, should read him,,, 4(11'1'Q)

he, e o n d e r whether he, should rvi~dhiin,,, Qk:

A whcrhcr he, should read him,,, Y N Q

wonder

I I

? he, should scad him,,, 1'Q

he, should rcad him,, Assurning that hpl skor,/d rt~arlhhncrtranslates to should' ('read~(".vl, ".Y(~)), the top line of the above analysis tree translates to an expression equivalent to the onc given in

(51).

It is a point in &I\.-orof the proposed analysis that the derivation ot'qucstions like (49) poses no difficulty either syntactically or semantically. However, it should also bc notcd

400 Lauri Karttunen that the bW-Quantification rule is nluch too powerful in its present form. Not only a n (49) be generated but so can questions such as (52).

( 5 2 ) *Which lnnn does Mary wonder whether should read PTQ?

/

That is, the rule does not take into account the Cact that thc crtraction of the subject pronoun from the enlbeddecl whether-question in (52) results in a clearly ill-formed ) sentence while the extractioi~of the object pronoun in (49) is acccptablc. Problems of this kind have been discussed in the literaturc (Kuno and Robinson 1972; Chomskv 1973; Hankamer 1974) in connection with the I.ZfH-Movement transformalion, which in its unconstrained form also fails to distinguish bctween (49) and (52). I will return to the probIen1 of limiting the power of the WII-Quantification rule in section 2.13.

2.10 Ambiguity in multiple Wh-questions In his dissertation (196S), C. L. Baker observed that- questions of the sort in (53) anlbiguous; they can be answered in two ways.

ilre

(53) Who rcmembers where Mary kceps which book? T h e two kinds of admissible answers are exhibited in (54). (54) (a) Bill remembers where Mary keeps which book. (b) Joe remembers where Mary keeps ..lsfiec/.s and h l a x remen~berscvhcre Mary keeps Sl~ntci~.til. Strul-lures. There have becn some dissenting opinions (Kuno and Robinson 1972), but the majority of linguists (Rach 1971; C;homsky 1973; IHull 1974; J,angackcr 1974; I-Iankamer 1951) and native speakers seem to agree that Baker was right in regarding (53) as ambiguous. T o account for the ambiguity, Raker proposcd that each Wig-phrase be associated with some higher S-node by mcans of indexed Q-markers. I-Ie represented the two readings of (53) in the manner sho\vn in (55).

c Ql

whoi remembers

P,l.k

S

wherek Mary keeps lvhich, book

s a,, who, remembers S Qr

wherei. Mary keeps which, hook

Syntax and Semantics of Questions 401

I 1

In Raker's system, a preposcd H'H-phrase moves next to the Q-operator which c~rricsa matching index. This conception of PVH-Movement rules out (56) as a possiblc representation of (53).

s

Qi.k

who; remembers

S

wherex, -Mary keeps which; book

'

I

I 1

, I

The structure in (56) cannot bc generated because n?h~reand the Q-operator to which it has been n~ovecldo not have matching indices. In addition to the indcxiilg of LVIIphrascs and Q-nlarkcl-s (or, alternatively, bYI-1'-phrases and S-nodes, as in Hankamer 1974), Baker's system rcquires some interpretive principle such as (57). (57) In answering a direct qorstion, ICW-phnscs indmed lo thc Q o f the mot S arc to be replaced by non-intcrrogativc !VP's. This principle pairs the structure in (55a) with answers like (54a), and (5%) with answers of the kind given in (54b). It also accounts for the intuition that ncithcr one of the two examples in (58) is an appropriate reply to (53). Joe remembers w-hich book Mary keeps in the drawer and Max rcmcnibcrs which book Mary keeps under her pillow. in thc drawcr and hlnx (b) Joe renienlbers that Mary keeps .5'ynta(.tic. Stl-uc,/rrrt>s remembers that slie keeps i4spec.ts undcr hcr pillow.

(58) (a)

(58a) is inappropriate because (53) does not hiwe a reading w51ch associates n711cre with the highest S-nodc and u~/ziihbook with the cn~beddedclause, as implied by the answcr. (58b) is also inappropriate as an answer to (53); it presupposes a non-existent reading of (53) where all the three WH-phrases are bound to the root S. In the following I will show that, under the analysis proposed in this paper, it is not necessary to assign any indices to PVH-phrases in order to account for the ambiguity of (53). There is also no need for additional interpretive principles such as (57). In fact, tlic rules given above account for the tn-o readings of (53) without any substnntive modification. We only need to improve the WH-Quantification rule in some appropriate way to deal with interrogative adverbs such as J I ~ ~ PTY h~e. two analysis trecs corresponding to (SSa) and (55b), respectively, are givenn in (59) together with their translations. (I& us assume here that mhrw translates to P V ~ [ ~ l a c e ' (~s )P j s } ]i.e. , that it has the samc translation ils z~~krit plirc-e, and let us also adopt the convenient fiction that where is il noun phrase rather than an interrogative adverb. This distortion has no bearing on the main issue and saves us the trouble of having to introduce new syntactic rules.)

402 Lauri Karttunen who remembers where Mary keeps which book, WHQ, 2

? he, remembers where Mary kceps which book, P Q

who

he, remembers whire Mary keeps which book, 4 ( P T Q ) s

he,

remember

e

e Mary kecps which book, QE

r

here -Mary keeps ~vhichbook, IVHQ, 1

/----l

which book, WHP

I

book

where Marj- kceps him,, W H Q , 0

/ '.

where

? Mary keeps him, in him,,, PC1

I Mary kccys him, in him,,

who remembers where Mary kceps which book, WIIQ, 1

1

which book, W-HP who rememl3ers where Mary kceps him,, \iz.Tl-I(l,2

I

book

A ? he2 remembers where Mary keep him,, P Q

who

hc, rctneinbers +I here ]I/

I

ps him,, 4 (P'TQ

rerneinbcr where Mary keeps him,, QE

mWI-IQ, 0

remember

where

where Mary keeps him,, ! hlarq'

keep him, in him(,, P Q

I

Mary kcep him, in him,, who-remembers-where-Mary-keeps-which-o 3 VJI V .c [ b o ~ k ' ( .A~'r,~ ) q = *remember1 (:z, " where-Mary-keeps-?;I)] = V.1)V c [booki(y)A ' q r\ y = remember' (c,p" V x[ylacel(x) r, -p n p = ^keep;(~?z,:)I, 's)l)l (Here keep',(ril, :)I, ',v) translates ;l/Iaqf k ~ ~ e .ll p sin .v.) As shown in (59), the indirect question corresponding to ( 5 3 ) can he derived in two ways which differ with respect to the point at which the WfI-phrase ~nhzl./rbook is introduced. It can be inserted either into the Q-phrase n~lrcrc.Mliql Xltc~pshim,,as in

Syntax and Semantics of Questions 403 (59a), or into the Q-phrase ~ ~ reme~nbers h o where Mary keeps him,, as in (59b). Since i~hichbook is not preposed in (53), there are no other possible derivations for this sentence which would differ with respect to the order in which the three VfH-phrases are introduced. The two analysis trees in (59) produce two non-equivalent translations for ~ ~ l z o rtmei~zb'nv lvhere hfnr;.ykeeps jghich book. The top line of (59a) denotes a set of all true propositions expressed by sentences of the form ''2 remembers where Mary keeps which book". T h e top line of (59b) picks out all true propositions expressed by "2 remembers where Mary keeps .y", where "y" denotes a book. These are just the two readings we wanted. What this example shows is that the analysis I am proposing accounts for all of Baker's observations about the syntax and meaning of (53). There is no need for additional indexing of CV-H-phrases or interpretive principles of the kind in

(57). It is important to note that it is the syntactic part, not the semantics of WH-Quantification, which disallows the third reading of (.53), the one represented by (56) in Baker's framework. When applied to a proto-question, the quantification rule produces the same effect as the CW-Movement transformation. Subsequent applications of WH-Quantification to what now- has become a wh-question only result in the replacenlent of pronouns by lVf1-phrases. Consequently, in (53) the preposing of inhere in the embedded wh-question indicates that WI~PIP wiiS quantified into a proto-question and thus has "minimal scope" wit11 respect to the two other CYHphrases. In languages, such as Turkish and Japanese, where there is no preposing of WH-phrases, wc can expect to find Inore ambiguities. An example of this (clue to Hankamer 19'74) is given in (60a). According to Ilankamer, it has aH the threc readings jointly possessed by the two possible English translations in (6Ob) and (60c). (60) (a)

Charley'nin kimi nerecle vurclugunu kin1 hatirliyor.; Charley who were shot who remembers (b) Who remembers tvhcre Charley shot who? (c) Who remembers who Charley shot wl~ere?

Hankamer comments on (60a) as follows (p. 70): "even though no WH has undergone CIVI movement in the e~llbedtlcdQclause, cve know that one of them must be indexed to that clause; it is just inlpossible to tell which one." In other words, since there is no preposing of WH-phrases in Turkish, the surhcc structure of (60a) does not betray how the embedded wh-question became a whquestion. Under m y ani~lysis, he only way to get a wh-question is to form it form a proto-question by quantifying in a WH-phrase. IIere it coulcl be either ki111i "who" or it~redtj"where". ,4 Turkish versioil of the FIW-Quantification rule, which differs from the one in (47) only in 11ow FIVHQ,,,(x, 4)is defined, can thus account for both the facts that Hankamer dcscribcd in ternls of Baker's indexing mechanism:

404 Lauri Karttunen (i) at least one of the two WH-phrases in the embedded question in (56) has "minimal scope" (= is indexed to the embedded Q clause). (ii) it can be eithes one (or both). T h e analysis predicts, without any additional interpretive principles, that (61) is not an answer to any of the questions in (60). (61)

Bill remembers that Charley shot Orhan in the garden and Hasan remembers that Charley shot hfehmet in the forest.

2.1 1 Universality of the WH-Quantification rule There is an implicit assumption in the above discussion that tlic basic concept of tlie kVH-Quantification rule (that wh-questions are derived fronl proto-questions) and the associated translation rule are universal. It is worth noting here that this view leaves u-ide room for language-specific variations. By defining FcbllQ,,,(a, (/,) in a suitable way, one can describe languages where the syntactic interaction of WH-phrases and other question markers cliff'ers considerably from their bel~aviourin English. In Kussian, for instance, all wh-phrases are yreyosed in multiplc wh-questions, as illustrated in (62). (The example is from Wacl~owicz1974).

(62) Kto fto kogda slrazal? "Who said what when?" who what when said In Japanese there is no preyosing (or postposing) at all and the question particle, ha, which by itself marks yes/no questions, is also retained in wh-questions. (I<xamples from Kuno 1973, p. 13.) Kore wa hon desu kii? "Is this a book?" this book is (h) John $a dare o butta kr7 siranai. "I don't know whom John hit?" John who hit know-not

(63) (a)

Variation of this kind is easily accommodated under the proposed analysis.

2.12 Other scope ambiguities One of the consequences of treating W-phrases in the proposed manizer is that, in a simple wh-question, the interrogative noun phrase always has widcr scope than any non-interrogative noun phrase. For examplc, in (64) )])hat~ I ' L I L / Cllas wider scope than ez7er)l sluiLtnt. (64) what grade every student dcserves

This indirect question can only be deri.c?edin the manner shown in (05a); tlie resulting translation is given in (6%).

Syntax and Semantics of Questions 405 what grade every student deserves, W H Q , 0

0

? every student dcserves him,,, P Q

what grade, W H P

I

I

every student deserves him,,, 10, 1 ( P T Q )

grade

every s

t

I

u

d

-

student

(b)

c

what-grade-every-studcnt-deserves ' ji = [student'(y) 4 deserve$('j/, 's)]] A

n

i

r

r

e

l him,,

V .z.[gradef(.r)A "b/\p

In other words, (64) denotes the set of all true propositions expressed by sentences of' the form "every student deserves gradc .x." This set is non-empty just in case there is n grade that every student deserves. Any attempt to reverse the scope of quantifiers in (61) Cails. 'I'llis is sho\vn in (66). (derivation blocks)

/

every student, 0 ( P T Q )

I

student

\

what grade he, deserves, WHQ, 0

e

what grade, W H P ? hel desesves him,)

I

grade

I

he, descrves himo

In (66), hel cannot bc replaced by e:*tJr:ysruc/cnt becausc u)i/crt griltlc ht>l (i'cs~rzlcsbclongs to the category of indirect questions and, thcrcfore, is not of the sort required by the quantification rulcs in PTQ for ordinary noun phrases (S 14, S 15, and S 16). 1:urthcrmore, for semantic reasons these rulcs cannot be generalized to permit quantification into Q-phrases. 1 S This rcsult seems at first problematic because sentences such as (67) are clearlj ambiguous with respect to cluailtifier scope. (65) John knows what grade every student deservcs. On one of its readings, which we can easily obtain by embedding (64) under know and connecting the result withJohn, (67) means that John knows what grade it is that evcry student deserves. However, (67) also has anothcr reading which does not inlply such uniformity of student performance - in fact this is the more natural one of thc two. I11 thc second sense of (67), e z v r y srurlent is understood to have wider scope than I I ) / I ( I / ~ C I ~ L J . This sccond reading cannot bc derived in the manner illustrated in (66). Under thc proposed analysis, it can only bc obtained by quantifying in ezjrqy s ~ u d ~ at n tthc very last stage of the derivation. This is shown in (68a) and the resulting translation is given in (68b).

406 Lauri Karttunen (68)

(a) John knows what grade every student deserves, 10, 1 ( P T Q )

Q John knows what grade hel deserves, 4 (PTQ)

every student, 0 ( P T Q )

I

Student

s

John

know

whi~tgrade hel deserves, WHQ, 0

0 ? he, deserves himo, P Q

what grade, W H P

hel deserves 1 himcr

grade

(b) John-knows-what-g-rade-every-student-deserves A,)/Istudent'(y) know' (3,;V x[gradel(x) "p A p = ^deser~ek(:~l, 'x)])]

+

/\

As (68b) shows, under this analysis (67) is true just in case John knows, for cach student ,)I, the true propositions expressed by 1 ' 11 deserves gradc ,r". Obviously this does not implicate that every student deserves the same grade, like the first reading does, although it does implicate that every student deserves some gradc or ot1.1er. It is interesting to observe in this connection that direct questions exhibit just the sort of ambiguity cliscussed above. Although (64) seems unan~big~~ous, the corresponding direct question, (69) is ambiguous in exactly the samc way as (67). (This observation is due to Hull 1974.) (69) What grade docs ever>-student dcscrve? In one of its two senses, (69) requcsts information as to the membership of the set of true propositions exprcssed by sentences like "every student dcscrves grade s." In this sense, (69) can bc answered by saying, for example, "Every studel~tdcscrves a C-," or simple, "C-.-." Under the second interpretation, (69) is not one but sevel-al requests for information at once. It can be paraphrased roughly as "For eycry student.)), I ask you (to tell me) what grade J J deserves." This reading of(60) requires multiple answers; for esample, "Mary deserves an A, Rill deserves a B, . . . " and so on fils each of the students. T h e existence of this second reading for (69) is consistent with the viems exprcssed in scction 1.1 about the relation between direct and indirect questions. If direct questions are equivalent to dcclarativc sentences of a certain kind containing the corresponding indirect question, we should ii~dccdfind that (69) is ambiguous with respect to q~~antifier scope in the same way as (67).

2.13 Island constraints on WH-Quantification When applied to a proto-question, the IV1-I-Qyantification rule of English has the same eff'ect as the WH-_Movement transformation. An adequatc formulation of the synracric part of the rule, therefore, should incorporate all the "island constraints" on movement transformations discussed in Ross (1967) and in subsequent studies. The

Syntax and Semantics of Questions 407 csumples in (70) illustrate the kind of ungrammatical sentences that arc escludcd by Ross' constraints.

(70)

I

I

'Mary found out what subject Bill wants to meet a girl who studies. (b) *John wonders who that the president fircd was not mentioncd in the press. (c) *Max discovered which boy Bill met Jane and. (a)

Relative clauses, sentential subjects, and coordinate constructions are isla~ldsti-om which no constituent can be extracted by movemcnt rules. I-Iowever, it will not suffice to invoke Ross' constraints just in cascs where PWQuantification results in the extraction of a pronoun from ail island. In thc abo\;e constructions, replaceincnt of a pronoun by a PP-H-phrase results in questions of dubious grammaticality even in cases where no "movement" is involved. This is shown by the strangeness of the multiple nh-questions in (71). (N.B. Hcrc "#" is a mark of dubious gramma ticali ty.)

(71) (a) # Who wants to meet a girl u-ho studies what subject? (b) # iQ11ere was that thc president fired whom not mcntioncd? (c) # LVho met Jane and which boy? This correspondence bet\vccn extraction possibilities and quantifying in ("qi~antiiicr lowering" in the ternlinolog!; of generative semantics) was first noticcd by J. 1). k1cCawley (in 1968) and it has becn discussed at length in Lalioff 1970, Postal 1971, and other works (though not wit11 respect to interrogativc noun pl~rases).R. Kodman (1976) has proposed a way to introduce island constraints into Montague grammar. His solution is to let hIontaguc's relative clause and conjunction rules marli all 1he i~nbound pronouns in the resulting constructions in such a waj- that the7 cannot bc catractcd or rcplaced by quantification rules. The only cluantification-typc operation ;~ffcctingsuch island pronouns ("supcrscript R \-ariablcs", as lie c~illsthein) is binding. 'Tlic saille technique could also bc used to capture thc ct'fect of Ross' Scntcntial Subject (:onstraint. Since the I/l.'FI-Quantification rule in (47) is lihe hlontaguc's cluantification rulcs in all the relel-ant rcspccts, bj- adopting Roctman's proposal, all scntcnces of the type in (70) and (71) can be excluded. Rodman points out, the Fact that Montaguc grammar makes it casy to associate constraints on extraction to resi-rictions on cl~~;uitifier scope gives it thc same advantage that generati\-c scinantics has ovcr tllc standard version of transformational grammar. Unfortunately, it is not cleal- that thc connection between extraction constraints and scope phcnon~enais as close as Rodman and generative seniantiuists havc claimed. Therc are apparent counterexamples, at least in the case of relative dauscs. Onc such example (duc to Cooper 1975) is given in (72). (72) John wants to date every girl m-11o goes out with a professes \\.]lo flunked him out of Liilguistics 10I. (73) secins to have a reacling nhere the existential cluantifler has \\;ider scope than contrary to \\-hat Rodman's constraint predicts. In other \vords, the quantification rulc

~ z l c ' q ~ .

408 Lauri Karttunen for noun phrases sllould permit the replacement of hiinl in lrco wants to ri~ttrczjrql girl ./lzirrked himo nut ld'l,i~~guist ir- 101. The cxt111/10 gofiSout t j ~ i r l llzilrl /?)I a prt,Jt.sso~ n~ho raction constraints are stricter; therc is no cluestion about the ungrammnticality of (73). (73) *The professor ~ v h o mJohn wants to date a girl who goes out with is a boring lecturer.

In the case of LVH-Quantification, it also appears that the constraints on cxtraction are stricter than the constraints on replacement. T h e exarnplcs in (70) sccm a lot worse than those in (71). Consider also the kind of examplcs discussed in scction 2.10. Example ( 5 3 ) seems to have a reading where rl?ki~.hhook has !vide scopc, that is, an analysis tree like (74), which duplicates thc top part of (59b), should be permissible.

(74) who ren~emberswhere Ahfar?kccps which book, W H Q , 1

! who remembers where Nlal-ji keeps him,, WI IQ, 2 -----7

which book

who

? IIC? remembers where Mary keeps him,

-

Fiere therc is no rnovemcnt because the main clausc already begins with a wh-phrasc. However, in a case like ( 7 9 , whcre the application of bb,'ff-Q~antificationrcsi~ltsin the extl-action of a pronoun from an embedded wh-question, thc rule perhaps should be prevented from applying. (76) is the corresponding direct question. (75)

which book Jane rcnlcmbers n-here Mary kccps, W H Q , 1

!Jane remembers whcre Mary kccps himl, P Q

which- book

I

Jane remembers where -Mary keeps himl, 4 (P'l'Q)

------7

Jane

(7G)

remember where Mary keeps him,

# Which book does Jane remember where hlary kccps?

Although there clearly is a great similarity between cstraction constraints and rcstrictions on quantifier scopc, this connection scclns too impesfect to justify the acloption of a policy on ilua~~tificalion 13-llich is as inflcxiblc as Rod~man's"suycrscript R variablcUconvention. These is also another reason to be skeptical of it. Kcccnt ~vol-kon extraction islands (Ertrschik 1973; Rodman 1975) suggests that tllcrc is littlc hope for finding clear-cut criteria for grammaticality ec:en in the extraction cases. lt is now proposed that there is no sharp distinction bets.c.cn islands and non-islands, that islandliood is a graded notion. Furthermore, the acccptabilit!- of a given estraction also scerns to rlcpcnd on thc "primacy" of the extracted twm. Consider the contri~stbetween (77a) and (77h).

Syntax and Semantics of Questions 409

(77) (a) Which book does Mar!; wonder whether she should read? (b) "Which man docs Mary wondcr whether shoulcl read PTQ? (773) sounds inarginally acceptable, which presumably indicates that whether-clauscs are "weak extraction islands". T h e fact that (7%) is so much worsc is said to inclicatc that subject terms are higher on thc "primacy scale", hence less extractable, than objects. It is not clear how the interplay of such factors is to be taken into account in 1 formal description of English syntax. 111 an\; case, it is not cvident that a tsansf(1rmational approach to this problem is supcrior to the one proposed here.

2.14 Other constraints on WH-Quantification In addition to island constraints, there ma! bc other restrictions on Wll-Q~rantificiltion. I i i ~ n oand Robinson (1972), who present their findings in Baker's framework, propose the three constraints given in (78), (82), and (89). (78) C1,AUSE: M A T E CONSTRAINT: Multiple WH-phrases bound bj- the same Q must be clausemates at the time of application of WfI-Movement. This is designed to account fol- the sort of data displayed in (79). (79)

Tell me who is a better linguist than 1~110. (b) *Tell nie who is a better linguist than who is. (c) Tell me what seemed to whom to be idiotic. (d) "Tell me to whom it sccmed (that) what was idiotic. (a)

As Hankainer (1974) points out, there arc man!- countcsexan~plesto (78); most spcakcrs don't find anything wrong with exiniplcs such as (80), which is ruled out by this constraint. (80) Tcll me which student expects that he will pass ivhicli exam. ?'he Clause Mate Constraint would also disallo~z-one of the two readings of (53). (Kuno and Robins011 find ( 5 3 ) unambiguous.) Although it is clear that the Clause hlate constsaint is too general, there arc cases, such as those in (79), where it makes correct predictions. How-ever, if one thinks of the matter in the hlontague framework, it seeins that thcse examples clo not slio~vanything more than what Ive observed above: thc restrictions on the replaccmel~tof pronouns by WH-phrases are siinilar (although w~caber)than the constraints on extraction. 'l'hc extraction cases corresponding to the bad examples in (79) also have to be ruled out, as shown in (8 1). (81)

(a) (b) (c) (ci)

Tell me who Hill is a better linguist than. *Tell me who Rill is a better linguist than is. Tell me what seemed to Harry to be idiotic. "Tell me what it sccined to Harry (that) was idiotic.

410 lauri Karttunen T h e ungrammaticality of (81b) and (81d) presumably is duc to some combination of island constraints and primacy considerations. If we call make the WH-Q~a~~tification rule u7ork correctly in the case of (81), then the examples in (79) are easily accounted for. C;onsequently, there does not seen1 to be any need for a special constraint of the sort proposed in (78). T h e second one of the three Kuiio and Robinson constraints is given in (82). (82) CROSSING C O N S T M I N T : No INH-phrasc can be preposed crossing over another WH-phrase except that mhen and rr~heuecan cross over a WH-phrase u~hicliis not in the subject position. This is designed to account for the kind of data illustrated in (83).

(83) (a) 'Tell me u.ho killed w-hom. (b) (c) (d) (e) (f)

"Tell me whom who killed. Tell me who wcnt where. "Tell me where who went. Tell me what you bought where. Tell me where yo11 bought what.

This constraint also seems too general. Many spcakers who reject (83b) and (X3d) nevertheless accept scntcnccs like (81)which are similar in othcr respects cxccpt lhat interrogative pronouns are replaced by longer IYH-pllrases.

(84)

# Which girl did which boy kiss?

Furthermore, as Hankamer notes, all examplcs of the sort in ( 8 5 ) , where a pronoun is cxtrautcd from an embedded wll-question, are countcrcvnmplcs to tlie C:rossing Constraint.

(85)

'Tell me whicl~book Hill said 11c couldn't remember who cvrotc. (b) 1 wonder what Bill was saying he didn't know what to clo about. (c) Can you guess which crimes thc FBI doesn't know how to solve? (a)

However, it appears that (82) is at least partially correct. It turns out that, in the frame\vork proposed here, one can easily reformulate the Crossing Constraint in such a way that it rules out (83b) and (83d) but permits the grammatical e-uamplcs in (8.1) i1s well as those in (85). (This was pointed out to me by Stanley Peters.) En its new form the constraint of course does not pertain to crossover; instead, it is a restriction on quantifying in. Tlic following change in (47) has the intended e f i c t of (82). (86)

a~nendmcntto (47): replace (ii) by (ii)' delete the first occurrence of PRO,, in 4 and replacc all unbound pronouns to the lcft of it by the correspo~idiiigrestricted pronouns (Rodman's superscript R variables) unless a is an interrogative adverb (r~~hen, 117hel-c,/IOU?, etc.) in which case onl!- the pronoun in the subject position is so affected. -

Syntax and Semantics of Questions 41 1 l'hc gist of this amended version of (ii) is that, once a wh-question is formed from a proto-question by replacing "?" with a WII-phrase which is not an intei-rog-atil-e adverb, then all the remaining pronouns to the left of the deletion site hccomc "closed", as far as quantifying in or extraction is concerned. An attempt to derive (83b), for example, blocks at the point. shown in (87). whom her killed, W H Q , 2

? he, killed him,,- P Q

I

he, killed him, Given Rodmnn's convention, the restricted pronoun her, in the top line of (87) c:rnnot be replaced by a WH-phsasc, hence there is no way to derive (83b).1° On the othw hand, the change from (ii) to (ii)' has no effect as fils as the derivation of (83a) is concerned. This is show11 by the analysis tree in (88). (87)

who killed whom, W H Q , 2

/'-',

~ 1 1 o who killed him,, WI-IQ, 1

A-

who ? hc, killed him,, P Q

I

he, killed him, Sincc the CVH-phrase here are insertcd "from left to right", no restricted pronouns are created. It is easy to see that the same is true of the derivations of (85a) and (8%). T h c reasbn why (85c) is not blocked is that the insertion of h o leaves ~ ~ a pronoun in the object position unrestricted. All things considered, it seems that the statement in (80) is a more adequate forn~ulationof the constraint than \+-hatKuno and Robinson 01-iginally proposed. T h e last of the three constraints Kuno and Robinson discuss is given in (89). (89) DOURTdE DlSLOC,4TION CONSTRAINT: Uo more than one constituent can be moved from its original location. In the data they discuss, there are only t\vo exa~nplcscvhcrc this restriction plays an essential role. These arc given in (90).

(90) (a) W h a t did John say where he bought? (b) *Where did John say what he bought? According to their interpretation, sentences of this sort are bad becausc two inter!-ogitivc noun phrases have been moved awaj- from their original location in the cmbcddcd question. Note that t-hese are just the sort of examples 11'c discussed earlier in section

412 Lauri Karttunen 2.13 (76). Sincc there are clear counterexamples to the doublc dislocation constraint, such as (8%) and (85c) abovc, I don't think it is the right explanation. T h c difference is that in (90) the embedded wh-qucstion contains a finite verb, in (85b) and (85c) the final extraction is from an infinitival complement. T h e best I can suggcst hcrc is that it is this feature of (90a) and (90b) which makes them unacceptable. That is, as far as extraction goes, wh-questions with a finite verb are strongcr islands than those \-vithout one. T h e same is true of u-hcthcr-questions as well. Although both examples in (91) are acceptable, (91b) is less so than (91a). (91)

(a) Which book does Masy wonder whether to rcad? (b) Which book docs Mary wonder whether she should rcad?

In conclusion, of the three constraints proposed by Kuno and Robinson, only the second one, the Crossing Constraint, looks basically correct as a syntactic principle for English, though not in thc form they state it. ,4 more adequate formulation of thc constraint has been proposed abovc. There are, however, many additional problems concerning 'VH-Quantification that still rcmain to be solved. See Chomsky (1973) for a comprchcnsive survej. of problematic data and for discussion of othcr proposals for constraining 6'H-hilovcmcnt in a transformational framework.

