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JOURNAL OF SEMANTICS Volume 13 Number 4

CONTENTS ATLAS 'Only' Noun Phrases, Pseudo-Negative Generalized Quantifiers, Negative Polarity Items, and Monotonicity

JAY DAVID

265

SHEILA GLASBEY

The Progressive: A Channel-Theoretic Analysis

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JOURNAL OF SEMANTICS Volume

13 {1996)

CONTENTS Articles JAY

DAVID ATLAS

'Only' Noun Phrases, Pseudo- Negative Generalized Quantifiers, Negative Polarity Items, and Monotonicity

26s

BART GEURTS

ili�

0

SHEILA GLASBEY

The Progressive: A Channel-Theoretic Analysis

33 I

R. HoRN Exclusive Company: Only and the Dynamics of Vertical Inference LAuRENCE

SHALOM LAPPIN

Generalized Quantifiers, Exception Phrases, and Logicality

ALEX LASCARIDES, ANN CoPESTAKE

and TED

197

BRISCOE

Ambiguity and Coherence

4I

fRANCIS RENAUD

The Definite Article: Code and Context JoHAN

VAN DER AuwERA

Modality: The Three-layered Scalar Square JAN

139

r8I

VAN ICUPPEVELT

Directionality in Discourse: Prominence Differences in Subordination Relations

36 3

ARNIM VON STECHOW

Modular Morphology and the Scope of 'Wieder'

87

HENRIETTE DE SwART

Meaning and Use of not . . . until

22I

Scope of this Journal The JOURNAL OF SEMANTICS publishes articles, notes, discussions, and book reviews in the area of natural language semantics. It is explicitly interdisciplinary, in that it aims at an

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journal of S�mantics IJ:

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© Oxford University Press

1996

'Only' Noun Phrases, Pseudo-Negative Generalized Quantifiers, Negative Polarity Items, and Monotonicityt

JAY DAVID ATLAS Department of Philosophy, Pomona College Abstract

t This paper is dedicated to my students Dr Peter Blok (Groningen), Dr Ana von Klopp (Edinburgh), Dr Michie! Lcezenbcrg (Amsterdam), Mr Thomas Rankin (Pomona).

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The theory of Generalized Quantifiers has facilitated progress in the study of negation in natural language. In particular it has permitted the formulation of a DeMorgan taxonomy of logical strength of negative Noun Phrases (Zwarts 1 996a,b). It has permitted the formulation of broad semantical generalizations to explain grammatical phenomena, e.g. the distribution of Negative Polarity Items (Ladusaw 1980; Linebarger 198 1 , 1 987, 1991; Hoeksema 1986, 1995; Zwarts 1996a,b; Horn 1992, 1996b). In the midst of this theorizing Jaap Hoepelman invited. me to lecture in Stuttgart about Focus, and I took the opportunity to talk about a seminal paper on 'only Proper Name' and 'even Proper Name' by Larry Horn (r969), a paper that I had admired but that had nagged at me for years. The result of Hoepelman's invitation was Atlas (1991, 1993), in which I believed that I had discerned difficulties for the formal semantics of Negative Polarity Item sentences; 'only Proper Name' sentences licensed Zwarts's "weak" Negative Polarity Items, e.g. 'ever', 'any', but 'only Proper Name' was not a downwards monotonic quantifier, thus refuting the broad semantical generalization that any NPI licenser was a downward monotonic quantifier. In fact 'only Proper Name' was the first of a new category of generalized quantifier: the pseudo-anti-additive quantifier. Though I have explained and defended the introduction of this new category in this paper, a particular interest of my analysis is that it opens up the theory of Negative Polarity Items for further development; it permits the formulation of entirely new questions for research (see 'Open Questions', Appendix I). Along the way I was also trying to present a correct account of the formal semantics and implicatures of 'Only a is F, a subject of theoretical investigation for the last 700 years, but without, in my view, any theory ever arriving at the truth. There had to be something wrong with our theoretical methods or theoretical bias towards the data. So I (Atlas 199 1 , 1993) have tried t o break out o f this logjam by introducing new constraints on the acceptability of logical forms (first introduced in Atlas & Levinson 1981 for the analysis of clefts, and in Atlas 1988 for the analysis of negative existence statements). The earlier theories ignored conversational implicatures entirely; it seemed of theoretical interest to examine statements containing focal particles like 'only' for their implicatures, especially as the correct prediction of implicatures tells one something about the truth-conditions and logical form of the statement itself {Atlas 199 1 , 1993). In this paper I review and modify my earlier theory of the logical form, semantical properties, and pragmatic properties of 'Only a is F. I also provide the correct general­ ization to the case of 'Only G is F. And I respond to the criticisms in Horn ( 1992, 1996b).

266 'Only', Quantifiers, NPis, and Monotoni�ity

As a corollary, I show that the logical equivalence that has been assumed since the thirteenth century, viz. 'All Fs are G' is logically equivalent to 'Only Gs are F', is mistaken. 'Only Gs are F' entails 'All Fs are G', but the converse is false. I also show that the familiar claim that 'only Proper Name' is a downward monotonic Generalized Quantifier is also mistaken; it is a non-monotonic but "pseudo-anti-additive" generalized quantifier. (A "pseudo-anti-additive" quantifier is one that is closed under disjunction.) Finally, I introduce a new DeMorgan taxonomy of strength of negative quantifier Noun Phrases, enriching and revising the proposals of Zwarts (1 996a,b).

I I NTROD U CT I O N

or more years of effort by logicians, until Charles Sanders Peirce and Gottlob Frcgc saw their way to a solution ca. I88o. Since the thirteenth century logicians and linguists have addressed the following questions: (i) what are the truth-conditions and logical form of only a is F, where 'a' is a Proper Name? (ii) is there an entailment Only Socrates saw an animal l­ Only Socrates saw an ass ? and (iii) arc the semantic and pragmatic properties of Only a is F and Only Gs are Fs similar? In the last fifteen years there have appeared the beginnings of a sufficiently rich theory by which these questions might be answered: the categorization of negative Generalized Quantifier expressions, the grammar of Negative Polarity Items, of NP/V inversion, of the occurrence of contrastive 'but', etc. An early, thirteenth­ century answer to question (i) offered by Peter of Spain (Horn I 989: 248-so) was that ( I a) consisted of the conjunction of (Ib) and (Ic), viz. (Ie): ( 1 ) a. b. c. d. e.

Only God can make a tree. God can make a tree. No one distinct from God can make a tree. A t most God can make a tree. God can make a tree & no one distinct from God can make a tree.

Peter Geach ( 1962/ I 980) criticized the medicvals for this analysis of the truth-conditions of (Ia); he proposed, in a Russellian spirit, that the "exclusive" component No one distinct from God can make a tree was what was essential to the meaning of Only God can make a tree. This analysis rejects the entailment of (Ib) by (Ia) and makes of only God a negative quantifier [ -..:3x ( •(x = g) . . .)]. In that case o ne would expect only a to have the semantical properties of "minimally" (Zwarts I 996a)/"sub-minimally" (Zwarts I996b) negative quantifiers, viz. downwards monotonicity in the

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A theory of logical consequence for multiply-quantified sentences, e.g. S omeone is l ov ed by ev ery one /f-- Ev ery one l ov es someone, defeated four hundred

Jay David Atlas 267

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sense of Barwise & Cooper (I 98 I). In that sense, no one is a downwards monotonic quantifier expression, since substitution of predicates whose extensions are subsets preserve the truth of the sentence, e.g. No one eats if­ No one eats rice. Ladusaw (I98o), Horn (I992), and Zwarts (I996a), among others, have hypothesized that the grammatical co-occurrence of Negative Polarity Items (NPis), e.g. any, ever, until Friday, bat an eyelash, with allegedly "negative" quantifier expressions requires that the quantifier expressions be downwards monotonic. On the converse hypothesis that downwards monotonic quantifiers will license the grammatical co-occurrence of Negative Polarity Items (Zwarts I 996b: I71), one would expect on Geach's (I962/I98o) analysis that only a license some Negative Polarity Items. Finally, since Only Gs are Fs seems logically equivalent to All Fs are Gs, and it is obvious that All Fs are Gs is downward monotonic in the F position, e.g. All Fs are Gs If- All F & Hs are Gs, it would seem that Only Gs are Fs is downwards monotonic in the F position, and so it would seem that Only a is F is downwards monotonic in the F position-that only a is a downwards monotonic quantifier expression. It is essential to these claims that the semantical property of downwards monotonicity is being used to explain the distributional facts of the grammatical co-occurrences of Negative Polarity Items with quantifier expressions. It is also essential to these claims that the quantifier only/\Proper Name and the quantifier only/\ Common Noun are treated equivalently. I shall argue in this essay that both these claims are incorrect. Though only a will license some Negative Polarity Items, it is not a downwards monotonic quantifier expression. So downwards monotonicity does not explain the co­ occurrence of Negative Polarity Items with only a (Zwarts I996b: 171). Yet, as I shall show, only/\ Common Noun is a downward monotonic, anti-additive quantifier expression-a "regular negation" (Zwarts 1 997a/"minimal nega­ tion" (Zwarts 1996b), so that it is also incorrect to treat the Proper Name case and the Common Noun case as semantically equivalent. Only a is not a "negative", downwards monotonic quantifier, even though Only"Common Noun is. 1 Of course there are theoretical alternatives to Peter of Spain's analysis besides Geach's. The "prejacent" proposition (1 b) God can make a tree has also been rejected by Horn (1969, 1979, 1992) and McCawley (1981, 1 993) as an assertion or entailment of (1a). Perhaps if it is not asserted, and not entailed, it is semantically presupposed (Horn 1969), conventionally implicated (Horn 1979), or pragmatically presupposed, or perhaps it is conversationally implicated (Horn 1992). Or, as in Geach's view, perhaps it is not inferred at all. By contrast with all of these alternatives, Larry Horn (1 996b) offers a new analysis that, in light of the analysis of Only a is F in Atlas (1991, 1993),

268 'Only', Quantifiers, NPis, and Monotonicity

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revises the analyses of the relationship of the "prejacent" { I b) proposition's schema a is F to the schema Only a is F of the assertion {I a), viz. revises the presupposition analysis of Horn (I969), the conventional implicature analysis of Horn {I979), and the conversational implicature analysis of McCawley {I98I, I983) and of Horn (I992). Since the propounding of my (I 99 I) nee-entailment analysis and its further development in Atlas (I993), analyses by deMey {I99I), Klooster (I994, I 995), and Horn (I992, I 996b), as well as informal suggestions by Sadock (p.c. I 996) and deSwart (p.c. I 996), have-along with many of the views mentioned in Horn (I996b)-raised questions about my analysis: its implications for only a and only Gs as Generalized Quantifiers, its relation­ ship to explanations of the distribution of Negative Polarity Items (Ladusaw I98o; Linebarger I 98 I , I 987, I 99 I ; Horn, I 992, I996b; Zwarts I 996a,b), the correctness of its account of the truth-conditions and the logical form of Only a is F, the generalization of that account to Only Gs are F, and its consequences for the typology of Generalized Quantifiers in work of Hoeksema (1995), Sanchez Valencia (1994), van der Wouden (1994), Zwarts (1996a), and Atlas (I995a). It is appropriate that I address these issues in a reconsideration of my view (Atlas I 99 I , I 993). Before I consider these issues I shall summarize the analysis of Only a is F in Atlas (I 99 I , I 993). The analysis was motivated by my criticism of the earlier views of Peter of Spain ( Tractatus Exponibilium, 2If£ in Mullaly I 945: I o8-7; Horn I 989: 24850), of William of Sherwood (1968), of Geach (I962/I98o), Horn, (I969, 1 992), McCawley I 98I, I 993), Taglicht (I984), and many others of similar views, e.g. Kuroda (I969) and G. Lakoff (I970). I was dissatisfied with the standard treatments of the logical form/truth-conditions of Only a is F as well as the absence of any account of its conversational implicata. My analysis was intended to remedy those defects. In this essay I shall modify my earlier account of Only a is F and generalize it to the case Only Gs are F. I shall contrast my analysis with the proposals of deMey (I99I) and Horn (I996b). I shall examine Horn's arguments in support of his I 996 theory and in criticism of the theory of Atlas (I99I, I993) and compare the explanatory advantages of Horn's (1996b) and my (I99 1 , 1 993) analyses, to see how well my nee-entailment theory can meet the challenge of Horn's new pragmatic theory. I shall show that however desirable the simplicity of the hypotheses of Ladusaw, Linebarger, Zwarts, and Horn might be as explanations of the distribution of Negative Polarity Items by appeal to downwards mono­ tonicity, the correct logical form of Only a is F does not support these hypotheses for the Proper Name case onlyi\Proper Name. As I shall show here, following Atlas (I995a), onlyi\Proper Name is a non-monotonic quantifier. Moreover there are subtleties i n the semantics and pragmatics

Jay David Atlas 269

of Only Gs are Fs that have been missed by these analyses, as I shall show in Section 4 · I shall also show that in addition to the official position in Horn (1996b), there is in Horn's essay an unofficial position, one that is strikingly similar to that of Atlas (1991, 1993), and so I shall, in good Derridean fashion, deconstruct Horn's text by showing that he is committed in his essay to inconsistent theories, his official view and a Sadockian (p.c. r 996) variant of my (199 1 , 1993) view.

2 T H E A NALYSES

(2) a. a. b. bl. c. c. d. dl. d". d"l. I

I

(

fl. f".

Only Muriel voted for Hubert. Only a is F. Muriel voted for Hubert Fa. Someone voted for Hubert. 3xFx. No one distinct from Muriel voted for Hubert. •:lx( •(x=a) & Fx) At most Muriel voted for Hubert. Vx(Fx ----+ x=aY Exactly one individual, and at most Muriel, voted for Hubert. 3xVy[(x=y � Fy) & (Fy __, y=a)]. 3xVy[(x=y � Fy) & (Fy __, y = iuAu)].

the view of Atlas (199 1 , 1 993) was that the truth-conditions of the statement (2a) Only Muriel votedfor Hubert were (2f, f') Exactly one individual, and at most muriel, voted for Hubert [(2f1) 3xVy[(x=y Fy) & (Fy y=a)] ]; so, (2a) Only Muriel votedfor Hubert entailed, but did not assert, the "prejacent" (2b) Muriel votedfor Hubert and entailed the boundedness condition (2d") At most Muriel votedfor Hubert [(2d1") Vx(Fx x==a ) ], what others call the (logically equivalent) "exclusion" condition (2d) No one distinct from Muriel voted for Hubert [(2d1) •3x( •(x=a) & Fx)]. Unlike other theorists I (Atlas 1 99 1 : 1 44) also discussed the lexical phenomenon of a Levinson Scale (only, also), Focal Stress Implicatures, an explanation of Horn's (1969) allegedly presuppositional inference, and the greater "informativeness" of only by comparison with also: �

__,

__,

(i) There exists a Levinson Scale (only, also) of lexical items (Grice 1 9 61 / 1 965: 459) that permits First Maxim of Quantity generalized conversa­ tional implicatures (Grice 1 975) from the assertion of verbal frames

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In the case of Horn's (1969) example (2a):

270 'Only', Quantifiers, NPis, and Monotonicity

By contrast Horn's (1996b: 24) new theory claims that the assertion of (2a) [Only Muriel voted for Hubert] requires an accommodation of the existential proposition that the set of voters for Hubert was non-empty [(2c) Someone voted for Hubert], which-combined with the asserted exclusion [(2d) No one distinct from Muriel voted for Hubert]-yields the inference that this set was the singleton {Muriel) [(2b) Muriel voted for Hubert].

In this analysis accommodation is the notion described by David K. Lewis (1979: 340): (3)

If at time t something is said that requires presupposition P to be acceptable, and if P is not presupposed just before t, then-ceteris paribus and within certain limits-presupposition P comes into existence at t.

Horn takes the traditional view that Only Gs are Fs is logically equivalent to All Fs are Gs, where 'F' and 'G' have Common Nouns as substituends. Since (according to Horn) an assertion of All Fs are Gs presupposes or accommodates that there are Fs, Horn assumes that an assertion of Only Gs are Fs presupposes or accommodates that there are Fs; in the case of Only Muriel votedfor Hubert, its assertion would presuppose or accommodate that there are Hubert-voters. The presupposition combined with Horn's truth-

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A( ) in which they occur (I use Frege's assertion sign f-- to denote that the utterance-type that follows the sign is asserted): a. (f-- A(also)) ---H A( not only) b. (f-- A(not only) ---H A(also) (ii) The Focal Stress implicature (f-- A(not ALSO)) ---H A(ONLY) is explained by Horn's (1985) "metalinguistic" denial and the Levison Scale (only, also): asserting a is not ALSO F metalinguistically denies a also is F, and so negates the Levinson Scale implicatum of also, i.e. negates not only, and therefore entails only (e.g. Was there also sugar in the coffee? No-ONLY sugar in it.). (iii) Horn's (1969) alleged presuppositional inference: [Not only a] is F. Therefore, a is F. is a two-staged inference, a scalar generalized conversation implicature and a "direct" entailment (Atlas 1 99 1 : 1 3 7): a. (f-- Not only a is F) ---H [a also] is F. b. [a also] is F If- a is F. (iv) Only is more informative than also both in Karl Popper's (1959) logico­ semantic sense, viz. in prenex forms 3\1 is more informative than 33 (Atlas & Levinson 1 981: 4 1 , n.1 3, 42, 48), and in the implicatural­ pragmatic sense of a Levinson Scale ordered by the semantical informativeness of lexical items.

Jay David Atlas

271

conditions (2d) No one distinct from Muriel voted for Hubert logically implies that Muriel voted for Hubert. (I shall discuss this argument below.) Horn (1996b: 32, n. 14) adds: The fact that only some universals-those with 'every' or 'all' rather than 'any'-tend to induce the existential inference might suggest that [existential) import is a conventional property of particular determiners. But there is growing evidence that free-choice 'any' is an end-of-scale indefinite and not a true universal, although its semantics mirrors that of universals in certain contexts . I shall remain agnostic here on how existential import in universals should ultimately be treated; for our purposes, the essential point is the correlation of existential import in universals and in 'only' statements. .

.

Existential import

Strawson (1 952) famously suggests that the assertion All Fs are Gs semantically presupposes There is an F. Since in the early 1 970s I, like Boer & Lycan (1976), defended an analysis of presuppositions as entailments by affirmatives and general conversational implicata of asserting negatives, and I treated the Russellian assertion All Fs are Gs as about Fs and so as implicating There is an F, by my (Atlas & Levinson 1 981) Principle of Informativeness (a correction of Grice's (1975) Second Quantity Maxim), I shall treat the accommodation of an existential "presupposition" as a generalized conversational implicature (GCI). Returning to the work of Strawson, Vendler ( 1967), and more current work by linguists, Horn has recently become dissatisfied with the treatment of existential import as a GCI, since he views the inference to the existential sentence as stronger than a GCI. Among other difficulties for the GCI view, the existential sentence does not seem cancellable in strong "categorical" predications Some F is G/Some Fs are G, which are about Fs and ''presuppose" that there is an F. By contrast, the "thetic" predications Sm F is a G/Sm Fs are G, i.e. There are F Gs [not, as is commonly expressed, There are G Fs], do not "presuppose" that there is an F (Kuroda 1 972). I have been sympathetic to such a distinction since hearing Philip Johnson-Laird (1 972) on the subject: Johnson-Laird convinced me that there is a distinction · between Some F is a G/Some Fs are G and Sm F is a G/Sm Fs are G. The former involves an indefinite partitive quantifier Some F/Some Fs, whose interpretation is a set of sets that contain at least one-two if one takes the plural seriously-F; the latter involves an absolute individual quantifier Smthing, constructed from its logical determiner Sm, which says that the set of FGs is non-empty, or otherwise from a relational determiner Sm, which says that IIG il non-emptily intersects I IFI I· It can be paraphrased by the first­ order absolute individual quantifier, viz. (3x) . Fx . . . . Likewise one could .

.

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2. r

272

'Only', Quantifiers, NPis, and Monotonicity

___,

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distinguish between All Fs are Gs and Everything that is an F is G. Since there is little sense or point in partitioning the null set. All Fs seems to "presuppose" that there are Fs, while the absolute individual quantifier NP Everything does not. The presupposition of the "total" partitive All Fs cannot be cancelled: (a) # All (the) seats are taken, but in fact there aren't any {seats). By contrast, cancellation is possible with Everything: (b) Everything that is a seat is taken, but in fact there aren't any [seats]. Statement (b) differs in this respect from (c): # Every seat is taken, but in fact there aren't any. Why this difference between (b) and (c)? One answer is that the Quantifier NPs are semantically distinct: Every seat vs. Everything. Clearly if the qualifier 'seat' is an essential part of the quantifier phrase, 'every seat' may be thought of as a restricted quantifier over seats. Thus the set of seats is a semantical determinant of the interpretation of the sentence, as in: (Vx: Seat(x) )(Tx) (Thomason 1973). It is the domain of quantification. If the domain is empty, no non-trivial interpretations of predicates are possible. 'In the dark of night, all cows are black.' And, annoyingly, the empty domain makes the following invalid: Everything is G If- Something is G. A semantical determinant of the interpretation of the sentence is not pragmatically cancellable. Since the interpretation of All Fs is a set of sets each of which has IIFII as a subset-a set of the supersets of IIFII-IIFII is a semantical determinant of the interpretation of All Fs. If IIFII is the null set, no non-trivial determination of the supersets has been effected, since any set is a superset �f the null set, and any predication is true. (This is just an elaborate reminder that (Vx(Fx Gx) ) is true for any 1Gxl if there are no Fs, but this fact is now built into the interpretation of All Fs. Hence the non-emptiness of IIFII is now "presupposed" by All Fs.) The "total" partitive quantifier All Fs and the restricted individual quantifier Every F may typically generate an inference that there is an F, but for quite different reasons. And they are both different from the absolute individual quantifier Everything, which does not "presuppose" that there is an F. But there are sentences for which this analysis is too simple. Consider the felicitous cancellations (h), (i), G), and (1). They are the redundant (h): All unicorns are mythical, and there aren't any, the cancellation sentences that Bretano's student Meinong would have thought non­ anomalously true, e.g. (i): All round squares are square, {and/ but} there aren't any, and of course the generic sentence Dodos are flightless, {and/ but} there aren't any, the truth-conditions of which are classically expressible by Everything that is a dodo is flightless, {but/ and} there aren't any, expressible by the just acceptable (?) All dodos, e.g. (j): ??All dodos are flightless, {and/ but} there aren't any (and definitely not expressible by Every dodo, e.g. (k): #Every dodo is flightless, {and/ but} there aren't any), and finally the felicitously

Jay David Atlas 273

2.2

The analysis ofrOnly

a

is

fland ronly

Gs

are

fl

Of course Horn's (I992) earlier analysis of Only a is F did not strengthen the inference to the existential statement. To pare it down to its essentials, Horn's (I992) former analysis of Only a is F was (4): (4) The statement Only a is F (Horn I 992) a. has truth-conditions No one distinct from a is F ((2d')]. b. implicates by Generalized Conversational Implicature a is F ((2b')]. His (I 996b) new analysis is (s): (s)

The statement Only a is F (Horn I 996b: 24) a. has truth-conditions No one distinctfrom a is F (the logical form (2d') is logically equivalent to (2d"'); the latter logical form is para­ phrasable in E nglish by Everyone who is F is a/ At most a is F.] b. presupposes by "accommodation" Someone is F ((2c')].

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cancellable (1): All myfriends and all your friends do not exceed in number all my friends, but then you don't have any. In sum, (I) All Fs and Every F, on these interpretations, typically but not universally generate an uncancellable i nference to There is an F; (2) Everything that is an F does not possess such properties; (3) there are certain cases in which the presuppositions of the "total" partitive All Fs fail. I n light of the cases (h), (i), G), and (1), it would be difficult to suggest that the "presupposition" that there is an F arises from the meaning of the determiner all in the quantifier NP All Fs alone. I am therefore inclined to weaken Horn's account of the inference from All Fs to There is an F as being an uncancellable "presupposition" to my original account of its being a cancellable Generalized Conversational Implicatum and deny the claim that existential import is an uncancellable presuppositional inference from All Fs that is "stronger" than implicature. Otherwise it would be quite unintelligible how Bertrand Russell ever felicitously expressed in E nglish his valid alternative (Nothing is both round and square If- All round squares are round ----+> Something is both round and square) to Meinong's invalid inference from the evidently true All round squares are round to the evidently false Some round squares are round, the latter entailing the evidently false Some squares are round. The problem of Meinong's inference also afflicts Strawson's (I952) account of the presupposition of All Fs, which would presuppose that there are round squares; since there are none, the evidently true statement All round squares are round would be on Strawson's view neither true nor false.

274 'Only', Quantifiers, NPis, and Monotonicity

Horn claims that it is a virtue of his new view that his analyses of Only a is F and Only Gs are Fs are parallel: (6) The statement Only Gs are Fs (Horn 1 996b: 10- 1 1) a. has truth-conditions All Fs are Gs b. presupposes by "accommodation" in asserting All Fs are Gs that II F II non-empty. IS

2.3

Horn's unofficial analysis of 10nly

a

is pl

f--t

�

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Actually one might have thought that Horn would have generalized from (sa) to Nothing other than Gs are Fs rather than to (6a). But at a late stage in his essay he specializes his analysis of (6) to account for Only a is F. In the section 'Conversion and NPI Licensing' Horn (1996b: 1 8 (ex. (46) ) make a remarkable emendation to analysis (6) when I Gil is a singleton set, e.g. {a}, an analysis that is incompatible with his analysis in (s) above. I shall call this emended analysis 'Horn's unofficial view'. I n his emendation to (6), he identifies Only {a} is F with Only a is F, the latter paraphrased by The Only F is a, not by his (sa) No one other than a is F.3 This is surprising because The only F is a II- a is F, while it is not the case that: No one other than a is F II- a is F. Thus in his essay he first defends his ( 1969) downwards monotonic logical form of Only a is F while later in the essay he unofficially adopts the analysis The only F is a that he admits, following Hoeksema (1986), is not downwards monotonic! This inconsistency in his essay is one that I welcome, since the emended view is one as close to my own as one can logically get without being mine, as it is syntactically distinct from mine but logically equivalent to my present view, as I shall discuss below. The logical form of Horn's unofficial analysis is, in fact, identical to a modification of my proposed logical form suggested by Jerry Sadock (p.c. March 1996)."� I shall now explain how such a remarkable emendation can have been made. In the section 'Conversion and NPI Licensing' of Horn's essay, he introduces the unofficial doctrine of Only a is B for a special case in which the extension II A II of A is a singleton set. Horn (1996b: 1 8, ex. (46)) writes, "the argument of only that corresponds to the restrictor of a universal is a downward, superior-to-inferior-licensing and NPI-friendly environment, regardless of its syntactic position." And then he adds, "where A is a singleton set, the relevant B position surfaces not as a standard restrictor of a universal but is instead introduced by the determiner the only, which semantically amounts to the converse of adverbial only: (46) (a) Only As are All Bs are As. (b) O nly A {Bs/ is a B} The only {B/ B'er} is A." Bs Consider the examples (i) Only Albert won the 1921 Nobel Prize in Physics, (ii)

Jay David Atlas

275

The only winner of the 1921 Nobel Prize in Physics was Albert. Where the determiner phrase the only B is paraphrasably by the sole B, or the unique B, and where, in fact, in these true examples, the extension of B, viz. II won the 1921 Nobel Prize in Physics!!. is a singleton set, lithe Bll=llthe only B ll, and the logical form of (ii) is (ii') ixWx = a. Only is now redundant in the only B. The logical form of (i), according to Atlas (1991, 1 993), is (i') :Jx\iy[(y=x f-t Wy) & (Wy -t y=a)] . Analysing (ii') by Russell's Theory of Definite Descriptions gives (ii") 3x\iy[(y=x f-t Wy) & (x a)] , or, in English, (I) Exactly one individual, who at most is Albert, won the 1921 Nobel Prize in Physics; (II) Exactly one individual, who is Albert, won the 1921 Nobel Prize in Physics. Horn's suggestion for Only a is B turns out to be a special case of one made by Jerry Sadock (p.c. March 1 996) as a modification of my logical form for Only a is B. In his Note 26 Horn (1996b: 33-4) agrees with Hoeksema's ( 1986) and Linebarger's (1981, 1 987) observation that Kim is the {youngest, only} American to have climbed Mt. Everest does not entail Kim is the {youngest, only} American to have climbed Mt. Everest with a 500 poutzd gorilla strapped to her back. Thus a the only B does not entail a the only B & C, so a the only . . . is not downwards monotonic. Since Horn will be committed to the view that Only a is B is logically equivalent to a is the only B, he must admit, as a consequence of his Note 26 in which he accepts Hoeksema's (1986) observation, that Only a is B is not downwards monotonic. But that is just the position of Atlas (199 1 , 1 993)! How, then, with an unofficial view simultaneously held in his essay with an official view inconsistent with it, does Horn argue himself into believing that the views are compatible? One argument in this direction was Horn's acceptance of Hoeksema's claim that though a the only B was not downwards monotonic, it was weakly downwards monotonic. If so, then Horn need not give up the notion of some kind of downwards mono­ tonicity that supports his view that Only a is B is semantically negative. Unfortunately, when one compares the original definition of downwards monotonicity with that of 'weak downwards monotonicity', one discovers a significant difference. If Only a is B were downwards monotonic, it would follow that for C � B, Only a is B If- Only a is C. Hoeksema's ( 1 986) definition of "weakly" downwards monotonic stipulates: for aEC and C � B, Only a is B If- Only a is C. But of course it is then trivial that Only a is B is "weakly" downwards monotonic, since on either Horn's official or unofficial account of the truth-conditions of Only a is B, the condition of weak downwards monotonicity is met if from {a} � C, C � B, and B � {a} [i.e. Only a is B], it follows that C � {a} [ i.e. Only a is C], which it does trivially; it even follows that B={a}. That is, from the claim that only a is 'weakly' downwards monotonic it follows: if only a is B, then a is B, which is not supposed to =

=

=

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=

=

276 'Only', Quantifiers, NPls, and Monotoniciry

follow according to Horn's official view of the entailments of Only a is B. If Only a is B is "weakly" downwards monotonic, as Horn seems to suggest in his Note 26, there follows an entailment that he specifically wishes to reject, viz. is B. So Horn's own official account faces this unhappy dilemma: either Only a is B is in no way downwards monotonic and so not "negative", or it entails a is B. For Horn's theory, either alternative is undesirable. But there is an even worse problem for Hoeksema's notion of weak downwards monotonicity. Consider the upwards monotonic generalized quantifier expression, the proper name John. john is "weakly" downwards monotonic: jEC, C � B, j is B lr j is C. Thus an upwards monotonic quantifier turns out also to be "weakly" downwards monotonic, which obviously reduces the notion of "weak" downwards monotonicity to absurdity. It's like saying that llamas are "weak" horses. Surely "weak" downwards monotonicity cannot support Horn's view that Only a is a semantically negative phrase on the grounds that it turns out to be, in some sense, no matter how bizarre a sense, a "downwards monotonic" quantifier expression. Horn's essay contains two analyses of Only a is B and of Only As are Bs, the official view and the unofficial view. The official view is the advertised view summarized in (s) and (6). It claims that Only NP is a NPI-licensing, because downwards monotonic, quantifier expression. It begins from the alleged logical equivalence between Only As are Bs and All Bs are As and claims that Only a is B is logically equivalent to Every B is a. The unofficial view claims that Only a is B is logically equivalent to The only B is a, which, following Hoeksema (1986) and Linebarger ( 1 981 , 1 987), Horn admits is not downwards monotonic in the B position, yet on the official view is supposed to be logically equivalent to a sentence that is downwards monotonic in the B position, viz. Every B is a! Having reached an unofficial analysis of Only a is B that, I have argued, is equivalent to Sadock's (p.c. March 1996) variant of my logical form for Only a is B, Horn might have reconsidered his strategy and captured the generalization in the way I shall suggest in this essay: treat Only As are Bs consistently with his unofficial, and Sadock's version of Atlas's (1991, 1 993), treatment of Only a is B. a

(6') The Unofficial View (Horn 1 996b: 18)

The statement Only a is F is true iff The only F is a.

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5

Jay David Atlas

277

Horn}s oj]i'cial analfis of 10nly a is F! Atlas's revised analysis of 10nly a is F, Atlas's analysis of 10nly Gs are fl 2.4

Horn's (1 996b) official analysis is essentially the same as deMey's (199 1 : 9 1 , 102) for the truth-conditions of Only Gs are Fs: (7) The statements Only Gs are Fs and All Fs are Gs are such that (in deMey's (199 1 : 9 1 , 1 02) generalized quantifier determiner notation): ALL(F,G) is true iff F � G. ONLY(G,F) is true iff F � G. Hence, ONLY(G,F) -lllr ALL(F,G) Asserting ALL(F,G) implicates that F is non-empty. So, asserting ONLY(G,F) implicates that F is non-empty.

In order to provide an analysis of Only a is F, deMey (I 99 I) follows Richard Montague (I974) et al. by introducing a generalized quantifier for the individual constant 'a' whose extension A is the set of extensions of predicates true of a from a domain D, e.g. JOHN {X � D; j E X}. Further, for each individual constant 'a' deMey (I99 I : 103) defines a generalized quantifier determiner ONLY-PNa that is the set of extensions of singleton predicates true just of a from a domain D, viz. ONLY-PNa = {X � D; X={a}}. Then deMey's (I99 1 : 1 03) analysis of Only a is F is: =

(8) The statement Only a is F (deMey 1 99 1 : 1 03, 102) a. is true iff ONLY-PNa(G,F), i.e.: (I) G={a}

(2) F

�

G.6

b. implicates that F is non-empty.7 Thus there are two competing theories of the relationship between Only Gs are F and All Fs are G, and of the inference from Only a is F to a is F. On the Horn (1 996b) and deMey (1991) view (i) Only Gs are Fs is logically equivalent to All Fs are Gs.8 Since asserting All Fs are Gs implicates, by generalized conversational implicature (deMey 1 99 1 : 1 02), or accommodates (Horn 1996b: 21), There is an F, Horn (1996b: 10) claims (iia) by virtue of {I) that (iib) asserting Only Gs are Fs accommodates There is an F. Since on Geach's (1 962/1 980) view, Horn's views (1969, 1 979, 1992, 1 996b), and McCawley's (198 1 , 1 993) view the truth-conditions of Only a is F are (2d) No one distinct from a is F [(2d')), it is not the truth-conditional content of Only a is F that entails a is F. It is the truth-conditional content of Only a is F conjoined with the accommodation There is an F, the total signification of the statement Only a is F, viz. There is an F & no one distinct from a is F, that

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a. b. c. d. e.

278 'Only', Quantifiers, NPis, and Monotonicity

entails a is F. This is a significant change from Horn (1992), where a is F is not an entailment of the statement Only a is F; there it was a generalized conversational implicatum of asserting Only a is F. By contrast with deMey's (1991) view, my current view, couched in deMey's terms, is the following: (9) The statement Only a is F (Atlas) a. has a generalized quantifier determiner representation ONLY­ PNa(G,F).

b. implicates There is someone other than a.9 is true iff the following obtain: c.

