Journal of Semantics, Vol.1 Issue 3-4 ,1982

JOURNAL OF SEMANTICS AN INTERNATIONAL JOURNAL FOR THE INTERDISCIPLINARY STUDY OF THE SEMANTICS OF NATURAL LANGUAGE VOLU...

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JOURNAL OF SEMANTICS AN INTERNATIONAL JOURNAL FOR THE INTERDISCIPLINARY STUDY OF THE SEMANTICS OF NATURAL LANGUAGE

VOLUME 1,

no.

3/4, 1982

Reprinted with permission of the original publishers by

SWETS & ZEITLINGER BV LISSE

-

THE NETHERLANDS

-

1994

EVALUATIVE ADJECTIVES AS ONE-PLACE PREDICA TE5 IN MONT AGUE GRAMMAR•

Kenneth Reid Beesley

Abstract

•

I

Introduction

Adjectives form a very diverse class and present a challenge to any linguistic or logical analysis. To avoid confusion in a field which has become a terminological jungle, I feel it is important to present a few definitions and clarify a few usages at this point. I will speak of 'syntactic predicates ' , ' syntactic predicate position ', or just 'predicate position ' when referring to the appearance of adjectives, without accom I will panying nouns, after copulas in strings such as The sky is blue. speak of 'syntactic attributives' or 'attnbutive position ' when referring to adjeCtives appearing in strings together · with the noun they modify, as in blue sky, big {lea and good plumber. From the semantic point of view, a 'predicate ' or 'one-place " p redicat e ' w i l l b e taken t o b e a iunction whose domain is the set o f entities JOURNAL OF SEMANTICS, Vol.!, no.3, pp. 1 9 5-249

195

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good, bad, In this paper I will argue that evaluative adjectives, such as clever and skilful, should be analysed as one-place predicates in, logical translation. This approach, which is basically the traditional logical trea tment of 'absolute ' adjectives, is to be contrasted with the approach in Montague (1974a) and Parsons (1972), wherein all adjectives are translated as two-place predicates, i.e. as semantic attributives. The move away from the Montague-Parsons analysis is not new: Bartsch (1972, 1975), McConnell-Ginet (1973), Kamp (1975), Siegel (1976a, 1976b, 1979), Keenan &. Fultz (1978) and Klein (1980) have similarly advocated one-place predicate sta tus, at least for fairly straightforward qualities (e.g. red, carnivorous, stony) and even for degree adjectives (e.g. tall, short, heavy and old). Evaluatives, however, remain troublesome: Kamp concluded that their status was uncertain, and Siegel classified them as two-place predicates after much argument. My remarks are directed primarily against Siegel's analysis; I intend to show that there are syntactic tests, some suggested by Siegel herself, which argue persuasively that evaluative adjectives should be interpreted as one place predicates.

K ENNETH R. BEESLEY in a model and whose range is the set { 0, 1 } . More simply, a predicate like bam ' takes one argument x, written bam'(:r), and returns 1 (true) if x is a barn and 0 (false) if it is not. Alternately, bam' can be seen as representing the set of all barns in a model, and bam '(:r) will be true iff x e: barn'. I will speak of 'two-place predicates' or 'semantic attributives' when referring to analyses of the Montague-Parsons type; examples w ill follow shortly. The distinction made here is important, but that does not mean that there are not significant correlations between syntactic and semantic predicativity and attributiveness. Indeed, by arguing that evaluatives can and should be interpreted as one-place predicates, .x [( tall '(jockey •))(x)] (John) (5b) tall '(jockey ')(John) (evaluative adjective) (6) John is a good jockey. (6a) A x [(good '(jockey')J{x)] (John) (6b) good'(jockey')(John) JS, voi. J , no.3

1 97


If big flea were analysed using the simple conjuction analysis used for red bam, then (2b) would follow automatically, and to hold that 'a big flea is small' would seem to involve a contradiction, that some thing can be big and small at the same time. Sim tlarly, If we know that someone is a good thief, then it follows that he is a thief, but not that he is absolutely good. A good thief can be, and usually is, a 'bad man. A woman can be a good· mother and a bad w ife simul taneously.

KEN N ETH R. BEESLEY In this analysis, whlie blue-eyed, tall and good can all be syntactically attributive, only ta ll and good correspond to semantic attributives, that is, to two-place rredicates. Blue-eyed' turns out to be semantically pre dicative even when the surface adjective appears as a syntactic attri butive. Conversely, these same adjectives can all appear in syntactic predicate posit 10n, but sentences like (8) and (9) must be taken as ell iptical versions of the more �:omplete sentences (8a) and (9a).

Before moving on to a more detailed discussion of these analyses and claims, it is worth noting that some adjectives (the 'non-standard modi and f iers' of Parsons 1972: 1 30) are even more troublesome than good tall. If we know that person x is a good thief, then we at least know that x is a thief. But if we know that x is an alleged thief, than we cannot even conclude that x is a thief . And if x is a pretend thief, then we must conclude that he is not a thief at all. Anxious to avoid any spurious logical consequences ansing from a conjunction analysis for such adjectives, Montague ( l 974a: 211 - 1 3; henceforht EFL) goes to the extreme of denying conjunction analysis (and so one-place pred icate status) to all adJectives. The result is an analysis where all adjec tives correspond to semantic attributives much as in (5) and (6) above. Montague rejects the idea of def ining multiple classes of adjectives, some of wh ich, the ' mtersect ives ' , would translate to allow (a) and (b) entailments as in (1), others of which, the ' subsectives', would translate to allow the (a) entailments as in (2) and (3), and still others of which, like reputed and a lleged, would allow neither; he felt such a solution would detract from the 'conceptual simplicity' of his untform treatment. As a result, all adjectives in EFL are treated as two-place pred icates, ad-common nouns denoting functions from intensions of properties to properties. ( 1 0) and ( 1 1 ) show typical syntactic and seman tic trees. ( 1 0)

(I I)


(7) John is blue-eyed. (8) John IS tall. (8a) John is a tall N. (where N is a noun) (9) John is good. (9a) John is a good N. (where N is a noun)

big '('flea')

/ big' .

"'

flea'

false ' ('friend ')

/

false '

� frtend'

.This blanket solution avoids invalid consequences; in fact it leaves_ Montague w ith no consequences at all. He cannot even show that a 1 98

JS, vol . l , no.J

EVALUATIVE ADJECTIVES red bam is red and a red bam is a bam are valid sentences. To patch up

this obvious deficiency, Montague mtroduces meaning postulates such as ( 1 2) and ( 1 3). every o r; is a r; I where 6 is an intersective or subsective adjective and r; is a common noun ( 13) I every 6z; is 6 I where 6 is an intersective adJective and c; is a common noun

( I 2)

I

In sp1te of Montague 's example, a number of writers in the general field of Montague Grammar, e.g. Dowty ( I 976: 2 10), continue to treat at least some adjectives as simple one-place pred1cates. Others like Kamp ( 1 97 5), Bartsch ( 1 973) and Klein ( 1 980) have argued that the Montague-Parsons analysis cannot be generalised to handle comparatives correctly; they claim that even degree adJeCtives should be translated as one-place pred1cates. Kamp ended his paper ( 1 975: 153-4) wondermg just how many other types of adject1ve could be g1ven predicate status; noting that alleged seemed a hopeless case, he contmued: "The same can be said to be true, to an almost equal degree, Where precisely we of adjectives such as fake, skilful, or good. should draw the boundaries of the class of adjectives [which are one-place predicates] I do not know. For example, does skilful belong to this class? Surely we must always ask 'skilful what? ' before we can answer the question whether a certain thing or person is indeed skilful; this suggests that the theory is not applicable to the word skilful . Yet there appears to be some plaus1billty in the view that having a good deal of skill does func tiOn as a predicate--be it a highly ambiguous one as there are so many skills." Siegel ( 1976a, 1 979) argued forcefully for treating degree adject1ves as a subset of the class of absolute adjectives, but she drew the line firmly at the evaluatives, which remained two-place predicates a!> in Montague ( 1 974a). I will proceed by f1rst examming the way in which degree adjectives have been elevated to absolute status. The challenge is to do this JS, vol. l , no.3

1 99


By way of example, red is an intersective adjective and tall 1s a subsec tive adjective in Montague's terminology. Meaning postulate ( I 2) allows one to show that a red bam is a bam and a big flea is a flea a r e v a I i d sentences. Sim ilarly, ( 13) supports the validity of a red bam is red but not a big flea is big. These rules allow Montague to ass1gn all adjectives the same syntactic category and logical translation while still getting out JUSt the nght consequences. However, Montague is getting no free lurtch: he avoids adjective subclasses m the grammar, but the meanmg postulates have to refer to such subclasses m the end.

