THOMAS
ON THE
PROPER
EDE
ZIMMERMANN
TREATMENT
CERTAIN
OF OPACITY
IN
VERBS*
This paper is about the semantic analysis of referentially opaque verbs like seek and owe that give rise to nonspecific readings. It is argued that Montague’s categorization (based on earlier work by Quine) of opaque verbs as properties of quantifiers runs into two serious difficulties: the first problem is that it does not work with opaque verbs like resemble that resist any lexical decomposition of the seek = try to find kind; the second one is that it wrongly predicts de ditto (i.e. narrow scope) readings due to quantified noun phrases in the object positions of such verbs. It is shown that both difftculties can be overcome by an analysis of opaque verbs as operating on properties.
1. INTRODUCTION The difference between (1) and (2) is well known: the latter cannot be analyzed in the same, first-orderly manner (1’) as the former. (1)
Caroline found a unicorn.
(2)
Caroline sought a unicorn,
(1’)
(3x1[u(x)& w x)1
There are at least two ways in which (2) differs from (1). The first is simply that (2), unlike (l), is ambiguous. On its specific reading, which is brought out more clearly by (2~9, it can be given a fairly satisfactory firstorder treatment, as indicated in (2’):’ (W
Caroline sought a particular unicorn.
(2’)
(wJ@) & S(c&l
* This is a strongly modified version of a paper entitled ‘Do We Bear Attitudes towards Quantifiers? that I have presented at conferences in Gosen (Gesellschaft fiir Sprachwissenschaft), Ithaca (SALT I), and Konstanz (Lexikon). I owe a special debt to Hans Kamp and Arnim von Stechow for shaping my views on the subject of this paper during the past ten years or so. Comments from and discussions with the following friends and colleagues have also led to considerable improvements: Heinrich Beck, Steve Berman, David Dowty, Veeile van Geenhoven, Fritz Hamm, Irene Heim, Wolfgang Klein, Angelika Kratzer, Michael Morreau, Barbara Partee, Mats Rooth, Roger Schwarzschild, Wolfgang Stemefeld, Emil Weydert, Henk Zeevat, and three referees. ’ Here and elsewhere in the paper I am ignoring matters of temporal reference. Natural LanguageSemanticsl, 149-179,1993. 0 1993 Kluwer Academic Publishers. Printed in the Netherlands.
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On its nonspecific reading, no such formalization is possible; not even the implication from the nonspecific reading of (2) to (3) or its first-order version (3’) is correct: (3)
There was at least one unicorn.
(3’)
(3
U(x)
The nonspecific reading of (2) is sometimes paraphrased by: Pa)
Caroline sought an arbitrary unicorn.
Although we shall see that (20) is not quite equivalent to the nonspecific reading of (2), it does give a rough idea of what this reading is. Let us note:
(4
Sentences with seek are ambiguous between a specific and a nonspecific reading.
The second difference between (1) and (2) concerns truth-preserving substitutions: the direct object position in (2) is intensional in that we cannot always replace one object by an extensionally equivalent one without thereby changing the truth value of the whole sentence. Clearly, under the assumption that NPs with extensionally equivalent nouns and identical determiners are extensionally equivalent, such substitutions are possible in sentences like (l), and the logical form (1’) would indeed justify these substitutions. Given some obvious biological facts,* we may thus conclude that (1) and (4) are both false, but (5) need not be false, even if (2) is: (4)
Caroline found a thirteen-leaf clover.
(5)
Caroline sought a thirteen-leaf clover.
And, given the same facts, the first-order same truth-value as (1’). (3x) [C(x) & TL(x) & F(w)] (4’) As a consequence, no such formalization thus have:
formalization
(4’) of (4) has the
for (2) would be adequate. We
z Maybe the nonexistence of unicorns is not a biological but rather a metaphysical fact, as Kripke (1972, 763) has argued; and in view of the possibilities of genetic engineering, (4) may even pretty soon become true. But I am confident that neither of these speculations affects the point I want to make.
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The direct object position of seek is intensional in that it does not always preserve extensions under substitution of extensionally equivalent noun phrases.
It is worth pointing out that (I) only concerns the nonspecific reading of sentences containing seek. In its specific sense, the verb seems to work pretty much like an ordinary transitive verb. This might suggest that seek is actually homonymous and that it is only one of its senses that creates all the trouble for a first-order formalization. But there is evidence to the contrary. For on the one hand, the two readings are closely related - so closely, indeed, that neither native speakers’ intuitions nor lexicographers’ work can find an ambiguity; and on the other hand, the English verb seek has various counterparts in other languages, giving rise to exactly the same logical puzzles. It thus seems that even (A) is a genuine problem for logical analysis, because the ambiguity must be explained, not just described. Of course, seek is not the only verb with such outrageous behavior. Indeed, probably the first such example to have been discussed in the semantic literature is the ditransitive verb OW,~ which also satisfies (A) and (I), as the following example shows: (6)
Rainer owes Fritz a barrel of Arctic wine.
(A) is satisfied because (6) may, e.g., concern an obligation to return a certain, incorrectly described barrel, in which case we have a specific reading; or it may be used in a nonspecific way and correctly report the outcome of a careless bet. In the second case (6) may well be true, although we cannot truthfully replace the direct object by the extensionally equivalent a bottle of lunar milk; so (I) is met, too. Following a .not uncommon practice, we may call verbs satisfying (A) and (I) (referentially) opaque. Although the majority of English transitive (di-transitive, . . .) verbs is certainly (referentially) transparent (= not opaque), referential opacity is a more widespread phenomenon than advocates of first-order formalization may guess. A list of clear cases would have to include, e.g., need, prevent, resemble, fit, and some more verbs to be discussed below; it could also be argued that certain ‘intentional verbs like imagine and paint belong in this category, but I prefer to leave this matter open here. Moreover, if we generalize the notion of referential opacity from (di-)transitive verbs and their direct objects to 3 Or rather its Latin counterpart in Geach (1965).
debere: see Buridanus (1350, 83-89)
and the discussion
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arbitrary verbs and their argument positions, we may also consider prepositional verbs like look for” and even raising verbs like appear5 to be referentially opaque. I know of no reason to exclude the former, but the latter will be excluded for reasons to be explained in section 4.2. Even though the examples given so far involve both (A) and (I), it is in principle possible for a verb to give rise to the specific/nonspecific ambiguity without being intensional. The following example, due to Mats Rooth, is a case in point: Mats owns 75% of the ball bearings in the basement.
(7)
(7) can be true if Mats holds a 75% share of the objects mentioned without thereby owning any particular ball bearing; it thus has a nonspecific reading in addition to the more obvious one concerning certain individual objects.6 On the other hand, (7) seems to allow for substitution of extensional equivalents: if the only metallic objects in the basement are ball bearings, it is obvious that (7) implies: Mats owns 75% of the metallic objects in the basement.