F);

(3) F � G (i.e. At most a is F). 10 Corollary. I G I = I. d. has topic NP F, so asserting the sentence can produce a generalized conversational implicatum There is an F, and in fact does produce the implicatum There is an F, i.e. that F is non-empty. 11 Though I did not discuss the matter in Atlas (199I, I 993), there is, contrary to the opinion reported in Horn ( 1996b: 24), an obvious general­ ization of that analysis of Only a is F to Only Gs are F. (10) The statement Only Gs are F (Atlas): has a generalized quantifier determiner representation ONLY(G,F). b. is semantically well formed (true or false) only if G is not identical to the domain of quantification D; so, on the classical assumption that D is non-empty, G is a proper subset of the domain D, i.e. there is a non-G in the domain, so that the complement G' is non­ empty (Atlas I 99 I : 1 28): •(G' = o). c. is true iff the following obtain: (I) G is a proper subset of D: G C D [G' is non-empty]. (2) F � G. d. has topic NP 'F', so asserting the sentence can produce a general­ ized conversational implicatum There is an F, and in fact does produce the implicatum There is an F (F is non-empty). a.

On the view of Atlas (I 99 I, I 993), the statement Only a is F entails a is F, i.e. Exactly one individual, and at most a, is F If- a is F. Thus despite Horn (1969, 1 979, 1 992), we now have convergence between Horn (1996b)'s official view and that of Atlas (199 I , I993) that a is F is entailed, though the explanations that Horn and I give for the entailment remain divergent. I believe that the

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( I ) G={a};

(2) I FI= I (i.e. the cardinality of set F is I; exactly one individual is

Jay David Atlas 279

3 NEGAT I V I T Y , NEGATIVE POLARITY, T H E N O N ­ M O N O TO N I C ITY A N D PSEU D O - AN T I - AD D I T I V ITY O F ' O NLY a', AND T H E ANTI - AD D I T I V ITY O F ' O NLY /\ COMMON NO UN' I

have clear logical reasons to think that �nly a is not downwards monotonic. argued in Atlas ( 1993: 3 1 4), intuitions about logical entailment su�gest that only a is non-monotonic. To review: singular terms, rmany N1 , most Nl, rall N1 , rsome N1 are monotonically increasing Generalized Quantifier expressions: the Quantifier contains every superset of every set that is an element of the Quantifier. Since rQ VP1 is true just in case the extension VP belongs to the extension of Q, i.e. I I VPII E I I Q I I , the monotonically increasing quantifiers Q are ones for which, if I I VP1 I I � I I VP2 11 , and ;-Q VP11 is true, then rQ VP 1 is true. Thus, since Some men [walked rapidly] vp, If- Some men [walked] vp2 but not conversely, 'Some men' is a monotonically increasing quantifier expression, as truth is preserved under the superset relation of the extensions of the predicates. Since 'No men' shows exactly the opposite pattern, e.g. No men walked I f- No men walked rapidly but not conversely, it is a monotonically decreasing quantifier expression, as truth is preserved under the subset relation of the extensions of the predicates. If As I

2

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entailment follows from the truth-conditional content of any instance of the sentence-schema ronly a is F1 ; Horn officially believes that the entailment follows from the total content of asserting any instance of the statement­ schema Only a is F. 12 Since I also believe that statements of Only a is F implicate There is an F, though not for Horn's reasons [see Section 6], Horn would think that my truth-conditions Exactly one individual, and at most a, is F are unnecessarily strong, since on his logically weaker (2d, d') No one distinctfrom a is F he can derive a is F from the total content There is an F & no one distinct from a is F of the assertion Only a is F just as I can from my logically stronger truth­ conditions of Only a is F, viz. Exactly one individual, and at most a, is F (Atlas, 199 1 , 1 993). So why, contrary to the methodology of my own Radical Pragmatics (Atlas 1 979; Atlas & Levinson 1 98 1 ; Atlas 1 984), should I hold on to my logically stronger truth-conditions? The answer is that I believe that only a expresses semantically a non-monotonic generalized quantifier exactly one individual, who is at most a, while McCawley (1981, 1 993) and Horn (1 996b) think that it expresses a negative, downwards monotonic quantifier no one other than a. 13 In the next section I shall show why theirs 1s an incorrect semantical analysis of only /\Proper Name. 14

280 'Only', Quantifiers, NPis, and Monotonicity

( I I ) Suppose Socrates and a cohort of young aristocratic Athenians are

conversing in the Athenian agora. As Plato puts a question to Socrates, a small mangy animal (a dog, perhaps) pushes his head through the crowd of legs and catches the alert Socrates's eye. No one else sees the animal. Then Only Socrates saw an animal is true. On the downwards monotonic view, it is entailed-entailed!!-that Only Socrates saw a Tibetan snow leopard. That is, in every possible model (world) in which Only Socrates saw an animal is true, Only Socrates saw a Tibetan snow leopard is true in that model. Surely this condition cannot be satisfied. The logical consequence relation cannot squeeze more information out of a conclusion than has been put into the premisses. But that is what downwards monotonicity does in this sentence. So much the worse for downwards monotonicity in only a sentences. (Notice, by contrast, that it is acceptable that: No man saw an animal if- No man saw a Tibetan snow leopard.) (12) Now consider the same premiss, but let the domain of quantification be finite with K elements; let the element i have the name 'a/, I ::::; i ::::; K. On the downwards monotonicity view Only Socrates saw an animal entails Only Socrates saw an animal named 'ano', for some n°, I ::::; n ° ::::; K. Then Only Socrates saw an animal entails a finite conjunc­ tion of N such statements, 1 ::::; N ::::; K. For N large enough, {Only Socrates saw an animal, There are no unnamed animals} entails Only Socrates saw every animal, which is an absurd consequence of down­ wards monotonicity. ( 13) The third argument is a reductio: Suppose that a noun phrase NP is

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Horn were right that the meaning of 'Only Muriel voted for Hubert' is logically negative, as is 'No one other than Muriel', or 'At most Muriel', 'only a' sentences should exhibit the semantic characteristics of mono­ tonically decreasing quantifier sentences. It seemed to me intuitively clear that Only Socrates walked does not entail Only Socrates walked rapidly, so 'only Socrates' is not a monotonically decreasing quantifier expression. Likewise, it seemed to me intuitively clear that Only Socrates walked rapidly does not entail Only Socrates walked, so 'only Socrates' is not a monotonically increasing quantifier expression. So 'only Socrates' is a non-monotonic quantifier expression. Despite some agreement with my (1991, 1 993) intuitions, e.g. L. T. F. Gamut (199 1 : 239) and Wim Klooster (1994, 1 995), I can understand that entailment intuitions are not always obvious, and I am more than aware of disagreement with these intuitions, e.g. Ladusaw (1980: 165-6) and Horn (I 992, I 996b: Is). So, following Atlas (I 995a), I shall give six arguments (I I )­ ( 1 5b) to show that 'only Socrates' is not a downwards monotonic noun phrase.

Jay David Atlas 281

downward monotonic, and the extension of VP1, I I VPd l, e.g. llwalks rapidlyll , is a subset of II VP2 11, e.g. llwalksll. Then NP VP2 lf­ NP VP1, e.g. Few men walk If- Few men walk rapidly. Suppose the parallel conditions hold for VP3 and VP2: NP - VP2 If- NP - VP3• It would follow that NP - VP2 If- NP- VP1 & NP VP3. But down­ wards monotonicity also implies (Zwarts 1 996a) that NP- VP1 & NP - VP3 If- NP - ( VP1 and VP3). 1 5 So NP- VP2 If- NP - (VP1 and VP3). For example, if 'only Socrates' were a downwards monotonic noun phrase, it would follow that Only Socrates walked If- Only Socrates walked rapidly and slowly. But that is absurd. So 'only Socrates' is not downwards monotonic. (Notice, by contrast, that it is acceptable that: Few men walked If- Few men walked rapidly and slowly.) ( 14) The fourth argument is also a reductio: If only Socrates were down­ wards monotonic, Only Socrates walked would entail Only Socrates walked rapidly. But: p (Walked(a) � (Walked rapidly(a) v Walked non­ rapidly(a) ). So it would follow: Only Socrates (Walked rapidly v Walked non-rapidly) If- Only Socrates walked rapidly. But that alleged entailment is absurd. So Only Socrates is not downwards monotonic. (Notice that it is acceptable that: Few men (Walked rapidly v Walked non-rapidly) If- Few men walked rapidly.) (I sa) The fifth argument is a reductio: If a Noun Phrase were downwards monotonic (Zwarts 1 996a,b; see (16a) below), then: -

-

-

or

VP2) If- NP- VP1

&

NP - VP21

e.g. Few men (smoke or drink) If- Few men smoke & Few men drink. Let VP1 df 'Walked rapidly' and let VP2 df 'Walked non-rapidly'. Then, again substituting the logical equivalence: =

=

p (Walked(only a) � ),x(Walked rapidly(x) v Walked non-rapidly(x) ) (only a).

in the left-hand side of the following we have via (OM): Only Socrates walked If- Only Socrates walked rapidly walked non-rapidly.

&

Only Socrates

which again is an obvious logical absurdity. (I sh) The sixth argument is a reductio: If a Noun Phrase were downwards monotonic (Zwarts 1 996a,b: 1 75, ex. (I I b) ); see (16b) below), then: (OM') NP- VP1 v NP- VP2) If- NP (VP1 and VP2), e.g. Few men smoke v Few men drink If- Few men (smoke and drink).

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(OM) NP(VP1

282 'Only', Quantifiers, NPis, and Monotonicity

Let VP1 df 'Walked rapidly' and let VP df 'Walked non-rapidly'. Then, again substituting the logical equivalence: 2 =

=

I= (Walked(only a) a) ).

+-t

(Walked rapidly(only a) v Walked non-rapidly(only

in the left-hand side of the following we have via (DM'): Only Socrates walked I I- Only Socrates (walked rapidly and walked non­ rapidly),

which again is an obvious logical absurdity. The conclusion from this argument is that only a is not a downwards monotonic Noun Phrase.

3- 1

The anti-additivity of 10nly CNl and pseudo-anti-additivity oj 10nly al

Nothing in these arguments (r r)-(rs) as formulated bears on the question whether or not 'only' followed by a Count Noun is a downwards monotonic Noun Phrase. By the criteria (r6a) and (r6b) employed for downwards monotonic Noun Phrases (Zwarts 1 996a,b), the corollary (r6c) of (1 6b), and the obvious, simpler consequences of the definition of downwards monotonicity (r6d), (r6e), and (r6�: (r6) a. NP(VP1 or VP2) II- NP- VP1 & NP- VP2. 17 b. (NP - VP1 v NP - VP2) I I- NP(VP1 and VP2). 1 8 c. NP- VP1 & NP- VP2 I I- NP(VP1 and VP2). d. NP- (VP1 or VP2) II- NP - VP1 . e. NP - VP1 I I- NP(VP1 and VP2). f NP - (VP1 or VP2) II- NP- ( VP1 and VP2). the intuitive judgements in (r6a'-f') make it plausible that Few CN, CN a count noun, is a downwards monotonic Noun Phrase, while the intuitive a'. b'. c'. d'. e'. f'.

Few women smoke or drink II- Few women smoke & ftw women drink. Few women smoke v ftw women drink I I- Few women smoke and drink. Few women smoke & ftw women drink II- Few women smoke and drink. Few women smoke or drink II- Few women smoke. Few women smoke I I- Few women smoke and drink. Few women smoke or drink II- Few women smoke and drink.

Judgements in (17) make it plausible that Only CN, CN a count noun,

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The conclusion from these six arguments (I I)-(r sb) is that only a is not a downwards monotonic Noun Phrase. 16

Jay David Atlas 283

(I7) a. Only women smoke or drink lr Only women smoke & only women drink b. Only women smoke v only women drink lr Only women smoke and drink. c. Only women smoke & only women drink lr Only women smoke and drink. d. Only women smoke or drink lr Only women smoke. e. Only women smoke lr Only women smoke and drink. ( Only women smoke or drink If-" Only women smoke and drink. is a downwards monotonic Noun Phrase:9 If the converse (18) of (DM)/ (I 6a) is also true: &

NP- VP2 lr NP(VP1

or

VP2)

then, by definition (Zwarts I 996a,b), the downwards monotonic Noun Phrase [satisfYing (I6a)J that is also closed under finite unions [as shown on the right-hand side of ( I8)] expresses an anti-additive operator, i.e. a "more negative" quasi-ideal on the VP algebra (called 'regular negation' by Zwarts (I 996a) and 'minimal negation' by Zwarts ( I 996b) )?0 Since it is intuitively plausible that: (I 9) Only women smoke & only women drink lr Only women smoke or drink it seems that only women in sentence-frames containing dispositional predicates expresses a quasi-ideal on the VP algebra. (Other anti-additive NPs are No N, Neither N, None of the N.) Since it is intuitively plausible that the following instance of (I 8) is true: (2o) Only John smokes & only John drinks lr Only John smokes or drinks but false that the following are correct instances of Zwarts's criteria for downwards monotonicity (I6a,b): (2 1 ) a. Only john smokes or drinks ? lr Only John smokes & only John drinks (2 ) b. Only John smokes v only john drinks ?l r Only John (smokes and drinks. some Noun Phrases, like only John, satisfY the essential (I6a)-converse condition (I8) for being a quasi-ideal, viz. closure under finite unions, without being downwards monotonic (and so satisfYing (16a,b) ). Only John is neither a quasi-ideal nor downwards monotonic, but it is closed under finite unions like quasi-ideals. Though Zwarts (1996a) calls the anti-additive operators 'regular negations', and Zwarts (1996b) calls them 'minimal negations' while the merely downwards monotonic negations are called 'sub-minimal negations', following Atlas (1995b) I call operators such as only a 'pseudo anti-additive'. This may make only "Proper Name semantically 1

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(I8) NP - VP1

284 'Only', Quantifiers, NPls, and Monotonicity

"negative" enough to license some Negative Polarity Items-though there is no theory to explain why it does, but it does not make it a semantically negative, downwards monotonic quantifier (satisfying (16a,b) ) like, e.g. Few N.Zl 3 -2

Negativity and the distribution of negative polarity items

I do not find the syntactic observation that only triggers [all, not 'some', of a theoretically relevant class of-JDA] Negative Polarity Items sufficiently well-grounded, and so I do not believe that there is yet sufficient ground to take only to be a negative lexical item.

The point here was evidence for the semantical negativity of 'only a', since McCawley (198 1 : so) had argued for the semantical negativity of 'only a' on the grounds that only a triggers Negative Polarity Items. I had assumed, perhaps wrongly, that McCawley (1981: so) had meant that the distribu­ tional fact of triggering all of some relevant if ill-defined class of Negative Polarity Items would be sufficient to establish the semantical negativity of 'only a'; I certainly did not think he meant to argue that the distributional fact of merely licensing some (at least one) Negative Polarity Item would be sufficient to establish the semantical negativity (downwards mono­ tonicity) of 'only a', but perhaps I misunderstood his intention.22 Perhaps McCawley, and Horn, thought that even licensing one Negative Polarity Item would entail that the expression must be downwards monotonic. But they should not assume [the falsehood] that (i) licensing even one Negative Polarity Item is sufficient to make the expression a Negative Polarity Item licensor in general. They should not assume Ladusaw's (1980) [false] generalization (ii) that an expression is a NPI licensor only if it is downwards monotonic; they would be begging the question that I had posed: 'Why does licensing one or more NPis make only a a downwards monotonic expression?' I thought then, as now, that the distributional facts alone would not justify the claim of the logical negativity of an expression unless the evidence from the syntactical environments, com­ bined with a semantical theory of those environments, could explain why the NP must be downwards monotonic. Anything less would beg the question that I had posed. Having granted that there were NPI contexts in which only a occurred

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Horn (1996b: 8) suggests that I have �laimed that 'only NP does not in fact license NPis [Negative Polarity Items]'. Actually I made no such claim. The only claim I made was for only /\Proper Name. Furthermore I (1993: 313) cited a datum to the contrary: Only John ever suspected David Alexander. My (1993: 313) claim was the one that Horn (1996b: 8) quotes in his text:

Jay David Atlas 285

grammatically, e.g. ever, I (Atlas 1993: 313) then exhibited some examples in which only a did not successfully license a Negative Polarity Item, e.g. the data in (22a,b,c): (22) a. b. c. d.

*Only Bill wants Sam to finish the report until Friday. ?Only I was all that keen to go to the party. ?Only Phil will give Lucy a red cent. Only john ever suspected David Alexander.

a

e. (Of all her friends,) only Phil would lift a finger to help Lucy. Only your wife gives a hoot about what happens to you. (McCawley f 1981: 83) g. My nose and my lungs are only alive at all because they are part of my body and share its common life. (C. S. Lewis; Jacobsson 1951) and there is similar data from McCawley (r988: 563): e'. Only Peter lifted a finger to help me. f'. Only Senator Claghorn gives a hoot about Namibia. But consider the following echoic and denial utterances negative statements or implicitly negative questions:

m

response to

h. Why am I alive at all? I'm alive at all because . . . Don't say that! I do too give a hoot about what happens to you! 1.

The negative polarity "minimizers", originally occurring without negatives in an echoic question or negative context, become conventionalized a. L. Morgan 1978) in clauses with focus NPs, no longer requiring the question or negative context, as in these acceptable statements with upward monotonic, non-Topic Noun Phrases: Of all her friends, Phil would lift a finger to help Lucy. [Phil is not a topic NP.] k. Even Phil would lift finger to help Lucy. I. PHIL would lift a finger to help Lucy. [On focus NP examples like (k) and (1), see Atlas (1989: 89-91).]

J-

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These data, I supposed, would undermine McCawley's and Horn's apparent argument that all NPis (of some relevant class) are licensed by 'only a', and thus 'only a' is essentially negative in meaning. Again, the issue was: what distributional facts will demonstrate an ill-defined "negativity" of the meaning of an expression? Horn (r996b) is not convinced of my claim that only is a weak trigger for NPis. To my data in (22b,c) Horn (r996b: 8, ex. (r6) ) and McCawley ( 1 98 r , r 988) counterpose data that contain minimizer NPis:

286 'Only', Quantifiers, NPis, and Monotonicity

So McCawley's and Horn's data (22e-g) do not show that because it licenses minimizer NPis only Phil is a semantically negative operator: an upwards monotonic, focused NP, as in the stressed utterance-type (22l) PHIL would lift afinger to help Lucy, and the non-monotonic, focused only a in Horn's and McCawley's data (22e,e',f,f') equally well make the occurrence of lift a finger acceptable in the utterance. Co-occurrence of non-monotonic, focused only"Proper Name and only "Pronoun with NPI minimizers seems explicable by conventionalization of the use of minimizers with focused NPs-the very feature of NPs that would occur in the original denial and question contexts. Non-monotonic, Pseudo-Negative, only a NPs in statements are apparently (i) assertorically Focused enough and (ii) semantically negative enough to co-occur with 'weak' NPis like ever and any.23 These data just make more pressing the question: why should one have thought that only" Proper Name sentences are "negative"? 3-3

Klima-McCawley negativity

Before I consider criteria by which formal semantics (e.g. Zwarts 1 996a,b) have characterized the negativity of quantifiers that license NPis, I shall examine the more traditional linguistic criteria for negativity originating with the tests for negativity in Klima (1964, originally written 1 959) and discussed more recently in McCawley (1988: 581 -9).24 I shall consider the Klima-McCawley so/neither test, reversal tag test, and the not even test, applied to sentences of the form Only a is F. I shall argue that these tests allow no conclusions whatever to be drawn concerning the possible negativity of Only a is F. I shall finish this discussion by a consideration of the too/either test (McCawley 1 988: 581 -6), and I shall conclude from this test that it is not possible to draw an inference that Only a is F is

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m. ?Phil would life a finger to help Lucy. [Phil is a topic NP.] m'. *Max lifted a finger to help me. (McCawley 1 988: 562) [Max is a topic NP.] n. 1-1!-would certainly lift a finger to help Lucy. [I is not a topic NP.] o. I would lift a thousand fingers to help Lucy. [As hyperbole: acceptable; as literal: a different utterance-meaning. On the use of the indefinite NP a finger, see Atlas & Levinson (1981: 48-so) and Horn (1984: 15, 1 9).] p. Listen to me, John! I give a hoot about what happens to you! [Accommodation; see Atlas (1975, 1 977).]

Jay David Atlas 287

"negative" in Klima's sense and that there is some evidence that it is "positive". After extensive discussion McCawley ( I 988: 58 I -9) concludes of the so/ neither test that so (McCawley I 988: s86): provides a useful test of negativity. Note that so is unacceptable in combination with subject NPs of the sorts that we have so far identified as negative: (18) a. *Few students voted for Carter, and so did not many professors. b. ??Few students voted for Carter, and so did Jew professors. c. ?Hardly any linguists eat Twinkies, and so do hardly any anthropologists. The unacceptabiliry of (18a-c) can be taken as grounds for classifying Not many professors voted for Carter, Few professors votedfor Carter, and Hardly any anthropologists eat Twinkies as negative

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On the other hand, though it may be only what McCawley calls Logicians' Pidgin English, I find just the reverse of the standard grammatical judgements for Few students voted for Hubert, and {*neither, ??so} did ftw students, Hardly anyone voted for Hubert, and{*neither, ?? so} did hardly anyone, with neither unacceptable (*) and so marginally acceptable (?), probably because the co-reference case in Muriel1 voted for Hubert and {so did Lady Bird21 so did Muriel�} is not ungrammatical even if not preferred, so implicating but not entailing so also (Horn 1984; Levinson 1 987a,b, 1 99 1 ; Huang 1994)?5 Hence the Klima-McCawley so test is not decisive. In the presence of a negative quantifier phrase, some so sentences are not ungrammatical; even if the ungrammatical cases of so imply negativity, the converse, of course, does not ·follow and is, I believe, false: non­ ungrammatical cases of so do not imply non-negativity. Since I find grammatically acceptable, even if pragmatically odd, Only Muriel voted for Hubert, and so did only Muriel, the so/neither test for negativity fails to yield a verdict for the case of only" Proper Name. The reversal tag test, excluding the rising intonation reduplicative tag (McCawley 1 988: 588), yields: Hoboken is in New Jersey, { ' isn't it?, * ' is it?}; Hoboken isn't in Pennsylvania, {is it?, *isn't it?}, but, as McCawley notes, when one is testing the negativity of a subject, the test is problematic (the pronoun of the tag being outside the scope of the quantifier): Few students failed the exam, {*did they?, *didn't they?}. Thus for only Muriel: Only Muriel voted for Hubert, {*did she?, *didn't she?}. Thus the test yields no conclusive result for only" Proper Name in subject position. As an example of the not even X test (Klima 1 964: 262-3; McCawley 1 988: 588-9), where X matches, or is a specialization of, a constituent that is in the scope of a negation of the host sentence, we find a contrast between: Sam won't let his friends use his car, not even Otto, *Sam will let his friends use his car, not even Otto; and between: No friends of Sam can use his car, not even Otto, *Friends of Sam can use his car, not even Otto. But again the test is not decisive, as it shows that the grammatical occurrences of the not even X

288 'Only', Quantifiers, NP!s, and Monotonicity

�

A

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implies that the host sentence is ' megative", but the converse is not the case; the test does not show that when the occurrence of not even is not grammatical the host sentence is non-negative. For we have already seen that o nly"'Count Noun and No "'Count Noun are semantically downwards monotonic. Thus it is no surprise that the following is grammatical: No birds like this weather, not even web-footed ones. But from the ungrammati­ cality of *Only birds like this weather, not even web-footed ones, it would be a mistake to infer that there was nothing negative about Only birds. Thus the ungrammatical data: *Only Sam will let his friends use his car, not even Otto, *Sam will only let his friends use his car, not even Otto, are inconclusive. They do not show that only"'Proper Name or only "' Verb Phrase is non-negative, and, of course, they do not show that it is negative either, which brings us to the too/either test (McCawley 1 988: 581 -6). In the negative example Few linguists eat Twinkies, and not many anthropologists do either/*too, the too must be replaced by either if the host V plus its subject comprise the scope of a negation (McCawley 1988: 584). In the sentences Muriel voted for Hubert, and Lady Bird did too/*either, Pat wouldn't vote for Hubert, and julie refused too/*either, the word either must be replaced by too in the positive host clause. Though marginal, the following is not grammatically unacceptable for me: Hardly anyone eats Twinkies, and onlyJohn does ?1too/*either, with too just barely in (?}, but either definitely out (*). I infer that Only John is not negative. At least it is clear that one cannot infer that Only John is negative. The same observations hold, on my semantical view of the truth-conditions, for the inconsistent but gramma­ tical Bill eats Twinkies, and only John does too/*either (if Bill is not John), and for the oddly underspecified (referentially general) but grammatical Bill eats Twinkies, and someone does too/*either, by contrast with the more acceptable too in Bill eats Twinkies, and someone else does too/*either (Horn 1984; Levinson 1 987a,b, 1 99 1 ; Huang 1994). Thus, on the Klima-McCawley tests of negativity: the so/either test, the reversal tag test, and the not even X test, nothing follows concerning the negativity of only"' Proper Name. On the too/either test it is clear that one cannot infer that only "'Proper Name is negative; there is some evidence to infer that it is non-negative. Of course such syntactical conclusions are inconsistent with the views of McCawley ( 1 98 1 , 1 993) and the official view of Horn ( I 992, I 996b) that only"' NP is "negative" even in the case of only Proper Name. By contrast, such syntactical conclusions are consistent with the views of Atlas ( 1 99 1 , 1 993), and with the unofficial view of Horn ( 1 996b) , that only"'Proper Name is non-monotonic, unlike the anti-additive, semantically negative No one, the merely downwards monotonic, negative Few N, et al. and unlike the upwards monotonic, semantically positive Proper Name, Someone, et aF6

Jay David Atlas 3-4

289

Semantical negativity and NPis

Besides the syntactical Klima-McCawley characterization of the negativity of a sentence, how shall we characterize the semantical negativity of generalized quantifier NPs? Zwarts's (1996a,b) typology of negative Quantifiers makes use of Quantifier versions of DeMorgan's laws, noted in (Z): Q(F or G) I I- QF & QG; QF & QG I I- Q(F or G); Q(F and G) I I- QF v QG; QF v QG I I- Q(F and G).

to rank quantifiers in negativity. A "minimal" negation (Zwarts 1996a), renamed 'sub-minimal' negation (Zwarts 1996b), like few N, is merely downwards monotonic; it satisfies (ia) and (iib). "Regular" (Zwarts 1996a), renamed 'minimal' negations (Zwarts 1 996b), like No N, Only N, and Only a few N, 'N a Count Nun, satisfy (ia,b), i.e. they are anti-additive operators (also known as quasi-ideals), and their downwards monotonicity suffices to satisfy (iib) as well. So every regular (Zwarts 1 996a)/minimal (Zwarts 1 996b) negation is a minimal (Zwarts 1 996a)/sub-minimal (Zwarts 1 996b) negation. Negative NPs that satisfy (Z(iia,b) ), e.g. Not all N, not everyone, are anti­ multiplicative operators. Of course classical sentential negation, e.g. sentential or main-verb not, satisfies the negation versions of the four DeMorgan relations (ia,b) and (iia,b); Zwarts (1996a,b) suggests the possibility that a negative Proper Name, e.g. not John, is a DeMorgan Noun Phrase, satisfying all four relations, but Atlas (1996) argues against this possibility and for the emptiness of the class of DeMorgan Noun Phrases. The Noun Phrase only 11 N, 1..1. = 'one', 'two', 'three', . . ., satisfies none of (i) and (ii); by these criteria it cannot be considered negative at all.27 Zwarts (1996a) shows that some NPis require the anti-additive minimal (Zwarts 1996b) negation for triggering grammatical NPI sentences; others only require the "weaker" merely downwards monotone sub-minimal (Zwarts 1996b) negation. For example, if one thought, like Geach (1962/1980), Horn (1969, etc.), and McCawley (1981) that only a meant -NO ONE OTHER THAN a - , then only a would be a relatively strong negation, satisfying (ia,b) and called 'anti­ additive'. If one thought that only a meant ·AT MOST a·, then only a would be a weaker negation, satisfying (ia) or (iib) and called 'merely downwards monotonic'. If one thought, like Atlas ( 1 99 1 , 1993) that only a meant ·EXACTLY ONE I N D IVIDUAL , WHO IS AT MOST a · , then only a would be a non­ monotonic operator that is a "pseudo-anti-additive" operator, satisfying

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(Z) (ia) (ib) (iia) (iib)

290 'Only', Quantifiers, NPis, and Monotonicity

a. Only sentences in which an expression of monotone decreasing negation occurs can contain a negative polarity item of the weak type. b. Only sentences in which an expression of anti-additive negation occurs can contain a negative polarity item of the strong type. c. Only sentences in which an expression of classical negation occurs can contain a negative polarity item of the superstrong type (e.g. one bit happy).

These laws provide necessary conditions in semantic terms for posltlve distributional facts of grammatical co-occurrence, e.g. (a) a weak NPI occurs grammatically only if there is a merely monotone negation in the sentence. But there are two further relevant observations: first, as Zwarts of course notes, every anti-additive negation is also a merely monotone negation; second, weak NPis occur just as grammatically with the "stronger" anti­ additive negations as with the merely monotone negations. Thus the crucial data are, e.g. No one batted an eyelash, ?Few students batted an eyelash, *john batted an eyelash. These data distinguish the weak from the strong NPis: the ungrammatical/unacceptable strings contain the intuitively less negative quantifiers with the NPis that co-occur gramatically/acceptably with the intuitively more negative anti-additive quantifiers.3 1 What these data justify is Zwarts's (b) above: a strong NPI, e.g. batted an eyelash, occurs grammatic­ ally only if there is an anti-additive negation, e.g. no on, in the sentence. What the data do not justify is (a), that a weak NPI occurs ungrammatically unless there is a merely monotone negation in the sentence. The data merely show that it is grammatically impossible to have merely downwards

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only (ib).28 What the negative polarity data (22) of Atlas (1993: 3 1 3) showed, couched in terms of the theory of Zwarts (1996a,b), was that only a was not DeMorgan negative, was not anti-additive, but was at most a merely downwards monotonic quantifier, comparable to few N and at most m N. What is shown by the distributional facts, that certain NPI contexts exclude grammatical occurrences of'only a', is that only a is at most a merely downwards monotonic quantifier, not that it is a downwards monotonic quantifier. For the theory of Negative Polarity Item distribution has not demonstrated that the grammaticality of an expression's co-occurrence with a "weak" (Zwarts 1996a) Negative Polarity Item, e.g. ever, which at most requires a merely downwards monotonic quantifier, is sufficient for downwards monotonicity of the licensing expression. 29 There can be no such demonstration, for as my six reductio arguments (I I )-(1sb) above show, only a, which co-occurs with ever, is, unlike few N, not downwards monotonic. As I have shown, only a satisfies only (Zib), e.g. (2o) above.30 Of course Zwarts (1996a,b) and others have made the claim for a theory of Negative Polarity Items that I have just refuted, e.g. Zwarts's ( 1 996a, 1996b: r 86) Laws of Negative Polarity:

Jay David Atlas

29 1

(23) a. Only John ever suspected David Alexander. b. Only John kissed Mary anymore. c. Aileen Frans kan hem luchten of zien. Only Frans can stand him. d. ?Only I was all that keen to go the party. e. *Aileen Franz zal er een zier voor voelen. *Only Frans will be one bit interested. (24) a. Few men ever suspected David Alexander. b. Few men kiss Mary anymore. c. Few men were all that keen to go to the party. d. *Few men will be one bit interested. e. *Few men want Sam to finish the report until Friday. correct to claim that in respect of licensing NPis the data for only a above "are quite parallel to another quantifier whose downward monotonic status is widely conceded, NPs of the form Jew + CN." But what Zwarts's (r 996a,b) data and typology show is that the roughly parallel distributional data in (23) and (24) of licensing NPis do not permit a valid inference to the claim that only a is semantically the same as the downwards monotonic Jew CN. Zwarts's (r996a,b) Law (a) of Negative Polarity was never justified by the data. And that is just what the passage from Atlas (I99J: 3 1 3) quoted by Horn ( r 996b: 8) implies.

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monotone negations with strong NPis, i.e. that in a grammatical/acceptable sentence if a quantifier is merely monotone, then the NPI is not strong. Equivalently, merely monotone negations are sufficient ceteris paribus for the grammatical occurrence of weak NPis. These data do not show the converse, viz. (a), that merely monotone negations are necessary for the grammatical occurrence of weak NPis. Zwarts's (a) is not justified by his data, which is fortunate, since the behaviour of only a is a clear counter­ example to (a), and had the data justified (a), one would have wondered at the anomalousness of only a. Since the data do not justify (a), there is no peculiarity in only a being an exception to (a). Proposition (a) is not a law of negative polarity. A question that remains open, then, is which, if any, ofZwarts's ( r996a,b) "weak" NPis co-occur only with merely downwards monotonic quantifier expressions. Obviously ever is not among then. A question that is closed, obviously, is the logical character of any expression that licenses the occurrence of every NPI in English, German, Dutch et al.. Such an expression must be a classical negation. The English and Dutch data in (23) and (24), except for the contrast between (23d) and (24c), show that Horn (r996b: 9) is

292 'Only', Quantifiers, NPis, and Monotonicity 3·5

Horn's argument for the downward monotonicity of 'only

a'

�

On our Russellian, set-theoretic understanding of ALL(B,A), B � A. The first, "restrictor" position in 'ALL( , )' is monotonically decreasing, while the second position is monotonically increasing. Horn is at pains to point out, correctly needless to say, that Only As are Bs does not entail As are Bs, by contrast with my (1991, 1 993) view that Only a is F entails a is F. Of course, as I have shown, the cases are semantically different; only a is a non­ monotonic, pseudo-anti-additive quantifier, while only Count Noun is a downwards monotonic, anti-additive quantifier (Zwarts 1 996a,b). Since only Count Noun is downwards, it is allegedly "negative"; since only Proper Name is non-monotonic, mutatis mutandis it is "non-negative". Since both are specifications of Only Noun Phrase, it is unsurprising that the quantifiers share a semantic property: closure under finite disjunctions. In the case of only CN, this property is predictable from the entailment (29) alone; it is not predictable from the converse of (29). Thus the logical equivalence (28b) is otiose in explaining the semantical property common to 'only' in the various instances of only Noun Phrase. For explanatory purposes we do not require the logical equivalence of ALL(B,A) with ONLY(A.B), which is fortunate, since even if we needed it, we cannot have it, as I shall now argue.

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So what does justify Horn in thinking that only a is downwards mono­ tonic?32 Let us look at Horn's semantic argument in (28) on which he (1 996b: ro) centrally relies [I quote]: (28) '. . . only phrases MUST be downward monotonic, given the converse relation between only and all, recognized since the medievals: a. Tantum animal est homo convertitur in istam: omnis homo est animal, per istam regulam: Exclusiva affi.rmativa convertitur in universalem. Gohn of Holland, in Bos 1 985: 27) Only animals are human is converted into this: All humans are animals, by this rule: An affirmative exclusive is converted into a universal. [which Horn glosses by:] b. ONLY(A,B), All Bs are As.' Notice that John of Holland, unlike Horn in (28b), claims only that: (29) ONLY(A,B) If- ALL(B,A).

