JOURNAL OF SEMANTICS AN
INTERNATIONAL
JoURNAL FOR THE
INTERDISCIPLINARY
Snmv
OF THE
SEMANTICS OF NATURAL LANGUAGE
MANAGI NG EDITOR: PETER BoscH (IBM Scientific Centre, Heidelberg and University of Osnabriick) A SSOCIATE EDITOR S: NICHOLAS AsHER (University of Texas, Austin) R oB VAN DER SANDT (University of Nijmegen) R EVIEW EDITOR : ANKE LiioELING (University of Tiibingen) ASSISTANT EDITOR : ANKE LiiDELING (University of Tiibingen) EDITORIAL BOAR D: M. BIERWISCH ( MPG and Humboldt University
Berlin)
B . BoGURAEV (Apple Computer Inc)
M. BORJLLO (University of Toulouse) K.. BROWN (University of Essex) G. CHJERCHJA (University of Milan) �N CoPESTAKE (Stanford University) 0. DAHL (University of Stockholm) PAUL DE (University of Amsterdam) CLAIRE GARDENT (University of Saarbriicken) B. GEURTS (University of Osnabriick) M. HERWEG (IBM Scientific Centre, Heidelberg) L. R. HoRN (Yale University) J. JAcoBs (University of Wuppertal) P. N. JOHNSON-LAIRD (Princeton University) !vfl!GUMI KAME Yt>MA (SRI International Stanford)
KKER
H. KAMP (University of Stuttgart) S. LO&NER (University of DiisseldorO SIR JoHN LYoNs (University of Cambridge) J. McCAWLEY (University of Chicago) M. MoENS (University of Edinburgh) E J. PELLETIER (University of Alberta) M. PINKAL (University of Saarbriicken) T. SANFORD (University of Glasgow) A. VON STECHOW (University of Tiibingen) M. STEEDMAN (University of Pennsylvania) ANArou SrruGIN (Max Planck Gesellschaft, Berlin) HENRIETTE DE SwART (University of Utrecht) B. WEBBER (University of Pennsylvania) H. ZEEVAT (University of Amsterdam) T. E. ZIMMERMANN _(Univer�ity of Stuttgan)
_
EDITORIAL A.DDRESS: Journal of Semantics, c/o Dr P. Bosch, IBM Germany Scientific Centre, Vangerowstr. 18, D-691 15 Heidelberg, Germany. Phone: (49-6221-) 59-4251/4437· Tclcfax: (49-6221- ) 59-3200. Email:
[email protected]
© Oxford University Press All rights reserved; no part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without· either the prior written permission of the Publishcn, or a licence petrnirring restricted copying issued in the
UK by the Copyright
Licensing Agency Ltd, 90 Tottenham Coun Road, London W1P 9HE. or in the USA by the Copyright Clearance
Center, 222 Rosewood Drive, Danven,
jounu>l of &mantia (ISSN
0167
Massachusetts 01921, USA.
)Ill) is published
quarrerly in February, May, August and November by Oxford
Universiry Press, Oxford, UK. Annual subscription is US$140 per year. journal ofSnnantia is distributed by MAIL America, 2121 Randolph Avenue, Avenel, New Jersey 07001, USA. Periodical postage paid at Rahway, New Jersey, USA
US
and at additional enrry points.
POSTMASTER: send address corrections to Journal of Snnantia, c/o MAIL America, 2323 Randolph Avenue,
Avenel, New Jersey 07001, USA.
For substription information p� su inside b..ck cover.
JOURNAL OF SEMANTICS Volume 14 Number 1
CONTENTS K.AI VON FINTEL
Bare Plurals, Bare Conditionals, and only JoosT ZwARTS Vectors as Relative Positions: A Compositional Semantics of Modified PPs
57
Book Review
Please visit the journal's world wide web site at http://www.oup.eo.uk/semant
•
Scope of this Journal The JOURNAL OF SEMANTICS publishes articles, notes, discussioiu, and book reviews in the area of natural language semantics. It is explicitly interdisciplinary, in that it aims at an integration of philosophical, psychological, and linguistic semantics as well as semantic work done in artificial intelligence and anthropology. Contributions must be of good quality (to be judged by at least two referees) and should relate to questions of comprehension and
interpretation of sentences or texts in natural language. The editors welcome not only papers that cross traditional discipline boundaries, but also more specialized contributions, provided they are accessible to and interesting for a wider readership. Empirical relevance and formal correcmess are paramount among the criteria of acceptance for publication.
Information for Authors: Papers for publication should be submitted in 3 copies to the managing editor. They should be typed on
A4
(or similar format), one-sided, double-spaced,
and with a wide margin and must be accompanied by an approx. 200 word summary. Notes and bibliographical references must appear at the end of the typescript All bibliographical references in the text by author's surname and year of publication. Diagrams must be submitted camera-ready. All papers submitted arc subject to anonymous refereeing and are considered for publication only on the assumption that the paper has neither as a whole or in part already been
published elsewhere nor has elsewhere been submitted or accepted for publication. Unless
special arrangements have been made, copyright rests with Oxford Uriiversity Press. Authors receive 20 offprints of their published articles and 1o offprints of their published reviews, free of charge. Larger numbers can be supplied at cost price by advance arrangement.
Subscriptions: The Journal of Semantics is published quarterly.
Institutional: UK and Europe £78.oo; USA and Rest of World US$140.00. (Single issues: UK and
Europe £23.00; USA and Rest of World US$4o.oo.)
Personal:* UK and Europe £38.oo; USA and Rest of World US$71.00. (Single issue: UK and
Europe £n.oo; USA and Rest of World US$21.00.)
*Personal rates apply only when copies are sent to a private address and payment is made by personal cheque/credit card.
Prices include postage by surface mail or, for subscribers in the USA and Canada by Airfreight or in Japan, Australia, New Zealand and India by Air Speeded Post. Airmail rates are available on request. Back Issues. The current plus two back volumes are available from the Oxford University Press,
Great Clarendon Street, Oxford OXl. 6DP. Previous volumes can be obtained from Dawsons
Back Issues, Cannon House, Park Farm Road, Folkestone, Kent CT19 sEE, tel +44 (o)1303 850101, fax +44 (o)1303 850440. Volumes 1-6 arc available from Swets and Zeitlinger, PO Box 830, 2160 SZ Lisse, The Netherlands.
Payment is required with all orders and subscriptions arc accepted and entered by the volume.
Payment may be made by cheque or Eurochcque (made payable to Oxford University Press), National Girobank (account 500 1056), Credit cards (Access, Visa, American Express, Diners Club), or UNESCO coupons. Please send orders and requests for sample copies to the Journals Subscriptions Department, Oxford University Press, Great Clarendon Street, Oxford OXl. 6DP,
UK. Telex 837330 OXPRES,
tel +44 (o)1865 267907, fax +44 (o)1865 267485-
Copyright:
It is a condition of publication in the Journal that authors assign copyright to
Oxford University Press. This ensures that requests from third parties to reproduce articles are handled efficiently and consistently and will also allow the article to be as widely disseminated as possible. -In assigning copyright, authors may
use
their own material in other publications
provided that the Journal is acknowledged as the original place of publication, and Oxford University Press is notified in writing and in advance.
Advertising: Advertisements
are welcome and rates will be quoted on request Enquiries
should be-addresse(ho Helen-Pearson, Oxford Journals AdvertiSing, PO Box 347, Abingdon SO, OX14 sXX. UK. Tel/fax: +44 (o)1235 201904- Email:
[email protected].
jou1711Jl ofSnntzn!W 14'
©Oxford Univenity Press
1- S6
Bare Plurals, Bare Conditionals, and
1997
Only
KAI VON FINTEL MIT
Abstract The compositional semantics of sentences like
Only mammals give live birth and Theflagflies only ifthe Queen is home is a tough problem. Evidence is presented to show that only here is modifying an underlying proposition (its 'prejacent'). Mter discussing the semantics of only,
I INTRODUCTION We will attempt to provide a compositional semantics for the following kinds of examples: (I)
a.
Only mammals give live birth. b. The flag flies only if the Queen is home.
What do such sentences mean and how do they come to mean what they mean? The overall meaning of our target sentences is reasonably clear. (Ia) excludes the possibility that among a realm of relevant individuals there are any who give live birth but are not mammals. (1b) excludes the possibility that the flag flies in circumstances other than ones in which the Queen is home. Apart from these negative claims, both sentences also seem to impose positive requirements. ( ra) is taken to signal that some (or even all?) mammals give live birth. (Ib) seems to signal that the flag does in fact fly if the Queen is home. We'll get more precise later on. There are two main avenues of analysis: (i) proposition, or
only modifies
(ii) only relates two subconstituents.
an underlying
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
the question of the proper interpretation of the prejacent is explored. It would be nice if the prejacent could be analyzed as having existential quanti£cational force. But that is difficult to maintain, since the prejacent structures when encountered on their own are naturally read as having a lawlike flavor, which in many analyses is attributed to the semantics of implicit operators alleged to be present in them. In the end, an analysis is presented which attributes some very particular properties to these operators and thereby succeeds in providing the target sentences with intuitively adequate interpretations. These complex constructions can therefore be used as a probe into the nature of implicit quantification in natural language.
2
Bare Plurals, Bare
Conditionals, and Only ------
Option (i): If we surgically remove only from these sentences, we are left with sentences that involve bare plurals or bare conditionals: (2)
a.
b.
Mammals give live birth. The flag flies if the Queen is home.
The idea behind Option (i) is that the logical form of the sentences in (I) involves only combining with essentially the structures in (2):
(3)
only [mammals give live birth] b. only [the flag flies if the Queen is home] a.
(4)
a. It is only true that [MAMmals]F give live birth. b. It is only true that the flag flies if [the QUEEN is home]p.
Medieval scholars called the structure that only appears to combine with its prejacent, a convenient term that I will adopt.2 The term bare plural as applied to sentences like (2a) should be familiar. The term bare conditional for a sentence like (2b) derives from a particular view of conditional sentences which assumes that if-clauses typically restrict some kind of (quantificational) operator, a view to be discussed later. Bare conditionals like the one in (2b) contrast with explicitly quantified or modalized conditionals such as The flag always flies if the Queen is home. If we pursue Option (i), we have to spend some time on saying what the prejacent structures mean. We will see that it would be nice if they could be analyzed as having existential quantificational force. But that is difficult to maintain, since the sentences in (2) by themselves are naturally read as having a lawlike flavor, which in many analyses is attributed to the semantics of implicit operators alleged to be present in them. To provide an adequate analysis of our target sentences, we will have to attribute some very particular properties to these implicit operators. Within such a view, we can use the semantics of the sentences in {I) as a probe into the semantics of lawlike statements.
Option (ii): The competing analysis would maintain that the sentences in (2) do not represent any ingredient of the structure of the sentences in ( I ). Instead, the idea behind Option (ii) is that in the logical form of the sentences in (I ) only is a quantifi.cational element relating two constituents: two predicates in ( Ia) and two clauses in (1b):
(s)
a.
only [mammals] [give live birth] b. only [if the flag flies] [the Queen is home]
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
This approach receives some initial plausibility from the fact that the following (slightly artificial) sentences seem equivalent to our target sentences:1
Kai von
Fintel
3
To specify the meaning of only is in such structures, we could draw inspiration from the logic textbook doctrine about the sentences in (I ). What we are told is that only As are Bs is equivalent to all Bs are As: only is the converse of all. It is further claimed that only ifp, q is equivalent to if q, p: only if is the converse of if So, our sentences in (I ) are said to be equivalent to these ones:
(6)
a.
All animals that give live birth are mammals.
b. If the flag flies, the Queen is home.
converse of only ifp, q, does not presuppose ifp, q. Hence, convertibility can only be said to hold as long as we ignore presuppositions. Perhaps, the champion of convertibility should maintain that while only if p, q is not equivalent to if q, p, it does entail it. Similarly, only As are Bs may not be equivalent to all Bs are As but it might entail it. The second reason why the convertibility doctrine can only be almost right is that conversion typically destroys the temporal/causal dependencies signaled by the original version: (7) a. We will celebrate only if John wins the race. b. If we (will) celebrate, John wins the race. We get a disturbingly different meaning if we put (7a) in the converse form as in (7b). The latter seems to suggest quite bizarrely that the celebration precedes and brings about John's victory. Something is wrong. McCawley ( I993) presents a lot of similar examples that make the traditional doctrine look thoroughly ridiculous.3 Note, though, that the traditional idea does have a plausible core. Intuitively, (7) asserts that John's winning the race is the only condition under which we will celebrate. This should entitle the listener to conclude that if she fmds us celebrating, John must have won the race. That is (7a) should entail something like:
(8)
If we celebrate, John must have won the race.
Note that (8), unlike (7b), maintains the temporal/causal dependencies carried by (7a). So, the traditional doctrine, suitably refmed, seems to have an ounce of truth to it.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
While there does seem to be something right to these logical teachings, the recipe that gets us from ( I ) to (6) can't be quite right. First, it is often thought that only triggers a certain kind of presupposition (or implicature, or what have you; we'll discuss this a little further in section 3). For example, only John left is said to presuppose that John left. Similarly, only if p, q is said to presuppose that if p, q is true as well. Of course, the latter can't be an entailment; otherwise q only if p would be equivalent to q if and only ifp, which it isn't. Now clearly ifq, p, which is the
4
Bare Plurals, Bare Conditionals, and Only
In the case of the claim that only as in (1a) is the converse of all, it is just as easy to come up with such counter-examples, although McCawley does not present any. As soon as we provide temporal material, we find analogues to the example in (7):
(9)
a.
Only runners who win races celebrate.
b. All people who celebrate are runners who win races.
These are not equivalent. So here, too, we will at least have to rethink the traditional doctrine.
2
ONLY
IS NOT AN ORDINARY QUANTIFIER
In this section, I will reject Option (ii), which maintains that only is a quantificational element that relates two constituents of the prejacent structure. For (ra), the claim would be the that only is a determiner relating the common noun predicate (mammals) and the verb phrase predicate (give live birth). For (rb), the claim would be that only is an operator with the if-clause (if the Queen is home) and the main clause (the flagflies) as its two arguments.
2.1
'Only'
as a
determiner?
Recall the pair: (ro)
a.
b.
Only mammals give live birth. All anima1s that give live birth are mammals.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Here is how we will proceed. In section 2, Option (ii) is considered and rejected (albeit perhaps not decisively). To explore Option (i), we first need to say something about the meaning of only when it is analyzed as applying to a proposition. This is done in section 3· Then we need a sketch of the basic analysis of sentences with bare plurals and bare conditionals. This is provided in section 4· In the following three sections, three possibilities for the interpretation of the prejacent structures are considered. While I do end up endorsing most strongly the solution discussed in section 7, the main purpose of this paper is to lay out the intricacies of the analysis of our target sentences. One might have thought that this is not much more than a simple homework assignment for a graduate course in natural language semantics. Instead, we get quickly entangled in a thicket of issues, including most prominently the semantics of lawlike statements in natural language. I hope that other researchers will venture into this terrain and make sense of these issues.4
Kai von
Fintel s
Since it seems that only and all are intimately related by being mutually convertible, why not just take the usual semantics for all and tum it around? Let us assume a simple analysis of all where it denotes the subset relation between its two argument sets, the common noun set and the predicate set:
(u ) [all](A)(B)
iff A
� B, for any two sets of individuals A and B.
We might then say that only is a determiner that denotes the converse of alZ.S (12) [only] (A)(B) iff B � A. for any two sets of individuals A and B.
(13)
a. I like only (FRENCH]F movies. b. I only like [FRENCH]F movies.
Now, even if we adopt the determiner analysis, we have to give an account of how the meaning of (13b) comes about compositionally. But there we seem to be forced to treat the bare plural as a full NP, since it by itself fills the object position. Then it would be unparsimonious not to use a parallel analysis in the case of (13a) as well. One way out for the determiner analysis is to claim that (13b) is actually syntactically derived from (13a) by some kind of 'shallow' placement rule. Something like such an operation is called 'only-separation' by McCawley (1988: section 18, 6II-I8). It is also considered favorably by Hajicova and Sgall (Partee, Hajicova, & Sgall 1994). I fmd it dubious at best that there should be such a rule. It would have to be an accident that it only arises with the 'determiner' only and not with other determiners. For example: (14)
a. I like both books on the table. b. *I both like books on the table. c. The books on the table are both expensive.
Note that (14c) shows that both is an item that can in fact float off its noun phrase. Nevertheless, (14b) is hopeless. The positional &eedom of only is much better explained by treating it as an adverb, not as a determiner.7 Secondly, we can see that (1oa) is roughly synonymous with examples more clearly involving full NPs under only: (15) Only mammals give live birth. Only a mammal gives live birth.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The analysis in (12) would be faithful to logical tradition. There are, however, a number of considerations that speak against this determiner analysis.6 First, when there is an only-NP in object position, we can construct apparently synonymous examples with only as a VP-operator:
6
Bare Plurals, Bare Conditionals, and
Only
Only the mammal gives live birth. Only the mammals give live birth. We would need to solve the problems brought up by these examples anyway. Here, only obviously attaches to an NP and therefore cannot be a determiner. Again, the determiner analysis would be too specialized to cover all examples that share the basic semantics of (10a). A third problem with the determiner analysis is that the putative determiner only as defmed in (12) would be non-conservative, in violation of a dearly held semantic universal which states that all natural language determiners are conservative (Barwise & Cooper 1981; Keenan & Stavi 1986; Westerscihl 1989). Recall the definition of conservativity:
This equivalence clearly holds for run-of-the-mill determiners: (17) Every man smokes{::} every man is a man who smokes. Some man smokes{::} some man is a man who smokes. No man smokes{::} no man is a man who smokes. Most men smoke{::} most men are men who smoke. Few men smoke{::} few men are men who smoke. Many men smoke{::} many men are men who smoke.
But it does not hold for only: (18) Only men smoke� only men are men who smoke.
The second sentence is trivially true. In set-theoretic terms, it says that the men who smoke are a subset of the men. But, for any two sets A. B, it always holds that A n B � A From this, it does not follow that A � B as claimed in the first sentence. So, only is not conservative. One could argue that non-conservativity is a property that only shares with some uses of weak determiners discussed by Westerst:ihl (1985) and more recently Herburger (1993, 1997):8 (19) Few [inCOMpetent]F cooks applied.
The observations is that (19) can be read as saying that a small proportion of the cooks that applied are incompetent. Under this reading, the restriction of the quantifier is not given by its surface argument, but somehow computed by using the focus structure of the sentence. Friends of the determiner analysis could then say that only works exactly the same way and that both weak determiners and only contrast with strong determiners in this respect:
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
( r 6} A determiner 8 is conservative ifffor any two sets of individuals A and B: [ 8] (A}(B}{::} [ 8] (A}(A n B).
Kai von
(2o)
Fintel 7
a.
Only (inCOMpetent]F cooks applied. b. Most (inCOMpetent]F cooks applied.
While the focus in (2ob) is most naturally interpreted as contrastive on a discourse level, the focus in (2oa) crucially affects the proposition expressed. What is claimed in (2oa) is that the set of cooks who applied is a subset of the set of incompetent cooks.9 But going against the parallel between weak determiners and only, we have the following contrast: (21)
a. Few incompetent cooks [apPLIED]F. b. #Only incompetent cooks [apPLIED]F.
2.2
'Only'
as
an adverb of quantification?
My somewhat tentative rejection of the determiner analysis gets re-enforced as soon as we tum to only if First of all, it would be unparsimonious to introduce a special analysis for the collocation of only with if, given that we need an analysis of synonymous cases where the two items occur at a distance: (22)
a.
We will play soccer only if the sun is shining. b. We will only play soccer if the sun is shining.
Of course, one might claim that only ... if is a discontinuous item, but that should be a last resort.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The determiner only would still be special in that it demands that the focus be somewhere in its syntactic argument.But anyway, in the absence of an analysis that salvages conservativity in the face of examples like (19), the conservativity argument cannot be taken as a severe problem for the determiner analysis.10 What is the upshot of this discussion? Clearly, 'whatever only is categorized as, it's an oddball, and its oddity has to be localized somewhere' Uim McCawley, p.c.). Much of our analysis has to be tailored to this one particular item.So, saying that in one of its senses only is a determiner with a number of very peculiar properties is not in any sense crazy.11 Never theless, if a general analysis of only as an adverb were available that could be naturally applied to the cases where only seems to be a determiner, we would prefer such a uniform analysis. The idea, floating in the folklore, is that noun phrases like only mammals should be analyzed as cases where only is modifying a bare plural noun phrase. That is, only doesn't make a noun phrase out of a common noun, but modifies a constituent that is already a noun phrase in its own right.
8 Bare Plurals, Bare Conditionals, and
Only
One obvious idea would relate only to the adverb of quantification by the near paraphrase relation illustrated here:
always, inspired (23)
a.
We only play soccer if the sun is shining. b. If we play soccer the sun is always shining.
(24)
[always (if p) (q)] iff all p-cases are q-cases. [only (if p) (q)] iff all q-cases are p-cases.
Again, one of the problems with this analysis would come from the non-conservativity of the putative adverb of quantification only. Work on adverbial quantification has shown that conservativity holds for adverbs of quantification as well as for determiners (Schwarzschild 1989; de Swart 1991). So we would have to give up or modify this result as well. A more serious problem comes from the fact that only if-sentences come in a variety of flavors: (25)
a.
We only play soccer if the sun is shining. b. John will only be arrested if there is evidence against him. c. John would only have been arrested if there had been evidence against him.
The examples in (25b and c) are what are sometimes called on-case conditionals: they are about a specific event not about a set of cases. (25b) is an indicative conditionals, (25c) is a counterfactual conditional Now, these kinds of readings never arise with adverbs of quantification: there are no one-case conditionals involving always, often, never. The proper conclu sion is that in these examples only combines with a conditional sentence that has a semantics of its own: only is not the only logical operator in these sentences.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The paraphrase relation is not entirely convincing, of course, for reasons we mentioned early on: (23b), but not (23a), carries a suggestion that our playing soccer somehow makes the sun shine. But let's assume that we can clean up the analysis enough to get rid of that problem. An account of (23b) that we might want to base our analysis on comes frcm Lewis ( 1975). The adverb always quantifies over 'cases': it says that all the cases specified by the if clause are cases in which the consequent is true. The role of the if-clause is to restrict the adverb of quantification, there is no other meaning to if. Kratzer (1978, 1986) has proposed to generalize this analysis to all conditional structures: if-clauses in general are used to restrict quantifiers of various sorts. We could now attempt a move parallel to the determiner analysis of only considered in the previous subsection. Why not say that only in (23a) is an adverb of quantification that denotes the converse of the adverb always:
Kai von
2.3
Fintel 9
Moving on
For only if-constructions, then, it is clear that we need an analysis where only semantically combines with a prejacent proposition (a conditional structure with its own operator). Since we want to maintain a certain amount of uniformity between the two kinds of constructions we are concerned with, also motivates us to look beyond the determiner analysis of only for examples like only mammals give live birth. We would prefer an analysis of the structures in (1) that does not introduce new meanings for only. We want to treat the combination of only with bare plurals and with bare conditionals in a compositional manner. The analyses should respect independently motivated accounts of only, bare plurals, and bare conditionals. Early attempts at analyzing only if into only and if can be found in Geis (1973) and McCawley (1974); see also McCawley (1993). Recent work includes Lycan (1991), Barker (1993), and Appiah (1993). I do not know of any explicit attempts at treating the combination of only with bare plurals, other than the determiner analysis. The severity of our problem can perhaps best be appreciated by looking at Geis's attempt (which is adopted in Lycan's work) and McCawley's response in his 1974 squib. According to Geis/Lycan, if p, q means 'all p-cases are q-cases'. Sometimes the universal force of this analysis is disguised by using a bare plural paraphrase 'p-cases are q-cases'. Now, attach only. 'only all p-cases are q-cases'. Clearly that is not the right meaning for only if p, q. One can disguise the failure of the analysis by using the bare plural paraphrase 'only p-cases are q-cases', in which the universal force has mysteriously disappeared. In fact, now we might even want to give the paraphrase 'only some p-cases are q-cases' (with focus on 'p'), where we have existential force. This kind of analysis cannot be called compositional: we are merely given paraphrases for the two ingredients
this
work compositionally. He fmally despairs of fmding a compositional analysis of only if. His last sentence is 'Have I missed an alternative?' Let's try. First, we need a semantics for only. Then, we will need to figure out what the semantics of the prejacent construction is. We will end up with the same problem we just saw: the prejacent is naturally analyzed as involving universal quantification, but once only is attached it's as if the prejacent is now existentially quantified. How can that be? I will consider three solutions: (i) the prejacent is in fact existentially quantified and the fact that without only it is read as universally quantified is due to some extraneous factor; (ii) the prejacent is universally quantified, but its focus
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
where one of the paraphrases gets different readings depending on whether it stands on its own or is combined with the other paraphrase. In McCawley's squib, he clearly shows that the Geis/Lycan analysis doesn't
10 Bare Plurals, Bare
Conditionals, and
Only
structure is such that when it is combined with only we automatically get the meaning we want; (iii) the prejacent is universally quantified, but the implicit quantifiers involved crucially validate the Law of the Excluded Middle and the Law of Contraposition, which together derive the correct meanings for our sentences. I will argue that the third solution is most generally applicable, while special cases may be analyzable along the lines of the other two proposals. We will thus end up having used the analysis of the sentences in ( r ) as a probe into the semantics of implicit quantification in conditionals and generics. THE SEMANTICS OF ONLY
We have decided to pursue the idea that only modifies a prejacent proposition. What goes on in such structures? And how do structures work where only doesn't appear to be attaching to a proposition? J.l
'Only'
as
a propositional operator
It is easily seen that only is an item that can attach to constituents of a wide variety of syntactic categories, a property it shares with some other 'logical' operators like negation and conjunction. Here's an illustration: (26)
a.
b. c. d. e.