(8)
Rooth’s example shows that (A) and (I) do not always co-occur, which raises the terminological problem of what to call verbs (like own) satisfying the former but not the latter. I will simply call them (referentially) opaque, even though this may evoke wrong associations; but then, examples like (8) seem very hard to find anyway:7 opaque verbs are normally intensional in the sense of (I). 2.
THE
CLASSICALANALYSIS
AND
ITS PROBLEMS
There is a very simple and elegant account of referential opacity that not only avoids any problems resulting from first-order formalization but also explains why we should expect features like (A) and (I) in opaque verbs. This analysis is essentially due to Quine,8 but it is better known in the more abstract, type-theoretic version developed by Montague.’ I will refer 4 As proposed in Geach (1965,425). 5 As suggested in Montague (1973,222). 6 The matter is not entirely clear; the nonspecific reading may be the only one, because it covers the specific cases. ’ I even used to think that they do not exist and that their nonexistence constitutes an adequacy problem for Montague’s analysis of opacity: see Zimmermann (1983, 73, fn. 9). I am very grateful to Mats Rooth for having supplied me with a counterexample. 8 Quine (1960, $32); the title of the chapter is ‘Opacity in Certain Verbs’. 9 Montague (1973, 237f.); the title of the article is ‘The Proper Treatment of Quantitica-
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to Quine’s and Montague’s account of referential opacity as the “classical analysis.” Although the classical analysis is well known, I believe that it has too often been misconstrued and mistaken for its type-theoretic implementation; an aura of logical technicality frequently obscures the simple and straightforward idea behind it. In the following subsection, I will thus present my account of the classical analysis of referential opacity; then I will point out some of its weaknesses. 2.1. The Class~caiAna~ys~ The key to Quine’s analysis lies in the observation that (9) can be roughly paraphrased by (10). (9)
Caroline is seeking a neighing unicorn.
(10)
Caroline is trying to find a neighing unicorn.
Let us, for the purpose of this exposition, assume that (10) can be represented by the Ty2-formula (lo’), where T (E Con,,,,,,,) denotes the propositional attitude of trying to make true.‘O
(lo’)
Ti(c7Pj@Y>Pj(Y> & Nj(Y)& Fj(c,Y)ll)
(10’) can be glossed as ‘Caroline is trying to make that proposition true that consists of all worlds in which there exists a unicorn that neighs and is found by her, Caroline’. In order to obtain (10’) as the result of a Montague-style translation, we may lexically decompose try reducing it to the attitude expressed by T: l
try’
= [APAx Ti(x, [AjPj(x)])].
tion in Ordinary English’. The analysis was already sketched in Montague (1969, 174177) and Montague (1970,394ff.). *” Ty2 is Gallin’s (1975, $8) two-sorted type rheory, which I prefer to the standard interlingua IL for reasons explained in Zimmermann (1989, 76). I hope that the notation is self-explanatory; ‘i’ denotes the free variable corresponding to the real-world index. Under Kripke’s (1972) standard assumption that proper names are rigid designators, the ZLversion of (9’) is :
T(c, A (3~)I U(Y)& N(Y)& FCC,~11) 0) The assumption that try expresses a propositional attitude is actually an oversimplification, because it is better analyzed as a de se attitude towards a property, in the sense of Lewis (1979). The categorization of try is one of the differences between Quine’s (propositional attitude) and Montague’s (de se) version of the story. I believe that this simplification does not affect any of the points I want to make.
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Given the paraphrase (10) of (9) we can now conjecture that seek is just short for try to fir&. This leads to the following, Quinean formulation of the classical analysis of opacity:
(Q>
The referentially opaque verb seek can be decomposed into a propositional attitude (a try) and a binary relation among individuals ( = find).
Before we go into the details of this lexical decomposition, let us see how (Q) deals with the characteristic ambiguity (A) induced by referentially opaque verbs. We may first note that the paraphrase does not resolve the ambiguity but retains the same two readings. However, in the case of attitude reports like (lo), there is a straightforward way of predicting this ambiguity as one of (quantifier) scope: on the first, nonspecific (or de ditto) reading (lo&& the existential quantifier” expressed by the NP a neighing unicorn takes scope over the complement ‘[Caroline] Jind y’; and the specific (or de re) reading (lo&) is obtained by quantifying in (or quantifier raising), i.e., by letting the same quantifier take wide scope over the whole report:
(lodr)
PY) Pi(Y) & Ni(Y) & Ti(c, [G Fj(cT Y)l)l
There are various ways of actually arriving at this prediction, and the details are of no concern to us. Only two points about the de re/de ditto ambiguity are important: it is (i) a structural ambiguity that is (ii) quite independent of referential opacity in transitive verbs. In particular, whatever mechanism of quantifying in we may use to produce (lo&), (i) it will not be attached to any particular words, and (ii) it will be needed anyway. So we may indeed expect the same mechanism to apply to the paraphrase (9) of (lo), thus yielding the reading (lob) in addition to the initially expected (lo&). (I) is just as simple: it is the attitude verb try that creates the intensional context in the usual way such verbs operate. Again, we may have different theories about what precisely this amounts to,i2 but it is clear that any ” I use the term qunnfijier in a highly context-dependent manner, sometimes referring to (arbitrary) sets of sets, sometimes to (arbitrary) sets of properties, and sometimes to (arbitrary) properties of properties. Moreover, the term intensional quantifier covers the last two possibilities, whereas extensional quantifiers are sets of sets. ” This question is another point of disagreement between Quine’s and Montague’s version of the classsical analysis. But the disagreement only concerns the foundations, not the descriptive aspects of the analysis. I have tacitly assumed a Montagovian account of intensionality.
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such theory will have to explain that, on its de ditto reading, (10) does not imply Caroline is trying to find a thirteen-leaf clover.