Jay David Atlas

4

293

I S ONL Y ( G , F ) L O G I CALLY E Q U IVALENT T O ALL(F , G) ? A D I RE CT ARGUMENT

ONLY(G,F) If- ALL(F,G) Uohn of Holland] • ( ALL(F,G) If- ONLY(G,F) ] • ( NO( •G,F) If- ONLY(G,F) ] ONLY(G,F) (i) grammatically presupposes that G' (the comple­ ment of G] is non-empty. (ii) implicates F is non-empty. (iii) implicates G is non�empty (for (believed to be) consistent G]. e. NO(•G,F) (i) implicates G' is non-empty (for (believed to be) consistent •GJ. (ii) implicates F is non-empty. (i) implicates F is non-empty (see Section 2). f ALL(F,G) (ii) hence, it is inferrable that G is non-empty.

(3o) a. b. c. d.

To put the point of (3o.d(i)) intuitively first, if an "excluder" like Only Gs is to exclude, there must be something excluded; otherwise the meaning of 'only Gs' is distorted. I argued (Atlas 1 99 1 : 1 28): (3o) g. Consider the sentence *Only everyone is running. This is a ungram­ matical sentence ofEnglish.33 If one states Only a,b,c, . . . are running, one "implies" that not everyone is running, i.e. that someone is not running. One "implies" that 'a, b, c, . . .' does not list everyone. Likewise the sentences, *Not only everyone is running, *It is not the case that only everyone is running, are ungrammatical English sentences,

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The answer is: no; ONLY(G,F) is not logically equivalent to ALL(F,G). I realize, of course, that mountains of opinion, for centuries, have held the contrary view. Well, lots of people, some immensely acute and perceptive ones among them, once thought that the earth was only 6ooo years old. (Dr John Lightfoot of Cambridge University put creation at Sunday, 23 October 4004 B C at 9:00 a.m.) Even one of the greatest of nineteenth-century physicists, Lord Kelvin, who formulated the First Law of Thermodynamics (conservation of energy) in 185 1 , calculated in a paper in 1863 that, contrary to geologists Lyell and Hutton's views, the earth could not be more than 1 oo million years old, far too young to explain geological formations and biological evolution. So let us accept the fallibility of received, even sophisticated, opinion and look at the matter. For the English Noun Phrase� only G, all F, and no non-G what is true, I shall argue in what follows, is (30):

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'Only', Quantifiers, NPls, and Monotonicity

and likewise if one states It is not the case that only a,b,c, . . . are running, Not only a,b,c, . . . are running, one "implies" that 'a, b,c, . . .' does not list everyone. I now would infer from these data:

'

For example, when one asserts Only birds have feathers, there is the semantical well-formedness condition: there are things other than birds. Since the following (i)-(iii) are ungrammatical (*) or semantically anom­ alous (#): (i) *Only everything has feathers, (ii) #Only furry or non-furry things have feathers, (iii) #Only self-identical individuals have feathers. Only As are B requires that the complement of A, viz. A', is not empty (that A is not the domain D), which is to say that birds aren't everything!3 5 There is also an inference from the statement Only birds are feathered to There are feathered things, a proposition of existential import. Notice that the analogue to Horn's truth-conditions No one other than a is F for Only a is F in the case of Only As are B would be No non-As are B, not his All Bs are A. The statement No non-birds are feathered has the same existential implicatum as Only birds are feathered, viz. There are feathered things. (The statement-schema No Cs are both D and not D shows that asserting No Cs are Bs merely implicates that there are Bs.) But 'no' is a "denier", not an "excluder", of individuals from the extension of the predicate 'feathered'. If non-birds are denied by 'no' from the extension of 'feathered', there need not be non-birds to deny; No round square is feathered is grammatically acceptable. So the non-emptiness of the extension of 'non-birds' is not required for semantical well-formedness, i.e. the semantical well-formedness of No non-As are B does not require that A' be non-empty. Asserting No Cs are B would merely implicate that there are Cs. (It might typically be misleading to deny of Cs that they are Bs unless there are some Cs.) But for the statement-schema Only As are B the

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(3o) h. To simplify, what is GRAMMATICALLY PRESUPPOSED by Only Gs are F is Gs are not everyone [•(G = D)]. It then follows that it is at least presupposed that if the domain D is non-empty, then G' is non-empty, i.e. that if D is non-empty, there is at least one non-G, but it is not presupposed that there is a G ( 1G1 is a focus NP, not a topic NP). IfD were empty, contrary to the classical assumptions, in the null model M0, M0 I= VxGx, i.e. Everyone is a G. So G s are not everyone does entail that D is non-empty. Thus it is grammatically presupposed: (1) D is non-empty; (2) G' is non-empty. On the further assumption (not presupposition) that there is a G, since there is at least one non-G, it follows that there are at least two individuals in the domain of quantification D.34

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295

ONLY(G,F) If- ALL(F,G) Uohn of Holland] ..., ( ALL(F,G) If- ONLY(G,F) ] ..., (NO( •G,F) If- ONLY(G,F) ] ONLY(G,F) (i) grammatically presupposes G' is non-empty. (ii) implicates F is non-empty. (iii) implicates G is non-empty (for (believed to be) consistent G]. e. NO(•G,F) (i) implicates G' is non-empty (for (believed to be) consistent •G]. (ii) implicates F is non-empty. (i) implicates F is non-empty. ( ALL(F,G) (ii) hence, it is inferrable that G is non-empty.

(3o) a. b. c. d.

s

I S O N L Y ( a , F) L O G I C ALLY EQ UIVALENT T O ALL( F , a ) ? A N I N D I RE C T ARGUMENT

The argument in Section 4 relies upon a linguistic judgement in support o f a semantical well-formedness condition for 'only CN to be an "excluder". There may be some who do not find such semantical intuitions compelling but are convinced by the entailment intuitions and reductio arguments that only a is not downwards monotonic. I shall now demonstrate that if you agree with me that only a is not downwards monotonic, you cannot

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admissible models are ones in which the complement of A, viz. A', is non­ empty, while the models for the statement-schema No non-As are B are not so restricted, though both statements implicate that B is non-empty, and the statement-schema No non-As are B implicates, not requires for either truth or falsity, that A' is non-empty for (believed to be) consistent non-A. Thus it is false that No non-As are B entails Only As are B (for it is false that every admissible model in which the first is true is one in which the second is true). Horn-type truth-conditions No non-As are B do not even logically imply Only As are B. So (3oc) is correct. Since asserting All Bs are A only implicates that B is non-empty (see Section 2), its class of admissible models does not require that A' be non­ empty; e.g. this sentence is semantically well formed: All birds are self­ identical. But then it is false that All Bs are As entails Only As are B. Any admissible model in which All Bs are As is true need not be a model in which A' is non-empty, and so Only As are Bs will not necessarily have a semantical value in that model, hence need not be true in that model. So (3ob) is correct. 36 In sum:

296 'Only', Quantifiers, NPls, and Monotonicity

consistently believe that Only a is F is logically equivalent to All Fs are a/ Every F is a. As reported by Horn { I996b: I S) the fourteenth-century English logician Walter Burleigh claimed that the monotonic entailments of only (tantum) and all (omnis) held for the alternate predicate positions. {3 r ) a. b. c. d.

Tan tum Sor videt animal. Tantum Sor videt asinum. Omnis homo est animal. Omnis albus homo est animal.

Only Socrates sees an animal. Only Socrates sees an ass. Every man is an animal. Every white man is an animal.

(32) a. Tantum homo movetur If- Omne movens est homo. Only a man is moving If- Every moving thing is a man. b. Omne movens est homo If- Omne currens est homo. Every moving thing is a man If- Every running thing is a man. c. Omne currens est homo If- Tantum homo currit. Every running thing is a man If- Only a man is runni11g. d. So, by transitivity (a), (b), (c): Tantum homo movetur If- Tantum homo currit. 37 Only a man is moving If- Only a man is running. Of course the logic of the argument is unchanged if one substitutes a Proper Name for the Indefinite NP 'a man'. Since I have demonstrated the falsity of the Proper Name version of (32d), of the downwards monotonicity of ONLY(a,F) in the second position, at least one of Burleigh's claims (32a), (32b), (32c) is false for the Proper Name case. I have already accepted John of Holland's entailment (32a) and shown why it is correct. I also accept, with the standard view, the downwards monotonicity of ALL(F,G) in the first position, i.e. I accept (32b). So what must be rejected is (32c). Every running thing is a man does not entail Only men are running.38 Thus, given the arguments I have offered against the downwards monotonicity of ONLY(a,F) in the second position, those arguments now suffice to show, while accepting (32a) and (32b), that ONLY(a,F) is not entailed by, and so is not logically equivalent to, ALL(F,a).

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Allegedly {3I a) entails {3I b), and {3I c) entails {3I d). That is to say that ONL Y(a,F), 'a' an individual constant, is downwards entailing in the second position, and ALL(F,G) is downwards entailing in the first position. In Atlas (1993) I rejected the view that ONL Y(a,F) was downwards monotonic in the second position, so I reject the alleged entailment from (3 I a) to (3 I b). By contrast Walter Burleigh offers an argument in support of the downwards entailment in the second position of ONLY(G,F), 'G' and 'F' count nouns, viz. an argument from double conversion, as in (32):

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Even Horn ( 1 996b: I S) admits that the alleged downwards entailment of

ONLY(a,F) in the second position is "odd", but asserts that:

the oddness of the downward inference . . . in the case where the animal Socrates sees is an ox rather than an ass is no more problematic than the well-established downwards inference from [Jic] to [Jrd], which remains valid in the absence of white men. The issue of existential import is to be handled similarly in both cases.

6 O N A CC O M M OD A T I N G Th ere is a n F FROM THE STATE ME NT ONL Y Cs a re F Horn's new view offers a derivation of the non-implicatum a is F from the statement Only a is F. Horn ( 1 996b: 16) claims that "no specific rule­ entailment, presupposition, implicature-need be stipulated for deriving" a is F. The "purported positive entailment/presupposition . . . is simply the existential import of the corresponding universal . . . ". Horn's argument is: The statement Only Gs are Fs is logically equivalent to All Fs are Gs. But stating All Fs are Gs implicates or accommodates There is an F (existential import). Thus the total signification of the statement Only Gs are Fs entails Some Fs are Gs.

In the case in which IIC I I={a}, the entailment is equivalent to Fa. This new argument is still subject to my ( 1 993: 3 1 6, n.s) old objections to his ( 1992)

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But the oddity of the downwards entailment for only a is more problematic than the entailment for all. The oddity is not merely a matter of a failed existential import of a predicate in the case of only a as it might be for all F if there are men but no white men. The all inference is valid because the extension of white man, even if it is the null set, is a subset of the extension of man, and the validity depends only on the partial order of the predicate extensions under the subset relation. The only a inference is dubious because it alleged validity cannot be explained by a partial order of the predicate extensions under the subset relation without assuming the equivalence between ONLY(a,F) and ALL(F,a). But to assume that equivalence in the current context of argument, the point of which is to show that there is no such equivalence, would merely beg the question. (Since my arguments in Section 4 against this equivalence are independent of my claim that only a is non-monotonic, I am not begging the question against my opponents.) The claim of the validity of the downwards entailment must be supported on its own merits, not by merely assuming the alleged equivalence between ONLY(a,F) and ALL(F,a) and merely assuming the validity of Walter Burleigh's double conversion argument. The reductio arguments in Section 3 show that the claim is without merit.

298 'Only', Quantifiers, NPis, and Monotonicity

There is an existential inference, generally assumed to hold in pragmatics, that characteristically associated with the assertion [my emphasis] of a universal.

IS

Since All Fs are Gs is not stated, on Horn's own grounds it is hard to see how the existential import is to be communicated. As I have observed elsewhere (Atlas I 995c), the theorist's need for an assertion somewhere tends to push the asserting back into the mind, so that when I assert Only Gs are Fs I am not just thinking All Fs are Gs; I am also "mentally asserting" All Fs are Gs. It makes for a very busy, parallel processing mind. The problem is, "mentally asserting" is not really something I'm aware of doing, and it seems something that I'd be better off not positing if an alternative theory could be found. Earlier I spoke of a convergence between my (I99I, I 993) view and Horn's official view. As he graciously observes, there is now not the earlier difference in our semantical views, since we both think that something entails Fa. The difference remains in what the something is. I think it is the truth-conditions of any statement of the schema Only a is F. Horn now thinks that by virtue of accommodation what entails Fa is the total signification of the statement. The difference is that the total content of the assertion seems to depend for Horn upon an indefeasible but pragmatic inference, viz. accommodation, and so, unlike an entailment, on his official view Fa does not necessarily follow from Only a is F. (See my discussion of Existential Import in Section 2.) One advantage of Horn's new official view is that it explains the Anita Mittwoch-Rogers Schwarzchild data of (33):

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version of this argument, which I shall not rehearse again here. To evade my original objections to this sort of argument Horn must claim that pragmatic inferences from Only Gs are Fs, including accommodation, are "trans­ derivationally generated", e.g. from the statement's equivalence class under the relations of synonymy with, or at least logical equivalence to, All Fs are Gs. Since I showed in Atlas & Levinson ( 1 98 1 : 1 -2, 8-9, 12-13) that the implicata of a statement are not preserved under logical equivalence, there is no general theoretical reason to expect that a logical equivalent to Only Gs are Fs preserves the latter's implicata or other pragmatic inferences. Finally, since it is false that Only Gs are Fs is logically equivalent to All Fs are Gs, an essential premiss of Horn's argument is, I believe, incorrect. Alternatively, he must claim that the "existential import" There is an F of All Fs is not a pragmatic inference of stating All Fs are Gs, since the latter is not stated, but somehow inferrable from an understanding of the meaning of Only Gs are Fs. The obstacle to Horn's taking this way out of the problem posed by my original objections to his (1992) similar conversational implicature view is that he (I 996b: 1 0) states:

Jay David Atlas

(33) a. b.

__

__

299

Who's coming tonight? Only John (is coming).

7

ASYM METRY, NEGATIVITY, A N D D I STR I B U T I O NAL FACTS

What pushes Horn to his official view that the truth-conditions of Only a is F are No one distinct from a is F is that a "negative" formula predicts alleged data: pragmatic facts of the suspension of implicata and distributional facts of the occurrence of negative polarity items (NPis) and facts of NP/V inversion. The alleged facts are claimed to be inexplicable on an analysis, like mine, whose truth-conditions entail the positive sentence a is F. If what I have said above about the logical semantics and implicatures of Only a is F is correct, either there must be alternative explanations of the data, or the data must be reanalysed. That is what I shall now proceed to do. Horn (I996b: 2) claims that the positive a is F can be "suspended" with

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As Horn explains it, the interlocutor who poses the question in (33a) must "accommodate" from the respondent's reply merely that someone is coming, not, as on Horn's (I992) earlier view, that John is coming. An advantage of my (I99 I , I 993) view is that it explains the Anita Mittwoch/Rogers Schwarzchild data of (33). I have a different analysis from Horn's. The posing of the question Who's coming tot1ight? already forces on the respondent an accommodation that someone is coming. Then the answer Only John informs the questioner that one person, John, is coming. Thus the data of (33) are compatible with my (I99 I , I 993) neo-entailment analysis as well. Furthermore, my analysis will help Horn out of the difficulty that his "trans-derivational' account brings upon him. Since I (Atlas & Levinson I 98 I ; Atlas I 988, I 989, I 99 I , I 993) have emphasized the crucial logical role that the Topic-Comment structure of assertions plays in the logical analysis of cleft statements, negative existence statements, and focal particle statements, my analysis of the Topic NP role of F in Only a is F suggests that it is a feature of asserting the sentence 'Only a is F' with the focal particle 'only' that there should be a generalized conversational implicatum (which includes, on my view, accommodation) There is an F. Horn does not need to appeal to the alleged logical equivalence of Only Gs are Fs with All Fs are Gs to get an inference to There is an F from Only Gs are F, and a good thing too; for there is no such logical equivalence to appeal to, and even if there were, it would not yield the inference. But if he wants the inference, he's got it from my (I99 I , I 993) analysis.

300 'Only', Quantifiers, NPis, and Monotonicity

the help of an "epistemic" rider possible while the negative no one distinct from a is F cannot be.39 An analysis that predicts that both are entailed by Only a is F cannot, Horn suggests, explain the difference in the alleged data of "suspension". Horn's judgements are given in (34), where (34a) is allegedly acceptable, and (34b) is unacceptable. Of course Horn ( I 996b: 2, ex. (3a,b)) admits that one cannot acceptably assert (3sa) [and, I would add, (3sb) as well]: (34) a. b. (35) a. b.

Only Kim can pass the test, and it's possible even she can't. #Only Kim can pass the test, {and, but) it's possible that someone else can. #Only Kim can pass the test, and she can't. ?Only Kim can pass the test, and maybe she can't.

(36) #Everyone passed, but {for all I know/it's possible that) someone didn't. where one who asserts (36) recognizes that {Everyone passed, Someone did not pass) is not satisfiable. Horn claims that 'possible' in (34a) is the speaker's epistemic 'consistent with all I know/believe'. I find the following version of (34a) acceptable: (34) a'. Only Kim can pass the test, and maybe even she can't. Where even is inserted in (34b), I find it much less deviant (in fact marginally acceptable (?7)): (34) b'. ?10nly Kim can pass the test, {and, but) it's possible that even someone else can. On the non-epistemic understanding of 'possible' as 'logically possible', I would find the following sentences acceptable: (37) a. Only Kim can pass the test, {but/and} it's possible/ she can't. b. Only Kim can pass the test, {but/and} it's possible/ even she can't. But on the epistemic understanding of 'possible' as 'for all I know/believe', my judgements differ from Horn's on (38b)/(34a) and coincide with Horn's (1972) on the maybe even sentence (38c)/(34a') when the second clause is a retraction or modifier of the first:40 (38) a. #Only Kim possiblee that} b. ?Only Kim possible, that}

can pass the test, {and/ but) {for all I know/it's she can't. can pass the test, {and/but) {for all I know/it's even she can't.

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but despite the essential occurrence of the "epistemic" qualifier possible even in the allegedly acceptable (34a), he believes that (34b) is just as unacceptable as (36) (Horn 1996b: 2, ex. (3c) ):

Jay David Atlas 301

c. Only Kim can pass the test, {and/butJ maybe even she can't. d. ?Only Kim can pass the test, but she may not have been able to pass the test.

:

(39) a. No even two years ago could you swim there. b. In not many years {does, wilij Christmas fall on (a) Sunday. 43 Thus according to Horn the following 'only' sentence requires mverston (Horn 1 996b: 3): (4o) a. Only one feature did I notice in the landscape . . . b. *Only one feature I noticed in the landscape . . . Horn's explanation for the similarity in inversion in (39) and (4o) is that 'only' sentences, e.g. only J-L N sentences, are also "negative", supporting his, Geach's (1962/I 98o), and McCawley's analysis of only a as the "negative" no one distinct from a .44 But inversion is certainly no less obligatory in the following sentences (4 1) as in (40) :

(41) a. Exactly one feature did I notice in the landscape . . . b. ?Exactly one feature I noticed in the landscape . . . Nevertheless exactly one NP is not downwards monotonic; it is non­ monotonic (if card jjNPjjM � 2 (Gamut 1 99 1 : 239, 328).45 So it cannot be necessary for syntactic inversion that the generalized quantifier expression be semantically downwards monotonic. Thus the fact that only NP can trigger syntactic inversion permits no inference to the claim that only NP is downwards monotonic and so is "negative". Inversion is not confined to

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Again for the reasons given by Alan White ( 1 975: so- I ) I find (38d) deviant. It seems to me that the relevant question is the acceptability of (38a) and of (38d), where the absence of even makes the sentences test cases of epistemic cancellation of Kim can pass the test without the semantic effect that even introduces in Horn's (38bf34a, 38c) (see Horn 1 969; Kay 1 990; Lycan 199 1 ; Barker 1 991). Even if one were to find the possible even sentence (38b) acceptable, as Horn does, its acceptability would not determine the issue at hand, which is an alleged difference in the epistemic cancellations (grammatically acceptable denials) of a is F and no one distinct from a is F, not in their suspensions, viz. blockage of an inference to a is F or to no one distinct from a is F, from the conjunction.41 I do not find in the data Horn's difference in acceptabili.ty between denying a is F (38a,d) and denying no one distinct from a is F (34b) while asserting Only a is F.42 Horn also believes that giving the official "negative" analysans no one distinct from a is F for only a is F will explain inversion that is allegedly restricted to "negative" sentences (Klima I 964: 300- I ), e.g. (39)

302 'Only', Quantifiers, NPls, and Monotonicity

phrases of semantically negative character, so inversion is not a sufficient reason to think that only NP is negative.46 Finally, the fact that only NP licenses some negative polarity items is also no evidence that all 'only' sentences, including 'only a' sentences, are semantically downwards monotonic and hence "negative". Horn cites Klima's (1 964: 3 1 1) example: (42) Only young writers ever accept suggestions with any sincerity. But, as above, the sentence with exactly one licenses the same negative polarity items ever and any in (43): (43) Exactly one young writer ever accepted suggestions with any sincerity. Downloaded from jos.oxfordjournals.org by guest on January 1, 2011

To infer from examples like (43) that exactly one writer is downwards monotonic, on the grounds that only downwards monotonic expressions license any negative polarity items, is to make a false prediction, viz. that exactly one writer is downwards monotonic (unless llwriteriiM =o (Gamut 1 99 1 : 328) ). S o i t is false that only downwards monotonic expressions license any negative polarity items. Hence data like (42) provide no conclusive evidence to support the hypothesis that only NP, for any NP, is downwards monotonic and hence semantically "negative'. My argument is straightforward. If the explanation of a quantifier expression's licensing NPis is supposed to be that the meaning, i.e. at least the extension, of the expression is a downwards monotonic quantifier, then there is no semantic explanation of exactly J-L N licensing a NPI, since it is not downwards monotonic and hence not semantically negative. What Linebarger (1987, 1 99 1 ) tried to explain (?), by the hypothesis that Exactly J-L N licenses a NPI if and only if asserting Exactly J-L N- VP implicates the allegedly downwards monotonic Only J-L N- VP, can be more parsimoniously explained. I never knew how to take Linebarger's claim. Is it a descriptive generalization? Is it an explanation of some kind? I grant that only"Count Noun is downwards monotonic. For the sake of argument, I'll even grant the claim that sometimes asserting exactly QP implicates 'only QP'. Are we supposed to explain the licensing of the NPis by the fact that only QP is implicated by asserting exactly QP? How does this explanation go? If the implicature is a conversational one, even the downwards monotonicity of Only Count Noun will not explain why the meaning of exactly CN should be "negative" and NPI licensing. There is no inference from the negativity of an implicatum to the negativity of the implicans, otherwise some would be negative because asserting it implicates not all. On the other hand if Linebarger is offering a descriptive general­ ization, then we ought to explain by deeper theory why her generalization holds.

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For example, when Exactly NP is used as a focal expression, asserting Exactly NP- VP will seem to implicate the focal particle sentence Only NP - VP. It is clear in certain extreme cases that exactly is focusing, and not semantically adding to, the NP, when it is used in sentences like There is exactly one even prime natural number. Thus in Exactly one even prime natural number ever played an important role in anything that DesCartes wrote, Exactly one even prime natural number occurs compatibly with NPis ever and anything. Without focus the utterance-type ?One even prime natural number ever played an important role in anything that DesCartes wrote sounds deviant, but with focus stress and intonation the utterance-type ONE even prime natural number EVER played an important role in anything that DesCartes wrote sounds much more acceptable.47

Horn (1 996b: 2) has asked: If orzly sentences have positive entailments [e.g. Only God can make a tree II- God can make a tree], how do we account for the data [of suspension of the positive entailment by an epistemic rider, of licensing negative polarity items when it is assumed that only downwards monotonic quantifiers do so, and of syntactic inversion] . . . which seem to demand an asymmetric theory of only on which the negative exponent [No one distinctfrom God can make a tree] is somehow more equal than its positive counterpart [God can make a tree]?

My answers are: (i) There is no suspension of the positive entailment by an epistemic rider-the data are symmetrical. (ii) Some non-monotonic quantifiers, e.g. just/exactly one N and only a, also license some negative polarity items, e.g. ever, any. (iii) Not only downwards monotonic quantifiers require syntactic inver­ sion: syntactic inversion is not a symptom of downwards monotonicity, as just/exactly one N illustrates. These observations undermine Horn's inference from the alleged facts on only NP to the conclusion that only NP in general, much less the case only Proper Name in particular, is downwards monotonic and hence semantically "negative". (iv) Though only CN is anti-additive, hence downwards monotonic, only a is a non-monotonic but "pseudo anti-additive"expression. (v) The non-monotonicity of only a is inconsistent with the logical equivalence of ONLY(a,F) to ALL(F,a). So they are not logically equivalent. ALL(F,a) does not entail ONLY(a,F).

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8 C O N C LU S I O N S : A NEW TYPOLOGY F O R N E G A T I VE QUANTIFIERS

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(vi) Horn wishes to explain the inference to There is an F from asserting Only Gs are Fs or Only a is F. On his new official theory there is no adequate explanation. On my (199 1 , 1993) theory and on the revised theory of this essay, there is. (vii) My theory is also consistent with the Mittwoch/Schwarzschild data of (33). (viii) I continue to think it obvious that it is impossible for Only a is F to be true and a is F to be false. Horn's official new theory has no explanation; Horn's unofficial new theory does-it is a version of my current theory. (ix) Thus the symmetrical analysis of Atlas (1991, 1993} has not been ruled out by the alleged data and official analysis of Horn ( 1 996b) .

(x) NON-NEGATIVE < PSEUDO-MINIMAL < SUB-MINIMAL < OUTER < MINIMAL < CLASSICAL (where CLASSICAL is empty [see Atlas (1996}]:48 NON-NEGATIVE {no deMorgan

PSEUDO-MINIMAL

Only J1 N Exactly J1 N

Only a

rule satisfied)

SUB-MINIMAL

OUTER

(downwards monotonic)

(anti-multiplicative)

few N At most a At most m N

Not all N

MINIMAL (anti-additive)

No N No one other than a Only a few N Only CN

It should be especially noted that the English quantifier expressions (i} At most John and (ii) No one distinct from John have distinct logical properties, the former being a merely downwards monotone NP, the latter being an anti-additive NP, even though their respective formalizations in classical first-order quantification theory with identity are logically equivalent: (i'} Vx(Fx ---+ x=John), (ii') -.3x( -.(x=John) & Fx). It is intuitively obvious that the latter formalization is syntactically the "more negative", which is consistent with the logical judgement that at most John is merely down­ wards monotone and the judgement that no one other than John is the more negative anti-additive quantifier of the English quantifier expressions being formalized. In Atlas (199 1 , 1993} I misleadingly used the English quantifier expression No one distinctfrom John interchangeably with At mostJohn, even though the formalization that I (Atlas 199 1 : 138} chose (i' above), by contrast with that of the official Horn (1969, 1 979, 1992, 1996b) (ii' above), was explicitly noted by me as best expressed by At most John (Atlas 1 991: I 33). Mea culpa!

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Modifying the typology of Zwarts (1996a,b) I (Atlas 1995b) shall introduce the following ordering of non-negative to increasingly negative Noun Phrases:

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305

(xi) only a means exactly one individual, who is at most a

(xii) In Atlas (I993) I earlier criticized two arguments, Horn's reduction of the entailment theory of only by his reductio of only ifto if and only if and McCawley's (I98 1 ) argument in support of the semantical negativity of only a is F. Surprisingly neither of my criticisms is addressed in Horn (I 996b) ; his original arguments are merely restated without further defense. So I have attempted to add to those criticisms in Appendices II and Ill, in hopes that the point will have been made more clearly. Horn ( I 996b: 24) concludes his discussion with the remark: The position on which Atlas alights is thus not entirely at odds with the one defended here, although we differ in many respects . . . Recall that Atlas's assumption of an entailed prejacent [Muriel votedfor Hubert] results in his denial of downward inferentialiry for only XP, and correspondingly in his failure to appreciate the significance of the monotonicity efforts (polarity licensing, inversion triggering, suspension, illocutionary scoper associated with exclusives.50 Since Atlas evidently accepts the standard non-conjunctive line on universals, he is also incapable of capturing the Burleyan insight recognizing the conversion of only A is B +-> all B is A.

In this paper I have shown that Burleigh was mistaken; only A is B entails all B is A but not conversely. I have distinguished the anti-additivity of only Count Noun from the non-monotonicity of only a, 'a' an individual constant. There is no general downwards monotonicity property for only XP. In the table for negative NPs above, one can distinguish the different semantic properties of non-monotonic but pseudo-anti-additive only a, anti-additive only Count Noun, and non-negative only J.l N. And I have discussed polarity licensing, inversion triggering, and suspension associated with exclusives, the appreciation of the importance of which in the case of 'only a' I owe to Horn (1992). In Atlas (I993) I had earlier discussed briefly

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On this point Horn remarks, 'while Atlas is certainly correct in claiming that Only Muriel voted for Hubert does not "say" that Muriel voted for Hubert, there is no reason to believe that it "says" that exactly one individual did so either.' By the criteria used by Karttunen & Peters (I 979) and appealed to by Horn to distinguish "what is said" P from what is conventionally implicated or non-trivially entailed Q, the statement form I know Q but P? should be acceptable. Thus the acceptability of I know Hillary trusts Bill, but does ONLY Hillary trust Bill? should be paralleled, on Horn's theory, by the predicted acceptability of #I know that only Hillary trusts Bill, but does exactly one person, {who is at most Hillary, who is none other than Hillary}, trust Bill?. But that is a false prediction of Horn's theory. And the simplest explanation of that datum is my analysis (xi).

306 'Only', Quantifiers, NPis, and Monotonicity

If the Williams of Ockham and Sherwood, Walter Burley, and their colleagues had only taken the trouble to consult Grice on implicature, Lewis on accommodation, and Stalnaker on assertion and presupposition, the reign of the conjunctive analysis might have been far shorter-lived. I would have thought that they would have done much better to have consulted their English countrymen Grice (I975) on implicature, Strawson ( 1 950, I 964) on presupposition, and Geach ( I 972b) on assertion: the D. K. Lewis (I979) notion of "accommodation" they could have invented for themselves in five minutes on a rainy afternoon (as I did, though not under that name, in Atlas (I 975, I 977) ). Let us late twentieth-century American philosophers and linguists not be too intellectually self-congratulatory about the achievements of our historical age. Those monasteries crammed to the spires with specialists on only, as Horn charmingly puts it, were to be found nowhere on the North or South American continent. As this paper shows, Peter of Spain and William of Sherwood were wrong, but not as wrong as Horn ( I996b) thinks. As I cautiously interpret him, John of Holland, my Groningen colleagues will be pleased to note, was actually right.

Acknowledgements I

am indebted to Henriette deSwart, Ivan Sag, Frans Zwarts, Jack Hoeksema, and others in the Semantics Workshop, June 1996, Center for the Study of Language and Information, Stanford University, for helpful discussion. I am likewise indebted to Jerry Sadock and the graduate students of his Spring Term, 1996, Pragmatics Seminar, University of Chicago. For conversation and advice I am indebted to Jerry Sadock, to James McCawley and Larry

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the non-monotonicity of only a, suspension phenomenon, and the polarity licensing by only a, where I distinguished the licensing of any and ever from the failure of only a to license until Friday. I had failed to appreciate how critical for current theories of the licensing of Negative Polarity Items the (erroneous) claim of downwards monotonicity for only a was until I heard Klooster (I994) give syntactical reasons to distinguish the minimizers in (22) from the "weak" NPis and give support to my claim for the non­ monotonicity of only a. In light of my discussion of the data of (22), and of the arguments of Klooster (I 994, I995), I now believe that the minimizers form a special class of NPis, co-occurring with both upwards and downwards monotonic, Focused NPs. An adequate explanation will have to account for the role of negative and question discourse contexts, assertorically Focused NPs, and the semantical pseudo-anti -additivity of only" Proper Name. Horn's paper concludes with the followingjudgement on Peter of Spain's conjunction analysis:

Jay David Atlas 307 Hom, especially for their extensive written comments on the January 1996 version of this essay, Rene Coppieters for helpful suggestions, Frans Zwarts, Jack Hoeksema, Sjaak deMey, Victor Sanchez Valencia for much useful discussion; Wim Klooster, Henny Klein, Charlotte Koster, Henriette deSwart, Eric Krabbe, Michie! Leezenberg, Ton van der Wouden, Sharon Parry, Jason Linder, Thomas J. Rankin, and John Francis Walter. For my Visiting Professorship in the Fall Term, 1995, I am indebted to the Department of Philosophy, University of California, Los Angeles. For the invitation to be a Visiting Research Scholar in the Department of Dutch Linguistics and in the Institute for Behavioural, Cognitive, and Neuro-Sciences in the University of Groningen, The Netherlands, in the Spring Term 1995, I am indebted to Frans Zwarts, Jack Hoeksema, and the Faculty of Letters. This research was supported in part by Nederlandse Organisatie voor Wetenschappelijk (NWO)-The Netherlands Organization for Scientific Research-and by the Institute for Behavioural, Cognitive, and Neuro-Sciences, University of Groningen, The Netherlands. Received: 09.02.96 Revised version received: 25. 1 1.96

APPE N D I X I Op en Questions

( 1 ) A question that remains open is: which, if any, of Zwarts's ( 1996a,b) "weak" NPis co­

occur only with merely downwards monotonic quantifier expressions? Obviously 'ever' is not among them. (2) McCawley's and Hom's data (22e-g) do not show that because it licenses minimiser NPls only Phil is a semantically negative operator; and upwards monotonic, focused NP, as in the stressed utterance-type (22!) PHIL would lift a finger to help Lucy. and the non-monotonic, focused only a in Hom's and McCawley's data (22e,e',f,f) equally well make the occurrence of lift a finger acceptable in the utterance. Co-occurrence of non­ monotonic, focused 'only" Proper Name' and 'only"Pronoun' with NPI minimizers seems explicable by conventionalization of the use of minimizers with focused NPs-the very feature of NPs that would occur in the original denial and question contexts. Non­ monotonic, Pseudo-Negative, only a NPs in statements are apparently (i) assertorically Focused enough and (ii) semantically negative enough to co-occur with "weak" NPis like ever and any. But is this right, and exactly how does this work? (3) There is the possibility that the semantical explanation for 'only"Proper Name' co­ occurring with "weak" NP!s is quite other than the semantical pseudo-anti-additivity of 'only"Proper Name'. The hypothesis that downwards monotonicity was necessary for licensing NPis was a noble attempt, but at this moment there is no theory at all for the behaviour of 'only "Proper Name'. The observation that the quantifier is closed under finite unions is just an observation that one DeMorgan relation is satisfied. If that explains

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JAY DAVID ATLAS Department of Philosophy Pomona College 551 North College Avenue Claremont, CA 917H - 6355 e-mail: [email protected]

308 'Only', Quantifiers, NP!s, and Monotonicity why it licenses "weak" NP!s, no one had a theory that shows why that is an explanation. The young man or woman who comes up with a good theory wins a US$soo Atlas Prize. Contrastive 'but'

( I ) a. Only Muriel voted for Hubert, but {she did/#nobody else did}. b. Muriel and only Muriel voted for Hubert, but {#she did/#nobody else did}. The data of ( I a) are incorrect: the correct judgement, instead of ( u), is ( I c): c. Only Muriel voted for Hubert, but {#she did/#nobody else did}.51 The pattern for only a is the same as for the admittedly non-monotonic a and only a in Horn's data. Whatever the force of these data, if they show anything, they show that only a shares distributional patterns for the case of "contrastive" but with a non-monotonic quantifier expression. The analysis of Atlas (1991, 1993) predicts this datum. Hom offers another argument, from Barwise & Cooper (1981: 193},,that Noun Phrases with different monotonicity must combine with but not and, as in the following JUdgements: ·

(2} a. John {#and/but} no woman b. Few women {#and/but} many men c. Many men {#and/but} only three women52 d. No men {and/#but} only three women and that Noun Phrases with the same monotonicity must combine with and not but: (3) a. No men {and/#but} very Jew women b. No men {and/#but} only three women. I doubt the strength of the Horn, Barwise & Cooper's (198I} argument, for there are cases of parallel monotonicity that prefer but to and, e.g. (4):

(4) Some men {#and/but} every woman driver Even if a case could be made for sameness of monotonicity being sufficient to permit grammatical occurrences of and or to forbid grammatical occurrences of but, its converse would not follow, viz. it would not follow that an ungrammatical environment for but is sufficient for sameness of monotonicity. Yet that converse is the interesting and relevant hypothesis for attempting to show the monotonicity of only phrases (e.g. (zd) ). It is also false, since (3b) would imply that Only J1 N is downwards monotonic. To the extent that I have reliable intuitions about these null-context sentences involving and and but at all, I have different intuitions from Horn, Barwise, and Cooper.