3 Discussion In the following I will first briefly sun~n~arize the main points of' my anal+ questions and then comment on its relation to prcvious analyses.

of

3.1 Summary I start by accepting the common view that indircci questions arc- best anal!xed by relating them to declarative (alternatively, imperative) sentences of-a ccrtain kind which contain the corresponding indirect question. Consequently, my major objcctivc is to givc an adequate account of indirect questions. I leave open for the timc being thc p-oblcni of exactly how direct cluestions are to be derived. I consider indirect alternative and yes/no questions and singlc and multiple whquestions as belonging to the same syntactic category. According to Montague's t11eor.y of grammar, it follom-s from this that all indirect questions should bc scmi~ntically interprctcd in a uniform way; they must have the same typc of meaning. hfodifying a suggestion by C:. L. Hamblin, I propose that indirect questions derlote sets of propositions. Roughly speaking, thc meaning of an indircct question is identified with a function which picks out, for any givcn situation, the set of propositions which in that siti~ationjointly constitute 11 complete and true answer to the question. The deilotation of ,oher/ze~.Jokw n~a1X.s in a given situation, is a set whose only mcmber is either the proposition that John u-alks or the proposition that John doesn't walk depending on ~vhicliof these happens to be the true one. Thc denotation of ndro mnlks is the set of true propositions expressed by sentences of the form ".r walks". This

Syntax and Semantics of Questions 413 semantic analysis seems to have the right d c ~ r e eof generality to enable us to account for the ineaning of all kinds of constructions that embed indirect questions. The syntax of English questions is described by extending the description of English given by Montague in P T Q with the following syntactic categories and rules (here informally outlined): New syntactic categorics: Q( = I / / / ) - category of indirect questions I ? / Q- category of question cmbedding verbs (k~zorll,wmenrbn; n,o??r/er, usk, dcl.ir/c>, i~~restigute, deter.minc, etc.) R7H( = t//IV) -- category of interrogative noun phrases (1140, ~ ~ k n 117hir,h r, 6 0 , ~ 1 , rr?/~lrt hook, etc.)

Ncw syntactic rules: PROTO-QUESTION RULE ( P Q ) - fi)rms indirect proto-questions horn declarativc sentences by prefixing them with "?". ALTERNATIVE QUESTION RULE (AQ) forms alternative u-hether-questions from sequences of proto-questions by removing "?"'s and inserting- ndelhcr and 01- in appropriate places. YES/NO Q T E S T I O N RULE ( KVQ) forms yes/no whether-questions by substituting 1)7httht3r(or not) fi)r "?". WH-PHRASE RUTX (lVHR) - forms interrogative noun phrases from comlnon nouns by prefixing them with n)hir./?or i ~ h a t . WH-QLXNT11.'IC14TION RULE (WHQ, n) - forms 0-h-questions by inserting a PVH-phrase into a proto-question or a wh-question that contains an occurrence of the corresponding unbound pronoun (that is he,,, him,,, or his,,). The pronoun is either replaced in its 01-iginallocation by the incoming- 1VH-phrase or deleted in casc the MiH-phrase is preposed. T h e rule also rnaltes a number of other changes whidl involve gcnder agreement of anaphoric pronouns, case assignment, and restrictions on furtllcr applications of W19-Qiantification. QLF,SrI'ION EMREDDING RULE ( Q E ) forms intransitive verb phrases hy combining question embedding verbs with whether- and wh-clucstions. -

-

-

As in P T Q , each of'the six syntactic rules above is accompanied bj. a translation rulc which assigns to each resulting English construction an ;ippropriatc expl-cssion of intensional logic as a representation of its meaning. T h e main innovation in the proposcd syntactic analpis is the derivation ol' 1~11questions. T h e category of interrogative noun phrases (FW-phrases) is syntactically distinct from Montague's category of ordinal-y noun phrases (T-phrases). Iio\vcvc~-, semanticall?; the!- are of the same type. In fact, the meaning assigned to IjVfI-phrases such as 117hoand ruhic.h rnan is the same as the meaning of thc csisteiltiall quantified noun phrases someone and a rrl~ln.T h c I4TI-Quantification rulc is sj-ntacticallg morc complicated than Alontague's quantification rules, bccause it also does thc work of the WH-movement transformation, but its semantic cffect is similar to thc cffec~of Montague's rules for quantifjiing into common nouns and intransitii-e verb phrases.

414 Lauri Karttunen

3.2 Comments on previous analyses of Wh-questions T h e main advantage of treating PW-phrases in this nlanncr is that the derivation of single and multiple wh-questions poses no problems either syntactically or sc~nantically. T h e proposal accounts in a very natural way for man!- propcrtics of such questions which iulder prel-ious analyses require additionrrl descriptive apparatus. 11 also nla kcs it relatively eilsy to relate the island constraints on c~trilctionto facts abour the scope of CvH-phrases, which the standard transforn~ationalanalysis cannot do. In spite of its unfamiliar appearance, this ncw analysis of English wh-questions is in many respects sinlilar to the transformational description first de\clopcd by J. Katz and P. Postal (1964) and subsequently improved in Baker (1068). In fi'lct, 13akcr's t \ ~ orules for deriving wh-questions constitute a close analogue to what is proposed hese. His firs[ rulc applies to sentences prefixed with the symbol Q and i~lscrtsa M711-m;lrkcr to a constituellt containing the clement S O ~ ~ I(or C TklA'l'). 'l'he rulc also marks the scope of the resulting WH-phrase by assigning matching indices to the Q ilnd WYl-symbols. T h e second r ~ ~mo\,es le a I$'H-phrasc to the beginning of the sentencc that constitutes its maximal scope. 'The only substantive sj-ntactic difircnee, asidc from those that come from doing the analysis in h4ontaguc's framen-ork, is that my description 111aIics it possible to dispense with Baker's ad hoc con\,ention for indicating the scope of !YHphrases. Since the tn-o descriptions are so close in other respects, it is not surprising as Baker's in accounting for the rangc of that the new analysis is just as successf~~l possible readings of multiple wh-questions. T h e idea that w1-h-phrases are quantifier-type expressions is not in itself new; i t l ~ a s been discussed by Baker (1968) ancl C h o m s l i ~(1975), among othcrs, \vl~o,hon-cvcr, (lo not concern themselves with tlle semantic interpretation of wh-quantifiers. The scnlantics of w-h-cluantification has been discussed b!. IIintikka (1074, 1076) and I-Iull (1974), but the new proposal seems superior to theirs in thc follonring rcspccts:

(i) it relates wh-questions to yes/no questions in a 1-ery natural \yay. (ii) it enabics LISto genci-ate and interpret multiple wh-questions \vith the S~\IIIC rules that are needed anyivaj- for single 11-h-questions, and (iii) it accounts for some of the puzzling propertics of' niultiplc wh-questions in an especially natural way n i t h less descriptive apparatus than any of the prc~ious proposals.

3.3 Outstanding problems , 7

1 he analvsis of qucstions proposed in this paper is in some respects tentative. 'She specific formulations of the syntactic rules undoubtedly call be improved with further w r k . This is especiall! true of the H7H-Quantification rule. T h e present shortcomings of that rulc are mostlj- due to our c u r r c ~ ~ ignorance t concerning the proper s~nlactic constraints on quantifier scope and ~novementtransfi)rmarions, not to carclessness or to the choice of the particular descriptive framc\vork. 'I'he relation between direct and indirect questions yet remains to bc spcllecl out in detail. T h e view advocated in section 1.1 is essential]\- the traditional "pcrfori~~ativc

Syntax and Semantics of Questions 415

1/

hypothesis," which receives some support from the facts about scope ambiguity discussed in section 2.12. T h e details, ho~vever,nccd to be ivorkcd out, and there remain other viablc alternatives (e.g. see Cresswell 1973) that should he esplorcd. Some difficulties can be expected in the case of dil-cct negative yes/no questions. Undcr- the analjrsis proposed h e x for indirect questions, ~llhelherthi.c Avn )I II plriilt I ' ~ ~ ~ J ,is cTS C ~ I ~ ~ I ~ I 17 tically equivalent to ~ ~ h r t h [his e r is LL pret
Notes

I

The rcscarch for this papa. \vils supported by a workshop on alternative theories on semnntics and syncas conducted by the Mathematical Social Science Board at UC; Berkeley in tlle Sumlncr of 1075. 1 am especially indebted to David 1,cwis and Stanley Peters, who took part in the workshop, for their encouragement and helpful criticism in the earlv-stages ot'this investigation. I h ~ v ealso benetitcd 17). tliscussing these matters with C. A. Anderson, C. L. Baher, R. Cooper, J. IIintikka, I), Laplan, I;. Karttuncn, ancl E. Kccnan. Preliniinar!- versio~lsof this paper have heen presented at the 1075 Winter LSA Meeting and at the Third Tntcrnational C;onfercnce of Nordic ant1 C;enual 1,inguistics in the Spring of 1976. I am especiall? grateful to Stanley- Pctcrs for his comments which rcsulted in many imyrol-ements in both the style and the content of the presentation.

416 Lauri Karttunen 1 Alternative questions have also been called nexus-questions; another name ii)r wh-questions is s' questions (Jcsperscn 1924). T h e term "wh-question" is somewhat niislcoding because t h ~ presence or absence of this marker does not precisely corrclatc with the intcnclcd division. Not( that FF-lietlicr-questionsarc alternati~e questions, not ~vh-cluestions,and thal questions hcginninl with honj are wh-questions. A better term for wh-qucs~ionsmight he "search questions", sincr semantic;~llythese cluestions involce 3 search for a suitable valuc for A variable (single seitrcf questions) or a set ot' variables (mul~iplcsearch questions), not B choice between itlternativc propositions. One might also consider using the contrasting tern1 "choice question" t i ~ alternative r questions. In tliis article, however, I !\-ill stick to the current terminology. 2 In written English, qucstions like Do you nwut I L ' ~or ~.c![Ji~t? citn be interpreted cithcr as simplt ycs/no questions ("Do you want either tea or coffcc?) or as elliptic forms for longer alternativt questions ("Do you want tea or clo you want coffee?"). Scc section 2.3 for a discussioll of this typc of ambiguity . 3 One might argue that the phrase l?,kr// /he)! srrrc./i)r br.cuk/irs/ in (5a) is not an indircc~question a1 all but an entirely different construction called the tirce relative, as i r i (i) What they serve for hreahfast is too fattening for me. One characteristic of indirect u~h-cluestionswhich distinguishes them li*oni bee relatives (see Baker 1968) is that t h q z may contain more than one wh-phrase. 'The fi~ctthat scntenccs likc (ii)

4

It is anlazing who thcy nominated for which office.

arc grammatical scclns to indicate that bc (ivia.zi17,yinclced cmheds inclirect wli-questions. Actuall> Hintilika thinks that (10a) and wh-questions in general arc anibiguous betviecn a universal and an existential reading of the interrogative quantifier. In the latter sense (10a) would be equi~alent,not to (lob) but, to the sentcncc. -

(i)

-

Someone camc and John remembers that hc came.

It ilppears that Hintihka is mistaken on this point. If (10a) had sucli a rcittli~tg,it sho~rldbe possible to say without any contradiction (ii) Jolin remembers who camc althougl~he docsn't remember that Mitr!: cilnlc. ITowevcr, sentences of the abovc sort arc gener;llly fklt to he contradictol-5 (cf Hnher 1068, p. 50). In ot.her words, (103) is true just in casc Jolin rcniembcrs of all the pcoplc who canic that the! camc. IIintikka may have been misled by the fact that rltrc~./wh-qu~'stionsoften get asked with the underst;lnding that :in cuhaustivc answer is not expected. This a person u h o ashs (iii) Lfiho, for instance, calile to the party last night? may be perfectly satisfied ~vitlian ans\\.er that lists some but not all of the p a ~ p l e\ ~ h ocalnc to the party. (The phrase-fir rn.s/nnl,eseems to he a con\-cntional clevice for indicating that csl~austivencss is not desired.) Since intlircct u-h-questions tlo not admit an! "for instance"-inrcrpret;ltio~~,I am inclined to think that there is no semantic ambiguity of the sort I~Iintikkitpostulates. \+'l.l;~twc do need, of course, is an ~iccountofsthe pragmatic tact that direct wh-questions clin be usccl to solicit more or less complete answers depending on the 1)articular question and the circumstances of its use. As fir as I can see, tliis task is not fi~cili~atecl at all by postulating a strict semanric dichotomy between universal and existential \vh-questions. Ucsides, in the casc of indirect wh-cluestions, this would lead to wrong results. Multiple wh-questions in particular do not sccm to have as many possible interpretations as Hintikka assumes.

Syntax and Semantics of Questions 417

-5

6

In this paper ~h-questions are alnays intcrprctcd "universally" although the t\h-wol.ds thenisclvcs are interpreted as existential quantifiers. (See the next section li)r details.) As (17) indicates, Haiiiblin interprets questions "univa.sally" i.c. as denoting all propositions of a certain kind. This feature of his treatment is implicit in (17) in the use of LLj", wliicl~ abbreviates " i p " . Note that the quantifier corresponding to 117lio in (17b) is the existenlial quantifier. (Cf fn. 4.). For cxample, this could be done in the following way. Let depend-on1 bc the translation of rlepettd on, let 5 and Yf be variables ranging over intensions of' indirect questions, i.c. over properties of propositions, and let ,? be a variable over fi~nctionsfrom scts ol'proposirions t o scts of propositions. As the first approximation, let us consider the possibility of constraining the interpretation of dcpend-on' with the meaning postulate in (i). = "X (i) dcpend-on1(%)(X) --t VROg("3)

This meaning postulate says, in essencc, that the denotation of the question in the subjcct position of ri'tpc~ndon is determined in all possible worlds by the denotation of the cluestion in thc objcct position. For csamplc, (18) would come out true just in case the election has a certain necessary outcome for each selection of people that might bc running. That is, in i~n!,two situations ~vhcrethe same people are running, thc same person wins. T h e above meaning postulate is undoubtedl!; too strong for the x r b rlcpmd ~ I I ,although i t niight he appropriate for a phrase likc bt ~ie~erraint>d by or depend e.~c.lirsizlel)!on. Scntencc (1 8 ) , for cxaniplc, does not rule out the possibility that the outcome of the clcction niight also dcpcnil on, say, when the election is held in addition to being dependent on who the candidates arc. To do justice to the intuition that depend on only means something like "be determined it1 part by", we must replacc (i) with '%) = '7{ (ii) depend-on1(8)("36)c; VRV '4[nR(-9,

7

V/'u./'("%) = '?{I,

:',T 7

whcrc % is of the same type as 9 and YC representing whatev-cr other factors might iatlucnuc the extension of "3"in addition to tile membership of '9. (The second colijunct in (ii) is needed to make sure that these other iactors arc not by themselves decisive, i.c. that the ansvt-cr to thc question in the subjcct position indeed in part dcpencls on the answer to the qucstion in the object position.) In echo-questions the wli-phrase has the widest possible scope. .As an echo-question, (21a) is ecluivalent to

(i) Which book isn't Mar!- sure about whetller to read? This involves taking (21%) as a whole to be a direct qucstion, not a cledarntite sentence containing an indirect qucstion, as indicated here. Note that an acceptable ansnw to (211-3) taken as ;In echo-cluestion - must itself be a question, e.g. "Did hlary read Sl!tr/or.iic..Y/riri~//ire~?". 'The analysis of such "sccond order" questions lies outside thc scope of this paper. 8 For the sake of making the prescntation shorter and easier to fbllow, I will discuss liere on14 vcrbs which embcd indirect questions in the objcct position. Morc sptactic categories arc obviousl!~ necdcd to accon~modatevcrbs likc h17 t/tipr)l.ir/lli and r/c.pen// orr. W n spoken English (29) can be disan~bi~watcd by a rising intonation contour on sn~okcsfolloncd by a drop in pitch and a tilling intonation un or Btll drinks. This marks the cni1-3cdclcd clausc as an alternative qucstion. Sonie languages malic thc corresponding distinction n~orpl~c~logicalI_v. Finnish, for example, niarks altcrnativc questions with a special form of "or" (zlai in altern;~tirc cluestions, / ~ i clsetj-here). i 10 Due to the shortcomings on Montaguc's syntactic frame\\-ork, thc present anal~vsisc:lnnot account for the rcli~tcdambiguity in sentences such as -

41 8 Lauri Karttunen (1)

Tcll mc whether Rill wants coffee or tea.

In order to produce the alternative question reading for (i) one ought to have a transformational rule which generates n~herherRill r ~ ) a r l (.(!fie f.~ or ira from mlietl~rrBill n?owls or BIN alutzts Ieo, where the latter has becn dcrivcd by the AQ rule. There are no syntactic operations of this kind in PTQ. By treating ~.r![fit or tell as a disit~nctivenoun phrase, as Montague docs, wc can gcnerate n~hethrrBill wants c@e or fell only by the )iNQ rulc from .illill n~rrnrnI . ( ! [ / ~ L L oi. [err. In other words, the only rcading we get for (i) is the onc which calls for a simple yes/no i1nsM;cr. 11 Actually we should distinguish here between the cluestion embedding verb knowfr j o and its that-clause embedding counterpart knon7,. Thcse are distinct lcxicat items under thc proposed analysis and belong to diffcrenr syntactic categories. T o assign proper semantic interpretations to sentences convaining X~nnrz?~~ ,p, we need a meaning posttulatc that relates their translations, know;, jp and know1, in the appropriate way. As the first approximation, let us consicler the following proposal. c.(![)i~!li.cl

-

T h e effect of this mcaning postulate is to make -7oIin kizttn~swhether Mrrr:]~ cooks or Bill O~II true just in case John k n o w every proposition in the set denoted b!; s l t r / / ~ r/ rI ~ L I Yr.noX.s ~ or Rill elrrs or// provided that the set is non-empty, and in the event it is, juvt in case John hnons that it is emptj-, i.e. hnows that Mary doesn't cook and Bill doesn't eat out. ?'he problem of the indiwct question possibly denoting an empty set does not arise in connection with simple ycs/no questions. Thus John knon~sr??hrtlrer.Mtrr11 (.(/oh is true just in case John eithcr knows the

proposition that Mary cooks or the proposition that Mary

doesn't cook. expect, given the fact that in transfor~nationaltreatments (c.g. K a t ~and Posta] 1964) mhl, and o,hd/ have been rhoughr of as being t r . ; l ~ ~ s f b r ~ ~ ~ a t i~~~~~i\.ctf o ~ ? i ~ l Ifrom > n7h + S O I I I L O H ~ancl J P t ~ SII~~IPIIZJYI~. I.? Uircct wh-questions and sentences containing indirect wh-clueslions are comn~onl>said to have esistential presuppositions. For example, J~"ILI/ 11oe.t John rc~nd?and 11 dmevn 'I mrrtl~rt?~hn[ j'oAj7 r~i/i/Simplicate that John reads something, i.e. that the set denoted by n7hn1 3ob11n~irifxis nonempty. This aspect of the meaning of wh-questions is not accounted for b; the present analysis. It is the topic of Karttuncn and Peters (1976), \vhich also presents a solution to a similar problcn~ concerning alternative qucstions that was mentioned at the end of sectioll 2.2 See section 3.3 For furtlier discussion. t proposed by laker (1968, p. 50) with tlic I4 This analysis of indirect wh-questions has in f ~ c becn difference that Baker (like Hintikka) interprets intlirect questions onlj- "contextually", that is, as part of a larger construction. Baker regards (41) as cqui\alent to

12 This is as one

(i)

For all

.Y,

John l i n o ~ ~ a shethcr .s datcs Mary.

1.5 If we were to generalize our quanlification rules in such n way as to 3110~.quiintif).ing P ~ * C V : ~ ! s/lr(Iri~linto the indirect question n711crl pwdc. /?el dt..cerzvs, the resulting translation would presumably be (i)

i; /\ ylstudent'(.jl) --. V ~ [ ~ r a d e ' ( . v")p n p = "descrve:(:)~,

".v)]]

Unclcr any reasonable interpretation of English, this formula is totally inappropriate ;IS a semantic representation for (64). In any world where there is more than one student (i) denotes the null set. 16 I am assuming here that restricted variables arc only used to restrict wh-quantification, not quantification with ordinary noun phrases as Roclman proposed. Otherwise tv-c could not generate analysis trees such as (682).

Syntax and Semantics of Questions 419 17 It is not entirely clear whether this is the correct result, given the fact that negative whcthcrquestions sound awkward in many contexts (cf. # ir isn't entireIy cLor 1~7hzrlrer/ / ? I S lsir 't //re I.ort-ec.t result). Furthcrnlorc, in somc cases wherc they do sound natural (c.g. I ~~orrr/i~r n7hethi.r 11~e .i.horrMir'I try n1zntl7cr (rppruaclz.) onc can plausibly argue that the negative questions is accompanied by somc sort of conventional or conversational implicature which the affirmative counterpart lacks.

References ,iqvist, Lcnnart. 1965. -4 ,Vem .4ppr',nt.h l o tlrr L o x i ~ n lTheory 01' lntt.rrogcrtiz'rs, Uppsala, Swcdcn: Filosofisha Fiireningen. Bach, Iimmon. 1971. Ques~ions.Lingzd~srii.Ii7yzrrr)! 2: 153-60. Hakcr, Carl L. 1968. lndirect Questions in Englisll, Ph.L). dissel-tation. University of Illinois. Urbana, Ill. Baker, Carl L. 1970. Notes on the description of English questions: the role of an abstrict question morpheme. Fourrdcrtiotzs ~!f'lafzgull,~e 6 : 197-2 17. Rclnap, Nuel. 1963. . i n -4rraIj~isr!/'Q~tstions,Technical Memorandum T M 1287/00/000, Systcrn Development Corporation. Santa Monica, Calif. Cliomsky, N o s n ~ .1973. Conditions on transformations. In Stephen R. Anderson and Paul Kiparsky (cds), -4 Fc.~tsc-lrrifi./i~r Mnl.rjs HiilIe. Ncv York: I-Iolt, Rinehnrt, and Winston. Chomskp, Noam. 1975. Rc:fr~~tlO~rs 0 1 1 L ~ I ~ ~ LNew I N ~York: c . Pantheon. Cooper, Robin. 1975. Montilgue's Semantic Theory and Transfbrmational Syntax. Ph.U. disscrtiltion. University of' Massad~usetts.,lmherst. Cresswcll, Mau J. 1973. Logics anrl Liriigirirges. London: Methuen & Co. Lrteschili, Nomi. 1973. On the Nature of Island Constraints. Ph.D. disscrtation. RI.1.T.. Canlbridgc. Gricc, TI. P. 1955. I,ogic and con\-ersation. In Ilonald Ilavidson and Gilbert Hasman (eds), Tlrrc, Logti. r!/'C;r.r/)trnrm~Lncino, Clalif: 13ickenson. Hamblin. C. L,. 1973. Questions in Alont;lgi~eEnglish. Forrizrl~rtionsr!f'I,trnpllr~~~ 10: 41-53. Hanliamer, Jorge. 1974. On WH-Indexing, NE1.S V : Papcrs from the Fifth Asleeting of the Northeastern Linguistic Society, Ilepal-tmcn~of I.inguis~ics,I Iarvard Universit!-, Cambridpe, hfnss. Hintikkn, Jaakho. 1974. Questions about questions. In Milton K. Munitz and Pctcr Lngcr (cds), Scnrawlics rri~ilPlrllosop/r,)~,NY University Press. New York, N.Y. Hintikka, Jankko. 1956. The se~nanticsof questions and the questions of sen~antics.case studies in thc interrelations of logic, syntax, and semantics. A i . ~ i lPkilnsopk~lzlFr'nnirrr 28(4). Hull, Robert David. 1974. A Logical Analysis of Questions and .Ins~vers, Ph.D. dissertation. C:am bridge. Jcspcrscn, Otto. 1924. The Ph~losc~phjt i!/'Gra~nr~znr. London: Allen ik Lnwin. Karttunen, Lauri and Stanley Peters. 1975. Conventional implicature in Montague grammar. In BLS 1: Proceedings of the First Annual Mccting of the Herlieley Ihguistics Society, Rerkcley, (,aliC. Kar~tunen,Lauri and Stanley Peters. 1976. whal indircct questions convm~ionalll;implicate. In CLS 12: Papcrs from the Twelfth Regional Mccting. Chicago Linguistic Socictj-. Chicago, Ill. Katz, Jerrold J . and Paul M. Postal. 1964. .-ln I n ~ e ~ r n / eTr /h r o ~qfLinguMtic. j~ L)i~scriptions,Cambridge, Mass.: M1T Press. Keenan, Edward and Robert TI. Ilull. 1973. T h e logical presuppositions of questions and ansbvers. In J. S. Pctijfi and D. Franck (cds), P ~ ~ ' s u p p o s i / i o ninm Philnsophlc ~itzii'I,i~grtis/ik.F r a n k f ~ ~ r,Athet: naum. Kuno, Susumu. 1973. Tllc Str*l~iturr/!/'/heJ [ r p i ~ i mLL~rrgrj?ll~rg~ ~ Ca~ilhridgc,Mass.: hllT Press. Kuno, Susurnu ancl Jane Robinson. 1972. hjlultiple W71H-Questions. Li'?rgzdzsir~.Ji~quii:)~, 3: 463-87. I,alioff, George. 1970. Ropartce. Fou~rdn/ionsqf jStrngurrge 7: 389-472. I.,angacker, Ronald. 1974. T h e cluestinn of Q Furrndtrtions ~ ! j " L n t z p ~ ~11: i ~ g1-37. t

420 Lauri Karttunen I,cwis, Davitl. 1072. Gcncral semantics. In Donald Ilaviclson ant1 Gilhert Harman (erls), .S'einr~~t/rr~ q/' n;trlrir.(rlI,rrngllrrpe, Dordrech: D. Rcidel. Lewis, Ilavid and Stephanie. 3975. Review of R. Olson and A. Paul, cds. "Contcniporary Philosoph!: in Scandinavia", T/zrorrtr 61: 39-60. A,lontague, Kichard. 1974. T h e proper treatmcnl of quantification in ordinnrj- English. in R. Thomiison (ed.), ForrmI Phrlosoplzy, Sz/ei.tt~rlPnper-s c!/'Rii/inrll :Mot~/ngue.New Haven, Conn.: Yale Uni\ ersit!- Press. Postal. Paul. 1974. On certain ambiguities. Lin,cz~is/irInquiry 4: 367-424. Rodrnan, Robcrt. 1075. The Non-discrete Nature of Islands, Indiana University Linguistics C:lut> Papers, Bloon~ington,Ind. Rodman, Robcrt. 1976. Scope Phenomena, "Movement Transformations," and Relative C:lauscs. In Harbara Partee (ed.), Mont~zgueGrammar, New York: Academic Prcss. Ross, John Robcrt. 1%:. Constraints on Variables in Syntax. Ph.13. disscrtation, M.I.'T. Cambridge, Mass.

Thomason, Richmond 1-1. 1976. Sonle extensions of Montague grammar. In Harbara Partcc (ed.), Monritpu~Grummar, New l'ork: Academic Press. Wachowicz, Krystpna. 1974. Multiple questions. Lirrplilstii.n Sileslutiu 1. Wundcrlich, Dieter. 197.5. Frizgesitze und Ft-agen (preliminary version), unp~~blished paper.