(11)
And this explanation then just carries over to the paraphrase (9) and its de ditto reading. In our Ty2-formalization (lo&) substitution fails because, I take it, the two NPs a neighing unicorn and a thirteen-leaf clover do not intensionally coincide, so that, e.g., (11 dd) may be false even though there are no unicorns or thirteen-leaf clovers, i.e., even under the additional premise (12):
(12)
(VY) [[u,(Y)
& N,(Y)]++[C,(Y) & TLi(Y)ll
(12) only guarantees the equivalence of the two quantifiers at one (real world) index (designated by free i); but this does not justify the conclusion (11 dd), because substitution under the A-operator necessitates equivalence at all indices (designated by bound 1). And if (9) and (10) are paraphrases of each other, we should get the same failure of substitution for (9). Let me repeat that these observations about (I) only concern the nonspecific or de ditto readings of (9) and (10). But this need not worry us. For it seems that either sentence possesses an additional, maybe more remote and trivially false reading according to which neighing unicorns exist and Caroline is trying to find one of them. Under such a reading substitution does work, again yielding a trivially false quantified attitude report: as was already mentioned, if we only concentrate* on specific readings of sentences involving opaque verbs, the latter behave like ordinary transparent verbs, a fact which the classical analysis of opacity can also explain pretty well, although I will not go into this here. In order to give a compositional account of the classical analysis, we still have to find a suitable decomposition of seek in terms of try and find. This can be obtained by considering the schematic paraphrases underlying our above considerations: (13) a. subi is seeking OBJ b. subj is trying to find OBJ Using standard Montagovian devices of indirect interpretation, (13b) translates as (14), where subj’ is the translation of the nonquantificational subject of type e, and OBJ’ translates the object as a quantifier of type (s(et))t: (14)
T,(subj’, [Lj [Ii OBJ’l,(lk
Ay F,(subj’,y))])
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We can now convert this scheme into the classical decomposition reinterpreting the schematic translations as functional arguments: (CD)
(CD) by
seek’ = [AQ 1~ Ti(x, [Jj Qj(lk AJ’ F&, Y))])],
where ‘Q’ is of type s((s(et))#); this move to intensions is obviously necessary in order to get the schematic OBJ’ into the scope of the ‘Aj corresponding to the intensional context created by try. The categorial asymmetry between subject and object is, of course, accidental in that the former may also be treated as a quantifier. On the other hand, it is essential for the decomposition (CD) that the object is taken to denote a quantifier; for otherwise it would not get the narrow scope needed for the opaque reading. (CD) is thus not a decomposition of the kill = cause to die kind:r3 (15) a. kill
= [Ly k CAUSE,(x, [Aj DIEj(y)])]
b. seek’ # [Ay Ax Ti(x, [lj Fj(x,y)])] So Montague’s version of the classical analysis says that referentially opaque transitive verbs are relations between individuals and properties of properties of individuals: (M)
The referentially opaque verb seek denotes a certain (decomposable) relation between an individual and an intensional quantifier.
There are some differences between (Q) and (M), about which I will say something in the next subsection. However, I think that the two analyses have enough in common to justify their being taken as variants of each other. Given suitable paraphrases in the style of (13), we can apply the same kind of analysis to other verbs. Here are some examples: (16) a. subj prevents OBJ b. subj prevents that OBJ happens (17) a. s&j owes OBJ to obj b. subj is obliged to give OBJ to obj r
I3 (1 Sa) is simply a translation of part of the decomposition given in McCawley (1968, 73) into the present framework. A somewhat more complicated though essentially equivalent version can be found in Dowty (1979, 202f.). Note that such decompositions do not, and are not meant to, produce intensional relations; but see von Stechow (1992) for a criticism of this lack of intensionality.
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(18) a. subi appears VP b. it appears that su& ITS In (16) the verb prevent occurs both in the analysandum and the analysans. It should be clear, however, that logically speaking we have two distinct attitudes, directed at quantifiers and propositions, respectively. (17) is the paraphrase provided by Montague (1969, 175f.); as a first approximation, the embedded infinitive can again be replaced by a propositional attitude. In (18) the result of the analysis is not an attitude toward a quantifier but rather a relation between a quantifier and a property; in particular, this analysis would lead to a recategorization of intransitive verbs as properties of quantifiers. As I have already said, there are good reasons to keep raising verbs out of the present discussion. Still, this small selection reveals some of the power and generality of the classical analysis of opacity. Let me now turn to its less delightful aspects. 2.2. Its Problems That there is something wrong with the classical analysis is best seen by trying to apply or adapt it to verbs that seem to resist any paraphrase of the ‘seek = try to jind’ kind. The claim that there are such verbs is not new; indeed, Montague mentions worship,14 which does not license inferences like the one from (19a) to (19b): (19) a. Mary worships a Greek goddess. b. There exists at least one Greek goddess. However, it may well be argued that worship does not belong in the same category as seek, because it does not give rise to a nonspecific reading: the truth of (19a) depends on Mary’s relation to each specific real or mythical Greek goddess. Thus (19a)‘s only reading is one of the form PO)
(3Y) FqYl
&Wow
YI17
where the variable y may range over real individuals as well as at least some “non-existent objects”; this is so because worship, unlike many other transitive verbs, is extranucZear15 with respect to its direct object position,
I4 See Montague (1969, 177), where the example is attributed to Hans Kamp (who does not support it anymore). That worship is not like seek has already been observed in Bennett (1974,82&), where Saul Kripke is credited. I5 In the sense of Parsons (1980, 22ff. and pas&n); a fuller discussion of the difference between opacity and extranuclearity can be found on p. 47f. of the same work.
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i.e., it may (actually) be true of objects that do not (actually) exist - or so one may argue in defense of Qume’s (!) analysis. But there are other verbs whose logico-semantic behavior is pretty close to that of seek although they cannot be given any straightforward decomposition: (21)
Tom’s horse resembles a unicorn.
(22)
Tom compares his horse to a unicorn.
The above sentences both satisfy the criteria (A) and (I). Thus (21) may express a similarity between a particular horse and a particular (mythical or existent) unicorn (de re); or it may be used to characterize the shape of a certain horse’s forehead (de ditto). And (22) may certainly be true without thereby licensing the substitution of the noun phrase a unicorn by the extensionally equivalent a centuur.16 So both verbs are semantically close enough to seek to be classified as referentially opaque. I doubt, however, that any suitable paraphrases for resemble or compare can be found. In the absence of any concrete proposal, a negative claim like this is hard to defend. But I shall at least indicate why certain obvious candidates do not work. In particular, the following kinds of paraphrases, though close enough, are of no help for the classical analysis of opacity: (21’)
Tom’s horse has a form which seems to be like a unicorn form.17
(22’)
his horse looks like a unicorn.
The trouble with (21’) - and many other conceivable paraphrases of (21’) - is that the NP a unicorn has no (proper) occurrence in it: (21’) does not tell us how to mm the quantifier denoted by a unicorn into the property of resembling a unicorn. Rather, it gives a recipe for obtaining the latter from the property of being a unicorn (denoted by the noun unicorn). It is thus not compositional, which it would have to be to fit a scheme like (16) - (18).‘*
I6 In view of the above discussion of extranuclearitv,__one may_ argue I that the two NPs are not extensionally equivalent because they may be used to quantify over different nonexistent beings. In that case we would have to replace a unicorn by something like a unicorn mentioned in some saga and assume that sagas are the only places where unicorns have ever appeared. Again, it seems that the substitution is not necessarily correct. I7 This paraphrase was suggested by an anonymous referee. l8 One
may
object
that (21’)
could
be derived
compositionally
once
we have
a systematic
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The trouble with (22’) is that it reintroduces referential opacity of the irreducible kind: look like is sufficiently close to resemble for the conjecture that (22’) leads to the same compositionality problem as does (21’). It is time to address a possible objection that can be raised in favor of formulation (M) of the classical analysis. For it seems that decomposability is only marginal to Montague’s type-theoretic version of Quine’s analysis: all that examples (21) and (22) show is that opaque verbs cannot always be decomposed in the way suggested by (Q); but their analysis as operating on quantifiers still appears correct. In fact, Montague has argued in precisely that way and, in one place, has even presented an analysis of seek along the lines of (M) but without any decomposition.19 Let us therefore briefly consider what may be called the real Montugovian version of the classical analysis: (RM)
Referentially opaque transitive verbs denote (not necessarily decomposable) attitudes of individuals toward intensional quantifiers.