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Consider the following data in which Horn (1996b: 4) contrasts the non-monotonic a and only a with the allegedly downwards monotonic only a. Horn claims that the non­ monotonic, neutral expression Muriel and only Muriel in (1b) blocks "contrastive" but when concatenated with his negative truth-conditions for Only a is F, viz. with no one distinctfrom a, or when concatenated with the positive entailment a is F of the total content. He claims that in ( u) only a, by contrast, does not block "contrastive" but with the entailed positive a is F, since, on his view, only a is negatively orientated and can contrast with a positive statement a is F, while it does block "contrastive" but with his negative truth-conditions no one distinct from a is F for only a is F.

Jay David Atlas 309

A P PE N D I X I I McCawley's

(1981)

p araphrase of A

only if B

If McCawley ( 1 981: so) were right that A only ifB is better paraphrased by Not A if not B than by B ifA, Not A only if not B would allegedly be better paraphrased by Not not A if not not B than by not B if not A. But who could believe that? (I am not confusing the oddity of a double negation sentence with its inaccuracy as a paraphrase.) The question is, which is the better paraphrase of Not A only if not B, not B if not A or not not A if not not B? If I were trying to judge among paraphrases of not A $ not B, $ a dyadic connective, and my choices were among: (•A ........, •B), (•( •B) ........, ( •A )) and (B -> A), I think the obvious choice is (•A -> •B), not McCawley's (•(•B) -> •(•A )), i.e. $ ; ->, not . . . +- •. . . . The interesting argument in support of McCawley's view is not offered by McCawley. It is: Go only ifyou want to! would be better expressed by Don't go ifyou don't want to! than by *You want to go if go!. And that is hard to deny. My (1993= 312- 13) earlier argument against McCawley's analysis was the following: •

,

•

McCawley's second argument concerned Negative Polarity Items. For discussion of that issue, see Section 3-

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McCawley ( 1 98 1 : so- t ) offers rwo arguments in support of the negativity of only sentences. One argument relics on alleged facts of paraphrase. First, he states rwo alleged facts, 'The fact that only can be paraphrased by expressions involving rwo negatives in combination such as No X other than Y, e.g. John read only thefirst chapter by John read nothing other than thefirst chapter, and Only Susan has a key to this room by No one other than Susan has a key to this room, and 'the fact that not A if not B is so much better a paraphrase of A only ifB than is IfA then B (or B ifA)', i.e. that only if is best paraphrased by an expression combining rwo negatives. These alleged facts suggest to McCawley (198 1 : so), and to Horn, that the only of A only if B is the same only that will combine with NPs and be analyzed as containing rwo negatives, e.g. no and other than. Let me begin with problems for the second alleged fact. Though it is true that IfA then B and A only if B do not seem to be paraphrases in cases like (a) If Mike straightens his tie once more, I'll kill him and (b) Mike will straighten his tie once more only ifI'll kill him, McCawley (t 98 1 : 49) fails to notice that what on his theory would be the preferred paraphrase of (b) Mike will straighten his tie once more only if I'll kill him, viz. (c) If I {don't/won't} kill him, then Mike won't straighten his tie once more, is in fact a good paraphrase of (a) IfMike straightens his tie once more, I'll kill him. Thus we have the following: (a) is a bad paraphrase of (b) (McCawley's fact]; (c) is a good paraphrase of (b) (McCawley's theory]; (c) is a good paraphrase of (a) (Atlas' fact]. But by the symmetry and transitivity of 'x is a good paraphrase of y', it follows that: (a) is both a good and bad paraphrase of (b), which is absurd. So it is not obvious to me that, in general, we should accept McCawley's theory that Not A if not B is the preferred paraphrase of A only if B. Thus it is not obvious that only if can be paraphrased by expressions involving rwo negatives as McCawley ( t 98 1 : so) claims. The problem with McCawley's first alleged fact, viz. that only NP can be paraphrased by No X other thart Y, is that this so-called fact is just what is in dispute berween me and Horn and McCawley (for the Proper Name case]. I deny that their paraphrase even correctly gives the truth-conditions for only NP [in the Proper Name case]. So it avails Horn and McCawley nothing to appeal to this alleged fact in the current debate; they would just beg the question at dispute.

3 1 0 'Only', Quantifiers, NPis, and Monotonicity

APPE N D I X I I I Horn's reduction ONLY IF to IF argument

-

-

-

-

-

•

•

-

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Horn ( 1 992: 180, n.10) offered an ingenious argument against a positive entailment if A from an only ifA clause. He alludes to that argument again in Horn (1996b: s), when he writes, 'the distribution and meaning of only if re-inforce the conclusion that the positive component of only clauses is not simply entailed, or else A only ifB would be equivalent to A if and only ifB.' Horn (1992: 180, n.w) had written similarly, 'If the semantics of only !farc compositional, they re-inforce the conclusion that the positive proposition is not entailed, or P only if Q would be equivalent to P if only and only if Q, which it clearly is not.' I (Atlas 1993= J06) argued in detail against the claim, but Horn (1996b: s) repeats this claim without discussing my argument. To say that only ifis compositional is to say, according to McCawley (198 1 : 51), that since 'expressions such as only if, even if, except if, and especially if appear to be immediately intelligible to anyone who knows the words of which they are composed (i.e. they are in no sense idioms), an analysis in which only if is treated as ordinary only plus ordinary if seems to be inescapable.' But the mere fact of compositionality of only if does not entail the particular compositional analysis preferred by Horn and McCawley for only if, viz. Geis's ( 1973) in no cases other than. This 'negative' analysis just begs the question against the entailmentist, since the question is just the correctness of the 'negative' analysis. We want to describe how A only if B supposedly entails A if and only if B on the entailmentist's alleged assumption that the clause only X entails X. As a first approxima­ tion, consider the following rough argument: treating only if as if it were like a coordinating rather than subordinating conjunction, A only if B might be thought immediately to entail A if B on the entailmentalist's assumption that the clause only X entails X. On the coordinating conjunction model, X only Y entails X 0 Y just as X and Y entails X and entails Y. Since only if is not a coordinating conjunction, this simple argument surely cannot be all that there is to Horn's argument against the entailment view. The exact form of this argument does not matter. No entailment theorist thinks Only a R b has the sentential-operator structure Only[a R b], with only modifying the clause a R b, which then allegedly entails [a R b], and no entailment theorist thinks that Only Gs are F entails Gs are F.53 So Horn's if-clause argument is a strawman account of the entailmentalist's position, with only applied to an if-clause, where no entailment theorist has ever applied it. Why should an entailment theory of generalized quantifier NPs be extended to a theory of S-modifiers? Furthermore, though again I thought that I had laid the argument to rest (Atlas 1 993= 3 1 2-IJ), Horn (1996b: 5) repeats the 'negative' analysis if B then A for A only ifB that McCawley (1981: 49-54; 1993: 81-8) and Barker (1993) have defended. 54 Consider that if A only if� were semantically negative, Horn would expect felicitous epistemic cancellation of the alleged positive entailment to occur while no felicitous epistemic c�ncellation of the negative entailment should be possible, just as in the case of Only a is F he (incorrectly) thinks that there is felicitous epistemic cancellation of a is F but none of no one distinct from a is F. So (46a) and (47a) should be acceptable rather than, as in fact, deviant because of the undermining by the second clause of the Felicity Condition on asserting the first:

Jay David Atlas J I I

(46) a. He'll go to church only on Sunday, and {it's possible/for all I know} {# 0/?even} not on Sunday. 55 b. #He'll go to church only on Sunday, and possibly on some other days as well. (47) a. He'll go to church only ifyou do, and {it's possible/for all I know} {# 0/?even} not ifyou do. b. #He'll go to church only ifyou do, and possibly in some cases in which you don't.56

These data do not support the asymmetry between the positive and negative entailments that Horn expects. There is no difference between the positive and negative entailment cases; there are no felicitous episternic cancellations of the positive entailment. So far as I can see from Horn's data, the predicted asymmetry between Muriel voted for Hubert and No one distinctfrom Muriel votedfor Hubert does not exist. Epistemic cancellation does not operate in only one case; there is no epistemic cancellation at all.

Criteria for assertion/non-assertion

Referring to Karttunen & Peters' { I979) criteria for distinguishing between "what is said" and "what is conventionally implicated', Horn notes that in the frames of higher illocutionary, attitudinal, or epistemic predicates, e.g. I just discovered that only Hillary trusts Bill, the natural interpretation suggests that Hillary trusts Bill is outside the scope of discovered. In Atlas ( 1991 : 1 44) I pointed out that the "presuppositional" inferences from only a is F to a is F, characterized by the implicatural inference from Not {only a is F} to a is F, could be given an explanation on my analysis of only a is F. Entailing predicates, like discover, for which I just discovered P If- P, permit the same "presuppositional" inferences. Hom ( r996b: n.Jo) subtly observes that it must be allowed that in certain contexts both Perrine conjuncts do indeed fall within the scope of a propositional attitude predicate. Thus the utterance of a sentence like (i) Mary will be upset if only Bill makes it to her dinner party may be taken to express the corresponding conjunction in (ii) Mary will be upset if Bill and only Bill makes it to her dinner party.

He has suggested elsewhere (Horn 1 992: r82-3) that: this case requires an invocation of the notion of explicature or pragmatic enrichment (a Ia Sperber & Wilson I 986, Carston I 988), so that the prejacent, while not constituting part of the linguistic meaning contributed by only, enters into the determination of what is said and hence into the (enriched) propositional content.

Of course, if one starts with an impoverished account of the linguistic meaning of Only a is F. one will, indeed, need to enrich it by the usual pragmatic inference (a discussion of the pragmatic enrichment by Gricean inference of the content of a statement beyond the literal meaning of its sentence is in Atlas I979) · The difficulty is explaining why some contexts require both Perrine conjuncts and other contexts do not. I would rather avoid that difficulty, if possible, though if Horn turns out to be right in his analysis, he will have to provide such an explanation. As yet, that is just a promissory note. Hom also points out focal stress data, also discussed in Atlas ( 1 99 1 : I4o-3), for which the prejacent seems outside the scope of what is asked, whence the acceptability of: I know Hillary trusts Bill, but does ONLY Hillary trust Bill? (Horn, r 996b: ex. (6 I d)), but even on Peter of Spain's view this sentence would be acceptable, as of the form: I know P, but P & Q'. Of course even without the focal stress, I know Hillary trusts Bill, but does only Hillary

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APPE N D I X IV

3 I 2 'Only', Quantifiers, NPls, and Monotonicity

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trust Bill? is also acceptable in my view, as the complement of the first clause is only part of the truth-conditions of Only a is F. Horn also notes statements of Horn's "exclusion" truth-conditions which when questioned in the same sentence allegedly produce anomalous utterances: I know nobody besides Hillary trusts Bill, but does only Hillary trust Bill? (Horn 1 996b, ex. (6 I e)). Horn explains the alleged difference between (6 I d,e) by the hypothesis that the prejacent Hillary trusts Bill is outside the scope of what is asked in (61d) while, asymmetrically, the exclusion Nobody besides Hillary trusts Bill is not outside the scope of what is asked in (6Ie}. As Horn (I996b: 22) remarks, 'as seen in the contrast between (6Id,e), once the discourse model contains the exclusion, the only sentence is pragmatically deviant-whence the anomaly of (62} # I know that nobody besides Kim is coming, but {I wonder if only Kim is coming, I just found out only Kim is coming, if (only Kim is coming}, we'll be all right}.' It seems to me that were (6Ie} to be parallel to (6Id}, there should be the same stress on only in (61e} as (61 d); (6 1e') I know nobody besides Hillary trust Bill, but does ONLY Hillary trust Bill? This stress suggests a contrast with besides: I know nobody BESIDES Hillary trusts Bill, but does ONLY Hillary trust Bill? But why is this last utterance anomalous according to Horn? I hear it as acceptable, since the first clause is used to state the exclusion of Hillary while the second clause is used to question the inclusion-in fact the unique specification-of Hillary. Furthermore, if Horn is reporting the anomaly of an utterance, as contrasted with a sentence-meaning, on his own theory that Someone trusts Bill is accommodated in the utterance, the utterance-type (61e) should not be anomalous, pace his own reported intuitions. On the other hand if he is reporting intuitions about sentence-meanings in sentence-type (6 1e), then it is hard to see what is 'pragmatically deviant' about the sentence-meaning 'I know P, but is it the case that P?'. Assertions can be 'pragmatically deviant', but can sentence-meanings? (The data of Horn's (62) raise the same questions for me as (6Id,e).) Horn also claims that the symmetrical account cannot explain why it is only the negative component that falls within the propositional attitude expressions in his (6Ia-c): a. If only Hillary trusts Bill, all is well; b. I just discovered that only Hillary trusts Bill; (c) It's too bad that only Hillary trusts Bill. The strength of Horn's intuition about (6Ia-c) is puzzling to me. The very theorists who believes in accommodation now claims that in the case of hypotheticals, or of propositional attitudes like 'discover' or 'too bad', there must be presupposed (or conventionally implicated (Karttunen & Peters I 979)) prejacent proposi­ tions 'Hillary trusts Bill'. On Horn's Karttunen-Peters' view what one has discovered is that no one besides Hillary trusts Bill; what one must presuppose in that discovery is that Hillary trusts Bill. On Horn's own view of the truth-conditions of No one besides Hillary trusts Bill, they do not entail that Hillary trusts Bill. But in discovering that only Hillary trusts Bill why couldn't one discover rather than presuppose that Hillary trusts Bill? It seems perfectly possible (Atlas I975, I977}: call it 'super-accommodation'. It also seem possible for one to discover that exactly one person, who is (at most} Hillary, trusts Bill. If Horn were to consider the consequences of his own theory of accommodation, what one has discovered is that no one besides Hillary trusts Bill: what is accommodated in asserting Ijust discovered that only Hillary trusts Bill is that someone trusts Bill (or possibly I just discovered that someone tmsts Bilry. So how do we arrive at the result that Hillary trusts Bill is outside the scope of 'discovered'? Moreover, unremarked by Horn, the stressed I know nobody BESIDES Hillary tmsts Bill, but does ONLY Hillary trust Bill? is acceptable. But if Only Hillary trusts Bill just means, as Horn believes, the downwards monotonic Nobody besides Hillary trusts Bill, substituting clauses salva significatione the following statement should also be pragmatically acceptable: #I know ONLY Hillary trusts Bill, but does ONLY Hillary trust Bill?, a statement that is, to the

Jay David Atlas 313 contrary, pragmatically deviant. Thus Horn's theory cannot explain the contrastive stress data. My theory has no difficulry providing an explanation, which, crudely, is of the Perrine form: I know P, but P & Q?.

NOTES I

4

Jerry Sadock (p.c. March I996) asked why I would not prefer the analysans Exactly one individual, who is a, is F, i.e. 3xVy[(x y ,...... Fy) & x=a], to my Exactly one individual, who is at most a, is F [3xVy[(x=y ,...... Fy) & (Fy -> y=a)] ]. One should note that Sadock's logical schema is equivalent to one of the form 3x[x & .r-a], which is equivalent to (a). The latter schema is equivalent to Fa & Vy(Fy -> y=a), i.e. to Fa & -.3y[•(y=a) & Fyj. Thus if we adopt Sadock's suggestion, we have, as we do on my analysis (and on Hom's "unoffi­ cial analysis" The only F is a, which is representable by Sadock's logical form), the logical equivalent of Peter of Spain's analysis. Peter, as did the other Scho­ lastic logicians, thought of Only a is F as somehow containing a is F as a syntac­ tical constituent, which is what Sadock's proposed analysis Exactly one individual, who is a, is F does. Horn (I992, I996b) ingeniously argues against any entail­ ment analysis that in that sense contains a is F. (For discussion of Horn's argu­ ments, see Atlas ( I 993= 306-8) and Appendix Ill of this paper.) My analysis Exactly one individual, and at most a, is F does not in that sense contain a is F. Horn's unofficial analysis is the same as the analysis of Only a is F that the arguments of deMey (1995: 227) would support, though, astonishingly, deMey contradicts his own argument by sug­ gesting the analysis a is the only F instead of The only F is a. Correctly noting that the statement (though deMey writes 'sentence') Only John is ill cannot be a =

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2

A downwards monotonic quantifier Q will satisfy the DeMorgan principle 1Q(F or G) If- QF & QG1 ; an anti­ additive operator in addition satisfies the converse as well, the DeMorgan prin­ ciple 1QF & QG If- Q(F or G)l . I shall introduce from Atlas (1995b), which revises Zwarts (I 996a,b), a new seman­ tical category of operator, a non-down­ wards-monotonic pseudo-anti-additive quantifier, to which only a belongs; unlike Zwarts's (I996a) "regular" nega­ tion, which is anti -additive, it satisfies only the latter DeMorgan principle (closure under finite unions). This "pseudo-negative" semantical category is the counterpart to the syntactical category "weakly negative" suggested by Klooster (I995). For future reference I note here the following sentence and logical form: (2e) There is someone distinct from Muriel. (2e') 3x(•(x=a)). This tacit identification of a with {a) sometimes is useful in mathematics, but it causes havoc in logic and set theory. Consider this remark of Bertrand Rus­ sell's (I959: 67): 'The second important advance that I learnt from Peano was that a class consisting of one member is not identical with that one member. "Satellite of the Earth", for instance, is a class and it has only one member, namely, the Moon. But to identify a class with its only member is to intro­ duce utterly insoluble problems into the logic of collections and, therefore, of numbers, since it is to collections that numbers apply.'

314 'Only', Quantifiers, NPis, and Monotonicity

7

8

9

=

-+

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shall use his determiner notation to show how the views of Atlas (1991, 1993) can be translated into deMey's (1991) framework. I do not thereby endorse the theory that only in only John is a determiner. What matters in my essay are the properties of the generalized quantifier NPs of the form only"Proper Names and only"Com­ mon Noun. The existential inference for 'only a', I shall argue below, can be had without Horn's and deMey's 'trans-derivational' rule of inference from All Fs are Gs. Among many holding this view are Lohner (1987), Chierchia & McCon­ nell-Ginet (1990: 427), Johnson-Laird & Byrne {I99J: 1 28), apparently as far back as the medieval logicians Walter Burleigh (Hom 1996b: 15), Pinborg (1981), Sanchez Valencia (1994)) and John of Holland (Bos 1985: 27). Notably, James McCawley does not hold the equivalence view, except for certain special cases. Atlas (1991: 133, 139; 1993. 304-5) mis­ takenly claimed that the assertion (2a) Only Muriel votedfor Hubert was seman­ tically well formed only if there was some individual distinct from Muriel (what I [Atlas 1991: 1 28] called 'a grammatical presupposition'), i.e. {a) is a proper subset of the domain D. I have now given this condition up for Only a is F, though I preserve it for Only Gs are F; I shall discuss this below. I am indebted to James McCawley for caus­ ing me to reconsider this. This presupposes that 'a' is non-vacu­ ous. In Atlas (199 1 , 1993) the truth­ conditions of the assertion (2a) Only Muriel votedfor Hubert were, in addition to the mistaken and now abandoned truth-or-falsity condition (2e) There is someone distinct from Muriel [(2e') 3x(-.(x=a) )], (2� Exactly one individual, and at most Muriel, voted for Hubert [(2f) 3xVy[(x=y ,..... Fy) & (Fy --> y=a)] ] ; so (2a) Only Muriel voted for Hubert entailed,

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felicitous answer to How is John?, deMey should have concluded that likewise The only one who is ill is John cannot be a felicitous answer to How is John? (without abnormal stress and intonation), unlike John is the only one who is ill. DeMey's (1995: 277) variant a is the only F of Hom's "unofficial" analysis The only F is a could plausibly seem to be about a. But on my focal Noun Phrase Limitation Principle, the correct analysis for Only a is F cannot be about a (Atlas 1991: 135), and my analysis is not about a. Hence there are good reasons to prefer my analysis to the plausible suggestion that Sadock has made and to deMey's (1 995) variant of Horn's unofficial analysis. The virtue of Horn's "unofficial" paraphrase The only F is a is that, like my analysis, paraphrasable by The (only) F is at most a, it satisfies my Noun Phrase Limita­ tion Principle. Hoeksema's (1986) main point, the simi­ larity of the only N to a superlative the F-est N, is unaffected by the fate of his notion of a "weak" downwards mono­ tonicity. I speculate that he constructed this notion because both phrases license the "weak" NP!s any and ever, and he presumed that some notion of down­ wards monotonicity would be required to explain the distributional facts. 6 DeMey's truth-conditions are most directly expressed by the first-order logical formula (2d"') Vx(Fx --> x a) corresponding to (2d") At most a is F, adopted by me (Atlas 1991, 1993) as part of my representations (2� Exactly one individual, and at most Muriel, voted for Hubert, (2f) 3xVy[(x=y ,..... Fy) & (Fy y=a)], or in the case of a definite description: (2f') 3xVy[x=y ,..... Fy) & (Fy --> y iuAu)]. for (2a) Only a is F. DeMey is aware that ONLY is not a conservative determiner and that there are syntactic reasons not to take only to be a determiner at all, e.g. onlyJohn, *all John, only a Jew girls, *all a Jew girls. I

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I 2 I should note that Atlas & Levinson {198I) and Atlas (1992) claim that It is John that is F is logically equivalent to Only John is F. Horn's official analysis of the assertion -schema Only John is F is just Atlas and Levinson's {1981) truth­ conditional analysis of the sentence­ schema 1It is John that is F1 . But I do not claim that It was a pizza that Mary ate is logically equivalent to Mary ate only a pizza; the latter entails the former but not conversely. Again, I distinguish between the logic of Proper Names and of Indefinite NPs; see Horn (1981) and my {1992) belated reply. Thus, though I disagree with Horn's official view of the truth-conditions of Only a is F, I agree that he has come within a logical equivalence of the total content of an assertion of 10nly a is F1 even on his official view. I3 On my view the statement Only a is F entails There is an F ('a' non-vacuous), and the asserting of the sentence 1Only a is fl , 'a' vacuous or not, will gener­ ally-conversationally implicate that there is an F. The latter is a defeasible inference; the former is not. The former is a matter of sentence-meaning and truth; the latter is a matter of the assertion's being Informative {Atlas & Levinson 1 981) or Relevant {Horn I984; Sperber & Wilson 1986). I 4 Henriette deSwart {p.c. June I 996) asked why my truth-conditions for Only a is F could not be weakened to Some individual, who is at most a, is F. In addition to what I have just said in the text above, my answer, of course, is that besides the entailment: Only a is F If- a is F. I not only want the entailment: Only a is F If- Exactly one person is F, I want the latter entailment to be a direct entailment {Atlas 1991: 1 37), i.e. (approxi­ mately) the entailment of a constituent (a sub-formula). If one does not impose that condition, which intuitively amounts to capturing the "uniqueness" part of the meaning of only he as a

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but did not assert, the "prejacent" (2b) M11riel voted for Hubert and entailed the boundedness condition (2d") At most Muriel voted for Hubert. In Larry Horn's essay I find myself described as an intellectual ally of the Scholastic logi­ cian Peter of Lisbon and Compostela {Petrus Hispanus), known to history as Pope John XXI ( 1276-7). {More accu­ rately, I'm the ally of John of Holland, as we shall see.) Peter provided the "conjunctional" analysis a is F and no 011e distinct from a is F [Fa & •:3x(•(x=a) & Fx)] of Only a is F (Tractatus Exponi­ bilium, 2 1 ff in Mullally I945: 106-7.) Peter's analysis treats the two compo­ nents of the meaning symmetrically and independently: my {Atlas 1 991: I33, 1 39; 1 99J: 304-5) logical analysis Exactly one individual, and at most a, is F [3x\iy[(x=y +-> Fy) & (Fy -> y=a)] ] opposes Peter's conjunctional analysis; my analysis subordinates one compo­ nent to another in a prenex logical form, disagrees with Peter's on the identity of the components, but agrees with Peter's in entailing a is F. I I Given Horn's unofficial paraphrase of Only a is F by The only F is a, where the only F is a singular term, equivalent to a Russellian definite description ixFx, it will be useful to contrast Horn's unof­ ficial truth-conditions with mine. The Russellian C(ixFx) is represented in determiner notation by THEsg{F,G), which is true iff I F! I and F � G. For the case The only F is a, the notation is: THEsg(F,{a}), which is true iff: {I) I F! = 1; (2) F � {a). Thus it is easy to see that on my analysis Only a is F entails Horn's The {only) F is a and conversely. So Horn's unofficial proposal is logi­ cally equivalent to my present analysis of Only a is F. {My earlier {199 I , I993) analysis containing the grammatical presupposition There is someone other than a would have entailed Horn's unofficial view, but the converse entail­ ment would not have obtained.)

316 'Only', Quantifiers, NPis, and Monotonicity

walked, Socrates walked rapidly} II- Only Socrates walked rapidly. (2) {Only Socrates walked, Someone walked rapidly) II- Only Socrates walked rapidly. But nothing about the downwards monotonicity of the NP only a follows from the correct­ ness of these entailments either. Ordin­ ary entailments from enthymemetic premisses do not constitute a special kind of 'downwards' entailment for only a, unless it is a "non-downward down­ ward" entailment. 17 If the interpretation of an 'or' com­ pound Verb Phrase is the union of the interpretations, and the Noun Phrase is a generalized Quantifier expression that is downwards mono­ tonic, then if the union of X and Y belongs to IIQII . i.e. X U Y E IIQII, then X E II QII and Y E IIQII. Actu­ ally it will suffice that Q is closed under VP 'or' weakening: II VP, or VP2 11 E IIQII II- I I VP, II u II VP2 11 E IIQII . i.e. that disjunction is always a part of the meaning of 'or'. 18 If X E IIQII or Y E IIQII . then the intersection of X and Y belongs to IIQ I I , i.e. X n Y E IIQII. It suffices for the conclusion that: II VP, and VP2 II E IIQII if I I VP, II n II VP. II E IIQII . i.e. that 'and' in these Verb Phrases expresses no more than the truth-func­ tional conjunction. For reasons dis­ cussed in Atlas (1996) I prefer (16b) to (16a) as a criterion for downwards monotonicity. 19 If a Noun Phrase is downwards mono­ tonic, then the NP satisfies (x6a) and satisfies ( 1 6b). But as I (Atlas 1 996) show elsewhere, (x6b) is a 'more negative' criterion for downwards monotonicity than ( x6a) is. Rene Coppieters (personal commun­ ication) has suggested that the entail­ ments in (17) might be open to the same objections that I made above for the case of only" Proper Name. For example, (16e') is intuitively acceptable, but cop­ pieters fmds (I7e) dubious for the

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separable component of the literal sentence-meaning rather than as a syncategorematic expression of part of the sentence-meaning, one could accept deSwart's suggestion as one that respects the entailments of the sentence but one that fails to respect the literal meaning of the sentence as composed from the literal meaning of the Noun Phrase only he. (See Grandy (1990); Geach's (1962/1980) analysis and deMey & Horn's analysis (8) amount to denying that the literal meaning of only he is a compositional component of the literal sentence-meaning.) Accepting deSwart's suggestion gives Only a is F the same truth-conditions as Atlas and Levinson's (198 1) analysis of It is a that is F. The truth-conditional redundancy attached to my representation of Only a is F, viz. Exactly one person, who is at most a, is F, which differs from the representation of Some individual, who is at most a, is F, respects the non­ synonymy of Only a is F with It is a that is F despite their logical equiva­ lence. I distinguish between Only a is F and It is a that is F by distinguishing their logical forms. (Note that deS­ wart's suggestion also disagrees with Horn's official view: cp. also Sadock's modification of a different sort to my logical form.) 1 :i Where the NP is a generalized Quanti­ fier expression Q, Q - VP is true iff II VPII E II Q II - If Q is downwards mono­ tonic, and the interpretations of a con­ junctive VP is the intersection of the interpretations of the conjuncts, the downward monotonicity of Q will imply that if II VP, II E II QII and II VP3 II E II Q II . the subset II VP , and VP3II E II Q II. Thus NP- VP 1 & NP - VP3 I I- NP- (VP1 and VP3). This requires that 'and' be interpreted as no stronger than logical conjunction &. 16 Nothing I have said is incompatible with the (obvious) correctness of the following entailments: ( 1) {Only Socrates

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women smoke and saw the light change at Main and Elm Streets at 2.JJ pm. I confess I disagree with this intuition, for the reasons given above. The only plausible apparent counterexample to down­ wards monotoniciry for only Count Noun that I have constructed involves referential equivocation: Only women saw the light change If- Only women saw the light change at Main and Elm Streets at 2.JJ pm. If the event predicate of the premiss characterizes a different light change from the event predicate of the conclusion, there is no entailment. But on the usual stipulation that no refer­ ential equivocation is allowed in the interpretation of sentences in an argu­ ment, the apparent counter-example is spurious. The effect of the semantic character of the Verb Phrase on the monotoniciry of the generalized quan­ tifier expression requires more analysis, but so far the data do not force me to modify the claim that only CN is down­ wards monotonic. Classical negation is anti-additive on the Boolean algebra of propositions: (a) •(p v q) If- •q & •q; (b) •p & •q If- •(p v q). Let B be a Boolean algebra. A quantifier Q is a quasi-ideal [i.e. anti­ additive] iff for each two elements X and Y of the algebra B: (a) if the union of X and Y belongs to Q, i.e. X U Y E Q, then X E Q and Y E Q [(r6a)J; (b) and, conversely, if X E Q and Y E Q, then the union of X and Y belongs to Q, i.e. X U Y E Q [(r8)]. (The empry set is not excluded.} See Chellas ( 1980). I shall call only a 'a pseudo-negation' because it has seemed to so many linguists to be downwards monotonic and because it satisfies ( 1 8), and so it seems to be anti-additive. When I pointed out this distinction between only a and only CN to Jerry Sadock, he immediately mentioned that if I were correct, in other languages the same operators should have distinct lexical realizations, and instantly confirmed

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reasons I gave against the entailment in the Proper Name case, viz. that the entailed sentence seems to add infor­ mation to the information in the pre­ miss: Only John smokes 1 If- Only John smokes and drinks. I do not share his semantic intuition; Coppieters would push me into an even more radical position than the one I hold in this essay, viz. the position that Only"Count Noun is not downwards monotonic in sentence-frames like those of (r7) con­ taining dispositional predicates like 'smoke' and 'drink'. There are intuitive problems, as usual, with understanding models in which the predicates receive the null set as an interpretation, e.g. the (d) instance Only women are non-self­ identical or smoke If- Only women are non­ self-identical, where the latter sentence requires that there are non-women and means At most women are non-self-iden­ tical and hence is trivially true, as is therefore the entailment. I am also willing to accept the (e) instance: Only foxes run If- Only foxes run faster than a speeding bullet, because it seems to me that it is impossible for simultaneously the first to be true and the second false: if only foxes run, there are non- foxes and there is no individual non-fox that runs and runs faster than a speeding bullet. By contrast it seems to me clear that it is possible simultaneously for it to be true that only John smokes but false that only John smokes and drinks; thus onlyJohn is not downwards mono­ tonic. I wish that ended the complexities, but, alas, it does not. When one replaces the dispositional predicates in (17) with event predicates like those I appealed to in my reductio arguments above, e.g. 'saw the light change . . .', where a specific light is referred to and a parti­ cular seeing is being described, Coppi­ eters find the following (e) instance an intuitively questionable downward entailment: Only women smoke If- Only

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3 1 8 'Only', Quantifiers, NPis, and Monotonicity may be forgiven a personal note, the first paper in generative grammar, from Fodor & Katz's (1964) The Structure of Language: Readings in the Philosophy of Language, that I read as a young Prince­ ton student of Dana Scott's in logic and philosophy that convinced me that Chomskyan grammar could shed light on logical aspects of ordinary language. 25 If the co-reference cases were unaccep­ table, reduced English statements of the conclusions of valid arguments of the form ¢ If- (¢&¢) would be linguistically unavailable. For another theoretical use of such reduced sentence forms in a discussion of sentential negation m natural language, see Atlas {1994). The standard judgements are: Pat didn't vote for Hubert, and {neither,*so) did {hardly, 0) anyone else. Muriel voted for Hubert, and {*neither, so) did Hubert. 26 The Klima-McCawley too/either test applied to only" VP, combined with McCawley's (1988: 584) argument con­ cerning ambiguity, leads from the observation that Tom only beats his wife because he loves her, and Dick only does too/ *either is ambiguous to the conclusion that only" VP 1s not negative (see McCawley op. cit.). Though contrary to Hom's expectations, this syntactical conclusion is consistent with the entail­ ment intuitions for only" VP sentences, which are simply inconclusive by the criteria in (I 6), since they are ill defined when applied to sentences of the form John [only [Fs] ]. Intuitively if the F position were downwards monotonic, one would expect the following to be a correct entailment claim: John only smokes If- john (only [smokes and drinks] ], but clearly it is not. 27 Zwarts ( I 996a) surprisingly classifies only J.L N as downwards monotonic. Klooster (1994) correctly observes that it is non-monotonic. 28 Atlas (I996) shows that what is essential to the negativity of negative quantifier Noun Phrases is (Z(ib) ) and (Z(iib)), i.e.