Type-shifting Rules and the Semantics of Interrogatives Jeroen Groenendijk and Martin Stokhof

0 Introduction T h e aim of this paper is a modest one. In what follou-s, we will argue that if one takes into consideration certain constructions involving interrogatives, a flexible approach to the relationship between syntactic categories and semantic types may be of great help. More in particular, we will tr>-to show that if one uscs something like an orthodox intensional type theory as one's se~nantictool, a more liberal association bctwccn syntactic categories and semantic types becomes imperative. Howcver, we will also see that such flexibility is by no means easily introduced into thc grammar, and that it nceds to be properly checked in order to avoid undesirable eonsequcnces. T h e paper tries to make b o ~ ha descriptive and a mcthodological point. First of all, we want LO demonstrate that type-shifting rules, when combined with general notions of coorclination and entailment, are useful tools in the semantic description of various constructions involving interrogati~es.And second, we hope to show that they arc important n~ethodologicaltools as well, which can guide us in finding the proper semantic types for interrogatives, and in arriving at a "unification" of the two major approaclles to the semantics of interrogatives: the catcgorial approach and thc propositional approach. T h e constructions involving interrogiltivcs which we will bc conccl-ned with in this paper, are mainly coordination of interrogatives ancl entailment I-elations between them. Coordinated in~errogatives,i.e, conjunctions, sequences, and disjunctions of' intcrrogatives, may appear to be pretty- rare phcilomena and not be worthy of too much attention. Similarly, entailment between interrogatives may seem a qucstionablc thing. Entailnlent is defined in terins of truth (conditions), and arcn't questions the prime example of sentences that are not true or fcllse.>True, but there are Inally other liinds of expressions hat, ils such, cannot be said to be true or false either, but of which we can meaningfully sa!- that the one does (or does not) entail the other. In fi~ct,this holds for all conjoinable expressions, i.c. all expressions of a scinantic type of the form (. . . t ) . For all such types one can define in a general schematic way, what coordination, conjunction and disjunction, within such typcs amounts to. 111 a similar way, n general

422 Jeroen Groenendijk and Martin Stokhof definition can be given for erltailment which tells us h r any two exprcssions of any particular conjoinable type under what conditioils the one entails thc other. T h c inductive basis of this clefinition is, as is to be expected, that of entailment between exprcssions of tj-pe 1 , entailment between indicative sentences. Entailment is a fundamental semantic notion. Other basic semantic notions, such as synonymy, antinomy and meaning overlap, can be defincd in terms of it. And in descriptive semantics, one of the major goals is to account for semantic phenomena in terms of these and similar notions. I'his holds for interrogative constructions as much as it does for the inore familiar indicative ones. Being the fundamental senlantic notion that it is, entailment, especially when it is coinbiilcd with generalized notions of coordination, is also an important methodological and heuristic tool. Semantic theories can be evaluated with its help, and this holds for theories of the semantics of interrogatives, too. If a particular theory assigns a certain kind of scmantic object, of a certain semantic typc, to interrogati~esentences, we can test it by applying these general definitions, and see ivl~etherthe interpretation it givcs to coordinated intcrrogatives and the predictions concerning entailment relations it n~akcs on the basis of thcse definitions, stand to reason. Consequently, entailment anit generalized coordination will help to find the right scnlantic tyyes for interrogative sentcnces, and the right Lind of semantic objects within thcse tj-pes to serve as their interpretation. \hlc will argue that the most adequate theory will assign a number of different semantic types to interrogatives, depending on the syntactic construction in which they occur. Type-shifting rules will play an important role in incorporating the results in the grammar. One of the most striking features of type-shifting is that it nllo\\,s for flexibility in associating semantic: interpretations with expressions. Vl'ith t l ~ chelp of pencrally defined semantic operations, a basic interpretation of an espression can be lifted and shifted to derived interpretations. So, one and the same expression can llave ;I wide iwicty of possible intcrprctations, which can be chosen from in different contests. Type-shifting can be put to different uses. E.g., as a descriptive tool, it plays a role in the analysis of coordination. Let us give a familiar exsmplc. For reasons of simplicitj and cleganee, it is attracti~eto assign to proper names, and possibl!- certain other NP's as well, a semantic object of type e as their basic interpretation. This cannot be the only type for propcr names, horn-ever, since the?- can also be conjoined with other proper names, and with other kinds of NP's. Type e is not the sight type to appl\.-coordination to. l'hcrefore, in the context of coordination proper na~ncsshould rather be interpreted as denoting the set of properties of an object of t 3 . p ~e. 1.e. we need a scco~ld interpretation of proper names, that of objects of type ( ( e , ~ ) , r ) which , is also thc lowest possible type for quantified NP's. We will see that, for similar reasons, such shifting in meaning is also recluired for coordination of interrogatives. Apart from this rather "standard" use of tvpe-shifting in the sun~anticsof interrogatives, involving well-known lifting and shifting yrinciplcs, there is something nlol-c. Among the proposed senlantic theories for interrogatives, two approaches can be distinguished: the categorial approach and the propositional approach. One rnajor difference between thc two is that they assign different types to intcrmgativcs. So, one may rush to conclude, "(at least) one of them must be wrong". No, not necessarily so, according to n flexible, typc-shifting methodology. If the types employed by each of the two approachcs can be related to each other by means of a significant uniform semantic operation, both

Type-shifting Rules 423 might prove to be (at least) partially right. We want to argue that there are reasons to look upon things this way. PVe will show that the successes and failures of thc catcgorinl approach and those of the propositional approach are complementarj-, and that by providing a more flexible theory that combines the two, we can add up their successes and eliminate their failures. However, a l t h o u ~ hwe will see that such a unification of the two approaches is possible, the cluestion remains whcthcr the semantic operation that is needed to get from the categorial type of interpretation to the propositional ripe, can really be viewed as a general type-shifting procedure. It certainly is not an orthodox one, and one lllight say that rather than adducing further support for a flexible approach, it raises foundational questions. If a flexible approach is to be more than a nlere technical descriptive device, i.e. if it is to be part of a substantial theory about the relationship between syntax and semantics, it has to be based on restrictive principles. T h c paper is organized as follo\vs. In section 1 \ye give a rough sketch of the ideas underlying the categorial and propositional approaches, outline why the two cannot be straightforwardly combined, and indicate how this problem can be solvcd. Section 2 deals with coordination of interrogatives and entailments between t h c n ~ and , discusses the various t p e s in which interrogatives should be analyzed. In section 3, a flexible approach is developed which deals with the filcts discussed in section 2 and which overcomes the difficulties indicated in section 1. Section 4, finally, sums up the results. A final remark in this section concerns terminology. In what follom-s, we shall use the phrase inlevrognlice to refer both to interrogative complements and to interrogative scntcnces. Further, we shall discriminate between senlcntirrl and ~.ons/i/uellljnterro~4ti\-cs meanins expressions such as "Does John love Mary?" and "whether John loves Marv" bv the former, and constructions such as "MTho atc the cake.?", and "who bought tvhich books where" by the former (using the phrasc n-c.ortsriturnl (intcrroptive) to indicatc the number of wh-phrases that occur in an interrogative). Finally, it should be notcd that intfrrugtctive shall denote linguistic expressions, wl~ilcyu~s\ioti is rescrved for the semantic objects they express.'

1 Caterpillars and Butterflies 1.1 Introduction In this section wc \\rill outline two appsoaches to the semantics of interrogtivcs and the question-answer relation. Each of these two approaches, we will argue, solves somc important issues, yet, oil the fi~ceof it, the tn-o are incompatible. However, 1t.e ivill sl~oviithat if we take n flexible view, the conflict may be an appl-vent one, and that a type-shifting process may serve to unifq- the insights of both. T h e situation we will sketch, bears a striking resemblance to the situation one finds in the semantics of noun phrases. Concerning the latter, Barbara Partee writes in her 1986 paper (which was a source of inspiration for the present paper): 'I'he goal [ . . . ] is to attempt a rcsolutioll of thc apparent conflict between txvo i~pproaches [ ... 1. 1 believe that thc most iniportanr insights of both sides arc basically correct and mutually compatible. T o try to show this, 1 \\ill draxx- on nancl extend the idea of general type-shifting principles [ . . . 1. (Yartee 1986, p. 1 15)

424 Jeroen Groenendijk and Martin Stokhof 'Thc tmro approaches we will discuss, can be dubbed the ~utegoriwland the proposiliolral approach. In the former much ernyh~sisis placed on the differences in syntactic category and semantic type between different kinds of intersogativcs, whercas in the latter the postulate of a uniform, propositional, type is the starting point. Our own analysis, if it is successful, will be one that covers both, in the sense that it ivill allow us r o treat interrogatives in a variety of types, which are systcmatieallv rclatcd to each other. Such an analysis would provide additional support for the kind of use of typeshifting that was made for the first time by Partec in her diseussion of NP-interpretations, a kind of use that considers type-shifting as an explanatory device, rather tliaii as a descriptive tool.

1.2 The categorial and the propositional approach If we restrict ourselves to the (modcl tlicoretic) semantics proper of intersogativcs, two main approaches call be distinguished: the catcgorial and the propositional approach. Disregarding details of concrete iinplementation (at least fbr the moment), they can be charactcrizcd as follows. O n the categorial view, the main semantic property of an interrogative is that it is in some sense an "incomplete" object. This object requires for its completion an answcr. Diffcrent kinds of interrogatives, it is observed, call for different kinds of ansmrcrs. Sentential interrogatives, for example, are characteristically answered by "Yes." or "No. ", and constituent interrogatives are typically followed by constituents such as "John,", "In the park.", "John, by Mary.", and so on. These constituents do not form a homogeneous category. Some are terms, others adverbs, and others again, like "John, by Mary.", are of a category not ordinarily h u n d in sentence grammar. Still, in the context of an interrogative, all these different kinds of constituents are meant to convey information, to express a proposition. And, of coursc, ivliich proposition a characteristic linguistic answer expresses dcpends on the interrogative it is meant to ans\i7er. On thc categorial approach this is accounted for by analyzing intesrogatives and answers in such a iv3y that the!; fit togcther and make up a proposition. Hence, since consti ti~en t answers arc of all kinds of di fcerent categories, different kinds of interrogatives are to be of different categories as well. Taking the orthodox vieiv, on which there is a fixed category-to-type correspondence, this mcans that the following general principle undel-lies categorial theories: /lrp .x)~i/tol.til. c-ntegoql and thp S C I I Z N I / ~ ~1L y. p ~(~f'i~i~i.r.og~1tiz1e.s C~W ( I ~ I P ~ I I I /!)I ~ I II ~PL ~' ~ ' ~ ~ l c gunl/ oi:)~ type of' their. ~-hurr~l.ic~tstic I I ~ I ~ U ~ Snnsn7er.s. ~ZL. This gencral idea leaves rooin for many different implementations, but all theories have in common that intcrrogntivcs arc treated ils relational expressions, expressing 17-place relations, and that constituent answers serve to fill in the argument places. T h e other kind of approach, the propositional one, takes a different view on thc scmailtic contcnt of interrogatives. Answers to interrogatives, it is obscrved again, convey information, hence the)- are taken to express propositions. C:onsequently, the answerhood conditions of an interrogative are a detern~inationof which proposition(s) count(s) as answei-(s)to it. From this point ofvic\\7, the semantic contcnt oEall kinds of intcrrogativcs can and must be ailalyzed in a uniform way, viz. in tcrms of propositions.

Type-shifting Rules 425 In view of this, there is no reason not to consider interrogativcs of different kinds to form a homogelieous category. So, the gist of the propositional approach can be formulated in the following gencral principle: int~vryqnti~les ore of'n unijorm syntactic catego!)! llnd a un?/irrrnt,ypr, ~ h srrt~antic r i?ztcrpret'lntinngi71ing I ~ lP~ . n . ~ ~ ~ ~ ~conrli~ions. r h o o ( i Again, this idea can be worked out in a number of different Brays. In most cases, the meaning of an interrogative is taken to be a function .cvhicl-~determines for each possible world a (set of) proposition(s) which constitute(s) the true semantic answer(s) to that interrogative in that world. 'l'hc differences between thc various individual theories mainly reside in what truc scnlantic answers are taken to be. As we said above, the situation we are confi-onted with in developing a semantic theory for interrogatives resembles the situation concerning the semantic interpretation of noun phrases which Partee analyzes in Partee (1986). Tliere are two radically different approaches, each one based on an intuitively clear idea, and each one capable of explaining an interesting and important class of phenomena. Each approach makes predictions about the kind of semantic object that an interrogative represents, arid these predictions are incompatible, if, that is, one takes the orthodox view on the relationship between syntactic categories and semantic types. If one assumes that to each syntactic category there corresponds a unique semantic type, the two approaches are incon~patible in two ways: the propositional one postulates a uniform semantic type, whereas the categorial one assumes interrogatives to be of a large number of different types; and even taking only one kind of interrogative into consideration, the two will not meet, since on the categorial approach an interrogative expresses an 11-place relation, ~vhercas in the propositional approach it determines a (set of) proposition(s). 1-Iowever, if w-c take a closer look at the phenomena that each of these al>proaclies deals with successfully, it can be observed that these are largely complementary. Hence, there is good reason to suppose that the incompatibility between thc two is only an apparent one which originates from the assumption that there is such a thing as tlre semantic type of an interrogative, and that oncc this assumption is given up, thc two can fruitfullj~be combined. In effect, this is what we want to argue for. So, let us first turn to the alleged colnplementarity of the two approaches.

1.3 A puzzling situation In order to get a clearer picture of what exactly is going on, let us start by formulating two intuitively plausible recluireli~e~lts that a semantic analysis of interrogativcs slioulcl meet. (This is not to suggest that this is all there is to such an analysis, but it suffices for our present purposes.) T h e first requirement concerns the question-answer relation as a linguistic relation, i.e. as a relation between an intcrrogative and its characteristic linguistic answers. It is the demand that the semantic content of the interrogative, and the semantic content of the constituent that forms a linguistic answer, togcther determine the semantic content of that linguistic answer. T h e second, cclually plausible, requirement is that a semantics of intersogativcs should give a proper account of systematic semantic relationships that exist bctwccn interrogatives (and between interrogativcs and indicatives). Especially in the cnsc of interrogatives, where intuitions about the kind of semantic object that is thcir propcr

426 Jeroen Groenendijk and Martin Stokhof interpretation are slim, meaning relations are the prime data to bc accounted for. A central relationship between interrogatives is the one that holds if every complete and true answer to the first also gives a complete and true ansurer to the second. In effect, onc might dub this "entailment" between intcrrogatives. 'This relation holds, e.g., between "Who will go to the party? And what will they bring along?" and "Who mill go to the party?", and between the latter interrogative and "Will John go to the party?". It will need no argumentation that a categorial theory will be able to meet the first requirement, at least in principle, since it assigns to an inteuogativc a semantic tjrpe which, when it is combined with the type of its characteristic linguistic answcrs, "cancels out" to t . And it will also be clear that, again at least in principle, a propositional theory will be able to meet the second requirement, for it identifies the semantic content of an interrogative with its answerhood conditions, and stipulates a uniform semantic type, to which a generalized notion of entailment may be applied in a straightforward way. And it is exactly the kature of a categorial theory that enables it to meet the first requirement hat makes it doomed to fail on the second. For in a categorial approach a multiplicity of types of interrogatives is postulated chat matches the multiplicity of types of constituents that form thcir characteristic linguistic answers. And it is this multiplicity of types that prevents the application of any standard notion of entailment, since entailment is typically a relationship between expressions of one and the same type. We can illustrate the rather paradoxical situation we find ou~.selvesin as follows. Suppose there are two interrogatives that are equivalent under the notion of entailment indicated above, i.e. for which it holds that each complete and true answer to the first gives a complete and true answer to the second, and vice versa. And suppose further that there is a characteristic linguistic answer that as an answer to the first interrogative conveys different information, expresses another proposition, than it does ss an answcr to the second. If such a situation exists, it is clear that neither a propositional nor a categorial theory will be able to deal with it. For the first assumption implies that on the propositional theory the semantic content of the two interrogatives is the same. I-Ience, combining it with the semantic content of one and the same constituent cannot but give the same result in both cases. O n the other hand, a categorial theory might very well cope with the second assumption, but only in virtue of failing to deal 1vit11 the first. For accounting for the fact that the constituent answer expresses different propositions in each of thc two cases, requires giving the two interrogatives a different interprctation, thus failing to account for their assunled equivalence. Examples of such pairs of interrogatives are not only theoretically possible, they actually exist. A simple case, involving almost no assunlptions about the details of an actual propositional or categorial theory, is the following. Take the taro interrog-ativcs: "Who of John, Bill and Mary will go to the party?" and "LVlio of John, Bill and Mary will not go to the party?". These two are equivalent in the sense that they have the same answerhood conditions. Each proposition which complctcl!: settles the first question, also fully answers he second one, and vice versa. However, a constitucnt answer like "John and Bill." expresses a different proposition according as to which interrogative it is used to answer. In the first case it expresses that John and Bill are the ones that will attend the party, whereas in the second case it conveys the information that John and Bill are the ones that won't go to the party.

Type-shifting Rules 427 As we said, this situation is rather puzzling. We have formulated two reasonable requirements on semantic theories for intesrogatives, and we seem to have found out that a scmantic analysis that meets the onc cannot at the same time meet the other. So what arc wc to do? There are many ways in which one might react to this predicament. Before briefly discussing three of them, we want to point out the following. It should be borne in mind that we are not discussiilg actual theories here, but overall approaches. And we take it for granted that thc insights on which the two approachcs are founded are basically sound. In fact, the sounclness of the ideas underlying the two approaches is rcflected, we feel, in the plausibility of the two requiremcnts we have singled out and discussed. Of course, both kinds of theories are wrong in so far as they take their respective starting points to say ull there is to say about the nleaning of' interrogatives. That is exactly what the paradox shows. But, we thiilk that this should not lead one to reject the underlying ideas as basically correct insights about rlspccts of the meaning of interrogatives. Now, we can envisage (at least) three different reactions. T h e first one runs along thc following lines. It hooks on LO the failure of the propositional approach to meet the first requirement. Logical equivalence, so it goes, is simply not a sufficient condition for sameness of semantic content (sameness of nleaning). Rather, meaning is a more finegrained notion, and what the first requirement amounts to is that in the case of interrogatives it should be at least so finely structured that within the overall meaning of an interrogative, which in the propositional approach gives the answerhood conditions, we can distinguish as a distinct "part" the n-place relation that the categorial approach considers to be the semantic interpretation. So, instead of the usual iinstruct u r d notion of a function fkom worlds to (sets ot) propositions, onc should use structurcd meanings, interpreted derivation trees, or lvhat have you. We feel that the use of structured meanings that this reaction proposes to make, is improper, or, at least, is not in line with the usual motivation fbl- using structurcd meanings. In the analysis of propositional attitudes, somc have proposed the use of structured meanings, because they feel that in such contexts, which, on their view, are essentially tied up with mental representations, we nced not just the semantic content of an cxpression, but also its semantic structure, assuming that this structure and our mental representation bear enough resemblance to let the one go proxy for the other. However, such use of structured meanings differs essentially from the one proposed above. There, no use of the structure of the entire meaning is made as such, it is only used to get at a certain part of the meaning that helped to gcnerate it. Once you've got hold of the relevant part, the rest of the structure can be discarded. T o our minds, this goes against what our two requiremcnts actually state about the meaning of an interrogative. They arc both requirements on one and the same notion of meaning. For consider what will happen if we follow this strategy in the case at hand. According to the proposed strategy, wc nced the meaning of a predicate (to meet the first requirement), and we need the meaning of a sentential structure (to meet the second one). In both cases, the meanings we use, are "normal" unstructured meanings, i.e. intensions. It is only by means of a trick that the two are unified. T h e two separate, unstructured intensions arc rake11 together in one "structured meaning", but to our minds, this is just a cosmctic movc, for no structure of the meaning as such is used in any essential way (in fact, we just use a pair of intensions as the meaning).

428 Jeroen Groenendijk and Martin Stokhof So, we feel, there are theoretical reasons to be dissatisfied with this appcal to the notion of structured meaning for this particular problcm. On the practical side, it may bc remarked that it may lead to a thcory that, extensionally, so to speak, meets the two requirements. Howcver, structured meanings are no sure cure for any propositional theory. It depends on the way in which such a theory derives its function from worlds to (sets of) propositions whether, taken as structured objccts, they do contain thc required relations as retrievable parts. For example, quantificational propositional theories, such as Karttunen's and Bennett and Belnap's, may structure their meanings any way they like, the required relations just ain't in there. T h e second possible reaction we want to discuss, starts from the categorial point of view, i.e. it takes illterrogatives basically as expressing- n-placc relations. T h e diagnosis it gives for the failure of this approach to meet the second requirement, that of accounting for entailment between interrogatives in a general, non ad hoc way, is that it lacks a uniform type to associate with different kinds of interrogatives. Now, property theory is designed to provide such a uniform type, for it allows for thc possibility of analyzing expressions which are of different types in the ordinary vicw, as being of one and thc same type, vix. that of entities. This suggcsts that the two semantic objects we need in our semantic analysis of interrogatives can be gotten as special instances of the general relationship that exists between abstract ohjccts and the corresponding relational "entities". However, a uniform type is one thing that is needed in order to be able to satisfy the second requirement, but it is not sufficient. What is needed on top of it, is an cntailment structure on (the relevant part of) the domain of objects. And the main question is how to get the proper structure. One kind of structure we need to impose on the donlain of objects anyway, is the structure that is inherited from the original domains of the respective relational types of entities. For example, we can view propositions as objects, and these objects will bear structurally the same relations to one another as their propositional counterparts. And the same goes for one-placc properties, two-place relations, and so on. Idowever, it must be clear that this kind of structure of the respective parts of the domain of objects \\-ill be of no use at all for accounting for meaning rclations between interrogati~es.First of all, the structures in question remain restricted each to their own subdomain. If we identify these subdomains with sorts, m-e can exprcss this by saying that these relationships arc essentially "intra-sortal". But, and this is the important point, entailment relations between interrogatives are cross-categorial relationships, and licnce \vould have to be "crosssortal" relationships on the entity domain in this approach. And second, the intsasortal relationships we do get, are not the proper ones to account for cntailment betnrecn interrogatives of the samc kind. For example, sentcntial interrogatives are not related by entailment to each other (e.g., "whcther 4" and "\vlicther cf, and !I/'' do not entail one another), but the corresponding propositions (in the example, "that dl" and "that cf, and $"), and hence the corresponding pl-opositional objects, have a very rich entailment structure. It seems that the only nray to get the proper cross-sortal relationships on the one domain of objects, is tlisough an analysis (at some lcvel) of interrogatives as objects of a propositional type. Of course, this does not show that intcrrogatil-es can't be, or shouldn't be, analyzed as entity denoting expressions. On the contrary, it can be argued that in certain

Type-shifting Rules 429

constructions and relations in which they enter, it is profitablc to analpze thcni as denoting an object. But what it does show is that such an analysis will not solve our present problem. We still need the two kinds of semantic objects that thc categorial approach and the propositional approach postulate. Property theory will enable us to analyze both (also) as abstract objects, and this may be uscful, but it does not enable us to avoid postulating a propositional type of semantic object, besides a variety of relational types, as an interpretation of interrogatives. T h e third reaction is the one that wc think is most adequate. It anal>-zcsthe situation in terms of type sl-rifting.T h e paradox occurs, so it goes, because in both rcqi~irerncnts mention is made of "the meaning of", or "the semantic interpretation of" intcrrogatives. T h e propositional approach assigns a uniform type to all intcrrogatitcs, and, disregarding ambiguities, in that type each has a unique semantic interpretation. T h c categorial view postulates various semantic types, but each kind of interrogative occurs in one type only. And again, in that type it has a unique semantic interprctation. So, both approaches takc it for granted that each particular interrogative belongs to a unique type and, in that type, has a unique interpretation. If we want to stick to that, the paradox is unavoidable. Or, to put it differently, the paradox shows that this is something w e should not take for granted. What the paradox indicates is that interrogatives are among those natural language expressions which do not have a unique interpretation in a unique type. Rather, taking different perspectives, such expressions can be said to have different (but related) meanings, that arc of different types. So, the third strategy proposes to solvc the apparent paradox b~ introducing a relativization to a perspcctive, In this case, it claims that the t n o requircn~entsare cquallv reasonable, but are madc from different perspectives, taking different constructions as their starting point, and hence are requirements on different domains. Interrogatives have to be analyzed in (at least) two different domains, as expressions of (at. least) tn-o different types. On the one hand, they have a clearly relational meaning, as is most prominently sl~ownin the way in which the; interact with thcir characteristic linguistic answers. On the other hand, they also behavc as propositional objects, and it is as objects of the latter type that they enter into systematic relationships, such as entailment, to each other. (In section 2.3 we \%-illsee that interrogatives belong to other domains as well.) Within a certain conception of how to incorporate such flexibility into the gran1mar, about which we \+-illsay some more in section 3.3, this implies that thc onc major sq-ntactic category of interrogatives has to be associated with different semantic types. And each individual iilterrogative \\rill have to he given an interpretation in a suitable relational type, and also an interpretation in a i1nifol.m propositional type. An additional requirement is that these two interpretations be systen~aticallyrelated. Giving up the assuinption of a unique interpretation in a uiiiquc type ~ncansthat thc two intuitive rccluirements on the semantics of interrogatives have to be rephrased along the following lines. T h e first requirement now rcads that an interrogative has to be analyzed as being of (among others) such a type that its semantic content as itn expression of that type and the semantic content of the constituciit that forms it linguistic answer together determine the proposition cxprcsscd by that linguistic answer. And the second requirement will now state that interrogatives also have to bc analyzed as expressions of one uniform type in which a proper account of thcil-

430 Jeroen Groenendijk and Martin Stokhof -

sj-stenlatic semantic relationships, in particular of thcir entailment structure, can be given. And the concept of a flcxible granlmar adds to these the additional requirctnenr that these two should be systcmatical1~-related. In order to gct a clearcr view 011 what a flesiblc analysis of interrogatives amounts to, we will first concentrate on an area where the use type-shifting and flexibility is inore familiar, \-iz. coordination. We discuss various F~ctsand their conscq ucnces in section 2, and outlinc a flexible framework in sections 3.1 and 3.2. 111section 3.3, we will return to the possibility of implementing the third strategy to solve our puzzling situatioi~.

2 Coordination, Entailment and Types 2.1 Coordination 011e has to k with a lot of questions, and solnetin~csone cannot wait to havc them answered only one by one. In such situations, one map usc a conjunction (or sequcncc) of interrogatives. :In example of such a conjunction, and of thc way in which it can be answered is gii-ell in (I): (1) \Vhom does John love? And whom docs A4ary love? -John loves Suzy and Rill. And Mary loves Rill and Peter. In this exanlplc a simple conjuncti\-e sequence of two iiltcrrogati\:cs is given, which, as the answer that follows it shows, in filct poses two separate questions: the spcaker wants to know both whom John lo\:es, a i d whoin Mary loves. Another example of an interrogative that ii~volvesconjunction is (2):

Example (2) is ambiguous between what wrc call a r1jrec.l reading, on which it is equivalent with (3):

(3) W-ho is such that both John and M a p love h i n ~ / h e r ? and what we call its prrir-liii reading, on which it means the sanie as (1) above, i.e. on which it aslis for a specification of the individuals that John lo\~cs,and for a specificstion of thosc that arc loved by Mary. A similar ambiguity can be observed in interrogatives such as (4):

I

I 11 I

i

(4) \IZThomdoes every man love? This example, too, has a direct reading and a pair-list reading, as the fi~llowing paraphrases, and the corresponding ansm-crs, illustrate:

(4)

(a) N7ho is such that ever!. man loves hirn/her? - Peter and Rilary .

;

1

Type-shifting Rules 431 (4) (b) \Whom docs Peter love? And whom does Bill love? And . . . - Peter loves Mary. And Bill loves Suzy and Fred. ,4nd . . . ,4n interesting point to note is that on its pair-list reading, as paraphrased in (4) (a), (4) behaves like (5). T h e latter is a two-constituent interrogati\;e, i.e. an interrogative containing two wh-phrases. i2lthougli (4) on thc relevant reading contains only one \vh-term, it is answered in the same way as (5):

( 5 ) Whom does which man love? (5) asks for is a specification of a list of pairs of individuals .v and , ) I , \vliere .I, is a man and .y an individual such that s loves ,)I. T h e same holds fbr (1)on its reilding (I)), which is whj- it is called what it is callcd. _4n example of a disjunction of interrogatives is given in (6):

(6) Whom does John love? Or, whom does Mary love? - John loves Suzy and Hill. -- Marj- lakes Bill and Peter. John loves Suzy and Bill, and Mary loves Bill and Peter. -

Disjunctions of interrogatives, like their conjuncti\-e counterparts, formulate two separate questions, hut, unlike conjunctions, they posc only one: they Ica\.e the hearer a choicc ilS to which one of the formulated questiotis she wants to answer. As thc answers in (6) show, a disjunction of interrogai-ives ]nay be ans\vercd b!. ans~vcring either disjunct or both. 1)isjunctive i n t e r r o p t i ~ e snccd ilot consist of t ~ v oseparate intel.rogati\.es, as (7) shows: (7)

Whom does John or Mary love?

1,ike its conjunctive counterpart ( 2 ) , (7) is ambiguous between a direct reading and what we call a r.lloi~-' reading. On the latter (7) is equivalent to (6), on the former it call be paraphrased ils (7) (a): (7) (a)

Who is such that John or A'rary (or both) loves him/hcr? Suzy, Bill and Peter. -

As m-e saw ahovc, pair-list readings are not restricted to interrogatives I!-ith overt conjunctions. In the same way choice readings can occur without ovcrt disjunctions, as a simple example like (ti) shows:

(8) What did two of John's friends givc him for C:hristmas? 'I'his interrogative is ambiguous. 11 has a direct reading, on which it ilsks for a specification of the presents that t ~ v oof his fiicnds gave him. Ancl it has a choicc reading, on which it invites the adclrcssec to choose an)- two friends of John's and

432 Jeroen Groenendijk and Martin Stokhof specify for each one of them wlzat he/shc gave him for Christmas. Obviously, it is a matter of the iilternal semantic structure of a term phrase whether it will givc rise to a 7 pair-list or a choice reading or not.- Again, it should be noted that choice rcadings of iilterrogatives are like two-constituent interrogatives, as is cvident from the w-ay in which they are answered. Like ordinary interrogatives, coordinated ones can be embedded under cxtensional and intensional verbs, such as know and wonder respectively. Also, thc ambiguity between a direct reading and a pair-list reading, and between a direct reading and a choice reading is preserved ill such contexts. As fbr thc distinction bctncen extensional ancl intensional embedding verbs, it should be noticed that there is a difference when disjunction is involved, as (9) and (10) show: (9) Peter knows whom John loves or whom h,iarj- loves (10) Peter wonders whom John loves or whom h'larj- loves. Sentence (10) is ambiguous, allowing for the disjunction in the complement to have either wide or narrow scope with respect to wonder. T h e wide scope reading occurs when the speaker knows that Pctcr wants to know- the answer to one of the two questions, but she herself docs not know which onc this is. On the narrow scopc rcading (10) expresses that Peter will be satisfied when he gets an answer to eitllcr onc of the questions involved, no mattes which one. A last observation that should be made here, is that coordination of interrogatives goes across kinds. It is not restricted to expressions of tbc same kind, i.c. to scntentirzl interrogatives, single constitucnt interrogatives and multiple constituent interrogativcs, but combines them freely, as the follow-ing examples show:

(1 1) m7ho \Lent to pick up John? And are the!- back alreacll*? (13) Peter knon-s who went to pick up John and \vhether they are back already ( 1 3) \Fihich woman does which Inan admire most? O r do they all detest each other? 'This fact, too, can be used to argue for uniformity in assigning types to thcse different kinds of interrogatives. So much for coordination, let us now tusn to the second part of our empirical domain, that of entailment.