K ENN ETH R. BEESLEY without causing undue problems for logical consequence. I will then show that evaluative adjectives can be handled in much the same way. Some new tests involving adverbial modification of adjectives will lend support to my clai ms. In the end, it will be shown that extending one-place predicate status to evaluatives results in more consistent syntax and semantics, with a closer mapping between the two. 2 Degree Adjectives as One-Place Predicates 2.1

Traditional Analysis o f Degree Adjectives a s Two-Place Predicates

( 1 4) John is a tall man. ( 1 4 ') Tall(John, >.x(x is a man))

&

John

£

>. x(x is a man)

The translation in ( 14') contains two clauses. In the first,tall is shown to translate as a two-place predicate holding between an entity and a set of entities. The set of entities, in this case the set of men, is the comparison class by which John's tallness is to be judged. This first clause is properly read as 'John is tall compared to men' rather than as ' John is tall for a man'. The second paraphrase presupposes that John is a man, and it is important to preserve a notation for representing a comparison between an entity and a set of which it is not a member. The second clause in ( 1 4') supports the intuition that if John is a tall man is true, then John is a man is also true, making the latter follow as a logical consequence. As we saw in section I, the less abstract Montague-Parsons analysis of tall man does not produce this logical consequence; meaning postulate ( 1 2) must be invoked. The relativity of tall is captured in the variability of the comparison class. John is a tall dwarf receives the interpretation in ( 1 5), which indicates that John's height is now to be considered relative to the set of dwarves. ( 1 5) Tall(John, >.x(x is a dwarf))

&

John

£

>. x(x is a dwarf)

Intuitively this accounts for the fact that the tallness of John can vary significantly when the comparison class changes from dwarves to men to basketball players or whatever. At first sight, ( 14') appears to be a simple and correct solution for characterising the relativity of degree adjectives. Any syntactically attributive construction A+N, where A is a degree adJective and N is a noun, will be translated with N representing the relevant comparison class. There are, however, two reasons why ( 1 4 ' ) is an incorrect transla200

JS, vol. l , no.3


We may take Wheeler ( 1 972) as a typical analysis of degree adjectives as semantic attnbutives. Wheeler translates ( 1 4) as (14 ').

EVALUATIVE ADJECTIVES t ion of degree adjectives: First, I will show that the translation is too rigid to account for the data, and second, I will show that the relativity of degree adjectives can be better handled by appealing to context. 2.2 Deriving the Comparison Class 2.2. 1

Syntactic Attributive Constructions

( 1 6) Jones is a tall old man. These two readings, which involve, presumably, different bracketings of the noun phrase elements following tall are representable in Wheeler 's system as ( 1 7) and ( 1 8). ( 1 7) Tall(John, AX(old(x, Ay(y is a man)) & x E: Ay(y is a man))) & John E: A x(old(x, A y(y is a man)) & x E: A y(y is a man)) ( 1 8) Tall(John, AX(x IS a man)) & John E: A x(x IS a man) & Old( John, A x(x is a man)) & John E: A x(x is a man) Sim ilar examples are discussed in Parsons ( 1 972: 1 32-3), Keenan & Faltz ( 1 978: 3 1 8- 1 9), and in most other works on the subject (Siegel 1 976: 1 30-4; 1 979: 247-8; McConnell-Ginet 1 973: 89, 1 33-4). The formalisms start getting unmanageable, and the intuitions start failing, however, as the noun phrases get more complicated. A sentence like John is a tall old fat man has one reading, for Wheeler, where the tallness is relative to old fat men, and "given the present order of its attributives, the sentence can be understood m at least two other ways", which again appear to involve different surface bracketmgs (Wheeler 1972: 32 1 ) . I will spare the reader the translations given for these readmgs (which are all, not unexpectedly, full of errors in the original paper anyway) and concentrate on the qualification by Wheeler that there are "at least" two other readings. It is com mon be under practice to Cite the simplest cases where "it will generally stood that the relevant class for grading is that specified by the noun" (McConnell-Ginet 1 973: 89; emphasis mine) and to avoid anything nastier. There is some uneasiness in the observations. If comparison classes are derived mechanically from syntactic structures, then it should JS, vol . 1 , no. 3

201


The problem with the Wheeler analysis is that it is not so easy to derive the relevant comparison class mechanically from the syntax. ( 1 4 ') shows the modified noun functioning automatically as the compari son class, but there arise difficulties with more complex noun phrases. Wheeler himsel f ( 1 972: 3 1 4) claims that ( 1 6) has two. readings, one ascribing tallness to Jones relative to old men and the other ascribing both tallness and age to him relative to men.

KENNETH R. BEESLEY always be possible to predict exactly how many readings are theoretical ly possible for any finite noun phrase construction involving degree adjectives. Siegel ( l 976a: 1 29- 1 35; 1 979: 247-8) goes farther than most in discuss ing the problems of interpretation of double degree adjectives as in ( 1 9) and horrors like (20). ( 1 9) Btlly is a heavy fast runner. (20) Btlly is a tall little red-headed basketball player.

"Presumably, it is the context of utterance that allows us to understand how much is included in the comparison class. It would appear that w ith prenominal measure [ 1.e. degree] adjectives, the comparison class may be taken as bemg either the set p1cked out by the basic common noun modified, or by another, more complex common noun to the right of the measure adject1ve." Going a step beyond Siegel, I claim that the comparison class, even in the simplest A+N constructions, may not be the set denoted by the noun at all. Consider the following conversation at a lmgu1stics convention. ( 2 1 ) Q: Which of the men over there is Quang? A: Quang is the short Vietnamese. Now there is a perfectly good, even preferable reading of short Vietnam ese in (21) which involves men' rather than Vietnamese 'as the comparison class for tall. That is, short Vietnamese can be paraphrased as 'short

compared to men and a Vietnamese '. It is perfectly possible to hold that Quang is a short Vietnamese but that he is not short for a Vietnam ese. Wheeler 's analysis, with its mechanical, syntactic translation, is incapable of captunng such usages. 2.2.2 Syntactic Predicate Constructions Another problem for any Wheeler-like theory is to account for degree adjectives in syntactic predicate position. (22) John is tall. If such adjectives are · taken to be semantically attributive, then the 202

JS, vol. l , ;)u.3


Noting that (20) seems to allow a reading where tallness is measured in comparison to little basketball players, skipping over red-headed alto gether, S iegel concludes, as did McConnel-Ginet, that context rather than syntax must p1ck out the comparison class.

EVALUATIVE ADJECTIVES noun (or predicate or set) used for comparison must be slipped into the translation by some fashion. There are basically two ways of doing this, both of which amount to the same thing for the purposes of this discussion.

For convenience, I will call such a process 'dummy noun deletion ' regardless of the actual mechanism involved. Any actual attempt to interpret a degree adjective in predicate position would seem to involve something like (23B), which ulti mately relies on context. There have been claims, however, that the comparison class in such cases can be derived m an orderly way from semantic codings in the lexicon. Katz ( 1 967) presents the examples in (24), where the comparison classes are claimed to be named by the nouns m square brackets.

{

(24) The

skyscraper man flea United States tarantula

is big

[buildings] [humans] [insects] [countries] [spiders]

In general, "the class of entities with which something IS compared IS a category to which that thing belongs" (Katz 1 967: 1 86-1 87). Katz The sky even claims that "we cannot render The skyscraper is big as scraper is big for a physical object or in a more extreme case, The flea is big, as The flea is big for an animal". The choice of comparison class is taken to be li mited to the next highest concept in the great semantic chain of being. Sim ilar notions have appeared in Chafe ( 1 970: 1 95) and even in Bartsch ( 1 972), but the inadequacies of this approach are notorious (see McConneii -Ginet 1 9 7 3: 89; Damerau 1 97 5; Siegel 1 976a: 1 29; 1 979: 243 -244; Bierwisch 1 969: 1 65- 1 68). For instance, it is clearly possible, Katz ' claims to the contrary notwithstanding, to interpret The {lea is big as 'The flea is big for an animal', and such a reading can be useful and natural in the context of science fiction. The problem of determining the comparison class for derived lexical item s, which have no dictionary codings, will also be a problem. Chafe, Bierwisch JS, vo1. 1 , no.3

203


(23) (A) An adjective like tall can be taken to apply to a noun as usual, yielding strings like John is a tall boy. Then a transformation can apply, deleting the noun (and deleting or suppressing the indefinite article) yielding John is ta ll. The predicate boy', or what ever, will remain in the semantic translation. (B) Alternatively, tall can be taken to apply to a dummy noun, call it b. , which never receives phonological form and so never has to be deleted. In the semantics, b. is instantiated with a nominal predicate by the context.

KENN ETH R. BEESLEY and Bartsch appreciate- that genericness and specificness can weight the choice, and Bartsch ( 1 972: 1 65) and Sampson ( 1 970: 257) point out further that proper name subjects like John give little clue as to what comparison class applies - so the context has the last say again. While attempts to assign comparison classes mechanically from lexical codings may have something to say about default assignments, it is clear that context can be an overriding factor.