Although (RM) frees the descriptive semanticist from the burden of having to provide a decomposition for every opaque verb, it does not make his or her life easier. For what precisely is the relation denoted by a given referentially opaque verb? How do we know whether or not a given individual bears the corresponding relation toward a given quantifier? If we can decompose the attitude, tine; it simply reduces to an attitude toward a proposition definable in terms of the quantifier. But what if we cannot? One may be tempted to say, “Well, look at what happens in such a case: we certainly do know the intuitive truth conditions.” So let’s take resemble. We have no trouble in understanding a sentence like (21) on its opaque reading. It says that a certain horse (specified by the subject NP) shares some contextually relevant features with all typical (and possibly nonexistent) members of the family of unicorns. Maybe this paraphrase is not entirely clear or adequate; but surely something like it is. It thus seems that we do know when a given individual (Tom’s horse) bears the relation of resemblance to a given quantifier (denoted by a unicorn). But the trouble is that, just like (21’) our paraphrase does not make clear what the quantifier’s contribution to the truth conditions of (21) is: only the property of being a unicorn occurs, but not the result of relativizing the way of deriving the property of being a unicorn from the quantifier denoted by a unicorn. I will return to this possibility in section 3.1. I9 Montague (1970, 394ff.). The argument against decomposition in general can be found in Montague (1969,177); it involves worship as the principal witness.
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(binary) existential quantifier to it. So our paraphrase is merely anecdotal, not systematic. It does not tell us whether or not a given horse stands in the relation of resemblance to some arbitrarily picked property of properties: if we try to save the classical analysis by admitting nondecomposable attitudes, it loses its intuitive basis, trading comprehensibility for abstractness. So, whether we use lexical decomposition or try to specify truth conditions, we are left with a Compositionality Problem: It does not always seem possible to describe the meaning of a VP containing an opaque verb as depending on the meaning of its (quantified) object. I now turn to a second, seemingly independent weakness of the classical analysis of opacity. Let us compare the following two sentences: (23)
Amim compares himself to a pig.
(24)
Amim compares himself to each pig.
(23) is ambiguous: it may truthfully describe a situation in which Amim sees a pig and utters something like “That guy doesn’t look a bit like me,” or it may be used to express that Amim describes (or considers) his degree of piggishness. However, no such ambiguity appears in (24): the sentence can only mean that Amim makes a comparison between himself and each pig in the domain of discourse. This is the transparent reading; an opaque one appears to be missing. The lack of a certain reading may in principle be explained with a variety of reasons. For instance, it is clear that the following sentence also has one reading only: (25)
Amim compares himself to Porky.
But it is a well-known fact that the de re and de ditto readings of (25) are logically equivalent once we interpret the proper name Porky as a rigid designator (or the quantifier corresponding to it)?O So maybe the ambiguity missing in (24) is eliminated in a similar way. I will briefly return to this suggestion in section 3.1; for now let us just note that we seem to have no idea as to why the two readings of (24) should coincide. Another possible explanation for a missing reading is that it would be *O In Ty2 a rigid designator (of an individual) is simply a constant intensional language like IL, a meaning postulate like (1) in Montague have to guarantee rigidity. This may be seen as a small technical advantage
of type e. In an (1973, 235) would of Ty2 over IL.
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too absurd, too trivial (or otherwise semantically marked) to ever be considered. I see no reason why this should or should not be so, but then I do not even know what the missing reading could be. This uncertainty can be removed by drawing our attention to a decomposable verb: (26)
Alain is seeking a comic-book.
(27)
Alain is seeking each comic-book.
Again, it seems that (27) lacks a de ditto reading, but this time the classical analysis makes a clear prediction as to what this reading would be, viz. (270), which is at least not logically equivalent to the transparent reading (27t): (270)
Ti(a,Aj(vY)
[CB~(Y) +
Fj(a~ YN
(27t)
(VY) lCBioI) - Ti(a, GFjta, YI)
(270) expresses that Alain is trying to find all comic-books, ditto reading of (28)
i.e., it is the de
Alain is trying to find each comic-book.
This reading is not available for (27). There are more cases of missing opaque readings, but they usually involve plural noun phrases, to which I do not want to turn before section 3.2. Let me nonetheless give two examples: (29)
Alain is seeking most comic-books.
(30)
Alain is seeking at most five comic-books.
So, in addition to the above compositionality analysis induces a certain amount of
problem,
the classical
Overgeneration: Not all sentences involving opaque verbs are ambiguous in the way predicted by the classical analysis. There are also some problems having to do with the specific form of the paraphrases suggested for the analysis of certain (reducible) opaque verbs. One of them is that, given the classical decomposition (CD) of seek involving Q, it is possible to define the latter’s intension in terms of the former%. Thus, it would appear that one could learn the notion of attempt by, logically deriving it, from .the notion of search, or that knowledge of the entire extension of seek implies knowledge of the entire extension of try: if you know who is seeking what, i.e. which quantifier, you know who is
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trying what, i.e., to make which proposition true. The reason for this rather surprising consequence of the classical theory lies in its unlimited use of intensional quantifiers. Here is a complete characterization of the attitude T appearing in (CD)? (31)
T = Ai Ip Ax seek’(x, Aj APpJ
Similar reductions of propositional attitudes to opaque verbs could be given for the other decompositions discussed above and elsewhere in the literature. I leave both the task and the conclusions to the reader. 3. AN ALTERNATIVE
ACCOUNT
We are now in a position to evaluate the above discussion and draw conclusions about the categorization of opaque verbs and their objects. We will then see how the above problems almost entirely dissolve. 3.1 Existential Quantifiers and Properties The problem of Overgeneration and the reduction (31) of try to seek can be seen to have a common source. For in both cases we find that the classical analysis allows the extensions of opaque verbs to relate individuals to too many quantifiers. More specifically, (31) makes essential use of a very weird kind of intensional quantifier denoted by the Ty2-formulae
(32)
Aj lPpi
It is the assumption that the extension of seek is defined for these quantifiers that makes the reduction (31) possible. Similarly, de ditto readings involving, e.g., noun phrases with each would be avoided if opaque verbs did not accept the kinds of quantifiers denoted by them. It is therefore tempting to restrict the range of the relations they express to a certain class of acceptable quantifiers. Two questions immediately arise, once we give in to this temptation: Which quantifiers are acceptable to an opaque verb? And, what does it mean to restrict the range of a verb? The first question is partly empirical, whereas the second one seems to be purely technical. We will answer them in turn. In order to find out about acceptability, we might first eliminate those 21 (31) is easily proved by replacing seek’ by its paraphrase given in (CD) and then applying the familiar reductions of d-calculus. - Incidentally, German morphology seems to confirm the classical analysis: seek translates as suchen, whereas try is versuchen, so that the meaning of the prefix ver- could be defined by ARAp Ix R,(x, LjjnP p,)!