2.2 Entailment Let us first of all recall a fl:r~miliar fact concerning eiltailrnent relations betwcen coordinated indicatives and thcir coordinates: a conjunction entails its conjuncts, a disjunction is entailed by its disjuncts, and a conjunction entails the corresponding disjunction. Analogous Facts hold for coordiilated structures in general, and properly generalized notions of coordination and entailment should account l'or them. Considering interrogati~es,we can observe that someone who asks ( 1 1 ) also asks (14), and that someone who answers ( 1 5 ) also answers (10): (14) Who went to pick up John?

Type-shifting Rules 433 (IS) IVhcre is your fiather? (16) Where is your fiather? O r your mother? c a notion of entailment between interrogatives which might be In section 1.3 ~ : used described informally as follows:

.An interrogative A entails an interrogative B iff whenever a proposition gives a complete and true answcr to A, it givcs such an answer to B. It is easy to check that this clescription conforms with the observations just made, and that it likewise predicts that (17) entails (16): (17) Where is your father? And your mother? These examp1es of entailments between interrogatives depend on their coordination structure. There are also other types of entailn~cntsto be observed. T,ct us give two more examples. T h e single constituent interrogative (18) entails thc sentcntial interrogative (19): (18) Which men does Mary love? (19) Docs h'larp love John? Getting a complete answer to (18) implies getting a complete answer to (19). Notice that in this case cntailnient is a relation between different kinds of interrogatives, a oneconstituent interrogative and a sentential interrogative. Another example is providcd by (18), (20) and (21). A complete answer to both (20) and (21) givcs a complete answer to (18) as well:

(20) Whom docs Mary love? (21) Whoare themcn? Notice that (20) oil its own does not entail (18), for knowing the ansnrcr to (20) is knowing which individuals (within the relcvai~tdomain of discourse) Mary lovcs, and this entails knowing which inen hh4ary loves only in conjunction with knowledge of which individuaIs are men. In line with recent work, we assume that coordination and entailment are ger~cl.irl syntactic and semantic processes. Elements of all major categories can be coordinated, and a number of people have proposed general definitions to account for this." Entailment, too, is a relation that holds between cIements within any major category: indicative sentcnces, of course, interrogatives, as we have seenabove, hut also termphrases (every i n a n cntails John), verbphrases (to walk cntails t o move), nouns (woman n and so on. In all cases it is the same relation that is at stdie, viz. cntails h u l ~ ~ abeing), that of the denotation of one element being included in all models in that of the other. T o put it tlifferently, employing a semantic n~eta-languagebased on set theory brings along a definition of entailment for all categories: incl~~sion of denotation in all models.

434 Jeroen Groenendijk and Martin Stokhof T h e following definitions of generalized conjunction and disjunction are based on the work referred to above. First, the notion of a "conjoinablc type" is dcfincd:

C q the set of conjoinable types, is the smallest set s ~ ~ that: ch (a) t E C ' T ; (b) if b E C T , then ( a , h ) E CT. Then generalized conjunction is defined as follows:

n Y = X A Y, for ,Y, Yof type t n 1-= i.r [lY(s)n Y(.r)], for any other conjoinable type. T h e definition of disjunction, U, is analogous. Entailment, C,can be dcfincd gcncrally as follows:

-

-X 2 Y = X Y, for X, Y of type t X C_ Y = b'.~[X(x)C_ Y(.v)j, for any other conjoinable type. It should be noted that cinploying such general notions of coordination and cnta]'1ment means that one is kept to assign seinantic interpretations to cxprcssions in such i1 way that the entailment relations that can he obscrvcd arc accounted for by these indcpcndently defined and m o t i ~ i ~ t enotions. d Exceptions to this should be well-argued tbrT4 It should be stressed that this is a methodological requirement. Of course, a tlleory that uses different and unrelated notions of entailment 01. coordination for diff'erent domains, may very well be empirically adequate, in the sense thitt it makes the right predictions. T h c point we want to make, is that a theorj t h ~ makes t the same predictions but does so on the basis of gcncralizcd and uniform notions, is to be prefcmcd on inctl~odologicalgrounds. It provides a simpler account of the relevant facts, and, hence, has greater explanator, force. In the nest section, we ivill shou how this requirement can be used to evaluate theories that PI-oposc ;I certain type of semantic object ;IS the interpretation of interrogati~es.

2.3 Types for interrogatives In this section we will investigate which types are to be assigned to interrogatives. In a flexible framework, there need not be a rrnique propcr semantic t!pe for all expressions of a certain category. Interrog;~tivesare no esccption to this rulc. I-Io\vevcr, for cvery ~ * u i ~ s t ~ u l . t in i n nu-hich interrogatives occur, there is, as we shall scc, a k q ! typr: tlzc type in which tllc intuitive entailments bet\veen interrogatives in that construction ilre accounted for by the general definition of entailment that our framework provides.' Also, we will arguc in this section that employing general notions of coorclination and entailment ivill enable us to ej-aluate various proposals within the t u o main approaches to tke senlantics of intelarogntives which were discussed in section 1. As we saw above, the main characteristic of the categorial approach can be sun~mcd LIP:IS follo\vs:('

Type-shifting Rules 435 'The syntactic category and the semantic type of an interrogative arc uniquely determined by the catcgory and type of its characteristic linguistic answers. T h c idea is that the type of an interrogative and the tj-pe of its characteristic linguistic answers should cancel out, b>-functional application, to that of sentences, i.e. to type /. Let us illustrate this with a few examples. First a single constituent interrogative: (22)

Whom does John love? Mitry,

-

Applying the criterion just mentioned, it follows that the (simplest possible) type of a single constituent interrogative is that of a property of individuals (a one-place relation). Next, consider a multiple constituent interrogative: (23)

Which man does which woman love? Mary, Bill; and Suzy, Peter.

-

Here the resulting type is that of a two-place relation between individuals. The last example is that of a sentential interrogative: (24)

Docs John love Mary? Yes.

-

If u-eapply the criterion in this casc, the outcome is not unique, but the simplest solution is to give sentential intcrrogatives type t , and hence consider "Yes." and "No." as expressions of type ( t , t ) , which is one of the solutions 11-e find in tho literature. Considering I to be he lypc of zero-place relations, we can vie\%- sentential interrogatives as zero constituent intcrrogati~.es.Generalizing from these examples, we conclude that in thc categorial approach, n-constituent interrogatives are interpreted as 11-place relations. Although this approach has attractive features, for one thing, it leads to a simple and intuitive analysis of the interpretation of characteristic linguistic answers, it also has its shortcomings. These concern coordination and entailment, ils ~ v cshall see. First of all, the approach ils such does not account for coordination and entailment across dififcrent kinds of interrogatives and it is hard to see hen- it could, without giving up its fundamental char;icteristics. For entailment and coordination require a uniform type, \vhiuh the categorial approach simply does not provide. 12 forecj r w - , e [-enit' n-eii~nit ou1;selv-esto interrog:itir-csof the same kind, in [vhichcase the general definitions arc in principle applicable, we find that the n-1.ong predictions are made. E.g. it is predicted that (25) and (26) are equivalent, which is not the casc: (25) (26)

Who walks? And who tallcs? Who walks and talks?

T h c conjunction of intcrrogatives (2.5) asks to specify both the individuals that walk and the indi~;idualsthat talk, whereas (26) asks to specify the individuals that both w:llk and talk (so, (25) entails (26), but no1 the other way around).

436 Jeroen Groenendijk and Martin Stokhof A second example. Analyzing one-constitucnt interrogatives as properties, predicts that (27) elltails (28), which again is not the case: (27) Who walks? (28) Who moves? If one is told which individuals walk, onc is not therebj told which arc all the individuals that move. A straightforward conclusion that can be drawn, is that if one wants to cmploy general definitions of coordination and entailment, tllcil, first of all, onc has to analyze, at some level, all interrogatives as being of one and the same type, and, sccondlj-, within this type one has to associate them with the right kind of objecte7 -4s we saw above, theories in the second main approach, the propositional onc, do assign one single type to all interrogatives. We characterized the main idca of this approach as follows: T h e meaning of an interrogative is given bj- its answerhood conditions. Within intensional semantic theories answers arc of a propositional naturc, hence intersogatives arc of a "propositional" typc. Hcre, several choices arc still opcn. The best-known analysis, that of ~ a r t t u n c n , 'nlakcs them expressions of tj~pc{(s, I } , I } . I.e., on this analysis an interrogative denotes a set of propositions. Karttuncn interprets this set as consisting of those propositions which J o i i ~ t ! ) i constitute the true and complete answer. T w o things should be noted. First of all, harttunen's theory is, what Relnnp calls, a "uiliqile answer theory", i.e. a thcory that assumes that each interrogative has il uiliquc true and complete answer. Why this is i+elevanlwill become clear shortl!,. Second, siilce Karttunen's theory employs a uniform (conjoinable) type, it makcs predictions about coordination and entailment generally, also aesoss different kinds of interrogatives. 1,ct us consider some of these predictions. T h e schema of generalized conjunction tells us that the conjunction of two interrogatives is interpreted as tlle intersection of the sets of propositions denoted by each of thc conjuncts. Gi\-en the interpretation of these sets of propositions on Karttunen's theorj-, the result is that a conjunction of inten-ogatives (almost) never has an answer. T h e follovl-ing exalnplc ill~lstratesthis:

(29) Does John walk? And docs Mary walk? Suppose it happens to bc the case that John walks and that _Marydoesn't. 'Then the first conjunct dcnotes the set consisting of the proposition that John wallis, and the second denotcs the set consisting of the proposition that hlary doesn't walk. 'I'hc intcrsection of these two sets is empty, which means that (29) cannot be answered. A similar result holds for interrogatives on pair-list readings. Disjunction corresponds to taking the union of sets of propositions. Again, the prediction that the Karttunen analysis nukes is not in accordance with the facts. Consider the disjunction of interrogatives (30):

I

Type-shifting Rules 437 (30) Does John walk? Or does Mary walh? Taking the union of the set denoted by each of the disjuncts results in thc set of jxopositions which jointly constitute the complete and true answer to the conjunction (29), rather than to the disjunction (30). For entailment, too, the rcsults which we get when we combine the general schema with Karttunen's interpretation of interrogatives, are not correct. A simple example is the entailment relation between (31) and (32):

(31) Who walks? (32)

Does John walk?

In the intuitive sense, (31) entails (32). But the set of propositions that is the denotation of (31) in Karttunen's thcory is not generally a subset of the set denoted by (32). Hencc, the theory fails to account for this entailment. Providing a semantic account of intersogati\-es which dcals with coordination and entailment adequately, then, is not just a matter of kinding a uniform and proper type, but also of associating each interrogative with the right object of that typc. One might think that Karttunen found the right type, but hit the wrong objects within that tyljc. However, as our discussion of a second proposal intends to show, therc are reasons to doubt whether this is indeed the case. Bcnnctt and Belnap have developed at1 analysis of the semnntics of intelsrogatives that is explicitly set up to deal with those constructions of interrogati\~eson which they allow for more than onc complete and true answer, such as disjunctions and ehoiccrcadings."~hev assign the same semantic type to interrog~tivesas Karttunen does, i.c. thcy, too, take intcssogatives to denote sets of propositions, but they interpret thesc denotations in a different way. In their analysis, each of the propositions in the set denoted by an interrogative on its o~v-nconstitutes a cornpletc and true answer. For "ordinary" intcrrogatives, i.e. for thosc which have a unicluc answ~er,this means that they denote a unit set. Here we h a w an analysis which differs froill Karttunen's, not in the type that it assigns to interrogatives, but in the objects of that type that intcrrogatives arc taken to denote. And we might ask whether this change overcomes the difticultics wc noted earlicr. As is to be expected, the Bcnnett and Belnap approach does well with rcspoct to those interrogatives for which it was designed, viz. interrogatives which have more than onc unique answer. Sticking to our general definitions, disjunction still comes down to taking the union of the denotation of the disjuncts. Ho\{ever, givcn the kind of set of propositio~~s that an interrogative denotes on their thcory, thc result is corrcct. Consider the disjunction (30) again. Each of the disjuncts now denotes a unit set, and taking the union thereof results in a set with two elements, each of' which is a proposition which is a complete and true answer to the disjunction. It is also clear that on the 13cnnett ancl Bclnap analysis a disjunctiotl is entailed by eilcll of its disjuncts. On this score, Bcni~ettand Belllap do better than Kasttunen. But this does not mean that now we have the right objects of thc right type, at l a s t not in all cases, as the fi~llowingconsiderations show. Take the conjunction (29). Here ivc still have the sanw

438 Jeroen Groenendijk and Martin Stokhof kind of problems as ivc met in Karttunen's theory. Given the general definition of conjunction, the denotation of a conjunction is the intersection of thc (unit) sets of propositions denoted by the conjuncts, and this still results in the empty set (at least in most cases). Also, u7edo not get the dcsirecl entailment betwcen a conjunction and its conjuncts. So, we must col~cludethat the Bennett and Eelnap approach is not satisfactory cithcr . Let us take stock: we have seen that atomic interrogatives, i.c. 11011-coordinatecl interrogatives which are not embedded and are not given a pair-list or a choice reading, conjunctions of intcrrogat-ives and disjunctions of interrogatives b e l ~ i l ~dit'fercntl?; e with respect to types and entailment. An atomic interrogative has il unique true and complete answcr (in each possible kvorld). This means that the simplest denotational type for atomic interrogatives is tl-pe (s, r ) (giving it a sense of typc (s, (s, I ) ) ) . -4s for conjunctions, if we disrcgard their relations with disjunctions, they could be analyzed at the same level. Since a conjunction, too, has a unique true and complete answcr: the conjunction of the propositions that answer the t.onjuncts, also answers their conjunction. For disjunctions, however, things are different. They do not havc a unique complete and true answcr, hence they simply cannot be of type (s, I ) . If' we look at entailment relations between disjunctions on the one hand and conjunctions and atomic interrogatives on the other, we see that in order to account for them we need a rrnifirnl type for all, since generalized entailn~entrccluircs a uniform type for all elcillcnts in\;olvcd. T h e need for such a uniform type is underscored bj- the observation that in ordcr to construct disjunctions in accordance with thc general procedure, atomic interrogatives should (also) hc of the same type as the disjunctions which ilre constructed from them. Such considerations, by the ivav, constitute a gcncral argument against the type that Kartruncn, and Bennett and Helnay emploj-. For, although the objects of type ((s, I ) , t } that the latter associate with interrogatives give a propcr interpretation for disjunction, it simply cannot be the uniform type which is required, as the exanlples discussed II above have shoivn. 50 here we do have a case against the typc as such. T h e question that now arises, is what this unifbrm type is, and wl~ctherit is ! sufficient to account for all entailments. T h e situation wc find ourselves in with reg~rd to intcrrogati\-es, resembles that of term phrases in some important respects. Thc loit-est type for a proper name is type r. 1,ooking at disjunctions of proper names in ' isolation, we find that we can analyze them as being of tj-pe (17, t ) . For conjunctions this I will not do. There we need a more complex tj~pe,viz. the Familiar ((e, I ) , I ) (disregarding intensionality). Once we take entailmcnts into account, wc see that the lattcr is the uniform type u-c need, hence that all proper names should 11:lvc type ( ( c . I), I ) at a certain level of analysis. Traditionally, this is achieved I>!- "generalizing to the worst case" and treating all proper names in all contexts as expressions of that type. \h7ithina flexible approach, however, we takc ((e, t ) , I ) as one of' the derived types that propcr names can have, a type that thcy must have e.g. when occurring in a coordinate structure. I . With respect to interro~ativeswe can follow the same lead. T h e ke! tqpe of atomic interrogatives, i.e. the type in which thc entailnlellts among them can be accounted for, ' is type (s, I ) . Looking at disjunction in isolation suggests ((s, t ) ,/) as the proper typc (cf. Bennett and Belnap), but taking a broader view we see that tlie level at which

i

I

Type-shifting Rules 439 coordination and entailinent can be accounted for is that of type (((s,l ) , r , ), r). And within a flexible frame of mind, thc relation between thc basic type (s, r ) and thc latter is a fiin~iliarone: we get from the onc to the other by the type-shifting rule of "lifting", the same procedure we use in analysing term phrases. T h e flexible approach is not rnotivatecl by reasons of elegance and simplicity alone. As is argued c.g. in Partee and liooth (1983), the strategy of generalizing to the worst case is not only unnecessarily complicated in many cases, sometimes it is also empirica 1 1 ~inadequate. T h e "wide scope or-cases" they ctiscuss, show that there is no rr priori worst casc to generalize to. A similar argumentatio~ican be distilled from the scmantics of sentences containing an intensional vcrb with a disjunction of interrogatives as its complement (see (10) in section 2.1. above. We return to this examplc later on). But the semantics of' intcrrogativcs provides yet anothcr argument for the necessity of flexibility. T o 1x2 able to account for entailment rclations between atomic intcn-ogatives, such as hold e.g. between (31) and (32), we need to analyze thcm in the licy r!*pe (s, t ) . If w-e lift thein to type ( ( ( 3 , I ) , t, ), t ) , we losc entailment rclations that liolcl at thc basic level (s, t). Hut in orcler to be able to account for entailment relations betwcen coordinated interrogatives, or between such interrogatives and atomic ones, we do need the liftecl level to get the right results. So, w-e cannot assign all intcrrogativcs a uniform type in all cases. What the proper type is, in terms of the predicted entailment relations, depends on the context (e.g. on the construction in which an expression occurs)."' Summing up, \-lie have found that there is no uniform key type for all intcrrogativcs. Rather, there is a key type for each of the various constructions and rclations that involve interrogatives. But these types do not constitutc a heterogeneous set, thcy arc related to each other in a systematic fashion. It is our purpose in the next section to Y' sketch a theory in which this is accounted for.

3 A Flexible Approach

3.1 Questions as partitions Lct us now sketch the outlines of a theory that satisfies the three scquirements which we fbrmulated at the end of the section 1, and which accounts for the \~ai.iousobservations niade in section 2. We start by giving the general idea on which the theory is based. T h e theorv stays within the possible worlds fran~ework.Following Stalnakcr, who formulated this vie\\. o n possible worlds in various places," r e view the set of possible worlds that is given m-ith the model as thc set of all possible alternatives, as thc set of all situations which, in that model, are distinguished from one another. In this vicw, sincerely uttering a proposition, or accepting it as true, is rest]-icting oneself to a subset of some initial set of alternatives. In the same vein, a question can be viewed, not as a restriction on the set of alternativcs, but as a division of it, as a grouping togctl~erof alternatives from a ccrtzin perspective. Each question has a particular subject matter, and it n~akcsa division of the set of alternatives by grouping together those which do not distinguish thcn~selvee with respect to this subject matter. Each such group is a set of altcsnatives, i.c. it is a

440 Jeroen Groenendijk and Martin Stokhof ynrposition. In each of the worlds tt-ithin such a proposition, the answer to the question is the same. Hence, the proposition they make up togcthcr can bc vie~vcdns a possiblc answer to a qucstion. J,ct us give some examples. (:onsides the simple sentential interrogative "Is Amstcrdam the capital of the Netherlands?". T h e question expressed by this interrogative divides a given set of alternatives (which need not be the entire sot of all possiblc worlds) into two, depending on the truth value of its subject matter in those alternatives. T h e one group of alternativcs consists of those ulorlds in which it is true tllat Amsterdam is the capital of the Netherlands, thc other of those in which this is false. Hence, the first group forms thc proposition that Amsterdam is the capital of the Nethcrlands, and the second the proposition that it is not. If the inten-ogatit-e in question has any presuppositions - say regarding the existence of Anlsterdam and the Netherlands, and the existence and uniqueness of capitals the set of altel-natives that the question makes a division on, is restricted to those worlds in which these presuppositions are true. As a second example, take the interrogative "Which city is the capital of the Netherlands?". This question, too, makes a division of thc rele\.ant set of alternatives. In this case the division need not be in two, it can have n~embel-s,as nlany ils there are cities that could be thc capital of the Netherlands. Arain, the alternativcs within such a group are indistinguishable as Llr as the subject matter of the question, i.e. thc extension of the propcrty of being the city that is the capital of the Netherlands, is concerncd. Together, they form a proposition that asserts of a certain city that it is the capital of thc Netherlands, i.e. they specify a possible extension of the propcrty in question. And each such lproposition is a completc answer to the question. From these two examples, the follou-ing picture emergcs. Each interrogative in natural language expl-csses a question the subjcct matter of ivhich is the extension of an 11-place relation (sentential interrogatives being the limit case where n = 0). Each such question is a partition of' the set of alternatives, i.e. divides this sct up into a certain numl~erof nlutually exclusive propositions. 'I'his general characterization of the notion of a question, of the mcaning of an interrogative, is made from the propositional perspective, i.e. from the point of view of ansm~e~~l~ood conditions. In fact, the description of the meaning- of an inlcrrogative that we just gave, is nothing but a statement of its answerhood conditions, i.e. il statement of the conditions under which a proposition gives a complete answer to it. Hut noticc that in our gcncral characterization of these anstverhood conditions the s t ~ b j c cmattcr ~ of a qucstion pla?;s an essential role. This subject matter is, generally speaking, thc cxtension of some n-place relation, and this brings in the second pcrspcctive on the semantics of interrogatives, that of the catcgorial approach. It is also possible to describe the nleaning of an interrogative in terms of the relation that is its subject matter. And in fact, as we saw above, this is u~hatwe need to d o in order. to be able to account for tllc relationship between interrogatives and their charactcristic linguistic answers. Of course, the two perspectives are systematically related: each possible denotation that IVC can distinguish tiom thc categorial point of view corresponds to a unique proposition that we distinguish ti-om the propositional point of view. We get the latter by collecting those alternativcs where the former is thc same. In this sense, \ire can say that a theory which gives intesrogatives interpretations -

Type-shifting Rules 441 both of a rclational and of il propositional type, but which lidis thcsc two in the way just dcscribcd, still gives them a unified meaning. Let us nou- turn to the fi~rmaldetails of a theory which is based on this idea. U7ehave concluded above that the key type for atomic interrogatives is tj-pe (s, t ) , But tixing a type is not enough, we must also say which objects of this type interrogatives dcnotc. ,\gain, observations concerning entailment relations will give us a clue. Under the ass~~mption that we talk about a fixed domain of individuals and that proper names are rigid designators, it holds that for every name A, (33) entails (34): (33) Who ~valks? (34) Does _d walk? Given our characteriza~iollof eiltailment between interrogativcs (scc scution 2 above), this means that ever$ proposition that gives a complcte and true answer to (33), also givcs a completc and tsue answer to (34), Given that atomic interrogatives such as (33) and (34) arc of type (s, I ) , we should take them to denote the proposi~ionthat is the con~pleteand true answer, which means that an atomic interrogalive -1 entails an atomic interrogative B iff in every situation he proposition denoted b? .-I enr-ails the proposition denoted by B. For that is in conlplete accord;.ulce wit11 the general definition of entailment. Since (33) entails (34) for cvery name A, this implies that thc proposition denoted by (3.3) givcs a complcte specification of' the extension of the walking-property. Hence, a single constituent interrogative will denote in each u-orlcl the proposition that gives a complete specificat-ion of tlie extension of n property in that ivorld. This generalizes to n-consti~uenrinterrogatives. For example, thc tvrro-constituent interrogative (35) entails for every two names A and B the interrogative (36):

(35) Who loves whom? (36) Does love B? T h e two-constituent interrogative (36) asks fbr, i.e. denotes, a complete specification of the extension of the relation of loving. In general, a complete answer to an n-constituent interrogative givcs 3 complcte specification of a possible extension of ;111 11-place relation, and thc propositions tllat cxpress these specifications are its possiblc complete and true answers. This tells us which object of type (s, t ) , i.e. m-I-hichproposition, an atomic interrogative denotes. At the same time, it also determines what constitutes the sense of such an interrogative: it is a function from possible \vorlds to such propositions. We conclude that: every interrogative is based on some underlying PI-placc ~.clation (where wc take scntenucs, which undcrlic seiltcntial interrogatives, to he zero-place relations). Every such relation has a set of possible extensions. T o each possiblc extension corresponds a possiblc answer, the proposition which specifies this cxlension. Such a proposition is the denotation of the interrogative in the ~ o r l din which the underlying relation has that extension. And the sense of an interrogative is il fi~nction from possible urorlds to possiblc answers. T h e latter object we call a y ~ t e s ~ i o Sclicmatn. ically, wc cnd up with the following analysis of atomic interrogativcs:

442 Jeroen Groenendijk and Martin Stokhof rl-p Ilici~r d i 17on

yuc.s/ion yow(D1') q,. : bV 4 {0, l}I' where q , - ( 0 7 ) = that p s.t h . p ( ~ ~H ' ) r(w) = I'

: Id'

4

1r(m').

This means that cluestions can be viewed as relations between worlcls of a special kind. '['hey arc cquivalcnce relations bctwcen the clcments of kt', i.c, they constitute partitions of W: T h e blocks in these partitions, sets of possible worlds, arc the propositions that are the possible answers to the questions. In what follo\\rs we will make use of this, and sonletimes represent the meaning of an interrogative, i.e. the question it expresses, as a partition of kI/. Lie will use the language of two-sorted type theory, in which quantification and abstraction over worlds is possible, as our rcprcscntation language. Let us then q ~ ~ i c h review ly horn- sentential interrogatives and constituent interrog~tives are interpreted according to this schema. First, consider the sentential interrogative (37):

(37) Does John walk? T h e underlying zero-place relation (formula) is: (38)

walk

(IV) ( j ) .

Here, n) is a variable of type s, I-anging over possible worlds. Obviously, (37) has two complete answers. In a world in which John walks, this is the proposition that he docs, and in a world in which he doesn't, it is the proposition that hc docs not. 1.e. (37) asks to identify thc actual world as belonging to one of tnfo disjunct sets: those in which John walks, and those in which he doesn't. This means that (37) partitions the set of worlds in two:

that John docsn't lvulk

T h e two blocks of this partition are the two propositions which constiti~tethc two possible complete and true answers to (37). 'I'he meaning of (37) can now be represented as follows:

As a second example, consider thc one-constituent interrogativc (40):

(40) IYho walks? In principle, this interrogative has as many ansllrers as there arc subscts of the domaill that it ranges over. Or, to givc a different but equivalent formulation, each proposition

Type-shifting Rules 443 that specifics a possiblo extension of the one-place relation of walking is a possible complete and t-rue answer- to (40). I.e., (40) induces the following partitiol~of :'$I

t no one walks

a is thc one that walks

h is the one that walks

N

and h is the ones that walk

everyone walks

W The meaning of (40) can thus be represented as follows:

,4 representation of the meaning of the two-constituent interrogative (42) is (43): (42) which man does n-hich uvman lovc? A n~an(m)(y)A lovc(w)(x,.li)] = (43) Lr~Ru7'[;lwi~y[woman(u?>(.v) i,rlt)l[won~an(n~')(x) A m a n ( ~ d ) ( . ~A/ )lo~e(n?')(,z.,.)!)]]. Generallj-, any n-place relational expression x can be tul-ned into a question that is the interpretation of the corresponding atomic: n-constituent interrogative, by means of'the f'ollow~ingschema:

This gives a satisfactory treatment of atomic interrogatives, but, as we havc scen above, we also need to raise thc type of atomic interrogatii-es (s, t ) , in order to bc able to deal with coordinated intcrrogatives and pair-list and choice readings.