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his own hypothesis in German: allein and nur. Hom (1996b: 1 8), m discussing deMey's (1991) examples, Hom's (49): (a) Only students read books, (b) Only John slept, (c) Only three pilots slept, writes that "while conversion (i.e. F ONL Y(G,F) <-> ALL(F,G)] is always possible, the strongest case for only phrases defining strict downward inferential patterns are those where only takes common noun or adverbial focus." I argue (i) that the logical equivalence claim on which conversion rests is a false claim, (ii) that Horn is correct that when the focus of only is a common noun there is a strong case for downwards mono­ tonicity, and (iii) that the claim that downwards monotonicity holds for adverbials in focus is premature, since the formal definition of downwards monotonicity in the theory of general­ ized quantifier NPs is not extended by the theory to adverbial phrases. 22 For a similar methodological problem of 'all' vs. 'some' in Bertrand Russell's account of logical types, see Atlas ( 1989: 1 ) 1 -61). 23 Of course there is the possibility that the semantical explanation for only" Proper Name co-occurring with "weak" NPis is quite other than the semantical pseudo-anti-additivity of only"Proper Name. The hypothesis that downwards monotonicity was necessary for licen­ sing NPis was a noble attempt, but at this moment there is no theory at all for the behaviour of only" Proper Name. The observation that the expression is closed under finite unions is just an observa­ tion that one DeMorgan relation is satisfied. If that explains why it licenses "weak" NPis, no one has a theory that shows why that is an explanation. The young man or woman who comes up with a good theory wins a US$soo Atlas Prize. 24 Klima's paper is justly famous for a number of reasons, and it was, if I

Jay David Atlas 3 1 9 tence-types i s alternatively described as a distinction between sentences and utterance-types; the difference in description in the present case is merely terminological. As I did in my discussion of Every­ thing and Every seat above, James McCawley (p.c. May 1 996} also points out the distinction between everyone and every N, e.g. the acceptability of Only every man is running-why aren't any gazelles running too? 34 A grammatical presupposition, in my sense, is a semantical well-formedness condition on English sentences; or as I would prefer to put it, it is a linguistic constraint on the admissible models in a formal semantical interpretation of English sentences. One could try to make a case that the condition in question is a Gricean (1975) conven­ tional implicatum instead of a seman­ tical well-formedness condition ('grammatical presupposition'). I have a contrary intuition: the case does not see to me analogous to but/and in which a semantical contrast is conventionally implicated by the lexical meaning of but without affecting the truth-condi­ tions but shares with and, as my (1991 : 1 28) observations from Atlas (199 1) above will confirm. Also, unlike the case of Only a is F, where the condition seems to be a Generalized Conversa­ tional lmplicatum, the condition char­ acterizes the meaning of 'only G'. Finally, I don't think one can correctly argue that the condition is merely a felicity condition on the assertion of the sentence; that also would not explain the observations above. Atlas (199 1 : 128) mistakenly inferred from (Jog): 'To simplify, what is GRAMMATICALLY PRESUPPOSED by Only a is F is a is not everyone . . . that, on the assumption that 'a' is non­ vacuous, there are at least two things in the domain of quantification D.' Thus I mistakenly inferred that it is

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one form of downwards monotonicity and closure of membership in a quan­ tifier Q under disjunction. which amount to anti-additivity. 29 Remarkably, that would be the same pattern of erroneous inference made famous in Generative Semantics by Haj Ross (1969) when he argued that, (incorrectly) assuming that definite pro­ nouns are anaphoric only with full Noun Phrases, the grammaticality of John is happy, but he doesn't look it, is sufficient for the adjective 'happy' to be an underlying Noun Phrase. Cp. also the (incorrect) assumption in Zwarts's ( 1996a,b} Law {a) of Negative Polarity [see below], that "weak" Negative Polarity Items are acceptably contained only in sentences with merely mono­ tone negations. (I was serendipitously reminded ofRoss's argument by reading the informative Newmeyer (1 996: r 14}.} 30 Klooster (1995) calls 'only a' syntactically 'weakly negative'. Even that is too strong a term, but it is in the right spirit. 3 1 James McCawley (p.c. May 1 996, 1 988: 584, 586, s88) points out that what he calls 'a loosely negative word', viz. hardly, will license batted an eyelash when it occurs with hardly anyone, e.g. Hardly anyone batted an eyelash is accep­ table. But this is not incompatible with Zwarts's observations. The question is not hardly; the question is the logic of the generalized quantifier hardly anyone. And that is not "loosely negative"; in fact, quite to the contrary, it is very negative, as is evident from the para­ phrase 'nearly no one'. 32 For Hom's arguments from contrastive 'but', see Appendix I. 33 There are different sentence-types asso­ ciated with the same string (system­ sentence), e.g. echoic or contrastively stressed Only EVERYONE is running, that are grammatical; see Atlas (r989: 89-91) where the present distinction between system-sentences and sen-

320 'Only', Quantifiers, NPls, and Monotonicity

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formedness of Only a exists cannot require its own falsehood (Atlas I988). My ( I99I) well-formedness condition for Only a is F could be maintained if 'exists' could not be a substituend for 'is F but I csee no principled reason to restrict the substitutions for 'is F in this way. Nonetheless it is worth noting that 'exists' is a semantically special case. James McCawley (p.c. May I996) raised an interesting puzzle for my view: the apparently acceptable Only self-identical individuals exist would seemingly require the truth of a well-formedness condition that seems to be necessarily false, viz. There are non-self-identical things. In my view a semantically correct account of 'only', and hence a felicitous use of the sentence, requires that when asserting the sentence an explicit con­ trast is being drawn between types of entities, the self-identical ones and the (actually, even necessarily, non-existent) non-self-identical ones. To take a leaf from Horn's book, the assertion seman­ tically requires the "accommodation" of the non-self-identical type or class. The speaker is tacitly denying that the impossibly non-self-identical entities exist, which does not mean that he presupposes that they do (Atlas I988)! Thus Bertrand Russell could have feli­ citously asserted to Meinong Only logi­ cally consistent entities have being, not because there were any logically incon­ sistent entities, i.e. no entities of which logically inconsistent predicates are true were values of bound variables from the domain of quantification (Quine I98o: I2; White I963: 85-7), but because (i) Meinong believed that there were; that such inconsistent entities at least had being, and because (ii) speaking from Meinong's point of reference (Scott I970) in order to correct him, Russell's domain of discourse, though not his domain of quantification, could include virtual entities as extensions of terrns like Meinong's the round square (see Scott

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a semantical well-formedness condi­ tion on Only a is F that there be someone other than a. After all, if only a is an 'excluder', it must exclude something, which is not a, from the extension of the predicate 'F'. This inference to the conclusion that the domain was at least cardinality two for non-vacuous 'a' I now believe was mistaken, though the linguistic evi­ dence from which the inference was made is still correct. I mistakenly spe­ cialized a conclusion for predicates in Only Cs are F to a conclusion for Proper Names in Only a is F. How ironic! This is the mistake noted in Note 3 above. If there were an argument for a not being the only element in the domain of quantification, it might have been something like this: If a is alone in D, then in that class of models M.: Ma f= •3x(•(x=a) ), from which it follows trivially: M. f= -,:Jx(•(x=a) & ¢x), no matter what ¢ is. That is, on my paraphrase it would follow At most a is ¢, no matter what rjJ is; and on Horn's truth-conditions, it would follow Only a is ¢, no matter what rjJ is. On Horn's analysis it might seem odd to have: Only a is F, Only a is C, Only a is H, . but the natural inference to draw from the truth of these statements would be that a is alone in D. {On my paraphrase At most a is ¢, there is less oddity with the statements At most a is F, At most a is C, . . .) Except for special domains the natural inference from a statement of the form Only a is rjJ is the Generalized Conversational Implicatum There is someone other than a. But this is merely an implicatum. For example, After the nuclear war only John was left alive on earth is semantically acceptable even when John is alone in the domain of persons. So I do not now accept my (I 99 I) claim that the seman­ tical well-formedness of only a is F requires that someone other than a be in the domain, for the semantical well-

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amiss in the expression Some things/ entities have logically inconsistent properties, particularly if the sentence should be thought false. There may turn out to be no non-As, or no non-A species of the relevant genus, but the speaker of the sentence is nonetheless committed semantically by his utterance to there being at least non-A virtual entities or virtual non-A species. That is the logic of the language; �hether it matches the facts of the world is another matter. So McCawley's puzzle sentence is not a counter-example to my semantical account of Only Gs are F. Of course any reader who is dubious about the judgements *Only everything has feathers, #Only self-identical indivi­ duals have feathers, will be dubious about this conclusion that it is false that All Bs are A entails Only As are B. In the next section, Section s. I shall show for the Proper Name case that such a reader need only grant me the non­ monotonicity of Only a in order to demonstrate that All Fs are a/Every F is a does not entail Only a is F. The indefinite NP a man in the accepted English translations straddles the logical distinction I have been careful to draw between the Proper Name and the Count Noun cases. For purposes of logic, not of translation, I would prefer: Only men are moving /f- Only men are running. This argument reinforces the conclusion independently reached in (3ob) above. In Horn (1972) the concept of suspen­ sion is used to describe the way in which presuppositions or implicata of a sentence could fail to be inherited by compound or complex sentences of which the original sentence was a component; e.g. the presupposition of The king of France is bald would be suspended in, i.e. fail to be inherited by, a sentence containing the original sentence plus an if-clause: The king of France is bald, if there is a king of France.

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(1967, 1970: 144-48), Parsons (198o) ), or, the Quinean alternative, Russell's theory of his own language would contain a theory of contextual defini­ tion for such terms by which they are rendered mere fafons de parler. In the same way Set Theory makes good use of virtual classes as distinct from actual classes, i.e. sets. For example, the cardinal number of a set (an actual class) is, usually, a virtual class, not an actual class (a set). (See Quine ( 1963/ rev. 1969); Quine (1976: 272-82)). On the account of Only As are B sketched above, the "complement", in the · required extended sense, of the actual class (set) of self-identical entities con­ sists of virtual non -self-identical enti­ ties in the domain of discourse, a superclass/set of the domain of quan­ tification. (I shall ignore some of the complications: virtual classes of virtual entities; actual classes of virtual entities, etc.) Similar considerations are required for sentences like 'Only self-identical entities are feathered or non-feathered'. Thus I shall preserve my account of the semantical acceptability of the statement-schema Only As are B even for these sentences. The word 'only' means what it says: alone in its class or kind. Like Geach (1972a), who notoriously held that identity is relative, that x is identical with y is elliptical for x is the same A as y, where 'A' stands for some contextually understood Count Noun, I, rather less notoriously I trust, hold that 'only As' means just what it says: alone in its class or kind K, where the class or kind K is not exhausted by As, and where 'only As' excludes the non-As from being Bs. The sentence a is a thing or a is an entity does not analytically imply a has consistent properties (a is the value ofa bound variable does analytically imply a has consistent properties); logical consistency is not part of the concept of a thing. There is nothing linguistically

322 'Only', Quantifiers, NPis, and Monotonicity

the test is not a gradable predicate: it is an accomplishment/achievement pre­ dicate. Consider the unacceptable accomplishment/achievement cases: #Only you and I swam the Channel, and you didn't; #Only you and I swam the Channel, and even you didn't; #Only you and I swam the Channel, {but/and) it's possible, you didn't; #Only you and I can swim the Channel, {but/and) it's possible, that you can't; #Only you and I can swim the Channel, {but/and} it's possible, that even you can't. Of course with the non­ epistemic 'possible', we have the accep­ table: Only you and I can swim the Channel, {but/and) it's possible that even you can't. For more discussion of degree predicates, see Atlas (r984). 43 These sentences are distinct from sen­ tences where the 'not' does not attach to the main verb, e.g. Not even two years ago, you could swim there (i.e. You could swim there not even two years ago). 44 Zwarts (r996a) (incorrectly) lists only J1 N as a monotone decreasing noun phrase, but since it fails to satisfy: NP(VP1 or VP2) If- NP- VP, & NP - VP2, a necessary condition of its being downwards monotonic, I do not believe that it is monotone decreasing. Thus it is not even semantically "nega­ tive" by Zwarts's criteria. For agreement with the view that only J1 N is non­ monotone, see Klooster (1994). 45 E.g. the following alleged entailments fail: Exactly one man entered the race early ? If- Exactly one man entered the race, Exactly one man entered the race ? If- Exactly one man entered the race early. Exactly one N satisfies none of the DeMorgan rules; by Zwarts's ( 1996a) criteria, it is non-negative, which is the intuitively correct judge­ ment. I should mention that (4ra) is unac­ ceptable in Larry Horn's idiolect. Hom notes that in his speech exactly fails to license inversion, e.g. {Only/#Exactly} on the High Holy Days does he go to shu/. In

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For the reasons given by Alan White (1975: 52), I do not believe that the epistemic possibility that P [ •K •PJ is coherently expressible by English 'may' or 'it is possible that P'. So I have long had doubts about the coherence of linguistic discussion on these points, though in this section I shall pretend otherwise. 40 James McCawley (p.c. May 1 996) also shares Horn's intuitions that (38b) is acceptable. Both, I suspect, are not taking the Felicity Conditions on asser­ tion seriously enough. One could not felicitously ASSERT Only Kim can pass the test and in the next breath withdraw the epistemic commitment to the first part of the assertion. (38cf34a') is not such a withdrawal. On Horn's official view the total content of asserting 'Only Kim can pass the test' entails Kim can pass the test. It should be infelicitous to assert as well: For all I know even she can't. 4 I On the difference between cancellation and suspension, see Hom (1972) and Levinson (r98J: I rs, 1 42). 42 Horn also argues that an exception clause can be cancelled without the use of the epistemic modifier, as in the acceptable All the world is queer save thee and men, and even thou art a little queer (attributed to Robert Owen r828). Since the attribution of mental oddity is a gradable predicate, it is unsurpris­ ing that the adjective 'queer' can be modified by 'a little'. The statement Only you and I are not queer, and even you are a little queer is acceptable because a is a little queer cancels a generalized conversational implicatum a is not at all queer of the assertion a is not queer. The degree interpretation of 'queer' in the second clause triggered by 'a little' forces a reinterpretation of 'not queer' in the first clause as a negation of a gradable predicate; one that produces the cancellable implica­ tum a is not at all queer. By contrast pass

Jay David Atlas 323

.

· chauvinists. It would be perfectly pos­ sible for Q to be replaced by 'no' in the appropriate context. But Horn's (r985) explanation by appeal to meta­ linguistic negation would fail to explain these compound assertions: SOME men are chauvinists?-NO men are; SOME men are not chauvinists­ NO men are. For Horn's (1985) analysis would claim that questioning or utter­ ing 'not' denies the implicatum of asserting 'Some men are chauvinists', viz. denies 'Not all men are chauvi­ nists' to give 'All men are chauvinists', followed by the assertion NO men are. The analysis thus predicts a contrary content to the compound utterance, viz. {All men are chauvinists, No men are chauvinists}, from which it follows that no one is a man. But that surely is not the intended communicated con­ tent of the compound assertion. A theory of metalinguistic negation fails to explain Some men aren't chauvinists­ no men are, because the phenomenon essentially depends on FOCUS, not on negation. Thus I (r983) preferred to describe Horn's ( 1985) data as cases of Focus Negation, not metalinguistic negation. 48 It is to be noted that of the DeMorgan principles: (Z) (ia) (ib) (iia) (iib)

Q(F or G) If- QF & QG; QF & QG If- Q(F or G); Q(F and G) If- QF v QG; QF v QG If- Q(F and G)

the Pseudo-Minimal operator satisfies (ib); the Sub-Minimal operator satisfies (ia) [or (iib)]; the Outer operator is anti­ multiplicative and satisfies (iia,b), and the Minimal operator is anti-additive and satisfies (ia,b). Another reason for rejecting Peter of Spain's analysis of only a as a and no one other than a is that the latter satisfies only (ib) and (iia) it is non­ downwards-monotonic but pseudo­ anti-additive (i.e. satisfies (ib)) and pseudo-anti-multiplicative (i.e. satisfies

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this sentence exactly is much worse than only for my speech as well, but it is not impossible, as it is for Horn. I fmd the following acceptable: just on the High Holy Days does he go to shu/. McCawley (p.c. May rgg6) finds both (4 u,b) deviant, with (b) more normal than (a). He notes the unacceptabiliry of On Tuesdays and only on Tuesdays {?he receives, ?does he receive} visitors, suggest­ ing that the two conjuncts in the preposed PP make conflicting demands on word order. In my view what is odd about (4rb) is that it is Chicago/Ger­ manic/Yiddish English, while what is acceptable about (4 ra) is that though in a Lord Tennyson register alien to American ears, it is not only English English. 46 The data of (4r), (42), and (43) work as well (or better) with the phrase just one . . as with exactly one . . .. Just' is acceptable with both Count Noun Phrases and Proper Names; 'exactly' is odd with Proper Names: just one feature did I notice in the landscape . . . , just john did I notice in the landscape . . . ?Exactly John did I notice in the land­ scape . . .. 47 See my discussion of the data in (22) above. In a similar way I said in my (1 983) comments on Horn (1985): In Horn's analysis by metalinguistic nega­ tion of Some men aren't chauvinists-all men are, the not is supposed to negate the implicatum Not all men are chauvi­ nists of the assertion Some men are chauvinists to yield 'All men are chau­ vinists', which is then redundantly but reinforcingly asserted. The same phe­ nomenon arises independently of negation, as I pointed out then. For example, the focused "rhetorical" ques­ tion SOME men are chauvinists?-ALL men are chauvinists, which implicates the propositional schema rQ men are chauvinists1 , where Q could be sup­ plied by the conversational context or by a further assertion, e.g. ALL men are

324 'Only', Quantifiers, NPis, and Monotonicity

49 so

51

53 54

55

He goes to church only on Sunday, and not even then if there's a football game on television, McCawley's (p.c.) allegedly (but not really) acceptable ?He'll go to church on Sunday, and (it's possible,/for all I know) he won't go even on Sunday, and my unacceptable epistemic cancellation (46a). {As I indicated above ·POSSIBLE· = { = ·MAY·.) Further, I think that Horn's even suspension works because the second clause is semantically a

restrictive modifier of the main clause, despite superficial syntactical appear­ ances, and on that interpretation Horn's ( 1996b: 6; ex. (ro'a)) statement: #[sic)He goes to church on Sunday and only

on Sunday, and not even then if there's a football game on television. is also acceptable rather than not. Thus the asymmetry Horn wishes between the acceptable first statement and the allegedly unacceptable second state­ ment vanishes. My {46a) is deviant because it is really an attempted epis­ temic cancellation that fails, not an if­ clause modification of the main clause. 56 The paraphrase of only if as only in all cases in which is taken from McCawley (r98 1 : 52), who relies on Geis ( 1973). Horn accepts this analysis. I don't. Horn {1996b: 5-6) also mentions an analysis of Lycan's (199 1 : 126-7) in which I'll go only if you do is analysed by I'll go only in (the event that/events in which) you go, and so on Horn's view *I'll go in no event other than one in which you go. I hope that this is not really their view, since the latter analysans is not even a grammatical sentence of English, and the former analysans is one in which the relevant sense of in the event that you go that paraphrases ifyou go has no plural in English, especially not in events in which you go. If it did, it would, I suppose, express *ifi you go. Of course Geis's (1973) analysis of the meaning of if by in all cases in which is not correct. On that analysis If it's cold enough tomorrow, it will snow, but not if it rains would incorrectly be analysed to mean In every case in which it is cold enough tomorrow, it will snow {in that case), but not in every case in which it rains.

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52

{iia)). Only a is non-downwards-mono­ tonic but just pseudo-anti-additive. this intuitively the correct result; and and no one other than a is more negative than only a but less negative than at most a and obviously less negative than no one other than a. See Appendix IV. and the distribution of but vs. and that according to Horn "speaks to the same point" as illocutionary scope; see Appendix I. As Jerry Sadock notes, these intuitions about the only"Proper Name case may be reinforced by these paraphrases of (rc): (rc') Muriel alone voted for Hubert, but (she did/ nobody else did,) (rc") Solely Muriel voted for Hubert, but (#she did/ #nobody else did). (2c) is a particularly dubious judgement, e.g. Surprisingly many men and only three women went to Hollywood's latest chick­ flick. For a discussion of criteria distinguish­ ing sentential from predicate operators, see Stalnaker & Thomason ( 1973). See Appendix II. There is no inconsistency between Horn's (r996b: 6; ex. (roa) ) acceptable even suspension phenomenon:

Jay David Atlas 325

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journal of Semantics I J: B I -J61

© Oxford Univmity Press 1996

The Progressive: A Channel-Theoretic Analysis S HE I L A G L A S B E Y

Centre for Cognitive Science, University of Edinburgh Abstract

1 I NTRO D U C T I O N Considerable effort has been expended over the last twenty-five years or so in attempting to capture the exact meaning of the English progressive. We will argue below that, while a great deal of progress has been made, no-one has yet produced an adequate account. In this paper we will present an analysis which, we argue, remedies some of the deficiencies. We will review some of the problems associated with pinning down exact truth conditions for progressive constructions. In particular, we will examine two recent accounts of the semantics of the progressive, those of Landman (1992) and Asher (1992). We argue that while neither account is completely satisfactory, both contain important insights which can be combined and made more precise in the treatment we develop based on Barwise & Seligman's (1994) Channel Theory, a recent theory of informa­ tion flow and reasoning with incomplete information. Our account is inspired in part by Hinrichs (1983), who gave an analysis of the progressive in terms of situation-theoretic constraints (a precursor to some of the notions of channel theory), and Cooper (198s), who made further sugges­ tions along these lines.

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In this paper we review some of the problems associated with giving a precise semantics for the English progressive. We begin by examining two recent accounts of the progressive, those of Landman (1992) and Asher (1992). While neither account is, we argue, completely satisfactory, both contain important insights which can be combined and made more precise in the treatment we develop based on Barwise & Seligman's (1994) Channel Theory. We show that the notions of natural regularity and channel embodied in channel theory provide exactly what is needed to give an account of the progressive which is precisely expressed and explains the data. In particular, we show how our account allows us to separate out the licensing conditions for the progressive from the existence of a 'default rule' as employed by Asher. This enables us to explain some examples that are problematic for a default-based account. Finally, we show that our analysis can be successfully applied to a range of examples, many of which have proved problematic for earlier accounts.

332 The Progressive: A Channel-Theoretic Analysis

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We will argue that the notions of natural regularity and channel embodied in channel theory provide exactly what is needed to give an account of the progressive which is precisely expressed and explains the data. In particular, we will show how natural regularities, while related to 'defaults' as used, for example, by Asher, are different in some significant respects which allow us to account for some examples that are problematic for a default-based account. We show how channel theory allows us to separate out the 'existence' of a natural regularity from the way in which we may, under certain circumstances, reason on the basis of such a regularity. We will show how our account can be successfully applied to a range of examples, many of which have proved problematic for earlier accounts, including those of Landman and Asher. It should be stressed that, while the intention is to introduce a new perspective (that of channel theory) to the analysis of the progressive, we do not claim that the present version of our account solves all the problems. More work is required in certain areas, including some basic issues of channel theory and its formalization. However, we believe that the present account sheds some useful new light on some of the traditional problems, and offers promise for a future account of increased precision. Our account is a truth-conditional one, in that it sets out to define the precise conditions under which a progressive sentence can be truthfully used. In this respect it is similar to the accounts in (for example) Dowty (1979), Landman (1992), and Asher (1992), while differing from these accounts in other significant respects that will become clear shortly (we do not, for example, use possible worlds). Our account might also be termed 'compositional', in that, again like those of Dowty, Landman, and Asher, the truth conditions of a progressive sentence are defined in terms of the truth conditions of the corresponding non-progressive! It will be noted, too, that we say very little in this paper about the 'context change potential' of progressives, which is emphasized in accounts of the progressive in DRT (see Kamp & Reyle 1 993). This does not mean that we consider the effect of a progressive sentence on the temporal structure of discourse to be unimportant. It is simply that one paper cannot do everything. The interested reader is referred to Glasbey (1994a), where the 'stative' view of progressives proposed by Vlach ( 1 981) and employed by DRT accounts is criticized, and an alternative proposed.

Sheila Glasbey 333

2 A B RI E F H I ST O R Y A N D S O ME PROBLEMS An early truth-conditional account of the progressive was given by Bennett

& Partee (1972), using interval semantics. The idea was that a progressive

( r ) Mary was building a house but she ran out of money and had to stop. That is, 'Mary was building a house' can be true even though she never finished it. In order to get over this problem, Dowty (r979) used a possible­ worlds framework, employing the notion of inertia worlds. The non­ progressive is no longer required to be true in the actual world, but it must be true at a larger interval in all the inertia worlds. The inertia worlds for an interval i and a world w are defined as those worlds which are identical to w up to i, but in which from then on 'nothing unexpected happens' and 'events take their normal, natural course'. It is not clear, however, what it means for events to take their normal, natural course. For example, it has been argued that in the example: (2) Mary was crossing the road when she was hit by a truck. if events take their normal, natural course, then Mary will still be hit by the truck, because the truck will still be hurtling towards Mary in the inertia worlds. Landman discusses this objection, and suggests that a way round it is to require that in the inertia worlds the event of Mary crossing the road (but not necessarily everything else) takes its normal, natural course-that is, we are allowed to remove the truck from the inertia worlds. Landman also considers the problem of what happens if there is a second truck behind the first one, also on course to hit Mary. In order to make the progressive true, we have to go to a world where neither truck is present. In other words, as Landman puts it, we have to 'remove all danger of the event being interrupted'. We remove everything 'external to the event' and see if this allows the complete event to be realized. If this is the case, then the progressive is true. However, Landman (1992) points out that this proposal runs into problems with sentences like: (3) Mary was wiping out the Roman army.

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sentence is true at a time interval t if t is part of a larger, later-ending interval t' at which the corresponding non-progressive sentence is true. The problem is that this predicts that a progressive sentence is only true if the corresponding non-progressive is also true. In other words, there is no allowance for interruptions. Yet it is clearly possible for the progressive of an accomplishmene to be true even if the complete event never occurs­ this is the familiar 'imperfective paradox'. We can say, for example:

334 The Progressive: A Channel-Theoretic Analysis

(4) John is walking to the shops.

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This sentence is generally agreed to be unacceptable when used to describe a scenario where Mary, a normal human being with only conventional weapons at her disposal, has (for example) killed two Roman soldiers and is about to attack a third. The reason we judge such a progressive unac­ ceptable seems to have to do with the fact that the project is absurd-Mary hasn't the remotest chance of achieving her objective. Yet, if we are allowed to remove anything 'external to the event' which prevents the complete event from being realized, then we are presumably allowed to remove the whole of the Roman army, which would make (3) an acceptable way to describe the scenario. Landman proposes a way to overcome this problem. The idea is that we follow the progress of an event e (corresponding to the complete event, as described by the non-progressive). If e stops in the actual world w, we go to the closest possible world where e doesn't stop, and follow its progress there. But we can only move to the closest world if that world is what Landman calls a 'reasonable option' from w, on the basis of what is 'internal to e'. If e is interrupted in this new world, we move to the closest world to that one, provided, once again, that this closest world is a reasonable option from w. This process is continued until a world · is found in which e goes to completion, or until we come to a point where going to the closest world is no longer reasonable in the above sense. If the latter happens, the progressive fails to be acceptable. Landman is thus able to explain why (3) is no good. Suppose Mary gets killed by a soldier after the first few minutes. Then we can go to a world where everything is the same except that the soldier does not kill her. Of course, she will probably get killed very shortly by another soldier. It is arguably by a reasonable option to go to a world where that soldier does not kill her, either. But there is a limit to how long we can keep on doing this. After removing a few soldiers, Landman argues, it is no longer a reasonable option to remove any more, and we are forced to abandon Mary to her fate. The notion of reasonable option is not made precise. Landman might argue that this is just what we want-it gives us some flexibility in which progressives are allowed, depending on what the hearer considers to be 'reasonable'. This flexibility seems appropriate, but what is less satisfactory is that there is no explanation of where the notion of what is reasonable comes from. There is no way to capture formally the fact that what is reasonable to one speaker may be unreasonable to another. Neither is the notion of what counts as 'internal to the event' made precise. Let us explore in detail what this notion might actually mean, and whether it always gives us what we want. Consider first of all the example:

Sheila Glasbey 335

Now suppose John habitually takes a walk from his house to the shops. A neighbour observes him daily, setting out and returning with his shopping. Suppose that on the way to the shops, there is a turning which leads to the park, and one fine morning John decides, as he sets out, to forgo his shopping and take a stroll in the park instead. John's neighbour, watching him set out, is of course unaware of the change of plan, and says to herself (s) John is walking to the shops.

(6) For many billions of years, the universe was contracting back to a singularity. Then, in the last hour or so, the interactions between black holes prevented it from ever reaching that point, and it began to expand agam. According to Landman's account, the progressive 'The universe was contracting back to a singularity' is acceptable provided that the complete event is a reasonable option on the basis of what is internal to the event. This forces us to regard the interactions between black holes as being external to the event, which seems rather counter-intuitive given that the contraction event involves the whole universe. 2. I

Progressives with contradictory outcomes

Landman admits that pairs of progressive like (7a) and (7b) are problematic for his account as it stands:

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We would want to say that she is wrong-the progressive (s) does not correctly describe this scenario. But of course it's a reasonable option for John to walk to the shops after leaving his house-he does so every day. What is different today is John's intention, which is invisible to his neighbour. How does Landman's account rule out (s) in the case? Landman could point oue that his notion of reasonable option depends upon factors that are 'internal to the event'-and it seems reasonable that such factors should include the agent's intentions in at least some cases. If we can argue that John's intention to go to the park is internal to the event, then we can say that on the basis of this intention it is not a reasonable option to go to a world where he doesn't turn off to the park, but goes to the shops. Yet there are many cases where an agent cannot be said to have intentions, or where the intentions of the agent are simply not relevant. It appears that more work is needed on how to make the notion 'internal to the event' precise. There appear, too, to be example where the notion 'internal to the event' is problematic. Consider the following:

336 The Progressive: A Channel-Theoretic Analysis

(7) a. We were flying to Manchester. b. We were flying to Havana. It appears that there are single scenarios which are correctly described by both (7a) and (7b). Suppose that we bought tickets to Manchester and got on the plane which took off and headed for that city. On the way a band of hijackers forced the pilot to take us instead to Havana. In retrospect it seems quite possible to say: (8) We were flying to Manchester but some hijackers forced the pilot to take us to Havana. and also to say: This

example is similar to the following one (attributed by Asher to Irene Heim) which, as Asher and others point out, poses problems for Dowty's analysis. (IO) Irene was making fish stew but the cat was eating the fish.

Just as in (7), the two outcomes are mutually incompatible, so there are no worlds in which both events can be completed. Yet the sentence containing the two progressives is perfectly comprehensible. This is a problem for Landman as well as Dowty. Landman proposes extending his account to deal with this kind of example by incorporating some notion of perspective. Depending on the perspective of the speaker, one or other of the progressives may be true. However, he does not attempt to formalize this idea, and it seems that he would need to introduce a considerable amount of new machinery into his account in order to do so. We will show below how channel theory provides us with the theoretical tools to make the notion of perspective precise.4 2.2

Asher)s account

Asher (I 992) gives a semantics for the progressive which employs defeasible reasoning. Use of the progressive relies on the existence of a default to the effect that, in the absence of any information to the contrary, we may conclude that the corresponding non-progressive sentence is true. If, however, there is information to the contrary, as is the case in: (I I ) Mary was crossing the road when she was hit by a truck.

then the default is overridden by the more specific information to the contrary, and we may not conclude that she crossed the road.

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(9) We were, although we didn't know it at the time, flying to Havana.

Sheila Glasbey 337

( 1 2) Mary was crossing the minefield. Here, the problem is that the progressive is judged acceptable even though there appears to be no default that people crossing minefields generally arrive at the other side. A more likely outcome (or, at least, an outcome that is equally likely) is that the person will be blown up en route. Now, a possible rejoinder is to say that special knowledge about Mary or the minefield might allow us to use the progressive. If, for example, Mary is an expert in crossing minefields and has suitable mine-detecting equipment, the default may well be that she gets safely across. Another possibility, raised by Asher, is that (12) may be used if Mary is unaware that it's a minefield she's crossing. This might allow us, says Asher, to take a perspective, corres­ ponding to Mary's viewpoint, which excludes the information that it is a minefield. However, it is possible to construct examples which pose problems for both these strategies. Consider the following discourse: (13) I looked out of the observation hut window and was horrified at what I saw. Mary was crossing the minefield. I realized, remembering her state of despair when she spoke to me the day before, that she was trying to get herself blown up. In this scenario, Mary not only knows that it's a minefield that she is crossing, but is exploiting that fact-she is deliberately trying to get herself killed. The narrator, too, is fully aware that what Mary is crossing is a minefield. It is therefore extremely difficult to see how any perspective which left out the fact of the minefield could be justified. In conclusion, we do not see how Asher's notion of default can account for this example.

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Asher uses a possible-worlds semantics which makes no use of events or event types, and thus in order to capture what he calls the 'relevant features' of the progressive state 5 that participate in the default, he introduces a theoretical notion of perspective,6 which excludes those aspects of the state which are not considered relevant. Thus, which characteristics we can count or discount depends on the perspective taken. This is Asher's way of removing 'interruptions to the event'-we are allowed to take a perspective which excludes the interruptions. Exactly which perspectives are licensed at a particular point of the discourse is a matter that Asher does not make precise, and it appears that further work is required here. Rather than examine this matter in detail, we will concentrate on what appears to be a more serious problem. There are some progressives where the default notion does not seem to be correct. One example, considered by Asher himself, is:

338 The Progressive: A Channel-Theoretic Analysis

Another similarly problematic example is: (14) John is writing a novel. He won't finish it, of course. Hardly anyone ever does.

3 TOWARDS A N I M PROVED A C C O U N T I t seems that both Asher and Landman have succeeded in capturing something important about the semantics of the progressive, yet neither of their accounts is entirely correct. Let us try to analyse what is right and what is wrong with their proposals. Certainly, there seems to be something right about Asher's notion of defeasible reasoning. On many occasions it appears that we do infer from our knowledge of the 'progressive event' that the event was completed, unless we know otherwise. And Landman's notion of 'reasonable option' seems to go some way towards capturing the idea of 'normality' that earlier accounts such as Dowty's set out to express but failed to do adequately. Our challenge is to combine the above insights by making the notion of 'reasonable option' more precise and also to characterize how people (may) reason with the information content of progressive sentences. In

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A speaker uttering ( 1 4) feels able to describe what John is doing as 'writing a novel', even though she clearly perceives no default to the effect that people writing novels normally finish them. Indeed, her second and third sentences indicate that she believes that the default goes the other way and that people generally don't finish the novels they start. It does not seem possible to find any other perspective here which might license the default, as this is simply a piece of directly reported speech. So we are left with the same kind of problem as in the minefield example. The minefield example is also problematic for Landman. In the scenario described by (r2), Landman would need to explain the acceptability of the progressive by being able to move to successive closest possible worlds, removing 'one mine at a time', just as in (3) we remove one Roman soldier at a time. Remember, though, that we can only remove another mine, at each step, if to do so is a reasonable option from the actual world w. Now we might well argue that there comes a point, long before Mary reaches the other side, at which it is no longer a reasonable option to remove any more mines. This is certainly the case if we except Mary not to get across, as in (12). So Landman is left without a way to explain why (12) is acceptable. The problem is that, while it does not seem to be reasonable option for Mary to get across the minefield, the progressive may still be correctly used to describe the scenario.

Sheila Glasbey 339

'X is crossing Y'

>

'X crosses Y'

where ' > ' signifies non-monotonic entailment, as used by Asher, and 'X crosses Y' corresponds to a complete crossing. The notion of default we are using looks something like what Barwise & Seligman (1994) call a natural regularity. A natural regularity is a constraint which holds between types of things in the world-for example, between the type of situation where my doorbell rings and the type of situation where someone is standing on my ·doorstep. If my doorbell rings, than I am generally safe in assuming that someone is standing on the doorstep. It is quite possible that there is another explanation-such as the doorbell being broken-but this is the exception rather than the rule. We appear to use such regularities much of the time to allow us to reason with the often incomplete information we receive about the world we live in. Natural regularities are both reliable and fallible. In general, they work well, which is why they are useful to us, but they also tolerate exceptions and thus our reasoning may fail to reflect reality on a particular occasion-! may go to the door to find no one standing there. Channel theory is a mathematical theory of information flow based on the notion of natural regularity (see Barwise & Seligman 1 994; Barwise 1 993; Seligman & Barwise 1 993). This notion is derived from the earlier situation­ theoretic notion of a constraint-see (Barwise 1989). Channel theory considers information flow to be a two-level process, involving the type level and the token level. The type level contains regularities or constraints between types of objects, where the objects themselves may be individuals, situations, etc. The token level contains connections between the tokens themselves. It is this two-level structure which, as we will show below, enables us to account for the fact that a regularity may have exceptions without invalidating the general rule.