PROPER
TREATMENT
OF OPACITY
IN CERTAIN
VERBS
163
quantifiers that violate some well-known and independently motivated restrictions on NP denotations. In particular, if we assume that the extensions GBi of natural language determiners are always extensional in the sense of (EXT) and, moreover, satisfy the principle (VAR*) of Strong Variefy,22 we could show that (for nontrivial propositions p) the quantifiers (32) cannot be expressed by any noun phrase of the form ‘Det + IT (EXT)
(VP) (VP’) (Vi) (Vj) [Pi = Pi + Al,
(VAR*) (VP) (Vi) [Pi #
[AX
I]
+ (W)
=
GSj(F)]
(3P”) G9i(P)(p’) f Sj(P)(P”)]
Of course, this does not mean that the quantifiers in question are not at all expressible, though maybe somehow even this stronger result could be established. However, instead of following this line of reasoning, let us directly look at what sort of quantificational noun phrases induce de ditto readings in opaque verbs and see whether their denotations form a natural class of quantifiers. We will, for that purpose, consider singular noun phrases only, leaving the plural to section 3.2. Ignoring coordination and other complications, it seems that we are left with essentially two kinds of noun phrases acceptable for opaque verbs, viz. indefinites of the form ‘a N’23 and definite descriptions of the form ‘the N’, as illustrated in (33) and (34) respectively: (33)
Jones is seeking a secretary.
(34)
Jones is seeking the boss.
What the two kinds of object NPs have in common (according to the classical theory) is that both denote existential quantifiers, i.e. (intensional) quantifiers of the form (3) where B refers to an arbitrary property: (3)
Izi AP (3x) [P,(x) & Bi(x)]
Clearly, for the object of (33), B may be taken to denote the sense of secretary, whereas the property of being the one and only boss is suitable for (a Russellian account of) the boss. Let us therefore hypothesize: F-9
An intensional quantifier Q is a suitable argument opaque verb just in case it is existential.
for an
22 (VAR*) is adapted from van Benthem (1984, 446); (EXT) is folklore. I am indebted to Veerle van Geenhoven for pointing out an error in my original formulation of (EXT). 23 In some dialects we also find opaque readings with negated indefinites like ‘no N’. We may, however, safely ignore these cases because semantically the negation always takes wide scope over the opaque verb, so that the argument is again equivalent to a positive indefinite: Tulaneis looking for no cow means that it is not the case that Jane is looking for a cow, and not that she avoids finding cows. See also fn. 44.
164
THOMAS
EDE
ZIMMERMANN
Writing ‘EX(Q)’ to express that, for some B, Q is of the form (!I), we may restrict the lexical decomposition of seek to existential quantifiers by postulating (35)
EX(Q) + [=k’(x,Q)
* Ti(x, [G
Qi(nk1~ F,(x,
Y))])]
for arbitrary quantifiers Q, individuals x and worlds i. This certainly rules out the reduction (31) of try to seek: the quantifiers (32) do not satisfy (I), so that (35) cannot be applied to them.24 In order to also avoid the problem of Overgeneration, we could then stipulate that whenever (35) does not apply, there is no de ditto reading: (36)
1 EX(Q) + [seek,‘(x,Q) ++ Qi(izilzy Ti (X7[AkF/c(X, Y)]))]
(36) says that, with respect to direct objects denoting nonexistential quantifiers, seek behaves like a transparent verb. Taken together, the postulates (35) and (36) can be used to give a formal account of (HJz5 But there is at least one good reason for not adopting it. For it does not tell us just why referentially opaque verbs make their scope behavior dependent on whether their argument satisfies EX: in having each referentially opaque verb satisfy something like (36), such account obviously misses an important generalization. Fortunately, we can do better than that. To see this, we should first observe that the relativizing property B of an existential quantifier Q is always true of exactly those individuals whose essence is accepted by the quantifier: (37)
B = Ai i2x Q,(x+),
where ‘x+’ abbreviates ‘[Aj Izy x = y]‘. This means that B is uniquely determined in (3). As a consequence, we have a one - one correspondence between existential quantifiers and properties, so that the latter may play the role of the former as objects of opaque attitudes.26 We could thus reduce the type (s((et)t))(et) of opaque verbs to that of relations between individuals and properties. And instead of applying it directly to the sense of the object, we could apply the opaque verb to the relativizing property determined by the NF’ sense: (38)
seek+V(Ai
AP
(3x)
[Pi(X)
& Bi(X)])),
24 There is one exception: if B in (3) denotes the necessarily empty property, the existential quantifier relativized to it can be defined as ‘Lj IP I’. However, in order for the reduction (31) to work, all quantifiers of the form (32) would have to be existential. 25 I am indebted to Heinrich Beck for pointing this out to me. 26 This observation is not new. See Partee (1987) for a more general setting.