2. 3

Appeals to Context

The solution of McConnell-Ginet ( 1 9 7 3: 1 1 5) is to employ 'delineations ' , contextual variables which f ix the extension o f degree adjectives. The basic idea is that predicates apply with respect to a relevant delineation, and the formalism indicates a ' d ' , for delineation, as a subscript to any degree adjective. (25) John is tall. (25') talld(John) In the same spirit, Klein ( 1 980: 1 4- 1 6) indicates contextually specified comparison classes, written 'c', as a subscript to formulas. (26) [ tall(John))c ' For reasons which will become clearer later, I prefer Klein's notation and w ill use it whenever the notion of compar ison class needs to be made explicit. Along the same general lines are analyses proposed by Bartsch ( 1 972: 1 65) and Keenan & Faltz ( 1 9 78: 1 78- 1 79). These grammars interpret degree adjectives in such a way that compar ison classes (or, in the case of Bartsch, averages over comparison classes) are built directly into them. The important point, for this discussion, is that all these schemes translate degree adjectives as one-place predicates.

20�

JS,

vo!. l,

no.)


Given that only context can be the ultimate arbiter in the choice of a comparison class in the examples 1iscussed above, the question remains of how this comparison class 1s to be represented in logical translation. Wheeler's analysis ( 1 4 ') cements the class in as one argu ment of a two-place predicate. It is not wise, however, to treat a contextual factor on the application of a predicate as a syntactic argument. In addition, the fact that syntactically attributive A+N constructions may have companson classes distinct from N destroys any. syntactic justification, by analogy, for semantic attributives.

EVALUATIVE ADJECTIVES 2.4 Syntactic Analogy Arguments 2.4. 1

Introduction

The common way of defending a solution like Klein's (26) over on€ like Wheeler 's ( 1 4') is to show that degree adjectives behave syntactical ly like absolute adjectives rater than like other adjectives thought to be irredeemably relat'ive. Then by analogy, if absolute adjectives translate as one-place prPdi:::a tes, so should the degree class.

S tege! ( 1 976: 52-54 ; ' 1 979: 228) believes that there is, m most languages, a strong correlation between predicate position and one-place predicate status for adjectives. Degree adjectives are like absolute adjectives, and unlike many of her relative adjectives, in their ability to appear gram matically in predicate position. (27) Mary is pregnant. (28) Mary is tall. (29) *Mary is: •nere/alleged/ostensible.

(absolute) (degree) (relattve)

If tall is taken as a relative adjective so that (28) has to be generated by way of d4m my noun deletion, then something would have to be added , to the grammar to prevent the transformation from producing the strings in (29), which also involve relative adjectives. For Siegel, who has but one class of relative adjective, thts would involve the ad-hoc assignment of a feature [+dummy deletion] to all those relatives, like tall, which happen to appear in predicate position. If, however, tall is taken to be a subtype of absolute adjectives, then both (27) and (28) can be generated directly by a rule which adds be to absolute adjectives to form syntactic predicates. The strings of (29) will never be generated by such a rule, and dummy noun deletion can be defenes trated. The net result is one less transformation and a closer translation between the syntax and the logtc. Si milar arguments for ' less abstract' analyses are found in Thomason ( 1 976), Klein ( 1 980: 1 4- 1 5), Keenan & Faltz ( 1 978), and McConneli-Ginet (1973). We shall see that Siegel's analysis of evaluative adjectives forces her to retai'n dummy noun deletion and adopt ad hoc lexical exceptton features. 2.4.3. The One Preform Argument Only certain adjectives seem to allow their arguments to be referred to by one as in (30) to (33). Aga11;, deg•ee adif'ctives behave 'like the absolutes.

;!05


2.4.2 The Predicate Position Test

KENNE TH R. BEESLEY (JO) This ( 3 1 ) This (32) *This (33)?*This 2.4.4

is is is is

a red box, a big box, an alleged an alleged

and that is a blue one. and that is a small one. thief, and that is a mere one. thief, and that is an ostensible one.

The Very Test

1 44, 1 50; Levi 1 978: 20; Keenan & Faltz 1 978: 1 64; Bartning 1 976: 9- l l , 58-59; Vendler 1 968: 1 09; Bolinger 1 972: 1 5). That is, pregnant, car nivoroWJ, virgin and other such all-or-nothing adjectives must take on secondary readings in very pregnant, very camivoroWJ and very virgin. might A woman either is pregnant or isn 't pregnant, but very pregnant refer to a woman' s size, degree of morning sickness, craving for pickles, etc. Lees ( 1 963: 1 80- 1 8 1 ) sug g ests that all 'bona-fide' adjectives can be modified by very and Levi ( 1 973: 344) goes so far as to say that words l ike pregnant and virgin, by virtue of their resistance to very, are not adjectives at all but rather nouns. To add to the confusion, Wheeler ( 1 972: 3 3 1 ) holds that the possibility of modification by very is a sure sign of a two-place predicate.

It seems clear that if the present class of absolute adjectives is to be retained, then an internal distinction must be made between gradables and non-gradables. The gradables will allow modification by very, extremely, remarkably, quite and other such words. Semantically, the difference lies in the way an adjective div1des up the universe of a model. A predicate like pregnant ' sharply divides all entities into the pregnant and the non-pregnant, with nothing left over. The bounda ries of tall, on the other hand, will be a bit fuzzy, and between the group of tall entities and the group of short entities there may be a group of entities which are neither short nor tall. This last group lies in the ' extension gap' . (34) (35)

-pregnant

+pregnant

+short

+tall extension gap

If we postulate that very can modify any one-place predicate with a possible extension gap, then we can show once again that degree adjec t ives act more like the absolutes than like the relatives. 206

JS, vol. l , no.3


The use of very as a syntactic test for adjectives is very tricky. Because *very a lleged and *very mere are so grcssly ungram matical while very red and very tall are so natural, one is tempted to advance modification by very as a test for one-place predicates. But some adjectives usually classified as absolutes par excellence do not a llow modification by very w ithout taking on secondary meanings (Sapir 1 944; K iefer 1 978:

EVALUATIVE ADJECTIV ES (36) (37) (38) (39)

The very red woman finally left the beach. The very tall woman got the job. *They sent me a very mere boy. *The very alleged thief was freed.

This test, if it is useful at all, can only provide posttJve evidence that an adjective is a one-place predicate. Failure to take very could in dicate either that the adjective lacks an extension gap or that it is not a one-place adjective at all. We shall see that Stegel's c lassification of evaluative adjectives forces her to deny even limited validity for the very test.

Yet another test proposed by Siegel ( 1 976a: 52, 1 2 3) is that only one place predicates can function as non-restrictive modifters of noun phrases. (40) (4 1 ) (42) (43) (44)

We all know naughty Nancy. We all know btg Bertha. *We all know mere Jonathan. *Ostensible Jonathan went home. *Say hello to alleged Bill.

(absolute) (degree) (relative) (relative) (relative)

2.4.6 The See-Catch-Find Test S tege! argues ( 1 979: 237-239; 1 976a: 76ft, 92) that the see-catch-find and there construction in (45) and (46) select unerringly for one-place predicates, and she uses these tests as a key tool in motivating her classification. Her examples again show degree adjectives behaving like absolutes. (45) (a) The warden saw the swimmers nude. (b) I've often seen the grass tall around that house. *(c) The warden saw the swim mers veteran.

(absolute) (degree) ( relative)

(46) (a) There is a bat asleep in the bathroom. (b) There were two pigs clean in the whole pen. *(c) There are several crt mes actual in the story.

(absolute) (degree) (relative)

In fact, Siegel gravely misunderstands these tests, which select not for one-place predicates as a whole, but rather for one-place predicates which are 'temporary' in the carefully defmed technical sense of Bolinger ( 1 952: 42-43; 1 967: 9- 1 4), Bauer ( 1 975: 1 1 3, 1 1 9) and Dowty ( 1 975: 582-583). Dowty prefers to use 'temporary' and 'permanent ' rather than Bolinger 's terms 'accident ' and 'essence' (Bolinger 1 972: 38-39, 47-48; 1 973) because he thinks the latter terms to have inappropriate, JS, vol. l , no.3

207


2.4.5 The Non-Restrictive Modifier Test

KENNETH R. BEESLEY m isleading connotations from their other uses in philosophy. Ironically, Bolinger adopted the terms 'accident' and 'essence ' because of a similar concern about the connotations of 'temporary' and 'permanen t ' . In Siegel's case, Bolinger 's fears are justified; she misinterprets 'temporary' and 'permanent' in literal, everyday senses, and goes to great lengths to demonstrate that some adjectives appearing in see-catch-find sentences are not temporary at all. This misunderstanding seriously flaws Siegel 's analysis, for English as well as for other languages she considers. 1 2.4.7 Nominalisation and Verbalisation Tests

(47) Adjective red tall big intelligent mere alleged ostensible

Noun redness tallness, height bigness, size intelligence *mereness, *merity *allegedness *ostensibility

The general intuiton is this: being red or tall involves partakmg of the qualities of redness or height respectively. But there is no way to make sense of a property of *mereness or *allegedness in the same way. The nouns a llegation and ostentation are, of course, related to a lleged and ostensible, but these are abviously not essences of a predicate like redness and size. Similarly, verbalisations, verbs with rough ' make Adjective' readings, and actual 'make Adjective' phrases appear to correspond only to one place predicates and never to relative adjectives.