3.2 Types for coordination and embedding As we saw abok~e,for coordinated interrogatives we need the type that is the lifted version of the type of atomic ones. 1.e. wc follou- a familiar procedure: Gced with incorrect rcsults when we apply generalized coordination to expressions of seine t!l>c (1, we go over to the lifted level, i.c. to type ((a, t ) ,t ) . The general type-shifting rule of

444 Jeroen Groenendijk and Martin Stokhof lifting gives us for every expression a of the "basic" type il a corresponding one which gives the nleaning of a as an expression of the lifted type ((a, I ) , 1 ) :

This is familiar from the analysis of NP's. Let us consider application of this soheina to a simple exanlple of coordination of two one-constitucnt intcrrogativcs:

(46) Who cvalks? And, who talks? At its basic levcl each conjunct of (46) is represented as an expression of t j pe (s, t ) . The first interrogative for exainplc is represented as:

Applying the lifting procedure of (45) we get:

If we apply the same procedure to the second conjunct, and then use the gencralized detinition of conjunction, we get (49) as the representation of the conjunction of interrogatives (46):

T h e conjunction of the two interrogatives is thus taken to denote a set of sets of' propositions, viz, thosc which contain the answer to the first interroptivc and the answer to the second one. Obviouslj~,m7eobtain as a result that, given thc gc~~eralizcd detinition of entailment, a conjunction of interrogatives entails each of its conjuncts, for every set of propositioi~sthat contains a complete and true answer to both conjuncts, contains a complete and true answer to each conjunct. Next, consider disjunction. Again, ive first lift the disjuncts, a r ~ dthcn apply gcneralized disjunction. (50) is thcn represented as (51): (50) Who N-allts?Or, who talks? = L.r[walh(m')(s)l]) V ( 5 1) I q i S ,),, ,;[Q(lmf[lr[a-alk(~.)(.r.)] Q()Ll~~'[2,v[talk(~~~)(*r)J = /2a[talk(m')(.v)]]).l. ,4pplying gencralized entailment, Fve see that a disjunction of interrogatives is entailed by each of its disjuncts, and, moreover, that a conjunction entails thc corresponding disjunction. Again, bearing the intuitive content of entailment bct~jlceninterrogativcs in mind, these results are what we want. As a matter of fact, it can be noticed that generalized conjunction and disjunction is defined at type (s, t ) (interrogative denotations) and (s, (s, 1 ) ) (interrogative meanings) as well. A little reflection shows that conjunction could be treated at this level, but

Type-shifting Rules 445 disjunction can't. 'The reason for this is simple. As wc saw above, atomic intcrroga~ives induce partitions of IY. Pointwise intersection of two partitions (which is what conjunction would amount to) results in a partition again. That is, we get an object, not only of the right type, but also of the right sub-type, i.e. one which inherits thc defining properties. However, taking the pointwise union of two partitions (which is what generalized disjunction does) in general does izot result in a pastition again. What we get is of the right type, but not of the right sub-typc. So, as a additional requirement on dealing with coordination in general, we can state that coordination should be performed at the lowest type that can be reached from the key type, procidttt.rl' thnt it uespel.ls (i.r. sriq~sroithttz) the rrln:at~rruhllomnin.~thew. Let us now turn our attention to embedded interrogatives. Given the tjpc (s, I ) of atomic interrogatives, the lowest possible type for interrog-ative-embedding vcl-bs such as know is ((s, t), (e, t ) ) . Taking these verbs to denote basically relations between individuals and propositions has some agreeable consequences. First of all, given he kind of object we assign to interrogatives as thcis meaning (and some f~miliar,though not always uncontroversial, assumptions about the semantics oE epistemic verbs) we get an account of the validity of such scheinas as (52) and ( 5 3 ) :

''

(52)

.Y

knows whether

4

4 x-knows that

4

(53) s knows whether q5 not-(/> .-

x knows that not-@

Also, given this type-assignment there is no problem in allowing for coordination of sentential and interrogative complements, using standard generalized coordination rules:

(54) John knows that Peter has lcft for Paris, and also whether Mary has gonc with him. Notice that the following schemata are iiituitively valid:

4 and whether ~bH s knows whether 4 and s knob$-swhether q!. s knows whether cl, or whether ~b .v knows whether (1) or s knows whether I//.

( 5 5 ) x knows whether (56)

Above we observed that conjunction at the (s, r)-level respects subdomains in thc casc of interrogatives. However, the lowest level at m-l~ichdisjunction respects su\~domains is that of type (((s, t), t), t). This means that the type of know when it takcs a coordinated interrogative complement has to be ((((s, t), t ) ,t ) , ( c , ~ ) ) . We gct the required results when we apply a second general type-shifting operation, that of c iargument-lifting": l'

446 Jeroen Groenendijk and

(57)

(11,

a

c)

art in Stokhof

+ ( ( ( i l , I ) , r), (-), provided

is a conjoinable type =+ t ) , ,) LQ(-x,.~,,, a(.ll))l where Q ( X , j f 6, ) = X(?,y6), if 6 is of typc I 1.

Ax{((,,

=

R.~,I[Q(X, .11,6(.~,1))1, if 6 is of type (d,,f).

This type-shifting rule allows us to lift the argument of a fi~nctor,and provides a semantics for the resulting functor in terms of its original interpretation. T h e example of lifting know of type ((s, t), ( e , t)) to ((((s, I), I), I ) , (r, f)) illustrates this. Application of (57) gives the following result:

If we apply this translation of know to a disjunction of interrogatives, such as (50) above, we get the required distributive result. Summing up, for extensional interrogative-embodding vcrbs, such as know, we can ernploy a key type ((s, t), (e, t)) for dealing wit11 embedded atomic interrogatives, and for conjunctions. For dcaling with embedded disjunctive interrogative complcmcnts we need the cterived type ((((s, t), t), t)(e,t)), which we get by applying thc typeshifting p~.ocedureof "argument-lifti~lg" clctinecl in (57). T h e latter procedure alloitw us to deal in general with cases where a functor is to be applied to an argument that itself has bccil lifted. Besides ex~ensionaleir~becldingvcrbs there are intensional ones, such as wonder. What basic type is to be assigned to thcm? One might think that a simple intcnsionaliz:ltiori of the basic t ~ p of e exte~~sional vcrbs woulcl do. But the semantics of coordinated interrogative conlplements again provides a counter-argumcnt. Above, in section 3.1, wc observed that whereas extensional verbs distribute over disjunctive complements, intensional ones don't, at least not always. Cimsidcr (.50): (59) John wonders who wallis or who talks. T h e point is that (59) is an~biguousbetween a wide scope o r and il narrow scope or reading (with respect to wonder). These different readings can be paraphrased as (60) and (61): (60) John wants to know \vllo walks or to know who talks. (61) John wants to know who walks or hc wants to Iinow who tallts. Trying to lieel) the analogy between extensional and intensional verbs as close as possible would suggest- to give thcin a basic typc ((s, (s, t ) ) , ( c , I ) ) . In orcler to deal with ( 5 0 ) , ive have to apply argument lifting again. But then we would get a distributive rcacling only. In order to get the non-distributive reading ivc nced another, higher type, and it is clear what this type should be. O n the non-distributive reading of (59) wonder takes the intension of the entire disjuilction as its argument, hence, in this case it is of typc ((s, (((s, t), I), f)), (e, I)). This, then, is the ke). type of intensional interrog-ativc embedcling vcrbs. I11 order to accounl for the wide scopc o r reading of (59), paraphrased in (61), we might proceed in two different n7ays. In the line of Partcc and

Type-shifting Rules 447 Rooth's treatment of ordinary intensional transitive verbs, u-e could apply disjunction at the lev-el: lift(,,,) (intension (lift((s, t)))). Or, we could first apply an operatio11 of argument-lowering, and then argument-lift again to get back the original type of wonder. For several reasons, we prefer the latter option. First of all, we think there are arguments against the function-argument "flip-flop" that the former strategy involves (see also section 3.3). Secondly, we need argument-lowering anyway, in order to arrive at simple representations of sentences with atomic intcrrogativcs embedded i~nderintensional verbs. O n the basis of the disc~~ssion so far, we can distinguish the following interpretation domains for interrogatives in natural language:

INT

1 EXT

INT

f 1FXT

Figure 1

In Figure 1, we see the four interpretation domains for interrogatives which we discussed above, and the type shifting operations wrhiel~connect them. T h e first domain, that of typc (s, t), is the dcnotational key type for atomic interrogatives and contains the objects that are the interpretations of the arguments of extensional interrogative-embedding verbs. T h e sccond domain, that of type (s, (s, r)), is the key type for meanings of atomic interrogatives, i.e. the level at which entailments bctween them arc to be accounted for. T h e third domain, that of type (((s, t ) ,r ) , I ) , is the denotational key type for coordination of interrogatives. And thc fourth domain, that of type (5, (((5, t ) , I), t ) ) ,contains the proper objects to be recognized as the meanings of such coordinatcd interrogatives: they are of the proper t y ~ to c be associatcd with the arguments of intensional interrogative-en~beddingverbs, and they contain the right structure for an account of entailment bctween coordinatcd interrogatives. T h e donlains I and 11, and 111 and IV, arc related by the type shifting rules of I N T (intensionalization) and ~cx.r (extensionalization). T h e key type for atomic interrogatives and the hey typc for coordinated ones are related by the operations L I F T (lifting) and LowF;n (lowering). Notice that the lattcr is a partial function. Notice also that only a proper subset of each of these domains contains the sight objects to serve as interpretations of interrogatives in their \~ariousroles. 7'hese subsets are characterized by the specific semantic interpretation rille (14) that we gave for atomic interrogatives, which defines the characteristic ("partition") properties which are "preser\-ed" by the general type shifting principles. _41-ethese four all the interpretation domains for interrogatives? Probably not. One domain one might also want to use is D,,which is to serve as the domain for norninalized interrogatives (e.g. 21s in "Whether cl, is a difficult question"). And others

448 Jeroen Groenendijk and Martin Stokhof --

might be distinguished as well. Prominent a i ~ ~ o nthem, g at least in thc context of this paper, are the relational types that the categorial approach uses. 110 thcg, too, form a possible interprctation domain for interrogatives that can be fitted into a flexible framework such as outlined in this section.; That is the topic of the next section, the possible unification of thc categorial and thc propositional approach.

3.3 Type shifting as unification? T h e discussion in the prcccding sections was largely ;limed at finding the propcr typcs of scmantic objects for the interprctation of interrogatives in the contcsts of coordination, cntailment and embedding. We found that no one unicli~etype serves as /he proper typc in all contexts, and that wc 11ced to pursuc il flexible approach in which various domains, connected to each other by general type shifting procedures, arc used. In this subsection we want to consider another (set of) tyye(s) for interrogativcs, the relational ones, which thc categorial approach uses to give ;In account of anothclconstruction into which interrogativcs enter, viz. intessogativc/answcr pairs. 'I'his consideration will lead us to illustrate yet another aspect of the use of t!.pc shifting, viz. that of unifying equally well-motivateil hut different semantie approaches clealing with differcnt parts of some empirical domain. Abovc wc saw that there arc two main approaches to the semantics of'interrogatives: the catcgorial and thc propositional one. T h e first assigns different relational types to different kinds of intcrrogatives, thc lallcr postulates a unique, propositional typc. Also, we that nrgumcnts in hvour of each can bc given, arguments which by and large arc complementary. l'his suggests hat at some level of analysis the two approaches necd not be in conflict. T h c semantics we outlined above may well contain the elements that such a unitication needs. Kccall that it is based on the following rule: n-plarr rullition qliestior? : nT+ ~OM;(D") 41 : cv {o, l}lq where ~~(777) = that p s.th. p(l71) r(w) = r(lvl).

On the left hand side we find the kind of'scnlantic objects that the categorial approach typicall} associates with interrogatives. And on the right hand side, wc havc a p~.olx)sitional type. So the basic rule of our semantics nlig-ht also bc looked upon as turning a categorial analysis into a propositional onc. Couldn'l: we, then, view this rule, too, as a type shifting rule, i.e. add to our stock of semantic domains t i ~ interrogatives r that of'rrplace relations, and postulate the rule as an additional typc shifting tool? T,ct us first indicate what lvould be thc advantages of such il move. As we saw above, the categorial approach is i~lspiredby the semantics of characteristic linguistic answers to interrogatives. And it deals with them in a natural way. C:onsiclcr the following example:

(62) Which man walks in the park? (63) M7ho walks in the parh!

Type-shifting Rules 449 (64) Hilary. (65) Hilary walks in the park. Given the sex-neutral status of the proper nanze "Hilary", this example clearly shows that thc semantic interpretation of a linguistic answer depends on the semantic intcrpretation of the interrogative it answers. T h e information that (64) and (65) convey differs according to whether they answer (62) or (63). Exactly which semantic property of an interrogative it is, that is necdcd for the interpretation of a linguistic ~ I I I S Wwe - ~ illustrated ~, above, in section 1..3, with an c s ~ i n ~ p l c like the following: (66) Who will come to the party? (67) Who will not come to the party? (68) John and Mary. Above \$re noticed that on a propositional approach, there tends to be no scnlilntic difference between (66) and (67). T h e proposition (or propositions) that give a coniplete spccitication of the positive extension of some property 01- relation are thc same ils the one(s) that give(s) a specification of its negative extension. I-Iowevcr, the nzcaning of (68) differs dependi~zgon whether it answers the positive 01. the negative question. From this we drcw the conclusion that the scnlantic interpretation of characteristic linguistic answers essentially involves the ruliltion that underlies the question expressed by an interrogative. O n the othcr hand, tve have seen that thcrc is ample reason for a propositional level as well. So, it seems that there are two con~plementarysemantic analyses, each accounting for different aspects in thc meaning of interrogatives and their answers. Unifying them could be done by postulating n-place rclations as a possible intcl-prctation domain for interrogatives and by regarding the rule speciticd above ils it t>pe shifting rule. It should be remarked at the outset that we are entering largcly uncharted tessitory here. One reaction to the afore going question, whether our basic scmantic rule can be viewed as a type-shifting principle, might be one of distrust: it certainly does not look like the ones we are fimiliar with. But another reaction might be: "VC'hy not, if it does the same kind of work as the others, and does that properly?" What we seem to lack is a thuoi:])of type shifting rules. Although investigations have been made into the formal properties of barious conglomerates of type shifting rules," a body of general and intuitive constraints characterizing the notion of a type shifting rule as such still remains to be formulated. Unfortunately, we do not have anything to offer on this score. We just want to point o i ~that t thcre may be a relation between what one wants to ~/l~ and the vimv one takes 011 their place in the grammar. If consider as a l ~ o i l n & f iprinciple one considers them to bc part of the s>-ntaxone's attitude might be just tl little more conservati\-e than if one takes them to play a role in the relation between syntax and semantics. m7ithout taking a very firm sta~zdon the mattcr, we suggest that the discussion so fils has provided evidence for the claim that it is possible and profitable to take the ri~lcin quostion to be a type shifting principle. However, there is a potential problcm that such

450 Jeroen Groenendijk and Martin Stokhof a move meets. And this problem raises some further rcaching questions regarding thc place of type shifting principles in the grammar. T h e problem is that of potential ovcrgeneration of meanings of expressions, and it occurs not only with this particular type shifting rule (if such it is). In order to discuss this problem, let us first givc a very rough indication of our view on the place of type shifting in a grammar. Vcrv roughly speaking, we might distinguish tmo ways of incorporating flexibility in thc grammar. On the first one, what we 11avc called type shifting rulcs are in fact considered to be cvttgoTy clzangd~grulcs, which form an integral part of the systcm of' syntactic rules and categories.'" This appmach is orthodox in so far as it adhcles to ij rigid and unique category-to-type correspondence, and consecluently to strict compositionality. For example, accounting for scope-ambiguities by meails of category-changing rules leaves unchallenged the principle that non-lexical ambiguity in the semantics should be based on derivational ambiguity in the syntax. However, the view in question also has some unorthodox features, the most surprising and interesting, perhaps, bcing the willingness to give up the traditional notion of constituent structure."' In view of what follows, it should be noted that in a categorial s!mtactic framework giving up constituent structure means giving up a notion of syntactic function-argument structure. Another view on the place of type shifting rules in the grammar is more semantic. On this approaclz, one of the uses of type shifting is to keep the syntax free from unnecessary complications, such as syntactically unmotivated derivational structures. T h e notion of constituent structure, with its associated function-argumcnt structure, is retained. In Fict, as we will arguc shortly, it can be usecl to deal with onc of the problems that the incorporation of type shifting in the grammar posits, viz. that of overgeneration. T h e unorthodox aspect of the senlantic view on type-shifting resides in the attribution of meanings to syntactic structures. In giving up a rigid and unique category-to-type correspondence, it also gives up strict compositionality. Flexibility does not play a role in the syntax, nor in that part of the semantics that consists of'the abstract theory of semantic objects that serve as meanings, but it concerns the relutian.vl?lp betwcen svntactic structures and nzcanings. Of course, this does not imply that there ma]- not be any need for flexibility in the other components of the grammar as \ve11." However, we arc convinced that in man\: cases, e.g. coordination (including non-constituent conjunction), scope ambiguities, type/tolien distinctions, embedding constructions, and so forth, the semantic approacll to flexibility i s the nlorc advantageous one. It keeps the syntax simple, and it links the phcnonlenon of flexible interpretation to syntactic constructions and contexts. So, the basic tenet of the approach to type shifting that we favour, can be summarized in the follom-ing three stalements: No fixed category-to-type assignment is assumed, but a family of types, generated bg type shifting rules from a key type, is postulated for each syntactic category. 13asic expressions go to a key type in the family associated with their category, and have potential meanings in the other types of the family prcdictcd by the type shifiing rulcs. Interpretation of syrltactic structures is liberalized to a relation: "anything gocs that fils", I.e., a syntactic structure has as many meanings as ciln bc generatcrl from thc potential n~eaningsof its constituents.

Type-shifting Rules 45 1

A simple, and familiar, example is provided by the anal>-sisof (extensional) transitive verbs and their arguments. We postulate one syntactic categorv for these transitive verbs, TV, and one for noun phrases, NP. T h e key type corresponding to the category 1'V that the grammar specifies, is (LJ,(e, I)), and that corsesponding to Nlj is L). On these types, type sllifting rules may operate generating new types. Lexical expressions are given a basic translation (arc assigned a basic meaning) of one of these types, ancl they obtain derived meanings in various (though not necessarily all) of the other types which arc associated with their categor} by the type shifting rules. If a T V occurs with two proper names all expressions iniwlved \$-illtit on the basis of thcir basic typc and meaning. Hence, no tj-pe-shifting is called for. If one NP, say the ohject, is a properly quantified expression, which is given ( ( r , r), t) as its basic type, the basic type of the 'I'V is inadequate. How-evcr, one of its derived types is ( ( ( e ,t), I), (e, I ) ) , the result of the application of argument-lifting to its basic type, with which is associated a clcrivcd meaning for the T\I within that typc. Combining these gives a tjtting result. Scope ambiguities of NP-arguments of TV's can be accounted for as follows. It can be i ~ l ' g ~ e d quite generally that type shifting principles which operate on arguments of functions, must be able to operate at arbitrary depth.'' Different relative scopes of NP-arguments then result from lifting argument places in different orders. No derivational ambiguity is needed in t-he syntax, the readings vc-e want, simply arise because generating the relevant type for TV's in two different ways, generates t\vo diffcrent ~neaningsfor a 'I'V in that type. Clearly, this approach does not eliminate the complexity of tlic syntactic view, but it places it in il different part ofthc grammar. This can be moti\-atcd not only by an appeal to a certain kind of intuition or to elegance, but also by pointing out empirical differences. T o sce why this can be so, it is important to note that adding tleuibility in tlic fi)rm of type shifting principles to the grammar, whether in the slntax or in the semantics, faces a potential problem. These mechanisms inay enlarge the power o f tlic gran~mar.On the syntactic approach, this means that expressions may be recognized which do not bclong to the language. And if we sol lo\^^ the semantic view, we run the risk of giving an expression a potential mcaning it docs not have, i.e for which no context can be found in which that expression must be assigned that meaning. T o cvhat extent this actually happens, depends, of course, on the actual set of type shifting rules onc adopts. For csnmple, in Partee and Rooth (1983) t!-pe-shifting principles are used to give iln account of so-called "wide scope or" readings of sentences such as "Tlic department is looking for a pl~onologistor a phonetician". T h e way the?; proceed differs from thc strategy we have followed in the previous section. They use a type shifting rule which allo~vsthem to interpret the disjunctive object N P as a function which talics the T V as an argument, thus giving it the required scope. However, the same mechanism \vill also predict impossible readings in certain cases. ]:or example, the mechanis~liemployed by Partee and Rooth also predicts that the sentence "Every student Failed or got a D" has as one of its readings "Every student hiled or every student got a D", ivl~ichit docs not. Partce and Rooth do not offer a solution for this problem. In the present case, i.e. if we add the question formation rulc to our stock of type shifting principles, overgeneration occurs as well. Adding the rule in question has the rather unpleasant consequence that our grammar predicts that any expression that expresses a relation, also, potentially, has the meaning of the corresponding question.

452 Jeroen Groenendijk and Martin Stokhof 1:or example, any simplc indicative sentence also gets assigned the interpretntion of thc corresponding sentential interrogative, which is clearly something \tic do not wish. A possible solution can be found along the following lines. We restrict the tisc of typc shifting in generating meanings by combination. Suppow that, its usual, fiiiictional application of lneailings serves as the interpretation of the synt;lctic operation of concatenation, i.e. that we have rulc pairs like the follou-ing: syntactic rule:

B / A + -4 + B

semantic rule:

;I'= F A (P', a')

I>'

a

7)

In an unrestricted flexible frame\vork, such a semantic rule is a rulc schema, allowing 2' aild 1' to be atzy possible translation that can be obtained by means of the type shifting rules, as long as ordinary functional application applies to such n pair of translations. So, a whole set of translations y' will be the result of applying the semantic rule. Wc propose to put the following constraints on the possible translations of a a11d I>':

/I should ' be a possible translation of /3 which is ohtained f r o n ~ils basic translation hy only applying argument shift rules. should be a possible translation of only applying global shift rules. M'

2

which is obtained from its basic translation by

T h e syntactic function-argument structure should be respectccl. (Of course, for other syntactic rules, we might want to formulate other rest-rictions on the corresponding translation part.) Thus restricted, functional application allows 11sto oht:ain only certain semantic objects as meanings o f eon1ple-u expressions. (E.g. Partcc and Rooth's treatment of widc scope or \vould bc prohibited, sincc it implies il reversion of the function-arg-umcnt structure of tlzc VP in question.) J x t P M (a) bc the sct of possible meanings of 2. For basic expressions, this is a unit set (disregarding lexical ambiguity). For derived expressions, it ma?; contain more than o~zcclement. l'hc possible meanings of a complex expression -y built by concatenation fi-om 2 and /I can then also be defined as follows:

I b E phi(/)), it E P M (a)} = F A (/?, 2') where/'is anj composition of argument shifts, and g is any composition of global shifts.

Y M(;!) = (/'(b)(g(n))

(The differc~zcebetween "global" and "argument" shifts is the diffcrc~zccbctwecn c.g. lifting and argument-lifting, intensionalization and argument-intensio~~alization,ctc.) Notice that this way of implementing type shifting in the grammar has a remarkahle consequence: it makcs the notion of the meaning of an expression relatiic to its syntactic context. T h e meaning of' a as a part of P with inca~zinpb is that possiblc meaning a of a that is used to derive /Iwith meaning b. We think that this conscqucncc is i~ltuitivelyapl~ealing.Consider the example of a proper name. Basically it has just one meaning, that of being the nalne of an individual. It is onl!. in certain (syntactic) contexts, such as in coordination with a qilailtified term, that we consider giving it il

Type-shifting Rules 453 derived meaning as well. Or, consider the ease of an atomic interrogative. In isolation, they must be given a meaning of the proper relational type. It is only e.g, in the context of an embedding verb, that we assign them their meaning in the type of questions. As for entailn~ent,we saw that that requires this propositional t>-pe of meaning, too. Hut then, entailment is a rel~ztionof which the interrogatives are arguments. We want to end this admittedly rough sketch with the following remark. In view of the fact that overgeneration is a potential problem both fbr the syntactic and fbr the seniantic approach to flexibility, thc latter, we think, lias this going fix it that it can employ independentlv motivated and restricted notions, such as the function-argument 10 . structure that is inherent in a suitably restricted account of constituent structure, In dealing u7ith this problem. This seems to square n-ith the semantic relcvancc that constituent structure can be assumed to have. But we do not want to suggest that the syntactic view on type-shifting couldn't he sufficiently restricted too. T h c entirc enterprise of incorporating flexibility in the grammar is only just beginning, and it seems wise therefore to explore various options.

4 Conclusion In this paper we have tried to show that generalized notions of coordination and entailment can he fruitful nleaiis to obtain more insight into the nature of the semantics of interrogatives. Their usefulness, both on a descriptive, and on il mctlzodological plane, has been demonstrated in the foregoing, we feel. 113 the course of doing so, wc have made some critical remarks about existing thcol-ies n~ithinthe propositional and the categorial approach. We want to emphasize that the observations and remal-1;s that me have made, in no way pl-etend to show that these i~ppro~~ches as such are wrong. On the contrary, wc feel that both are right. Our discussion does show, however, that ~ h c y cover only part of what an adequate semantic theory of interrogatives sliould account for. Lie also have tried to sketch a thcory that incorporates the insights of both approaches. And in a more speculative manner, have indicated that a flexible way of relating syntactic structure and semantic interpretation may be of great help in achiei-ing this. T h e exact format of a grammar that encompasses these principles, is still in need of further investigation. For one thing, one would like to have some intuitive and independentlv motivated constraints on what arc adequate and natural typcshifting mechanisms. Despite the many interesting contributions one can find in the literature, we feel that this is still largely an open question. T h e last remark we want to make, concerns the necessitj- of incorporatin%a senzantic analysis like thc one presented above, into the framework of a theory of intensional objects. T h e reason for being interested in this, is that one ~ o u l dlike to r c p r d questions, tlie meanings of interrogatives, as constituting a separate categos!. of intcnsional objects, in much the same ~vavas properties and propositions do, and for similar reasons. Notice that, since the analysis is carried out in a standard possihle worlds framework, qucstiolzs arc treated extensional1~-,in the sense that two questions wlzich every~vl~ere have the extcnsion (i.c. the same complete and true answers), are identified. In other words, ivhat the fran~eworkprovides is only an tsicw.sionn/ idcntitj criterion for questions, just as it only gives extensional identit>- criteria for propcrtics and

454 Jeroen Groenendijk and Martin Stokhof propositions. I.e., we are able to give an account of the find of intensional objects that questions are (viz. equivalence relations between possible worlds), but we do not have the means to represent all of the intensionality that they comprise. Just as being true of the same i~lclividualsin every world is a necessary, but not a sufficient condition for identification of two properties, having the same true and complete answers in all situations is not all there is to two questions being identical. 'l'l~creis, of coursc, a relation between these two fiacts. Take an! two different properties which, in sonic suitably chosen set of alternatives, apply to the samc objects in aH situations. Consequently, the question that is based on the first onc, will be eutensionallj. equivalent to the question which is fbrnled fiom the second. But the questions are not the same, just as the properties are not. For somcone might wonder what the extension of' the tirst propcrty is without also wondering whicl~objects the second one applies to. How would one incorporate this fact in something like Chierehia and lurncr's theory of properties?"' Onc might think that oncc one has an intensional theory of properties and/or propositions one automatically also has an intensional thcory of questions, sincc questions are defined in terms of properties and propositions. What one jvould do, then, is define possible worlds using the notion of a proposition and, given that, define questions are equivalence relations on them. But this is in fact still an e.z.tewsiontr/approach to the semantics of interrogatives: it still identifies any two extensionally ecluivalenl interrogatives, i.e. interrogatives which have the same true answers evcrj~n~here. T h e proper \tray to go about, then, is to extend property theory to a general theory of intensional objects, which recognizes besides properties and prol,ositions, also relations, individuals and questions. Another argument to thc cffcct t h a ~questions constitute an intensional category in their own right, can perhaps be talcen from the m u t ~ ~dependal ence of questions and ~~ropositions, interrogatives and indicatives. lt is, at least so since Frege, a commonplace to regard the sentence (statement} as a funclan~entalbuilding block of language. But this is only part of the truth. One of the main functions of language no doubt is to discriminate the actual world (state of affairs) among the possible ones. 13ut this fi~nctionis triggered only when the question of whcrc the actual wo1.1d is located, is raised in the first place. 'To be sure, the depcndencc is mutual, for raising a question clearly presupposes the possibility of malting the discriminations which the question calls for. So functionally, at least, questions and propositions ase mutually dependent, a fact which we might see reflected in the f ~ c ttl ~ a tan extensional derivation of either category to the other is doomed to fail. Within the context of a general theory of intensional objects these considerations call for the introduction of a new basic typc in ous ontology, that of questions, and for thc concomitant fi)rmalization of a new cxccnsionalization relation, between questions and propositions. This relation is, of course, the relation of answerhood, i.e. the relation of being a con~pleteancl true senlantic answer. But an account of that is another topic.

Notes 1 This paper is a further development of some ideas in Grocncntlijk and Stolihof (l084), cspccially chaptcr Vl. Also, ~ a r i o u other s aspects of thc approach described 11cl.c arc exp1:lincd and dcfcndcd there in more detail. We have refrained from bothering the reader with detiiilcd refkrcnces.