PROPER
TREATMENT
OF OPACITY
IN CERTAIN
VERBS
165
where ‘W denotes some operation that picks out the relativizing property when applied to an existential quantifier.*’ Unfortunately, this type shift does not make much of a difference, because we still have to take care of the nonexistential quantifiers; and it seems that this still requires some ad hoc device like (36). There is a simple way out. For if we analyze opaque verbs as operating on properties, we should not really expect quantifiers to occupy their object positions at all. Hence, instead of resorting to complicated type maneuvers, we might as well regard the result of combining an opaque verb with a quantifier as undefined. But what about existential quantifiers, then? The answer is all too obvious: they can be identified with their relativizing properties, thus giving rise to a distinction between quantified and referential noun phrases advocated by some contemporary semantic theories.28 The latter would have to be categorized as expressing properties. So, instead of something of the form (38), the @m-educed) result of a compositional translation of seek a unicorn would be: (39)
seek,‘(Aj unicorn,‘)
which is, of course, equivalent to (39’), the analysis I am proposing: (39’)
seek,’ (unicorn ‘)
Before investigating how the present treatment of referential opacity deals with the problems and phenomena discussed in section 2.2, we must still complete it. What is chiefly missing is an analysis of the de re readings of sentences involving referentially opaque verbs. From the point view of the present analysis, these fall into two quite distinct classes, according to whether the object noun phrases are quantificational or referential. As in the classical analysis, quantificational NPs will be treated by allowing quantifiers to take scope over a matrix containing a variable in the original object position; and this variable will be interpreted like a proper name, i.e., as a special case of referentiahty. So it is referential object NPs that we must look at first. The rest will follow easily. I can only sketch my analysis of de re readings, because a more detailed presentation would force me to make more assumptions and decisions about the overall framework than necessary for the limited topic of this
27 See Lerner and Zimmermann (1983,295) for a possible definition ofX. 28 Heim (1982) and Kamp (198 1). - I should point out that by ‘referential’ I do not mean ‘directly referential’ in David Kaplan’s (1977) sense but something more general (or maybe independent): a referential NP is one that can be used to refer to an individual, i.e., one that ‘introduces a discourse referent’ in the terminology of Kamp’s DRT.
166
THOMAS
EDE
ZIMMERMANN
paper. I will therefore rely on the reader’s ability to translate everything I say into his or her favorite framework. Now consider a famous example: (40)
Richard is seeking a unicorn.
Asuming that seek denotes a relation of type (s(et))(et) and that unicorn’ = a unicorn’ = U, this is how we can get the de ditto reading: (4Odd) Izx [x = f & see&‘(x, Ai U,)] The outermost A-operator reflects the fact that the proper name Richard is a referential noun phrase describing some particular object. This description denotes a set that combines with a verb phrase denotation by intersection, thus forming a more complex description that can, e.g., be intersected with further descriptions following it. We may also read (40) as a claim about the world (denoted by i), in which case (4Odd) would have to be read as expressing that the set it denotes is not empty (existential closure or embedding). Truth-conditionally, (4Odd) thus boils down to: (4O’dd) seek,‘@, U)]
It should be clear that on this approach, the more referential noun phrases a sentence contains, the more places the relation it expresses should have. However, (40) contains two referential NPs although according to (4Odd), it expresses a unary relation. The reason for the missing I-prefix is obvious: the object NP is not used referentially and, consequently, does not describe any particular object. But, surely, it could be understood in a referential way, in which case (40) would translate into a binary relation: (40dr)
ly Ax [x = r & UXy) & seek,‘(x, 1~’lz z = y)]
This time the result is truth-conditionally (4O’dr) (3Y) Pi(Y) & =&(r,
equivalent to:
Y+)l
(40’dr) can be glossed as ‘There is some unicorn such that Richard stands in the relation of seeking to (the property of being) that unicorn’. We thus obtain essentially the same first-orderly de re reading as Montague’s version of the classical analysis, except that individuals y get represented by essences y+ rather than by name-like quantifiers y*. The precise way of obtaining (40dr) from some syntactic representation underlying (40) will not concern us here. But I take it that any standard scoping mechanism would do, as long as it semantically dissects the underlying structure into the referential object and an open property:
PROPER
(40t)
TREATMENT
lzy i2X
[X
ui
OF OPACITY
= f & U,(y) & Y
See&(X,
IN CERTAIN
VERBS
167
y+)]
Izx [x = r & seek:(x, y+)]
So much for de re readings involving referential noun phrases.29 Nonreferential NPs are treated as intensional quantifiers; as such they are unable to occupy the object position of an opaque verb. So the only way of combining them should be by scoping, i.e., by applying them to an open property, as in:
(41) (419
Theo is seeking each unicorn. Ix [x = t & (VY) [u,(Y) + =4(x, lbp PY) Pi(Y) + pi (y)]
The truth-conditional t41’)
y
AX [X
=
Y’)]] t
&
Sf?dCi’(X,
y+)J
content of the result can, of course, be expressed by:
(‘Y) Pi(Y) + seeK(t7 Y+)l
Again, this is essentially the de re reading predicted by the classical analysis; but we got rid of the de ditto reading, thus avoiding the problem of overgeneration. As to the compositionality problem, a case in point was resemble, where we gave the rough paraphrase ‘share some contextually relevant features with all typical (and possibly nonexistent) members of and complained that it cannot be combined with a quantifier. As a matter of fact, it relates an individual to a property, just as the present analysis would have it. Now maybe the case of resemblance is misleading because it is an external relation, as opposed to an intentional attitude like search. But clearly, primitive attitudes toward properties are much less controversial than attitudes directed toward quantifiers. Thus, e.g., we may have a preference for a certain color, taking the latter to be a property of extended objects; this does not necessarily mean that our preference always extends to the objects of that color. Preference thus seems to be a natural candidate for an irreducible attitude toward properties.30 29 More could be said about this. In particular, a full account of de re attitudes would have to deal with double vision problems as discussed in Quine (1956), Kaplan (1969) or Kripke (1979). (The term ‘double vision’ is due to Klein (1979, 73), I believe.) I tend to favor solutions along the lines of Lewis (1979, sec. 13) or Cresswell and von Stechow (1984), but incorporating them in the present approach does not seem to be a trivial task. I cannot go into this here. 30 Lewis (1979, sec. 1) argues that, for reasons of theoretical homogeneity, the objects of
168
THOMAS
EDE
ZIMMERMANN
Finally, let me point out that the present analysis is perfectly compatible with Quine’s decomposition of seek. For we may well have: (ED)
seek’ = [IP AX Ti(x,
Aj (3~) [q(y) & Fj(X, Y)])]“’
On the other hand, we are not forced to adopt anything like (ED), but may instead regard seek as an irreducible attitude a person bears toward a property. But even in the presence of (ED) (or a similar decomposition), the counterintuitive reduction of the meaning of seek to that of try (or some such attitude appearing in the decomposition of the former) is no longer possible, because neurotic quantifiers of the form ‘dj I P py are not accepted as arguments to opaque verbs. In fact, one can show that there can be no (logical) reduction of try to seek as analyzed in (ED); but I must leave the matter to a footnote:32 3.2. Plural Properties
Let me positions reasons. de re/de (42)
now briefly turn to plural noun phrases occupying the object of opaque verbs, which I have excluded mainly for expository As mentioned in section 2.2, not all plural noun phrases induce ditto ambiguities; but some certainly do: Tom needs five toy monsters.