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the remainder of the paper we will develop an account based on channel theory which attempts to do these things. Suppose we say that by stating (12), the speaker is not making use of a specific default about crossing minefields in particular, but is making use of a more general default-perhaps one concerned with 'crossing things' in general. Then, we might argue, it doesn't matter that there is no specific default 'available' for minefield crossings. Certainly, it appears rnore psychologically plausible that we use general rather than specific defaults-the load on memory would be very great otherwise.7 Let us suppose for a moment that there is such a general 'crossing' default-to the effect that if someone (or something) is crossing something, then the default is that they get to the other side of it. We might express this provisionally as:

340 The Progressive: A Channel-Theoretic Analysis

Information flow takes place by means of channels. A regularity can only be true or false with respect to a channel, which in the former case is said to support the regularity. More formally, a channel is an informational link between two classifications, where a classification is a structure which divides up the world (or part of it) into tokens and assigns types to those tokens. The tokens may be individuals, situations,8 other classifica­ tions, etc. If a channel C links two classifications A and B, we write: C : A =:> B C is itself a classification, the tokens of which are connections, written: where t is a token of A, t' is a token of B and t is said to signal t'. The types of C are constraints, written ¢ - 'lj;, where ¢ is a type of A and 'lj; is a type of B. If C classifies t f-t t' as of type ¢ - 'lj; we write: :[

¢

-

If t f-t t'

:c

¢

t f-t t'

'lj;

-

'1j;

then (by means of a soundness condition) t : ¢ carries the information that t' : 'lj;. It is possible for a constraint to be supported by a channel C even though not all the connections in C are classified by that constraint. If --,[t f-t t1

:[

¢

-

1f;]

then t : ¢ does not carry the information that t' : 'lj;, even when t : ¢ holds. [n this case, the connection t f-t t' is said to be an exception to the regularity.9 Thus the key to the treatment of exceptions is that while regularities exist at the level of types, whether or not the appropriate reasoning goes through is determined by whether or not the connection between two tokens is of that type. For example, suppose that we have a channel C supporting a constraint between situations of a type we could call 'X crossing Y' (call this a) and those situations of type: 'X cross Y' (call this (3).10 That is, C supports a - (3, which we write as: c :

(X -

{3.

Now consider a particular occasion where Mary is crossing the road. In general, we might expect her to get across-this is reflected by the fact that the channel in question supports the above constraint.1 1 Now consider the

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t f-t t'

Sheila Glasbey 341

situation (call it s) that corresponds to 'Mary crossing the road' on this occasion. s may support facts about Mary's position at a given time, her direction of travel, her intentions, etc. s may be linked by a signalling relation to another situation s', which is a situation that contains s and continues until a few minutes after the end of s. The signalling connection is denoted by s � s'. Whether or not the particular connections s � s' is of the type a ---+ (3 is determined by the channel C, which, as we saw above, classifies the connections of C according to whether or not they are of the type of the constraint(s) supported by C. For example, C may in this case tell us that:

If an utterance of a sentence of the form 'X was V-ing Y can be correctly used to describe a situation s, this shows that:

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If this is the case, then the soundness condition ensures that s' : (3-that is, Mary gets to the other side in s'. However, if C does not classify s � s' in this way, then we may not conclude that s' : {3-that is, we may not conclude that Mary reaches the other side. This captures neatly the fact that progressives may sometimes 'fail' in the sense that the complete event is not realized, while the progressive sentence is nevertheless true. There may, however, be a problem in identifying the situation we have called s'. We proposed above that s' should be thought of as the situation supporting facts about Mary which ends a few minutes after she is in the middle of the road. In other words, the 'end time' of s' is associated with the time that Mary would have been expected to reach the other side, had she done so. If Mary does indeed reach the other side, then there is no problem in picking out the time of s'. However, as we explained above, the progressive sentence may still be true even if Mary never reaches the other side. It then becomes difficult to identify the end-time of s', because we have no way of knowing exactly when Mary would have reached the other side. This, in turn, makes it difficult to know exactly which situation we are call.mg sI . 1 2 In order to get around this problem, we propose that in cases where Mary does not reach the other side, we go a step further than saying merely that s f---t s' is not of a type a ---+ (3. We propose that in this case, s is a pseudosignal (in Barwise & Seligman's terminology) for the relevant constraint in channel C. This means that s is not connected to any other token in this channel-there simply is no s' such that s ---+ s' in C. We can now express the semantics of the progressive as follows:

342 The Progressive: A Channel-Theoretic Analysis

There is a channel C : A =? B and a type o: such that s : o: in A, and o: ---t /3 is supported by C (where /3 is the type of the corresponding 'complete event', 'X V-ed Y).

s : a & C : a ---t /3 but -{3s' s.t. s �---? s' :c a

---t

/3) .

In cases where it is not appropriate to use the progressive, we may simply say of the situation s in question that ..., (s : o: ) . Our above characterization of the progressive does not, as it stands, say anything about how we reason with the information given to us by progressive sentences. Channel theory, as presented by Barwise & Seligman in the aforementioned papers, does not attempt to model how we reason with channels. It is, however, very natural to assume that some kind of defeasible reasoning is often involved. Cavedon (1995) presents a system which models defeasible reasoning with channels. 1 3 He argues that if we are to model this kind of reasoning, we need to minimize the number of exceptions in a channel. He does this by defining a suitable maximal normality constraint (MNC), which basically imposes the assumption that there are as few exceptions as possible within a channel. Effectively, the MNC ensures that a token is not the LHS of an exception unless information about it contradicts the 'background assumptions' of the channel. In Cavedon's model, this background of information is represented by means of a channel hierarchy. This is most easily explained using an example. Suppose we have a channel C which supports the constraint bird ---t fly, where bird is the property of a being a bird and fly is the property of being able to fly. Now, suppose that b is a particular bird, and the (reflexive) connection b �---? b is one of the tokens of C. If we have no further information about b, then the MNC allows us to assume that this connection is not an exception to the above regularity, i.e. that:

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Is there is a situation s' such that s �---? s' is one of the tokens of C, and if C classifies s �---? s' as of type o: ---t /3, then the soundness condition ensures that ' s : (3, which means that the complete event is realized. However, as we saw above, s �---? s' need not be of type o: ---t /3 in order for the progressive to be true-indeed, there may not even be an s' . Thus an utterance of a progressive sentence may correctly describe a situation s even in cases where the complete event does not take place­ which is exactly what we require. In these cases-where the progressive is appropriate but the complete event is not realized-we say that:

Sheila Glasbey 343

b 1---7 b

:c

bird � fly

and thus we can infer from the soundness condition that b:fly. Now, suppose that we know that b is a penguin. In this case, some means of blocking the above reasoning is required (because we know that pengui11s

carmot fly). One way to do this might be to change the constraint to:

(bird & -, penguin) � fly A similar approach is taken by Barwise (1989), who (in a treatment of conditionals) expresses this as: bird � fly I B

(bird & -, penguin) � fly The presence of channel C' as a superchannel of C in the hierarchy is wh�t blocks the use of C to reason that b (where b is a penguin) can fly. What is blocked is the serial composition of C (supporting bird � fly) and the channel we will call L which supports the 'logical regularity' (bird & penguin) � bird. Such composition would give a channel C' supporting the constraint (bird & penguin) � fly. In Cavedon's model, serial composition is blocked here by virtue of C being a subchannel of C', which supports the constraint {bird & -, penguin) � fly, the antecedent of which is incompatible with the antecedent of the constraint supported by L (see Cavedon 1 996, 1 995 for more detail). By this method Cavedon obtains a logic for defeasible reasoning with channels, whereby 'more specific contrary information' can block the derivation of new channels by serial composition. We will see shortly how a slight modification of our analysis of the progressive, combined with Cavedon's model of reasoning with channels, allows us to account for the 'minefield' examples, (13) and (14), that were problematic for Asher's analysis. First, however, we will show how the

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where B is the property of not being a penguin. The property of not being a penguin is seen here as a 'background condition' to the constraint bird � fly. A problem in this approach is that it may well not be possible to specify all the background conditions that are required in order for a given constraint · to be applicable. Cavedon overcomes this problem by encoding such background conditions implicitly in a channel hierarchy. The background assumptions associated with a channel C ar� not encoded in C at all but are captured by the way that C relates to other 'more informative' channels. In the case above, C is a subchannel of a 'more informative channel' {or superchannel) C' which supports the constraint:

344 The Progressive: A Channel-Theoretic Analysis

notion of 'situation type' that we have been using to formulate some of our constraints can be made more precise using situation theory, and how we can build temporal information into the constraints. 3. 1

Situation types and the PART-OF relation

o Situation Aspect: This corresponds at least roughly to what is usually

called 'aspectual class' or 'Vendler class'.

o Viewpoint Aspect: This concerns the speaker's perspective on the

situation described. Viewpoint aspect acts as a kind of window on situation aspect, determining how much of the situation is 'visible'. Smith defines three viewpoints perfective imperfective, and neu­ tral. Viewpoint aspect is independent of situation aspect, giving rise to the two-component nature of the theory. The essential properties of a particular situation aspect are not obscured by the viewpoint aspect imposed upon it, but continues to be visible. Perfective aspect presents an event in its entirety-'complete with both endpoints'. Imperfective aspect, on the other hand, presents an 'internal portion' of an event, without either of its endpoints. -

,

In Smith's theory, progressives and statives are distinct. The English progressive is a manifestation of imperfective viewpoint, while 'state' is a particular situation aspect. Smith circumvents the imperfective paradox, by not addressing the issue of what must be true about an eventuality for it to

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So far, we have not given an exact characterization of 'situation type'. In order to do this, we need to introduce some apparatus from situation theory (for an introduction to situation theory see, for example, Barwise & Perry 1 983; Barwise 1 989; and Barwise & Cooper 1993). First, however, let us consider how we might build some kind of temporal information into our account of the progressive. Bennett & Partee's original analysis, although incorrect in that it required a 'completed event' (see Section 2), contained the important intuition that the 'progressive event' occupies a time interval which is included in the time interval for the 'completed event'. Other more recent analyses of the progressive encode a similar notion of temporal inclusion. Smith (1991), rejecting earlier analyses such as that ofVlach (1981) of the progressive as a 'stativiser', presents an analysis whereby a progressive sentence is seen as conveying an 'interval viewpoint' on the corresponding complete event. Here, the notion is one of event inclusion rather than temporal inclusion, but the idea is intuitively very similar. Smith presents a two-component theory of aspect, which analyses what is traditionally called 'aspect' into two orthogonal properties, these being:

Sheila Glasbey 345

qualify as part of a bigger (conceptual) eventuality. We will address this further below. Smith develops a DRT formalization of her accounts of the progressive, which works as follows. For a progressive sentence such as:

( IS) Mary was climbing Ben Nevis. she takes the corresponding 'complete event' e (this being an event where Mary climbs Ben Nevis), and enters this into the set of discourse referents. Thus the DRS for (IS) contains the following: e , x, y

She then encodes the imperfective viewpoint by introducing an interval [I] (this being a temporal entity) into the DRS. [I] is the viewpoint of the sentence, and she includes a condition which specifies that this viewpoint is imperfective. Thus her DRS for (Ist is as follows: e , x, y, I x : M a ry y:Ben Nevis e = climb(x,y) e = { Ac c o mp l is h m e n t } viewpoint(l,e)

=

imperfective

There is a problem, however, concerning the interpretation of this DRS. We have an event referent e corresponding to the complete event, and yet of course it is not necessary that such a complete event exists in the model. In attempting to express her ideas in DRT, Smith has thrown away the highly intuitive notion that the complete event is of 'conceptual' rather than 'real' status. What is missing from her account is a notion of conceptual event or event type. Now channel theory, with its distinction between the token level and the type level, can provide us with what is required here.

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x:Mary y:Ben Nevis e = climb(x,y) e = {Accomplishme n t}

346 The Progressive: A Channel-Theoretic Analysis

First, however, we need to see how we can represent an event such as 'e = walk(x,y)' above in terms of situation types.15 In order to do this, we use the version of situation theory given in (Barwise & Cooper 1 993), expressed in the Extended Kamp notation (EKN) introduced there. Barwise & Cooper use a box notation for situation­ theoretic objects such as infons, situations, and propositions, based upon the graphic notation of DRT. However, in EKN the boxes directly represent semantic objects, in contrast to DRT where the discourse representation structures (DRSs) are expressions of a language which require interpretation in a model. Another .important difference is that EKN boxes may contain situations. Propositions in EKN include objects of the form:

i mb (X , Y , T )

which is the proposition that a situation S supports an infon lclimb(X,Y,T)I, where T is the time argument of the relation climb. 16 Under certain conditions, we can think of T as the 'time role' of the situation S, or what is sometimes called the 'run-time' of that situation. But this is only the case if the infon lclimb(X,Y,T)I is related to a particular way to S. Intuitively, we require that S is the 'minimal situation' or 'smallest situation' that supports the infon-that is, S corresponds to the climbing event and noth.mg more. 17 We can make this precise by ensuring that lclimb(X,Y,T)I is a 'key infon' of S. This notion is taken from Cooper ( 1 985). A key infon of a situation S is defined by Cooper as an infon whose temporal duration (corresponding to its time ar ument T) includes those of any other infons supported by S. If climb X,Y,T is indeed a key infon of S, 18 then we can say that T is the time role or run-time ofS. More formally, we introduce a binary type TIME-OF which hold berween a situation S and a time T if T is the run-time of S. That is, we write:19 S,T

I

TIME-OF

Situation-theoretic objects may have restrictions imposed on them, as shown below, where the object P is restricted by the proposition Q. That is,

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cl

Sheila Glasbey

347

the representation below denotes P iff the proposition Q is true, otherwise it fails to denote.

(16) Mary climbed Ben Nevis.

named(X, 'Mary')

climb(X,Y,T)

named(Y,'Ben Nevis') S,T J TIME-OF

From a proposition such as the one above we can form a type by abstracting over one or more of the parameters, using the technique of simultaneous abstraction developed in Aczel & Lunnon (I 99 I) and Lunnon (I99I). For instance, we can abstract over S in the above proposition to give the situation type:

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The use of restrictions allows us to represent certain kinds of 'back­ grounded' or 'presupposed' information such as the naming of individuals. Cooper (1 993) motivates the use of resource situations (e.g. R, R' in the example below) to support such information. We can then represent the meaning of

348 The Progressive: A Channel-Theoretic Analysis

r1

w

---?

S

� named(X,'Mary')

� climb(X,Y,T)

S ,T J TIME-OF

where the role corresponding to the parameter S which is abstracted over is labelled by the role index r1. Such indexing of roles is necessary with simultaneous abstraction, in order to keep track of which role corresponds to which parameter (see Barwise & Cooper 1993 for further details). Situation theory thus allows us to make precise the notion of situation type or event type, and, moreover, allows us to speak of the realization or instantiation of such types. We can represent an event of conceptual status as an event (situation) type, without necessarily claiming that the type is realized as an actual event. This allows us to think of the speaker referring to an event type, and claiming only that an internal portion of that event type is instantiated. For example, we might say that an utterance of (17) Mary was climbing Ben Nevis. describes a situation s, where s : a and a is an 'internal portion' of an event type of (3, (3 being the type of the complete event, which is the type shown above. Smith admits that her account is not a truth-conditional one, in that it does not attempt to cover the 'normality' component of the progressive. We can remedy this by adding the semantics for the progressive we developed above, which requires that some channel C supports the constraint a ___, (3 (see below).

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named(Y,'Ben Nevis')

Sheila Glasbey 349

Next, we need to make precise the notion of 'internal portion'. We want to say that, in those cases where the complete event is realized (that is, there is an s' such that s t--t s' and s t--t s' :c o: ---+ {3), then s is an internal portion of ' s . In order to formalize 'is an internal portion of' we use the notion of PART­ OF (or �) from situation theory. This is defined in Barwise (I 989) as follows: For all situations supported by s,.

s.,

S2, S2 � s, iff any infon is supported by 52 is also

If an utterance of a sentence of the form 'X was V-ing Y can be correctly used to describe a situation s, this shows that: There is a channel C : A ::::} B and a type o: such that s : o: in A, and o: ---+ {3 is supported by C (where {J is the type of the corresponding 'complete event' 'X V-ed Y), and if 3s' s. t. s t--t s' :c o: ---+ {3, then s � 1 s' . Our semantics for the progressive now incorporates two notions: firstly the idea that some channel must support an appropriate constraint between the type of situation described and the complete event, and secondly that, in those cases where the event goes to completion, the described event ('progressive event') is PART-OF, in the sense defined above, the complete event. However, our task is not yet complete. We will see below that some further refinement is needed.

4

S O ME EXAMPL E S A N D S O ME C O M P L I CAT I O N S

Let us now test our account on some further examples. We discussed above how we can capture the semantics of:

(18) Mary was climbing Ben Nevis. To summarize briefly, we say that there is a channel C which contains a number of connections between situations. In addition, C supports the

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For all situations s,, 52, s2 � s, iff any infon supported by 52 is also supported by s,. Based on this, we can define a new relation TEMPORAL PART­ OF (�,) which requires also that the run-time of 52 is temporally included in the runtime of s,. Adding this requirement gives us the following semantics for the progresstve:

350 The Progressive: A Channel-Theoretic Analysis

constraint a ---+ {3, where a is a situation type corresponding to an incomplete crossing, and {3 a situation type corresponding to a completed crossing. We proposed that if the described situation s is of type a, then s may be described using the appropriate progressive ('X was crossing Y'). Now we have to explain why sentences like: (19) Mary was wiping out the Roman army. as discussed earlier, are not acceptable. This sentence, and the similar example: (2o) Mary was swimming the Atlantic. Downloaded from jos.oxfordjournals.org by guest on January 1, 2011

are judged by speakers to sound odd, unless we know that Mary has superhuman capabilities and is actually capable of wiping out the Roman army or swimming the Atlantic. We cannot use (2o) to describe, for example, a situation where, for example, Mary sets out from the coast of Cornwall and swims for several hundred yards in the direction of America. But why can't we use a 'swimming constraint' that holds between 'incomplete swims' and 'complete swims' in the same way that we used climbing and crossing constraints in our examples above? The existence of such a swimming constraint appears intuitively as plausible as that of a crossing or climbing constraint-the constraints say nothing about what is being swum, climbed, or crossed, remember. The point is that if we employ constraints at this level of generality, we have no way, as yet, of ruling out the use of the progressive in examples like (2o). We want to keep the general swimming constraint (which we will abbreviate to 'gsc'), but to rule out the use of the progressive in a case where the subject is Mary and the object is the Atlantic. Note that this is not the same thing as saying that a particular connection between situations is not classified as being of the type of the constraint. This would only tell us that the complete event was not realized-it would not rule out the use of the progressive per se. We propose the following explanation. Let us suppose that there exist (in the sense that human beings perceive them and use them to reason with) channels supporting constraints at a fairly general level, that we might informally call crossing constraints, swimming constraints, etc. We do not want to commit ourselves at this stage to saying exactly what constraints we use, or at what level of generality we perceive them. Much further work would be required in order to establish this, possibly lying outside the realm of linguistic semantics. We will merely explore here the idea that constraints may exist at different levels of generality. Imagine someone hearing a progressive like (2o). In order to make sense of it, the hearer starts with the general swimming constraint (gsc), which we will call 'Y ---+ 8, 8 being the situation type we label 'X swims Y', with X and

Sheila Glasbey 351

Y unspecified. Now the hearer checks to see if the substitution of 'Mary' for X and 'the Atlantic' for Y in 8 yields a situation type 81 which is 'conceivably possible'. In this case, the situation type obtained by the substitution is the one corresponding to the complete event 'Mary swam the Atlantic'. This situation type fails the 'conceivably possible' test, if Mary is a normal human being receiving no miraculous aid, and for this reason the use of the progressive is ruled out here. Now compare: (21 ) Mary was crossing the road.

(22) Mary was crossing the minefield. is acceptable? Once again, the hearer starts with the gee, o: � (3. Now she tries to instantiate (3 by substituting 'Mary' for X and 'the minefield' for Y. Doing so produces the situation type corresponding to a complete crossing of the minefield by Mary. As long as we can see this situation type as 'conceivably possible', we may use the progressive. We do not require the complete event to be the default outcome, nor even that it is likely or expected, but simply that it is (in the mind of the hearer) a possible outcome. Provided that the hearer believes it is possible for Mary to get to the other side of the minefield, it is correct for her to use the progressive. This is the case even though the hearer may believe t}at by far the most likely outcome is for Mary to get blown up. On Cavedon's model of reasoning with channels, discussed above, we say that the channel C supporting the gee is a subchannel of a channel C' which supports the constraint: ('X crossing Y' &

-,

'Y a minefield')

�

'X crosses Y'

This blocks (by the mechanism described earlier) the formation by serial composition of a channel supporting the constraint:

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where the hearer may readily substitute 'Mary' and 'the road' in the RHS type of the general crossing constraint (gee), to give the situation type corresponding to a complete event 'Mary crossed the road'. Now, this situation type is seen as conceivably possible, and the progressive is therefore licensed. The impossibility of the 'instantiation' in (19) and (2o) is thus responsible for the fact that these are judged as unacceptable progressives. Of course, if the hearer believes that Mary is superhuman, or receives divine assistance, then the instantiation may become possible, thus allowing her to accept the progressive. This allows us to account for the so-called 'miracle scenarios' discussed by Landman. Now, what about Mary crossing her minefield? Can we explain why:

352

The Progressive:

A

Channel-Theoretic Analysis

('X crossing Y' & 'Y a minefield')

-----+

'X crosses Y'

Thus, there is no 'default' to the effect that someone crossing a minefield succeeds in getting to the other side. Nevertheless, the use of the progressive in (22) is licensed, by virtue of the existence of the channel C supporting the gee, and by the fact that getting across a minefield is seen as conceivably possible. Similarly, consider: (23) John was writing a novel.

'Mary crossing Y' & 'Y a minefield'

-----+

'Mary crosses Y'.

We can now give a revised semantics for the progressive, taking the above modifications into account. If an utterance of a sentence sent of the form 'X was V-ing Y' can be correctly used to describe a situation s, this shows that:

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Here, the use of the progressive is licensed by virtue of a channel supporting what we can call a 'general writing constraint', which tells us that if someone is writing something they generally finish it (with the added proviso, once again, that we can see the situation type corresponding to a complete writing of a novel by John as conceivably possible). Once again, there does not need to be a default to the effect that ifJohn (or anyone else) is writing a novel he (or she) will finish it. We can therefore explain why most speakers are happy to accept (22) and (23) to describe the appropriate scenarios, while rejecting (2o). We differ from Asher in that we do not require there to be a default that someone crossing a minefield succeeds in getting to the other side, or that someone writing a novel completes it. It is the fact that some channel supports the appropriate general constraint (e.g. the gcc)-together with the 'conceivably possible' requirement-that licenses the progressive. Our account differs from Landman's, too, in that we do not require Mary's getting to the other side of the minefield to be a 'reasonable outcome', but simply possible.2 1 Our proposal can be summarized as follows. Correct use of the progressive is licensed by the fact that some channel C supports a general constraint of the appropriate kind (such as the gee or gsc). We also require that the consequent (RHS) type of the constraint can be instantiated (by the particular referents supplied by the utterance) to give a situation type that is 'conceivably possible'. The latter requirement rules out examples like ( 19) and (2o). However, the fact that the progressive is licensed in (22) does not require there to be;a channel supporting the constraint:

Sheila Glasbey 353

There is a channel C : A ::::} B and a type o such that s : o in A, and o ---+ f3 is supported by C, (where f3 is the type of the corresponding 'complete event 'X V-ed Y'), and f3 can be instantiated by substituting values of X and Y in sent to give {3', where {31 is a 'conceivably possible' situation type, and if 3sl s.t. s � s' :, o ---+ {3, then s � , s'.

s

S O M E F U RTHER EXAMPLES

5.1

Perspectives revisited

Earlier, we discussed examples like:

(24) We were flying to Manchester/We were flying to Havana. We will now see how the notion of channel allows us to deal with such examples. We have seen that a channel C contains a number of connections, supports one or more constraints, and classifies which connections are of which types. Thus a channel may be thought of as a perspective-one particular way of classifying reality. Alternative ways of classifying reality are possible, and we may think of these as corresponding to different channels. We may want to associate different channels with different participants in an event, or even with the same participant, reflecting the fact that it is possible to switch viewpoint mid-sentence. The example below should make this clear. Suppose we say that one channel, C. , supports the constraint between the situation type (o) of sitting in the appropriate plane, with the appropriate tickets to Manchester and the situation type (/3) of flying to Manchester. Let us call this constraint o ---+ {3. Another channel, C2, supports the .constraint (-y) between the situation type of sitting in the appropriate plane, with the appropriate tickets, and having hijackers bound for Havana on board, and the situation type (b) of flying to Havana. Let us call this constraint "f ---+ 8. If s is the particular situation of our being in the plane (etc.), then it may be true that:

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In this section we will look briefly at some further examples which are problematic · for Landman, Asher, or both, and show how the channel theoretic account can help us to address the problem.

3S4 The Progressive: A Channel-Theoretic Analysis ·

in which case we fly to Manchester. Alternatively, it may be true that:

' s�s

:,,

1 ----?

8

(25) Irene was making fish stew but the cat was eating the fish. Here, we can view the channel C" corresponding to the first progressive, as reflecting the perspective of Irene (given her intention to make the stew) and the channel C2, corresponding to the second progressive, as reflecting the perspective of the cat (given its intention to eat the fish). Either outcome (or neither) may be realised, but it is not possible for both events to be completed. Thus we can deal with examples of 'conflicting' progressive which are problematic for Dowty, and for Landman's basic account. 22 5.2

Intentions

Let us now investigate briefly how the channels proposal would work in examples where intentions are important, such as: (26) John was walking to the shops. In Section 2, we describe a scenario where this progressive is not licensed, because John's intentions are inappropriate. First, let us suppose that there is a general 'walking-to' constraint ¢ ----? '1/J, where '1/J is the type of situation 'X walks to Y'. In order to capture the requirement that John's intentions must be right, we must build information about the intentions of X into ¢. Thus a situation s will only be of type ¢ if s supports the information that John intends to walk to the place in question. 2 3 This prevents a situation where John intends to walk to the park rather than to the shops from being classified as of type ¢, and hence the progressive cannot be licensed.

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in which case we fly to Havana. Of course, it is not possible for both of these to be true on the same occasion. And it is not necessary, of course, that either of them are true-we may not reach either destination. As we have seen, all that is required to license the use of the progressive is for the described situation to be of the type of the antecedent of the constraint (together with the 'conceivably possible' requirement). Thus each 'perspective', in the informal sense used by Landman, can be seen to correspond to a distinct channel in our framework. The different channels correspond to alternative perspectives that may be taken by the speaker depending on her knowledge or point of view of the time of evaluation. Or, as we suggested above, the different channels may in some cases correspond to points of view taken by different participants in the event. Consider the example given earlier:

Sheila Glasbey 3SS

In contrast, we have examples like: (27) Mary was making John a millionaire. where the progressive may be true even when the agent does not intend the outcome to happen. In this case, suppose we have a general constraint a --+ (3, where (3 is 'X makes Y a millionaire'. In this case we do not need to place any restrictions on a concerning the intentions of X.2 4 Thus, by taking care to define precisely the situation types which make up the antecedents of our constraints, we can build in information regarding the intentions of the agent in cases where this is relevant, and exclude it where it is not.

Drinking bouts and paper marking

Finally, let us look briefly at some examples that Ogihara (1 990) identified as problematic for analyses of the progressive, and which Asher confesses are problematic for this account. These include: (28) Mary is marking so exam papers. which is acceptable when used to describe a situation where Mary has marked, say, eleven papers and is taking lunch before starting work on the twelfth. Compare, however: (29) ??Mary is drinking three cups of tea and five glasses of whisky. which sounds distinctly odd, even if I say it in the middle of a day when Mary does in fact consume all these drinks. Things improve dramatically if I can somehow see Mary as having an intention or plan to carry out this feat.2 5 Suppose someone has bet Mary a tenner that she couldn't possibly consume all these drinks, and she is in the middle of attempting it when she begins to feel sick. Then she might say afterwards: (3o) I was drinking three cups of tea and five glasses of whisky when I started to feel sick and gave up. In this context, the progressive sounds perfectly natural and correct. In a comment on Ogihara's paper, Caenepeel & Moens (1 990) suggest that an account of the progressive needs to capture the difference between something that can be seen as part of a plan26 and something that can't. They take this to suggest that the semantics of the progressive cannot be captured in purely temporal terms, but they do not formalize the notion of 'plan'.

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5·3

356 The Progressive: A Channel-Theoretic Analysis

5·4

The universe

We now return to our earlier example (6), repeated here as (31).

(3 I) For many billions of years, the universe was contracting back to a singularity. Then, in the last hour or so, the interactions between black holes prevented it from ever reaching that point, and it began to expand agam.

which we argue posed problems for Landman's account. We now can explain why the progressive is acceptable here, by virtue of the fact that some channel supports a general 'contracting constraint', which we can write as: 'X contracting back to Y'

---+

'X contracts back to Y'

and the fact that the situation of the universe contracting back to a singularity is conceivably possible to us. Whether such an event is possible according to the laws of Physics does not appear to be relevant here. This leads to the question of what exactly is the nature of channels and constraints-do they exist independently of reasoning agents as part of

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Can we make some progress here for using channels? One way of thinking about it is to say that, in the case of a pre-planned scenario like the marking of a set of papers, we can employ a channel supporting a constraint between the type of situation where one is in the middle of such a marking task (with the intention of finishing it) and the type of situation that corresponds to completing the task-what we might call a 'general marking constraint'. Similarly, if we know that Mary is attempting some drinking feat, then we can employ a channel supporting a constraint between the type of situation where one is partway through a drinking feat (with the intention of completing it) and the situation type where one completes it. If, however, the drinking was not planned but simply the result of Mary having a bad day (or, perhaps, a good party), then we cannot classify the described situation as being of the required antecedent type, and the progressive is not licensed. Notice, once again, that Asher's notion of default does not seem to work here. A hearer may accept (29), provided he believes that Mary intends to consume all these drinks, while being very sceptical of Mary's ability to achieve her aim. Thus we have another example where it seems wrong to identify the correct use of the progressive with a licence to perform default reasoning in the particular case described.

Sheila Glasbey

357

(32) Peter's sins are being forgiven. while a sceptical outsider might question the truth of this progressive. We might say that the religious community perceives the existence of a channel supporting the constraint: 'X prays to God'

--4

'X's sins are forgiven'

and this is what licenses their use of the progressive. Looking from the outside, we might say that this progressive is appropriately used to describe the situation in question, in a context where the conversational participants are attuned to the above constraint. The channel supporting the constraint reflects, as we have seen, the perspective taken by this community of believers. We are thus able to take an informational perspective which saves us from having to worry about which constraints 'actually exist' independently of the agents who perceive and use them. Of course, many questions remain about exactly how we reason with channels. The answer to some of these may have to wait for further developments in channel theory. But at least we have been able to make a start towards the precise analysis of some problematic progressives that other accounts have not been able to deal with.

6 CONCLUSION I n this paper, we have reviewed some recent accounts o f the progressive and argued that they are unsatisfactory in certain respects. In attempting to decide what was going wrong, we showed how moving from a default analysis like Asher's to an account based on the notion of natural regularity,

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the natural order of things, or are they part of the way that agents like ourselves perceive and attempt to make sense of their environment? Perhaps in many cases we want to think of channels and constraints as somehow being part of the way things are, and in a sense existing independently of the agents that employ them for reasoning. There are some difficult philosophical questions here which we will not attempt to answer. One thing that seems clear, however, is that it is useful to be able to model the fact that one community may be 'attuned' (to use Barwise & Perry's term) to constraints to which the rest of us are not. Consider, for example, a community of religious believers, who believe that when they pray, God forgives their sins. Someone from such a. community, on seeing Peter at repentant prayer, could describe the situation as:

358 The Progressive: A Channel-Theoretic Analysis as

given by channel theory, allows us to deal with some of the problems, while at the same time capturing important insights from both Asher's and Landman's approaches. In particular, we showed how the idea of channels supporting constraints of varying degrees of generality allows us to account for the problematic 'minefield' examples. In addition, we have shown how channel theory can make precise the notion of perspective introduced informally by Landman. Our analysis has enabled us to explain a number of examples that are problematic for earlier accounts. Acknowledgements

SHEILA GLASBEY Centre for Cognitive Science University of Edinburgh 2 Buccleuch Place Edinburgh EH8 9LW UK e-mail: [email protected]

Received: 07.01 .96 Revised version received: 19.08.96

N OTES The reason we d o things this way is that it is not all clear to us how a truth­ conditional account of the progressive might otherwise look. It seems very natural and intuitive to try to define truth conditions for a progressive sen­ tence in terms of the truth conditions for the corresponding non-progressive. Attempts to take a non-compositional approach (e.g. Parsons 1 990), do not, we believe, achieve the objective of defin-

ing precise truth conditions (see the criticism of Parsons 1 990 in Lascarides 1991, for example). 2 We use the terminology of Vendler ( 1 967). 3 He does not discuss this kind of ex­ ample. 4 As will be seen below, Asher's account also contains the notion of perspective. However, he employs perspectives for a different purpose (in order to pick out

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This work has benefited greatly from discussions with Lawrence Cavedon, Robin Cooper, and Jerry Seligman. My thanks also go to the two anonymous referees for the Journal of Semantics, and to Karen Brown, Janet Hitzeman, Alice ter Meulen, and members of the Tense and Aspect Group and Meaning and Computation Group at the Centre for Cognitive Science, University of Edinburgh for helpful and perceptive comments. I am grateful for the questions and comments of the participants of the Conference on Information-Oriented Approaches to Language, Logic and Computation, Saint Mary's College of California, June 1 994. where an earlier version of this work was presented. Earlier versions of some of the material from this paper appeared in the proceedings of that conference (Giasbey 1 996), and in (Glasbey 1 994a). The research is supported by an EPSRC postdoctoral fellowship.