(Only John] was awake in time for breakfast. John [only voted by proxy]. John invited [only a couple of old friends]. John watches TV [only during dinner]. John solved the problem [only after Mary gave him a tip].
The best-known among the serious semantic analyses of only is probably the one found in Mats Roath's dissertation (r985).12 Roath's idea is that the . various manifestations of only can be reduced to a base case where only combines with a proposition and asserts that no other proposition is true. Here's as good an example of only applying to a propositional argument as one finds (&om Irene Heim, class discussion):13 (27) The barbecue went fairly well. It only rained. It wasn't windy, there are enough beer, and there weren't any mosquitoes. Imagine that the logical form of it only rained is s
r-'5 . .
only
1t rame
d
this:
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
3
Kai von
Fintel
II
on
s �s
rY""c
it rained
or as we will write from now on:
S
�s
onlyc
1·t ra1ne . d
Putting C into the logical form is just a matter of convenience and not the only possible way of dealing with the context-dependency of quantifiers. Various issues having to do with contextual restrictions on quantifiers are discussed in von Fintel ( r 994: section 2.2), where further references are given. The semantic value of only is a function that takes a set of propositions C and a prejacent proposition p and asserts that no proposition in C other than p is true. The basic intuition here is that only is a funny kind of general negation, it denies all the (contextually relevant} alternatives to its sister proposition: (3oa) For all sets of propositions C, propositions p, r, and worlds w: [only] (C}(p) is true in w iff'v'r E C (r =J p- r is false in w) iff'v'r E C (r is true in w - r = p). or {equivalently) In addition to the negative claim about alternatives to rain, it seems that (27) also conveys that the prejacent is true, that it actually rained. Is that part of the truth-conditions, i.e. is the prejacent entailed? Or is it presupposed, or is it merely implicated? There is a major industry devoted to this question (Hom 1992, 1996; Atlas 1993). I will assume for concreteness that we are dealing with a presupposition. Hom (1990) argues that we actually don't want to say directly that the truth of the prejacent is presupposed. Rather, he effectively suggests that what is presupposed is that there is at least one alternative in C that is true. Taken together with the assertion that no proposition in C other than p is true, we will be able to infer that p is true. The difference between the two
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The claim is that (28} is interpreted as saying that no proposition other than the one that it rained is true. But clearly, what (28} says cannot literally be as sweeping as that; there will always be numerous other true propositions beside the one that it rained. The negative quantification has to range over a restricted domain of propositions, here apparently propositions about the occurrence of annoying circumstances. None of those propositions other than the one that it rained is true. The restricted set of propositions quantified over are called the 'alternatives' by Rooth (1985) and the 'neighbors' by Bennett (1982). This context-dependent nature of only is a property it shares with all other quantiflcational constructions in natural language. What we will do is assume that, at logical form, only is provided with an implicit argument of the type of sets of propositions. That is, the logical form of our sentence is really this:14
12
Bare Plurals, Bare Conditionals, and
Only
options will only show up when we embed the only-proposition in various matrix contexts. Hom argues that the weaker presupposition is more adequate; we will not review the discussion here. Here is how we could formalize the Hom-presupposition in our framework: (3ob) For all sets of propositions C, propositions p, r, and worlds w: [only (C)(p} is defined for w only if 3r E C: r is true in w. If defmed, �only (C)(p) is true in w iff 'Vr E C (r is true in w � r = p).
]
]
(31)
It only rained in [MEDford]F·
Quite clearly, the only propositions whose falsity is asserted here are propositions that talk about rain in places other than Medford. Proposi tions about John's reading War and Peace are irrelevant. This phenom enon has become known as 'association-with-focus'. We subscribe to Rooth's 'alternative semantics' for focus. The principal effect of focus is to introduce into the context a set of alternatives to the focused item. This can then be passed on 'up the tree' and lead to sets of alternatives for bigger expressions. The focus on Medford in (31) first evokes a set of relevant contrasts to Medford. Higher up what we get are alternative propositions about rain in the places contrasting with Medford. In a sentence with only, we can look at the focus structure as providing us with information about the set of propositions among which only is roaming semantically. How exactly these evoked alternatives come to enter into the interpretation of sentences with only need not concern us here.17 Let us just put things this way:
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Hom himself tries to derive this presupposition by appealing to the well known existential import of all in natural language.15 Since all As are Bs arguably presupposes that there are As, we have that its converted equivalent only Bs are As presupposes that there are As as well. And, if there are As and we assert that nothing other than Bs are As, we can infer that (some of ) the Bs are in fact As. In this paper, however, we cannot go this way: after all, we cannot directly say that only is the converse of all, which would only work under the determiner analysis which we rejected. Our project is to derive convertibility while not treating only as a determiner. How do we fmd out what the set of contextually relevant alternatives C is in any given case, a daunting task since this set is only implicitly given? We need to read the speaker's mind16 and one way of doing that is by looking at the focus structure of the argument of only. Here's an example (again from Irene Heim):
Kai von
Fintel 13
(3oc) For all sets of propositions C, propositions p, r, and worlds w: [only] (C)(p) is defined for w only if (i) 3r E C: r is true in w, (ii) the focus structure of p constrains the extent of C.18 If defined, [ only] (C){p) is true in w iff'v'r E C (r is true in w r p). �
=
(3od) For all sets of propositions C, propositions p, r and worlds w: [only] (C)(p) is defined for w only if (i) 3r E C: r is true in w, (ii} the focus structure of p constrains the extent of C. If defined, [only] (C}{p) is true in w iff 'v'r E C (r is true in w p � r). �
Alternatively, we could let the contextual restriction do the work, by requiring that these propositions just aren't legitimate alternatives: (3oe) For all sets of propositions C, propositions p, r, and worlds w: [only] (C)(p) is defined for w only if (i) 3r E C: r is true in w, (ii) the focus structure of p constrains the extent of C, (iii) no proposition in C is entailed by p. If defmed, [only] (C)(p) is true in w iff'v'r E C (r is true in w r p). •
�
=
I will choose the latter approach for concreteness. A further modification: when it rained in Medford last week, some raindrops fell on the mayor's house. Now, it is not logically necessary that rain in Medford will drop on the mayor's house; nevertheless it just happened to be part of that particular rain episode. So, there is a proposition that is true, which is different from and not entailed by our prejacent proposition. This problem was noted by Kratzer (1989), who cited the following dialogue with a lunatic:19
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
There is another problem with the strong assertion of only as formalized in (Joe): if it rained in Medford, then there are presumably quite a lot of further propositions that have to be true, all the logical entailments of the proposition that it rained in Medford. For example, if it rained in Medford, then there must have been some drops of water falling on some part of Medford (note that this is a unilateral entailment). Such true propositions do not threaten the assertion made by only. There are two ways we could get rid of this problem: we could change the entry for only so that it says that all true propositions have to be merely entailed by the prejacent proposition instead of being identical to it:
14 Bare Plurals, Bare Conditionals, and Only
{32) Lunatic: What did you do yesterday evening? The only thing I did yesterday evening was paint this still Paula: life over there. Lunatic: This is not true. You also painted these apples and you also painted these bananas. Hence painting this still life was not the only thing you did yesterday evening.
(3of) For all sets of propositions C, propositions p, r, and worlds w: [only](C)(p) is defined for w only if (i) 3r E C: r is true in w, (ii) the focus structure of p constrains the extent of C, (iii) no proposition m C 1s entailed by p, (iv) no proposition m C 1s lumped by p. If defined, [only] (C)(p) is true in w iff\lr E C (r is true in w � r = p). For the moment, I J.2
will
leave things at that.21
'Only' combining with non-propositional constituents
Convincing cases where only is plausible modifying a proposition, such as Heim's examples in (27) and {31) and also McCawley's (1970) example in footnote 13, are not easy to fmd. Perhaps the tp.ost common position for only is in the auxiliary system (around Infl). It then typically associates with a focus somewhere in the VP. This kind of behavior, somewhat troublesome &om the point of view of the claim that only is a propositional operator, is also shared by natural language negation, which doesn't naturally occur in sentence-peripheral position. Here are a couple of possible responses. In accordance with the predicate-internal subject hypothesis in recent GB syntax (or its analogues in other frameworks), we could maintain that VP-level only is in fact attached to a propositional constituent. What happens is just that for extraneous reasons the subject has to raise out of the predicate phrase (either for case reasons or to satisfy the Extended Projection Principle).
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Kratzer proposes to thwart the lunatic by saying that the proposition I painted this still life lumps the proposition I painted these apples, and that propositions that are lumped by a target proposition are not legitimate alternatives to that proposition. A proposition p lumps a proposition q in a world w iff in every situation s in w in which p is true, q is true as well. To execute this, we have to move to a situation semantics. What we have then is this:20
Kai von
Fintel 1 S
Kim.
But Rooth's project was to reduce such non-propositional uses of only to the basic case of only operating on propositions. It is in fact easy to translate our talk above about properties into talk about propositions: the set of alternative propositions includes Kim went to the opera', Kim read War and Peace', 'Kim cooked a five course dinner', 'Kim prepared her tax return', and so on. The sentence claims that those propositions in C that are not the proposition 'Kim watched The X-Files' are false. To reduce the verb phrase-level only in (33) to a proposition-level only, Rooth {1985) takes a cross-categorial approach, where a family of meanings for only is defined, a different meaning for each syntactic environment. These meanings are related by a general type-shifting schema. What we do is posit an operator onlyVP, which is systematically related to the proposi tional operator onl/. The semantics of this new operator takes a set of properties C and a property P and gives a function that for any individual x gives us the same proposition as the propositional only would give us for the set of propositions that we get from applying all the properties in C to x and the proposition resulting from applying P to x. In symbols: (34) For all sets of properties C, for all properties P, all individuals x, all worlds w [onlyVP] (C){P)(x) is true in w iff [only]( { Q(x): C(Q)} )(P(x)) is true in w. In general, we can find a reducible meaning for only whenever it combines with an expression that is a function that given the right arguments will give a proposition. For more in-depth discussion, see Rooth (1985) and K.rifka (1991). Three consequences of this view are particularly interesting in the context of this paper: (i) the putative determiner only would have a meaning that is not reducible to the propositional base-case; (ii) even for the seemingly simple case of Only John left, we will need a rather complicated analysis; John here will have to '
'
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The other option, the one pursued by Rooth (1985), is to reduce the semantics of VP-level only to that of the proposition-level only. Here's an example: (33) [What did Kim do last night?) Kim onlyc [watched The X-Files]p. The straightforward way to treat (33) would be to say that there is a VP-operator onlyVP that says that among a certain set of properties C none other than its sister VP truthfully applies to the subject. The set of alternative properties C in (33) presumably contains properties like 'went to the opera', 'read War and Peace', 'cooked a five course dinner', 'prepared her tax return', and so on. The sentence claims that those properties in C that are not the property 'watched The X-Files' do not truthfully apply to
16 Bare Plurals, Bare Conditionals, and
Only
be treated as a generalized quantifier to which only applies-more on this in Appendix B; (iii) unless very complex types are introduced, the prediction is that only takes scope over its local proposition. Instead of Rooth's cross-categorial semantics for only, one could pursue an LF-based approach, where only moves covertly to adjoin to a proposi tional constituent (if it isn't already adjoined to one).22 To mimic the strict locality of the scope of only, mentioned under (iii) above, one might limit scopal movement to the local clause. Scopal movement of only would not be the same as the focus-movement that Rooth argues against, where
this
the focused constituent associated with only raises to a position next to only. An LF-approach to only could be combined with a Roothian in situ
J.J
Wh ere
we are now
Let us turn to the main problem we want to explore in this paper:
( I)
a.
Only mammals give live birth. b. The flag flies only if the Queen is home.
Strictly speaking, we will have to work on analyses that involve the cross categorial operator only combining with a bare plural noun phrase in ( u) and with a verb phrase containing an if-clause in ( I b). As mentioned, I will instead pretend that we are dealing with logical forms in which only attaches to the whole prejacent sentence: (35)
a.
onlyc [mammals give live birth] b. onlyc [the flag flies if the Queen is home]
Our task is now to figure out what the semantics of the prejacent is and what the relevant alternatives in C are like. Wrong choices will lead to wrong meanings. The analysis of section s assumes an existentially quantified prejacent. The analysis in section 6 assumes a quasi-universal prejacent with wide focus on the quantifier restriction. The analysis of section 7 assumes a quasi-universal prejacent with potentially narrow focus inside the quantifier restriction, which makes it necessary to attribute certain interesting logical properties to bare conditionals and bare plurals.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
approach to focus semantics. But I will not attempt seriously to pursue such an account here. Nevertheless, using the cross-categorial semantics for only quickly gets somewhat intricate, and so I will tend to use (pseudo-) logical forms at various points where I pretend that we are dealing with the propositional operator only. But for current purposes, this should clearly be seen as merely an expository device; I do not want to adopt seriously an LF-approach.
Kai von
Fintel 17
But first we will briefly have to discuss the interpretation of sentences with bare plurals and bare conditionals. This will be woefully sketchy but that's unavoidable.
4
IMPLICITLY QUANTIFIED STRUCTURES
(36)
a.
I made cookies last night. 3 [Ax cookies(x) & Ax I-made-last night(x)) b. Professors are usually confident. usually [Ax professor(x)][Ax confident(x)] c. Professors are confident. GEN [Ax professor(x)][Ax confident(x))
In (36a), Existential Closure turns the complex predicate cons1stmg of the bare plural cookies and the rest of the sentence into an existentially quantified statement. In (36b), the adverbial quantifier usually quantifies over individuals that satisfy the bare plural predicate. To analyze (36c), we posit an implicit quantifier, called GEN to remind us of 'generic'. The factors that determine which procedure applies in a given case are multifarious and the object of intense study in recent work. In the absence of overt operators, bare plurals are preferentially read existentially when
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Sentences with bare plurals in them of course sometimes have existential force and sometimes have universal/generic force. This 'quantificational variability' is an effect that has been at the center of much work in contemporary semantics. There are two main approaches: (i) bare plurals are names of kinds and the quantificational force of the sentences they appear in comes from the predicate; (ii) bare plurals are indefinites and the quantificational force comes from overt or covert operators.23 I will have some comments on the reference to kinds approach later on. For the moment, I will assume the indefinites approach. This approach has two variants: the unselective binding account and the event/situation-based account. Although I have strong sympathies for the latter (von Fintel 1997b), I will here work within the unselective binding account, mainly for reasons of convenience. In this account, bare plurals are interpreted as predicates that are either conjoined with the other predicates in the structure or serve as the restriction of some operator. In structures where no overt operator is available to take care of the predicate, two covert procedures can apply. Either a default process of Existential Closure kicks in or an implicit quasi-universal quantifier is introduced. A few samples:
18 Bare Plurals, Bare Conditionals, and Only
they are VP-intemal in various senses. One of the more solid generaliza tions is that bare plural subjects of 'individual-level' predicates (such as confident) are forced to be read generically. This fact that will play a central role in the next section. In conditionals, implicit quantifiers are at work as well (Kratzer 1978, 1986). Consider: (37)
a.
We always play soccer if the sun is shining. always [..Xs the-sun-is-shining (s)][..Xs we-play-soccer (s)] b. We play soccer if the sun is shining. GEN [..Xs the-sun-is-shining (s)][..Xs we-play-soccer (s)]
Consider:
(38)
a.
Professors are confident. 'All normal/relevant professors are confident' b. We play soccer if the sun is shining. 'All normal/relevant situations in which the sun is shining are situations in which we play soccer'
The function of the adjectives normal or relevant in these paraphrases can be formally captured by a selection function which from the domain of quantification supplied by the bare plural or the bare if-clause selects a set of cases about which GEN then makes a universal claim. 25 I will assume for convenience that at logical form there is a variable over selection functions associated with GEN. The lexical entry for GEN will look like this:
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
While in (37a) the overt adverbial quantifier always relates the restrictive if-clause with the matrix clause, this is achieved by an implicit operator in (37b). One thing to note is that there do not seem to be cases where bare conditionals are read as having existential force: for some reason, the process of Existential Closure seems inapplicable to conditional structures. I will assume that the very same implicit operator is at work in generic sentences and conditional sentences. This rather adventurous assumption is discussed with considerable sympathy by Krifka et al. (1995: 49-57). I will not argue for it here. If it turns out to be mistaken, the account developed here would not suffer much; we would just have to separate more carefully the bare plural cases from the bare conditional cases. The fact that GEN gives rise both to generic sentences and conditional sentences could be explained by treating it as an unselective quantifier. We need to keep in mind that the quantificational force of GEN is not strictly speaking universal. Both generic sentences and conditional sentences-let us call them lawlike sentences with an umbrella term notoriously allow exceptions. One way of accounting for that is by assuming that GEN only quantifies over 'normal' or 'relevant' cases. 24
Kai von
Fintel 1 9
s
EXISTENTIAL PREJACENTS?
It would be easy to get the right meanings if we could convince ourselves that the prejacents modified by only in our target examples invariably had existential force. In this section, I consider this possibility. In the end, I will say that some examples do actually have this property, but others probably don't, so at least for those we will need a different account. How existential prejacents interact with 'only' Take some existentially quantified propositions: (4o) a. Some professors are confident. b. Sometimes, if the sun is shining, we play soccer. 5.1
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
(39) For u either e or s, for all p, q E D(.,.,t)• f E D(s.(cn,m))• and worlds w: [GEN](�(p)(q) is defmed for w only if 3 x E f{w)(p). Where defmed, [GEN](f )(p)(q) is true in w iff 'Vx E f{w)(p): q(x). This defmition is schematic in that it is supposed to cover both the use of GEN as a quantifier over individuals (in which case the type u will be e) and the use of GEN as a quantifier over worlds/situations (in which case u will be the type s). The selection function f differs potentially with the evaluation world. It will select a set of relevant individuals or worlds/situations from the domain of quantification p. There is an existence presupposition: that the selection function will select a non-empty set of relevant cases. About the set of relevant cases, GEN then makes a universal claim: all of them are q-cases. One might want to speculate what factors determine whether a generic sentences or a bare conditional sentence is chosen. Clearly it would be awkward to replace Mammals give live birth with Ifsomething is a mammal, itgives live birth. Similarly, Thejlagjlies ifthe Queen is home is preferable to Occasions on which the Queen is home are occasions on which theflagflies. Nevertheless, since in all of these GEN is at work, the pairs seem roughly equivalent. To fill out this sketch, which is not something we can do here, we will have to say much more about the nature of quantification over 'normal' or 'relevant' cases and much more about the covert processes of Existential Closure and the licensing of GEN. I hope that what I have said here will be enough to let us go on in our investigation. For details, I have to refer to the large literature on bare plurals, indefinites, adverbs of quantification, genericity, conditionals, and so on.
20
Bare Plurals, Bare Conditionals, and
Only
The interpretation of (4oa) is unproblematic. The interpretation of (4ob), in accordance with the Lewis-Kratzer thesis, is something like: some situations/cases in which the sun is shining are situations/cases in which we play soccer. Now, add only to these propositions and associate it with focus on the restriction of the existential quantifier: (41)
a.
Only [some [proFESsors]F] are confident. b. Only [if [the SUN shines]F do we sometimes play soccerV6
5.2
Do we have existential prejacents in our examples?
Consider then: (42)
a.
Only [proFESsors)F are confident. b. We play soccer only if [the SUN shines]F.
Can we reasonably assume that only here applies to an existentially quantified prejacent proposition? I will argue that we can make this assumption in some cases but not in all of them.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The interpretation of these examples is straightforward, based on our previous discussion. What happens in (41a) is that only denies all relevant alternative propositions of the form 'some Xs are confident'. What is denied is that some students are confident, some administrators are confident, etc. Take all the individuals that at least one of the alternatives to 'professor' is true o£ The truth-conditions of (41a) then amount to the claim that among all those individuals the only ones that are confident are professors. Whether there is any commitment to the claim that there are in fact such individuals depends on the status of the Hom-ingredient. If we say that the truth of the prejacent is presupposed, then it is presupposed that some professors are confident and it is denied that anyone else is confident. Note that in this way, the assertion of (41a) amounts to the claim that everyone (in the relevant domain) who is confident is a professor. In effect, (41a) is the converse of All confident people are professors. We can now see that we would get close to salvaging the convertibility doctrine for the target sentence Only professors are confident, if we could argue that it contains an existentially quantified prejacent. For (41b), matters are essentially parallel, except that there we are dealing with quantification over situations or cases. Only denies all alternatives of the form 'we sometimes play soccer if X', where we consider alternative weather conditions X That results in the claim that any situation in which we play soccer has to be one in which the sun is shining. In effect, (41b) will be the converse of If we play soccer the sun must be shining.27
Kai von
5.2. 1
Fintel 21
Bare plural prejacents
When we look at bare plurals that naturally get an existential reading, we can safely assume that when such structures are embedded under only we will have no difficulty in getting the right interpretation: (43)
a. I made cookies last night. b. I only made [COOkies]F last night.
(44) Professors are confident. One of the well-known results of the research on bare plurals cited earlier is that bare plural subjects of individual-level predicates like be confident are reliably read as being universally/generically quantified. (44) means that professors in general are confident, not merely that some professors are confident. In isolation, then, the putative prejacent proposition of the sentence Only professors are confident does not have an existential reading. How should we react to this situation? There are three possible reactions. First, we could take this to be a demonstration that we should not assume that our target sentences involve prejacent propositions, i.e. we could abandon Option (i) and return to Option (ii). But since we had reasons to be wary of Option (ii), let's not give up just yet. Second, we could try to heroically maintain that while (44) by itself does not have an existential reading, when this structure is embedded under only something somehow licenses Existential Closure. Third, we could take the observation at face value: the prejacent is a generally quantified proposition, and we'll have to fmd some way of getting the right interpretation for when only gets added to it. In the rest of this section, I will go through some evidence that may help us decide the matter. There is one argument for existential prejacents (other than the fact that it would make the interpretation of our target sentences straightforward). And there is one argument for generic prejacents in at least some cases (other than the fact that it might be hard to come up with a story of how existential force comes to be more widely available under only). I do not want to reject once and for all the possibility that we have existential prejacents throughout; but I do have a neat account which gets
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The example in (43a) is one where it is unproblematic to assume that Existential Closure applies to give cookies existential force: there are some cookies that I made last night. When only is added, as in (43b), alternatives to that existential claim are denied: it is false that there are some cakes or ice-cream sundaes that I made last night. Things get more difficult when we tum to cases where bare plurals occur in a context where they normally cannot get an existential reading:
22 Bare Plurals, Bare Conditionals, and Only us the right interpretations even in the case of generic prejacents. So I will try to convince myself and the reader that it is worth considering that account. 5.2.2
Maybe we do have an existential prejacent
The best argument for an existential prejacent even in apparently recalcitrant cases such as only professors are confident comes from thinking about the Hom-ingredient of the meaning of only. Remember that we might want to claim that the truth of the prejacent proposition 1s presupposed or implicated. Consider the following examples: Only Only Only Only
(proFESsors]F are confident. [DEmocrats]F supported Clinton. [inTELligent people]F are physicists. [WOmen]F have blue eyes.
from Hom ( 1 996) from Barker (1993) from Kiss ( 1994)
It is obvious that speakers who utter these sentences do not have to presuppose that professors in general are confident, that all democrats supported Clinton, that all intelligent people are physicists, and that all 28 women have blue eyes. So, .if what we feel these sentences as signaling about the speaker's presupposition is a straightforward clue as to what the prejacent proposition is, we have to conclude that we are dealing with existentially quantified prejacents. And that would be so even though the putative prejacents uttered on their own are not readily understood existentially. Let me also consider one only if-example where the presupposition seems to be less than universal: (46) George is a cat only if he is a mammal. Barker (1993) thinks that this does not presuppose that if George is a mammal he is a cat. He must have a reading in mind where (46) means the same as (47): (47) George can be a cat only
if he
is a mammal.
(Otherwise, he must be something else). Then (46) may actually involve an existential prejacent, as made explicit by can in (47). The presupposition of (46)/(47) would be that if George is a mammal he gn or � be a cat, which is harmless enough. I'm not sure however that (46) can be read that way. To my ear, it does presuppose that if George is a mammal he is a cat, absurd as that sounds at first glance. A natural context would be one where we have established that George is either a cat or a small lizard. Then, (46) and its (universal) prejacent are true.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
(45) a. b. c. d.