(42) is clearly ambiguous: it may express that Tom needs to have a particular collection of five toy monsters; or it may report him to be in need of some collection or other, as long as that collection has five members each of which is a toy monster. This ambiguity is obviously well accounted for by treating five toy monsters as a referential plural NP
intentional attitudes should all be of the same type, so that preference may seem to be at odds with propositional attitudes like belief. However, a de se account would get the two closer to each other: both belief and (a de se version of) preference are relations. 31 T can actually be taken to be the translation of another sense of seek, as in seek to embarrass her. If so, (ED) falls under the same pattern of metonymic lexical relations as a reduction of risk one’s life to risk losing one’s life. Note that this reduction goes in the opposite direction from the one contemplated in fn. 21. 3z A proof can be given as a variation of Padoa’s (1901) theme: the idea is to make a change in the intension of try without affecting seek so that the former cannot functionally depend on the latter. To be specific, let m and m’ be Ty2-models (= interpretations of constants plus variable assignments) satisfying all relevant postulates including (ED) and differing only in their interpretation of T: whereas m verifies Ti(xJj 7 (3~) F,(x, y)), the same formuIa is false in +B’. It is easily seen that such models exist, under certain natural assumptions about our system of postulates. In particular, due to (ED), 112and tm’ agree on the interpretation of seek’; but they differ in their evaluation of T, as required.
PROPER
TREATMENT
OF OPACITY
IN CERTAIN
VERBS
169
expressing a plural property, i.e., one that only collections can have. In order for a collection to have this particular property, it would have to consist of toy monsters and to have (exactly) five members. Although in principle, collections may be thought of as sets, it is better to think of plural structure as distinct even if it should be isomorphic to set structure.33 In particular, we will assume that collections of individuals are themselves individuals of type e. Under these assumptions, the above sentence can be analyzed as: (42ild)
;Ix [x = t & neeG(x,Aj rly [toy monsfer$(y) &five’(y)]]
(42ilr)
Izy k [x = t & toy monster$( 7) &five’(r)
& needi’(x, r+)]
I have used the Greek letter ‘f (for group) to indicate a variable ranging over collections. As in the singular, a plural referential noun phrase like five toy monsters allows for two distinct combinations. In (42’&), the object NP’s intension is the object of Tom’s need whereas, according to (42’&), it is the essence of a particular individual falling under the concept expressed by the object. I believe these to be the intuitively correct truth conditions. Let me now turn to a more complicated case of plurality: (43)
Tom needs many toy monsters.
There is strong evidence that many is ambiguous between a cardinal and a proportional interpretation. 34 On the former option, many toy monsters is a (context-dependent) referential plural NP denoting the property of being a sufficiently large collection of toy monsters. Using the same analytical tools as with (42), we would thus predict a de re/de ditto ambiguity for the cardinal variant of (43): (43&Y) b [x = t & nee~(x,~~2jr2y[toymonster~(y) (43Vr)
& many~~,d(~)])]
Izy Ax [x = t & toy mon.sters~(~) & many&&)
& need,‘(x, y+)]
(43Zr) expresses that Tom needs some particular toys and that the number of these toys exceeds a certain (contextually given) standard, whereas (43’M) says that he is in need of a sufficiently large monster collection, the exact composition of which is immaterial Obviously, (43) can indeed have these two readings. 33 See Link (1983, sec. 1) for ontological details, 34 See Partee (1988), where this distinction, already hinted at in Milsark (1977, 2Of.), is made precise and justified. I am very much indebted to Angelika Kratzer for the suggestion to relate my analysis to Partee’s work on many.
170
THOMAS
EDE
ZIMMERMANN
Now for the proportional reading of many, according to which (44) expresses that the number of pupils I have met is large in comparison to the number of those I have not met: (44)
I have met many pupils from Alain’s class.
As has been argued by Partee (1988), the main difference between the cardinal and the proportional reading of many is that the latter behaves like a quantificational determiner relating two (singular) properties, so that (44) gets the following kind of analysis:35 (44’)
rnar~y~,~~(i)(~j2jkpupil-porn-Alain’s-cZuss~(x), Z-have-met,(x))
Ljjilx
The interesting prediction we now get from Partee’s analysis of many and the above treatment of opacity is that the proportional reading of many can only be a de re reading: the quantifier many;, cannot occupy the object position of need’ and hence can only be quantified into this position, thus arriving at: (43Prop)
k [x = t & many~,(i)(Lj,jily n+‘(x,
toy monster;(y),Lj
ly
Y+))]
(43prop) seems to represent a possible reading of (43): the sentence may be true if Tom needs seven particular items out of a collection of ten, so that the absolute number of toys needed is relatively small and (43S) likely to be false. On the other hand, it looks as if (43) cannot express that Tom needs a relatively large proportion of toy monsters, so that the proportional reading of many must be de re, just as Par-tee’s analysis of many combined with the present analysis of need would have it.36 The de re/de ditto ambiguity is not the only one that typically arises when a plural referential noun phrase serves as the object of an opaque verb; in general, there is also room for a collective and a distributive reading. To see this, we must change the example because, maybe due to the distributivity of have, need does not seem to allow for this ambiguity. But resemble certainly does: 35 The extension of proportional many depends on the index, because it combines with properties (rather than sets), so that at each index it will have to extract the extensions of its arguments. This variability of the extension of proportional many must not be confused with the contextual dependence of the standard of comparison. 36 Note that a classical acocunt of need combined with a generalized quantifier analysis of many would get such a reading. Using the obvious decomposition of need into musf have, the overgenerated reading would be: k
[x =
t & must’,{&
many,,,(j)(lk
ly
toy mon.ster~(y),
Ak dy have’,(x,
y))]
PROPER
(45)
TREATMENT
OF OPACITY
IN CERTAIN
VERBS
171
Nessie resembles two monsters.
On the above analysis, we get the following two readings for (45): (45&f)
ilx [x = n & resemble,‘(x, Aj A y [monsters;(y) & two’(y)]>]
(45’dr)
Ayl.x [x = n & monsters~(~) & two’(y) & resemble,‘(x, r+)]
(452.U) says that Nessie bears the relation of resemblance to the property of being a two-membered group of monsters. Given what we have said about resemblance in general, this means that Nessie has the contextually relevant attribute(s) of any typical collection of two monsters: maybe Nessie is doubleheaded, maybe she eats twice as much as an ordinary monster, maybe both. (45&j, on the other hand, expresses that Nessie bears resemblance to a particular group of two monsters: maybe her two heads look exactly like Grendel’s and the Cooky Monster’s, etc. Although (45) does have the two readings paraphrased, there is a third one: (45’dis) Ay k [x = n & monsters,‘(~) & two’(~) & (Vy) [y E y -, resemblej(x, y’)]], where ‘y E y’ expresses that the individual denoted by ‘y’ is a member of the group denoted by ‘7’. (45S) says that there is a pair of monsters such that Nessie resembles each member of that pair. This is certainly one way of reading (45). And we get it if we assume an “optional distribution” device, which essentially reinterprets any predication of the form ‘q(y)’ as ‘(Vx) [XE y -P qqx)]‘.” 3.3. Talking about Properties Both the classical analysis and the present approach assign two readings to (46) viz. (46dd) and (46d~):~~ (46)
Geach is seeking something Quine is not seeking.