(48� Adjective

red tall old big small dead pregnant mere alleged 208

Verb redden, make red, rubrify make tall make old, age make big, increase, augment make small, decrease kill, cause to become dead impregnate, make pregnant *make mere, *merify *make alleged, *allegify JS, vol . I , no.�


Some people working on relative adjectives (e.g. Bartning 1 976; 1 0) have claimed that only those adjectives which are one-place predicates have meaningful nominalisations or corresponding nominal forms. Allow ing some slightly abstract, stilted nouns, the results of this test seem to support the others.

E. VALUATIVE

ADJECTIVES

but this verb is not reA llege, of course, is a verb related to alleged, lated to an adjective in the same way that impregnate and age are. 2.5 Rescuing the Conjunction Analysis

A major problem remains. The decision to treat degree as a kind of absolute adjective means that both will receive tion analysis. Yet it was the apparent failure of degree to support a conjunction analysis which origmally led to their tion as semantic attributives. Geach ( 1 956: 33) wrote

adjectives a conjunc adjectives classifica

" 'Big' and 'Small ' are attributive; 'x is a big flea' does not split up into 'x is a flea' and ' x is big ' , nor 'x is a small elephant' into 'x is an elephant' and 'x is small ' ; for if these analyses were legitimate, a simple argument would show. that a big flea is a big animal and a small elephant a small animal." In fact, a proper appreciation of context makes the problem disappear. Geach assumes that for a sentence like 'x is a big f lea ' , the comparison class must necessarily be the set of fleas. This is the same assumption which I showed to be inadequate in section 2.2. 1 . Even for simple A+N constructions like short Vietnamese and big flea, context can force comparison classes different from N altogether ( 2 1 ) . Also, Geach as sumes that 'x is big ' , where x is a flea, will necessarily have the com parison class of animals. This is an implicit statement of the Katz ( 1 967) method for automatic computation of comparison classes f rom lexical codings, which is similarly inadequate (see section 2.2.2). I have shown that context must choose the comparison class by which any sentence of the form 'x is big ' will be evaluated. Let us assume that (49) is evaluated in a context where the compar ison class is c ' , where c' is the class of fleas. A conjunction analysis with contextual specification w ill look like ( 50). (49) x IS a big flea (50) [big'(x)]c• & flea'(x) Now let us assume that the pair of sentences in ( 5 1 ) is evaluated relative to the same context c ' . The translation will be (52). ·

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2 09


In summary, I have shown some of the h istory of degree adjective analysis, �hich shows an increasing trend toward interpreting them as one-place predicates. I have shown how syntactic computation of comparison classes is inadequate, and how an appeal to context is both necessary and natural. I have also outlined a number of arguments designed to show that degree adjectives behave syntactically like absolute adjectives, which lends support to a common translation.

KENNETH R. BEESLEY (5 1 ) x is bi� and x is a f lea [big'( x)]c ' & flea'(x)

( 52)

The equivalence of (50) and ( 52) shows that the conjunction analysis can indeed hold for degree adjectives. In fact, the conjunction analysis for degree adjectives holds whenever the context remains constant over the original clause and the constituent clauses of the conjunction.

(53)

{ [x is a big flea]c 1 } I= { [x is big]c 2 and [x is a flea] }

Given that context may assign different comparison classes for evalua ting a sentence of the form :r is big, the same type of contextual equiv ocation can make the evaluation of :r is big different from the evalua tion of another sentence with the same surface form. \54)

{ [x is big] c 1 }

I= { [X is big] c 2 }

And as I showed that contexts can force short Vietnamese to be evalua ted relative to the heights of V ietnamese, men, or any number of other classes, even (55) is possible. (55)

{ [short V ietnamese]c 1}

I= { [short V1etnamese]c 2 }

A s 1t I S hardly t oo much to require that context remain fixed throughout the various stages of an analysis, there is no barner to adopting a conjunction analysis for degree adJectives. 2.6 Hedges as Overt Specifiers of Context Before leaving degree adjectives, I wish to add one final argument to support the treatment of compar ison classes as contextual subscripts rather than as syntactic arguments. So iar we have considered cases where context alone must select comparison classes. Tr.ere are, however, a variety of ways in which comparison classes can be spec ified syn tactically. ( 56) John is tall for Pygmy. For a Pygmy, John is tall. John is tall for i:l Pygmy but shor! f.;r 2!0

, t >. There are two such predicate classes in Montague ' s ( 1 9 74b) PTQ:syntactic predicates and common nouns. To preserve the syntactic distinctions between them, syntactic predicates are assigned the category t/e and common nouns t/ /e. As Siegel proposes to treat some' adjectives as one-place pred1cates, and as their syntactic behaviour is different from both syntactic predicates and com mon nouns, she assigns them the category t/ I /e. Rule (7 5) forms a syntactic predicate from an adjectival predicate by adding a be. (75) If a £ Pt /// ' then F 2 0p) £ P 1 y where F 2 o(l) e

=

be a

For our purposes, the corresponding semantic interpretation rule may be taken to simply preserve the original interpretation. Rule (7 5) will allow Siegel to generate strings such as (76) and (77), but (78) will not be' generated by this rule because mere is not of cate gory t/I /e. ( 76) John is carnivorous. (77) John � nude . ( 78) *John is mere. To generate absolute adjectives in syntactic attributive position, Siegel resorts to an awkward version of the old relative clause reduction JS, vol. J , no.J

717


(74) is a tree showing a derivation including jective.

KENN ETH R. BEESLEY transformation from transformational grammar. Such a solution, mtxmg TG and MG, is the sort of thing pursued by Partee ( 1 97 5, 1 976b). The reduction rule is shown in (79) and an example using it in (80). (79) If a e: P e N and a is of the form 6 such that hen be y where 6 e: P e N and y e: P t ///e , then F22 ( a ) e: P e N where F22 (a ) =y 6 The red barn collapsed t

(80)

/

�

/

barn e N

1s red t h eo'\. / '\_oe hea r

red 1 v

""' red t ///e

As ·we have seen, Siegel included degree adjectives among the absolutes. By using rules (75) and (79) she properly generates the strings in (8 1 ) and (82) without any recourse t o dummy noun deletiOn. (8 1) The basketball player is tall. (82) The tall basketball player sat down. When taken to its full conclusion, this analysis makes some interesting predictions about possible readings for adjectives in attributive vs. predicate position. If there are adjective forms which have both a CNICN and a tl I le reading, then only the tl I le reading should be possible when the adjective is in predicate position. The adjective in attributive position should be ambiguous: absolute if derived by way of relative clause reduction and relative if derived directly. Consid er the case of moral in moral philosopher. A moral philosopher is either a practitioner of moral philosophy (Siegel's 'relative' reading), or he is a philosopher who is moral (Siegel ' s 'absolute' reading). But moral has only the absolute readmg when it appears in syntactic predicate position: The philosopher is moral. So far the predictions a re borne out. This test works for moral philosopher, plastic surgeon, abnormal psychologist,

fuzzy logician, legal secretary, deviant logician, Chinese restauranteur, mediaeval scholar and a number of similar examples discussed by Bolin

ger ( 1 967). In fact, Siegel's absolutes and relatives correspond nicely with Bolinger 's 'referent modifiers' and 'reference modifiers' or with the traditional dist inction between 'inherent' and ' non-inherent' modifiers (Quirk et a!. 1 972: 259ft). Unfortunately for Siegel's analysis, evaluatives refuse to act as 218

JS, vol. l , no.3


the red bar n r collapsed1 v I red barn e N I barn such that it is red e N

EVALUATIVE A DJ ECTIVES her classification would predict. Good is taken to be a doublet, but unlike other doublets like moral, a good in predicate position can still have what Siegel calls a relative reading. (83) John is good. Since Siegel's relative readings come from semantic attributives, any relative reading of (83) must derive from John is a good 6 , where 6 is a common noun. This forces Siegel to retain dummy noun deletion. 3.4