Type-shifting Rules 455 This terminolog! ma! be slightlj, confusing. C:crlainly to the hlontogovian, the use of t w o different nnlnes suggests lhat there arc two different underlying derivational processes at work. Ho~vcver,this is not the case. Both readings are thc ~.csultof one and the sarnc dcrivationnl process. It is the internal senlantic srructure of the tern1 phrase that is used that dctcrmines ~vliichreading is thc result. Moreover, notice that the tcvo readings, in a sense, arc not con~plcnicntary. T h e result we get if we use a term such as Imo i!f hzs~/i~icirr/.v gives a choice reading, but oncc a certain choice has been made H hat is requilacd is a list of pairs. Likewise, a siniplc proper name can be view-ed as a t r i ~ i a lone-item list. In what follon.~,we will not go into the details of the derivation of I?air-list and choice readings, since in this paper me are only interested in the rele\-ant types. Cf. Gazdar (19XO), Keenan and Faltx (1985), Partec and Rooth (1983). An example is conjunction which functions as "addition". See Partee and Rooth (1983), Partec (1086). Notice that thc kex type is not necessarily thc niinilnal t!pc, in tlie sense of the leas1 comples type, of an exl>rcssion. For example, the least coniplex type of proper names is e but their key t>-peis ((e, t ) ,I ) . See e.g. Ilausser (1983). It should be noted that for interrogatives of the same kind, a categorial theory might obtain correct results by appealing to the same niechanisrn that we bill propose to USC,viz, lifting (see below). T ~ v oremarks are in order. First, in a sense such a move against the nature of the approach. Second, this observation does suggest an adjustment of' the use 01' coordination and entailnienc u-e arc making hcrc. !4s an evaluation measure i t works if' we constrain tlie use of such t!-pc-shifting proccdures as lifting in order to account for coorcliniition. 'The following sccnis intuitively justified, and prevents the move just mentioned: coordination should be accounted for in tlic lolvest common t!-pe in which it respects "subdoniains" (scc section 3.2). Scc Karttunen (1 977). See Bennett (1979) and Belnap (1982). Whiit is said hcrc about their approk~chis a kind of rational reconstruction of just one aspect of it. The reader is urged to consult tl~cirpapers li)r niore information. Notice that son~c~liing similar would hold for expressions of type e if the domain 1)'. \vould have an entailment structure clefincd on it. See c.g. Sralnakcr (1984). &%gain,it should be notcd that this is not characteristic for coordination of interrogatives. T h e same applics to other domains that are structured I)y cntailmenr. Cf, also notc 10. See Partec and Rooth for another application of this rule. There is a difference in the way they ;~ccounth r wide scope or readings and the way in which we proceed. O n their analysis, thcrc is m hat the!- call "function-argument flip-flop". We keep thc f~inction-arguiiic~it structure intact. For a moti\7atin~i, see section 3.3. See e.g. \an 13entheln (1986). See e.g. Ades and Stecdnian (1082), van Uentheni (I986), Dowty (1988). A clear and well-argued u s e is presented by Z~varts(1986). For exomple, Mourtgat (1988) argues that wc need flexibilit?. in the n~orpholog?,and tlic "right node raising" constructions discussed in Dowt) (1988) ma!. be presented i1s argunicnts for s o n ~ e kind of flcxibilit!. in the syntax. In hct, the distinction is rather particular to a functional formulation of type-thcchr!. I f n c norc to use a relational version (see Muskens (1986) for an exposition kknd some ,lr-gumcnts in livour of nt using such a theor)), we would simply sa! that argument-lifting ma!- OpcriIte on an!, a r g ~ ~ m eof a relation. T h c restricted framc~vorlideveloped in I.andman and Moertlijl, (1083) sccnls to oll'cr a good starring point. Scc Chiercliia and Turner (1987).

456 Jeroen Groenendijk and Martin Stokhof

References .4des, .4. and h4. Steedman. 1982. On thc order of ir-ords. Lit~~uis/I'r.s a~rtlPhilo.zopl1)~5: 517- 58. 1 Bclnap, N. 1082. Qi~estionsand answers in hlontaguc grammar. In S.l'cters lind E. Saarine~i(cds), Proc.c.\:\.cr, B~liy/.ir/mrl Qut~.srinn.s.Dordrecht: D. Reidel, 1 05-98. Bennett, hl. 1979. @u.v/rons in Montugu~'Crlttnnarrr.. Blooniington, 111d.: Indiana Uni.vcrsity 1.iiiguistics Club. , Bcnthem, Joliarl v.m. 1986. T h e semantics of vnricty in categorial grammar. In Wojciccli 13uszkowshi, Wirold Marciszc~vskiand Johan \an Benthem (eds), Ctr/egori(//Grl~wrrnrrr,m s r c r d a m : Rmjaniins. Chierchia, G. and Turner, R. 1987. Semantics and yropcrty theory. I , i ~ ~ ~ t l i rtl~il s / i ~ Philo.sop/~)/ s 11: 263 1 -302. Dowty, David. 1988. Type raising, functional con~position,and non-constituent conjunction. In Richard T . Oehrlc, Emmon Bach and Dcirdrc LIiheeler (eds), C i r / r ~ ~ / ~(;~.nttrtrrlr,:s r/r// otrtl .A;tr/rrrt/l Lrrl~gl~/ige Struclures, Dordrccht: D . Rcidd. tiazdar, Gerald. 1980. A cross-categorial semantics li)r coordination. L~rlLqrrr~rr.s trrrd Plrrl~~so~)/t)l 3: 407-1 0. Groencndijk. Jcrocn and Martin Srokhof. 1984. Studies on thc Sem;~nlicsof (k~estionsand the Pragmatics of .4ns\ver-s. P h D dissertation, University of Amsterdam. Hausser, R. 1983. T h e syntax- and semantics of English mood. In F. Kiefcr (ed.), @rtsliorrs irr~rl -,-lnswen, Dordrecht: D . Reidel, 07-1 58. Karttuncn, Lauri. 1977. Sxntax and semantics of questions. Lirrgrrrs/ir:~irrrd P/ri/osop/~)lI : -3 44. Keenan, Edward 1,. and Leonard hi. Faltz. 1985. B O O I ~ I, SI NC I I I I O I I I girlrlrl(/ I . S / ~ ~ ~I , I I I I ' ~ N 13or1lrccht: (~~L'. D. Rcidcl. Landman, F. and I. Moerdijk. 1983. Compositionality and the analysis of' un;~pliora./,rriprris/ir..v rrrril PI~i/os~)p/?)! 6 : 89- I 1 4. I Moortgat, M. 1988. h,lixed composition a i d discontinuous dcpendcncies. 111 Ricliarrl T. Ochrlc, Einnion Bath and Dcirdrc MTheclcr(ecls), C ~ r q ~ ) r t(;rn~trttrtrr.s af l r l l l / Nri~rrrr~l Ltrtrgrli!~~ S/r.rri.~rrr.us, Ilorclrecht: D . Reidel. Muskcns, R. 1986. Relational Formulation of the 'Thcory of Typm. I'T1.I prcpublicntions 5, mstcrdam. Partce, 1Earbarn. 1986. Noun phrnsc interpretation and tjpc-shifting principles. In jcroen GrocncndijL, Dick de Joiigh, and h~lartinSlokhof (cds), S/~ii/rr~s irr J)i.si.o/rfi~ R L ~ ~ ~ ~ ' X CT/r(~o/:)) ~ I ~ ~ (otrt/ / / ( /I IhI ~ T f ~ c . ~ ~!/'Grlrerdl/ic.t~d )rl~ @ ~ a r r / ! / i ~ Dordrceht: n, Foris, 1 1-5-44. Partec, Barbara and Mats Rooth. 1983. Gencralizcd conjunction and type ambiguity. In Rainer Biuerlc, Christoph Schwarze, and Arni~nvon Stecho\\- ((eds), ;lleo~rjl~,q, Z,'s(,, onrl l t ~ ~ r r p r ~ ~ n I!/'/ i o ~ r Lir~r,y~(.l,trgt?, Berlin: Walter dc Gruyter, 361-83. Sralnakcr, Robert C. 1984. I ~ ~ q u l lCambridge, :)~. Mass.: M1T P1.ess. Zmarts, F. 1986. Categoriale Gramniatica en Algebraischc Yemantick. I>isscrtation, T)cpartmcnt 01' Linguistics, Unil-crsity of Groningcn.

I

i

On the Notion Affective in the Analysis of Negative-polari ty Items William A. Ladusaw

1 The Question Several approaches have been taken to limiting the distribution of Icxical items like r r l y , Pi'e/+,y ' t , and ar~linrol-' since Klima's account in "Negation in English" of the cliffcrcnce in acceptability of sentences like those in (1) and (2). (1) (a) (b) (2) (a) (b)

Chrjsler dcalers don't ever sell any cars anymorc 'I'he 6:OS hasn't arrived yet *Chrysler dealcrs ever sell any cars a n y l o r e "The 6:05 has arrived yet

A11 of these approaches have madc the acceptability of a sentence which contains onc of these so-called negative-polarity items conditional on the presence of a licensing negatib-e clen~entelsewhere in the sentence. Klima showed that the rangc of such licensing lexical items extends far bcyond what could reasonably be called negations on any morphological or obvious seniantic grounds. It includes members of several syntactic categories, and lexical iteins with otherwise parallel syntactic properties may differ in whcther or not they license negative-polarity items. He assumed that some semantic property unified this diverse class and postulated the feature z$[fi~.ti~~e to govern the rules he proposed to restrict the distribution of Negative-polarity itcms. T h e sentences in (3) give an indication of the difficulty of providing a definition of this semantic feature.

458 William A. Ladusaw

(a) Defenizi7i~ls no one at most three people fcw students

I

.

*someone *at least three people *many students

who had erer read anything about phrenology attended aqt of the lcctures

( b ) Quant~ficnlaonni/z)crDs never rarely seldom ez5er eat r~nythingfor breakfC~st anyiloue

*usually "alwa~-s "sometimes

I

( c ) Prepo"tion.s John finished his homework against John i i r e d {++for

}

John will replace the n1onejr

I/;t'rhs lend ~djectislrs ( hard difficult

(i) It's "easy "possible

( i ) John

1

~ c n ) )help

i i i r apl~rovingany of the propsrls

(d) r l h e r b i n l conjun~.tions

(e)

{

without *with

[ lllen 1 *after

~ ~ ~ O 'zlcr T I Pmisses

to find rrn,)10r7ewho has e w r read

nn,ythirzg n~uc/zabout phrenology

that LIYI.)IOYIE would LTCT discover that the money was missing

it

The Analysis of Negative-polarity Items 459 ' is unlikely

(iii)

is doubtful amazed John *is likely *is certain

It

+

that rrn)!onr could ezler discover that the money was missing

)

to return m y of the money

is surprising ,"is unsurprising '

refused for got failed

(iv) John *agreed "remembered , "managed avoided *cncountcred (t)

any scandal

Degree nzorrls John is

too smart "smart enough

to eaer do ar~yrhinglike that again

Much about thc distribution of negative-polarity items can bc accounted for by taking Klin~a'sgencralization in (4) as one of thc neccssarq- conditions on thc acceptability of sentences which contain them.

(1)

i\, sentence which contains negative-polarity items will be acccytablc only if the>-

are c-commanded by an affective cxpression. It is clear, though, that a detinition of affective is essential to il principled account of thc distribution of negative-polarity items. We havc said vcry little when we say that a scntencc containing negative-polarity items is acceptable only if it also contains an nffcctive to license them if our only evidence that some word or phrase is affective is that it licenses negative-polarity items. In the absence of a definition of ~![jec117~, thcre is no alternative to listing arbitrarily the appropriate lexical items in (3) as semantically [i-afkctiveJ. T11erc is, hoaever, reason to think that such an approach is inadequate. C:onsider sentenccs like those in ( 5 ) and (6) which were, to my knowledge, first discussed in lioss' dissertation. 111(5) negative-polarity itcms occur only in the NOM of the subject Noun Phrase. In (6) they occur only in the Verb Phrase.

460 William A. Ladusaw (6)

':

{ n o student " e ~ - e rstudent ~~ (c) *some student

}

who attendcd the lectures had ever read anything about phrenology

No and Ezleql must be marked [+affective] and sonte I -affective) to account for thc sentences of ( 5 ) . T h e negative-polarity items in (53) and (jb), but not those in (5c) would then be c-commanded by a licensing affective. T h e sentences in (A) pose a problc~n.Since the negative-polarity items in (ha) arc not c-coinmandcd by Iro, (4) is not met. Yet the sentence is acceptable. We might considcr substituting conrrnarrd for I.c,owimand in (4)) the strategy taken by Jackendoff in his analysis of similar sentences in the reference in the bibilograph!, but since no and pzlci:)t differ in their ability to license the ncgitive-polarity items in the verb phrases of the sentences in (A), any revision of ccolnniand in (4) to account for (ha) \vould incorrectl!. predict (At?) to be grammatical ils mrell. No single feature assignecl to thc lexical items rro a i d ez:eq~will be ablc to predict that ei:ety should act like no with respect to c-commanded negative-polarity items, but like some with respect to those which it commands but docs not c-command. The sentences in (3a) show that .fL;117 and at tnos~thvte pattcrn with ?lo. T h e other unikersal determiners (all, each, and universal-a);)!) pattern 1vit1i ecery. We need not conclude from ( 5 ) and (6) that the licensing cf'fcct of trc~?:y and no cannot be reduced under a single generalization nl->outaffecrives. t\!c can maintain (4) as it stands by saying that the any in the verb phrasc of (ha) is licensed not by thc affective determiner no, but by the affective N P rzo stzii/~'~~ts, n~hichdoes c-comm;~ndit. But since we callnot lcxical1~-specify a noun phrase like no s~~uktzt~ as affective, such il proposal \vould require us to provide principles to predict that it is affcctivc, whilc ez.fyy stziiient, wl~ichalso has an affective determiner, is not. It requires a definition of <[fic.tii+r which can predict for determiners and iloun phrases alikc which arc affective and which arc not on independent grounds. Bj- thc end of this paper, I hope to have shown just horn- this can bc done.

2 The Answer Gilles Fauconnier and Janet k'odor have independently found definitions of y[7ictjz?e which capture a correlation bctw-een the kind of infcrcnces which may bc made from sentences containing affectives and the licensing of n c ~ a t i v c - p c r titenis. Fauconnier (1975) presents an analysis of superlative NP's like the one in (7) which seem to have the force of a universal quantifier.

( 7 ) Jolin can solve the hardest problem (8) John can solve any problem According to his anal!sis, (7) may be used to convey (8) because in conjunction with the pragmatically reasonable assunlption that if one can solve some particular problem, one can generally solve ally problem simpler than it, (7) entails (8). Fauconnier noted that affectivcs have what he called an "implication reversing" effect on these quantificational superlatives. Whenever the superlative fills in the scopc

The Analysis of Negative-polarity Items 461 of an affective, as in the sentences in (9), the direction of entailment is reversed. Hence in these sentences it is the noun phrase the simplcsl problem rather than tlzc lzarl/es~ problem which has the force of a universal quantifier.

(9) (a) John can't solve the simplest problem (b) I doubt that John could solve the simplest problem (c) It's hard for John to solve the simplest problem ( 10) expresses thc correlatioil Fauconnier found bctween being an implication reverscr

and licensing ncgative-polarity itcins. (10) If rj entails II/, thc result of enlbcdding result of embedding 51, in that context.

I)

in an affective context will entail the

Fauconnier concludcd that negative-polarity items like n q t , ez7er and Izfi-a+itlgcr and superlatives are sensitive to the same class of scmantic contests: the q~~antificational those which reverse the direction of entailment. In her work on the logic of negation, Fodor also noticed this correlation betu.een "direction of entailment" and the property of being an affective. In uncrnbcddcd contexts, entailnlcnts proceed from scts to their supersets, from what shc calls "strong v;llues" to "weak values." Because the noun .firthrr. must denote il sul~setof the denotation of ?77un, a sentence containing the noun Jirrhel- will typically entail one lvith its superset noun tnan, as in ( I 1) and (12). (11) (a) (b) (12) (a) (b)

J o h n i s a '~ther tJohn is a man Some fathers walk Somc me11 walk

t

I will call entailn~entslike those in ( I 1) and (I 2 ) from a subset to a supersct "upwarcl entailments". Affectives crcnte contexts in which cntailn~entsare reversed: superset values cntail subset values. T h e affcctives not and no in (13) and (14) reverse the entailment pattern in (1 1) and (12).

(1 3)

(a) (b) (14) (a) (b)

John isn't a man t John isn't a father Nu man w l k s k Vo father walks

These cntailincnts from scts to their subsets I \%-illcall "do~vn\vardentailments". It is this correlatioil between licensing downu7ar-d entailments and licensing negativepolarity items which predicts the facts of (5) and (6) about rvc3?)/and no. Parallel to the subsct/superset relation of the n o u n s . / i t / ~and ~ ~ . man, u-c will consider the verb phrase mnlk S/OIP/)~ to denote a subset of the denotation of nlalh. (Everything which walks

462 William A. Ladusaw slowly also walks, but not vice versa.) T h e direction of entailment in (1.5) and (16) parallels exactly the grammatically judgments in (5) and (6). Only if the entailment in (15) and (16) is downward from a superset to a subset is thc corresponding sentence in (5) and (6) grammatical. ( 15 )

(a)

(b)

(c)

(16)

(a)

(b)

(c)

no man walks k no father walks (downward) every man walks k every father walks (downward) some father walks k some man walks (up~vard) no man walks k no man walks slowly (downward) every man walks slowly k every man walks (uyward) some man walks slowlv Isome man walks (upward)

This correlation extends, with some hedging about proportional quantifiers liltcjcr?) and nzilq~,to the determiners in (j),as the entailments in (17) and (18) show.

(17) (a) at most tl~reemen walk k a t most three fathcrs walk

(downward) (b) at least thrce fathers walk k at least threc men wall; (upward) (18) (a) few men walk Ififw nlcn walk slowly down^\-ard) (b) man!- men walk slowly k many men walk (upward) Loolting beyond the cletern~iners,we can consider (19a) to rcprcsent a suhset of its entailment, (19b). T h e entailments in (20) show. that all and only the af'fective sclitcnce adverbs in (3) reverse this entailment. (19) (a) John eats brussels sprouts for dinner k (b) John cats a green vegctahle for dinner

The Analysis of Negative-polarity Items 463

(20) (a) John

r:m

{ } } { } } rarely

eats a green vegetable for dinner k

neyer ~ o h n{rarely eats txussds sprouts for dinner seldom (downward) usually (b) John always eats brussels sprouts for dinner k sometinles usually John {always sometinles (upward)

eats a green vegetable for dinner

In a sense in which it would take too long to formalize here, we may also considcr the noun phrase a red jl~cket to denote a subsct of thc denotation of a j ~ l c k e l . T h e entailments in (21) establish zvithout as downward-entailing, and with as upwardentailing.

(21)

(a) John left without a jacket k John left without a red jacket (downward) John left with a red jacket k (b) John left with a jacket (upward)

Sinlilar intuitions would show that the other affectil~esin (3) are downward-entailing (though there are some problems posed by intensional contexts). We now know what unifies Klima's class of gffictiiles: (22)

An expression is ojfictivr iff it licenses inferences in its scope from supersets to subsets.

Given (22), we can raise the question of how best to state this correlation in a grammar of English so that the facts of ( 3 ) , ( 5 ) and (A) are predicted by some principle like (4).

3 A Theory 111 the renxlinder of this paper I will sketch how this correlation between dow-nnrard enrailmcnt and thc licensiilg of negative-polarity items nlay be captured in a gramn1ar whose semantic component provides a model-theoretic interpretation of the language it generates. Such a semantic component associates with each of the sentences generated by the syntactic rules a set of functions which represent its truth-conditional

464 William A. Ladusaw meanings. These interpretations are assigned in two stcps. 'l'he lexical itenls of thc language are first assigned functions which express the contributions that they consistently make to the meanings of sentences. Then the syntactic rules of the glxnlrnar are cach paired with a senlantic con~positionrule. This semantic rule specifies how the interpretations of syntacrically complex expressions formed by the syntactic rule may be determined from the interpretations of its immediate constituents. M y proposals are based on the extensions made of Richard hfontaguc's work by Rohin Cooper, and are discussed in more detail in Cooper (1975) and 1,adusaw (1980). M y purpose here is only to show how a certain mathematical property of the functions which serve as the denotations of affective cxprcssions captures the fact that they license dou.nward entailments and serves as the definition of q[/ec.tiz!e. Let us begin by considering the three functions which are used as the denotations of the determiners sonze, no, and ezwy. Consider first the function which takes as its arguments two scts X and Y ilnd returns as its valcle the truth value of the sentence in (23a). (23) (a) FI: T h e intersection of X and Y is not empty (b) ), X ;1Y 3x[X(x) A Y (x)] 'l'his function is equivalent to the onc dcnotcd by thc expression of intensional logic in (23b), which serves as the denotation of some. W-hen applied to the sets F and W in Figure 1, F1 will yield truc. Given that FI is truc for sets F and W, it is obvious that the result of applying F1 to V \ and any supcrsct of F, say h/I in Figure 1, must come out true as well: if set I.' had some intersection with W, then any set which contains F must intersect W as well. In general, (24a) is true of F1.For any sets X, Y, and Z, such that X is a suhsct of Z, (X, Y) entails FI (2, Y). (24) (a) VX W t'Z (b) b'X t'Y VZ

[[X [[Y

C Z] 4 [./'(X, Y) 4 J'(Z, Y) 1 j Z]

+ [J'(X,Y)

i/'(X,Z)]l

Fl also has this property with respect to the argument represented by Y in the formula, because (24b) is true. By similar reasoning, the application of FI to sct F' and any superset of W in Figure 1 must be true if FI is true of F and W. When (24a) or (24b) is true of some function, it is said to be Iuonotnul) irl~.rccla.~i~f,q. For our purposes here, we will s a j that F1is monotonc increasing with resycct to its first argument becausc (24a) is true of it, and monotone increasing with respcct to its second argument because (24b) is true of it.

Figure 1

The Analysis of Negative-polarity Items 465

Now consider the fi~nctionrepresented by the sentence and formula in ( 2 5 ) , the denotation of the determiner no.

F2:T h e intersection of X and Y is empty (h) iX ;1Y n3x[X(x) A Y(x)]

(25) (a)

F L will be true of thc sets It4 and W in Figure 2. But note that neither (213) nor (24b) is true of F2.There could well be supersets of -M that would intersect with W and thereby falsify (24a), and similarly for supersets of W. F2 however shows a similar property with respect to subsets of its arguments. For example, M's subset F cannot intel-sect W in Figure 2 since it contains nothing which was not in -M, and M did not intersect W.

Figure 2

F2 then has the property in (26a) for subsets of its first argument, and that in (26b) for subsets of its second. (26) (a) 'v'X YY YZ (6) VX fl-'v'%

[[X 2 Z + [j'(Z, Y) [[Y Z + [J ' ( X , Z)

c

(X, Y)]]

4.f

J(X, Y)]]

+

(26a) and (26b) represent the property of being a monotone decseasing function with respect to its first and second argument respectively. Note the similarity of (24a) and (26a). They arc identical except that the positions of X and 2, are reversed in their consequents. In (24), the consequent represents an entailment from a subset value to a superset value. In (26)' the entailment is reversed, it is from a superset value to a subset. T h e property of being a monotone decreasing function is exactly the property of being an expression which licenses downward entailments. Now consider the function in (27). (27)

(a) F3: X is a subset of Y (b) 3, X 2 Y Vx[X(x) + Y(x)]

Figure 3

'This function applied to the sets M and IV in Figure 3 5-ields truc, but if \ye ask whetl~cr F; is monotone increasing or monotonc decreasing, the answer diffcrs

466 William A. Ladusaw depending upon which argument we consider. F3 will continue to yield true in Figure 3 if we choose to replace _M with one of its subsets, for example set F. This means that (26a) is true of F3 and so like F?, it is monotone decreasing with rcspect to its first argument. However, F3 will continue to yield Lrue only if we replace W in 1:igure 3 with its supersets. Like F 1 ,F3 is monotone increasing with respect to its second argunlent position. We have shown that these three functions have these properties independently of any linguistic considerations. We can solve the problem posed b } the sentences of (5) and (6) by putting these functions to work in our interpretalion of English by taking F 1 ,FL, and F3 to be the denotations of some, no, and e.t'ery respeclively. Thc semantic composition rules associated \+-it11the syntactic rules which combine determiners and NOM7s to form NP's will specify that the function denoted by the NP is the result of applying the function denoted by the determiner to the set denoted by the NP's NOM constituent. T h e con~positionrule paired with the syntactic rule which combincs Noun Phrases and Verb Phrases to form sentences will specify that the interpl-etation of the sentence is the result of using the set denoted by the VP as the argument to the subject NP's interpretation, in effect supplying the second argument to the determiner function. This will make the predictions in (28) about the truth-conditions of sentences which have these quantifier NP's as subjects. (XI stands for the denotation of X.) (28)

(a) Ls LNP some XI [VyY]] is true iff the intersection of X' and Y' is not empty no XI [vp YIl] is true iff the intersection of X' and Y' is emptv (b) [s r [vp Y]] is true iff X' is a subset of Y' (c) ISIhl, e ~ e q XI

Looking back at the Venn diagrams in Figures 1-3 and interpreting M, I?, and W as the denotations of man, father, and walk respectively, it is easily seen how such an interpretation predicts the entailments of (15) and (16). When we instantiate (26a) for no and euuy and the relevant sets, and (241) for some, we get the formulas in (29) which exactly parallel the entailments in (15). [[father' C nzan'] -. [no' (man', walk') + no' (father', walk')]] (29) (a) (b) C] [[fatl~er'C man'] + [every1 (man', walk') + every' (father', walkl)ll [somef (father', walk') -+some' (man', walk')]] (c) t3 [[father' C man']

-

T h e downward entailments in (15a) and (15b) are a consequence of having chosen functions which are monotone decreasing with respect to thcir first arguments as the denotations of no and ez)er)/. T h e second argument to the determiner function is supplied by the denotation of the VP. When we instantiate the definitions of monotone increasing ((24b)) and monotone decreasing ((26b)) for the second arguments, we get the predictcd entailments expressed by (30), which parallel those in (16). (30) (a)

(b)

C] [[walk-slowly'

C walkf]

+

[no' (man', walk') -. [no' (man', walk-slowly1)11 C] ]:[walk-slowly' C: u-alkf] + [every' (man', walk-slowly1) -+ every' (man', walk')]]

The Analysis of Negative-polarity Items 467 (c)

[[walk-slowly' walk'] + [some' (man', walk-slowly')

-

some' (man', walk')]]

Recall that F3, eaey11's denotation, is monotone increasing with respect to its second argument. Hence it patterns with some in (30) rather than with no, as it did in (29). Our choice of Elg as the interpretation of every predicts the switch in entailment pattern which it shows in (15) and (16). UTe defined an affective as a downward-entailing expression, thus prcdicting that negative-polarity items will occur only in the parts of a sentence whose interpretation serves as the argument to a monotone-decreasing function. It is thus a consequence of what eaery means that it should display its apparent ambivalence for licensing negativepolarity items. We can now recast the generalization in (4) in terms developed in this section of the paper. We define the semantic scope of a constituent by the way in which the functions which serve as the intespretations of the constituents of a sentence are related in its semantic interpretation as in (31). (3 1)

For any two expressions r and /l constituents , of a sentence 4, o: is in the scope of with respect to an interpretation of 4, d,' iff the interpretation of a is used in the formulation of the argument to p's interpretation in 4'.

(32) is our dcfinition of affrclii;r, or i/o~~muczril-entailing expression in terms of monotone decreasing. (~[flertive)iff its denotation 6' is a mono( 3 2 ) An expression 8 is ~hwn~~~arrl-~ntlIjling tone decreasing function.

6' is monotone decreasing iff'#X VY

[[X i Y]

-

[6'(~){$)6'(~)]]

By these definitions, the negative-polarity items in (Sa), (5b) and (63) are in the scope of a downwal-d-entailing expression (no, ezely, and no stuhnt, respectively). Those in (Sc), (6b)? and (6c) are not, since some, esery studtnt, and some studCni are all upw-ard-entailing expressions. These definitions are made simpler by taking the subject NP to denoie a one-argument function which is the result of supplying the determiner's denotation with its first argument. In this way, the noun phrase no student is predicted to be downw-ard-entailing, but the noun phsase cz:tr:y sfrader~tis not, despite the fact that its determiner is a downward-entailing expression. We can now predict the licensing behavior of thc determincrs sovnc, ezlcl:y, and no as well as the other affectives In (3) by replacing- (4) with (33) as a necessary condition on the accept~bleoccurrence of negative-polarity items.

(33) A negative-polarity item is acceptable only if it is interpretcd in the scope of a down\zrard-entailing expression. T h e foregoing account of eveqy extends directly to another welI-known asymmetry in the licensing properties of affectives. Negative-polarity items may occur in the an~ecedcnts of conditional sentences without a licensing affective, but not in their consequents, as the sentences in (31) show.

468 William A. Ladusaw (34)

(a) If anyone ever discovers the money missing, then John d l r e t ~ ~ ritn (b) "If John doesn't return it, then anyone will ever discover that thc money is missing.

This difference in grammaticality is paralleled by the same diffcrence in the direction of entailment noted above: he entailment in (Oh) represents thc substitution of n subset for a superset in the antecedent clause (a downw;ard entailment), while that of (35b) is the substitution of a superset for a subset (an upward entailment). If John eats a grceil vegetable for diililer then Mary will reward him k IfJohn cats br~lsselssprouts for dinner then Mary will reward him (b) If Mary rewards him, then John will eat brussels sprouts fi)r dinner t If Mary rewards him, then John will eat a grccn vegetable for dinner

(35) (a)

By making the common (but not uncontroversial) assumption that ~fexpresses the two argument ruth-function of material implication, u7e can show that it is downward-entailing with respect- to its antecedent argument, but upward-entailing with respect to its consequent argumcnt. Instantiating the definitions of monotone dccrcasing for the tirst argumcnt of if' in (36a), and that of monotone increasing for the second argumcnt of zf' in (36b), we get two tautologies of the propositional calculus.