Kai von
Fintel 23
But at least for bare plurals, the observation seems to stand: we do not reliably get strong universal presuppositions, instead the presupposition seems to have at most existential force. If this observation accurately reflects the actual interpretation of the prejacent, then we have an argument for existential prejacents. 5.2.3
Against assuming existential prejacents throughout
The best argument for generic prejacents in at least some cases involves negative polarity. Bare plural noun phrases in the scope of only can contain negative polarity items (NPis): this course.
NPis are not licensed in existential sentences of the relevant kind:
(49) #Some students who have any experience in math (managed to) master(ed) this course.
NPis are licensed in quasi-universal sentences of the relevant kind: (so) (All) students who have any experience in math (managed to) master this course. Finally, attaching only to a clearly existential prejacent does not rescue NPis:
(51) #Only sm students who have any experience in math (managed to) master(ed) this course.
As Hom ( 1996) observes, NPis are only licensed in a bare plural in the scope of only if there is a causal/lawlike force to the prejacent:
(52)
a.
Only (those) students who have any siblings need to complete the survey. b. #Only (those) students who have any siblings happen to have passed the exam. c. Only (those) students who have ever been to Europe need to complete the survey. d. #Only (those) students who have ever been to Europe happen to have passed the exam.
Lastly, NPis that are licensed in only-bare plurals are exactly those that are licensed in generic bare plurals. So-called strong NPis are not licensed:29
(53)
a.
#Members who have paid a red cent towards their bills can renew their membership.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
(48) Only students who have any experience in math (manage to) master
24
Bare Plurals, Bare Conditionals, and
Only
b. #Only members who have paid a red cent towards their bills can renew their membership. The obvious conclusion, arrived at by Irene Heim (MIT class discussion, 4/22/94), is that what licenses NPis in the scope of only is the genericity present in the prejacent.30'31 5.2.4
The prospects for the existential prejacents account
(s4)
a. Monkeys live in trees. b. Monkeys live in that tree.
While the bare plural subject of (s4a) cannot be read generically, an existential reading surfaces (and is preferred) in (s4b). These observations suggests that existential readings can be manu factured in ways that are as yet ill understood. Perhaps then, only somehow helps create existential readings in configurations where they are not normally available. Consider the case of the flag over Buckingham Palace: (ss) a. They only hoist the flag if [the QUEEN is home)p. b. They hoist the flag if the Queen is home. c. They sometimes hoist the flag if the Queen is home. The prejacent of (ssa) when read on its own as in (ssb) does not have an existential reading like the overtly existential example in (sse). In fact, (sse) couldn't even be embedded under only. (s6)
a. ?*They only sometimes hoist the flag if [the QUEEN is home)F. b. They only ever hoist the flag if [the QUEEN is home)p.
Only does not easily allow an existential quantifier sometimes in its scope as in (s6a). Instead, what is required is the negative polarity item ever as in {s6b). Now, we could try saying that only somehow licenses a silent ever, and that bare conditionals do not allow silent ever because they are not in the scope of a negative polarity licenser. I invite other researchers to continue this line of argumentation. I remain skeptical. To some extent, I would just like to stamp my foot and claim that we should not blithely assume that bare plurals can get existential force by magic when they occur under only. Compare:
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Recently, researchers have pointed out more and more observations which suggest that bare plurals can more easily be read existentially than was assumed in much of the earlier literature. Some discussion can be found in Fernald (1994), McNally (199s). and Glasbey (1997). Consider an example from Glasbey:
Kai von
(57) a. a'. b. b'.
Fintel 25
I like operas by Bellini. I like an opera by Bellini. I only like operas by Bellini. I only like an opera by Bellini.
·
5.2.5
What do with the Hom-ingredient
If I want to seriously consider the possibility that our only-sentences at least sometimes involve generic/universal prejacents, I need to say something about the argument in section p.2 from the Hom-ingredient.' How should we respond to the observation that someone who asserts the sentences in (45) is not committed to a quasi-universal claim? What is going on in examples such as (58)? (58) Only birds have feathers and
{
}
not even all of them do even among birds there are . some without feathers.
One possibility is that (45) and (58) somehow readily allow weakening or cancelling of the presupposition. Consider more familiar kinds of examples where the presupposition of truth of the prejacent is suspended: (59) I love only you and even about you I have my doubts. Hom
has
consistently used such examples to argue that the truth of the
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
For some reason, a generic reading is preferred in (57a), while (57a') seems to have only an existential reading, if it is at all felicitous. Now, if only were somehow to license existential prejacents, no matter whether they were felicitous in the structure without only, we wouldn't expect there to be a contrast between (57b) and (57b'). The addition of only should wipe out the difference between the prejacents. But that's not what happens. (57b) is read as having a generic prejacent: I like Bellini operas in general and no other operas. (57b') is read as having an existential prejacent: the only opera I like is a Bellini opera. Perhaps, a more serious version of this foot-stomping is the observation that there is no case where bare conditional sentences have existential force: they typically involve quasi-universal force or some kind of necessity. So, in distinction to bare plural sentences, which at least sometimes surface with existential force, bare conditionals never do so. While I do have these doubts about the prospects for the existential prejacents theory, I do not pretend to have disproved it. But I wish to present a solution to our problem which works even if the prejacent is generically quantified.
26
Bare Plurals, Bare Conditionals, and
Only
prejacent is not an entailment but a suspendable presuppositioiL Perhaps, we should read (58) in the very same way. Another possibility is that we cannot use the Hom-ingredient as a clue about the semantics of the prejacent. Perhaps, there is no such thing as the Hom-ingredient. Perhaps, the truth of the prejacent simply isn't presupposed or entailed. I leave the matter in this unresolved state and now propose to see whether we can arrive at a good analysis of what our target sentences mean under the assumption that the prejacent is not always existentially quantified, but at least sometimes has generic or universal force.
Consider again the prejacents of these examples: (6o) a. b. c. d.
Only professors are confident. prejacent: Professors are confident. We play soccer only if the sun shines. prejacent: We play soccer if the sun shines.
We are now working with the assumption that our only-sentences involve the following logical structure (again short-circuiting the complications of the cross-categorial approach): (61) a. onlyc [GEN [professors] [are confident]] b. onlyc [GEN [if the sun shines] [we play soccer]] We need to ask: what are the alternatives in the domain of only in these examples? What is the focus structure of the prejacent? For only if, there is an attractive option: assume that the focus is somehow such that the only relevant alternative to if p, q is if not p, q. Then, only would say that it is not true that if not p, q. This is arguably a fairly reasonable interpretation: from only ifp, q we get not (if not p, q). From there, we could proceed via the Excluded Middle to if not p, not q, and further via Contraposition to if q, p. Thus, we would be able to derive the convertibility of only ifp, q and if q, p. (We will discuss the status of the needed principles of Excluded Middle and Contraposition in section 7.) What would we have to say about the focus structure of the prejacent to get this result? Barker (1991, 1993, 1994) suggests that the relevant focus is on the auxiliary (if there is one) or on if itsel£ He gives some persuasive examples of even if-conditionals:
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
6 WIDE F OCUS ?
Kai von
{6z)
Fintel
27
a. Don't worry, the party will be fme even if Basil DOES tum up. b. But even IF Basil turns up-which is highly unlikely-it is very improbable that he will cause any trouble, so the party won't be ruined.
{63) It probably won't rain and a. the game will only be cancelled if it DOES rain. b. the game will only be cancelled IF it rains. These examples could thus also be analyzed as involving focus on the polarity of the if-clause.34 Unfortunately though, the analysis would not be able to carry over to the generic examples where there is no way of focusing that would signal the negation of the common noun phrase as the relevant alternative. Luckily, there seems to be another way in which we could get the right meaning. We could assume that (i) focus is on the whole restriction of the implicit quantifier, (ii) the domain of alternative restrictions includes very specific kinds of restrictors. To get the idea, consider the bare plural example Only professors are confident. Assume quite plausibly that there is focus on the common noun phrase professors, that the focus does not include the quantificational operator, that therefore all alternatives to the universal prejacent have (quasi-)universal force as well. If we assume that the domain of alternatives only includes propositions in which professors is replaced with contrasts like students, politicians, steelworkers, and so on, we would obviously get an incorrect meaning. In that case, the o nly-claim would be that not all (normal) students are confident, not all (normal) politicians are confident, not all (normal) steelworkers are confident, and so on. That would clearly be much too weak an interpretation. (6oa) excludes � (normal) student, politician, or steelworker from being confident (unless she is a professor as well). But now we could avail ourselves of a trick: imagine that the domain of alternatives is much larger. Contrasts to the property of
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The treatment of the example in (6za) is presumably unproblematic from the point of view of fairly standard assumptions. Focus on the auxiliary is interpreted as focus on the truth polarity of the sentence.32 The relevant alternative to 'Basil does tum up' is 'Basil does not tum up'. The example in {6zb} is a little more tricky: we would have to assume the relevant alternative to the complementizer if is if . . . not. Barker suggests that this is a problem for a Kratzer-style theory of conditionals since there if is not given much of a meaning, and he attempts to argue that these facts provide evidence for a pragmatic theory of if.33 Do such examples carry over to only if-conditionals? Perhaps they do:
28
Bare Plurals, Bare Conditionals, and
Only
(64) Only if [the QUEEN is home]F do they hoist the flag.
As pointed out to me by Satoshi Tomioka (p.c.), (64) does not convey that the flag is not hoisted if the King is home (too). It merely says that the flag is not hoisted if the Queen is not home. That means that even though there is a pitch accent on the subject, we would want to say that there is sentence focus here. This is unproblematic since pitch accents on subjects of unaccusative verbs are able to project to sentential focus, according to standard assumptions. But when we look further we fmd that we cannot always assume that we have wide focus on the entire quantifier restriction.35 Consider examples such as these: (6s)
a.
b.
Only (BLUE]p-feathered birds fly to the Galapagos Islands. A. Can I call you tomorrow about this issue? Or would that get you mad? B: No, go ahead and call me. I will only get upset if you call me [after MIDnight]F·
These examples can clearly be read as involving narrow focus internal to the quantifier restriction. (6sa) can be read as making a claim only about birds of various kinds of feathers, perhaps other kinds of flying animals, bats for example, migrate to the Galapagos Islands as well. (6sb), due to Irene Heim, only talks about the speaker's getting upset about the timing of phone calls; in no way does it exclude the possibility that she might also get upset about the garbage not having been taken out. We need to be able to account for such examples as well. Here, the trick of assuming a large domain of very specific alternatives will not work. On to the last candidate analysis.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
being a professor might include the property of being identical to Jane Smith, etc. Such a large domain of very specific alternatives would get us the right result. The same maneuver can be contemplated for only if-examples, as suggested to me by Roger Schwarzschild (p.c.). Imagine that the alternatives to if the sun shines include restrictions such as if it rains six and a half inches on Sunday September 8, 1996. Then, denying that all of those situations are ones in which we play soccer will result in the appropriate force. Can we safely assume that in all of the relevant examples focus is on the whole restriction of the prejacent quantifier? We can definitely find examples with such broad focus. The sun-shine example (6oc) is presumably a case in point. Consider also:
Kai von
Fintel 29
7 GENERICS, C ONDITIONALS, EXCLUDED MIDDLE, AND C ONTRAPOSITION 7.1
The puzzle restated
What would we need to assume to make the right predictions for cases where only attaches to a (quasi-)universal prejacent with focus inside the restriction of the (quasi-)universal quantifier?
(68) onlyc
[{ GE
..
[
\ . )q)]
iff -, [GEN{p')(q)] & -,[GEN{p")(q)]
{By the semantics of only and focus) At this point, it would be really nice if we could assume that GEN obeys two classic principles: the Excluded Middle and Contraposition. Because then we could proceed as follows:
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The schema in {66) covers both the case in {67a) where we have (quasi-) universal quantification over individuals (a generic sentence) and the case in (67b) where we have (quasi-)universal quantification over 'cases' (or situations, or worlds, or states of affairs; a conditional sentence): (67) a. Only [BLUE)p-feathered birds fly to the Galapagos Islands. b. Jane will only get upset if you call her [after MIDnight]p. Our semantics for only would say the following about such structures. The assertion of the only-sentence is that none of the relevant alternatives to the prejacent is true. The alternatives to the prejacent are (quasi-)universal claims that differ from the prejace�t in {part of) the restriction of the (quasi-)universal quantifier. Therefore, (67a) would deny that all normal red-feathered birds fly to the Galapagos Islands, that all normal green feathered birds fly to the Galapagos Islands, and so on for all relevant contrasts to blue. And (67b) would deny that in all normal cases where you call Jane before midnight she will get upset. But these predicted truth conditions seem much too weak. {67a) is actually falsified by the existence of one normal red-feathered bird that flies to the Galapagos Islands. {67b) is falsified if Jane got upset because of one late phone call. Let me lay out the logical situation here. For the moment, let me ignore the Hom-ingredient, the presupposition or implicature that the prejacent is true. Assume also that the relevant contrasts to p are p' and p". What we have then is this:
30 Bare Plurals, Bare Conditionals, and Only
{69) onlyc
[••{ /
J
l
The Excluded Middle There are two ways that I can see to validify the Excluded Middle for generics and conditionals. One approach assumes that these kinds of sentences involve reference to an entity about which a claim is made. Negating such a claim then amounts to the same thing as attributing the contrary property to that entity. The other approach traces the Excluded Middle back to a presupposition carried by the implicit quantifier in such structures. 7.2
7.2. 1
The entity approach
Take a sentence about the entity John: John left. Denying such a statement by It is not true thatJohn left amounts to the same as attributing the predicate did not leave to John. Proper names thus trivially satisfy the Excluded Middle. For conditionals, Stalnaker has argued that their interpretation involves reference to a single world selected &om among the worlds in which the antecedent of the conditional is true. Stalnaker's assumption can be cast within our sketch of an analysis of GEN as follows: the selection function selects one case &om the domain of quantification supplied by the if-clause.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
{q) .] , iff •[GEN(p')(q)] & •[GEN{p")(q)] (By the semantics of only and focus} iff [GEN{p1)(•q)] & [GEN(p")(•q)] (Excluded Middle) iff [GEN(q)(•p') & [GEN(q)(•p")] (Contraposition} If we then assume that in all relevant cases one of p, p', or p" is true, we can deduce that GEN(q)(p). We would have reached the traditional meaning of our sentences. Our problem now is that universal quantifiers do not in general obey the principle of the Excluded Middle. If not every A is a B, it doesn't follow that every A is a non-B, but merely that some A is a non-B. But of course, what we know about the semantic behavior of universal quantifiers like every is quite irrelevant here. The structures that we are investigating involve not the determiner every but the implicit quantifiers posited to give a semantic analysis of generic sentences and conditional sentences. Perhaps then, we should seriously contemplate the possibility that these implicit quantifiers do obey the Excluded Middle.36
Kai von
Fintel 3 1
(7o) a. Only [MAMmals]F give live birth. 'Among the relevant alternatives, the only kind that gives live birth is the kind "mammals" '. b. Only owners of [RED]F cars need to pay extra insurance. 'Among the relevant alternatives, namely owners of cars of a certain color, the only kind that needs to pay extra insurance is the kind "owners of red cars" '. c. I only like [FRENCH]F movies. 'Among the relevant alternatives, namely kinds of movies, the only kind that I like is the kind "French movies" '. Given that (7oa) denies that the kind 'reptiles' gives live birth can we infer that any animal that gives live birth is not a reptile? What we have is that the kind 'reptiles' doesn't give live birth. Does this entail that no reptile gives live birth? Offhand we wouldn't know, because we don't know what it means for a kind to give live birth or what it means to deny that a kind gives live birth. But, in Carlson's account, we have the necessary leeway to introduce stipulations about generic properties, about predicates generated by the generic predicate operator Gn. One such stipulation might be that if a kind has the generic properties Gn{P), then a significant number of k-individuals must have the individual-level property P. The stipulation that we need to get the right readings for only-sentences is this: {71) The Generic Excluded Middle For any kind k and any property P, if • [Gn{P)](k), then -, 3 x E k: P{x). When a kind is denied to have a generic property Pko then any of its individuals cannot have the corresponding individual-level property Pi.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
If we now deny the truth of a conditional ifp, q, what we are saying is that the selected p-ease is not a q-case. This amounts to asserting that the selected p-ease is a non-q-ease. Thus, Stalnaker's semantics for conditionals validates the Excluded Middle. Lewis (1973a, b) has attacked Stalnaker's assumption and Stalnaker (1968, 1981, 1984) has defended it. We will soon come back to one of the moves in this debate. Carlson (1977a) argues that bare plurals are proper names of {natural) kinds. For example, Mammals give live birth attributes to the kind 'mammal' the predicate 'gives live birth'. Whether such kind-level predications can be reduced to or supervene on (quantificational) facts about individual members of the kind is not relevant to the logical form of such examples, which is non -quantificational. Some of our problematic sentences would get the following meanings:
32 Bare Plurals, Bare Conditionals, and Only
Here then in a nutshell is this analysis of only + bare plurals: only Qs are Ps says that no kind R alternative to Q has the property P. If the property is a stage-level property, that means that R doesn't have any instantiations that satisfy P. If the property is a generic property that means that R doesn't have Gn(P), which in tum means that no instantiations of R have P (by the Generic Excluded Middle). Such an account would explain Carlson's observation (1977a: 84-5} that the negation of a generic sentence is always also a generic sentence: (72) Bill doesn't like wombats.
(73) a. #A bird is common. (vs. Birds are common). b. Only a bird has feathers. To analyze {73b) we have to posit a quantificational operator GEN. At least here, we cannot obtain the Excluded Middle from appealing to reference to kinds. I'd like to discuss one more example of an analysis that derives the Excluded Middle from reference to an entity. LOhner (1985, 1987a, b) argues that definite plural noun phrases have the logical property of completeness ('If the predicate P is false for the NP, its negation not-P is true for the NP'). Consider a situation where all of ten children are playing, among them are three boys and seven girls. The following judgments seem to be natural:37 (74) TRUE: The children are playing. FALSE: The children are not playing. ?: The children are boys. He writes: 'the referent of a definite NP cannot be split in case the predicate holds only for some part of it, but not for the whole. Without any differentiating modification of the predication, the alternative is just that of global truth or global falsity. If it is impossible to apply the predicate or its negation globally it fails to yield a truth-value' (1987a: 185). In LOhner (1987a: 83), he calls this the 'presupposition of argument homogeneity', which says that 'the argument of a predication is homogeneous with respect to the predication'. In the following section, I will sketch an approach that obtains the
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
This has no reading where the generic force is negated, no reading along the lines of'it's not true that Bill likes wombats IN GENERAL, just that he likes SOME of them'. Unfortunately, Carlson's analysis would not extend to other cases we considered. Singular indefinite generics do not allow kind-level predication, but they do give rise to the readings under only that we are interested in:
Kai von
Fintel 33
Excluded Middle for generic sentences and conditional sentences without making special assumptions about ontology. 7.2.2
The Homogeneity Presupposition
(75) The Homogeneity Presupposition [GEN](£)(p)(q) is only defmed for w if ['v'x E f(w)(p): q(x)] V ('v'x E f(w)(p): •q(x)] From this it follows directly that the Excluded Middle is obeyed: (76) The Excluded Middle [GEN](£)(p)(q) is false in w iff [GEN](£)(p)(•p) is true in w, or shorter:
•[GEN](p)(q) iff [GEN](p)(•q).
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Lewis criticizes as unrealistic Stalnaker's assumption that a single antecedent world is selected by the selection function involved in the semantics of conditionals. Taking for granted that what the selection function selects from among the antecedent worlds is the world(s) most similar to the evaluation world, it is unlikely that there is only one such most similar world. Stalnaker responds that one could simply assume that in such cases a supervaluation procedure is used to obtain the proper interpretation. If all of the most similar worlds behave the same with respect to the consequent proposition, it won't matter which one of them is selected. In effect then, conditionals :i la Stalnaker presuppose that all of the selected worlds are uniform with respect to the consequent. What I would like to suggest is that this is a presupposition tied to the implicit operator GEN. Here is a precedent: Janet Fodor argues in her dissertation (1970: 159-67) that both deftnite plurals and generic bare plurals carry what she calls an 'aU-or-none' presupposition. If someone says that the children are asleep, it is presupposed that either all of them are asleep or none of them, and it is asserted that all of them are asleep. This presupposition explains why saying that it is false that the children are asleep amounts to claiming that none of them is asleep. Similar thoughts apply to generic bare plurals. Note that this is very similar to LOhner's argument two decades later. However, LOhner takes an approach where plurals refer to higher-order entities and then assumes a principle that says that properties attributed to such entities have to be uniform with respect to the constituents of that entity. Fodor, on the other hand, assumes implicit quantification and attributes an 'aU-or-none' presupposition to the implicit quantifier. This then is what I propose to assume: GEN is lexically specified to trigger a Homogeneity Presupposition, which means that generic bare plural sentences and bare conditional sentences will obey the Excluded Middle:38
34 Bare Plurals, Bare Conditionals, and Only Ultimately, we would hope to explain why the Homogeneity Pre supposition is observed with implicit quantification as in (77) but not with overt quantification as in (78): a.
(77)
Are the children asleep? No. b. Do mammals lay eggs? No. c. Will this match light if I strike it. No. d. Would John have passed the test if he had studied for it? No.
(78)
a.
The idea behind the Homogeneity Presupposition is that a speaker who chooses a sentence involving GEN rather than one of the overt quantifiers signals that it is presupposed that the cases in the domain of quanti fication are uniform with respect to the property attributed by the scope of the quantifier. Take someone who asks Do mammals lay eggs? Choosing GEN signals that it is taken for granted that mere mammal hood will determine whether an animal lays eggs or not. Therefore, either all mammals lay eggs or none of them does (modulo irrelevant exceptions). The Homogeneity Presupposition may be subject to contextual cancellation. Paul Portner (p.c.) gave me the following example:
(79)
A:. I need a kind of bird which is always black (for my poem, I'm trying to finish the line 'Quoth the x, . . . '). I'm considering ravens,
B:
eagles, and vultures. I've seen black examples of each. Do you know whether any of them are consistently black? RAVens are black.
Clearly, B can't presuppose that ravens are all black or all non-black. That is what A is asking. What is important for my analysis of our only-sentences is that the Homogeneity Presupposition is at work there; no reason for it to be cancelled seems available. Larry Hom (p.c.) objects to the Homogeneity Presupposition. He finds himself unconvinced by my claim that we can't deny that humans are violent without asserting the contrary claim with inner negation. He admits that the most natural way of rej ecting the generic claim is by using an overt quantifier: 'No, you're wrong. Humans aren't necessarily violent.' But he
does think that one can deny the generic without an overt quantifier: 'No, you're wrong. Humans are NOT violent. Just SOME humans are.' For me,
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Are all the children asleep? No. b. Do all mammals lay eggs? No. c. Will this match necessarily light if I strike it? d. Would John necessarily have passed the test if he had studied for it? No.
Kai von Fintel 35
such examples, if possible, have to involve metalinguistic or echoic negation. Krifka (1996) talks about some of the same data that motivate us to propose a Homogeneity Presupposition but argues that they can be explained by a process of pragmatic strengthening.40 I don't know whether it is crucial that we assume that Homogeneity is a presupposition. Perhaps all we need is that it is an assumption that can feed the inferences that we automatically draw from a statement. Perhaps we don't have to conclude that the Excluded Middle is part of the lexical meaning of GEN, as long as certain pragmatically derived inferences are available to the semantics. •
39
Contraposition
We could stop here. Perhaps, only ifp, q is best paraphrased as if not p, not q, which is of course what we get in our analysis once we obtain the Excluded Middle. Perhaps also, it is enough to predict that only ps are qs amounts to the claim that non-ps generally are non-qs. But, just out of curiosity, what would be involved in going further to salvage traditional intuitions and getting only ifp, q to entail ifq, p and getting only ps are qs to entail that qs are ps? Let us consider what we would need:
[ c.. [c•{ .
\. )q)] "' G£Nh)(�q).
(8o) What we now predict (assuming the Homogeneity Presupposition): oniyc GEN
[.
\ . . ) (q)] "' GEN(q)(p).
What we might want: onlyc
.
[.
The obvious way to get this would be to say that the implicit quantifier involved in our structures allows Contraposition: GEN{•p)(•q) <=> GEN{q)(p). Contraposition is an inference that the standard universal quantifier supports. It is also supported by material implication and by strict implication. It is however not supported in the Stalnaker-Lewis semantics for conditionals. Since we drew considerable inspiration from that semantics, we should be skeptical about the prospects for Contraposition being supported by GEN. In the following discussion. I will concentrate on Contraposition in bare conditionals. But parallel considerations should apply in the case of generic sentences {Contraposition hasn't been discussed much in the literature on generics).