Evaluatives as One-Place

Siegel has two related arguments, both of which I must counter, for handling such 'relative' readings of evaluatives as semantic attribu tives. The first argument is based on the distinction between intensional and extensional modifiers which was discussed earlier. Siegel claims that to evaluate an expression like good car, which involves a 'relative' modifier, one must have a grasp of the intension of car - one must know what it means to be a car. But conversely, to evaluate expressions like red car or fast car, which involve absolute adjectives, one does not have to have a grasp of the intension of car; one needs simply to be able to identify car things and red-things or car things and things which move as fast as a car. Sim ilarly, to know what a bad library is, one has to have a grasp of the intension of library - a bad library IS poorly stocked, diff icult to use, badly designed in general for finding mformation. But a tall library, according to Siegel, can be understood with no reference to the characteristic functiOning of a library at all ( 1 979: 2 3 1 -232; 1 976a: 1 09ff). Relativ ity to the intension of a noun is taken to be explained by the form of the translations g•ven to so-called relative adjectives as in (84). (84) x is a bad library. (84 ') (bad '("library '))(x) That is, (84 ') shows bad mapping the intensiOn of library into a new predi cate which is predicated of x. · Extensionality of a modifier is taken to be explained by the structure of the conjunction analysis they receive. (85) x is a tall library (85') tall '(x) & library'(x) First, it must be pointed out that an analysis like (84 ) in itsel f explains nothing. Bad simply denotes a function mapping the intension of a CN library into a new CN bad libra r')'· There is no indication of how the '

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On Arguments Against Translating Predicates

K ENN ETH R. BEESLEY meaning of the new whole is constructed from the meanings of its parts - one simply knows that a new predicate has been created. Signifi cantly, there is not even a way to show logically that the x in (84') is a l ibrary at all. Both Montague and Siegel have to resort to meaning postulate ( 1 2) to do this. As for the conjunction analysis in (85'), it is every bit as 'intensional ' as the analysis in (84'). All functions in PTQ, before simplification, apply to the intensions of their arguments. Siegel's argument that good in good car is relative to the intension of car while fast in fast car is not is simply confused. She points out that

In addition, we saw that the extensional status of degree adjectives is somewhat in doubt, so Siegel 's contention that their extensional status requires "them to be translated as one-place predicates cannot be accepted. In fact, the question of whether an adjective is an intension al or extensional mo difier simply does not have anything to do with their status as predicates in logical translation. Any theory like Siegel's which can appeal to context to guide the application of a predicate can simulate intensional effects with simple one-place predicates. Siegel's second argument for treating 'relative' readings of good and bad as semantic attributives centers on the possibilities of vague read ings in sentences such as (86) and (87).

(86) That lutist is good. (87) That is a good lutist. Siegel claims that good in a sentence like (86) can be both ambiguous and vague. The claimed ambiguity is between being absolutely good (derived from a t/I /e) and being good as a something (derived from a CN/CN). In the case where (86) is derived from a CN/CN, the sen tence is vague; the something that the person is good as can be any noun in the lexicon. (86) might turn out, in the right context, to mean that ' That lutist is good as a chess player'. On the other hand, the good in (87) is claimed to be ambiguous but not vague ( 1 976: 55, 63-72). That is, the lutist m ight still be absolutely good or relatively good, but the relative goodness is limited to goodness as a lutist. It is impossible, 220

JS, vo!. l , no.3


a car can still be a car even if 1t does not run at all, and concludes from this that speed is not part of the intension of car - it is not a necessary attribute of car-hood. A fast car, therefore, can be charac terised without recourse to the intension of car. She claims that good car however, must be characterised relative to the intension of car. This ar gument simply does not hold. I may call a car good in the : 'relative' sense that it reliably transports me from point A to point B. But by Siegel's own argument, a car that does not run at all is still a car, so ability to transport me from place to place is not a necessary attribute of car-hood, and it therefore is not part of the intension of car any more than speed is. So, by Siegel's own argu ment, good is not an intensional modifier.

EVALUATIVE A DJECTIVES claims Siegel, for (87) to be read as 'Tnat is a good as a chess player lutist ' . Siegel believes that h e r analysis of (86) and (87) a s (86 ') and (87'), respectively, captures these observations about vagueness. (86'b) has. a variable slot ranging over common nouns. The same slot in (87'b) is filled by lutist, blocking a similar kind of vagueness. (86') a. b. (87') a. b.

good '(that lutist) good '(A ll ) (that lutist) good '(x) & lutist '(x) good '(Aiutist ') (x)

absolute reading vague relative reading absolute reading non-vague relative reading

Siegel also flaws her arguments by using only functional words in her examples showing the possibilities of vagueness. In practice, there is strong pragmatic pressure to evaluate goodness relative to just as there is lutist-like qualities in any construction like good lutist, strong pragmatic pressure to evaluate shortness relative to Vietnamese in a construction like short Vietnamese. It is easy to be fooled into think ing that the usual default readings for such constructions are the only readings available. Since Plato, however, it has been recognised that examples involving more general words like man, woman and person are much harder to explain (Bolinger ( 1 967: 26-30, 1 4 , 20; Vendler 1 968: 2 1 -22, 90-94; Hare 1 957: · 1 07- 1 09; Katz 1 966: 292-293; Berman 1 973: 1 99). (88) John is a good man. It is much easier to get a range of 'vagu e ' readings for (88) than it is for Siegel's example in (78). The sentence ·might be utte red, for example, by John's sergeant, his drinking buddy, his wife, the president of his chess club or even his religious leader, and each utterance could JS, vol. 1 , no.3

221

·


Siegel, however, is wrong. Semantically, it is indeed possible, despite her objections, to read the good in sentence (87) as 'good as a chess player'. Hare ( 1 957), Sampson ( 1 970) and Keene ( 1 9 6 1 ) have shown the futility of trying to derive standards of evaluation from the meaning of modified nouns, and they have shown how context can override even the strongest hints of functional nouns. Consider the hypothetical case of a chess school which specialises in teach!ng musicians. When asked how lutists, as opposed to oboists, take to chess, an instructor might say, ' V(e get some good lutis�s and some bad lutists' . In this context , the goodness will be relative not to lute playing but to chess playing. (Syntactically, Siegel errs in presenting the reading she wants to reJect in a way which is ungrammatical in surface English. Adjectives with explicit complements cannot be preposed, so good as a chess play er lutist is simply ungrammatical. The reading becomes clear and acceptable when the phrase is postposed: 'That is a lutist good as a chess player'.)

K ENNETH R. BEESLEY imply goodness according to a different standard. Yet for Siegel, any reading other than that of absolute moral goodness must be derived from a semantic attributive. Her translation in (89), with man plugging up the vagueness slot, is completely inadequate. (89) *good '( "man') (John) 3.5 Syntactic Tests and Evaluative Adject ives 3.5. 1

Introduction

3.5.2 The Predicate Position Test It is quite obvious that evaluatives appear freely in predicate position just like absolute and degree adjectives. (90) Mary is good/tall/pregnant : To defend her analysis, Siegel has to argue that free occurrence in predicate position is not a reliable test for t/ I /e adjectives in English. The problems Siegel runs mto in the attempt to. make her analysis work suggest strongly that something is basically wrong. After including evaluative adjectives among the CN/CN 's, Siegel is forced to retain an otherwise unnecessary dummy noun deletion transformation ( 1 976: 54; 1 979: 230). Given the modern standards for attractiveness of analyses, which place a premium on avoiding transformations and abstract analyses, this is a Bad Thing. The dummy noun deletion transformation causes its own difficulties, for it threatens to generate ungrammatical strings such as *John is mere and * Bill is utter. To compensate for this new problem, Siegel is forced to introduce an ad hoc feature [+dum my deletion] for every word in the CN/CN class ( 1 976: 93). In the end, Siegel lists a large class of CN/CN adjec tives with the features [+dummy deletion], [ +preposing] and [+subsective] (in the sense of Montague, see the meaning postulate ( 1 2)). This class, barrin g a few mistaken entries, is in fact the class of evaluative adjec tives ( 1 976: 1 8 1).

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We have seen that Siegel and others have used a number of syntactic tests to identify absolute adjectives. Siegel uses these to defend her classification of degree adjectives with the absolutes. I believe that her tests and her conclusions, as regards degree adjectives, are generally valid. I claim, moreover, that evaluative adjectives are also a subtype of the absolute adjectives and that the same syntactic tests w ill support my previous arguments.