Sheila Glasbey 359

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what he calls the 'relevant aspects of an I) See Glasbey (1994a) for further discus­ event'-effectively similar to our notion sion of Smith's analysis of an attempt to of 'event type' or 'situation type'). It is formalize her intuitions in a situation not clear to us how Asher's notion of theoretic framework. perspective could be used (at least, with­ I 6 S, X, and Y are parameters, denoted by capital letters in situation theory. out considerable further development) 17 It is necessary to pick out such 'minimal to account for (7). situations', as there may be many other Asher treats progressives are statives, situations of which S is a part, which following Vlach {I98I) and others. also support the infon in question (for 6 Not to be confused with Landman's notion of perspective, which is entirely example, the situation that we might call 'Mary's holiday in Scotland'). It is different. 7 This leaves us, however, needing to possible to identify such minimal situa­ explain why we can't use the general tions, because in situation theory, a 'crossing' default for 'Mary was swim­ situation is viewed as 'a part of the ming the Atlantic'. We will consider world as individuated by an agent'. This this below. means that it is possible for a situation S 8 We employ the situation theoretic to support only the infonlclimb(X,Y,T)I. notion of situation here (see, for ex­ without necessarily supporting other ample Barwise & Perry I 983; Barwise & facts about Mary and Ben Nevis, for Cooper I 99 I). exampie. Situations are not identified 9 Space does not allow us to explore in with (spatio)temporal locations, so there more detail here what exactly makes a is no problem about S having to support token relation exceptional. This is other infons with the same time (and clearly an interesting topic which place) coordinates. For further discus­ deserves further study, and where sion, see Glasbey (1994b: Ch. 3). We further work on the foundations of agree with the anonymous referee who channel theory may be required. pointed out that we need to formalize 10 We will show below how the notion of more precisely what makes a situation a situation type is characterized in situa­ 'complete event'. This brings us to a tion theory. consideration of how best to represent I I We will consider the minefield ques­ the aspectual class of situations, but tion below. space unfortunately does not permit I2 I am indebted to Jerry Seligman and this here. For a discussion and some Lawrence Cavedon for discussion of this proposals, see Glasbey {I994b: Ch. s). point. I8 Cooper's definition allows a situation to I3 Cavedon is actually concerned with the have more than one key infon, but we reasoning we carry out with the infor­ will not worry about this complication mation conveyed by generic sentences, here. See Glasbey (I994b) for further but the idea is basically the same. See discussion. Cavedon & Glasbey (in press) for an I9 See Glasbey (I 994b), especially Chapters analysis of generic sentences using 3 and s. for further discussion of situa­ channel theory. tions, infons, times, and the relations I 4 This is actually an abbreviated version between them. of Smith's DRS. We have omitted some 20 We ignore tense here, for simplicity. detail which spells out that imperfective 2 I It could probably be argued that our viewpoint excludes endpoints, and some account is not so very different from Landman's in this respect-that the information about temporal reference which is not relevant here. notions of 'possible' and 'reasonable'

360 The Progressive: A Channel-Theoretic Analysis require that s supports (a) certain infon(s) corresponding to John's inten­ tions. 24 Clearly, the general constraint used here must be sufficiently specific to allow discrimination between cases where intentions must be present, and cases where it need not. This is why we have suggested that the constraint spe­ cifies 'millionaire' rather than 'X makes Y a Z'. 25 Ogihara suggests that progressives like these are acceptable if we can regard the eating and drinking as comprising one 'coherent event'. However, he does not make this notion precise. 26 Caenepeel & Moens point out that the problem of speaking of a plan is that if has connotations of intentionality, which are not always desirable.

REFERE NCES Aczel, P. & Lunnon, R. (199 1), 'Universes and parameters', in J. Batwise, J. M. Gawron, G. Plotkin, & S. Tutiya (eds), Situation Theory and Its Applications, Vol. 2, Center for the Study of Language and Information, Stanford, CA, 3-24. Asher, N. (1 992), 'A default, truth condi­ tional semantics for the progressive', Linguistics and Philosophy, . 15, 5, 463-508. Barwise, J. (1 989), The Situation in Logic, Center for the Study of Language and Information, Stanford, CA. Barwise, J. (1993), 'Constraints, channels, and the flow of information', in P. Aczel, D. Israel, Y. Katagiri, & S. Peters (eds), Situation Theory and Its Applications, Vol. J, Center for the Study of Language and Information, Stanford, CA, 3-27. Barwise, J. & Cooper, R. (1 993), 'Extended Kamp Notation: a graphical notation for situation theory', in P. Aczel, D. Israel, Y. Katagiri, & S. Peter (eds), Situation

Theory and Its Applications, Vol. J, Center for the Study of Language and Informa­ tion, Stanford, CA, 29-53Barwise, J. & Perry, J. (1 983), Situations and Attitudes, MIT Press, Cambridge, MA. Barwise, J. & Seligman, ]. (1 994), 'The rights and wrongs of natural regularity', in J. Tomberlin (ed.), Philosophical Perspec­ tives, Vol. 8, Ridgeview, California, 33 1 65. Bennett, M. & Partee, B. H. (1972), Toward the Logic of Tense and Aspect in English, Indiana University Linguistics Club, Bloomington, ID. Caenepeel, M. & Moens, M. (1990), 'Pro­ gressives, perfects and the temporal structure of discourse', in H. Kamp (ed.), Tense and Aspect in English, Centre for Cognitive Science, University of Edinburgh, DYANA Report R1.2A, 3947· Cavedon, L. (1995), 'A Channel theoretic approach to conditional reasoning',

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are not so far apart. This may well be true in general, although we have argued that Landman's account would not predict the acceptability of the minefield example. But while recogniz­ ing that there are some strong intuitive similarities between Landman's account and ours, the channel-theoretic frame­ work gives us tools to begin to make precise some notions which are left unformalized in Landman's account. 22 Note that Asher's account can deal with such examples. In his theory, the sen­ tence content would be expressed in terms of conflicting defaults, giving a 'Nixon Diamond' from which no further information can be inferred. 23 Situation theory allows us to build in such requirements very naturally using the supports relation between a situa­ tion and an infon. We can simply

Sheila Glasbey 361 Semantics', in A. Chukerman, M. Marks, & ]. F. Richardson (eds), Papers from the Nineteenth Regional Meeting of the Chicago Linguistics Society, 171-82. Kamp, H. & Reyle, U. ( 1993), From Discourse to Logic: Introduction to Mode/theoretic Semantics of Natural Language, Formal Logic and Discourse Representation Theory, Kluwer, Dordrecht. Landman, F. (1992), 'The progressive', Nat­ ural Language Semantics, l , I , 1-32. Lascarides, A. (199 1), 'The progressive and the imperfective paradox', Synthese, 87, 3, 40 1 -7. Lunnon, R. (1991), 'Generalized Universes', Ph.D. thesis, University of Manchester. Ogihara, T. (1990), 'The semantics of the progressive and the perfect in English', in H. Kamp (ed.), Tense and Aspect in English, Centre for Cognitive Science, University of Edinburgh, DYANA Report, R2.3.A, 3-38. Parsons, T. (1990), Events in the Semantics of English, MIT Press, Cambridge, MA. Seligman, J. & Barwise, J. (1 993), 'Channel theory: toward a mathematics of imper­ fect information flow', unpublished MS, May 1993· Smith, C. S. ( 1 991), The Parameter of Aspect, Kluwer, Dordrecht. Vendler, Z. (1967), 'Verbs and times', in Linguistics in Philosophy, Cornell Univer­ sity Press, ithaca, NY, 97- 1 2 1 . Vlach, F. ( 1 981), 'The semantics of the progressive', in P. J. Tedeschi & A. E. Zaenen (eds), Syntax and Semantics, Vol. J4: Tense and Aspect, Academic Press, New York.

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Ph.D. thesis, Centre for Cognitive Science, University of Edinburgh. Cavedon, L. ( 1996), 'A channel-theoretic model for conditional logics', m ]. Seligman & D. Westerst:ihl (eds), Logics, Language and Computation, Vol. 1 , CSLI. Cavedon, L. & Glasbey, S. ( 1994), 'Outline for an information-flow model of generics', Acta Linguistica Hungarica, 42, 3/4. Cooper, R. ( 1985). 'Aspectual classes in situation semantics', Report CSLI-841 4C, Center for the Study of Language and Information, Stanford, CA. Cooper, R. ( 1993), 'Generalized quantifiers and resource situations', in P. Aczel, D. Israel, Y. Katagiri, & S. Peters (eds), Situation Theory and Its Applications, Vol. J, Center for the Study of Language and Information, Stanford, CA. Dowry, D. (1979), Word Meaning and Mon­ tague Grammar, D. Reidel, Dordrecht. Glasbey, S. (1994a), 'Progressives, events and states', in P. Dekker & M. Stokhof (eds), Proceedings of the Ninth Amsterdam Collo­ quium, ILLC/Deparcment of Philosophy, University of Amsterdam. Glasbey, S. (1994b), Event Structure in Natural Language Discourse, Ph.D. thesis, Centre for Cognitive Science, University of Edinburgh. Glasbey, S. (1996), 'Towards a channel­ theoretic account of the progressive', in J. Seligman & D. Westerstihl (eds), Logic, Language and Computation, Vol. 1, CSLI. Hinrichs, E. (1983). 'The semantics of the English progressive: a study in Situation

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Directionality in Discourse: Prominence Differences

m

Subordination Relations 1

JAN VAN KUPPEVELT University of Amsterdam Abstract

I I NT R O D U C T I O N I f one is confronted with the task o f structuring an extended answer to a question, there are, in principle, three options: first, operating towards the 'goal' of the question implying the so-called goal-subservient part to precede the part providing the goal-satisfying value; second, acting inversely, by firstly specifying that which is ultimately asked for and then elaborating on it for supportive reasons, e.g. providing a justification of the answer value given; and third, acting as it were in both directions, implying that the discourse units comprising the extended answer are mutually subservient in satisfying the goal of the question.2 However, it is generally assumed (especially Allen I983; Allen & Perrault I98o; Grosz & Sidner 1986; Litman I985; Mann & Thompson I988; Moore & Pollack I992; Pollack 1986; Wilensky I 983) that these options apply not only to the structure of complex answers to explicit questions but also to the structure of extended discourse in general.

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This paper proposes a new approach to discourse directionality, a phenomenon which, as is well known, is neither well defined nor adequately accounted for. Directionality is the property of (a part o� a discourse to be directed towards a 'goal', usually implying asymmetric functional relations between the discourse units involved. The direction of such an asymmetric discourse relation depends on whether the unit that provides the goal­ satisfying value precedes or follows the unit which is subservient to it. Fundamental to our proposal is an analysis of directionality in terms of the topic-comment distinction. Within this framework, directionality is defined as a recursive property assigned to higher-order and lower-order discourse relations central to which is the assumption that they are realized by explicit or implicit topic-forming questions. It will be shown that the distinction that can be made between three types of directionality is precisely a function of three different ways of quantitative/qualitative subordination realized by subquestioning. Apart from the resulting theory providing a solution to the definition problem, it also provides an answer to the determination problem which implies that we attribute a criterion to distinguish dominant discourse units from subservient ones. In addition, the theory contributes to the much discussed issue of an adequate formalization of those discourse elaboration processes that do not involve a new partial value but merely support an already introduced 'subject matter'.

364 Directionality in Discourse

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The phenomenon under discussion is that of discourse directionality, a phenomenon that is central in, in particular, the rhetorical and intentional approaches of discourse structure.3 Directionality refers to the property of (a part ofj a text to be directed towards a 'goal' or 'point', usually resulting in asymmetric functional relations between discourse segments. This asymmetry implies a division of {that part ofj the text into two related segments, one of which is subservient to the other, with the latter being identical to the part providing the goal-satisfying value or a part of this value. Various terms are used to refer to the phenomenon of directionality. A frequently used term is nuclearity in Rhetorical Structure Theory (RST; e.g. Mann & Thompson 1 988). In RST, nuclearity is considered to be 'a central organizing principle of text structure' ( 1988: 267), referring to a functional distinction applicable to rhetorical relations between discourse units ('spans'), namely that one of them, the nucleus, is functionally dominant while the other related unit, the satellite, is subservient. It is assumed that in most cases a functional asymmetry such as this is present in, e.g., 'If A is evidence for B, then B is not evidence for A' (1988: 266). Another term commonly used in the intentional approaches of discourse structure is the term dominance (Grosz & Sidner 1986). The term refers to one of the characteristics of intentional relations between discourse segments, namely that if one discourse segment purpose DSP 1 dominates another discourse segment purpose DSP2 , DSP2 contributes to DSP 1 (1 986: 1 79). As made clear in Moser & Moore (1993), dominance relations such as these correspond to the direction of intentional relations in RST, i.e. 'the satellite span, S, affects the purpose of the nucleus span, N, only if the intention that S realizes is dominated by the intention that S and N (and possibly others) realize together' ( I 993: 95).4 However, in spite of the central role of directionality in theories of discourse structure, we are nevertheless confronted with both a definition and a determination problem. The former is probably the most serious one and implies the absence of a fully adequate formal definition. For instance, RST, in which the notion of directionality is most central, does not provide so much a definition as a taxonomy of characteristic properties of this notion. The characterizations given are, among others, that the dominant discourse unit, the nucleus, is 'more essential to the writer's purpose', is 'more central', is 'more deserving of response, including attention, deliberation and reaction'. Although many of these characterizations present relevant descriptions of the phenomenon, they do not show the kind of phenom­ enon with which we are precisely dealing. In particular, they lack a full explanation of why the non-dominant part, the satellite, may be deleted while preserving the coherence and intention of the text. In addition, they

Jan van Kuppevelt

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leave unexplained why the dominant part is functionally more prominent, i.e. more deserving of attention, deliberation, and reaction than the functionally less prominent part. Obviously, if a definition is to be considered adequate, it must provide satisfactory answers to these ques­ tions.5 Closely related to the definition problem is the task of determining the relevant factor stating which of two related discourse units is functionally dominant. It is generally assumed that in the case of functional asymmetric discourse relations the order of dominant and non-dominant discourse units is not directly influenced by the discourse relation between them. The literature also fails to provide an adequate solution to this problem. In addition to the definition problem and the determination problem, one more issue, though a less central one, has to be mentioned, namel'· ,ne formalization of non-dominant, supportive discourse units. Usually a con< :Jerable part of discourse consists of justifications, motivations, etc. which in themselves do not introduce a 'subject matter' or 'independent value', but have a supportive function with respect to the dominant discourse parts which provide such a value. How can the effect of this supportive material be formalized in terms of, e.g., set theory, if the function of this material is merely a secondary, not providing independent values as such? We will propose an account of directionality which provides an adequate definition of the phenomenon including a corresponding criterion for identifying functionally dominant and non-dominant discourse units. In addition, the proposal provides the formalization referred to above. Essential to the proposal is an account of directionality in terms of the topic-comment distinction which, by definition, applies, in a uniform way, to individual utterances and larger discourse units. It is demonstrated how the phenomenon of directionality is determined by the discourse-internal topic-comment structure. Fundamental to the proposal is the underlying hypothesis that the topic­ comment structure of discourse results from the process of answering higher-order and lower-order explicit and implicit questions in discourse. This necessarily implies a distinction between the main structure of discourse and its embedded, lower-order subordinate structures. As we will see, the former is analysed as an answer to a (set o� leading higher­ order, topic-forming question(s) defining the global discourse topic, while the latter results from subquestions. By definition, substructures are hierarchically embedded in the main structure of discourse because of the specific completion function of the associated subquestions, namely to contribute to the unsatisfactory answer given to the overall, discourse-topic defining question.6

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in

Discourse

2

TH REE TYPES O F D I RE C T I O NALITY 2.I

Description of the phenomenon

In the introduction we have informally characterized the phenomenon of discourse directionality as the property of a (part of a) text to be directed towards a 'goal'. Usually this implies a division of this (part of the) text into two related segments, one of which is functionally less prominent. In the intentional approaches of discourse, this so-called non-dominant discourse unit is analysed as that part of the relation which is subservient to the discourse purpose associated with both discourse units, leaving unspecified the exact (intentional) status of the related dominant discourse unit. In this paper a distinction is made between the following three types of directionality: Forward (FW) Directionality, Backward (BW} Directionality, and Bi-Directionality. We will demonstrate (Section 4) the specific way in which these types correspond to three different types of subordination relations in discourse. In all cases of directionality the phenomenon applies to a succession of two related discourse units. We present the following description: FW Directionality,

BW Directionality, and Bi-Directionality Given two related discourse units U; and U;•n• the discourse relation R between them, R(Uh U;.0), is characterized by FW Directionality if U; is subservient to the succeeding discourse unit U;•n• i.e. the discourse unit that (in a sense which has to be explicated) provides the goal-satisfying value in this case, by BW Directionality if the reverse applies, and by Hi-Directionality if such a functional asymmetry is absent.

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Directionality is then characterized as a property assigned to a discourse relation between two discourse units. According to the framework this relation is realized by an explicit or implicit topic-forming question. It will be demonstrated that dominant discourse units providing goal-satisfying values are not determined by such a question but rather by the higher-order question defining the common topic of both the dominant and the related non-dominant discourse unit.7 In Section 2, we briefly illustrate the different types of directionality that can be distinguished, and include an illustration of the fact that these types may occur on different structural levels, corresponding to the discourse­ internal topic-comment structure. In Section 3, an account is given of this mostly hierarchical structure which, as indicated above, results from the process of the contextual induction of explicit and implicit topic-forming questions. Finally, Section 4 demonstrates how the different types of directionality are determined by this topic-comment structure.

Jan van Kuppevelt 367

(r)

At this telephone company we assume you enjoy a good natter. (Q 1 ) (What do you mean?) A 1 [ ] we've come up with an offer to make your ears prick up. FW (Q2) (What does this offer imply?) A2 It means that with this company, you can now phone all your family and friends in the UK for only 30 cents a minute, 24 hours on Saturday and on Sunday. No matter how fast they multiply in number. (The Guardian, r o April 1994, p. 9t •

•

•

FW Directionality holds for the discourse relatiun between the discourse units functioning as the answers A 1 and A2 • Answer A1 has given rise to the implicit question (Q2 ) that is answered by A2• The latter is more specific than the former. In Section 4 we illustrate that the more specific A2 is the dominant discourse unit that sufficiently satisfies the goal of the leading implicit question (Q 1 ) to which A1 and A2 together form an extended answer. In Section 3 we give an account of subordination relations such as that between the leading implicit question (Q 1 ) and the subordinate question (Q2 ). The latter is a subquestion embedded in the extended answer given to the former. Example (2) illustrates the phenomenon of BW Directionality.

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The absence of asymmetric functional relations in case of Hi-Directionality implies that the related discourse units U; and U;+n are equally prominent and that together they contribute to the goal of the text segment which comprises the two of them.8•9 One of the central hypotheses of the framework to be presented is that in this context every discourse relation R(U;, Ui+n) is determined by an explicit or implicit question introducing the topic of the (extended) discourse unit answering this question. By definition, such a topic-forming question is induced as the result of the discourse unit U; and is answered by the succeeding discourse unit Ui+n· In anticipation of a further explication of this hypothesis, we will illustrate the different types of directionality in terms of discourse relations realized by such questions. An illustration of FW Directionality is given in ( r ) , Two implicit questions are added to the original text, providing an analysis of the structure of this text in terms of questions and answers. Angled brackets indicate the implicit character of a question; arrows indicate the direction of a discourse relation. 1 0

368 Directionality in Discourse

(2) (Q 1 ) (Which countries have bad records with respect to

air safety?) China, India, Central Africa and the republics of the former Soviet Union [. . .] are the world's most dangerous locales for air travel [. . .] (Q2 ) (Why?) BW A2 These countries are especially plagued by hazards such as undertrained pilots, poor air-traffic-control systems, inadequately maintained aircraft, lax airport security and political unrest. (Time Magazine, I I April I 994, p. 4) A1

Questions about the effectiveness of therapy cloud decisions about treating the illness. (What are the problems?) BW Older patients, if left untreated for small tumors, may die of other causes. + (What else?) FW [. . .] many men-young and old-face impotence and incontinence as the result of the therapy. (Scientific American, April I994, p. 2) In line with the preceding two cases, the extended answer to the implicit question (Q 1 ) consists of the answers A1 and A2 • However, in this example A1 and A2 together provide the requested goal-satisfying value. They constitute the enumeration of problems asked for in the leading question (Q,). Apart from the fact that an account of the questioning process underlying the structural coherence of discourse is needed, a further explanation of the phenomenon of asymmetric discourse relations is also required. As far as the latter is concerned, we will advocate the view that the discourse units involved in asymmetric discourse relations share the same topic, though in agreement with this asymmetry the comment value to this topic is in fact provided by only one of them.

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As in example (I), the implicit question (Q 1 ) is a leading question superordinating the implicit question (Q2 ). However, in this case, it is not A2 but A 1 that is the dominant part of the extended answer to (Q1 ). It satisfies the goal of this question, i.e. what is ultimately being asked for by it: a list of the countries that have bad records with respect to air safety. The answer given in question (Q2 ) merely provides support for this list.12 Finally, example (3) illustrates the phenomenon of Bi-Directionality.

Jan van Kuppevelt 369

Operational criterion It is generally assumed (e.g. Mann & Thompson 1988) that an operational 2.2

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criterion to distinguish a functionally dominant discourse unit from a related non-dominant unit is that the latter can be deleted while preserving discourse coherence and discourse intention. Obviously, deletion of such non­ dominant parts may affect, among other things, the cohesion of the text thereby implying specific adjustments in formulation, e.g. the use of definite descriptions instead of a pronoun if the latter anaphorically refers to an entity introduced in the non-dominant part. 1 3 Preserving the coherence of a text implies that the structural relations between the remaining, undeleted discourse units are identical to those before deletion. In terms of the topical approach to be outlined this means that the relations between the (implicit) topic-forming questions answered by these discourse units are the same. Deleting non-subservient discourse units, on the other hand, results in discontinuities in the question-answer structure of the discourse. In the developed topical approach the preservation of discourse intention in case of the deletion of subservient material implies that the higher-order and lower-order discourse purposes associated with the corresponding topic-forming questions are still fulfilled at the end of the discourse, though this deletion is in fact only possible when we assume the presence of relevant background or situational knowledge. This is obvious, for instance, with those discourse units that merely have a supportive function with respect to that which is asserted in the related dominant discourse units. Examples form those subservient discourse units that only provide a j ustification or motivation for the related dominant discourse unit. The essential point is that the production of this supportive material is largely addressee-dependent, i.e. dependent on the addressee's knowledge of background and situation or, in case of implicit questions, the speaker's assumptions about these. Assuming that the answer value provided by the dominant discourse unit is accepted by the addressee, the subservient discourse unit may be omitted. An example of a specific form of deletion is that of answer A1 in (I). A, (and, of course, the implicit question (Q2)) can be omitted while the coherence and intention of the text is preserved. As a general rule, if a given answer is extended by a more specific answer, the former can be deleted because it is implied by the more specific answer. Both discourse intention and coherence in terms of question-answer structure are then preserved. Also, in a question-answer pair such as Who are laughing?-Two women, Ellen and Susan, the indefinite, less specific part of the answer may be deleted this way.

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An illustration of another type is the deletion of answer A2 in example

(z). The non-dominant discourse unit A2 has a supportive function only

2.3

Directionality on different discourse levels

Characteristic for theories of discourse structure in which directionality has a central role is the assumption that this phenomenon occurs on all structural levels. In terms of the topical approach this means that its occurrence ranges from the highest structural level that corresponds to a discourse unit for which a discourse topic is defined to the lowest level of individual utterances containing a sentence topic. 14 On each higher-order discourse level the phenomenon gives rise to the possibility of asymmetric binary relations comprising discourse units of which at least one embeds a lower-order discourse relation. As will be shown (Section 4), it is the dominant, non-deletable part of these lower-level relations that plays a role on the higher structural levels. We will now give illustrations of the three different types of direction­ ality realized at different structural levels in discourse, comprising both the highest structural level and all subordinate lower levels. In these examples the hierarchy of structural levels is (indirectly) represented by the given combination of arrows expressing which type of directionality is realized at which structural level.

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with respect to A 1 which, as long as relevant background knowledge is present, independently satisfies the goal of the leading question Q 1 • Answer A2 only provides a justification of the answer value provided by A 1 • However, in the case of example (3) neither answer A 1 nor answer A2 are deletable. In this case an �symmetric functional discourse relation such as that in the two preceding examples is absent. A 1 as well as A2 are functionally prominent in the sense that they provide an answer value to the leading question Q 1 • Clearly, the deletion of one of them would affect the intention of the text because of the resulting incompleteness of the remammg answer. The operational criterion to distinguish non-dominant from dominant discourse units is also important in another way. It provides an adequate explanation of the phenomenon of summarizing texts, i.e. those text summaries which under the assumption of specific knowledge on the part of the addressee are coherent and satisfy the same intention as the original version of the text. However, also in this case, we need a general characterization of dominant and non-dominant discourse units in order to guarantee adequate summarization.

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(4) (Q 1 ) (Why did the workers of the Philips computer A1 (Q2) A2 (Q3) A3

A1 (Q2) A2 (Q3) A3

j

In (4) a discourse relation determined by FW Directionality is embedded in a higher-order discourse relation of the same directional type. In (s) a relation determined by FW Directionality is embedded in one determined by BW Directionality, and in the narrative presented in (6), a bi-directional

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(s) (Q 1 )

division go on strike?) They are very worried about the managers' new economy plans. (Why?) According to these plans the managers would consider moving the production section abroad. (Why are the workers so worried about this?) This would imply that 300 of all those employed in this division would be dismissed. (Translation of a Dutch text) How can I be sure not to miss anything on BBC World Service? Subscribe to BBC Worldwide [. . .] Why? you'll get the full picture every day of every month of the year. What does this mean? As well as daily radio and TV listings; in-depth programme reviews and of course, the time and frequency details of every World Service broadcast in English, you can tune into feature articles; commentaries; reviews; worldwide reports, profiles and previews. (Scientific American, April I 994, p. I I ) Whatever happened to RJ? Six years ago, she mysteriously disappeared. (Then what happened?) Though the authorities had a suspect, their investigations stalled. (Then what happened?) Two years later her body was found in a North Coast grave. (Then what happened?) Now authorities have a chilling new theory about what might have happened to her. (San Francisco Chronicle, 7 June 1 992)

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higher-order relation embeds two discourse relations of the same direc­ tional type only one of which is directly embedded. Let us first take a closer look at example (s). The higher-order relation determined by BW Directionality is realized by the implicit question (Q2 ). It relates the discourse unit that functions as answer A1 to the remaining discourse which forms an extended answer to the implicit question (Q2 ). The implicit question (Q3), on the other hand, is a subquestion of question (Q2). It relates answers A2 to the more specific answer A3 , thereby constituting a FW directional discourse relation of which it will be shown that only the dominant, non-deletable part actually has a function on the higher discourse level. As stated above, the examples (4) and (6) are different from (s) due to the fact that one or more discourse relations of one directional type are embedded in a relation of the same type. Important to mention with respect to the narrative in {6) is the assumed distinction between event structure and discourse structure. The arrows indicate that though the presentation of the events forming the story line is sequential, the underlying structure of this discourse in terms of questions and answers is hierarchical (see van Kuppevelt 1 995b for more details about the analysis of narrative discourse in terms of questions and answers). 15 In the preceding section we have discussed an operational criterion to distinguish dominant from non-dominant discourse units. Our analysis of this distinction will make clear that applying this criterion to different structural levels implies a specific computation of non-deletable values provided by dominant discourse units: the output of a deletion operation executed on a lower discourse level is taken as input for such an operation carried out on a higher structural level. The computation of these values implies that non-deletable values on a lower level may function as deletable ones on a higher level. An illustration of this is the value provided by answer A 3 in example (s). After deletion of the non-dominant discourse unit A2, this value is taken as input for the computation associated with the deletion process carried out on the higher level which comprises the whole text (part). However, on the higher level the value provided by A2 is a subservient one. As a final result we predict that in {s) all discourse units can be deleted except answer A 1 the value of which satisfies the goal of the leading implicit question (Q 1 ).

Jan van Kuppevelt 3

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THE D I S C O U RSE - I NTERNAL TOPI C - C O M M E NT S T R U CTURE

3- 1 3- 1 . 1

The

Topicality and underdeterminedness

uniform topic notion

The developed topical approach of discourse structure starts from a context-dependent, question-based topic-comment notion that accounts for the topics of sentences and those of larger discourse units in a uniform way, including those comprising the discourse as a whole. We gave the following topic-comment definition: Definition Every contextually induced explicit or implicit (sub)question QP that is answered in discourse constitutes a (sub)topic Tp· TP is that which is being questioned. Comment CP

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We will now provide an account of the phenomenon of directionality in terms of the topic-comment distinction, thereby implying a solution to both the definition and determination problem discussed above. Before starting the analysis, we will present an outline of the developed theory of discourse structure in which this distinction is central (van Kuppevelt 1 99 1 , 1995a, and other publications). We have described directionality as the property of a higher-order or lower-order discourse relation between two discourse units, which expresses a functional asymmetry between them. In the theory of discourse structure we have developed, the hypothesis is central that the structural relations in discourse are essentially determined by the discourse-internal, mostly hierarchical topic-comment structure. It has been demonstrated that the segmentation structure of discourse corresponds to this topic-comment structure and, in particular, that this structure is the fundamental output of the process of the contextual induction of explicit and implicit topic­ forming questions. 1 6 In this section we present an outline of this essentially topical approach of discourse structure. In the succeeding Section 4 it will be shown how directionality applies to discourse structure, in particular to the discourse relations which are assumed to be primarily of a topical rather than a rhetorical or intentional nature. 17 Apart from the fact that topics are fundamental to the direction of the discourse relations, they also have another special function with respect to this phenomenon, namely, as will be argued in detail, that the nature of the direction, be it FW Directionality, BW Directionality, or Bi-Direction­ ality, is not determined by the topic of the discourse relation involved but by the higher-order topic superimposing it.

374

Directionality in Discourse

given by answer AP provides that which is asked for. If (the speaker assumes) A is fs satisfactory to the addressee, TP is closed off If not, AP gives rise to subquestioning. 8

(7) a. Q r: Who (is the one who) has been arrested? b. Ar: TP[The one who has been arrested] is cPUOHN] It is cPUOHN] TP[who has been arrested] cPUOHN] TP[(is the one who) has been arrested] 2 TP UOHN] 0 . (7)' a. Q.': The x [x has been arrested] by WH? b. A/: The x [x has been arrested] be JOHN. In (7a)' the topic of question Qr is expressed by the subject term The x {x has been arrested], to be read as 'The one who has been arrested'. As shown in (7b)', all answers of (7b) are assigned the same syntactic analysis A/. A/ is derived from the analysis of the question by replacing the WH-constituent by the proper answer to the question. 21 In semantic terms, a topic T P is the intension of the subject or topic term in the syntactic analysis of the corresponding question Qp. It is the contextually provided set of possible extensional values of this term which, in line with the analysis of Q p, is identical to the set of possible answers (comments).22 The related comment CP, on the other hand, is identical to that which is asked for by Qp , namely the actual extension Tp(Sa ct) of this topic term or, more generally, the extension of this term in the verification domain with which the discourse is compared. 23 "24 The topic set T P thus contains possible extensions of the type meeting the description of the topic term in the question. T P is contextually provided, implying that its elements are textually given or evoked. However, in many cases, knowledge of this set only consists of a characterization rather than an enumeration of its elements. In (7)" we give an illustration of topic set T., assuming that the introducing question Qr has arisen in a context in which someone has

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Clearly, the definition merely provides a global characterization of the notions topic and comment and requires further explanation. An explica­ tion will be given by accounting for both the syntactic and semantic status of this pair. 19 Later, in particular in Section 3.2.3, we will discuss the notion of satisfactory answer. Syntactically, a topic is analysed as expressed by the subject term in the grammatical analysis of both the question and the answer that is derived from it. A comment, on the other hand, is analysed as the constituent in the answer that has replaced the WH-constituent in the question. As an illustration see question Qr in (7a) and its grammatical analysis in (7a)'.

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actually been arrested and that this context only contains the relevant set of persons D = Oohn, Peter}.

(8) QP: Tp(Sact) WH? AP: TP(Sact) = Cp AP, forming the full answer to QP, contains the proper answer to this question. It selects a possible value from the topic set TP as the extension of the topic term in the actual situation. In the semantic analysis topics are thus not identified with questions, avoiding problems comparable to those signalled by Kartunnen (1 977), Tichy ( I 978), and others. A topic is the contextually provided set of possible values of the subject term in the syntactic analysis of the question. As will be argued in the next section, this term represents the indeterminacy that has given rise to the corresponding question. A question, on the other hand, is a request for the extension of this term in the actual situation. Identifying topics with questions would give rise to the following problems. First, it would disregard the fact that a topic is just a part of a questioning process. Asking a question involves both a topic set and an act of questioning, though the latter is not defined as a general request with respect to the set of possible values comprising the topic set but rather as a request for the specific value to be selected of this set. Second, the identification would imply the contextually undesirable result that a question like Has John been arrested? and its comparable negative version Has john not been arrested? are the same, because the related topic sets are identical and consist of the values that John has and that he has not been arrested?6 Important to note is that this semantic analysis of topic and comment explicates the relation it assumes between the two conceptually different notions of focus used in the literature, namely what is called Aljocus and linguistic or informationalfocus. 27 The latter type concerns the informationally prominent sentence part that is usually intonationally marked and that represents contextually new information (Sgall, Hajicova, & Bendova 1 973; =

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(7)" T, = {(S 1 , Oohn}), (�, {Peter}), (S3 , Oohn, Peter})} Topic T, contains the extensions of the subject term 'The one who has been arrested' in all possible situations Si. Comment C, on the other hand, is that which is asked for by question Q., namely the extension of this term in the actual situation (T,(Sacc) ).25 Important to note is that at the moment of questioning this extension is underdetermined in the discourse, implying that the extension of this term is not yet (exactly) known by all the discourse participants. Given this semantic analysis of topic and comment, question-answer pairs are represented accordingly.

376 Directionality in Discourse

3· 1 .2 Underdeterminedness

It is assumed that the underdeterminedness of the actual extension Tp(Sact) of the topic term of a question is a necessary condition for topichood. Questions are induced as the result of contextuality provided indetermi­ nacies which, as we have seen in the preceding subsection, are expressed by the subject or topic term in the syntactic analysis of the topic-forming question. The condition for topichood implies that there is more than one entity in the world (or verification domain) talked about that meets the

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Halliday 1 967; Kuno 1 972). The former type is assumed to be of quite a different nature and is closely related to the notion focus of attention commonly used in artificial intelligence (e.g. Grosz 1 978; Grosz & Sidner 1 986; Reichman 1978; and Sidner 1 979).28 Contrary to linguistic focus, it does not express informational prominence on the sentence level but rather referential prominence on the level of discourse. Among other things, this implies that only some of the entities introduced in the discourse are in focus of attention and, as a consequence, allow anaphoric reference. As demonstrated by these authors, the set of discourse entities in focus of attention is a variable set the content of which changes in accordance with the structure of discourse. In our framework, on the other hand, both focus notions are captured by the definition and semantic analysis of topic and comment. According to this analysis, the linguistic focus is expressed by the comment of a sentence, while the set of entities in focus of attention comprises the topic set the content of which changes radically depending on the structure of discourse. As said above, central to our framework is that discourse structure corresponds to topic structure, implying that a radical shift in topic results in the construction of a higher-level discourse segment. Finally, the analysis of topic and comment directly gives rise to the much requested account of the relation between topics of sentences and larger discourse units on the one hand, and discourse intentions underlying these segments on the other. In the topical approach we have developed this relation becomes fully explicit. 29 In this approach a discourse intention is characterized in terms of topic-forming questions, namely as the requested final comment value in respect of the topic defined by the question. One of the main advantages of this approach is that the discourse intentions associated with discourse segments can considered to be directly linguis­ tically marked, e.g. by accent distribution. This because of . the existing direct relation between the linguistic form of answers and the questions asked. As will be outlined later, discourse segments of all structural levels are considered to be answers to topic-forming questions.