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
7.J
36 Bare Plurals, Bare Conditionals, and Only
Here are two counter-examples to Contraposition for conditionals: (8 1) Failure of Contraposition a.
=
=
=
=
p
p
-
q
q
Counter-examples to Contraposition are often given in the form of even if-conditionals. The reason can be intuited from the picture: the crucial fact is that q is true throughout the selected ranked p and non-p-cases. We'll soon come back to this fact. Let us look again at the semantics of GEN, which at the moment looks like this: For a either e or s, for all p, q E D(a, t}o f E D(s,(cn,ut)}o and worlds w: [ GEN](f)(p)(q) is defined for w only if (i) 3 x E f(w)(p), (ii) [\fx E f(v1(p): _,(x)] V [\fx E f(w)(p): -.q(x)] . Where defined, � GEN](f)(p)(q) is true in w iff Vx E f(w)(p): q(x).
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
If it rained, it didn't rain hard. =fr If it rained hard, it didn't rain. (Even) if Goethe hadn't died in 1832, he would still be dead now. b. =fr If Goethe were alive now, he would have died in 1832. The basic move that invalidates Contraposition in the Stalnaker-Lewis semantics is this. Recall that the conditional does not make a claim about simply every antecedent case, nor even about every contextually salient antecedent case. The idea is there is a (contextually salient) selection function that for any conditional selects a subset of the antecedent cases to quantify over. Contraposition then fails because the fact that the selected p-cases are q-cases does not preclude a situation where the selected non q cases are also p-cases. Take the Goethe-example and suppose that the selection function here is based on a comparative similarity relation, so that the antecedent cases selected are those that are maximally similar to the evaluation world. The selected p-cases in which Goethe didn't die in 1832 are all q-cases where he nevertheless dies (well) before the present. But of course, the selected (in fact, all) non-q-cases (where he is alive today) are also p-cases where he didn't die in 1832. Here's a picture of the situation: p Goethe didn't die in 1832 (82) p Goethe died in 1832 q Goethe is alive now q Goethe died before now
Kai von
Fintel
--t -,
--t
-,
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The detail in here which gives rise to the particular logical properties of the Stalnaker-Lewis semantics is the fact that the selection function f is sensitive to the antecedent p. There is an alternative, dismissed in most work on conditional semantics but defended in my paper 'Conditionals in a Dynamic Context' (von Fintel 1997a). I argue there that what happens in the apparent counter-examples to Contraposition (and some other inference patterns) is that the context in which the conditional is evaluated shifts midway through the example. The positive proposal is that conditionals quantify over a contextually restricted set of relevant cases. They carry a presupposition that the antecedent proposition is compatible with the set of relevant cases. If that pre supposition is not fulfilled, because we have moved to considering a proposition not previously considered, the contextual domain will have to be adjusted. It is the dynamics of domain restriction that leads to non monotonicity, which is not a strictly semantic fact but a fact of discourse dynamics.41 The semantics for GEN that comes out of this proposal looks as follows: (84) For cr either e or s, for all p, q E D(,.,t)• f E D(s,ut)• and worlds w: [GEN](f)(p)(q) is defined for w only if (i) p is compatible with f(w): 3 x E f(w): p is true of x, q(x)] . (ii) [Vx E f(w): p(x) q(x)] V [Vx E f(w): p(x) Where defmed, [GEN](f)(p)(q) is true in w iff [Vx E f(w): p(x) q(x)] . Note that here the selection function is replaced by a function that assigns a set of relevant cases to the evaluation world. Since there now is no fickle sensitivity to the antecedent p. there will be fewer cases where logical inferences are disrupted. This perspective leads to the following diagnosis. Something very much like Contraposition will be valid under two additional conditions: (i) q is compatible with the context (i.e. if q doesn't hold throughout the domain of relevant cases), and (ii) q doesn't presuppose p. The counterexamples to Contraposition presented in the literature fail one or both of these conditions. Condition (i) is fulfilled by most ordinary conditionals. If q holds throughout the domain, then p is not a condition for q. Ordinary conditionals may even carry a presupposition that (i) holds (discussed among others by Kratzer in her dissertation). An exception are concessive conditionals/semifactuals/even if-conditionals:42 (8s) (Even) if Goethe hadn't died in 1832, he would still be dead now. =fr If Goethe were alive now, he would have died in 1832. The elements even and still explicitly signal that the consequent is true --t
•
37
38 Bare Plurals, Bare Conditionals, and Only
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
throughout the relevant sphere of cases. A new conditional with the negation of the original consequent as its antecedent would therefore have to move outside the previous contextual domain. The premise, (Even) ifGoethe hadn't died in 1832, he would still be dead now, explicitly signals that all relevant cases are cases in which Goethe is dead. The antecedent of the conclusion then clearly moves outside this realm of cases by supposing that Goethe was still alive. This kind of example therefore demonstrates that Contraposition appears invalid if the consequent of the conditional holds unconditionally throughout the relevant domain. There are counter-examples that lack the explicit marking seen in (8s): (86) a. If it rained, it didn't rain hard. -=/? If it rained hard, it didn't rain. b. If she wrote a letter to Santa Claus, she didn't get an answer from him. -=/? If she got an answer from Santa Claus, she didn't write a letter to him. Both examples still have the property that the consequent is true through out the relevant domain. (86a), due to Jackson I believe, explicitly says that in all of the cases in which it rained, it didn't rain hard. But of course, if there are relevant cases in which didn't rain, it must a fortiori have not rained hard in them. Thus, throughout the domain it didn't rain hard. The same goes for (86b), from McCawley (1993). In both cases then, the contraposed version will take us outside the relevant domain, thus creating the impression that Contraposition is invalid. Both examples have an additional property: they say ifp, not q, where q presupposes p in some sense. Thus, it becomes strange indeed to say ifq, not p. Not only do the contraposed versions take us outside the relevant domain, they can in fact never be true. This is then another possible source of counterexamples to Contraposition. And this may seem to be a much more pervasive problem than the one created by conceSSive conditionals. Here are some more example, due to McCawley: (87) a. If I do heavy exercise, my pulse goes above roo. -=/? If my pulse doesn't go above roo, I don't do heavy exercise. b. If the Police start tapping your phone, you're in danger. -=/? If you're not in danger, the Police don't start tapping your phone. McCawley's diagnosis of what goes wrong here seems correct: it matters which clause is the antecedent and which the consequent, because there are asymmetric temporal/causal dependencies involved. In effect, the conse quent depends on the antecedent in its interpretation. Such donkey
K.ai von
Fintel
39
dependencies, whether temporal/causal or having to do with the reference of noun phrases, are of course extremely common. Do we have to give up on Contraposition altogether? Not really. What these examples show is that Contraposition is not a recipe for constructing paraphrases by switching antecedent and consequent and inserting negation into both. Contraposition is a property of the semantics of the quantifier GEN . What we have is this: (88) For any f, p, q, true in w.
w:
[GEN] (f )(p)(q) is true in w iff [GEN] (f )(..., q)(• p) is
(89) If I call John at some time in the night, he calls me (back) ten minutes later. What should the contraposed conditional express? (89) leads us to infer that at any point in time at which John doesn't call me, I can't have called him ten minutes earlier. Otherwise, we'd have a situation that would falsify (89). There doesn't appear to be an ear-pleasing way of phrasing the contraposed version. But Contraposition still holds in a certain sense. Every relevant case in which the consequent is false is one in which the antecedent is also false. Let us try this a little more formally. Assume that the cases that (9oa) quantifies over are times (across a contextual domain of epistemically accessible times in epistemically accessible worlds). Assume that what the sentence expresses is formalized as in (9ob), which roughly says that all relevant times at which John wins the race are times that are followed (closely?) by a time at which we celebrate: (9o)
a.
If John wins the race, we will celebrate. ' b. GEN(f )(-\ t wins (j ,t))(-\ t 3t' � t (celebrate(we,t )))
Now, contrapose (9ob) and you get: ' (9o) c. GEN (f )(-\ t --, 3t' � t (celebrate(we,t )))(-\ t --, wins (j ,t)) This says that any relevant time that
not (closely) followed by a time at which we celebrate is a time at which John doesn't win the race. Under reasonable assumptions (which I leave to the reader to identify), (9oc) is now equivalent to the following:
is
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
But since there can be a number of implicit semantic ingredients in these structures we are not guaranteed that simple syntactic operations concluded at the surface will give us the proper contraposed form of a conditional statement. If part of the original structure was an implicit dependency between the two sets of cases, that dependency has to be maintained. Try it on a simple example that involves an explicit temporal dependency:
40 Bare Plurals, Bare Conditionals, and Only
(9o) d. GEN(f}(.Xt .., celebrate(we,t}}(.Xt .., 3t' � wins(j ,t')) This says that any relevant time at which we don't celebrate is one that is not (closely) preceded by a time at which John wins the race. Arguably, this is something we can express in English as follows: (9o) e. If we don't celebrate, John must not have won the race. t
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
So, once we consider the semantics of the original conditional in detail, we see that its contraposed version will have to be something like (9oe). The apparent counter-examples in (87) are not really counter-examples to Contraposition, they j ust show that the proper contraposed versions have to respect the implicit temporal/anaphoric dependencies between antecedent and consequent. The reader might perhaps think that I have been unfair to McCawley here. His claim surely is that the relation of temporal dependence is build into the semantics of the conditio11al operator and not part of the consequent, as I have assumed above. Such a complex operator, which contains the reference to temporal/causal dependency, then clearly does not support Contraposition. But note that the 'backtracking' conditional in (9oe) is a counterexample to such an analysis. Clearly, the temporal dependency here is reversed as signaled by the temporal/aspectual marking in the sentence. I submit therefore that temporal dependency is not built into the conditional quantifier, but is carried by elements in the antecedent and consequent clauses. If we can agree that the quantifier every should validate Contraposition (as the primordial universal quantifier of natural language, modulo the fact that it is a word in a rather recent language), we can see that we should not be too dismayed by McCawley-style counter-examples. Consider: (91) Every man who stole a car abandoned the car hours later. =fo Every one who did not abandon the car hours later is not a man who stole a car =fo Every one who did not abandon a car is not a man who stole the car hours before. There are two anaphoric connections between the quantifier restriction and the scope: (i) the dependency between the indefinite a car and the definite the car, and (ii) the dependency between the time of the theft and the time of the abandoning. Both dependencies need to be handled with gloves when we check the validity of Contraposition. But once we are careful we will see that (91) lets us infer that if there is someone who did not abandon a car, he is not a man who stole the car hours before. Eventually, I think there will be more to be said about how logical
.Kai von
Fintel 41
inferences fare in a setting that deals in a proper way with the dynamic of anaphoric dependencies. There are plenty of subtleties remaining in the analysis of anaphoric connections and dependencies in conditionals that we have to leave aside here. I have dealt with some of these issues in other work and will certainly return to them at some future occasion. When we control for the two factors isolated in this discussion (when we ensure that q doesn't hold unconditionally and that q doesn't presuppose p), we get intuitively valid instances of Contraposition:
(92)
a.
Thus, there seems to be something fundamentally right about the old doctrine of Contraposition.43 Counter-examples come from a well defmed class of cases. The dynamic strict analysis that I argue for in 'Conditionals in a Dynamic Context' gives us the right handle on where to find counter-examples and where to find supporting examples. One kind of counter-example will in fact never arise with only if There will be no cases of only if p, q such that the converse version if q, p is strange because there are no accessible q-cases. Since the prejacent ifp, q is presupposed, we are automatically presupposing that there are accessible q-worlds. That means that the contraposed conclusion will not force us to change the context to make the set of accessible worlds compatible with q. Let us end this section by considering a counterexample to the strong
analysis of only if advocated here. It is due to Robert Stalnaker and is cited by Appiah (1993):
(93)
Count Dracula is coming only if we invited him. Nobody in fact invited him. If he is coming anyway, he'll be here without an invitation. . ·.
The point is that the conclusion (which seems valid) is incompatible with the converse of the only if-sentence (If Count Dracula is coming, we invited him). So it seems that we shouldn't advocate the strong analysis of only if But that again commits the fallacy of shifting contexts. First note that from
the premises we can validly conclude that Count Dracula is not coming. All of the relevant worlds are such that he isn't coming. Then the antecedent of
the conclusion takes us to far-fetched worlds not previously considered. This new conditional in this new context can be true without the old
only if-conditional (and its converse) in the old context being false. But, now
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
If Harry is a cat, then he is a mammal. ::::} If Harry is not a mammal, then he is not a cat. b. [We don't know where Harry and Mary are, but. we know they avoid each other:) If Harry were in Athens, then Mary would not be in Athens. ::::} If Mary were in Athens, then Harry would not be in Athens.
42
Bare Plurals, B are Conditionals, and
Only
note that the old conditional in the new context is in fact false. We can with: respond to
(93)
(94)
But that means that you think that he won't be coming ONLY if we invited him. He might be coming without an invitation.
So, in the new context the first premise is in fact false, which means that the argument in argument in
(93) is built on contextual quicksand. In fact however, the (93) is misleadingly stated anyway since the conclusion follows
from the second premise alone. The
only if-conditional plays no
role in it. I claim that we can assume that our implicit quantillers obey the
Excluded Middle and validate Contraposition. Thus we can achieve a
8
CONCLUSION
Our aim was to develop a compositional semantics for sentences involving only and bare plurals and for only if-conditionals. We saw that an account that can deal with the whole variety of relevant sentences had to assume throughout that the structure modified by only was a quantifi cational construction, although there is no overt morpheme expressing the quantillcational force. For some examples, it may be enough to assume that there is an implicit existential quantification prejacent to
only.
For most
examples, and particularly for all of the conditional examples, we arguably need to deal with a prejacent (quasi-)universal quantification. Some of those can be dealt with by assuming wide focus on the entire quantifier restriction: the large set of relevant alternatives in these cases might suffice to account for the strong meaning of these examples. Lastly, however, we have to deal with examples where focus falls strictly inside the restriction. For those, the perceived meanings could only be accounted for by making substantial assumptions about the semantics of the underlying implicit quantillcation: those quantillers carry a Homogeneity Presupposition and validate Contraposition. What we learn from
this exercise then, is that we can fmd out about the
nature of implicit quantification in natural language by looking at how such structures combine into even more complex constructions. Another lesson, independent of the particular results argued for here, is that analyses in this area should attempt to account for both generic sentences and conditional sentences in some more or less unilled way, because of the close semantic parallels between them.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
compositional analysis of the investigated structures, which to a large extend does justice to some old intuitions about what such sentences mean.
Kai von Fintel 43 append some remarks about structures where the prejacent to only is overtly quantified. I also discuss seemingly simple examples where only combines with a name.
I
Acknowledgments
KAI VON FINTEL Department of Linguistics and Philosophy 77 Massachusetts Avenue Massachusetts Institute of Technology Cambridge, MA 02139
Received: 22.10.96 Final version received: 30.06.97
USA
e-mail:
[email protected]
APPENDIX A: O VERT QUANT I FIERS UNDER ONL Y What happens when only attaches to a prejacent that is overtly quantified? Here I have found an astonishing gap between theory and reality. Consider a simple example like (95):
(95)
Only every [YOUNG)F girl cried.
There are three important facts about (95): (i) it does not seem to allow the expected reading where the universal force is constant across all alternatives. In other words, (95) is not affected by focus in the usual way; (ii) largely, only one interpretation is available, namely the one where no one else cried; (iii) perhaps most importantly, (95) is (almost) unacceptable. Our theory so far predicts that in (95) the alternatives would all involve the same underlying quantificational force, here a universal force. All alternatives would be about girls of various kinds, here perhaps older girls. So (95) might in effect deny (96):
(96) Every older girl cited. This would of course not exclude that some older girls cried. That's the prediction. (95) would mean something like the following paraphrases:
(97)
a.
Only the [YOUNG)F girls all cried. b. Only among the [YOUNG)F girls did every one cry.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
I have benefited immensely from discussion and criticism by Irene Heim, Bob Stalnaker, Renate Musan, Roger Schwarzschild, Regine Eckardt, Larry Hom, Paul Portner, and from class discussions at MIT. Some of the material in this paper was presented at the LSA Annual Meeting in San Diego (January 6, 1996) and at a colloquium at the University of Massachusetts at Amherst (March 29, I 996). The audiences at those occasions helped this paper along quite a bit. Thanks especially to Jim McCawley, Angelika Kratzer, Maribel Romero, and Satoshi Tomioka. Two reviewers for the Journal ofSemantics provided many useful comments. Since in some cases I stubbornly refused to heed the good advice I was given, and since this is only a first attempt at broaching some difficult issues, there undoubtedly remain may shortcomings, for which I take full responsibility.
44
Bare Plurals, Bare Conditionals, and Only
I have my doubts that (95) can really have that interpretation. Here are some other examples that we would expect to have an interpretation where all alternatives have the same (strong) quantificational force: (98)
a.
b.
c. d.
On the whole, these examples are horrible.45 When pressed, native speakers seem to assign such sentences a meaning that excludes everything else having the property in question. (95) is read as claiming that no one else cried, no older girls, no boys, no one. My suspicion is that this is more of a rescue strategy than a genuine semantic analysis. But let's briefly see how we might account for it. We could ignore the normal focus projection principles and assume that the focus in (95) projects beyond the adjective. We could, for example, assume that the whole NP in (95), including the universal quantifier, is in focus. We would then have to figure out what the legitimate alternatives to the universal quantifiers are. Krifka (1993) proposes a stipulation. He argues that a focussed universal quantifier only competes with other ftlters. This would essentially predict that (95) means that noone other than the young girls cried. Irene Heim (p.c.) suggested another possibility: we could assume that the focus in (95) is on the whole restriction, excluding the universal quantifier. This would of course again violate the usual focus projection. We could then make use of the fact that for any entity in the universe there is the property of being identical to that entity. If all of these properties are legitimate alternatives, denying the family of universal statements that every entity that has such a property cried will result in the claim that noone else cried. (This is the strategy that we considered in section 5, where we argued it couldn't account for cases with genuine narrow focus. But here the narrow focus readings do not seem to exist.) A third possibility is to abandon alternative semantics at least for these examples and define a meaning for only that applies directly to the meaning of a quantifier without being focus-sensitive. This is suggested for example by Groenendijk & Stokhof (1984). I will not discuss their analysis because it does not obviously carry over to the focus-sensitive only that we have been talking about. Let me say again that I am deeply suspicious of sentences like (95). Why then should these configurations be unacceptable? I don't really know. Previous researchers have not tended to take the unacceptability of these structures seriously. Groenendijk & Stokhof (1984= 4 1 1, fn. 42) write: 'the least we can say is that we've grown accustomed to it.' Bonomi & Casalegno (1993: 7) write: 'some speakers find sentence such as Only {every boy}p cried a little unnatural, but whatever the explanation of this fact might be, there is no doubt that only can associate with NPs whose determiner is every, and we must account for this case, too.' Let us tum to examples where only combines with various kinds of 'conditional'
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
e.
can drink milk. Some native cats can, but not all. Some feral cats can, but not all. So we see with regard to the varieties of cats that only all [doMEstic)F cats are milk drinkers.'" While the referendum did in the end carry by a simple majority, most GROUPS of voters were against it. In fact, only most [WHITE MIDDLE-class MALES)F voted for it. There was not much support among blacks, women, and lower income voters. I only recommended every student who got an [A)F· Only everyone from Middletown was present at the meeting. (Hoeksema & Zwarts 1 991) Only every woman was present at the meeting. (Hoeksema & Zwarts 1991)
All domestic cats
Kai
von Fintel 45
quantifiers. First, recall that there is no problem with existential quantifiers restricted by if-clauses under the scope of only: (99) a. b. c. d.
Only if it rains may we cancel the game. Only if it had rained might we have cancelled the game. Only if the Queen is home do they sometimes hoist the flag. Only if you're over 21 are you allowed to buy alcohol.
The logical structure of these constructions is as follows: (roo) only (3c(if . . . [x)F . . .)(q)).
(ror)
a.
??Only if it rained must they have cancelled the game. ??They only must have cancelled the game if it rained. b. Only if the Queen is home do they always/invariably hoist the flag. They only always/invariably hoist the flag if the Queen is home. c. Only if you're planning to go to Mrica are you obliged to get a malaria shot. Only if you're planning to go to Mrica do you have to get a malaria shot. Only if you're planning to go to Africa ought you get a malaria shot. Only if you're planning to go to Mrica must you get a malaria shot. You are only obliged to get a Malaria shot if you're planning to go to Mrica. You only have to get a Malaria shot if you're planning to go to Mrica. You only ought to get a Malaria shot if you're planning to go to Mrica. You only must get a Malaria shot if you're planning to go to Mrica.
These sentences should all have the following logical structure: (ro2) only (Vc(if . . . [x]F . . )(q)). .
What only should be doing here is to deny alternative universally quantified conditions. What is different from our main examples is that oven universal operators do not obey the Excluded Middle. So we expect these sentences to have rather weak meanings, denying that all cases alternative to the prejacent antecedent verify the consequent. Because we can't apply the Excluded Middle, we can't go on to say that this means that all alternative cases such that the consequent does not hold. Such meanings are exacdy what we get in (10rb and c). The claim conveyed in (rorb), for example, is that the only kind of case in which they invariably hoist the flag is when the Queen is home. It is not denied that they hoist the flag once in a while when the Queen is not home. This distinguishes the weak claim made in (rorb) from the strong claim made in (91). There are two observations to be made that don't follow from our analysis in this paper. First, note that it seems to be rather odd to have an epistemic universal in an only if-conditional. The examples in (101a) are not very good. The only thought I have about this at the moment is to try and relate this behavior of episternic operators to Iatridou's discussion in her LI squib (Iatridou 1990).
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
What we get is that alternative existentially quantified conditionals are denied. (99a) for example denies that it is possible in case of conditions other than rain that the game is cancelled. This direcdy means that any relevant case of the game being cancelled can only be a rain case. Hence, these only if-conditionals with an existential prejacent also license the converse inference. Now, consider examples of prejacents that involve oven universal quantifiers: episternic must, deontic must/ought, adverbial always:
46 Bare Plurals, Bare Conditionals, and Only The second observation concerns the behavior of deontic ought and perhaps also deontic must in only if-conditionals: (103) You only ought to drink alcohol if you're over 21. You only must drink alcohol if you're over 21. Only if you're over 21 ought you drink alcohol. Only if you're over 21 must you drink alcohol. =>
If you drink alcohol you ought to/must be over 21.
(104) ought [onlyc{GEN {if you're [over 2I]F)(you drink alcohol))]. To get this, we would have to say that somehow the surface order 'only ought' is reversed at logical form. Such funny behavior of modals with respect to other operators is more widely attested, see for example the fact that need not means the same as not need to (c£ also fn. 27). The example then would be interpreted as saying that it ought to be case that (105) is true: (105) You only drink alcohol if you're over 21. We would treat this as only attaching to a universally quantified conditional prejacent. By our analysis, (105) will entail the converse of the prejacent: (106) If you drink alcohol, you're over 21. So (103) would end up to be saying something like 'it ought to be the case that whenever you drink alcohol you're over 21'. That would seem to be adequate.
APPENDIX B : ONL Y AND NAMES Perhaps the most counter-intuitive application of Rooth's cross-categorial semantics for only concerns cases where only combines with a proper name.
( �<>7) [Only Einstein] understands this theorem. Clearly, this means that no one other than Einstein understands this theorem (where the set of people quantified over is quite possibly restricted by the context). We don't, however, want to posit a sui generis operator onlfN, which combines with proper names and means 'no one other than since such an operator would not be reducible to the propositional operator on/1 (since proper names do not have a type ending in (s,t)). What we can do instead is treat Einstein as denoting a generalized quantifier, a set of properties, namely the set of properties that Einstein has. The type of intensional generalized quantifiers is ((e,st),st), a type that ends in (s,t), just what we need. Then ',
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
We seem to get a strong reading that entails the converse just as we did in our earlier paradigm cases. But it seems that we can't attribute this meaning to the Excluded Middle. These deontic operators do not obey the Excluded Middle. If it is denied that something ought to be the case, that does not amount to saying that the opposite ought to be the case. How then can we derive the meaning that (103) seems to have? One possibility is that in (103) the overt deontic operator has scope over the only if conditional, which itself involves an implicit quantifier over cases. We would have the following structure:
K.ai
von Fintel 47
we can define an operator on�, which combines with an implicit set of generalized quantifiers and a generalized quantifier. This operator is reducible to onlf: (Io8) For all sets of quantifiers C, for all quantifiers q, all words w [onlr](C)(q)(P) is true in w iff [onll]({r(P): qr)})(q(P)) is true in w. What we get then is that (I07} claims that no generalized quantifier in C other than the one denoted by Einstein gives a true sentence when combined with the predicate understands this theorem. Unfortunately, there seem to be far too many generalized quantifiers around. Clearly, Einstein in (ro7) is not competing with generalized quantifiers like at least one human. or the most famous modern physicist. On the level of propositions, (Io9) shouldn't compete with (IIo) or (n r ):
this
theorem.