EVALUATIVE ADJECTIVES 3.5.3 The One Proform Test Here again, evaluative adjectives act like absolutes and unlike real semantic attributives. (9 1 ) (92) (93) (94)

That's a red box, and that's a blue one. That 's a tall man, and that's a short one. That's a good boxer, and that 's a bad one. *That's an utter fool, and that 's a good/tall/fat/prize/consummate one. (95) *That's an abnormal psychologist, and that 's a normal one. (on CN/CN reading for abnormal)

Because evaluative adjectives occur freely with very and other extent adverbs, Siegel has to argue that very is not a reliable positive test for t///e status ( 1 976: 1 46; 1 979: 256ft). Gradability, she claims, is a feature ranging through all the categories of grammar, and she cites (96) as an example of gradability on a CN/CN. (96) I will follow Peter, because he is the more rightful king. This specific objection is a relic of the fact that the CN/CN class is poorly understood and analysed. R ightful properly interprets as some rightful thing like A PA x [rightfui'(1P { x } ]], so the interpretation of king turns out to be A X [nghtful'( 1king'(x)])]. We may read this as 'all x such that it is rightful (i.e. proper, legal, etc.) that x is a king'. R ightful turns out to correspond to a one-place predicate over formulas, which denote facts or states of affairs. If we believe that modification by very is characteristic of predicates of various sorts, then (96) follows quite naturally. CN/CN 's which do not translate as predicates of any kind, such as mere and utter, will be expected to resist modification by very. In conclusion, it is important to note that even if this syntactic test is totally unreliable, it still cannot rule out the classification of evaluative adjectives which I have proposed. 3.5.5 The Non-Restrictive Modifier Test In yet another "test, Siegel ( 1 976: 52, 1 23) argues that non-restrictive adjective modifiers can only be of category t/ I/e. Evaluatives work here too. (97) The crowd cheered for Good K ing John. (98) The king, good at warfare, suspected the abilities of his general.

JS, vol . l , no.3

223


3.5.4 The Very Test

KENN ETH R. BEESLEY 3.5.6 The See-Catch-Find Test

.)

The see-catch-find and there constructions are claimed by Siegel to be positive test for t///e status ( 1 9 7 6 : 7 6 f f ;92; 1 979:237-239). This is quite correct, but it means, of course, that failure of an adjective to pass this test is no guarantee of CN/CN status. Siegel cites examples like (99) to show that tall is necessarily a t/ I /e. Then she has to explain in away the perfectly good and perfectly devastating example of good ( I OO) by calling it an ' idiomatic' usage. (99) I ' ve often seen the grass tall around that house. ( I OO) I ' ve seen the children good, but not very often.

( 1 0 1 ) Nureyev was good last night; it's been a long time since we've seen him (so) good. Even degree adjectives, interestingly, can fail the see-catch-find test; Siegel has simply chosen her examples well. ( I 02)?*1've often seen Bill tall. In our world, grass is a type of thing which is constantly changing in height--it gets cut short and grows right back again. The height of grass, therefore, is a ' temporary ' or 'accident' state. (I use these words in their technical sense.) Humans, however, although they grow and change over time, have a characteristic 'permanent ' or 'essence' height. We don ' t expect people to be 6' tall one day, 5'6" tall the next, 6 ' 2 " tall the next, etc. In a world like Wonderland, however, where Alice constantly grows and shrinks by eating and drinking magic cakes, mushrooms, liquids, the Mad Hatter could utter a perfectly acceptable sentence parallel to ( I 02). ( 1 03) I 've often seen Alice tall. In conclusion, the see-catch-find test supports my classification over Siegel 's. The good in ( I OO) must be a t/ I/e. but is has a 'relative' reading in Siegel ' s sense; i .e. the goodness i s probably to be evaluated relative to proper be haviour for children. 3.5.7 The Nominalisation and Verbalisation Tests If one-place predicates have corresponding nouns representing their nominalised qualities and corresponding verbs w ith the reading ' make Adjective ' , then evaluatives also seem to be one-place predicates.

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Other devastating examples are easy to construct.

EVALUATIVE A DJ ECTIVES ( 1 04) Adjective

Verbalisation

red big good bad

redden, make red make big (bigger), increase, augment make good (better), improve, reform make bad (worse), harm , ruin, corrupt

mere

*make mere

Nominalisation redness size goodness_ badness *mereness

3.5.8 AU-or-Part Relativity Test

( 1 05) Bill is a tall little red-headed basketball player. ( 1 06) Bill is a former little red-headed basketball player. Quite rightly, Siegel points out that the comparison class for tallness in ( l 05) may well be the set of little basketball players, with red-headed m issed out altogether. Quite rightly again, Siegel points out that no such skipping is allowed in ( 1 06), which has the CN/CN former. But in a sin of om ission, Siegel never tries using evaluatives in the same con structions. ( 1 07) Billy is a good little red-headed basketball player. In ( 1 07) also, the goodness may very well be evaluated relative to some standard for little basketball players, with red-headed skipped over. Indeed, I have shown that standards of evaluation may have nothing to do with the following noun phrase, just as the comparison class for a degree adjective can be distinct from the modified com mon noun, even if that common noun is a single word. I conclude that Siege l 's own -syntactic tests show that her analysis is untenable. In all these cases evaluative adjectives behave syntactically like absolute and degree adjectives. 3.6 Rescuing the Conjunction Analysis Again The appeal to contextual standards, just like the appeal to contextual JS, voi . J , no.3

225


Siegel argues that CN/CN modifiers have the quality of applying ne cessarily to the ·entire common noun following them, and ' that therefore such adjectives are always relative to that whole common noun. Degree adjectives, on the other hand, are not similarly relative, for their comparison classes are not necessarily the class denoted by the full CN following them. The key examples are ( 1 05) and ( 1 06) ( 1 976: 1 32- 1 34 , 7 9 ; 1 979: 248).

KENN ETH R. BEESLEY comparison classes, allows evaluative adjectives to receive a conjunction analysis. As long as context remains co n stan t , the truth conditions of John is a good thief and John is good and John is a thief will be the same. The argument for this runs completely parallel to the one for degree adjectives in section 2.5. 4

An Adverb Test for Adjective Classification

( 1 08)

The red barn collapsed t the re

�

�

I

apsed 1 v

rn T

red barn c N

I

barn such that it is red c N ""' h eo ts red t barn c N

/

�T

'be red 1 v "red t

///e

Relative adjectives, on the other hand, apply very straightforwardly to their arguments, with no intermediate clause. ( 1 09)

A mere boy arrivedt / arrt":e d I V a me e boy r

T

""- ·

mere boy c N

/ mere

c NI c N

"

boy c N

The presence of the embedded t-node in ( 1 08) predicts implicitly that is, as well as the t-node of the whole sentence, should be susceptible of modification by sentence adverbs. Conversely, the absence of such an extra t-node in ( 1 09) would predict that only the sentence as a whole can take sentence adverbs. ( 1 1 0) ( I l l) 226

Obviously, the red barn collapsed. The obviously red barn collapsed. JS, vol. l , no.3


Siegel's ( l 976a, l 976b, 1979) analysis of adjectives in Montague Gram mar provides grossly different analyses for absolute and relative adjectives. Absolute adjectives in attributive position arrive there only after starting out in the predicate position of an embedded sentence which later undergoes relative clause reduction.

EVALUAT I VE A DJECTIVE�

( 1 1 2) Obviously, a mere boy arrived. ( 1 1 3) *An obviously mere boy arrived.

The tree corresponding to ( I I 0) is the same as (1 08) but w i th applying to the highest t-node.

( 1 1 4) obviousl

obvious!)

Obviously, the red barn collapsed t

{;

t

�

the red ba

/

the red barn T

I

"

collapsed 1 v

I

barn such that it is red C N

/

barn c N

"'1s red t / "' be red1 v heo T I red heo

t ///e


red barn c N

collapsed t

( 1 I 1) is not only grammatical and intelligible, but its truth conditions are different from those of ( 1 1 0). I n Obviously, the red bam collapsed, it is the fact that a paricular red barn collapsed which is obvious. In

The obviously red bam collapsed, it 1s the redness of the barn which is

obvious. Although Siegel's relative clause reduction rule provides no way to carry along a sentence adverb from a reduced clause, the tree in ( 1 1 5) would seem to be the analysis for ( I I I ). The obviously red barn collapsed t

( 1 1 5)

"

/

collapsed 1 v

the obviously red barn T obvious!