As a side note, where iJ'is taken LO denote a relation between set-denoting expressions (either propositions construed as sets of possible worlds, or sentences when they arc taken to denote sets of assignments of values to variables) then its denotation is in fact F3, be-a-subset-of, and thc parallel between ever)rand $is cvcn clearer. I have concentrated in this part of the paper on the dctcrmincrs and !f h r two reasons. First because thcir behavior was difficult or impossible even to describe as long as affective was treated as an arbitrarily assigned feature of a moryhcmc's meaning. The Fact that this definition of affective predicts their bcl~nviorprovides impressive confirmation of the correlation between direction of entailn~entand the ability to liccnsc negative-polarity items. T h e second reason for concentrating on these logical words is because we can show for thcse lexical items exactly what function is to serve for their denotation in our intcrpretation of English. This is not the case for most of the other downward-entailing ewpressions, like doubt, be suvp~zsed,for~~et, and mitkau~.T h e in~erpretationsof I:nglish based on hlontague's semantic theory typically specify only t l m lexical itcms should receive some function of a certain type as thcir denotations, using meaning postulates for the languagc to constrain this choice sonleu-hat. Our definition of (Iffi>l.~i~?c~provides some addi~ional content to the theory of lexical semantics in this framework. It rcstricts rhc choice of function which may be uscd to inlerpret an affective by specifying that it be monotone decreasing. T h e non-aff'ectives in (3) are all upward-entailing, and would have monotonic increasing functions as heir denotations.

The Analysis of Negative-polarity Items 469 Not all expression of English will be either upward-entailing or downward-entailing. n is T h e determiner e.rtlrfI)r tkriv, fbr example, receives a denotation f ~ ~ n c t i owhich neither inonotone increasing nor monotone decreasing. T h e theory sketched here replaces thc two-way distinction implicity in the use of thc feature affective with a three-way distinction: upward-entailing, do\vnward-entailing, and neither. We should, therefore, look for this contrast in the other generalizations which have becn based on af'fecti~~c or downu~ard-entailing,such as those governing the distribution of Fauconnicr's pragmatic polarity items and the constraints on the conjunction of quantifier NP's noted in Barwise (1979). In conclusion, I would like to point out one consequence of these rcsults for our ideas about the role of semantics in a grammar. \L7e have seen that the property of sentences like (38) which renclers then1 unacceptable is to be defined in terms of thc cntailincnts licensed by certain lexical items, rather than by simply marking certain morphemes with a semantic feature. It seems to follow directly then that no grammar can in a principled way distinguish the sentences in (37) as acceptable and those in (38) as unacceptable unless its scmantic component aims higher than at simply disambiguating sentences by deriving "logical forms'' for them to the goal of providing a thcory of entailment for the language it generates.

(37) (a) no studcnt who had ever rcad anything about phrenologJ- at-tcndccl the

(38)

lecture (b) every student \vho had ever read anything about phrcnologj attended thc lecture (a) *every student who attended the lecture had ever rcad an!.thing about phrenology (b) "somc students w h o attended the lecture had eye]*read anything abor~t phrenology

Note Paper presented to the 1959 .%nnual Meeting of' the LSA4,Los -$ngcles. This paper is based 011 Chapter VI of my dissertation and the peoplc I acknowledgc rherc arc hereb! thanked again, particulilrl! 1,iluri K;lrttunen for many good comments on that chapter and Sranlcy Peters for first making Barnrise's c\-ork accessible to me.

References Barnisu, J. 1951). On branching quantifiers in english. Joi.iiiirr/ of f'hi/osophl'rir/ Loytr. 8: 17-80. C:ooper, K. 1955. Montague's Semantic. Theory and Transformational Gmrnmar. Ph.11. disscrtation, University of hlassachusetts, Amhcrst. Fa~~connies, G. 1975. Polil~ityand the Scale Principle, in CLS I / . lauconnier, G . 1059. Implicalion rcversal in a natural language. In F. Gucnthncr and S. Schmidt (cds), Fomial St~in~lntrr..~ and Prmg~iri/lc.sFor i\'[riurrrl Lut~~.rlicge. Dordrccht: Kcidcl. Fodor, J. L). .A hTc\\-1,og-ic for Negation. Unpublished manuscript, Universiry of' Connecticut. Foclor, J. D. 1979. A Logic for Phrasal Negation. Paper delivered to rhc sulnnicr meeting ofrhe I.S?I, Siil~burg.

470 William A. Ladusaw Jackcndoff, R. 1972. Scnla~zticIntrrprrlulion in G't.n~rclriz.eG'rr~rt~~nur. Carnbridgc, Mass.: MI?' Prcss. Klima, E. 1964. Ncgation in English. In J. A. Fodor and I. Katz (eds), T h i ~S~rrrcttrr~ (!/'I1i/tlg~~itRr, NCW York: Prcnticc-I-Iall. L,adusaw, Mi. 1979. Polclrrt)~Srnsztii.ilj1 as TnIlet.cnt Sn~pcR~1rl1iun.r.. N c a York: Garland Press. -4lso distributed by IULC;. Montague, R. 1973. T h e proper treatment of quar~tificationin ordinary English. In R. Thon~astrn (ed.), Fosnial Plzilosupl~.)~. Selecled Pnpcvs (![Rirlran/ i2lor2tuLque,Neu Havcn, G ~ n n .Yale : University Press.

Index

.-I (type-shifting operation), 362, 366-8 ri(n), 19, 21, 26, 96, 124, 358, 366, 368 ti prtori truth, 150-1 operator, 150 abstraction operator, 135 acceytabilit?- in contest, 162-3, 169-73, 175 srcl mlso felicity accessibilit!- relation, 297, 320 moral, 320 accon~modation,163, 2 5 6 5 , 257-9, 259 n global, 254-5, 258-0 local, 254-5, 257-9, 259n rule of (Lewis), 16.3-4, 168-75, 3 1 1 accon~plishmentverbs, 261-2, 2635 achievement verbs, 264-5 .fir-advcrbials and, 42 activities, subdivision of, 285 n activity verbs, 26.5. 272-3 additivit~,328, 332 adjectivc(s) and modalit!., suc modality and adjectives null determiner and, 62-3 phrase, 292 admittance conditions, 252-8 aclvcrbs, 18 of quantification, 178-9, 182-4 temporal .fit.-adverbials, 42, 44 :ifSective, 457-8, 460, 463-4, 467-8 .4jdukiewicz, K., 32 n algebra, Boolean, 137 all, 96, 124 Allen, R., 324 alternative questions, sr.cJ clucstions, alternati~e Alternative Question Rule, 390, 413 [ ~ I ~ P ~178-81, ~ , ) I X , 184, 186-7 ambiguity, 22, 2%30, 43&2, 446, 45&1, 455 n in questions, SPC questions, ambiguity in analysis trees, 3, 21-2, 25 anaphor, null determiner and, 45-8 anaphora, 6, 225, 238-40, 243

anaphoric chains, 183 anaphoric relation, 239, 238-40 bound-\ ariable, 239 discourse, 360 resolution of; 194, 2 15, 220 n see r r k o pronouns, anaphoric cud, 106, 334-56 "And Next" operator, 269 "distributivc-rcadi~~g",35 1 < group-reading", 35 1

.

answer, 424,436 answerhood condition, 424, 426-7, 4i6, 440 anteccdcnt, 240, 243 antiadditivity, 332 anti-pcrsistencj-, srBeclctermincrs, pcrsistcnt a~ltis~ibdivisibility, 332 ( U I ) ~ ,4.55-8 rrn,))nlore,457-8 apprupriarcness u ill1 rcspcct to a fils, 233-4, 236-5 kqvisl, L., 159, 382 argument shift, 452 argument-lifting, 445-6 arlicle tlefinitc, 19, 26, 37 indelinite, 19, 21, 20, 35, 236-7, 36&8: ovcrt vs. uncxprcsscd, 366; opacity antl, 38 semantic category of; 23 1 aspect null determiner and, 62 tense and, 9 aspectual classifica~iun,324-5 verbs, bare plural and, 43 erbs, 11~11determiner and, 43 assertion, 9, 2.5, 147-61 content of, 154: effect on conlnlon ground, 1524 ncgatite csistential, 157-9

472 Index assignment of value, 181, 188 n admissible, 181 (11 IL>'IXI 11, 10.5 s m (11~0numerals (11 ~ t ~ o s/ I ,t 124 sctpn/so nun~erals atom, 136-7, 326 atomic eLent, 327 attribute noun, 370-5 predicate, 370-5 Rach, E., 3 4 , 7, 327-8, 340, 348, 350, 378 n, 400 Hach-Peters scntences. 10 I Baker, C;. I,., 382, 400, 403, 409, 414, 418 11 Ballmer, 'T.,344-5 -imr (German), 29Ik1, 3 1.3 bare plurals, 9, 371 as existential cluantifier, 36-7, 66 as proper name of a kind, -59, 68, 359 aspectual verbs and, 43 generic interpretation and, 64 indefinite plural use of, 36-7, 61-0 intonation and, 71 n mass nouns and, 70, 72 n SO-I.II//L'(/ and, hO subject 1s. object position ot; 44 sue ir/.co null determiner Bartsch, R., 4, 220 n Ijarwise, J., 0 , 123, 143, 246 n, 357, 359, 370,469 BE (operation), 365-8 ha, 357, 367, 375-0 extcnsioni~lity of, 29 oi' identit)., 30 of preclication, 30 Bcch, G., 289, 313 BECO&IF:,202-70, 285 n Behaghcl, O., 304 i ? i ~ / l ~1~ 0 l, ~38 f~, Belnap, N., 14511, 188 11, 382, 428, 430-8 Bennett, hl., 4-5, 73 n, 261, 265-6, 270, 272, 332 n, -340, 349, 370, 389, 428. 437-8 Boolean algebra, 137 nppro;lch, 144 n hierarch!- of possible denotations, 140 lattice, 137 operations, 366 structure, 369 "boosh" (Roolean n~odclstructure with hon~ogencousLernel). 137, 326 botlt, 84, 94, 124 .sr(' 11/50 determiners, presuppositional boundedness, intli\iduals and spatial, 66 branching cluantitication, 14.3

branching time, 274 7 Rrcsn'in, J., 5 I>ulctic moclnlity, 200, 3 10 ordering source. 310 Hurton-Roberts, N., 70 11 bllt, 107 C~alculusof Individuals, 128 cardinal nun~bcrs,370 Carlson, G., 4, 220 11, 330, 359, 375, 379 n Cartsun, L., 324, 328-0 Carnap, R., 1-2 Cartesian product, 24 Cartwright, H., 70, 71 n case, admissible, 18.3 cases, quantilication over, 180- 1 categorial approach to intcrrogativcs, spe interrogatives, catcgori;ll appro~ch categorial grammar, 4 category, syntactic, 18 10 category-to-t! pe mapping rules, 340 category-t!-pc correspondence, 337-42, 348-.i I, 357 CL4USJ:,262-5 c-con~mantl,220 CCP (context chnngc potontial), 2.53-7 as card tiles, 255 compositioni~li~ssig-nmcntol; 353 of complex sentence, 2.53 of conditionals, 253, 250 of negation, 2-54, 2.50 7 of sentences \tit11 free variahlcs, 250 of uni\cl.sal cluantifier, 256--7 rclation to heritage content, 353-4 relation to tr~1t11conditi~ni~l contellt (or content propert!,), 2.53-4 CG, st(- categorial granln1ar chains, ;~naphoric,183 changes of locarion, 207-8 Chicrchia, G., 4, 7-8, 330, 350, 36.3, 370 5, 378 11, 379 n, 454 choice reading, 431-2, 4.55 11 (:hornsky, N., 3, 5, 37, 1 1 I, 240 11, 4.00, 412. 414 Lhomsliyan syntas, Li~malscman~icsand, S Christopliersen, IJ., 223 circumstnn tial niodal base, gracling of; 308 111udalit?-,.301-3, 31 4 C;l:~rli, 0 Cl,irk. H., 0, 104 Clause Mate (:onstraint (Kuno ancl Robinson), 400 cleft scntenccs. H Il:.,

Index 473 CN, srr common noun coindexing, 229-30, 233, 238-9 semantically vacuous, 238-9, 246 n collective, 127 (~o/or,37 I--5 conlmon ground, 9, 151-1, 210 n status of a proposition, 160 n common knowledge, 1-51-4 cornmon noun (CN), 18, 28-9, 31 -. 'issification of, 140: MCN (mass noun phrase), 140; PCN (plural count noun phrase), 140; SCN (singular count noun phrasc), 140 comparative possibility, 290 complement of a sct, reference to, 47, 56 coinpositionality, 5 principle of, 1 concept, individual, 28, 3(k1 conclitional(s), 157, 159, 250-6, 317-21 CCP (contest change potential) of; 253-63 clausc. 183-6, 188 n contraposition (inTerence) and, 321 modality, 3 17-21 prcsi~ppositionprojection of, 250-1 semantic properties of, 250-2 scntcnce, 467-8 strengthening the antecedent (inference) and, 32 1 transitivity (inference) and, 321 conjoinable categories, 331 expressions, 421 types, 336, 122, 433 conjunction, 10, 33i-56 generalized, 334-56, 434, 436, 444 of interrogatives, 430, 444 oT NPs (noun phrases), 117 reduction, 348 rules ol; 20, 27 see also coordination, generalized conscrvnlivity, 84, 92 ~1~1' (//SO qu;lntitier(s), L'li~e~-on" consistency, 293 constituent con~plcx,23 1 interrogatii-es, 423-4, 435, 442: structure of. 450 questions, sce qucstions, ivhconstitution, 128, 135 contcxt, 147-61, 172-3, 240-53, 254-9 and non-logical determiners, 78 as card file, 2 5 5 as scclucnce-~vorlclpairs, 255-7 as set of propositions, 252

cliangc, 1.52- h, 249 -52, 254-5 defective, 152 local, 252 nondefective, 15 1 set, 1 5 1 4 , 1.58 speech, 147-01 "the fixed context assunIption", 78 continuation, 242, 244-5 trivial, 242 contraposition and conditionals. 32 1 conventional irnplicaturc, 287 11, 4 15 conversation, 162-77 rulcs governing, 162-77 conversational background, 203-0 bulctic, 296 deontic, 205 empty, 296 epistemic, 294-5 realistic, 295 stereotypical, 295 totally realistic, 295 conversational implicature(s) cancellation of, 2.50 conflicting, 250 C:oopcr, R., 3-4, 6, 143, 220 n, 240 11, 257-8, 25911, 337, 345, 357, 3-50, 370, 407, 404 coordinates event, 182 time, 182-3 coordinated interrogative, 432 coordination, 430, 43.5 generalized, 422, 4.13, 44-5 restriction on, W5 t!~k?cs, 443-4 see (t/so conjunction, gcnel-alized copula, 357 SPL, (I/SO h~ count term, relation to mass ta.111, ,726, 328.- 30 counterf~~ctual(s), 3 19 statement, 2 7 6 7 supposition, 157-8 count-mass-plural don~ain,324 Cress~xll,M. J., 1, 3-4, 8, 383, 41.5 Crossing constrain^ (Kuno and llobinson), 410 cumulative rcfi.rcncc property, 128, 130 dagger operator, I -50, 1 5 ( ~ X Dahl, 0, 49 Dai-idson. D., 2, 6, 8, 328 ( k c t/ic.io, 22, 20--10, 340 scr ~r/sononrcfercntial reading i/t YC, 22, 29-30, 346 set cilso refcrencc, rcfcrential rcading

474 Index definite(s), 2 3 3 4 , 243-1 article, 19, 26: zero, 364 NP (noun phtase), 357, 368 SLY also definite description definite clescription, 150, 159, 168-70, 234, 249-51, 2 5 4 7 , 359-61, 363-6, 368 denotation of, 169 multiple definitus in onc donlain of discourse, 168 prcdicativc reading of, 36.5 salience of; 169 semantic type of, 359-6 1, 363-6, 368 semantics of, 88, 90, 91, 124 sce rllso determiners, dcfinite tlefinitencss, 227, 234 feature, 234 Ileggau, G., 301 degrccs, as entities, 371 deixis, 193, 240 see ulso pronour~(s),deictic use of (/elink (operation), 369-7 1 Delorme, 70 n deinonstratives as definite determiners, 97 as strong determiners, 96 denotation, 24-5 possible, 24 see also extension deontic conversational background, see conversational background, deontic deontic modalit)-, 296 description operator, 131, 135 DET, see determiners determiners, 241, 357-8, 367-8 definite, 97, 364--6: as positive strong determiners, 1 19 denotation of, 8 1 determinerless NPs, 211 logical YS.non-logical, 78 persistent, 105, 120 presuppositional, 81, 93-5 the intersection condition for, 102 trivial, 95 1s. quantifier, 77, 82 weak vs, strong, 9, 95-5, 100-3, 120 weak, 367 S E E ril.~o definite description; gcneriilized quantifiers and the language L(GQ)); quantifiers rs. determiners; universals, semantic diagonal proposition, 119-50 cliagonalization, 158 direct object, lexical, 7 1 n dircct questions, SCE indirect questions

discourse referents, 195, 197, 208-0, 218 Discourse Rcprcsentation, set DR Discourse Reprcscntation Structure, see DRS disjoint refcrcnce, 233 disjunction, 2.5 1, 259 of interrogatives, 131, 436, 144 rules of, 20, 27 distributive, 136, 140 predicate, 132, 135-6 Dom(F), 229 domains algebraic structure of, 361 model-theoretic, 362 of discourse, 168-9 of entities, algebra structurc for, 35 1 of eventualities, structure of, 327-8 uf individuals, 137: structure of, 325--7 of sequences, 228, 233, 235, 237, 241 donkey sentences, 189, 197, 201, 201, 206, 218-19 truth conditio~lsof, 100-1 Doron, E., 379 n Doublc Dislocation Constraint (Kuno and Robinson), 4 1 1 Dougherty, 70 11 Dowry, D., 3-4, 7, 42-3, 70n, 71 n, 328-9, 332 n, 337, 340, 342, 348-0, 357 DR(s) (Discourse Representation(s)), 1g4, 21 1 as mental representations, 192-3 for conditionals, 197-9, 202, 210--12, 21 4- -10 indefinites in, 214 principal, 203, 2 14 pronouns in, 215 proper names in, 214 rulcs 01- formation for, 194, 207 subordinate, 204, 2 12-13 union of two, 2 13 universal quantification in, 200-2, 2 12-16 DRS (Discourse Representation Structtrrc), 200, 211, 24611 complete, 214-15 partial, 213: extcnsioii of; 214 rulcs of construction for, 214 dual, of a quantifier, sep quantifier, dual of dubitative vcrb, see verb, dubitative dynamic logic, 6 d j nanlic semantics, 5-6, 9 errch, 96, 124 Ebcrle, li., 137 echo questions, 389 Egli, U., 247 n embedded interrogatives, 445 embedding types, 44543

Index 475 emhcdding, of questions, see qucstions, embedding emotive factives, 383 empty conversational background, stJe conversational background, empty l!,nglish, see "fragments", syntactic, of English ensemble, 128 entailment, 31, 32 n as general proccss, 4 3 3 4 between interrogativcs, 422, 426, 428, 432-5, 437, 441 downward, 46 1-9 revcrscd, 461, 464, 468 upwiil.d, 46 1-3, 467-9 entity, 24 cpistcmic acccssibiliry relation, 297 conversational background, ser conversational background, epistemic modal base, grading of, 306 modality, 295, 306, 310 Erteschili, N., 408 Evans, G.. 6, 191, 205, 22011, 24611 events, 145 n, 3 2 t 5 , 327-8, 332 and processes, 324, 327-8: algebra of, 327-8 as entities, 37 1 atomic, 327 plural, 327 singular, 328 stages and, 64-70 subevents, 332 eventualities, 327-8 domain of, 327 properties of, 328, 332 ez'er, 157-8 iJoer:y, 19, 26, 84, 94, 96, 110, 124, 366, 460, 464, 466-7 vs. ??iOSl, 77 scc cilso quantiliers, universal r~:c>i:)/ihing, 87 L~.v(~c//J 71, 124 SPE also numerals e.vili.lly owc, 367-8 existence and identity criteria, 139 implicature, 415 predicate, 135 csistential quantifier, 359 sentences, 9, 9-5-6, 1 I S statcnicnts, negative, 157 e.t*rsl.\., set existence, yredicstc cxprcssions, basic, 19 extension, 24, 130

Ext (extension of). 232. 235. 241 rnixecl, 132 extensional operator, 1SO cstensionality, null detcrn~inerand, 47. 67 factives, emotivc, 383 Faltz, I,., 315-6, 340, 342-5, 366, 455 n familiarit!. theorv of dcfinitcness, 223, 227, 2334 Fauconnier, J., 160, 469 f-command, 360 features, 233-4 definiteness, 234 fklicity, 17+5 / r w , 77, 94, 96-7, 1 10, 1 17-18, 124 n jiv, 96-7, 110, 124: qrriii' LI j t ? ~I10 , lile (file change semantics), 225-6, 234, 255 card, 225-6, 240, 255-6, 259 n change, 241 : operation, 23 1, 233; potential, 227. 231-2, 234, 236, 2 4 g I ; result, 23-54), 243; rule of, 234, 245 satisfaction of, 228-9, 235, 238, 245 sequencc (of file cards), 228, 236, 238, 241-2 truth of, 228: Wse, 228, 236; true, 228, 235-6 update, 226-7, 2-71, 240-1, stc also file change Filln~ore,C., 282 filter, principal, 368-70 f i t ~ i79 ~~~, Finnish, 417 n first-order logic, quantification in, 77 SCP IIISO quantifiers, in standard first-order logic o d quantifiers, nun dctinablc- in terms of Lirst-order logic fixed context assumption, 78 see olsu context flexible analysis of interrogativcs, 430, 439 flexiblc grammar constraints on, 452 overgeneration by, 450-3 Flynn, M., 340, 377 F'odor, J. A., 1-2 Fodor, J. D., 3, 6, 460-1 formal pragmatics, 5 , 8 formal semantics historj- of, 2-7 Montague's papers in, 8 "fragments", 7 complexit!. of, 113 syntactic, of English, 18-73 Frege, G., 1-2, 378 n function characteristic, 25 "function-argument flip flop", 340, 447,4.5.5 n functional application, rule 01; 19-20, 26 ,

Index 477 CCP (contest change potential) of, 258 description, 170 indexing of, 258 logical form of, 258 noun phrase, 223 wide-scope, 347 n see also noun phrase, indefinite indefiniteness, 227 of quantifying NP, 259 n indexicalitp, 0 indices on NPs (noun phrases) as variables, 2301 indirect questions, 382-3, 395-6, 399, 402, 101, 406, 4 12 category ofi semantic, 384-8, 412-13; syntactic, 384, 380, 412 convcntionai implicature oi; 41 5 denotation of, ser indirect questions, category of, semantic game-theoretical semantics of, 385 relation with direct questions, 383, 406, 414-15 rule for embedding, 302 "individual sublimations", 367 individual(s), 21, 3 1, 325 atoms, -326 domain of, -325-7 generics and, 58 join. 326 hind versus individual denotation, 56, 59-60 matter that corresponds to, -335 part, 130, 135, 326 plural, 325 possible, -33 n spatial boundedness and. 60 sum, 129-31, 136 individuation, 332 indivisibility, 328 inferences, semantic, ;is c~idcncc lijr a scnlantic theory, 112 inhercnt modalit!., sac, moclalit!., inherenr intension. 24, 30 as normal unstructuretl meaning, 427 intensional logic, 3, S, 23-5, 27. 29 cnriclling, 359 SlJ'>

lllso

IL

intensional object, propcrty theory of. 4.54 semantic analysis of, 453 intensional opcrator, 151) intensionalit!., null determiner and, 47, 67-8 interpretation, 24 logicall! possible, 28 model-thcorctic, 4 6 3 4 interpretive semantics, 3-4

intmrogativc(s), 32 n as denoting sets of propositions, 430-7 as distinct tivrm question, 423 as 11-place relation, 424-5, 441 atomic, 438-9, 441, 443 categorial approach, 424-8,436,440,448,45.5 n constituent, 423-4, 435, 442-3 coordinated, 432 denotational, 428 disjunction of, 431, 437, 444 domains for, in natural language, N7-8 cmbcddcd. 445 entailment in, sar entailment flexiblc anal!~sis, 430 propositional approach, 474-8, 140, 448-0 sentcntial, 4 2 3 4 , 428, 435, 442 syntactic category and semantic type ol; 425 types of, 434-5: t! pe shifting analysis of, 420, 449451 sea olso questions interval, 26.5-7 1, 276 bounded, 266 closed, 266 final boundar!- of, 206-7. 259 for branching time, definition of, 27h initial boundar! of, 266- 7, 269 see illso subinterval intonation. 417 n bare plural and, 7 1 n intrinsic ordering, 13 1 intuitions, semantic, 112-1 3 invariant prcdicatcs, 129, 136 inr-ited inference, 272 i o ~ n(operation), 359, 362 0, .308 i-part, srr individual part islands, syntactic, 400, 406-9 i-sum, sre indi\citfu:~lsutn Jackendoff, R., 1-2, 400 Jacobson, P., 4 Jsnsscn, T, hl. Y.,5. 14.3, 145 11, 37.5 Japanese. r~h-in-situ in, 403 Jenkins. L., 115 Jcspcrscn, O., 223, 410 n Johnson, hl., 7 Johnson-Tird, P., 2 join operation, 131, 326-7, 330-7 scmil;ttticc, 131, 137, 326-7 Joshi, A., +.i Knmp, I-I., 0 , 8, 159 n, 246 n, 247 n, 325, 327, 350-60, 308-70. 378 n, 370 n Kanger, S.. 2

478 Index Kaplan, D., 2, 5, 8, 32, 123, 160 n, 246 n Kaplan, K., i Karttunen, F., 7 Karttunen, L., 4-7, 189, 220n. 224-5, 227, 24611, 249-55, 257-8. 25911, 280, 391, 415, 418 n, 428, 436-8, 455 n, 460 n Katz, J., 2, 414, 4181-1 Kcenilin, E., 4-5, 33.5-6, 340, 342-5, .i66, 382, 455 n Kenny, A., 332 n key type, 434, 439, 417, 455 n fi)r atomic interrogatives, 441, 447, 450 kinds, -330, 370 bare plural and, .59 individual versus kind denotation, 56, 59, 66 null determiner and, 53-70 syntactic expression of, 56 Klein, E., 7 Klima, E., 4.5-8, 463 kollelitionm, 128 X+'nrwn (German), 301, 309-10 deontic use of, 310 Kratzer, A., 5, 7, 173, 176 n, 220 n, 246 n, 259 n, 295 liritla, h'i., 8 kripkc, S., 2, 150-1, 246 n Kuno, S., 382, 400, 409, 41 1-12 Ladusaw, W., 7, 105, 464 I.akoff, G.. 1, 407 Lainbek, J., 347 I,angaclicr, R., 400 language of thought, 2 T.,arson, K.,2, 6, 372 Lasnili, H., 220 11 lattice, 137 atomic, 137 Boolean, 137 complt-re, 137 J,a\\;ler, J., 72 n Lewis, D., 1, 3, 5-6, 8, 159 n, 220n, 246 n, 254, 274, 298, 328, 371, 382-3 Lewis, S., 382-3 Lexical Fullctional Grammar, 5 lexical insertion rule, 86 Icxicnl item, 249-50. 2.53-4, 2-56, 259, 250 n content property of, 250, 253-4, 259 n heritage properr!; of, 250, 252-4, 259, 250 n presupposition property of, 250, 253, 259 n lcxical rules, 361, 36.; L T (Logical Form), 2. 5 see N I Slogical ~ fornl LTG, see Lexical Functional Grammar licensing

of downward entailnicnt, 401 of negative polarity itcni, 457--61, 467 -/ir.l~(Gcrnian), 200- 1, 3 13 / ! / I (operation), 362, 364, 366-8 lifting, -361 "likcness" relation, 270-7 likcness of worlds, 273-4 linguistic knowlcclge, world knowledge and, 72 n IiizX~(opcration). 300-7 1 I.inh, G., 3, 7, 324-31, 33211, 351, 367-70 logic as part of linguistics, 1 14 dynamic, 6 intensional, srz intcnsionnl logic niotlal, 148 logic of plurals and Inass terms, 135 model for, 137 theorems, 139 logical compatibility, 293 conscquencc, 293 equivalence, 28-9, 427 logical form, 2, 5, 10, 227, 229-30, 2 3 2 4 , 230-7, 241, 24.1-4, 251, 258, . s t t LI/.
inakc up, sre constitution t t i ( ~ n ) ~76-7, , 04, 00, 08, 117-1 8, 124 'ind the intersection condition for determiners, 102 ( i / t ) / i t i i t c l l ~ 111(11i,)~, 70, 10-5, 124 ~ 1 t ~ O l i t l ~ ~ 1 1IJfl17.)1, / 7 / ) ~ 105 mass noun(s), null determiner cmd, 46, 71 n,72 n opacit? and, 71 n plirasc, 368-7 1: prcdicativc, 370 mass predicates, 370 mass term, 370 correspondent, 132, 136 nominal, 120-30, 145 n predicatikc, 130, 132, 135, 145 11 relation to count term, 320, 328-30 mass-count distinction, 324 niatcrid equivalence, 131 fusion, 130-1, 136 implication, 3 18 part, set ni-part predicatc, 136 materialization function, 128, 137