Our task should be to derive which quantifiers Einstein competes with from general principles. If we have to stipulate that names only compete with names, we might as well adopt a special meaning for only when combined with names, Krifka (1991, 1993) has a special rule: names only compete with other names. · Actually, he says that names only compete with other (principal) fllters, but that won't work in an intensional framework (the most famous modern physicist is a fllter). There is no problem with at least one human: this quantifier is actually entailed by Einstein (in an extended sense of entailment), if we assume that Einstein is essentially human. On the level of propositions, (109) logically entails (no). The problem is much more complicated with the mostfamous modern physicist, this is not logically entailed by Einstein, since there are worlds in which Heisenberg is more famous. Unfortunately, it also not the case that the mastfamous modern physicist is lumped by Einstein (in the appropriately extended sense of lumping). According to Kratzer, a situation that supports the proposition about the mostfamous modern physicist has to be fairly large, it has to include all modem physicists at least. That means that the Einstein-proposition can be true in much smaller situations, which in tum means that it doesn't lump the modem physicists proposition. So co-extensional descriptions present a real problem. We obviously can't lift a prohibition against co-extensional alternatives to the level of propositions: we can't exclude all co-extensional propositions from the set of alternatives, at least as long as co-extensional for propositions means having the same truth-value. That would fatally trivialize the semantics for only. Can we make use of the fact that there is a lumping relation between the two propositions in the opposite direction? Any situation which supports the modern physicist proposition will also support the Einstein proposition. Can we exclude from the set of legitimate alternatives any proposition that is lumped by the prejacent proposition and also any proposition that in tum lumps the prejacent proposition? One might think that this move would create a problem with the proposition (1 12): (II2) The two most famous modem physicists understand
this
theorem.46
There is a world in which (r 12) lumps (ro9). Any situation that supports (r 12) will support (Io9). Can we exclude (1 12) from the domain of alternatives to (109)? Sure, why not? The only-claim will falter whether (I 12) is in C or not. It will falter because there is the
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
(Io9) Einstein understands this theorem. (no) At least one human understands this theorem. (I 1 I) The most famous modem physicist understands
48 Bare Plurals, Bare Conditionals, and Only competing proposition that Heisenberg understands the theorem. And that proposition is not excluded by any of our provisions about C. Is there independent motivation for adding the new bilateral lumping exclusion? Well, it does seem to work in the case of Paula's still life as well Here's the lunatic again:
(1 13) Lunatic: What did you do yesterday evening? Paula:
The only thing I did yesterday evening was paint these apples and these bananas over there. Lunatic: This is not true. You also painted this still life. Hence painting these apples and these bananas was not the only thing you did yesterday evening.
For all sets of propositions C, propositions p. r, and worlds w: [ only](C)(p) is defined for w only if (i) 3r E C: r is true in w, (ii) the focus structure of p constrains the extent of C, (iii) no proposition in C is entailed by p, (iv} no proposition in C is lumped by p, (v) no proposition in C lumps p. If defmed, [only] (C)(p) is true in w iff V'r E C (r is true in w
-t
r
=
p).
NOTES r
2
3
As we will discuss soon, the inter pretation of such sentences is crucially affected by their intonational structure. Where relevant then, I will indicate the intended intonation. The conventions used here: pitch-accented syllables are shown in capitals, where the focussed phrase is marked with an F-subscript. The relation between pitch accent and focus is investigated in the literature on focus projection. For a recent survey, see Selkirk (I 993). See Kretzmann (1982) for an overview of the relevant medieval literature. Hom (I996) employs the term 'prejacent' as well, citing medieval sources. McCawley (I 993= s66, fn. I I ) cites Sharvy (1979) as the first publication in which arguments are given that p only if q and ifp, q are not equivalent. Strangely
enough, McCawley doesn't cite his own earlier Ll squib (1974), which already contained a counterexample to the traditional doctrine. 4 It appears that the terrain was well travelled in the Middle Ages (the first golden age of semantics). Hom (I996) somewhat wistfully cites Ockham, who after mentioning some out-of-the-way uses of only writes that 'since they are not as widely used as the ones we have dealt with, I will leave them to the specialists'. Hom comments: 'A glorious picture indeed: monasteries crammed to the spires with specialists on only, labouring away on the fme points of the semantics of exclusive propositions. Those were the days!' (Hom I996: 27). 5 To accommodate a presuppositional component to the meaning of only, we
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Assuming that the still life is fairly minimalist and only contains those applies and those bananas, the still life proposition lumps, but arguably, is not identical to the apples and bananas proposition. The lunatic's response has to be rejected and the new bilateral lumping exclusion would do just that. (This may not be independent evidence, however, since it involves definite descriptions.) Perhaps, we should adopt the new principle:
Kai
i.
a.
They were advised to learn only [SPAnish)F· b. They were advised to only learn [SPAnish)F· c. They were only advised to learn [SPAnish)F·
The sentence in (ia) is ambiguous, while the sentences in (ib) and (ic), where only is separated from its focus, are unam bigous (keeping the focal structure con stant). Rooth (I985: 90) suggests that the explanation is simply that since only Spanish is an NP it can undergo Quantifier Raising, and since there are two possible landing sites, we observe ambiguity. In the other sentences, there is no constituent only Spanish and so it cannot undergo QR, no ambiguity arises. McCawley (I 988: 6 nf), who does assume that at some point there is a constituent only Spanish, has to appeal to rule ordering or level-ordering (since he works in a Generative Semantics frame work, what he says is that only-separation precedes Quantifter Lowering). 8 Recall that weak determiners are those that can occur in there-sentences, while strong determiners are those that can't; the relevant literature is large (Milsark I977; Barwise & Cooper I98I; Higgin botham I98T. Keenan I987; Lappin I988; Partee I988; de Hoop I99Sa). See Musan (I997= Section 4-2·3) for an alternative account of the non-conservative reading
of (19), based on a suggestion by Irene Heirn. See also de Hoop (I995h), de Hoop & Sola (I995). and Biiring (I99S= 98ff). 9 Note that (2oa) does not mean that all applicants are incompetent cooks, which is what the simple semantics in (I2) would predict. So, we would have to revise the semantics of the determiner only to make it sensitive to focus. 10. In fact, as suggested in Hom (I996), one can observe that the putative deter miner only would be conservative with respect to its second argument: only men smoke is equivalent to only smoking men smoke, at least if one is careful with the focus structure of the second sentence. I 1. One might think that the determiner analysis would help us understand the existence of the complex expression all and only, which is a conjunction of the (apparent) determiner all and the item only. But this argument is undermined by doubts that all is a determiner itself (Partee I99s). Consider, for example, all and only the foreign students, where the collocation all and only applies to a full NP (note that this cannot be reanalyzed as a partitive structure along the lines of all (of) the, since only cannot occur with a partitive, cf. only (*of) the foreign students). I2. Other relevant works include Szabolcsi (I98Ia, h), Groenendijk & Stokhof (I984: Chapter s). von Stechow (I99Ih), and Bonorni & Casalegno ( 1993). 13. An earlier example of this kind was given by McCawley (1970): i. The judge only sent you to prison; your wife didn't leave you too. McCawley (p.c.) notes that 'as with Heim's example, one "annoying circum stance" is being contrasted with others.' I<J. One refinement to the sketch given in the text is to acknowledge that C will have to vary with the evaluation world. Thanks to Paul Portner (p.c.) for discussion.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
could add to (12) the presupposltton that B is non-empty, which corresponds to the existential import that all argu ably has with respect to its ftrst argu ment A. We would also have to ensure that the determiner only can only apply to plural nouns, a property it would share with all and most, for example. 6 An early critical discussion can be found in Thijsse (I983). See de Mey (I99I, I996) for a dissenting opinion. 7 There is an observation, due to Taglicht (I984), that has received some attention in the literature:
von Fintel 49
so Bare Plurals, Bare Conditionals, and Only
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
IS For more on existence presuppositions 21 As mentioned above, Hom (I996) tries to connect the existential impon of only ofquantificational constructions, see for to the existential impon of all. While example, Heim & Kratzer (I997= section 6.2). my rejection of the determiner analysis I6 This talk of 'reading the speaker's prevents a direct adoption of his pro mind' is somewhat loose talk. Perhaps, posal, in a more general sense I share his outlook. I would like to explore the idea what the speaker is thinking never determines contextual parameters; see that all of the presuppositions about Gauker (fonhcoming) for discussion. the contextual domain C specified in (3of) follow from general principles of Two very different references on quantifier interpretation in natural mind-reading are Bolinger (I972) and Baron-Cohen (I99S)· languages. Keeping unwanted cases out I7 See Rooth (I98S. I992) for more on of a quantifier domain is a problem that also emerges in the case of adverbial this. There are in fact ways of ovenly quantification. There it is crucial to the constraining the domain of only, e.g. we can specify the domain with an prospects for an event-based semantics overt o/--phrase: (Dekker I 996; von Fintel 1 997a, in progress). i. Of the people at the party, only 22 See Bayer (1996) for a book-length [JOHN]p got truly drunk. study of such a theory. Someone should figure out how this 23 The reference to kinds approach is due construction works. to Carlson (I977a. b); see also Chierchia I8. This is a deliberately vague way of (1996). The indefinites approach is due stating the fact that focus tells us to Heim (1982); see also Wilkinson about what C is. (1986, 1991), K.rifka (1987), K.rifka et al. I 9 I am grateful to Irene Heim for letting (I99S). and Diesing (1992). me see unpublished notes of hers on the 24 For more on these options, see again topic of lumping and its consequences Krifka et al. (199s). for the semantics of only. Bonomi & 25 Selection functions are of course well Casalegno (I993: 20, fn. 16) note the known from the Stalnaker-Lewis seman problem but do not pursue it in any tics for counterfactual conditionals. For detail. Kratzer also discusses a pedantic mulating the semantics in terms of a response to Paula's claim: the pedant selection function is only possible under ignores the tacit restriction to inter what Lewis calls the Limit Assumption, esting things Paula did. Paula's and which says that there will always be a set Kratzer's response is too conciliatory: of maximally close antecedent cases. See they admit that strictly speaking Paula Stalnaker (I981, 1984) and Warmbrod was wrong: she also looked out the (1982) for a defense of this assumption, window once. But, really that wasn't in the face of Lewis's arguments against what Paula was talking about at all. it. So, the pedant should not be appeased. 26 Note that, to make the example mini 20. fu Paul Ponner (p.c.) points out to me, mally euphonous, we have to rearrange the notion of lumping that I have to the elements of (4ob) on the way to employ here is not quite the same as the (41b). I will not explore why this should one that Kratzer uses in the semantics of be. conditionals (for her, generic statements 27 There is an interesting type of case are true in any situation in any world where only combines with an existential they are true in). I will postpone dis modal: cussion of the differences to a future occas10n. i. John can only be at work.
Kai von Fintel 5 1 An example like this is discussed by von
operator above only. Otherwise, these data do not argue for a generic prejacent under only. The argument here depends on an observation due to Linebarger (198o, 1987): NPis are only licensed locally. The mere presence of a licensing
Stechow (1991a). Note that (i) is felt to imply: ii. John must be at work.
The way to get this, von Stechow shows,
operator somewhere above the NPI is not enough. For example, #Every boy has
is to assume this logical form: iii. onlyc [can (John be (at WORK)F)).
Understanding
can
any potatoes doesn't get any better when embedded under negation: #It's not true that every boy ate any potatoes. Conversely, Not every boy who had any potatoes ate them is okay because every licenses NPis
in the usual way as
existential quantification over worlds, denies that there are worlds where
(iii)
liaries: can not really means not can. Jim McCawley (p.c.) points out that this is a general property of modal auxiliaries except should/must/ought. He also points out that when we remove only from (i) we have to use may instead of can: iv.
a.
??John can be at work. b. John may be at work.
It seems that to express epistemic pos
sibility, may is preferred, but
when there is
in its first argument, even though the presence of the higher negation will eventually destroy the downward monotonicity in the ftrst argument of every. Thus, in the examples in the text, it can only be a generic operator in the scope of only that can license the NPis. 32 Two pieces of a complete analysis would have to be (i) Laka's work on the syntactic elements that manipulate the truth polarity, especially her hypothesis of a �:>phrase (Laka 1 990), (ii) Hohle's work on 'verum focus' (Hohle 1992). 33 One
is signalled by destressing constituents which have semantic content. This may
(I 996: 1 off) for further discussion of this point.
30 In an appendix, Hom (1996) discusses some of these data and suggests that NPI-licensing here is based on speak ers' confusion: somehow the downward monotonicity of only's second argument is illicitly extended to its first argu
ment. An explanation based on the assumption of a generic prejacent is clearly preferable.
3 1 As Paul Portner (p.c.) pointed out me, I have to exclude the possibility that the NPis here are licensed by a generic
reviewers pointed out
well. Hohle suggests that verum focus
28 See McCawley (1993: 3 1 1 f) and Hom
29 The observation is due to Hom (1 996: 28). The example in (s3h) was given to me by Jim McCawley (p.c.).
of the
that Hohle's analysis may help here as
can is used negation or only around.
34
leave stress on if, which according to Kratzer of course has little semantic content.
Thanks to Jim McCawley (p.c.) for help with these examples.
35 However, I have to report an example, due to Maribel Romero, that is some what troubling from my perspective:
i.
Only if at least one
man
with BLUE
eyes is among your ten guests will I come to your party.
In spite of the apparent narrow focus on a deeply embedded constituent of the if-clause, we can only get the right meaning if we assume focus on the
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
John is at home, at church, at the health club, etc. Hence, (ii) is implied. Note that to make this work, the logical scopes of only and can have to be the reverse of their surface order. This is of course reminiscent of other ill understood facts about all modal auxi
sz
Bare Plurals, Bare Conditionals, and Only thing like a homogeneity presupposition is Schwarzschild (1994), although his system is different from what we are doing here. Barker (1996) also postulates a 'homogeneity presupposition', but it is not at all the same condition I am using. It has to do with a solution to the proportion problem. 39 See Horn (1989) for extensive discussion of meta-linguistic negation. The data here differ from more run-of-the-mill cases of meta-linguistic negation in that in those it isn't negation that is focussed, as pointed out to me by a reviewer. However, note that what should be focussed in my examples would be the generic quantifier, which of course can't be focussed since it is silent. So perhaps stress shifts to negation as some kind of default. 40 See also Yoon (1996). 41 In the paper on conditionals, give references to other work which has pursued similar ideas. See especially McCawley (1993: Chapter 15, 1996). 42 For treatments ofeven if-conditionals, see the series of relevant papers in L&P (Bennett 1982; Barker 1991, 1994; Lycan 1991). Here, I cannot discuss these pro posals and the way they would help in spelling out the pragmatic story about Contraposition. Maybe I'll have a chance of doing that on some other occasion. 43 Other authors that want to maintain the validity of Contraposition are Hunter (1993) and Urbach (1988). 44 This example is from Barker (1993), who writes that the only-sentence 'is perhaps a little cumbersome, but perfectly intelligible'. 45 It would be nice to conduct a corpus search and see whether there are real life examples of this kind. 46 A completely unrelated aside: note the interesting problem this sentence poses for the analysis of superlatives.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
truth polarity of the antecedent. (i) clearly does NOT deny that the speaker will come to the party if there is at least one man with black eyes among the guests. Rather the claim is that the speaker will not come if there is not at least one man with blue eyes among the guests. This example thus can only be properly treated if the relevant alternatives are not signalled by the prominent pitch accent, but are com puted in some other way. What we would have to hope is that we can reasonably claim that the pitch accent on blue is motivated by matters of discourse contrast and that there is some secondary focus that signals the alternatives relevant to the domain restriction of only. 36 Barker (1993) also reaches the con clusion that the Excluded Middle is rather essential for an analysis of only if-conditionals. He remains skeptical about this move, however. He advocates an analysis where conditional sentences express conditional assertions, some thing that may be correct for certain kinds of speech acts, but can presumably not be generalized to all conditionals that can combine with only. His pro posal also does not extend naturally to cover the generic only-sentences that I see as posing the very same semantic puzzle. 37 Note that it is well known from the study of the semantics of plurals that for The students are playing to be true they don't all have to be playing, 'as long as they're behaving as some sort of coher ent group engaged in a play activity (maybe one of them is keeping score and another one is keeping watch for bullies, etc.)' (Jim McCawley, p.c.). This phenomenon is discussed most recently by Brisson (1997). 38 Another author who argues for some-
Kai
von Fintel 53
RE FERENCES Carlson, Greg (1977a), 'Reference to kinds in English', Ph.D. dissertation, University of Massachusetts, Amherst. Carlson, Greg (rmb), 'A unified analysis of the English bare plural', Linguistics and Philosophy. 1, 413-58. Chierchia, ·Gennaro (1996), 'Reference to kinds across languages', MS, University of Milan. Dekker, Paul (1996), 'Cases, adverbs, situa tions, and events', in Robin Cooper (ed.), Building the Framework, ECCS, Edinburgh. Diesing, Molly (1992), Indefinites, MIT Press, Cambridge, MA. Fernald, Ted (1994), 'On the nonunifor mity of the individual- and stage-level effects', Ph.D. dissertation, University of California, Santa Cruz. von Fintel, Kai (1994), 'Restrictions on quantifier domains', Ph.D. dissertation, Graduate Student Linguistics Association An Essay on Autism on Theory of Mind, (GLSA), University of Massachusetts, MIT Press, Cambridge, MA. Amherst. Barwise, John & Cooper, Robin (1981), von Fintel, Kai (1997a), 'Conditionals in a 'Generalized quantifiers and natural dynamic context', MS, MIT language', Linguistics and Philosophy, 4, von Fintel, Kai (1997b), 'A minimal 159-219. theory of adverbial quantification', in Bayer, Josef (1996), Directionality and LAgical Hans Kamp & Barbara Pattee (ed), .
Form: On the Scope ofFocusing Particles and Wh-in-situ, Kluwer, Dordrecht. Bennett,Jonathan ( 1982), 'Even-if', Linguistics and Philosophy, 5, 403-18.
Proceedings of the Workshop on Context Dependency in the Analysis of Linguistic Meaning, IMS, Stuttgart.
von Fintel, Kai (in progress), 'How to Bolinger, Dwight (1972), 'Accent is predict count events: an owner's manual', MS, able (if you're a mindreader)', LAnguage, MIT 48, 633-44Fodor, Janet Dean {1970), 'The linguistic Bonomi, Andrea & Casalegno, Paolo description of opaque contexts', Ph.D. (1993), 'Only: association with focus in dissertation, MIT event semantics', Natural LAnguage Gauker, Christopher (fonhcoming), What Semantics, 2, 1 -4S. is a context of utterance?' Philosophical Brisson, Christine (1997), 'On definite Studies. plural noun phrases and the meaning Geis, Michael (1973), 'If and unless', in Braj of all', SALT, 7. Kachru, Roben Lees, Yakov Malkiel, Biiring, Daniel (1995), 'The 59th Street Angelina Petrangeli & Sol Saporta (eds), Bridge accent: on the meaning of topic Issues in Linguistics: Papers in Honor of and focus', Ph.D. dissertation, Universitit Henry and Renee KtJhane, University of Tiibingen. illinois Press, Urbana, 231 -sJ. .
.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Appiah, Anthony (1993), 'Only-ifi', in James Tomberlin (ed.), Philosophical Perspectives, 7, LAnguage and LAgic, Ridge view Publishing Company, Atascadero, CA, 397-410. Atlas, Jay David (1993), 'The importance of being only: testing the neo-Gricean versus nee-entailment paradigms', journal of Semantics, 10, JOI-18. Barker, Chris (1996), 'Presuppositions for proportional quantifiers', Natural LAn guage Semantics, 4, 237 - 59· Barker, Stephen (1991), 'Even, still and coun terfactuals', Linguistics and Philosophy, 14, 1 -38. Barker, Stephen (1993), 'Conditional excluded middle, conditional assertion, and only if', Analysis, 53, 254-61. Barker, Stephen (1994), 'The consequent entailment problem for even if', Linguis tics and Philosophy, 17, 249-60. Baron-Cohen, Simon (1995). Mindblindness:
54
Bare Plurals, Bare Conditionals, and Only
Glasbey, Sheila (1997), '!-level predicates th.at allow existential readings for bare plurals', SALT, 7. Groenendijk, Jeroen & Stokhof, Martin (1984), 'Studies on the semantics of ques tions and the pragmatics of answers', Ph.D. dissenation, University ofAmster
dam.
,
Rede: Kontexttheorie-Modalworter-Kon ditionalsiitze, Scriptor, Konigstein/Taunus.
Kratzer, Angelika (1986), 'Conditionals', Chicago Linguistics Society, 22, I - I S· Kratzer, Angelika (I989), 'An investigation of the lumps of thought', Linguistics and Philosophy, 12, 607-53. Kretzmann, Norman (I982), 'Syncate goremata, exponibilia, sophismata', in Norman Kretzmann, Anthony Kenny, & Jan Pinborg (eds), The Cambridge
History of Late Medieval Philosophy: From the Rediscovery of Aristotle to the Dis integration of Scholasticism 1100-16oo, Cambridge University Press, Cambridge, 21 1 -45· Krifka, Manfred (I987), 'An outline of genericity', MS, Universitit Tiibingen. Krifka, Manfred (I991), 'A composi tional semantics for multiple focus constructions', SALT, 1, I 27-58. Krifka, Manfred (1993), 'Focus and pre-
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Heim, Irene (1982), 'The semantics of defi nite and indefinite noun phrases', Ph.D. dissertation, University of Massachusetts, Amherst. Heim, Irene & Kratzer, Angelika (I997), Semantics in Generative Grammar, Black well, Oxford. Herburger, Elena (1993), 'Focus and the LF of NP quantification', SALT, 3, 77-96. Herburger, Elena (1 997), 'Focus and weak noun phrases', Natural Language Semantics, 5, 53-78. Higginbotham, Jim (1987), 'Indefiniteness and predication', in Eric Reuland & Alice ter Meulen (eds), The Representation of {In)definiteness, MIT Press, Cambridge, MA, 43-70. Hoeksema, Jack & Frans Zwarts (199I), 'Some remarks on focus adverbs', journal ofSemantics, 8, s I -70. Hohle, Tilman (I992), 'Ober Verum Fokus im Deutschen', in Joachim Jacobs (ed.), Informationsstruktur und Grammatik, Niemeyer, Tiibingen. de Hoop, Helen (1995a), 'On the characteri zation of the weak-strong distinction', in Emmon Bach, Eloise Jelinek, Angelika Kratzer, and Barbara Partee (eds), Quan tification in Natural Languages, Kluwer, Dordrecht, 421 - 50. de Hoop, Helen (I995b), 'Only a matter of context?' in Marcel den Dikken & K. Hengeveld (eds), Linguistics in the Netherlands 1995, Benjamins, Amsterdam. de Hoop, Helen & Sola, Jaume (1995), 'Determiners, context sets, and focus', WCCFL, 14, I55-67. Horn, Larty (1989), A Natural History of Negation, University of Chicago Press, Chicago.
Horn, Larry (1992), 'The said and the unsaid', SALT, 2, 163-92. Horn, Larry (I996), 'Exclusive company: only and the dynamics of vertical inference', journal ofSemantics, 13, 1 -40. Hunter, G. B. B. (1993), 'The meaning of if in conditional propositions', Philosophical Quarterly, 43, 279-97. latridou, Sabine (I990), 'The past, the pos sible, and the evident', Linguistic Inquiry, 21, 1 23-9· Keenan, Edward (I987), 'A semantic defini tion of "Indefinite NP" ' in Eric Reuland and Alice ter Meulen (eds), The Repre sentation of (In)definiteness, MIT Press, Cambridge, MA, 286-317. Keenan, Edward & Stavi, Jonathan (1986), 'A semantic characterization of natural language determiners', Linguistics and Philosophy, 9, 253-326. Kiss, Katalin {I994), 'On generic and exis tential bare plurals and the classification of predicates', MS, Linguistic Institute of the Hungarian Academy of Sciences, Budapest. Kratzer, Angelika {I978), Semantik der
Kai von Fintel 55
supposition in dynamic interpretation',
journal of Semantics,
Kri£ka,
Manfred
10, 269-300.
(I996),
'Pragmatic
strengthening in plural predictions and donkey sentences', handout of a talk
given at Rutgers University, SALT, 6. Manfred, Pelletier, Je£( Carlson, Greg. ter Meulen, Alice, Chierchia,
Kri£ka,
McCawley, James (1970), 'English as a VSO
language', Language, 46, 286-99. McCawley, James (I974), 'If and only
if,
Linguistic Inquiry, 5,
632-5. McCawley, James (I988), The Syntactic Phenomena ofEnglish, Chicago University Press, Chicago. McCawley, James (1993}.
'Genericity: an introduction', in Greg
Everything that Linguistics have Always Wanted to Know about Logic* *but were ashamed to ask,
Book, Chicago University Press, Chicago,
Chicago University Press, Chicago. McCawley, James (I996), 'Conversational
Gennaro,
& Link, Godehard (I995).