)

I

red barn c N

barn such that obviously it is red C N

/

barn c N

obviously

obv

tu

h�

sly t / t

is

> is

he

/

heo T

red t

red t

"'be

red 1 v

I red

t /// e

The analysis of ( 1 1 2) requires only a straightforward addition· to 0 09), but ( 1 1 3) 1s ungrammatical. Obviously mere s e e m s u n i n t erpretable, and this intui tion fits in nicely with the observation that in the grammar JS, vol. l , no.3

227

KENN ETH R. BEESLEY there is no obvious way that a t/t modifier can apply to an argument of type CN/CN . There is simply no node in ( 1 09) for a sentence adverb to attach to other than the top node of the whole tree. All these ob servations are consistent with, and even explained by Siege l ' s dual handling of adjectives. Sentence adverb be very productive. ( 1 1 6) ( 1 1 7)

modification

of

absolute adjectives

turns out

turned

to

The close association of Wl(ortunately to mad in ( 1 1 6) is i n tuitively quite undeniable. A n 'unfortunately mad patient' is a patient such that ' un fortunately he is mad. If 1D1(ortW10tely were a modifier of the full sentence, it would clash with or cancel out w ith fortW10tely, w hich it ob viously doesn ' t . ( 1 1 7) shows a sentence modifier associated with either a single adjective handsome or with the conjoined pair handsome and dis tinguished--an ambiguity of the old men and women-type. Not only do all of Siege l ' s absolute adjectives allow sentence adverbs, but most of her exclusively relative adjectives seem to reject them. ( 1 1 8) *That is the obviously main reason. ( 1 19) *He is an obviously alleged cr iminal. ( 1 20) *Bill is an obviously blithering idiot. In cases where adjectives are ambiguous between relative and absolute readings (as in moral philosopher, plastic surgeon, fuzzy logician, ab normal psychologist and criminal lawyer), only the absolute reading is possible with sentence adverbs. ( 1 2 1) ( 1 22 ) ( 1 23) ( 1 24)

The obviously moral philosopher lost his job. The previously fuzzy logician got a shave. The occasionally abnormal psychologist needed help. John is an obviously criminal lawyer.

As a test for absolute adjectives, sentence adverbs are even better tests than very. It has long been known that very can disambiguate moral

philosophers. ( 1 25) ( 1 26)

Jane is a very moral philosopher. The very abnormal psychologist studied himself.

ex But some adjectives like pregnant, virgin and carnivorous and also treme ends of scales like perfect and fla wless resist very. Very pregnant, very virgin, very flawless, etc. take on secondary readings. But sentence adverbs can apply to the words with their literal senses. 228

JS, vol. l , no.)


Fortunately, the unfortunately mad patient was cured. The unmistakably handsome and distinguished actor politics.

to

EVALU ATIVE A D J ECTIVES ( 1 27) ( 1 28)

The obviously pregnant princess continued her engagements. My previously carnivorous friend became a vegetarian.

Siegel's work contains the claim that degree adjectives (tall, short, high, are a subtype of absolute adjectives, and that they should be generated in attributive position by way of relative clause reduction. Given the long history of degree adjectives being considered semantic attributives, this is a bold claim. If the sentence adverb test is valid and Siege l ' s claim is true, degree adjectives should appear freely with sentence adverbs; and indeed they do.

low, fat, thin, etc.)

The obviously tall ballerina was rejected. The previously fat capitalist lost 20 pounds. The presently low wages were once respectable.

For evaluative adjectives, however, which Siegel claims are ambiguous between absolute and relative readings, the adverb tests indicate other wise. The doublet moral, as was seen, can have only its absolute reading i n the presence of a sentence adverb. In parallel constructions, however, good is perfectly capable of retaining what Siegel calls 'relative' readings. ( 1 32) ( 1 33) ( 1 34)

He is an obviously moral philosopher. (only the absolute reading is possible) She is an obviously beautiful dancer. ( 'relative' readings are still possible) John is an obviously bad monk. (the 'relative' reading is even preferred)

Though it is impossible to read the moral in ( 1 32) as being 'relative' to the meaning of philosopher (i.e. in the sense of moral-philosophy), the beautiful in ( 1 33) can still be 'relative' to dancer. An obviously beautiful dancer can still be a 'dancer who dances beautifull y ' . Similarly, an obviously bad monk need only be relatively 'bad qua m o n k ' r a t h e r than absolutely bad. Siegel would represent her two claimed readings of bad monk w i th the following trees. ( 1 35)

John is a bad monk t

/

John T

be

ba

JS, vol . 1 , no.3

�

(relative reading)

ad monk 1 v

I

bad monk c N

(.

/C N

�onk C N 229


( 1 29) ( 1 30) ( 1 3 1)

KENN ETH R. BEESLEY (absolute reading)

John is a bad monk t

( 1 36)

/

Jotin T

" be a bad I

monk

/ monk c

monk 1 v

bad monk c N

J

ch that he is bad c N

N

he o

h

Only ( 1 36) provides a natural and consistent way to account for the presence of the sentence adverb in ( 1 34). Any attempt to allow sentence adverbs to apply to CN/CN words like bad m ( 1 35) will overgenerate producing *obvioU8ly mere, *allegedly moral (with its CN /CN reading) and *previOU8ly ostensible. This would also destroy the explanatory insights that the theory seems to support so far. In this as well as in other syntactic tests, evaluative adjectives consistently act like absolute adjectives. A gross syntactic and logical ambiguity in good is neither tenable nor necessary. The standard of moral uprightness which supposedly characterises Siegel's 'absolute' reading is simply one standard among the many possible. These results point to an analysis parallel to that suggested in Hare ( 1 957), where only one good is postulated, and it is a fuzzy one-place predicate. 5 The Grammar 5.1

The internal S tructure of Adjective Phrases

Absolute, degree and evaluative adjectives are all of category t// /e, reflecting their status as one-place predicates. Any grammar wishing to characterise their syntactic behaviour w ill have to deal with the following facts: ( A) Gradable t// /e's, those which can apply fuzzily over a universe of entities leaving an extension gap, can be modified by very. extremely, quite, a wfully and other such extent adverbs: very tall, extrem ely good,

quite red.

( B) Some adjectives of the t/ I /e class, whether modi fied by extent adverbs or not, can be further modified by certain manner adverbs: ostentatioU8ly (very) rich, quietly (extremely) assertive, discretely 230

JS, vol. 1 , no.3


�

" is

E V A L U ATIVE A D JECTIVES

(quite) powerful, wwssumingly intelligent, generously wealthy, graciously hospitable, lavishly generous, coolly defiant, etc. These constructions can themselves be preceded by very, etc., but the bracketing will always be thus: [very ostentatiously] rich. [very discretely] [quite powerful], [extremely stubbornly] defiant. It is clear that the extent modifiers of (A) must apply to a t/ I /e before the manner adverbials of (B): *very [os tentatiously rich]. An excursus here into manner adverbtals is i mpossible, and only the gross syntactic possibilities will be considered.

(C) Adject ives of class t/ I /e, whether or not mod i f ted by extent adverbs and by manner adverbs, are further modifiable by sentence adverbials:

The analysis must, therefore, accommodate constructions at least as complex as the tree in ( 1 37), ensuring that the hierarchy of modifiers remains fixed. (sent-adv (man-adv (ext-adv ( t///e))))

( 1 37) sent

�v

� v (t/I/e)))

(man-adv (ext

/ man-adv

"

(ext-adv (t///e))

e

xCadv

""'- t/I /e

The way to ensure that modifters apply in the correct order ts to distinguish the different levels of the tree by distmct categortes. As the semantic category at each level is always a one-place predtcate, we need only extend our analysis with a few extra slash categories. Mamtammg t/ I /e as the basic category of absolute adjectives, succeeding levels can be distinguished by adding an extra slash.

/

o

( 1 38)

�

� r ich t ///// e

ously o tentatiously v

obv iously t ( ///// e ) /( t///// e )

/

�

tentatiou

osten tat i ously t//// / e ) /( t//// e ) (

very rich t ///// e

/very � \.1///e

very t// ( 1 / e) /( t /// e )

rtch t

///e

The unusual abiltty of very to apply recursively to its own output (very very very rich) will be tgnored here. Other extent adverbs block

any possibil ity of other extent adverbs applying; this is reflected in their proposed category (t/ I I /e)/(t/ I /e). Even the troublesome ve·ry blocks further modification by extent adverbs other than very: *quite very rich. (See Backlund 1 973: 1 58; N ilsen 1 972: 1 1 3ff.) It does not seem possible JS, vol. l , no.3

231


obviously (ostentatiously) (very) rich, previously openly defiant, presently very peaceful. The modifiers of (A) and (B), if any, must apply before those of (C): *very [obviously defiant], *modestly [previously humble]. Some sentence adverbs may themselves be mod i fied: [very obviously] rich.

K E N N ETH R. BEESLEY to define hard rules about which lexical items can be graded, so the matter of constraining extent adverbs is left open. 2 Many adverb forms normally thought o f as manner adverbs seem also to have a reading as extent adverbs: impressively lucid, irrita tingly bad, a wfully good, horribly contagious, terrifica lly talented (Bolinger 1 972: 22-23; Backlund 1 973: 1 2, 1 65ft, 277; Zwicky 1 970). Nevertheless, i t cannot be concluded that all premodifiers of adjectives can be reduced to extent adjectives. The examples in (B) have typical manner force.