Index 479 May, R., 246 n McCawley, J., 5, 407 McConnell-Ginet, S . , 7 MCN (niass noun phrase), sre common noun, classification of; also niass noun me'ining lexical vs. constructional, 308 postulate, 417 n, 418 n psychologistic vs. nan-psychologistic \;icw of, 1 i.efercntia1, 225 structured, 427 truth-conditional, 189, 225 meaningful expression, 31-3, 27, 110 meaning-preserving transforniation, 382 mcct, 336-7 ni-equivalent, 136 Meseguer, J., -37 1 , -379 n LUG,sc>i7Montaguc grammar Milsarli, G., 9, 63, 65, 72 n, 95 minimal parts, 134 mixed extension. 132 Aiiy;lrd, s., 7 m-join, 326 ~nodal auxiliar>-,29 1 basc, 207-321 : grading of, 306--14; normal, 300 epistcmic, deontic use of; 310 logic, 148: two-diniensional, 150 operator, 150, 2.59: one- or two-diniensional, 150; of propositional necessity, 1.50 reasoning, 301--6 relatioa, 203 statement, 276 lcrhs, 173 modality, 0-10, 17.;-4, 259 2nd acljccti\.es, 290, 202 circumstantial, 30 1-3, 314 conditiontll, 317-21 dcontic, 173 cpistcniic, 173, 294, 302-3, 306, 310: and circun~stanti;ilcompared, .301-0 inherent, 289 relative, 173-4, 176 n root, 301-2 . ~ i ) 111~0circumstantial modalit!niodals, S P E modality or modal auxiliary model intensional, 24 of semantic interpretation, 227 par~ial,189 niodel-tlicorctic semantics, 2, 0-7, 59 moment, 300 moilotonc decreasing, 465-0

increasing, 464-9 rnono~onicity and NP conjunction, 305-7 Monotonicit! C:onstruint, 100 . r i ~quantifiers, monotonicit! Montague, R., 1-5, 8, 17, 22. 37, 59, OC-.i,67, 71n,76, 114, 145n, 191, 200,220n.2(,3, 273, 277, 325, 330, 3.3542, 348-9, 353 n, 358-60, 364, 366, 370-1, 375-6, 377 n, 37811, 382, 393, 464 category-to-type mapping rules, 349 11 rule of VP-quantification, 89 treatment of NPs (noun phrases) 13, 103 uniform categor! -type corrcspoiidcncc, 341- 2, 348 rcr also PTQ YIontague grammar, 1, 4-5, 358, 364 syntax of, 206--8 h4oortgat, M., 370 11 moral accessibility relation, 320 hloravcsili, J. h.1. E.. 17--18 Ailorgan, J., 5 ttrnsl, 70-0, 94, 96, 117-18, 121, 124 vs. CTL'I:)', 78 sc?r also quantifiers, lion-dcfinahle in terms of. first-order logic Mostorvshi, A , , 75 Mourclatos, A,, 324 movement, syntactic, constraints on, 400 rn-part (milterial part), 131, 137, 326. 330 11-term, 139 multiple quantification, 145 n multiplc rr~lr- clucstions, scc questions, multiple n>Aniultiplication, succcssi~~c, 185 mutual hnon lcdge, 1.5 1 19, 33 11, 25-0 necessary proposition, 1 50 nccessarl- truth, 150 ncccssity, human. 298 negation, 223, 230, 245-6, 254, 256-7, 457 CCP ofl257 defining ncw quantifiers in tcrnms of, 99 nionotonicity reversal by, 99, 12 1 niill detcrnminer and, 30-40 operator, 150 neg;lti\ e polarity (item), 10, 457-8 i~cpati\-cexistential construction, 157-9 negati\.c queslions, seep questions, negative ~rc,itlii~i., 84, 04, 00, 124 $1>cTrilso dctcrminers, prcsuppositionill Nerbonne, J., 7 n t i . ~ ~178, . , 18 1, 183-4 i~r~ic~ss~irit)~,

480 Index Ncwine!.er, F., 2-3 1 1 0 , 84, 94, 96, 124, 400, 464, 460 t/or?r (operation), 362-3, 368, 371 nonlinalizi~tion,359, 363, 371-4 Chierchia's theory of, 371-4 nonrcferential reading, 22, 31-2 see also iie (/ic10 nonrigid designator, 1 50 nonrigid individual concept, 375 normal nlodal base, 300 tiot, 108 / I O I I P ~ I Z ( ~ ~ ~ (German), C ~ ~ ~ ~ ~ I ~ L296.5 ' noun phrase (NP) as generalized quantifier, 81 conjunction of, 1 17 tiefinite, 357, 364-8 distinction between CN and, 362 empty, 230 first-order translations of, 80 generic, 5 1 , 58, hO indetinite, 3.59, 36&8. 370, see rrlxo indefinites interpretation o f ; 357-9 M o n t a ~ u e ' streatment of, 103 negation of, I08 of type P , 358-7 1, 378 n, 379 11 of type ((e,t),t), 357-76, 378 n, 379 n, see 11/.(0 generalized quantifiers parallels between scmaiitics of interrogatlvcs .md, 423, 425, 438 prcdicative, 357, 36&1, 365 quantiticational, 357, 3'71 referential, 3.57, 371 semantics of, 8-9 synractic distribution of in English, 70 syntactic structure of in English, 77, 86 types, 357-79 xc'e ([/so universals, senirlntic No\-elt!-/Familiarit!. Condition, 233-5, 243, 24.5 izonl, 150 n NP. see noun phrase null determiner adjcctires illld, 62-3 acli-erhials and, 43 anaphor and, 45-8, 51-3 as an~higuousderermincr, 49-50 as existential quantifier, 49. 61, 66 as rigid designator, 67 al 35-6, 49, 57, 63 as ~ ~ n i \ e r squantifier, aspect and, 62 hare plural versus, 35-74 evtcnsiol~alcontext and, 47 generic use of. 35-7, 48-58, 63 in coordinate strucrures, 45-8

indefinite article and. 37-8, 40- 1, 48-0. 61 -9 intcnsionality and, 47, h i 8 kind denotation and, 53-70 mass ~ i o u n sand, 46 negation and, 30-40 opacity and. 38-9, 5C.5, 67 prepositional plirascs and, 03 4 proper namc and. 60, 06, 08 scope properties of, 30-45, 68-0 stages and, 64-70 subjcct i s . object position, H, .SO, 53, 62 numcraks, 84, 94, 06-7. 124 adjectival intcrprctation ot; 370 as determiners, 370 see (~1st)(11 /errs/ ii object language, 7 1 n object plural, 130 singular, 130 y/; 07, 116-17 c!/i~n,178, 181, 183, 187, I88 n one-dimensional modal operator, 150 opacity existential qu;intitication and. 38 in coordiniite structures, 4.5-6 indefinite article and, 38-0 kind denotation i~nd,54 mass nouns and, 7 1 n null deterniincr ancl, 38-9, 54- 5 , 67 transparmcy ancl, 38-9, 45-8, 54 operations, Boolean, 360 operator, 220, 241-2 II prtori truth, 150 abstraction, 13.5 daggcr, 150, I -56 8 description, 131, 135 extensional, 150 intensional, 1 5 0 one-dimensional vs, ti\-o-dimcnsiond, 1-50 square-dagger, 1 50 star, plural operator, I40 temporal, 150 11 upside-down dagger, 1 SO 11 or, 106, 334-56 ordering semantics. 298 ordering source, 297 321 packaging, 328 byair-list reading, 43(k2, 455 11 Parsons, T., 3-4, 06, 22011, 370 part individilal, 130, 135 material, ste nl-part

Index 481 partake, 133, 135 Postal, P., 2, 60, 407, 414, 418n Partee, B., 3-5, 17, 31-2, 71 n, 72 n, 73 n, 220 n, p-part, 328 261, 265-6, 270, 272, 340, 357-8, 375, practical inference, 3 1C17 378 n, 389, 423-5, 439, 446, 45 1-2, 455 n pragmatic polarit!- itcni, 409 partial function, 1.55 p ~ ~ g m a tprinciples, ic 147-61 partial ordering, 137, 326 pragmatics, -5-6 l~artiallyordered set, 137 formal, 5 partition, 442-3 philosophical, 0 qucs~ionas, 439-40 pr-erl (operation), 302-3, 308, 371 partitive puzzle, 329-30 predicate calculus, 76, 205 part-whole relation, 320 predicate(s), 230, 232, 235, 24&1, 240 11 c 1characteristic" 1,s.event rcacling of, 5 0 PC:N (plural count noun phrasc), 1-10 Pcllctier, F. J., 328, 370-1, 37911 classification of, 328 perfecthe-imperfectix contrasts, 328 condition, 246 n performa tive(s), 174-5 distributivc, 132, 13.;-6 and non-performatives, 174 existence, 135 explicit, 174 in\ariant, 129, 136 hypothesis (for indirect questions), 382-3, material, 136 414-15 nominal, 23 1 sentence, 174 plural, 131, 135 utterance, 177 n proper, 131, 136 terb, .382, 414..15 predicative Perry, J., 6 mass term, 130, 132, 13.5, 145 11 persistence, s t p detcrnlincrs, persistent noun phrase, S P P dellnite description, Peters, S., 5 , 240--55, 257-8, 25911, 340, 342, lvedicativc reading of- noun phrase 349, 367, 391, 410, 415, 41811, 469n preposition, 18 pied-piping, 395 intensional, 30 Pinlcal, &20-5 I., phrascs, null tletermincr and, 03-4 plural present progrcssivc, null determiner and, 02, ct-cnt, 327 05 indi\.iduals, 325-7, 351, 369-70 presupposition, 5-0, 0, 150, 162-77, 170 11, 234, opcr3tor, 135 240 11, 249-59 predicate, 131, 135-0 iiccolnmodation of, 1A3 plurality principle, 134 as set of possible norlds, 253 contraction, 134 associated with cluantificrs, 93-5, wv. rrlso ',. cs" expansion, 134 SIL\ sj-n~mctry,134 cancellation of, 2.50-1, 255, 257-8 plurals, 32.5-7, 308-7 1 contradictor!,, 251 barc, set barc plurals cxistcncc, 33'9-5 1, 364 distributive readings of, 367, 371 f i ~ scorc, r 167--8 group readings of, 367 in qucsrions, 415, 418 n null determiner and, 42 kincmatics of, 163, 17.5 polarit). itcms, 105 lack of, 162 polarit!. questions. st9cJquestions, .)ws-tlo of definite description, 249-50, 2.52 Pollard, C., 4 of NP interpretations, 357, 304-6 portion of matter, 132, 130-7 of universal quantifier, 356-8 poscl, set partial ordering, partially orclered set p1;117 and, 175-6 possibilit>, comparative, 299 projection of, 249-59 grades of, 296, 3 14 projection problem, 24011, 415 human, 298, 316 rules governing, 103 slight, 298 semantic property of, 250, 253 possible situation, 147-8 speaker, 147, 151-5, 1.59 possiblc world, 6, 147--61,257, 259, 425-39 uniqueness, 304 semantics, 293 Prince, E., 5 16

482 Index principal ideal, 137 principal ultrafilter, 88 priilciple of compositionality, 1 process(es), 324-5 verb, 328 processing constraint on types, 348 semantic, 220 n PROG, 262-5, 269-70, 2 7 t 6 , 283, 28611 progressil e tense (continuous tense), 201-2, 269, 273, 285 n progressive, -329-30 furusate, 277--83, 286 n future, 286 n imperfective, 280 projection problem (in presuppositions), 246 n, 415 pronoun(s), 19-20, 32, 230, 234, 238-0, 21611 anaphoric, 191-2, 193-7, 215, 22011, 240, s t c i11.w anapliora bound variable, 191, 204-5, 358 deictic and anaphoric, 159 deicric use of, 191, 193, 195, 2 3 9 4 0 cl-type, 192, 205 gender agreement of, 19.5-0 of laziness, 32, 192 personal, 191, 197, 205 quasi-deictic, 240 translated as varinblcs, 89, 124 proper cnibcdding, 189, I9 1 and conditionals, 198 propcr inclividunl sum, 131, 136 proper name. .see proper noun proper noun, 28, 124, 157, 24611,422,438,455n a n ~ the l so-L-NIIEJconstruction, 60 as generalized quantifier, see generalized quantifiers, proper names as as type t p , .160 hare plurals as, 68 in existential senrences, 96 null determincr and, 60, 66, 68 propcr plural predicate, 1?. 1, 136 property, 2.5 entity-correlates of, 363, 372 null determiner and, 63-5 property-correlate in type r , 359, 372, set9 crlso properties, entity--correlates of set, 111111 determiner and, 65 stages and, M-70 l-wopel-tv theory, 454 iind interrogatives, 428 proposition, 147-61, 231, 235, 2.37, 216 n atomic, 231-3, 235, 243 closccl, 240

diagonal, 149-50 molecular, 231-2, 23G5, 241, 245 necessary, 150 propositional approach to interrogatives, sccl intcrrogatives, propositional approach propositional attitude, 148, 150 n verbs, 259 propositional concept, 147--5 1, 150, 1.58 Proro-Question Rulc, 389, 41 3 proto-questions, 389-90 see ~l.s!\'oProto-Question Rule pseudoclefts, 375 PTQ(Montagucls "The Proper Treaunent of ~ 140, Quantification in O r d i ~ i a rEnglish1'), 263, 283, 335.42, 350, 367-8 treatment of scope ambiguity in, 393

QR, -\.iBrquantifier, Q R quantification, 20, 3 1, 240 branching, 143 computational models lbr, 10t.5 existential, 170, 201-2: and negation, 40; and opacity, 38 multiple, 145 n restricted, 199 rilles of; 20, 27 syntactic rulc for, 80, XCP ~11.vogcneralizctl quilntifiers, and the language L(G0J uni\-el-sal, 19, 20, 242-5: andlir,-advel.bials, 42 cluantilicational logic, 238 quantilicational supcrlativcs, 460-1 quantified NP, lowest type For, 422 yuantiller(s), 224, 230, 238, 245, 24611 and NP-negation, 109 as "sieves", 93-5 cardinality, 75 CCP (contcxt change potenti;il) of universal, 2 56-7 dual of a, 109 existential, 76, 79, 84, 236-7 gcneralizcd, .we generalized cluantifiers in standilrd first-order logic, 75 in standard first-order logic as translations ol' English NPs, 80, 83 "lives-on", 84, 92, 119, srr also conscrvativity lowering (in Genel.ativc Scrnantics), 107 monotonicity, 97-103: and N1'-conjunction, 108; and NP-disjunction, 105, 108 nun-definable in ternis of first-order logic. 76-7, 121-2 over cases, 180-1 over events, 179 over times, 178 processing of, 104, 1 1 I

I 1 I

I I

I

i 1

I

Index 483 proportional, 462 QR (Quantifier Raising), 5 scope of, 225, 238-9 syntactic structure of, 77 topological, 73 universal, 76, 79, 84, 251, 256-8, 461: universally quantifying NP, 243 unselective, 180-2 vs. detcrmincrs, 78 witness set for, 103, 105 quantifying in, 393-4, 407 quantifying NP, 238-9, 246 n unix-ersa1l;v quantif? ing NP, 243 quantifying term, 3 1 qunntitv (of matter), 130 Question Embedding Rule, 392, 41 3 question-answer relation, 423-5, 440 questions, 10, 422, 382-420, 431-2 alternative, 3 8 3 4 . 390-2: ambiguity of, 302 ambiguity in, 392, 400-6 and quantifying-in, 3 9 3 4 as partition, 439-40. 442 direct, see inclirec~questions ccho, 389 embedding, 392-3 indirect, srr indirect questions multiple i d - , 397-8, 400-4 negative, 4 15, 4 18 n proto-. S ~ L ' proto-questions search, .set q~iestioiis,~ d m/~-, 38.3-4, 388-0, 395-4 12 r?>/Iu~/trr., 391, 39.5-6, 390-400, 418n )tcr.\-rro. 391-2, 41 5 , spe r~lsoTcs-No Question Rulc seiJ also Alternative Ques~ionRule; interrogative; It'h-Quantification Rule Quine, W., 30, 73 n, 246 n

eq~~ivalence, 1 35 in intension, 25 partial order, 13.5, 137 preorder, 135 reflexive, 135 symmetric, 135 transitive, 135 relational type for interrogati~e,448 relations bctwccn intcrrogativcs, 425-6 relations, temporal, 327 rdative clause, 142, 395 formation, 207, 2 13 reduced, 116 svntactic structure of the English, 86 rclativization, 3 1 Revised Estendcd Standard 'Theory, 246 n rigid dcsignator, 156 null operator as, 67 Robinson, J., 382, 400, 409, 41 1-12 Rodman, R.. 4, 407-8 Rohrer, C., 34 , 324 root modality, 302 Rooth, M.,-3, 8, 330, 357-8, 378n, 430, 447, 451-2, 4.55 n Ross. J. R., 353, 305, 406-7 Ross's generalization, 4.59 rules, 165 conjunction, 30, 27 constitutitc, 16.5-7 disjunctions, 20, 27 for file changc, 234 functional application, 10-20, 20 lexical, 361, 303 of sign, 20, 27 of tl'IlSC, 20, 27 quantification, 20, 27 regulative, 165 c rulc-b!--rulev interpretation, 3, 205, si,iz a l s ~ ) L

rcalistic conversational background, set con\-ersational bsckground, realistic recursive definition, 23--5, 3.3 11, 232 recursive set of rules, 2.36 redundancy rules, t!pe-lifting rules, 3.39. 348-9 Reed, A . , 361 reference, 223 - 5 , 240 disjoint, 23.1 nonrefcrcntial/~~oiirefcrring, 22.3 referent, 223. 227, 240: discourse, 2 2 4 4 , 227 referential reading, 22, 3 1-2, see (//SO ilt re rcfcrcntiality, 227 referring cxprcssions, 223-4 Reinhart, T., 246 n, 378 n relation, 25 antis.l;nimetric, 135

coinpositionality scniantic con~position,4hC-5 Russell, B., 188 11, 230 Russcllian anal>sis, 236 Ryle, G.. 202 S (Sentence), syntactic structure of in I
86 Sag, I., 4, 6-7, 340 salience, 169-70, 176 n comparative, 169-70: ranking ol; 169; rule of' accommodation for, 170 contextual. 240 contcxtuall! dctcrn~inctlranhing of, 160 kinematics of', 169 shift of, 170

484 Index SatlF), 229 satisfhction condition, 238, 246 n set (of ;i file), 229-45 SPP r~lsofile, satisfiction of Scha. R., 379 n Schabcs, Y., 5 Schiichter, P., 70 n Schcin, B., 6 Schubert, L., 370, 379 n SCN (singular count noun). 140 scope, 30, 229, 240, 246 scnrckccping. 162-77 con\-ersational score, 166-9, 17 1, 173-5: component of; 166-75; dependence, 169; function, lbi-7; kinematics of, 164-8 in a baseball game, lh4-6 language gamc, 168. 172 mentat scoreboard, 167 rules go\crning, 166-8 Scott, D., 6 search questions, SLY cluesrions, mhSegal, C;., 6 Scgcrberg, K.,159 n s~lrlon~, 178, 181, 183, 188 n ''s~nm'' (semiintic transparency), 37.5 semantic catcgorics, 220-3 1 sanantic competence, 1 semantic t!.pes association to syntactic cntegories, 338-42, 348 of interrogatives, 425 scmi~ntics carcgorial approach, 424 Diividsonian, 6 d.namic, -5-6, 9 epistcn~olog!- and, 58 generative, 3 4 interprc1i1-e, -7-4 model-tllcoretic, 2, 6-7, 50: il11~1psj-cholog!, 112; vs. representational, 2 of inren.ogatives, 421, 423 possible-~vorlds,203 propositional approach, 424--5 situation, 6 semilattice, 137 ioin, 137 sentence ildverb, 292 sentcntial interrogative, 423-4, 442 Se~~tcntial Subject Constraint (J. R. Ross), 407 sequcrrcc, scJr filc, sequence sequence-world-pairs, 2 5 5-7 sert~i-(11, 97, 1 24 Shicbcr, S., 5 Siege], M., 5 , 63

sicvcs". 03-5, 118 S ~ ilfso C dctermincrs, presuppositional o-tcrnm, 142 sign, rules of, 20, 27 Siliorski, R., 137 singular event, 328 sing-ulnr object, 1.lO situation, 1 4 7 8 semantics, 6 slight possibilit?, 298 Smabq-, R., 247 n Smith, C:., 71 n Smith, P., 21 .~O-c~ll~cr/, 60 Soames, S., 5, 25 1, 2 5 0 n .rout[), 84, 94-7, 10.5, 1 10, 360, 368, 460, 464, 466 S ~ Y NISO ? quantitiel.s, existential ~.ort/etlrirlg,87 sonre/it~zes,178, 181, 183-4 sort-shifting operators, 370 spoakcr prcsupposition, 147. 1.5 1-5, 159 specch act, 145- 6 1 speech context, 147-6 1 square-dagger opcr;ltor, 1 50 stage cvcnts and, 64-70 individuals and, 64 -70 11~111 dctern1incr and, 04- 70 Stalnilkcr, R., S 0, 8, 159 11, 246 n, 252- 3 star operntor, we pluri~loperator. 141 state, 325 null determiner and, 03--5 Stein, M., 7 stereotypical conversalionat background, srJc conversational background, stereotypical Stockwcll, R., 37 Stokhof; M., 6 18 strict implication, .i Stunll.,, Ci., 37.5 subdi\ isibility, 632 subdomain, 332 subinterval, 26.5-6 final, 206, 269, 273 initial, 266, 273 proper, 260 Subrahmanyam, R., 5 subscc~uence,235, 242 substance, 130 subslance name, 145 n supervaluation, 275 Suppcs, P., 17-18 supposition, 157-9 suprcn~um,137, 330 Sweet, I-i., 37 LC

Index 485 syn~acticcategories associ;ltion to scn~antictypes. 338-42, 348 of interrogntives, 425 syntactic rule, 19-21 s! n tax autononious, 5 integiltion of semantics with, 3-5 Montaguc's, 3 sec nlso categorial grammar; C:homshy;zn syntaa; GB; Generalized Phrase Structure Grammar; EIead-Driven Phlxse Structure Granimar: Lexical Functional Grammiu-; Tree-:idjunction Grarnlnilrs 'TAGS (Tree-4djunction Cir;~rnmars),4 target language, 7 1 n 'Tilr~hi,A , , 1-2, 114 Tedeschi, 1'. J., 26.3 temporal operator, 150 n reference, 14.5 n relations, 327 tense future, 27.5, 277-8 generic intcrpretiition and, 62 null determiner and, 62 progressi\ c, 261-2, 209, 273, 285 n rulcs of, LO, 27 sequence of; in discourse, 192 ter Meulcn, 370 term phrases, 349 tcrm, restrictive, 180-7 /hr//, 124 tllc~,10, 26. 3.55, 3 0 4 6 THL ( o ~ c r ~ t i o n304-6, ), 368 theory of spccch, 147 I/II.S, 124 Thomason, R., 4, 8, 275-7, 281, 380, 395 T I T I , (the logic of P T Q ) , 140 extended (TI?'L1),140 /or//orroa>,280-1 topology, 77 totally realistic con\.ersational bachground, see conversational background, totillly rcalistic tritnsfbrniation. ~~~eaning-;-preservi~~g, 382 t~nsfhr111ationiilrules, 37, 229 transitivitj , inference in conditionals, -721 translation, 25-9, 33 n, 88, 113-14 trllnsp;wencj-, sire opacitjTree-.ldjunction Graililnars, scr 'l'P1Gs truth L l pr;/11.;, 1 50- I iund clcnotation, 140 conditions, 227-8, 230, 240-1, 243: absolute, 6

criterion, 236, 241 definition of, 25, 189, 201, 203, 216-20 logical, 28-9 necessary, 150, 1 -56 of a discourse, 101 value, lack of, 102, 236 n l u c gap, 85, 155 Turkish, rvh-in-situ in, 40.3 Turncr, R., 8, 220 n, 378 11,370 11,454 two-dimensional matrix, 149-5 1, 1.56, 158 two-dimensional tnodal logic, 150 t~vo-dimensionalmoditl operator, 1.iO t!-pc-driven translation, 357 type-lifting rules, 348-9, 359, .iOl, 376 tppc(s), 23 association to syntactic categories, 338-42, 348 basic, 344 conjoinahle, 336 for coordination ancl cmbcrlding, 44.3 0 for interrogatives, 434 5, 4.78, 441 highest, 358 lo\vest, 338-42, 348: proccssing constraint, 341-2, 348; processing strategy of'tr!.ing first, 359; psycholinguistic atlvantages 01; 341-2 niarkcd and unniarhcd. 302, 364 semantic, unifonn, 3-53 simplest, 350 theory, 335-42 t\\ o-sortecl, for inte~.ropati\-cs,441 t! pe-lifting rulcs, sc,c t?pe-lifting rulcs s r trlso ~ kc! type; t!-pe-shifting tl-pc-shifting, 5 , 9, 422, 44(3 as unification, 448 functors, "natural", .300-8 in analysis of interrogatives, 420, 440-51 principles, 357 .70 rules, 358, 376, 421, 450 ultrafiltcr, 360, 36.3 unicorn, 17 19, 22, 20-32 uniform catcgol.y-type corresponilcncc, 341-2 unic]uc answer tlleorj~,430 Universal Grinder, 328, 371 Unil-crsal Pnchager, 328 uni\~c.rsals,semantic, 11 1 constraint on determiners that can create uildefincd NPs, 9.; constrilint on negating self-dual and doit-nnard monotone quantilicl-s, 109 dctcrminer univt.~.sal,92 dislocated phrase uni\'crsaI, 0 2 dual cli~ilntifieruni\-e~-sill,110 mono~onicit!- corrcsponclcnce uni\ ers;ll, 00

486 Index universals, semantic, ( ~ . o n t ' ~ / ) NP-quantifier uni1-ersal. 91 persistent determiner universal, 105 strong derermincr constraint, 100 upside-dolt n dagger, 159 n u s r ~ i ~ l / )179, l , 181-2, 188, 188 n vacuity, 246 n vagueness, 171-3, 176 n, 295 van Bentlicn~,J., 3-57, 378 n, 379 11 van Eijeh, J., 379 n variables, 23, 229-30, 232, 235, 237-9, 243 binding of, 369 event, 182 free, 369 variation, st! listic, 185-6 Vater. H., 291 Veltman, I?., 220 11 i i n d l e r , Z . , 265, 332 n verb(s) accomplishment, 261-2, 265 achievement, 42, 264, 265 activity, 265, 272-3 classification of. 321-5, 327, j.32 n decision. 384 dubitatikc, 383 extensional interrogative-cn~beddi~'~g, 445-h inquisitive, 385 intensional i~~tewogativc-emI>edding, 446 intransitive, 18-1 9, 28, 3 1 nonsubintcrval, 26 1 of acquir-ing knowledge, 384 of' coming and going, 170-1 of communication, 384 of conjecture, 381 of dependency, 385-6 of rclc\-ance, 385 of retaining knowledge, 384 opinion, 38.5 phrases, 3 1 : sptactic structure of the in English, 86

pl+ocess,328 transitive intensional, 28 uholistic, 26 1 Verkuyl, I-I., 332 11 Vctter, I)., 278 i~~ija~-Sh:tnker, K., 5 Vlach, F.,159 n, 329--30, 332 n von Stcchon, .4., 8, 336 Wachoivicz, K., 388 Wall, R., 340, 342, 349, 3h7 weah islands, (syntactic), 409 weak vs. strong, scJr dctcrminers, weak YS. strong Webhcr, A., 220 n. Zlicbber, B., 6 bVcgcner, 289 \Vcinrcich, U., 289 \vcllforincclncss constr;lints, 220, 23 1, 233 \\;cstcrstahl, I)., 379 n 12>ht/he~ questions, see clucstions, ~r~lrril~nb'liitchcad, ;l. N ., 188 n ,))/~-moccmcnt(transformation), 207, 213. 393 Il,7t-Phrasc Rule, 394, 4 13 mh-phrases, 393, 41.3 l4/'h-Oy'1tification Rule, 394, 398, 401, 4034, 406.- 13 ~~!lz-questioils, SPC C ~ U C S ~ ~ O 117~11S- , Williams, I., 301, .371-5 "\Villiams puzzle", 358, 301, 371-5 witness set, .see quantiiiers, \vitncss set for \Vittgcnstein, L., 155 Wunderlich, I>., 382 Yes-No Q ~ ~ c s t i oRule, n 39 1, 413 , ) t c J ~ - t z oclucstions, SL'L,questions, ,)~e~-110 Zcevat, I I., 36'9, 378 n, 370 n Zcrnach, E., 60 Zin~merm;~nn, 'l'., 257