Carlson & Jeff Pelletier (eds), The Generic
scorekeeping and the interpretation of
the nature of functional categories and
conditional sentences', in Masayoshi Shibatani & Sandra Thompson (eds),
projections', Ph.D. dissertation, MIT. Lappin, Shalom (I988), 'The semantics of many as a weak determiner', Linguistics, 26, 977-98.
Lewis,
David
(I973a),
Blackwell, Oxford. David (I 973b),
Lewis,
Counterfactuals,
77- IOI. McNally, Louise
(1995),
University Press, Cambridge, 3 - I S. Linebarger, Marcia (I98o), 'The grammar of negative polarity', Ph.D. dissertation,
MIT.
and grammatical
Linguistics and Philosophy,
representation', 10, 325-87.
LOhner, Sebastian ( I 985), 'Definites', Journal
of Semantics, 4, 279-326. LOhner, Sebastian (I987a), The conceptual
and
'Only as a determiner
and as a generalized quantifier', Journal
of Semantics, 8, 9 I - 106. de Mey, Sjaak (I996), 'Generalized quanti
fier theory and the semantics of focus', in Jaap van der Does & Jan van Eijck (eds),
Language,
Quantifiers, Logic, and
CSLI Publications, Stanford,
269-79· Milsark. Gary (I977), Toward an explana tion
Linebarger, Marcia (I987), 'Negative polar
'Stativity
theticity', MS, Ohio State University. de Mey, Sjaak (199I},
'Counterfactuals
and comparative possibility', Journal of Philosophical Logic, 2, 4I8-46. Lewis, David (I975), 'Adverbs of quantifi cation', in Edward Keenan (ed.), Formal Semantics ofNatural Language, Cambridge
ity
Grammatical Constructions: Their Form and Meaning, Clarendon Press, Oxford,
of certain
existential
peculiarities
construction
Linguistic Analysis,
3, 1 -29.
in
of the English',
Musan, Renate (I997),
On the Temporal Interpretation of Noun Phrases, Garland, New York.
Partee, Barbara (1988), 'Many quantifiers',
nature of natural language quantifi
ESCOL, 5, 383-40 1 . Partee, Barbara (I 995), 'Quantificational structures and composirionality', in
posium on Logic and Language, Akademiai
Emmon Bach, Eloise Jelinek, Angelika Kratzer, & Barbara Partee (eds), Quanti
cation', in l Ruzsa & Anna Szabolcsi (eds), Proceedings of the '87 Debrecen Sym
Kaid6, Budapest, 8 I -94LObner, Sebastian (I987b), 'Natural language and generalized quantifier theory', in Peter Gardenfors (ed),
Generalized Quan tifiers: Linguistic and Logical Approaches,
Reidel, Dordrecht, I 8 I -20 1 . Lycan, William (I99I}, 'Even and
Linguistics and Philosophy,
even if,
14, 1 15-50.
fication in Natural Languages,
Kluwer,
Dordrecht, 541 -601 . Partee, Barbara, Hajicova, Eva, & Sgall, Petr (1994), Topic-focus articulation, tripar tite structures, and semantic content',
MS, Charles University, Prague.
Rooth,
Mats
(1985),
'Association
with
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
I - I24-
Laka, ltziar (I990), 'Negation in syntax: on
56 Bare Plurals, Bare Conditionals, and Only quantification: a generalized quantifier approach', Ph.D. dissertation, Rijks universiteit Groningen. Szabolcsi, Anna (198Ia), 'Compositionality in focus', Folia Linguistica, 15, 141-61. Szabolcsi, Anna (198Ib), 'The semantics of topic-focus articulation', in Jeroen Groenendijk, Theo Janssen, & Martin Stokhof (eds), Formal Methods in the Study of Language, Mathematisch Centrum, Amsterdam, 513-40. Taglicht, Josef (1984), Message and Emphasis: On Focus and Scope in English, Longman, London. Thijsse, E. (1983), 'On some proposed uni versals of natural language', in Alice ter Meulen (ed.), Studies in Model-Theoretic Semantics, Foris, Dordrecht. Urbach, Peter (1988), What is a law ofnature? A Humean answer', British Journalfor the Philosophy of Science, 39, 193-210. Warmbrod, Ken (1982), 'A defense of the limit assumption', Philosophical Studies, 42, 53-66. Westerstihl, Dag (1985). 'Logical constants in quantifier languages', Linguistics and Philosophy, 8, 387-413. Westerstihl, Dag (1989), 'Quantifiers in formal and natural languages', in Dov Gabbay & Franz Guenthner (eds), Handbook of Philosophical Logic, Vol. 4, Reidel, Dordrecht, 1 - 131. Wilkinson, Karina ( 1 986), 'Generic indefinite NPs', MS, University of Massachusetts, Amherst. Wilkinson, Karina (1991), 'Studies in the semantics of generic noun phrases', Ph.D. dissertation, GLSA. University of Massachusetts, Amherst. Yoon, Youneun (1996), 'Total and partial predicates and the weak and strong inter pretations', Natural Language Semantics, 4, 217-36.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Focus', Ph.D. dissertation, University of Massachusetts, Amherst. Rooth, Mats (1992), 'A theory of focus interpretation', Natural Language Seman tics, 1, 75- 1 16. Schwarzschild, Roger (1989), 'Adverbs of quantification as generalized quantifiers', NELS, 19, 390-404Schwarzschild, Roger (1994), 'Plurals, pre suppositions, and the sources of distri butivity', Natural Language Semantics, 2, 201 -48. Selkirk, Elizabeth (1993). 'Sentence prosody: intonarion, stress and phrasing', in John Goldsmith (ed.), Handbook ofPhonological Theory, Blackwell, Oxford. Sharvy, Richard (1979), 'Transitivity and conditionals', Logique et Analyse, 81, 347-51. Stalnaker, Robert (1968), 'A theory of conditionals', in Nicholas Rescher (ed.), Studies in Logical Theory, Blackwell, Oxford, 98- 1 12. Stalnaker, Robert (1981}, 'A defence of conditional excluded middle', m William Harper, Robert Stalnaker, & Glenn Pearce (eds), Ifs: Conditionals, Belief, Decision, Chance, and Time, Reidel, Dordrecht, 87- 104. Stalnaker, Robert (1984), Inquiry, MIT Press, Cambridge, MA. von Stechow, Arnim (1991a), 'Current issues in the theory of focus', in Arnim von Stechow & Dieter Wunderlich (eds), Semantik: Bin internationoles Hand buch der zeitgeniissischen Forschung, Walter de Gruyter, Berlin, 804-25von Stechow, Arnim (1991b), 'Focusing and backgrounding operators', in Werner Abraham (ed.), Discourse Particles: Prag matics and Beyond, John Benjamins, Amsterdam, 37-84de Swart, Henriette (1991), 'Adverbs of
Journal of&man1Us 14: 57-86
Vectors
as
© Oxford Univenity Press
1997
Relative Positions:
A Compositional Semantics of Modified PPs1
JOOST ZWARTS Summer Institute of Linguistics, Kenya Abstract
Although there is a wealth of literature about many aspects of the interpretation of prepositions and PPs, little attention has been paid to the semantics of modified PPs, like those in (I):
(I)
a. one meter behind the desk b. far outside the village c. right under the lamp
The discussion of cases like these is mainly limited to some accidental remarks in the semantic literature, e.g. Cresswell (I978: 14, 29-3I), Jackendoff (I983: I67), Hawkins (I984: 330-6), Bierwisch (I988: 32, 44-5, 48-9), Lang (199I: I33), and Wunderlich & Herweg {I99I: 780). Only Wunderlich & Kaufmann (I990) and Rauh (I996) discuss the semantics of modified PPs in more depth. The purpose of this paper is not to give a complete and detailed treatment of modified PPs that would fill this gap or to discuss and compare the proposals in the literature just mentioned, but rather to demonstrate, by focussing on certain modifiers of locative PPs in Dutch,
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The interpretation of modified PPs, like one meter behind the disk, Jar outside the village, or right under the lamp, has never received much attention in the literature about prepositions. However, as this paper shows, the modification ofPPs presents an intriguing problem for a compositional semantics of PPs. This problem can be solved when the PP is interpreted, not as a set of points or mereological portions of space, but as a set of vectors, that represent positions relative to the reference object. Modifiers map a set of vectors to a subset. For example, if behind the desk denotes the set of vectors pointing backward from the desk, then one meter behind the desk denotes the subset consisting of those vectors that have a length of one meter. Given the familiar operations on vectors, the denotations of PPs can be studied in a systematic way, by formulating formal properties that characterize empirically relevant subclasses of locative PPs or that provide general constraints on their denotation. The examples are taken from Dutch, but the conclusions are valid for all languages that have the kind of PP modification that exists in Dutch and English.
sS
Vectors as Relative Positions
r
MODIFI CATION O F PP'S
The empirical scope of this paper is restricted to the most important locative prepositions of Dutch and the most common modifiers. The locative prepositions that will be discussed in this paper are given in
(2): (2) voor (in front of), achter (behind)
hoven (above, over), onder (below, under) binnen (inside), buiten (outside) links van �eft of), rechts van (right of) naast (next to, beside}, tussen (between) in (in), op (on, at), bij (near)
For the purposes of this paper, locative prepositions are to be understood as those prepositions which, in combination with a noun phrase object, are primarily used to denote locations, typically as the complement of the copula be. Directional prepositions like naar (to}, van (from), uit (from), door (through), and tegen (against} will be discussed only very briefly, because they do not denote locations but paths, which 1 will analyze as sequences of locations. Prepositions like langs (along), over (over), om (around), and voorbij (past, beyond) may be used locatively, either by distributing a plural or elongated object along a path (as in (3a)), or by identifying a location as the endpoint of a path (in (3b)}:
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
that PP modification presents a intriguing problem for any compositional semantics of prepositions and PPs and that the most natural solution to this problem involves the use of vectors, interpreting the PP as a particular set of vectors emanating from the reference object. However, the use of vectors has implications that go far beyond the domain of modification, because the notion of vector allows us to study the denotation of PPs (whether modified or not} in a systematic and precise way, making use of familiar algebraic operations on vectors. In this way natural classes of prepositions and general constraints on prepositional meanings can be formulated. After the introduction in section r of the basic problem, section 2 presents the outlines of a solution that is based on vectors. Section 3 provides some mathematical background for the semantic definitions of individual locative prepositions and modifiers in section 4 and for the formulation in section s of a range of relevant formal properties of PP denotations.
Joost Zwarts S9
(3)
a.
de bomen I het hek om het huis the trees I the fence around the house b. Het hotel is over de heuvel I om de hoek The hotel is over the hill I around the comer
(4)
a.
twee centimeter hoven de deur two centimeters above the door b. enkele stappen achter het doel a few steps behind the goal c. vele lich�aren buiten de melkweg many light-years outside the milky way
Some of the so-called dimensional adjectives, namely hoog (high), laag Qow), diep (deep), ver (far), and dicht (close) can also specify a distance in a particular direction:
(s)
a.
hoog hoven de deur high above the door b. diep onder de grond deep under the ground c. dicht achter de gouden koets close behind the golden coach
A group of special adverbs indicates a very short distance, close to zero:
(6)
a.
direct hoven de deur directly above the door b. net buiten de stad just outside the city c. vlak naast me right beside me
The direction modifiers specify the direction of the location, either by making reference to the angle that the direction makes with respect to an axis, like recht and pal (straight) and schuin (diagonally):
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
However, I will follow the conimon assumption in the literature that these prepositions primarily refer to paths and that their locative use is derived.2 Several locative prepositions, like aan ('on' in the meaning of 'attached to'), halverwege (halfway between), and tegenover (opposite) are absent from the list in (2) because their analysis involves complications that would go beyond the basic proposal of this paper. PPs formed with the prepositions in (2) can be modified in different ways, two of which will be discussed in this paper: modification of distance and modification of direction. The distance modifier can be a measure phrase:
6o Vectors as Relative Positions
{7)
a.
recht hoven de deur straight above the door b. schuin achter de tafel diagonally behind the table
or by means of the adverbs links �eft) and rechts (right), yielding phrases that have no straightforward translation in English: (8}
a.
links hoven de deur above the door and to the left of it b. rechts voor het doel in front of the goal and to the right of it
(9)
a.
links boven de deur
X
b.
rechts voor het doel
0
D
·-----··-'''''''''''''llr········
In (9a) the nail x is links boven de deur and in (9b) the ball o is rechts voor het doel (when seen from above). How do these modified PPs fit into the semantic analysis of prepositions and PPs? Traditionally, a locative preposition like boven (above) is taken to be a relation between a theme x (also called trajector or figure) and a reference object y (also called landmark or ground): (1o) BOVEN(x,y) However, in much recent work this relation is broken down into two parts, as in ( n ):
( I I ) LOC(x, BOVEN(y)} The function BOVEN maps the reference object to a region or place BOVEN(y} and the theme is located in this region by a general location relation.3 I will assume in this paper that this location relation LOC is actually not part of the lexical meaning of boven or any other preposition,
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
In order to make clear what these PPs mean, the following pictures will be helpful:
Joost Zwarts 6 1
but contributed by the predicative and modificational constructions in which a locative PP is used (e.g. de spijker (is) hoven de deur 'the nail (is) above the door'). The preposition hoven only contributes the function BOVEN; this means that the theme x is not part of the lexical meaning of the preposition, but provided by a 'type-shift' or 'coercion' operation that turns locative PPs into predicates. As a result the basic denotation of a locative PP like hoven de deur (above the door), corresponding to the region part BOVEN(y) in (I I), is a purely spatial object. Modifiers of PP apply to this region before the location operation maps the region to a set of objects, as in recht hoven de deur (straight above the door):
Suppose now for the sake of concreteness that the region corresponding to hoven de deur is a set of points, which is the natural mathematical way to model a spatial region. Then the modifiers of this PP in the a-examples of (4) to (8) each have to be interpreted as functions that map a set of points to a set of points, presumably a subset.4 These functions could provisionally be formulated in the following way, with [a] representing the denotation of an expressiOn a: (I3)
a.
b. c. d. e.
[z cm PP] [hoog PP] [direct PP] [ recht PP] [links PP]
{p {p {p {p {p
E E E E E
[PP] I [PP] I [PP] I [PP] I [PP] I
p is p is p is p is p is
2 centimeters} high} direct} straight} to the left}
However, a moment's reflection makes clear that these definitions do not make sense, because all by itself a point cannot be said to be 'two centimeters', or 'direct', or 'straight'. The definitions in (13b) and (IJe) make more sense at first sight, but even in those cases a point can only be 'high' and 'to the left' with respect to a reference point. In hoog hoven de deur (high above the door) and links hoven de deur (above and to the left of the door), hoog and links take the door as their reference point and not the ground or the speaker (which are the usual reference points for hoog and links). Relativity is the general characteristic of the modifiers in (I3): they do not specify absolute properties of the points of the region, but they specify the distance between the point and the reference object (in (13a), (I3b), and ( IJc)) or the direction of the point with respect to the reference object (in (I3d) and (IJe)). This relational character can be accounted for in the following way:
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
(12) LOC(x, RECHT(BOVEN(y)))
62 Vectors as Relative Positions a.
(15) [ [ver [P hoven]] [NP de deur] If this would be the case, then modifiers map relations to relations in a way that is both compositional and descriptively adequate: a. [2 em P] { (x,y) E [P] I 2 cm(x,y)} b. [hoog P] {(x.y) E [P] I high(x,y)} c. [direct P] {(x,y) E [P] I direct (x,y)} d. [recht P] {(x.y) E [P] I straight(x,y)} e. [links P] {(x,y) E [P] I left(x,y)} However, it is generally assumed in the syntactic literature that modifiers inside PP are not sisters of the preposition, but of the combination of preposition and object, a constituent that is sometimes called P-bar (e.g. Jackendoff 1973, van Riemsdijk 1978), and we would want to have good syntactic reasons to depart from this assumption, rather than just to get our semantics right. Furthermore, Dutch shows that modification of prepositions can never be a general solution to the problem In Dutch,
(16)
-
-
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
{p E [PP] I 2 cm(p, [NP])} [2 cm PP] {p E [PP] I high(p, [NP])} b. [hoog PP] {p E [PP] I direct(p, [NP])} c. [direct PP] {p E [PP] I straight(p, [NP])} d. [recht PP] {p E [PP] I left(p, [NP])} e. [links PP] Of course, the relation that defines a modifier would have to be worked out in order to capture its full lexical meaning. For example, direct requires that the distance between p and the reference object is almost zero and for recht the angle that the line between p and the reference object makes with the relevant axis is zero. I will come back to the specification of the lexical semantics of modifiers in section 4.2, but here the schematic interpretations in (14) suffice. The definitions in (14) make sense, but now another problem arises. The definitions in (14) are actually non-compositional: the interpretation of a modified PP is not a function of its immediate constituents (the modifier and the inner PP), but the proper interpretation ofPP modification requires access to the reference object NP, which is strictly speaking not visible to the interpretation process. When locative PPs are taken to denote spatial regions then a compositional interpretation of modified PPs becomes impossible. One possible way out worth considering is that modifiers are not sisters of PP (or P-bar), but of the preposition: (14)
Joost Zwarts 63
the reference object can always be replaced by a special proform that can come between a modifier and the preposition.5 (17)
a.
b. c. d. e.
In these examples the modifier can not be a functor applying to the preposition, mapping a relation into a relation. It must be the PP (or P-bar) that is modified. Concluding, if we want to interpret modifiers compositionally as functions applying to the denotation of a PP, then a denotation based on points is simply not adequate. The heart of the problem is that modifiers of PP do not refer to positions denoted by the locative PP, but to distances and directions relative to the reference object. PP modification can only be compositional if these aspects are somehow directly reflected in the denotation of a locative PP.
2
VECTORS AS RELATIVE P O S ITIONS
The proposal of this paper is to analyze a region as a set of vectors. The region denotated by the PP achter de kerk (behind the church), for example, will then be the set of vectors with their starting point at the church that point backwards and the theme of this PP is located at the end point of one of these vectors. The truth conditions of (18a) are as in (18b), with v a variable over vectors: ( 18)
a.
Jan is achter de kerk Jan is behind the church b. 3 v [v E [achter de kerk]
1\
loc(jan, v)]
How to define the region in (18b) will be explained in section 4.1, but the picture in (19) gives a good impression, with the shaded area representing the region behind the church and v being one of the vectors from this reg10n: 0
6
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
twee centimeter er hoven two centimeters above it hoog daar hoven high above that direct hier hoven directly above this recht waar hoven straight above which links ergens hoven above and to the left of something
64 Vectors as Relative Positions
(19) Jan is achter de kerk
(2o) a. bij de kerk (near the church): the set of vectors with their origin at the church with a length smaller than a pragmatically determined number r b. hoven de kerk (above the church): the set of vectors that point from the church in an upward direction c. tussen de leerk en de kroeg (between the church and the pub): the vectors that point from the church towards the pub and vice versa. The general idea should be clear at an intuitive level. What the vector does is formalize the notion of a relative position, i.e. a position specified in relation to a reference object that functions as a spatial origin. By its very nature the vector concept provides the parameters of distance and direction that prepositions use to specify relative positions and that can be further specified by modifiers. Using vectors, the general semantics of the modifiers is straightforward. Each modifier selects from the set of vectors in the extension of the PP those vectors that have a particular length and/or direction:
(21) a. [2 cm PP] b. [hoog PP] c. [direct PP] d. [recht PP] e. [links PP]
{v E {v E {v E {v E {v E
[PP] j [PP] I [PP] I [PP] j [PP]I
2 cm(v)} high(v)} direct(v)} straight (v)} left(v)}
The measure phrase 2 em selects those vectors from the PP denotation that have a length of two centimeters and the adverb recht (straight) picks out those vectors that point in a particular direction with respect to a reference axis. The exact lexical definition of these and the other modifiers is not important at this moment (see section 4.2 for this). What is crucial is that
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Other prepositions can be analyzed vector-theoretically along the same lines:
Joost Zwarts 65
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
modification of PPs can be done in a compositional and natural way, because spatial entities are used that are by their very nature relational and that carry infoimation about the reference object that would otherwise have only been accessible to the modifier in a non-compositional way. Let me briefly compare this proposal to two alternative approaches to the modification problem. The notion of relative position might be modelled more directly, by adding the reference object of a PP to each position p in the region, yielding a set of pairs of a position p and the reference object y.7 A modifier like 2 em would then single out those pairs (p,y) such that the distance between p and y is two meters. This seems to yield the same result as a vector-based approach. but within a more traditional point-based framework. Another possibility is explored by Wunderlich & Kaufmann (1990) and Wunderlich & Herweg (1991) within the 'two-level approach' that separates a compositional semantic level from a non-compositional conceptual leveL8 In the example hoog boven de deur (high above the door), the modifier hoog is a two-place predicate high (p,c) expressing the vertical distance between a point p and a reference point c. At the semantic level this variable c is left unspecified, but at the conceptual level it is identified with the reference object of the preposition in a non-compositional way. However, both alternatives solve the problem without gaining any extra insights into the nature of locative PPs and their modifiers. First, PP modifiers like recht (straight) and schuin (diagonally), that are also used to orient linear objects (e.g. een rechte/schuine streep 'a straight/diagonal line'), suggest that the relation expressed by a locative preposition behaves in this respect like a line segment, which is something we get with vectors but not with pairs of a point and a reference object or with modifiers that have an implicit reference point that needs to be specified conceptually. Second, a denotation based on vectors provides the algebraic structure that reveals the kind of properties discussed in section s. properties that can only be formulated in an indirect way without vectors. Although vectors are intuitively connected to movement and in physics used to represent change of position, here their function is exclusively restricted to represent position. The path or movement of a directional PP like naar de kerk (to the church), for example, is not treated as a vector pointing to the church. but as a sequence of positions, the last one of which coincides with the church (see, for instance, Langacker 1986, Habel 1989, Nam 1995). Given our proposal to treat positions as vectors, this means that a path leading to the church is a sequence of vectors, each having their starting point at the church and gradually going to zero length. There is a good reason why a path cannot be represented by one single vector: because the paths corresponding to some prepositions are not linear. For example, the PP om de kerk {around the church), denotes a set of paths that are
66 Vectors as Relative Positions
approximately circles enclosing the church. Clearly, a vector cannot be used to represent such a circular path, but we can represent a path around the church as a sequence of vectors. The following diagram gives a very rough idea of what such a path would look like: (22) on de kerk . .
. .
I \
- - --
/ The \ ',_church./ "
--
1
___
_ __ '
''
.. ...
:
.
,' The ', church / _ ,
--
..
�·,': (\ The ' , _church,/
, -·: \ ) , /
The ', church
.. .. ..
... ...
... ..
'
.. _ _ _ ...
3
THE ALGEBRA O F VE CTORS
We have seen that the PP denotes a set of vectors that all have their origin in the reference object of the PP. Mathematically, the set total of all vectors with the same origin corresponds to the algebraic notion of a vector space: (23) A vector space V over the set of real numbers R is a set that is closed under two operations: a. Vector addition For every pair v, w E V there is exactly one v + w E V, the vector sum of v and w b. Scalar multiplication For every v E V and s E R there is exactly one sv E V, the scalar product of v by scalar s The operations of vector addition and scalar multiplication are graphically illustrated in (24) and (25), respectively: (25) Scalar multiplication (24) Vector addition
• -v
E
0
v
2v
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
This much will have to suffice to indicate how a semantics of directional prepositions can be built on a theory with vectors. In the remainder of this paper we will deal exclusively with locative prepositions.
Joost Zwarts 67
A vector space has the following properties: (26)
In order to use vectors for the model-theoretic interpretation of natural language expressions, vectors have to be added to the standard domain E of objects. One vector space V is not sufficient, however; the model will have to contain a much larger set S of vectors, providing for each pair of points P and Q, a vector pointing from P to Q and a vector pointing from Q to P. S is then the union of an inftnite set of vector spaces, one for each point in space and this S is added to the traditional domain E of individual objects.9 In addition to E and S (with its algebraic structure), a general location relation loc is assumed that determines the spatial relationships between E and S and between vectors of different vector spaces. Loc is a subset of the set of pairs (E U S) X (E U S) that can be understood in the following way: (27) a. b. c. d.
loc(x,y) loc(v,x) loc(y,w) loc(w,v)
x=y the beginning point of vector v is located at object x object y is located at the end point of vector w the beginning point of vector w is located at the endpoint of vector v
The diagram gives a rough idea of the nature of this relation:
(28) Location relations loc(w,v)
w
� X
y,w)
loc(v,x)
Finally, it will be useful to assume a function I I that assigns to each vector v, the length or norm lvl of that vector.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
a. For all u and v E V, u + v = v + u b. For all u, v, and w E V, (u + v) + w = u + (v + w) c. There is an element 0 E V, the zero vector, such that v + 0 = 0 + v = v for all v E V d. For every v E V there is a -v E V, the inverse of v, such that v + (-v) = 0 e. For all u and v E V and every c E R, c(u + v) = cu + cv £ For every v E V and a and b E R, (a + b)v = av + bv and (ab)v = a(bv) g. For every v E V, I V = v
68 Vectors
as
Relative Positions
SEMANTIC DEFINITIONS O F PREPOSITIONS AND MODI FIERS The interpretation of a locative prepositional phrase has the general schematic form in (29). A locative PP denotes a set of vectors taken from a 'universe' of vectors that is determined by the reference object NP, i.e. space([NP]M): {v E space([NP]M) I . v . . } (29) [ (pp P NP ]]M The reference object becomes the origin of this spatial inverse by selecting only those vectors that are located at the su iface or boundary of the reference object, as shown in (3o), and that point outward (v for outside, near, on, and the other prepositions) or inward (v2, for in and inside). (3o) Vectors on the surface 4
.