(464 W&
(3~)
PTjWk F,(w))& Qw)l>
37 See Ramp and Reyle (forthcoming, chap. 4) for a detailed account of optional distribution. 38 Thanks are due to Mats Rooth and an anonymous referee for bringing up examples lie (46). A similar case can be found in Geach (1965, 430), where a higher-order analysis seems to be suggested. - For expository reasons, I am relying on Qume’s decomposition in the Ty2-translations to follow. Moreover, for simplicity, I have identified meaning and truth-conditional content; otherwise my account would have differed from the classical one by having L-abstracts in lieu of (some) existential quantifications. Finally, I am assuming that something means the same as an entity
172 (46dr)
THOMAS
EDE
ZIMMERMANN
(3Y) [ 1 Ti(q,iZj Fj(q,Y)) & T&G
F&Y))]
(46dd) could describe a (fictional) situation in which Geach avoids hunting for the same theorems as his American colleague; (46dr) would be true if both philosophers had lost their copies of &in und Zeit and both of them searched their respective studies. Both readings are possible for (46), I take it, but the most straightforward one is obviously: (46h)
('?I P"&lZj
('Y) [q(Y) & Fj(g, Y)I)
& 1 Ti(qJj
@Y>I'j(Y) & Fj(Q, YIl>I
(46h) expresses that Geach is engaged in some search but that either Quine is not or, if he is, their intentions differ. In particular, (46h) will be true whenever (46dr) is but not vice versa: (46h) would be true if Geach were looking for a detective novel without having a particular one in mind, whereas Qume wanted to get hold of Reagan’s memoirs. It is perfectly possible to truthfully describe such a situation by means of (46), but neither (46dd) nor (46dr) cover it. Both the classical analysis and the present approach can be easily modified to account for the additional reading (46h). Indeed, it is not hard to see that sentences like Lemon’s A working-class hero is something to be require the indefinite noun phrase something to quantify over or refer to properties:
(47e)
something’ = ;1P (P = P)
Using (47c), it seems possible to obtain (46h) within the framework of the classical analysis of opacity. 39 Similarly, (47e) suggests the following possible analysis of (46) within the framework sketched earlier: (46 t)
Geach is seeking something Quine is not seeking 1P lz Ix
IZ= 9 & lTi(Z, WY) IPj(Y)& F,izTY)I & x = g & T@, WY)
[e(y) & Fj(X, Y)I)I
something Quine is not seeking 1P Az[z = q & 1 Ti(z, pi 14(y) & F,& YII)I ’ /\ something IP(P = P)
IPlz[z
Geach is seeking P Wx = g & ‘I-i@, WY) 16(y) & F,(x, Y)I)I
that Quine is not seeking - q cQ~T~(z, ai (3~) lpi(y) & F,h Y)I)I
3g It may be noted that a detailed analysis of (46).would tionality problem discussed in von Stechow (1980).
have to deal with the composi-
PROPER
TREATMENT
OF OPACITY
IN CERTAIN
VERBS
173
Note that (46t) is a de re reading construed along the lines of (4Ot), but in this case res est qzditas; and clearly, (46t) truth-conditionally boils down to (46/z), as promised. Also, note that because of a type mismatch a corresponding de ditto reading is missing: properties are not the kinds of objects that one can find. Whereas (46) only involves reference to properties, there also seem to be at least some cases of quantification over properties. To see this, let us first note that seek is upward monotone in the sense that the nonspecific reading of (48) implies the nonspecific reading of (49): (48)
Geach is seeking a book by Quine.
(49
Geach is seeking a book.
Now consider: (50)
Geach is seeking an arbitrary book.
If (48) is true on its nonspecific reading, Geach stands in the relation of seeking to the property Q expressed by book by Quine; he thereby also stands in that relation to the property B expressed by book. But (50) would not be true in such a case, which shows that the unspecific reading of (49) cannot be paraphrased by (50), as was already mentioned in the introduction. The reason why we would then deny that Geach is seeking an arbitrary book is just that there is this special kind Q of books that he is seeking. In other words, in order to seek an arbitrary book, he would have to stand in the seek-relation to B without standing in that relation to any of its subproperties. The following analysis of an arbifrary book captures this idea:
(51)
IZPs((s(et))r) lpi(B)
& Pp)
Ip < B +
‘Sp)ll
where ‘P < B’ expresses that P is a proper subproperty of B: ‘(VI) (Vx) [pi(x) * Bj(X) ] & (3/) (3x) [ Bj(x) & 1 Pi(X) 1’:’ And it appears that we can obtain the meaning of arbitrary simply by abstraction from B. However, there are certain difficulties with this procedure: it does not tell us what to do with the indefinite article. I cannot offer a solution and will rely instead on the analysis (51) of the whole NP. Using the same scoping device as above, we then arrive at the following analysis of (50): ” (5 1) is actually an oversimplification. A more appropriate analysis, covering downward monotone contexts (like be allowed to read an arbitrary book) would be IV,(B) & (VP) (VQ) P = Ai [pi V Qi] + 7 [P,(p) & 1 e(Q)]]] which says th .t the notion of an arbitrary book does not differentiate between subkinds of books.
174
(52)
THOMAS
EDE
ZIMMERMANN
i2x[ x = g & seek,‘(x, B) & (VP) [ P < B + 1 seeki’ (x, p)]]
Just like the use of arbitrary induces a (special kind of) de ditto reading, so does the adjective particular indicate de re. It thus comes as no surprise that it can be given an analogous treatment in terms of quantification over properties. In fact, the following formula appears to be quite a plausible analysis of a particular book: (53)
%WW~
k [B(x) & Pi(
(53), too, can be combined with the translation of ‘Geach seeks P’ yielding the de re reading of (49); the details are left to the reader. Other instances of quantification over properties may be provided by the following kind of example: P-4)
Tom needs at most two blankets.
Under the natural assumption that ‘subj needs OBJ’ can be schematically paraphrased by ‘it is necessary for subj to have OBJ’, the classical account would assign (54) a de ditto reading (54~) according to which the number of blankets had by Tom must not exceed two: (54~)
N(W”*y)
(BiJ~ Hi& Y>>,
where both N( = necessary> and H( = have) could be interpreted in a context-dependent way. But although (54~) may be glossed as (55), it is not what (54) means on any reading. (55)
Tom needs to have at most two blankets.
Let me briefly sketch how to get a more adequate analysis of (54). The idea is to interpret at most as a polymorphic modifier:41 (56)
at most’ = Ax, AP,(,@x’)
[P,(x’) + x’
& Bj