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description of the topic term in the question and that may function as the extension of that term in the actual situation. Though the extension of this term is defined in the world, it is underdetermined in the discourse at the moment of questioning. At that point in the development of the discourse (exact) knowledge of the extensional value does not belong to the knowledge domain shared by speaker and addressees. All that is known is that the requested extension is identical to one of the possible extensions. The underdeterminedness of Tp(Sact) is thus expressed by its relation to the original or remaining set of possible extensions Tp(Si)·

=

(7)'" a. Tr(Sacc)

E

{{John}, {Peter}, {John, Peter}}

A full reduction of this underdeterminedness is realized by a satisfactory answer to question Q" as the result of which Tr(Sacc) becomes identical to one of the possible extensions. b. Tr(Sacc)

E

{{John}}

(ig'(Tr)l = 1 )

(7b)" ' shows that, in agreement with the principle of topic termination Section p.J), the necessary condition for topichood is no longer met and, as a consequence, Tr is closed of£ Relevant with respect to the underdeterminedness of Tp(Sact) is the related notion of discourse informativeness. In the framework it is presupposed that this notion is determined by answers. In the process of answering an explicit or implicit higher-order or lower-order topic-forming question an increase of informativeness results from a reduction of the underdetermin­ edness of the topic extension, implying a reduction of the original topic range �(Tp) or a further reduction of the already reduced actual topic range

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In (9) the variable set �' (Tp) is the actual topic range of TP' in this case consisting of the remaining possible extensions of the topic term, thus making it a subset of the original topic range �(Tp)· As will be explicated later, �(Tp) is reduced to �'(Tp) if an (un)satisfactory answer to the topic­ introducing question QP has resulted in the exclusion of possible extensions. As long as I�'(Tp) l > 1, the actual topic extension Tp(Sact) is under­ determined.30 Underdeterminedness only holds if �'(Tp) does not contain a unique extensional value, implying, as will be discussed further in Section p.J, that the corresponding question Qp has not yet been answered satisfactorily and will therefore give rise to subquestioning. As for the question in example (7), (7)" ' illustrates the underdetermined­ ness of Tr(S.c,) at the moment of questioning. We start from the same assumptions, including that the contextual domain D Uohn, Peter}.

378 Directionality in Discourse

�'(Tp)· Reduction of a topic range results from an (unsatisfactory) answer thereby implying the exclusion of possible extensions. J.2 J 2. I

Hierarchical topic processes

Feeders and main topic-forming questions

Definition A discourse topic DT; is the set of main, higher-order topics TP which have come into being as the result of one and the same feeder F;: DT; {TP I TP originating from F;}. =

In a coherent discourse a feeder Fi gives rise to the topic of the whole discourse which usually comprises lower-order topics. If only one topic arises out of a given feeder, the topic and discourse topic coincide ({Tp}:= Tp)· Example (ro) illustrates the contextual induction of i single topic­ constituting question as the result of a feeder. The questioning process initiated by this feeder is a simple, non-hierarchical one, involving an immediate (non-stage like) determination of a requested actual topic extension (F {x I friend(x,Harry)} = Uohn, Peter, William}). =

( 1 o) a. F 1 A: Late yesterday evening two friends of Harry called. Q 1 B: Which two friends? A 1 A: Peter and William.

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The process of explicit and implicit questioning which gives rise to a hierarchical topic-comment and corresponding segmentation structure of discourse involves the contextual induction of two functionally different types of questions, namely main, higher-order topic-constituting questions and subtopic-constituting subquestions. By definition, topic-constituting questions are contextually induced as the result of a linguistic nor non-linguistic feeder Fi. If Fi is linguistic, its function is to initiate or re-initiate the process of questioning in discourse. This process must be initiated when the context is empty, or when no more questions are induced by the preceding context and the discourse participants wish to continue the conversation. A linguistic feeder may be a single sentence, e.g. the opening sentence of a discourse, or it may be a larger discourse unit. Together with associated background knowledge, a feeder Fi supplies a set of actual indeterminacies the inducing power of which is contextually 1 unrestricted by preceding questions in the discourse.3 Therefore, Fi provides the means to open a discourse and to initiate a discourse topic DTi. The indeterminacies it provides give rise to a set of main, topic­ constituting questions that together constitute DTi.

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b. Q 1 : Which two friends? T I (Sw) E {X J X � f 1\ JXJ 2}. E {Uohn, Peter}, {Peter, William}, Oohn, William}} A1: Peter and William. T I (Sw) = {Peter, William}!32 =

3-2.2 Subtopic-forming questions

A programmatically bound, stage-like development of the discourse necessarily involves the contextual induction of subquestions. Subquestions introduce a topic which is subordinate to a preceding one introduced by a higher-order question. Contrary to topic-constituting questions, subques­ tions do not have an autonomous status in the process of questioning, but are subservient to the program imposed on the discourse by a leading topic­ constituting question. By definition, subtopic-constituting subquestions are contextually induced, in a recursive way, as the result of unsatisfactory answers and have the purpose of completing these to satisfactory answers. If a topic­ constituting question has been answered unsatisfactorily and, naturally, if no disturbance of the questioning process occurs, this unsatisfactoriness gives rise to subquestions until the original main topic-constituting question has been answered satisfactorily. Consider example ( I I ), an advertisement, in which the entirely linear

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As shown in (1 0b), the topic-constituting question Q1 introduces an, initially, underdetermined actual topic extension T 1 (Sact)· The determina­ tion of this extension is realized in a single step as the result of answer A 1 • That determination processes like that i n (10) are not always realized in one step is due to, among other things, the program associated with a main question. A program is associated with every explicit or implicit topic­ constituting question Qp, controlling the development of coherent dis­ course. It consists in the specific task, to be carried out by the speaker, of providing an answer to Q P which is satisfactory for the addressee. As is argued in Section 3.2.3, a satisfactory answer to QP implies unique determination of the requested actual topic extension Tp(Sact)· Main, topic-constituting questions are therefore considered to be responsible for a programmatically-bound development of the discourse. However, as indicated above, the program associated with a main question Qp may not be accomplished in a single step. It is a standard procedure that such a program is realized in stages, in which case it may comprise all or a considerable part of the utterances belonging to the main structure of the discourse.33

380 Directionality in Discourse

embedding of subquestions forms a clear illustration of the recurs1ve property of questions of this type.

(I I) Fl (QI) AI (Q2) A2

.

The implicit question (Q1) functions as topic-constituting question. All other implicit questions form subquestions linearly embedded under (Q1). Each of these subquestions is induced as the result of the unsatisfactory answer given to a directly preceding one. Subquestions thus fulfil a completion function in the program associated with a preceding topic-constituting question. We have given the following description in terms of topic underdeterminedness. Completion Junction of subquestions Given a leading topic-constituting question QP' the completion function of subquestions consists in a further reduction of the underdeterminedness of the extension Tp(Sact) in the discourse.

In the next two subsections we will briefly elaborate on the completion function of subquestions, making a distinction between quantitative and qualitative underdeterminedness. 3.2.2.1

Quantitative underdeterminedness Subquestions are contextually induced as the result of unsatisfactory answers. However, this induction is caused by a quantitative or qualitative unsatisfactoriness, implying a quantitative or qualitative underdetermined­ ness of the main topic extension. The former type will be illustrated in this subsection, the latter in the next one. A subquestion Qp may be contextually induced as the result of a preceding unsatisfactory answer Ap-n because of the quantitative under­ determinedness of Tp-n(Sa ct) implied by this answer. This quantitative

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(Q3) A3 (Q4) A4

For more than a century and a half, *** has been known as the finest watch in the world. [. . .] (What is the reason for this?) It is made differently. (In what way?) It is made using skills and techniques that others have lost or forgotten. (What kind of skills and techniques?) It is made, we have to admit, with a total disregard for time. (What do you mean?) If a particular *** movement requires four years of con­ tinuous work to bring to absolute perfect, we will take four years. [ . .] (Time Magazine, I I April I 994)

Jan van Kuppevelt 381

underdeterminedness presupposes that the comment value provided by

Ap-n is incomplete.

An illustration of the contextual induction of a subquestion as the result of a quantitatively unsatisfactory answer is given in ( 1 2) . In ( 1 2) question Q2 functions as a subquestion asked as the result of the unsatisfactory answer A1 (C {x I colleague(x, speaker A)} = {Michael, John, Brian, Susan}). =

Because of the occurrence of subquestion Q 2 , the determination of the actual main topic extension T1 (S.c,) is now realized in two stages. Initially, the unsatisfactory answer A1 reduces the original underdeterminedness of T 1 (S.c,) to those possible extensions which include the incomplete value Michael. Subsequently, answer A2 reduces the set of remaining possible extensions to one unique value, implying the determination of T1(S.c,)· After an answer has been given to subquestion Q2 , both topic T1 and subtopic T2 are closed of£ Subquestion Q 2 introduces its own subordinate topic, while continuing the main topic. 3.2.2.2

Qualitative underdeterminedness

If a subquestion Qp is induced as the result of a qualitative under­ determinedness, this means that the comment value provided by the

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( 1 2) a. F t A: Tomorrow I will go to the movies with some of my colleagues. Q l B: Which of them? A t A: Unfortunately Michael. Q 2 B: Who else? A2 A: John and Susan. b. Q 1 : Which of them? T t (S.c,) E {X I X � C 1\ lXI > 1 } A 1 : Unfortunately Michael. T1(S.c,) E {Tt(S;) E Q(T1) I {Michael} � Tt(S;)} E {{Michael, John}, {Michael, Susan}, {Michael, Brian}, {Michael, John, Brian}, {Michael, Brian, Susan}, {Michael, John, Susan}, {Michael, John, Brian, SusanW4 Q 2 : Who else? T2(S.c,) E {X I X � (C - {Michael}) 1\ lXI � I }) E {Uohn,}, {Susan}, {Brian}, Oohn, Brian}, {Brian, Susan}, Uohn, Susan}, Oohn, Brian, Susan}} A2 : John and Susan. T2(S.c,) = Oohn, Susan}! T1(S.c,) = {Michael, John, Susan}!

382 Directionality in Discourse

preceding unsatisfactory answer �-n is either not specific enough, or, as will be explained later, not yet accepted by the addressee. An illustration of the former is given by a variant of ( 1 2) given in ( 1 2)' . ( 1 2)' a.

Fl

Ql AI Q2 A2 b. Q 1 :

=

Q2: A2:

In this case, answer A 1 is unsatisfactory, not because it is incomplete but because it is not sufficiently specific. As in the preceding example ( 1 2) the determination of the actual topic extension T1(Sacc) is realized in two stages by means of a subquestion. 3-2-3

Topic termination by unique determination

In general, if no disturbance occurs, a process of subquestioning comes to an end once the program associated with the related topic-constituting question QP is fulfilled. Program fulfi l ment means that Qp has been answered satisfactorily, implying the unique determination of the actual topic extension Tp(Sact)· The principle of topic termination has been defined accordingly. Topic termination Once the actual topic extension Tp(Sact) is no longer underdetermined, i.e. when possibly after a process of stage-like reduction the condition is met that Tp(Sact) = CP, the topic set TP is no longer subject of questioning, which means that this topic and the introducing question are closed off If Tp(Sacc) = CP, I!J'(Tp) l = r thereby implying the unique determination in discourse of the extension of the indeterminacy that has given rise to the corresponding question QP.

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A1 :

A: Tomorrow I will go to the movies with some of my colleagues. B: Which of them? A: Two colleagues of my own department. B: Which two? A: Michael and Susan. Which of them? T I (Sacr) E {X I X � C 1\ lXI > r } Two colleagues of my own department. T I (S.ct) E {T I (Si) E �(T I ) I Tl (Si) � D (\ I T I (S i)l 2} E {{Michael, Brian}, {Michael, Susan}, {Brian, SusanW5 Which two? TiS act) E {X I X � D 1\ lXI = 2} E {{Michael, Brian}, {Michael, Susan}, {Brian, Susan}} Michael and Susan. T2(S.cr) = {Michael, Susan}! T 1 (S.cr) = {Michael, Susan}!

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=

4

D I RE C T I O N A L I T Y A N D THE T O P I C - C O M M E N T D I ST I N C T I O N

In the preceding section we presented an outline of the developed topical approach of discourse structure, fundamental to which is the relation it assumes between the notion of topic and that of (implicit) questioning in discourse. In non-procedural terms this relationship implies the following: first, the topic of a discourse unit is defined by the explicit or implicit question it answers, and, second, the hierarchical organization of discourse segments is determined by the relations between these topic-providing questions. However, as has been illustrated, discourse structure was also dynamically characterized. By definition, main topics are contextually induced as the result of so-called linguistic or non-linguistic feeders, while the contextual induction of subordinate topics results from unsa­ tisfactory answers, i.e. those which have not yet fulfilled that which is asked for by the corresponding question. Whereas the constitution of topics

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The principle of topic termination accounts for the standard cases in which topic closure is not the result of a disturbance of the questioning process, due to, e.g., a disruption or an epistemic limitation on the part of the answerer, i.e. if he does not know a satisfactory answer to the leading question. The satisfactoriness of an (extended) answer is linguistically marked by phenomena which many researchers have exclusively related to topic closure and segment closure. For instance, as far as the intonational aspects are concerned, Brown, Currie, & Kenworthy (1 980) observe that topic intro­ duction is marked by loudness and high pitch, while topic closure is marked by a relatively low pitch, by fading away in amplitude and by duration. In addition, many people have demonstrated that topic shifts on structurally different levels are intonationally marked by gradual differences in pitch accent.36 The state of unique determination is not always reached directly as the result of the (extended) answer given. It may be inferred from an apparently unsatisfactory answer. Obviously, this is only possible in the context of existing background or situational knowledge. However, other configura­ cp are also possible (van Kuppevelt I 996a, tions in which Tp(Sact) forthcoming), namely those involving topic-narrowing and topic-weakening processes, implying a qualitative or quantitative reduction of a subtopic range as the result of the discourse purpose associated with a higher-order topic-forming question.

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results from the process of questioning, it is also recognized as a standard procedure of topic termination that topic closure results from the satisfactoriness of answers given. The question-based topic notion has been uniformly characterized, comprising both the notion of sentence topic and that of larger discourse units. In this section we give an account of the phenomenon of directionality in terms of the topical approach just outlined. As stated above, directionality refers to the property of the functional asymmetry of discourse relations. It implies that, given a discourse relation between the two succeeding discourse units ui and ui+n• either ui or ui+n is the functionally prominent unit, or both are equally prominent. If Ui is the functionally prominent discourse unit, we speak of BW Directionality, and, inversely, if Ui+n is functionally prominent we refer to FW Directionality. In case of Bi­ Directionality both units are functionally prominent and, consequently, no functional asymmetry is defined for the relation between ui and ui+n· As for the phenomenon of directionality, we signalled two main problems, namely a definition problem and a related determination problem. In addition, we have referred to the issue of formalizing discourse units the function of which is not to provide an independent value but rather to support an already given value. The definition problem deals with the difficulty of adequately characterizing the kind of phenomenon we are dealing with, in particular the lack of an adequate explanation of the recognized differences in functional prominence. Rhetorical Structure Theory (Mann & Thompson 1 988), though it provides a valuable taxonomy, does not provide a definition of this phenomenon; nor does it explain why in the case of two related discourse units one unit is functionally more prominent than the other. The intentional approaches, on the other hand, do provide a definition. However, as said above, in these approaches directionality is defined in terms of a subsurvience relation between the discourse purpose associated with the non-dominant discourse unit and that associated with both the non­ dominant and related dominant discourse unit jointly. Due to this, neither the exact intentional status of dominant discourse units nor the typical relations that may exist between subservient discourse units and related dominant ones are made explicit. In relation to the phenomenon of directionality, the topical framework outlined above is relevant in two specific ways. First, it provides a topical account of the discourse relations R(Ui> Ui+n) to which this phenomenon applies. Fundamental is the view that R(Ui> Ui+n) is realized by an explicit or implicit topic-forming question. This takes place in the following way: ui gives rise to a topic- or subtopic-forming question Qi+n to which ui+n forms an (extended) answer. As can be seen from above, the discourse units

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ui and ui+n may comprise discourse parts larger than a single utterance, in

·

Directionality in discourse On every structural level in discourse the phenomenon of directionality applies to two related discourse units U; and Ui+n one of which is functionally dominant, except in the case of Bi-Directionality when both are functionally dominant. functional dominance is assigned to that unit which provides (a part oD the final comment value to the topic defined by the higher-order (sub)topic-forming (sub)question Q; to which U; and U;+n together form an extended answer, implying the subordinate status of the embedded question Q;•n·

Together with the topical approach outlined above, the definition makes fully explicit the functional status of dominant and related subservient discourse units in terms of the topic-comment distinction. In addition, it gives rise to an explanation of the implied asymmetric functional relation between them, including the distinction we have made between the three types of directionality. In contrast to subservient discourse units, functionally dominant units directly contribute to the higher-order topic-forming question to which both units jointly form an extended answer. By definition, they provide the requested final comment value to the topic defined by this question. Subservient discourse units, on the other hand, do not provide a definite value with respect to this higher-order question. Their contribution to this question is merely indirect, implying that their comment value is subservient to that provided by the functionally dominant unit. For instance, as will be discussed later, in case of BW Directionality the comment value provided by the non-dominant unit provides support for the definite, but not yet fully accepted comment value provided by the related dominant unit. The definition forms the basis of an explanation of the different types of directionality in terms of the topic-comment distinction. Directionality is

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which case they embed lower-order discourse relations for which the property of directionality is also defined. Second, as we will now go on to explain, the framework provides a topical account of the central notion of directionality. A discourse not only derives its structural coherence from the discourse-internal topic-comment structure, but also its directionality. Directionality appears to be an· essential structural property that depends on the topic-comment structure and is assigned to discourse relations on different structural levels. The topical approach will answer the intricate question of what precisely determines which of two related discourse units is the non-deletable, functionally prominent one. In addition, it will provide a formal characterization of what this functional prominence signifies. We can now present our definition of discourse directionality, central to which is the claim that this phenomenon is determined by topic-forming questions.

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considered to be a function of the different ways of quantitative/qualitative completion of an unsatisfactory answer. This implies that it is essentially a function of the three different types of subordination relations distin­ guished in discourse. The three types of directionality are thus explained as follows. First, Bi-Directionality applies to a quantitative extension of a given partial answer, implying the absence of a functional asymmetry between the discourse unit U; which functions as a partial answer to question Q;, and the related discourse unit Ui+n which functions as the answer to subquestion Qi+n by means of which the quantitative extension to U; is realized. U; and Ui+n together provide the final comment value to the higher-order question Q;. Second, in contrast to Bi-Directionality, FW Directionality applies to a qualitative extension of a given answer, making it more specific. In this case the final comment value to the topic defined by the higher-order question Q; is provided by only a part of the extended answer given to this question, namely by discourse unit Ui+n which is more specific than discourse unit U;. Ui+n functions as the qualitative extension of U; which, as in the preceding case, functions as an unsatisfactory answer to the leading question Q;. Finally, as is the case with FW Directionality, BW Directionality, too, involves a qualitative extension of a given answer. However, in this case the final comment value to the topic of the higher-order question Q; is provided at the beginning rather than at the end of the discourse by the unsatisfactory answer U;. The comment value provided by U; has not yet been accepted by the addressee and calls for support, e.g. a justification or motivation of the value given. This supportive material is provided by discourse unit Ui+n which forms an answer to the subquestion. In addition to giving an adequate explanation in terms of the topic­ comment distinction, the definition also provides a solution to the above mentioned determination problem. Given an asymmetric discourse relation R(U;, U;+n), the relevant factor stating whether U; or Ui+N is functionally dominant is thus not determined by subquestion Qi+n that realizes the relation between them, but by the higher-order question Q; to which U; and U;+n together form an extended answer. By definition, the dominant discourse unit is the one which provides the final comment value with the topic introduced by the higher-order question Q;. Clearly, this topical approach of directionality relates to the approach in terms of discourse intentions which, as indicated above, requires an adequate explication of the intentional status of dominant discourse units as well as an account of the specific relations between these and subservient discourse units. In the topical approach both points can be accounted for by making explicit the relation between discourse intentions and topic-forming

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questions. As said above, in the topical framework the discourse intention associated with a discourse unit is defined as the requested final comment value to the topic defined by the explicit or implicit question which this discourse unit answers. The intentional status of dominant discourse units is thus captured by the fact that, in contrast to subservient discourse units, they provide the overall intentional value functioning as the final comment with the topic shared by both this and the related subservient unit. We have argued that the full acceptance of this value by the addressees may require support which is then provided by a non-dominant discourse unit. On the other hand, as will now be obvious, the intentional relations between subservient and. dominant discourse units can be accounted for in terms of how their comment values contribute, directly or indirectly, to the topic of the higher-order question. As indicated in Section J. I . I , in the topical approach discourse intentions are considered to be just one aspect, be it an integral one, of discourse structure determined by topic-forming questions. Given the relation between topic-forming questions and discourse intentions, the definition also provides a satisfactory explanation of the deletion property of non-dominant discourse units. As said above, under specific conditions, subservient discourse units can be deleted while preserving discourse coherence and discourse intention. In the case of Bi­ Directionality in which both the discourse unit Ui and Ui+n directly contribute to the higher-order question Qi> neither of them can be deleted while preserving the coherence and intention of the extended discourse segment which forms an extended answer to question Qi. For instance, ifUi and Ui+n are part of a narrative representing events that constitute the story line, deletion of one of them will affect the coherence and the intention of the text. This is, for instance, the case if in the preceding example (6) we would delete the discourse unit functioning as answer A3 . On the other hand, deletion of one of the answers in (3) would only affect the intention of that discourse because of the resulting insufficiency of the value the resulting answer provides to the higher-order implicit question (Q ,). In contrast to Bi-Directionality, deletion of the subservient parts of asymmetric FW or BW directional relations has no effect on the coherence or intention of the discourse. In the case of FW Directionality the more specific discourse unit ui+n provides the final comment value, implying that not ui+n but uj may be deleted without any loss of coherence and discourse intention. Examples of deletable units in FW directional contexts are the answers A, in (1) and (12)'. In example (4) we may delete two units because of the occurrence of FW Directionality on two structural levels. On the lower structural level we may delete answer A2, while on the higher level we may delete answer A,. In case of BW Directionality, on the other hand, the

388 Directionality in Discourse

(13) a.

B: What would be a suitable birthday present for Harry? A: A monkey-wrench. B: {A monkey-wrench?) Why? A: He recently came to borrow one from me. What would be a suitable birthday present for Harry? TI{Sact} E P [P {x I present(x) 1\ •expensive(x)}] A1: A monkey-wrench. T I {Sm} E {{MW}, •{MWW7 [TI(Sact) = {MW} or TI(Sact) E Complementp{{MW})] Q2: (A monkey-wrench?) Why? . T2(S.ct) E R [R {x I reason(x, being_a_suitable_birthday_present}f8 A2 : He recently came to borrow one from me. Tz{S.c ,) C 2 ! T , (S.ct) = {MW}!

Q1 AI Q2 A2 b. Q 1 :

r

=

=

=

As far as supportive, non-dominant discourse units are concerned, the example illustrates their reducing effect on the specific underdetermined­ ness that results from related dominant discourse units. In (13b) it is

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discourse unit ui provides the final comment value, implying that ui+n forms the deletable subservient discourse unit. An example is answer A2 in (2). Multi-level structures like the one in (s) involve both discourse relations characterized by BW Directionality and FW Directionality. BW Direction­ ality applies to the discourse relation on the highest structural level, while a FW directional relation applies on the lower level. As illustrated above, deletion of the subservient discourse units on both levels implies that only answer A 1 remains. Also in this case, the deletion operation does not affect the coherence of this discourse which in general implies that the deletion operation has no effect on the remaining structural relations in terms of question-answer structure. Nor does the deletion operation influence the discourse intention associated with this discourse, because the final comment value to the topic defined by the higher-order question Q 1 is preserved by the remaining answer. Finally, what still needs to be explained is how the topical analysis of directionality accounts for the formalization problem of supportive discourse units. Subservient discourse units of this type belong to the category of BW directional phenomena. They provide a justification, a motivation or other kind of support for that which is asserted in the related dominant part of the discourse. The problem is the formalization of the supportive function of these discourse units. Consider, in this respect, example {13).

Jan van Kuppevelt 389

illustrated that in case of positive support such an effect consists of a reduction of the following form: Tp(Sact) E {p, •p} is reduced to T1(Sac,) E {{p}}. The contextual induction of subquestion Q2 indicates that the comment value provided by answer A1 has not yet been accepted by questioner B. This means that at this stage in the process of questioning either a monkey-wre�ch or something else is a suitable birthday present for Harry. The answer to subquestion Q2 lends support to the first alternative, implying the unique determination of the actual extension of the main topic (term). However, if the support given by A2 had been negative, i.e. if T1(S.ct) •{MW} had been the result, this automatically would have shifted attention to the complement set of possible values: T 1 (S.c,) E Comple­ mentp({MW}). In general, automatic shifts caused by negative support imply that the higher-order topic-forming question has not yet been answered satisfactorily which will then give rise to further subquestioning. =

University of Amsterdam Faculty of Arts Department of Computational Linguistics Spuistraat 134 1012 VB Amsterdam The Netherlands e-mail: [email protected]

N OTES 1

2

The research reported here was sup­ ported by the KNAW (Royal Nether­ lands Academy of Arts and Sciences). Besides the KNAW, I would like to thank the Department of Computa­ tional Linguistics of the University of Amsterdam for the appointment of guest researcher during the period in which I completed this paper. An earlier version was published in Bosch & van der Sandt (1994). Obviously, in the case of binary dis­ course relations the property of mutual subservience implies that the two dis­ course units involved are partially goal­ satisfying. If two discourse units are

3 4

mutually subservient in this respect, each of them constitutes a quantitative completion of the other only partially satisfying the goal of the question. For a discussion on the characteristics of both approaches, see Rambow ( r 993). As will become clear later, in this respect both the rhetorical and inten­ tional approaches of discourse do in fact deal with functionally different types of subordination relations in discourse. In relation to this a distinction has to be made between the phenomenon of sub­ ordination on the one hand and that of directionality on the other. While the subordination of a discourse unit B to

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Received: I 3.0S-9S Revised version received: 22.08.96

JAN VAN KUPPEVELT

390 Directionality in Discourse closed off and are taken up again after the interruption. 8 See also note 2. 9 The phenomenon of multi-directionality is analysed as a function of bi-direc­ tional relations realized on different structural levels. Examples of this phe­ nomenon are lists (Polanyi & Scha I984) comprising enumerations as well as those special cases of lists providing event sequences defining the story line of narrative discourse. An illustration of the latter type is given in example (6). 10 In all cases the arrows comprise both the (implicit) subquestion realizing the discourse relation R(Ui> U;.n) and the superordinating (implicit) question to which U; and U;.n together form an extended answer. I I Modified version. I 2 As will be argued for in Section 4, the direction of the relation between the text parts analysed as A, and A2 is determined by the superordinating implicit question (Q,). Assigning a dif­ ferent interpretation to this text by changing the content of (Q,) may result into a different order of dominant and non-dominant discourse units. For instance, the question 'As Jar as China, India, Central Africa and the republics of the former Soviet Union are concerned, how bad are their records with respect to air safety?' gives rise to an inverse relation characterized by FW Directionality. 13 Apart from the fact that deletion of non-dominant pans may result in a lack of cohesion, Mann & Thompson (I988) assume that such a deletion operation may also influence the 'gram­ mar of clause combining'. Although the latter is considered to be of a rhetorical rather than a topical nature, in line with our topical analysis of directionality {Section 4), the authors observe that the deletion of non-dominant parts does not affect the overall topic: '(after deletion) we still have a reasonable idea of what the text is about' (I988: 268).

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a preceding discourse unit A necessarily implies that B contributes to A in satisfying the associated discourse goal, the direction of the relation between A and B may be different depending on whether B's contribution is goal-satisfy­ ing or merely goal-subservient. As for the definition problem, the intentional approaches encounter other problems due to their characterization of directionality, namely in terms of the relation between a subservient discourse unit and the whole text pan comprising both the subservient and the related dominant discourse unit. They face the difficulty of adequately accounting for, in intentional terms, the status of this non-subservient discourse unit as well as the difficulty of providing an account of the characteristic subservience rela­ tion between non-dominant, subservi­ ent, and related dominant discourse units. In this paper in which both issues are central we provide a topical analysis in terms of topic-forming ques­ tions. 6 We abstract from so-called side questions which give rise to intervening side structures. In contrast to subquestions, they do not imply a continuation of the leading topic but result from a topic digression (for a discussion on the main structure-side structure distinction, see van Kuppevelt I995b). 7 In this paper the phenomenon of direc­ tionality will be only considered for cases in which a dominant and a related non-dominant discourse unit form an uninterrupted part of discourse (see also Carberry et al. I993 on this point). However, in contrast to RST which assumes discourse relations to be pri­ marily of a rhetorical nature, inter­ rupted discourse relations can in principle be accounted for adequately because of the fact that the overall continuity in discourse structure is maintained. The leading (implicit) ques­ tion and the topic it defines are not yet

Jan van Kuppevelt 391 14 As

that a topic-comment modulation is imposed on every non-elliptical ques­ tion-answering sentence, depending on the question it answers: TP is a topic part, CP a comment part. It is argued that comment parts are always can­ didates for accent assignment (capitals indicate main sentence accents). We have made use of Gussenhoven's (1984) accent rule SAAR which operates on semantic constituents often closely related to (but not necessarily implying) what is called traditional surface con­ stituency. See in this respect, Steedman (199 1 and other publications) for an isomorphism between syntactic, infor­ mational, and intonational structure based on Combinatory Categorical Grammar. 21 A grammatical treatment of question and answers is given elsewhere (van Kuppevelt 1991). As is argued in Gundel (I976), The x which is lexica­ lized as it in cleft sentences is not semantically empty bur refers to the topic of the sentence. 22 From the viewpoint of discourse repre­ sentation, a topic TP is the set of possible extensional counterparts of the dis­ course address denoted by the subject term in the syntactic analysis of the topic-introducing question Qp. 23 In line with Hausser (1983), Scha (1983), and Tichy (1978), we have opted for an individualistic, non-propositional analy­ sis of questions and answers. The ana­ lysis is in agreement with the view explicit in e.g. Belnap & Steel (1976) and, earlier, in Stout (1932) that the topic ('(psychological) subject') of a question is a set of alternatives. A topic can be taken as the set of entities referred to by that which in a given context can be inserted into the corresponding question frame or open proposition (Prince 1 986) introduced by the question. 24 Obviously, the verification domain does not need to be the actual world. In this respect it is claimed that both discourse

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to discourse topics, the analysis is in agreement with the observation that a discourse may contain several discontin­ uous discourse units that are internally coherent only in the sense that its sentences deal with the same general topic. 15 In this framework the analysis of narra­ tive discourse as a hierarchical rather than a linear structure accounts for the phenomenon of the structurally unrest­ ricted accessibility of antecedents for spe­ cific sentence-external anaphora, namely that the resolution domain of anaphora belonging to the story line comprises all possible antecedents of the part of the narrative. I6 As for addressee-oriented discourse, implicit questions are defined such as those anticipated by the speaker to have occurred to the addressee as the result of the preceding context. I 7 It will be illustrated in this and the next section that the approach in terms of topic-forming questions is not unrelated to other approaches of discourse struc­ ture. It relates, in particular, to the intentional approach which accounts for discourse structure primarily in terms of the discourse purposes under­ lying the production of discourse. I8 Central is the point of view that topic­ forming questions have a factual status, implying their actually occurrence in the given contexts. This discourse func­ tion of question is different to their function in so-called question tests (e.g. Sgall, Hajicova, & Panevoci I986) in which they represent possible contexts in which topic-bearing sentences may occur. I 9 For other question-based topic notions, see e.g. Bartsch (I976), Belnap & Steel ( I 976), Groenendijk & Stokhof ( I 993), Klein & von Stutterheim (1987), Stout ( 1896), Vennemann (1975), and Zeevat (1994)· 20 Among other things, the presented question-based topic notion implies

392 Directionality in Discourse

26

27

28

29 30

31

32 33

34

35

36

37

the extent to which at the moment of questioning the associated set of actual indeterminacies is unrestricted by pre­ ceding questions in the discourse. Topic closure is indicated by an excla­ mation mark. For an account of the main structure-side structure distinction, see e.g. Klein & von Stutterheim ( I987), von Stutterheim & Klein (I989) and van Kuppevelt (I995b). An unsatisfactory, incomplete answer A, is formally represented as A,:T,(S..,,) E (T,(Si) E Q'(T,) I c; � T,(Si)}, whereby c: is the comment value as mentioned in answer A,. An unsatisfactory, non-specific answer A, is formally represented as A,:T,(Sacr) E (T,(Si) E Q(T,) I T,(Si) � Y AIT,(Si) l 2 n}, whereby Y and n are given by A,. In this respect Hirschberg, Litman, Pier­ rehumbert, & Ward (I987), e.g., say the following 'When speakers increase their pitch range from one utterance to the next, they can signal varying degrees of topic change. Degree of final lowering in an utterance can be used to signal the "level" of topic which that utterance concludes; maximum final lowering sig­ nals the conclusion of major topics, for example' (I987: 637). However, see, e.g., also Hirschberg & Nakatani (I996) and Nakatani, Grosz, & Hirschberg (I99S) on this point. In fact the unsatisfactory answer A 1 gives rise to the clausal implicatures (Gazdar I979; Levinson I983) 'possibly p' and 'possibly ....,p', whereby p is '(That which would be a suitable birthday present for Harry is) a monkey­ wrench'. The clausal implicatures give rise to the corresponding topic range Q(T,) (p, ....,p}, comprising the set of possible answer values to question Q1• See van Kuppevelt (I996a,b) for an analysis of Quantity, conversational implicatures, in particular the scalar implicatures (Horn I 972). Obviously, the sets P and R are deter­ mined by background knowledge. =

38

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25

coherence and discourse satisfa ctoriness are not necessarily determined by its truth, implying that the discourse segments functioning as answers to topic-forming questions do not necessarily provide values identical to those of the topic terms in the actual world. An extended answer may be a coherent composition of smaller, lower level discourse seg­ ments, though the latter may provide wrong answer values. Likewise, an (extended) answer may be actually wrong, but perceived by the addressee as providing the value asked for and thereby satisfying the purpose of his question. The following sections will make clear that the so-called contextualization of the topic set implies that it is constrained not only by the domain of discourse, but also by processes of subquestioning implying a reduction of this set. The second point also forms an argu­ ment against the view referred to in the first point, namely that a question is a non-specific request directed to the whole topic set. See e.g. Vallduvi (I993) on this point. Clearly, the focus notion involved in Centering Theory (e.g. Joshi & Wein­ stein I 98 I) is also closely related to the notion of AI-focus. See e.g. van Kuppevelt (I993). Obviously, the underdeterminedness of Tp(Sact) is not a sufficient condition for topic hood. The contextual induction of the topic-introducing question Qp is also controlled or determined by a dis­ course topic DT;. namely in the sense that in a coherent discourse the answer to Q p must also contribute to the (set oD leading question(s) defining DTi. It was illustrated that higher-order topic-forming questions may restrict the set of actual indeterminacies asso­ ciated with a discourse unit functioning as an answer to a question (van Kuppe­ velt I995a). Discourse units functioning as feeders differ from such answers to

Jan van Kuppevelt 393

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