.
.
X
Evidence that location is relativized to a surface or boundary comes from examples like the following: (3 I ) a. diep in de boom deep in the tree b. ver buiten de stad far outside the city The use of the modifier deep in {3Ia) indicates that the reference point for the position is not the tree as a whole, but its surface. When the PP in de boom (in the tree) denotes the set ofvectors pointing from the surface of the tree inward, then diep can select those vectors that are long. In (3 I b) the modifier ver can only be properly understood as measuring the distance from the edge of the city. I will therefore assume that the vector universe space(x) of a reference object x consists of vectors like those in (3o).10 A formal definition of the function 'space' will not be given here, because the intuitive content is quite clear and a definition would lead us into many complexities. The preposition defmes a subset of space([NP]M) by imposing certain conditions on the length or orientation of vectors. For example, in the PP hoven de deur (above the door), hoven will take the upward vectors from the vector universe of the door: {32) [[PP hoven [NP de deur]]]M { v E space([de deur]M)I 'upward' (v)} =
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
u
Joost Zwarts 69
We already saw that generally a modifier of PP maps a set of vectors to a subset, for example: {v E [hoven de deur]M I (33) [ [PP recht [PP hoven de deur]]M 'straight'(v)} {v E space ([de deur]M) I 'upward' (v) 1\ 'straight'(v)} =
=
As discussed in section I, a locative PP usually functions as a predicate, which requires that the vector-denotation must be shifted to a property of objects. This interpretation can be defmed as the set of objects that are located at a vector from the region denotated by the PP:
(3s) {x E E l 3 v E [recht hoven de deur]M & loc(x,v)}
=
{x E E 1 3 v E space( [de deur]M) ['upward' (v) 1\ 'straight' (v) & loc(x,v)]}
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
(34) {x E E l 3 v E [PP]M & loc(x,v)} This is also the type of denotation that allows us to conjoin PPs, as in achter de schuur naast de auto (behind the barn beside the car) or achter Jan en naast Marie (behind Jan and beside Marie) by simply taking intersections. 11 There also seem to be modifiers that apply at this denotational level and not at the vector level. In the PP hoog achter de deur (high behind the door) hoog and achter de deur do not have the same point of reference: hoog does not take the door at its point of reference, but the ground. When the object level denotations of hoog and achter de deur are intersected, we get the correct result: the set of objects that are high and behind the door. Certain ambiguities with modifiers can possibly be derived from a distinction between 'object modification' and 'vector modification' of the same PP. The PP links hoven de deur (literally, left above the door) mentioned in section I , has another interpretation besides the one explained there and analyzed in terms of vectors in section 2: an interpretation in which links does not take the door as its point of reference, but a deictically given point (usually the position of the speaker). This second interpretation involves the intersection of the set of objects to the left of the speaker and the set of objects behind the door. The focus of this paper will be exclusively on the spatial meaning of PP, under the assumption that the predicative meaning can always be derived from this spatial meaning in a systematic way, without any cost, by a 'type-shift' or 'coercion' operation (Partee I987, Pustejovsky I99I) that maps a set of vectors to the set of objects located at those vectors, as soon as the locative PP is used in a position where a predicative expression is required. When the modified PP recht boven de deur is used as a predicate, the type-shift function implicit in (34) maps the set of vectors given in (33) to the following set:
70 Vectors
as
Relative Positions
I will now discuss the definitions of individual prepositions in section 4·1 and of modifiers in section 4.2.
4.1
Definitions of prepositions
Following Herskovits (1986), Landau & Jackendoff (1993) and others, I will distinguish between the prepositions in (36) and those in (37):
Roughly, the prepositions in (36) express basic topological notions, like 'inclusion', 'contact', and 'environment'. The prepositions in (37) are based on a particular direction, which is usually determined by an axis or by another object in the case of tussen (between). Some notion of direction also plays a role within the first class of prepositions: in/binnen and buiten express opposite directions with respect to the surface of the reference object. PPs with in and binnen denote the set of vectors pointing inward and PPs with buiten denote the set of vectors pointing outward (all interpretations are assumed to be relative to a model M): (38)
[in NP] = [hinnen NP] = {v E space([NP])I v inward to [NP] } {v E space([NP] )I v outward to [NP] } b. [huiten NP] = a.
The notions of inward/outward vectors with respect to a reference object not be defmed here. The illustration in (4o) will have to suffice. The prepositions op (on) and bij (near) can be defined in terms of the length lvl of the vector v: will
(39) a. [op NP] = b. [hij NP] =
{v {v
E E
space([NP] )I lvl space([NP] )I lvl
� <
o} r}
(r > o)
The diagrams (40) to (43) indicate what kind of regions are determined by these defmitions. Notice, however, that the diagrams only give bounded two-dimensional cross-sections of regions that are three dimensional and sometimes unbounded. The region is represented by the shaded area (unless the region is very small or thin, as in (42)) and the dotted line around an area indicates that the area is topologically open.t2
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
(36) in (in), binnen (inside), op (on), buiten (outside), bij (near) (37) voor (in front), achter (behind), hoven (above, over), onder (below, under), links �eft), rechts (right), naast (next to, besides), tussen (between)
Joost Zwarts 71
(4o) in I binnen x
(41)
buiten x
X
{42) op x
(43) bij
X
X
Of course, these are only very rough and idealized representations of the meanings of these items. They capture the central intuitions that we seem to have about them, but it is obvious that many of the subtle and interesting complexities of use, discussed in Herskovits (1986), Vandeloise (1991), Cuyckens {199 1), and others are ignored. How to capture the full range of meanings of prepositions like in and op clearly goes beyond the scope of this paper. Moreover, the prepositions in and binnen have received the same definition, in spite of obvious differences, like those in (44):
(44)
a. in het water in the water b. *in de grens *in the border
vs. vs. vs. vs.
*binnen het water *inside the water binnen de grens inside the border
What exactly distinguishes binnen from in must be left for further research. The same is true for the factors that may determine the 'radius' r in the definition of bij in (39b), like the size of the reference object, the structure of the environment, etc. The regions denoted by the prepositions in (37) (except for tussen) are 13 determined by an axis. There are three orthogonal axes. The vertical up down axis is determined by the line of gravitation usually. The horizontal front- back axis can be intrinsic to the reference object in virtue of its shape, movement, or function) or assigned deictically (from the point of view of an observer). The lateral axis goes side-to-side, is perpendicular to the other two axes, and has a left-hand side and a right-hand side. Again I will abstract away from the many different factors that may determine these
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
D
72 Vectors
as
Relative Positions
axes and simply assume that the model provides three axes, or rather half-axes, each defmed as sets of vectors:14 the set of vectors pointing upward (45) VERT FRONT the set of vectors pointing forward DEXT the set of vectors pointing rightward
(46) the inverse of an axis A is -A = {v E S 1 -v E A} Another useful notion is that of the so-called orthogonal complement .l.A, which is the set of vectors orthogonal to the vectors in an axis or plane A; (47) the orthogonal complement of A is .l.A = {v
E
S I "i/w E A [v _l. w]}
For example, the orthogonal complement _l.VERT of the upward vertical axis VERT is the set of horizontal vectors and the lateral axis LAT correpsonding to naast (beside) can be defmed as the orthogonal comple ment of VERT U FRONT. Given these axes, every vector can be decomposed into several components in the axes. This is illustrated in {48). The vector v is decomposed into a vertical component vVERT (its projection on the vertical axis) and a horizontal component v.lVERT (its projection on the orthogonal complement of the vertical axis). {48) Axes and projection VERT vvEJU
l.VERT
-VERT
X
v VERT
The notion of projection used here is defined in (49):
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Of course these half-axes correspond to the prepositions hoven (above), voor (in front of), and rechts van (to the right of). The respective antonyms of these prepositions, onder (below), achter (behind), and links van (to the left of) correspond to the inverses of the axes in (45). The inverse of an axis (and a set of vectors in general) is simply the set of vectors pointing in the opposite direction:
Joost Zwarts 73
(49) The projection vA of vector v on axis A is that vector u there is a w, such that w _l u and u + w v
E
A for which
=
This provides the necessary formal apparatus to define the most important direction-based prepositions. Herskovits (1986) shows that the size of the region corresponding to a preposition like boven (above) can vary: (so) b. boven x a. boven x c. boven x a
b
X
X
X d
In (soa), we can say that a is above x, but b is not, but in (sob), both a and b are above x, but c is not. However, when comparing a, b, and c with d in (soc), we can say that a, b, and c are above x, but d is not. So the region orresponding to above in a particular situation depends on the contrast we want to make. All of these regions can be expressed as sets of vectors emanating from the reference object x. For situation (soa), it is simply the axis VERT that is taken as the above-region, for (sob) it is the set of those vectors such that the projection on the vertical axis has a greater length than the projection on the orthogonal horizontal plane. The vector v in (48) is an example of a vector that satisfies this condition. For (soc), only those vectors count that have a non-zero component on the VERT-axis. What is common to these definitions is that they all impose conditions on the length of the vertical component: (51 )
a. [hoven NP] {v E space( [NP]) I lvVERTI lvl} b. [hoven NP] {v E space( [NP])I lvVERTI > lv_LVERTI} c. [hoven NP] {v E space( [NP]) I lvVERTI > o} For the purposes of this paper it is most convenient to assume that prepositions like hoven denote cone-shaped regions defined as in (s1b). The definitions of the other axis-based prepositions are very similar: =
=
=
=
(52)
[onder NP] {v E space( [NP]) I lv-VERTI > lv_L-VERTI} b. [voor NP] {v E space( [NP]) I j vFRoNTI > lv_LFRONTI} c. [achter NP] {v E space( [NP]) I lv-FRoNTI > lv_L-FRoNTI} a.
=
=
=
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
•
74 Vectors as Relative Positions
d. [rechts van NP] {v E space( [NP]) I lvoEXTI > lv_LDEXTI} e. [links van NP] {v E space([NP])I lv-oEXTI > lv_i-DEXTI} £ [naast NP] {v E space([NP]) I jvLATI > lv_LLATI} The definitions in (52a) to (52e) yield regions like those in (53) to (55) and the definition of naast in (52f) corresponds to the diabolo-shaped region in (56). (Remember that the diagrams only give ftnite cross-sections of these regions.) (53) onder x (front view) (54) voor x (side view) =
=
=
X
(55) links van x (front view)
(56) naast (front view)
The definition of tussen (between), finally, is of a slightly different nature. In order to keep things simple, the definition given here only covers those uses of tussen with two reference ojects, where the region is a line between the two objects, as shown in (57): (57) tussen x en y
• X
• y
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
X
Joost Zwarts 75
The definition is given in (s8}:
(s8) [tussen NP1 en NP2] =
{v E space( [NP�] ) I 3 s [s � I 1\ loc( [NP2] ,sv))} U {v E space( [NP2] ) j ::l s [s � I 1\ loc([NP2] ,sv))} Essentially, a vector located at x is between x and another object y if it would end in y when lengthened. This is sufficient for our purpose, but see Habel (I989) for an extensive discussion of the semantics of German zwischen that covers many of the intricacies of this relation.
Definitions of modifiers
Section 2 indicated how the introduction of vectors makes it possible to interpret modifiers as functions that map the denotation of a PP into a subset:
(59) [ (pp Mod PP) ]M = {v
E
[PP] M I · . . v . . . }
Each modifier imposes certain conditions on the length or direction of the vector v in (59) that will be explained in somewhat more detail here. The length of the vector can be specified in absolute terms by a measure phrase, for instance twee meter (two meters):
(6o) [twee meter PP] = { v
E
[PP] I lvl = 2 m}
where m is a real number representing the unit of the meter. There is no need to treat the measure phrase as the specifier of an invisible adjective Jar, as proposed in Wunderlich & Kaufmann (I990: 24I) and Wunderlich & Herweg (I99I: 780), because the measure phrase can directly apply to the PP denotation. This is also empirically more adequate, because in Dutch some measure phrases are possible with PPs even when they cannot be combined with a dimensional adjective:
(6I)
a.
b.
*
een eind buiten de stad a long distance (lit. end) outside the city een eind ver/hoogldiep a long distance far/high/deep
Adverbs like vlak (right) and direct (directly) express that the length is almost zero:
(62) [vlak PP] = [direct PP] = {v
E
[PP] I lvl
�
o}
The adjectives ver (far) and dicht (close) specify the length of the vector in relative terms, by comparing it with a contextually given norm r:
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
4.2
76 Vectors
as
Relative Positions
(63) [ver PP] {v E [PP]I l v l > r} [dicht PP] {v E [PP]I lv l < r} The same is true for the adjectives hoog (high), laag Qow), and diep (deep) but these adjectives carry additional information about direction, specifying that the vectors are downward (in the case of diep) or upward (in the case of hoog and laag):15 (64) a. [hoog PP] {v E [PP] I v E VERT & lvl > r} b. [laag PP] {v E [PP] I v E VERT & l v l < r} c. [diep PP] {v E [PP] I v E -VERT & l v l > r} The modifiers recht and pal (straight) both express that a vector v coincides with an axis that is taken as a reference axis (for example the vertical axis VERT), as illustrated in (6sa). The modifier schuin (diagonally) indicates that the vector v deviates from the reference axis and can be composed in two non-zero orthogonal components (6sb). (6s) b. schuin a. recht, pal =
=
=
=
=
V = VA
.L A
VA
.lA
X
V:' X
V.tA
The crucial difference is that in (6sa) there is no orthogonal component, but in (6sb) there is: (66) [recht PP] [pal PP] {v E [PP] I lv.LA I o} [schuin PP] {v E [PP] I l v.LA I > o} Finally, the modifiers rechts (right) and links Qeft) are defmed in terms of the DEXT and -DEXT axes: (67) [rechts PP] {v E [PP] I l vom l > o} [links PP] {v E [PP]I lvoEXTI > o} Rechts selects the vectors that have a component on the rightward axis and links selects the vectors that have a component on the leftward axis. The vector interpretation of modifiers makes it possible to relate the modifier use of dimensional adjectives like hoog and laag and directional modifiers like recht and schuin to their more basic adjectival uses, like in the following examples (with literal English translations): =
=
=
=
=
=
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
A
A
Joost Zwarts
(68)
77
a.
een hoge toren a high tower b. een lage toren a low tower c. een rechte toren a straight tower d. een schuine toren a slanting tower
5 C L O S URE AND C O NT I N U I TY PROPERTIES OF RE G I ONS The regions denoted by locative PPs (whether modified or not) have certain formal properties that crucially rely on their vector structure. A region may be closed under operations of scalar multiplication and vector addition and a region may or may not have certain continuity properties.16 I will explain such properties in this section and show their importance for the semantics of PPs. Some of the properties seem to express general constraints on prepositional denotations ('semantic universals'), others defme natural classes of prepositions with a characteristic semantic behaviour. It is crucial that all locative prepositions are interpreted in terms of vectors and not just those that involve axes or directions. It is only because all locative prepositions are of the same vector type that we can sharply formulate such properties as introduced in this section and discover where the sets of vectors denotated by, for example, inside-PPs and behind-PPs differ and agree. Compare
this to the theory of Generalized Quantifiers, where the
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
In these examples, the modifier picks out a subset of those objects that have a particular size or orientation with respect to the vertical axis. Suppose now that certain objects are associated with a vector that represents its main axis (like in the visual 3D models of Marr 1982). A tower, for example, will be associated with an upward vector that represents its main vertical axis. The definitions that we gave for the PP modifier use of hoog, laag, recht, and schuin can then easily be adapted for the adjectival use. The basic condition that is imposed on the length or direction of the vector is the same in both uses. A tower is hoog if its vector v satisfies the condition v E VERT & lvl > r and it is recht if the component in the horizontal plane is zero, i.e. lv .LVERT I = o. Although I am not able to provide a full treatment of such cases here and to do justice to the richness of dimensional and directional adjectives, these examples suggest that a semantics based on vectors can be extended naturally from locative prepositions to other expressions with a spatial meaning component.
78 Vectors
as
Relative Positions
uniform treatment of all noun phrases as sets of sets is the basis for a fruitful research program. Closure properties As explained in section 3, a vector can be multiplied by a scalar in order to change its length. If the scalar is greater than I , the vector will be lengthened, if it is between o and I , the vector will be shortened. Lengthening and shortening can be seen as operations on vectors in a region and regions may or may not be closed under these operations. Closure under lengthening can be defmed as follows: (69) Closure under lengthening A region R is closed under lengthening iff for every non-zero v E R, sv E R for every s > I . Given an arbitrary vector v in a region that is closed under lengthening, one can stretch this vector and the result will still be in the region. Intuitively, a region that is closed under lengthening is unbounded in the direction in which the vectors point. A region that is not closed under lengthening is bounded, because of the preposition used (e.g. bij ), because the reference object is bounded (e.g. with binnen) or because of modifiers like dicht (close) and hoogstens twee meter (at most two meters):17 (7o) closed under lengthening not closed under lengthening voor (in front of) bij (near) achter (behind) in, binnen (in, inside) hoven (above) op (on, at) onder (under) tussen (between) naast (beside) buiten (outside) ver achter (far behind) dicht achter (close behind) minstens 2 m achter hoogstens 2 m achter (at least two meters behind) (at most two meters behind) 5.1
(7I)
a.
twee meter voor I achter I hoven I onder I naast I buiten NP two meters in front of I behind I above I under I beside I outside NP
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
This distinction is significant, because the PPs that are closed under lengthening are the ones that can be modified by measure phrases like two meters, provided that they are not already modified. This is illustrated by the following examples:18
Joost Zwarts 79 b.
*
twee meter tussen I bij I in I op I binnen NP two meters between I near I in I on I inside NP
(72)
Closure under shortening A region R is closed under shortening for every v E
R, sv E R for every o
iff s < 1.
<
This property says that one can take an arbitrary vector from the region, make it shorter, and the result will again be in the region. {73)
closed under shortening
not closed under shortening
all simple prepositions recht hoven {straight above) laag hoven �ow above) minder dan 2 m buiten �ess than 2 m outside)
hoog hoven (high above) meer dan 2 m buiten {more than 2 m outside)
Intuitively, the regions that are closed under shortening make contact with the (surface of the) reference object. The diagram in (74) shows the region of meer dan twee meter buiten x (more than two meters outside x). The region does not make contact with the reference object, because there is a gap of two meters created by the modifier meer dan twee meter (more than two meters). {74)
meer dan twee meter buiten
x
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
This shows that measure phrase modifiers are not just functions from regions to subregions, but they apply only to regions that are closed under lengthening. The intuitive explanation is that measure phrases specify a value or range of values on a open-ended scale and the regions that are closed under lengthening are the regions that provide such a scale. Notice that the examples in {71) show that it will not do to say that measure phrases measure a distance on the spatial axis (like VERT, FRONT, DEXT) associated with a projective preposition, which would obviate the need for vectors.19 PPs with buiten (outside) can also be modified by means of a measure phrase, even though there is no axis. Closure under shortening is like closure under lengthening:
So Vectors
as
Relative Positions
Notice that in (73) all simple PPs (i.e. PPs without modifiers) are closed under shortening. This might be taken as a coincidence, but it would be more interesting to interpret it as a constraint on prepositional semantics: (75) Universal 1
All simple PPs are closed under shortening.
(76) Closure under vector addition A region R is closed under vector addition iff for every v, w E R, v + w E R shown in (77), this property, which is characteristic for direction-based prepositions like hoven (above) and achter (behind), can be lost with certain modifiers:
As
(77) Closed under addition hoven (above) recht hoven (straight above) hoog hoven (high above) minstens 2 m hoven (at least 2 m above)
Not closed under addition schuin hoven (diagonally above) vlak hoven (right above) hoogstens 2 m hoven (at most 2 m above)
The property of closure under addition corresponds with the transitivity of the underlying prepositional relation. This is why (78c) follows from the premises (78a) and (78b), while (79c) can not be concluded from (79a) and (79b) (talking about paintings on a wall): (78)
a.
Vermeer hangt (recht/hoog) hoven Rembrandt Vermeer is hanging straight/high above Rembrandt b. Rembrandt hangt (recht/hoog) hoven Van Steen Rembrandt is hanging straight/high above Van Steen c. Vermeer hangt (recht/hoog) hoven Van Steen Vermeer is hanging straight/high above Van Steen
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
This universal implies that simple PPs denote regions that overlap with every environment of the reference object. One clear and easily falsifiable prediction drawn from this universal is that there are no distal prepositions. This seems to be true for Dutch and English (and other languages I know of): the proximate PP bij NP (near NP) does not have a distal counterpart ver NP (far NP). Of course, this gap is filled by the expression ver van NP (far from NP), but this is not a simple PP, since it involves a combination of the directional preposition van (from) with the distal adjective for (ver).20 The universal would only be falsified by a distal expression which is a genuine simple PP. Some PPs have the property of closure under vector addition:
Joost Zwarts 81
(79)
Vermeer hangt schuin/vlak hoven Rembrandt Vermeer is hanging diagonally/right above Rembrandt b. Rembrandt hangt schuin/vlak hoven Van Steen Rembrandt is hanging diagonally/right above Van Steen c. Vermeer hangt schuin/vlak hoven Van Steen Vermeer is hanging diagonally/right above Van Steen a.
5.2
Continuity properties
(So) v linearly between
u
and w
(81) v radially between
u
and w
A vector v is linearly between u and w if v is a lengthening of u and w is a lengthening of v. A vector v is radially between two vectors u and w
that form an acute angle if the shortest rotation of u into w passes over v. Both of these notions of 'betweenness' correspond to a form of continuity: (82)
a.
Linear continuity A region R is linearly continuous
iff
for all u, w E R, if v is linearly between u and w, when v E R
b. Radial continuity A region R is radially continuous iff for all u, w E R, if v is radially between u and w, then v E R
The best way to grasp these continuities is by looking at two cases that each lack one of these properties. The region in (83) denoted by een even aantal meters buiten x (an even number of meters outside x) consists of an infinite set of concentric shells around the reference object x. This region is radially continuous but linearly discontinuous. The PP schuin hoven x (diagonally above x) in (84) denotes a region that is linearly continuous, but radially discontinuous.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The region denoted by a locative PP can be continuous or discontinuous. Continuity can be defmed in many ways, but the defmitions used here are based on the two ways in which a vector v can be 'between' two other vectors u and w:21
82 Vectors as Relative Positions
(83) een even aantal meters buiten x
(84} schuin hoven x
X
(8s} Universal 2 All simple PPs are linearly and radially continuous. (86) Universal 3 All PPs are linearly or radially continuous. CONCLUSION The primary goal of this paper was to give a compositional and natural account of the interpretation of modified PPs. I have shown that both prepositions and modifiers of PPs can be interpreted in terms of vectors. The insights from the literature about prepositions and other elements (e.g. dimensional adjectives) can be integrated in a general, formal framework. The vector-algebraic background of this framework makes it possible to study the meanings of PPs, both simple and modified, in a way that is reminiscent of the Generalized Quantifier Theory of NPs: in addition to precise definitions of individual PPs, algebraic properties can be formulated that either single out empirically relevant subclasses of locative PPs or that provide (universal?) constraints on their denotation. JOOST ZWARTS SH. PO Box 44456 Nairobi Kenya
Received: o8.o7.96 Final version received: I 4-07·97
NOTES I
The research for this paper was sup ported by the Foundation for Language, Speech, and Logic, which is funded by the Netherlands Organization for Scien tific Research, NWO (grant 300- I 7I -o33).
Earlier versions were presented at the TABU-day at the University of Gron ingen and SALT V at the University of Texas at Austin. I would like to thank the audiences there for their comments and
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
Two continuity universals can now be formulated, a stronger one for simple PPs and a weaker one for all PPs, whether they are modified or not:22
Joost Zwarts 83
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
their status and treat them as if they Johan van Benthem, Peter Gardenfors, Bill Philip, Martijn Spaan, Henk Verkuyl, were spatial primitives. and Emile van der Zee for their com IO For simplicity, reference objects are ments on earlier written versions (with assumed to be convex, ie. they contain the usual disclaimers), the anonymous no discontinuities, indentations, or pro reviewers of this journal, and especially trusions, but are basically like familiar Yoad Winter for extensive discussion geometric objects (spheres, cylinders, and fruitful cooperation. rectangles, etc.). How to deal with 2 See, for example, Bennett (I975), Cress non-convex objects or with objects well (I 978), Jackendoff (I 983), and Lakoff that seem to have no boundary (like (I987)· the universe) or vague boundaries (like 3 See Jackendoff (I983), Creary et al. mass objects) is a topic for future research. (I 989), Wunderlich (I 99 I). 4 Alternatively, regions could be seen as I I See also Creary et al. (I989). Conjunction primitives ('individuals') in a mereology of PPs with different reference objects of space, as in Bierwisch (I988), cannot be interpreted directly as inter Aumague (I995), and Nam (I995), for section, because such PPs usually denote instance. A modifier then maps a region disjoint sets of vectors. This is because to a proper subregion, but since both each PP is part of its own vector space argument and result of the modification that is not directly related to the spaces function are unanalyzed, it is hard to of other PPs. specify what the modifier does, unless I2 From the topological point of view all we have an idea of the mereological of these regions are open sets, the sur and geometric sttucturing of the spatial face region is a closed set. Two objects domain. touch if their surface regions overlap. 5 That this pronoun is not a clitic incor See also Hayes (I985). porated into the preposition is shown I3 See Herskovits (I986) for extensive dis by its ability to switch places with the cussion of axes and their relation to modifier: er twee centimeter achter, daar prepositions like those in (37) and also hoog boven, and by the possibility to Lang (I990). The treatment given here move it out of the PP to several posi can only be very sketchy. tions in the sentence, including the I4 In a more realistic account, these axes topic position (van Riemsdijk I978). would have to be relativized to objects. 6 This picture of a PP region and the For example, if x is a television, then ones to follow are given for clarification FRONT(x) is the set of vectors reaching only; they have no theoretical status of out from the screen, roughly. But if x is their own, unlike the diagrams used a tree, then we would need a second in the Cognitive Grammar literature argument: FRONT(x,y) would then be (Langacker I986, Hawkins I984). the set of vectors pointing from the tree 7 This formulation was suggested by an x towards an observer y. In this paper, anonymous reviewer. the model is set up in such a way that all 8 A full discussion of the two-level objects are oriented in the same way. approach to prepositions and PP modi IS I am not yet sure whether it would fiers would go beyond the scope of this perhaps be more adequate to say that paper. these modifiers do not measure the 9 Vectors are usually defined as pairs of length of the vector itseU: but its projec points or tuples of real numbers in the tion on the vertical axis, ie. lvVERTI > r, mathematics literature, but in this paper etc. Moreover, definition (64c) only I wish to remain neutral with respect to gives the 'downward' meaning of diep.
84 Vectors as Relative Positions may become closed under lengthening
However, we have already seen that diep also has an 'inward' meaning, as in diep
in de boom (deep in the tree) that I will not account for here. 16 Another property that I will not discuss
in this paper is closure under rotation: we can change the direction of a vector
19 That axes would be sufficient to explain the use of measure phrases was sug gested by an anonymous reviewer, who referred to Wunderlich & Herweg (1991: 78o).
20
That ver (far) is really an adjective in this construction and not a preposition is shown by its modiftcation possibilities: erg ver van het huis (very far from the
the proper use of a modifier like recht (straight): *recht bij de deur (straight near the door) vs. recht boven de deur (straight above the door). It would be interesting (but far beyond the scope of this paper) to relate the vector-based closure prop erties to geometric invariances: which properties expressed by prepositions are invariant under such operations as translation and rotation and under projective and topological transforma tions? See Crangle & Suppes (1989) for
house), te ver van het huis (too far from the house). 21 There is an interesting connection here with recent work of Peter Giirdenfors, who claims that natural properties (expressed by color terms and common nouns, for example) can be represented as convex regions in conceptual spaces, i.e. if points v and v, are in the region, then every point between v and v, is also in the region (Gardenfors 1994). The continuity universals of this section, defined in terms of between-relations over vectors, impose a sitnilar condition
interesting discussion of prepositions from this geometric �rspective. 17 The definitions in this section apply
22 Yoad Winter pointed out to me that this universal does not seem to be valid
to regions, but a PP can be said to be closed under lengthening when the region it denotes is closed under length
conjunction of two modifiers: e.g. schuin en een even aantal meters boven x (diag
ening in every model. Sitnilarly for the other properties, I will talk about PPs or prepositions having a particular
onally and an even number of meters above x). This PP denotes a region which is neither linearly nor radially
property when it is strictly speaking a property of the corresponding region.
continuous, because it is the inter section of the regions in (83) and (84). Given this, Universal 3 should be
This property might be relevant for
an
18 The pattern in Dutch is clearer than in English. where beside and next to have a meaning component of contact or proximity, absent in Dutch. which makes that they are not closed under lengthening. Binnen (inside) and in (in)
1
1
on the regions denoted by PPs.
for those PPs that are modified by a
reinterpreted as a universal for PPs that do not contain conjunctions and we would need another, more general universal that applies to all locative PPs, simple, modifted, and conjoined.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
while keeping its length ftxed and check whether the result is still in the region. This property only works when the reference object is idealized as a point. For instance, PPs with bij (near) are closed under rotation, PPs with boven (above) are not closed under rotation.
when the reference object itself is open ended (e.g. twee centimeter in de muur, 'two centimeters into the waUl
Joost Zwarts
85
REFERENCES Aurnague,
M
{I995).
'Orientation
in
XXIX. Akademie-Verlag, Berlin, I -65. Crangle, C. & Suppes, P. ( I989), 'Geo metrical semantics for spatial preposi tions', Midwest Studies in Philosophy, XIV, 399-422.
Creary, L, Gawron, M., & Nerbonne, J. (I989), 'Reference to locations', Proceed ings of the 27th Annual Meeting of the ACL,
42-50.
Cresswell, M ( I978), 'Prepositions and points of view', Linguistics and Philosophy, 2,
I -41.
Cuyckens, H
(I99I ),
The semantics of
spatial prepositions in Dutch: a cogni tive-linguistic exercise', dissertation, University of Antwerp. Gardenfors, P. ( I994), 'Frameworks for properties: possible worlds vs. conceptual
spaces', Semiotiques, 6-7, 99-I20. Habel, C. ( I989), 'Zwischen-Bericht', in C. Habel M. Herweg & K. Rehkaemper
Raumkonzepte in Verstehenspro zessen: Interdiszipliniire Beitriige zu Sprache und Raum, Niemeyer, Tiibingen, 37-69. Hawkins, B. (I984), The semantics of English prepositions', PhD. dissertation, University of California, San Diego. Hayes, P. J. ( I985), 'Naive physics I: ontology for liquids', in J. Hobbs & R Moore (eds), Formal Theories of the Commonsense World, Norwood, New Jersey, 7I - IQ1. Herskovits, A. { I986), Language and Spatial Cognition: An Interdisciplinary Study of the Prepositions in English, Cambridge (eds),
University Press, Cambridge.
Jackendoff, R
( I973),
The base rules for_
prepositional phrases', in S. R Anderson & P. Kiparskf (eds), A Festschriftfor Morris
Halle, Holt, Rinehart & Winston, New York, 345-66. Jackendoff, R ( I 983), Semantics and Cognition, MIT Press, Cambridge, MA. Lakoff, G. ( I987). Women, Fire, and Dangerous Things. Chicago: University of Chicago Press. Landau, B. & Jackendoff, R { I993). ' ''What" and "where" in spatial language and spatial cognition', Behavioral and Brain Sciences, 16, 2I7-65. Lang, E. ( I 990), 'Primary perceptual space and inherent proportion schema: two interacting categorization grids under lying the conceptualization of spatial objects', in Journal of Semantics, 7,
121-41.
Lang, E . ( I99I ), 'A two-level approach to projective prepositions', in G. Rauh (ed.), Approaches to Prepositions, Gunter Narr Verlag, Tiibingen, I27-67. Langacker, R ( I986), Foundations of Cognitive
Grammar, Stanford University Press, Stanford. Marr, D. ( 1982), Vision, Freeman, San
Francisco. Nam, S. ( I995), The semantics of locative prepositional phrases in English', PhD. dissertation, UCLA.
Partee, B. H
( 1987),
'Noun phrase inter
pretation and type-shifting principles', in J. Groenendijk, D. de Jongh & M
Stokhof (eds), Studies in Discourse Representation Theory and the Theory of Generalized Quantifiers, Foris Publica tions, Dordrecht, 1 15-44. Pustejovsky, ]. ( I991 ), The generative lexi con', Computational Linguistics, 17, 4,
409-41.
Rauh, G. ( I996), 'Zur Struktur von Prapo sitionalphrasen im Englischen', paper presented at the Jahrestagung DGfS, Freiberg.
Riemsdijk, H. van {I978), A Case Study in
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
French spatial expressions: formal representations and inferences', Journal ofSemantics, 12, J. Bennett, D. C. { I975). Spatial and Tem poral Uses ofEnglish Prepositions: An Essay in Stratificational Semantics, Longman, London. Bierwisch, M ( I988), 'On the grammar of local prepositions', in M Bierwisch, W. Motsch, & l Zimmermann (eds), Syntax, Semantik und Lexikon, Studia Grammatica
86 Vectors as Relative Positions Peter de Ridder Press, Lisse. Vandeloise, C. (1991), Spatial Prepositiosn: A Case Study from French, Chicago Univer sity Press, Chicago. Wunderlich, D. (1991), 'How do preposi tional phrases fit into compositional syntax and semantics', Linguistics, 29, 591 -621. Wunderlich, D. & Herweg, M (1991), Syntactic Markedness,
'Lokale und Direktionale', in A. von Stechow & D. Wunderlich (eds), Seman
tik: Ein internationales Handbuch der zeit Walter de geniissischen Forschung,
Gruyter, Berlin, 758-Ss. Wunderlich, D. & Kaufmann, L (rggo), 'Lokale Verben und Prapositionen: semantische und konzeptuelle Aspekte', in S. Felix et al. (eds), Sprache und Wissen, Westdeutscher Verlag, Opladen, 223-52.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
©Oxford University Press
1997
Book Review
Linda M. Moxey
&
Anthony J. Sanford. Communicating Quantities.
Lawrence Erlbaum, Hove (UK)/Hillsdale (USA), 1993. £19·95/$37·50 (cloth).
xii +
144 pp.
BART GUERTS
( r ) A survey has recently been carried out whether or not female students prefer to be examined by female doctors. Q [=Jew, a few, many, not many, . . . ) of the local doctors are female. Subjects were asked to specify what percentage of the local doctors they thought were female, and these estimates were compared with baseline expectations determined in a prior test. As might be expected, the choice of Q affected the proportion reported, but M & S found this effect to be curiously restricted, as there turned out be no reliable difference between Jew, very few, a Jew, only a Jew, and not many. That is to say, if one supposes that these quantifiers simply serve to denote percentages, one is forced into the unlikely position that they all mean the same thing. M & S conclude from this, plausibly enough, that the prospects of the psychometric approach are dim. Since the seminal work of Barwise and Cooper (1981), it has become
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
In this monograph, Moxey and Sanford (M & S) report on a series of psycholinguistic experiments on the subject of natural language quantifica tion. Several of these experiments were published before in separate articles, but here M & S draw together the various strands in their research, and treat in more detail some of the issues raised by their earlier work. Perhaps the most thoroughly explored psychological approach to quantification is based upon the prima facie plausible assumption that quantifying determiners correlate with points on a numerical scale. This assumption obviously makes sense for numerals, but intuitively it might also apply for quantifiers such as few, many, or most, for it evidently makes sense to ask how many As count as few, many, or most As (in a given context). Proponents of what M & S term the 'psychometric' approach have tried to an5wer precisely such questions, but M & S argue that the utility of psychometric investigations into the semantics of quantification is rather limited. In one experiment, M & S presented subjects with texts like the following (pp. 31f):
88 Book Review
{ :� }{ e ? w Not many ?Many
of the suspects were proved to be guilty, were they? lawyers are troubled by anything like a conscience.
}
One of the most interesting of M & S's findings is that, in addition to these negation-like properties, monotone decreasing quantifiers correlate with a distinctive pattern of anaphoric reference. I will discuss this point in some detail. From a pragmatic point of view, the interpretation of a quantifying determiner typically involves . one or two sets. On the one hand, most quantifiers may be interpreted, on a given occasion, as presupposing some domain of individuals. In Milsark's (1977) terms, a quantifier thus interpreted is 'strong'. When it is thus interpreted, the interpretation of a quantifier will generally involve a subset of this domain (what M & S call the 'refset'), which is made available for subsequent anaphoric reference. For instance, a token of (3)
a.
At least three volunteers were injured.
is most likely to be construed in terms of a contextually given domain of volunteers, A, and this sentence claims that there is some B � A such that the cardinality of B is 3 or more and that all members of B were injured. Once this sentence has been uttered, both the domain and the refset are available for anaphoric reference; for instance:
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
widely accepted that quantifiers may be construed as relations between sets. (I prefer this relational perspective to the functional stance Barwise and Cooper adopt themselves, mainly because on a relational construal the connections between the semantics and the pragmatics of quantification become more transparent, as I will try to illustrate in the following. But in most respects these two perspectives are mutually compatible, of course.) For instance, some is a relation that holds between two sets A and B if A n B =j; 0. A quantifier Q is monotone increasing (more accurately: monotone increasing in its second argument) iff, for all A, B, C, if Q(A, B) and B � C, then Q(A, C); Q is monotone decreasing iff, for all A, B, C, if Q(A,B) and C � B, then Q (A, C). All, most, some, a Jew, and many are monotone increasing quantifiers; no,few, not all, and not many are monotone decreasing. The latter class of quantifiers are negative in the sense that they pass the standard negation tests; for example, they accept positive tag questions and license negative polarity items, such as anything:
Journal of Semantics 89 (3) b. But they wouldn't give up. Here the plural pronoun might be construed as referring back to either the domain or the refset. On the other hand, most quantifiers can also be construed without presuppositions, as in:
(4)
There were at least three volunteers.
this
In case, at least three volunteers does not mean 'at least three of a contextually given domain of volunteers'. It therefore is interpreted here as
(s) ?Most of the names on this list begin with a J. They begin with an M. M & S's principal result, and the centrepiece of the second half of their book, is that these observations are not valid for all varieties of quantifica tion, because monotone decreasing quantifiers license, and sometimes even favour, anaphoric reference to the compset. This is shown by an experiment in which subjects were asked to continue text fragments like the following:
(6)
{
Not many
:�:
w
}
MPs were at the meeting
{
. They
.
.
.
because they . . .
}
Only a few The outcome of this experiment was that, whereas monotone increasing
a
Jew induces subjects to refer back to the refset (i.e. the set of MPs that were at the meeting), monotone decreasing quantifiers like not many and Jew bias them towards the compset (i.e. the set of MPs that were not at the meeting). These results hold for the full stop as well as for the because condition. The quantifier only a Jew is the odd one out: while in the full stop condition it
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
a 'weak' NP, as Milsark would say. The interpretation of (4) involves just a single set that may be picked up by a subsequent anaphor. In the following I confine my attention, as do M & S, to strong quantifiers, i.e. to quantifiers that are construed as presupposition inducers, and whose interpretation involves a domain as well as a refset. From what we have seen in the following it is natural to conclude that a strong quantifier introduces two objects into the discourse, a domain and a refset. Once these are in place it is of course possible to derive a third object, which is the set-theoretic difference between the two, but there are reasons to assume that this 'compset', as M & S call it, is less accessible than either the domain or the refset. For instance, the following discourse is obviously incoherent, the reason being, intuitively speaking at least, that in order for this discourse to make sense, the anaphoric pronoun has to refer to an object which becomes available only on second thoughts:
90 Book Review induces a preference for the refset, in the
because
condition subjects
predominantly refer to the compset. These data are surprising. Extrapolating from the behaviour of proto typical quantifiers such as
most,
one is prepared for quantifiers that draw
subjects towards their domains or their refsets, but not to their compsets.
A
natural initial reaction, therefore, is to question the data. For instance, one might suspect that, although it appears as if subjects were referring to the compset of a quantifier, they were actually referring to its domain, albeit perhaps in a somewhat vague or sloppy way. The idea is that, conceivably, when a speaker produces a discourse like the following, (7) Few of the MPs were at the meeting. They were too busy. (p. 63)
arguments. First, they observe that speakers themselves label their compset references as such, and that their assessment is confirmed by independent judges. Secondly, speakers often volunteer continuations with
instead,
like
the following: (8) Hardly any of the MPs attended the meeting. They were out at the pub or with their secretaries instead. (p. 64) Such continuations surely count as genuine compset references. Finally,
M & S report that compset references predominate even with the quantifier not quite all; for instance:
(9)
Not quite all of the MPs were at the meeting. They stayed at home instead. (p. 64)
Presumably, the compset of a quantifier like few or
not many will
not be
much smaller than its domain, so in these cases it is not unlikely that apparent compset references are in fact generalizing references to the quantifier's domain. However, the domain of much larger than its compset, and yet continuations
M&
not quite all will
typically be
S's subjects produce compset
9 out of 10 times {in the full stop condition), which is more
than for any of the other quantifiers M & S used in their studies. These arguments, the last one in particular, have convinced me of the fact that compset references exist, but they still leave room for doubts about the extent of the phenomenon. It seems to me that in some cases at least, it may be held that what appears to be compset reference is in fact a kind of
collective reference to the domain of a quantifier (this is similar to, but not quite the same as, the view M & S argue against). It is common practice to
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
he uses the pronoun to refer to the MPs in a quasi-generic manner, so that the speaker actually wants to convey that the MPs were 'generally' or 'mostly' too busy. M & S seek to discredit this account with three
Journal of Semantics
91
distinguish between collective and distributive uses of plurals and (other) quantifiers. (10)
a. Each of the pirates had a wooden leg. b. The pirates attacked the galleon.
(I I) The pirates were fishing. If all the pirates were fishing, then an utterance of (11) is obviously true. But is it to be construed collectively or distributively? This question may be hard if not impossible to decide. If the individual instances of fishing pirates are wholly unrelated (for instance, if the speaker is referring to pirates that live in different parts of the world, who, purely coincidentally, all happened to be fishing at a given point in time), then a distributive reading might seem more likely. But otherwise there may not even be a fact of the matter. M & S apparently take it for granted that the subjects in their continuation tasks always had distributive interpretations in mind. But perhaps this assumption is not as innocuous as it may seem. It is easily conceivable that the subject (call her 'Betsy') who produced the continua tion in (7) intended the pronoun to refer collectively to 'the MPs'. 'They were too busy' was therefore intended to mean that, taken as a group, the MPs were too busy-which does not exclude the possibility that some of them had time to spare. Now suppose Betsy is asked to specify to which of the following the plural pronoun in her own continuation referred (p. 6I): (12) MPs in general All MPs MPs who were at the meeting MPs who were not at the meeting Other (please state) Then she should conclude that none of these matches her original intention, if she doesn't want to use the escape hatch provided by 'other' -which she may not want to use because it is not clear to her what she should say. For, as I have argued in the foregoing, the content of 'the MPs taken as a group' (which is what Betsy should have said, ex
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
( wa) only has a distributive reading, according to which the predicate 'had a wooden leg' applies to each pirate individually. (Iob), by contrast, favours a collective reading, according to which the pirates attacked the galleon as a group. On this reading, not all and perhaps not even a majority of the pirates need have been involved in the attack; a group may be responsible for an action implemented by some of its members only. Now, although the collective/distributive distinction is intuitively sound, it does not by any means yield a clearcut dichotomy. Consider, for instance:
92
Book Review
hypothesi) is somewhat elusive, and
not always clearly distinct from 'all the MPs'. In such a situation it is understandable that Betsy should decide to slightly shift away from her original intention and decide that she was · referring to the MPs that were at the meeting. This is not to claim that Betsy doesn't know what she was saying, since for all practical purposes, what she said coincides with what she claims to have said. It is just that Betsy's reports on her own intentions cannot simply be taken at face value which is surely not a controversial point. I believe that this story is a plausible one, and that M & S's counter
(1 3)
Few of the fans went to the football match. They all watched the game on the television instead. (p. 74)
Here the plural pronoun refers back to the compset of monotone decreasing few, and the continuation explains why few of the fans went to the football match. This is in fact the general pattern: if a sentence of the form [[ Q N] VP] invites continuations with compset references, then these continuations will typically seek to explain why VP is true of Q N only. It is intuitively obvious that some such connection must exist. In reporting that few As are Bs a speaker conveys that the size of A n B is smaller than
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
arguments are not sufficient to prove that something along these lines didn't happen in at least some instances of what they call 'compset reference'. If this is correct, potential problems arise in more than one way. First, it may be that M & S's data are distorted to a greater or lesser degree, the actual number of domain references being higher than reported, and the actual number of compset references proportionally lower. Secondly, in the light of the foregoing observations about the distributive/collective distinction, it may even be that this kind of ' experimental setup is ill suited to separate reference to a quantifier's domain from reference to its compset. Thirdly, M & S's theoretical account of compset reference may be in jeopardy (see below). In order to explain their fmdings, M & S propose a model on which compset references are caused by two factors. First, and foremost, they hold that quantifiers such as few or not many focus upon their compsets. If this is correct, the context representation of such quantifiers not only involves compsets-they highlight their compsets, to boot. In combination with the widely held view that anaphors prefer to pick up referents that are at the focus of attention, this assumption explains how, say, few directs subjects towards its compset. The second factor involved in compset reference, according to M & S, is of a thematic nature. Analysing the content of the continuations produced, they fmd that there is a correlation between compset reference and the content of a continuation. The following example is a typical one:
Journal of Semantics
93
expected. It seems natural that subjects should want to explain why this expectation was disappointed, and in doing so they will almost necessarily concentrate their attention on the As that are not Bs, i.e. they will concentrate the compset. This line of explanation is confirmed by M & S's fmding that, while a sentence like { 14.a) yields hardly any compset references at all, (x4b) invites compset references in the majority of cases (p. 8 x): (14)
a. Only a few of the MPs were at the meeting. b. Only a few of the children ate their ice-cream.
(xs) Few of the children hated Santa Claus. They left him plenty of milk and cookies. (p. 67) M & S conclude from this that compset references do not always arise because subjects want to explain the situation reported in the opening sentence, and that it must be assumed, in addition, that a quantifier such as few focuses upon its compset. Judging solely on the basis of this example (which is the only one given by M & S), however,. I don't see that this conclusion is inescapable, because I am not convinced that (xs) must be
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
M & S explain this by assuming that, taken by itself, only a few does not bias the hearer towards its compset, and that it is the difference in content which makes the difference: as compared to (14a), the state of affairs reported by (x4b) is defmitely remarkable, and therefore it is more likely that subjects will want to 'account' for (1 4b) than for ( x 43-), with a larger proportion of compset references as a concomitant. At this point one may wonder if not all instances of compset reference can be explained along these lines. Ceteris paribus, such an account would be more attractive than M & S's two-factor theory, for at least two reasons. First, it would obviously be simpler. Secondly, if compset reference could be explained in purely thematic terms, it would not only be unnecessary to suppose that certain quantifiers focus on their compsets: one could even get by without the assumption that the context representation of these quantifiers involves compsets at all. For then we could return to the 'naive' view outlined earlier, according to which quantifiers are uniformly represented in terms of domains and refsets-compsets being derivable only if needed. M & S consider this alternative, and argue on the basis of experimental evidence that an independent focus effect must be assumed. M & S presented subjects with sentences that reported a quite unexc�p tional state of affairs, and therefore did not seem to call for an explanation. As it turned out, subjects indeed produced very few reason-giving continuations, and yet the proportion of compset references remained high. M & S give the following example:
94 Book Review
Universitiit Osnabrock
FB 7 49069
OsnabrUck Germany e-mail:
[email protected]
REFERENCES Barwise, J. & Cooper, R (1981), 'Gen eralized quantifiers and natural lan guage', Linguistics and Philosophy, 4, 159-219.
G. (1977), Toward an explana tion of certain peculiarities of the existential construction in English',
Milsark,
Linguistic Analysis, 3,
1 -30.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
classified as an instance of compset reference. Indeed, the most obvious interpretation of (Is), to my mind, is the one on which the plural pronoun refers collectively to 'the children', and the continuation provides evidence for the truth of the Hrst sentence, as suggested by the following paraphrase: {I6) The children left Santa plenty of milk and cookies, which shows that few of them hated him. Clearly, the children in {I6), which is the counterpart to the plural pronoun in {IS), is used here collectively. It is impossible for me to tell whether {IS) is typical of the results obtained by M & S, but it is obvious enough, I think, that the case for or against their two-factor model will have to be based upon a more detailed content analysis of their data. In my opinion, Communicating Quantities is a most welcome addition to the already impressive bibliography of natural language quantification. To begin with, this monograph charts a new and evidently fruitful approach to the mental processing of quantification. Secondly, and perhaps most importantly, it presents a range of intriguing data which should be relevant to the concerns of everybody with an interest in the pragmatic aspects of quantification. Thirdly, although I do not (yet) agree with it in all respects, as the foregoing remarks should have made clear, I do believe the theory M & S propose merits serious consideration. Finally, Communicating Quantities testifies to the fertility of the interdisciplinary approach to natural language, an approach that is preached by many, yet practised by so few.