The resulting structure of an adjective phrase bears a striking, hardly accidental, resemblance to the structure of a sentence. The analysis of absolute adjectives begins to resemble, i n overall respects, the adjective analysis proposed in Lytle ( 1 9 7 1 ; 1 97/f) and even that in Anderson & Bower ( 1 9 7/f), where all adjectives appear in sentence like structures. It is important to note that such sentence-like structures as ( 1 38) are not relative clauses which are reduced by some syntactic transformation; they are hierarchical semantic representations from which adjective phrase strings are computed directly. (For a related approach see Bartsch 1972: 1 66.) We can now look at the rules assumed so far. ( 1 39)

( l ifO )

If a

e:

� t////e)/ ( t///e )

then F 6( a , 8 )

e:

where F 6 (a , 8 ) If a e:

=

and 8 e:

P t///e

and 8

Pt/// e

P t//// e aS

P (t////e)/(t///e )

e:

and a and 8 translate as a� and 8 � respectively, then F 6(a , 8 ) translates as a � ( 8 �). A

These rules and translations will meet the present purposes. The seman tics of extent modifiers are surprisingly complex and have been described elsewhere (Kamp 1 975: l lf6 - l lf7; Keenan & Faltz 1 978: 1 71f, 228, 207- 2 1 0; Klein 1 980: 2/f-26).

p ( t//1// e )/( t//// e ) and F 6 ( a , 8 ) e: P t/////e .

( ! If ! ) If a

e:

( l lf2)

e:

then

232

If a

P(t/////e)/(t//// e )

8 e:

and 8

£

p t//// e

P t ////e

and a and 8 translate as a � and 6� respectively, then F6( a , s ) translates as a' ( "ll ' ).

JS, voi . J , no. 3


Manner adverbs on adjectives seem to block modification by any other manner adverbs; they too bump the category one slash higher. Sentence adverbs, however, allow recursive application: obviously pre viously rich, previously obviously rich. Their category is (t//1//e)/(t// (//e))

EVALUATIVE A DJ ECTIVES

This rule treats manner adverbs modifying adjectives as functions mapping intensions of , t > predicates into < < s,e> , t > p r e d icates, just as in PTQ and in Thomason & Stalnaker ( 1 97 3). The whole question of manner adverb analysis is vexed - Parsons ( 1 972) and R ichards ( 1 976) have even argued that they are formula modifiers. I have no desire or space to pursue the issue; these rules will suffice for the present purposes.

( 1 43)

( 144)

If a E If a E

;

Pt t Pt 1 t

then F s o(a ) E

and a translates as a '

( 1 46)

A P A y( a ' ( 1

then F s o ( a ) translates as

The application of is straightforward. ( 1 45)

P( t///// e )/{t/////e)'

sentence adverbs,

If a E

P (t/////e)/( t///// e)

a

y } ] )).

of class (t/ I II /e)/(t/ I I I /e),

E

P t/////

e

and 6 E

P t/////

e

P (t/////e)/( t///// e ) and 6 F 6( a ,6 ) E P t/////e .

If a E

then

now

P{

where F s o(a )

and a and il translate as a ' and 6 ' respectively, then F 6( a , 6 ) translates as a' ( � 6 ' ) .

5.2 Adjectives in Predicate Position To generate a sentence with an absolute adjective in predicate positiOn, rule ( 1 47) is used. Unlike the Montague-Parsons analysis, this rule generates adjectives in predicate position directly, with no recourse to a dummy noun deletion transformation. The class IV /(t/ II I /e) contains the copula verbs - for simplicity we will limit our example5 to be . ( 1 47)

If a E

P IV/(t///// e )

and 6 E

P t/////e ,

then F 6(a , 6 )

E

P1v.

In the interests of simplicity, I assume that the semantic rule correspond ing to ( 1 47) merely preserves the translation of the argument intact. Also, I assume that I V ' s map their subjects into truth values rather than vice-versa as in PTQ (Thomason 1 976: 79; Keenan & Faltz 1 978: 23). JS, vc-1. 1 , no. 3


The proposed class of (t/ I I I /e)/(t/ I I I /e) adverbs appears to be coexten sive w ith the class of t/t sentence adverbs. E ither ( l ) a class of (t//1//e)/ (t/1///e) adverbs can be defined in the lexicon, w ith the stipulation that i t is coextensive with the t/t class, or (2) a syntactic rule can be defined to bump t/t adverbs into (t/1///e)/(t/////e)'s, with a corre sponding change in the semantics. As there are complex t/t's like very obviously, � he second option offers some economy.

KENNETH R. BEESLEY The iota operator is imported for definite expressions; no other quanti fied expressions appear in the examples. Tense and the contribution of the copula be will be ignored in the semantic trees. Using rule ( 1 47), the analysis tree for John is obviously ostentatiously very Mch is ( 1 48). The corresponding semantic tree is ( 1 49). John is obviously ostentatiously very rich t

( 1 48)

/

'\.

Johnr be obviously ostentatiously very rich 1 v

be

OV(

11

obYi "'( y

obYiou•ly o•ten

HI/III o l/( . P >. x[bad'(x) & P{ x}]

J

d'

It is now possible to show the semantic and syntactic differences be tween ( 1 7 1 ) and ( 1 72) w i th no recourse to relative clause reduction. Obviously, the red barn collapsed. The obviously red barn collapsed. Obviously the red barn collapsed t

/

"'

the red barn collapsed t

obviously t/ t

/

the red barn T

I

"collapsed

red bar n c N

/

red c N I c N

I

red t

( l 7 l b)


( 1 7 1) ( 1 72) ( 1 7 l a)

" barn

1v

cN

/////e

obviously'(1collapsed ' ( � t x[red '(x) & barn'(x)] )] )

/

obviously' t

"

collapsed ' ( � t x[red'(x) & barn '(x)] )

/

"'

collapsed '

x[red'(x) & barn'(x)]

I

>. x[red'(x) & barn'(x)]

/

>. P >.x[red '(x) & P{ x }]

"

I

barn'

red' ( l 7 2a)

The obviously red barn collapsed t

/

the obviously red barn T I

"'

collapsed 1 v

obviously red barn c N '\ y red c N / C N barn c N obvio

;. I

ob

�

�

ously red t

/////e

obviou ly t / ( III/ e ) /( t /I II/ e ) obviously t / t 238

""' red t /

II Ile

JS, vol. l , no.J

EVALUATIVE ADJECTIVES collapsed '( " l x(obviously '( 1red '(x) ] ) & barn '(x)] )

(7 2b)

/

1 x[obviously ' < 1red'(x)l)

I

& barn '(x)]

"

collapsed '

>.x[obviously' < 1red'(x)] ) & barn'(x)]

/

>. PA x[obviously'< 1red'(x)] ) & P{x} ] I

"

bar n '

>. y[obviously'( 1red'(y)] )]

/

AP>.y[obviously'(1P{ y }] )]

red '

obviously ' 5.4

Postposed Adjectivals

Certain 'tempo rary ' or with complements, will they modify. ( 1 73)

( 1 7 4)

If a £ P t

lllll e

'accident ' adJectives, as well as adjectives require a rule postposing them to the noun

where

a

denotes an 'acciden t ' state

or where a is an adjectival with a syntactic complement then F o(a) £ P c N II c N. (Same translation as in rule ( 1 68).) If a £ p C N II c N

and a £ p C N

then F7 (all ) £ P c N

where F 7 (,. , a) aa (Same translation as in rule ( 1 64).) =

If adjectival prepositions are viewed as trans1t1ve adjectives with their objects representing a kind of complement, then rule ( 1 7 3) also serves to order and interpret such prepositional phrases. Note that the tentative rule for preposing and postposing attributive adjectives in EFL, which states ·that all multi-word adjectivals must be postposed, is totally madequate; it would even postpose very good (Hamblin 1 976: 249; Thoma son 1 976: 8 1 -82). Bartsch 's ( 1 973: 57) slightly better rule, which preposes those adjectivals which end in an adjective, will still incorrectly order examples such as ( 1 7 5). ( 1 7 5) *The

+

eager to help you become famous

+

man

Present participles are derived from I V ' s (both trans1t1ve and in transitive), by rules parallel to ( 1 67) and ( 1 68). Lees ( 1 963: 33, 97) JS, vol. l , no.3

239


I

"

K ENN ETH R. BEESLEY notes that only those -ing forms which are genuine i n t ransitives are likely to be preposed to a noun. A transitive present participle with its object may never be preposed. ( 1 76) *the stealing/eating boy ( 1 7 7) the shivering/walking dog ( 1 78) *the walking the dog man

(pseudo-intransitive) (true intransitive) ( transitive)

If we view the object of a transitive participle as a type of complement, analogous to seeing the object of a preposition as a complement, then a generalised rule ( 1 73) will handle participles as well. the man walking the ,dog

Intransitive post pose .

present

participles

with

other

types

of complement

also

( llSO) the man shivering with cold. 5.5

HedgP-s as Overt Context

Context figures decisively i n the analysis of both degree and evaluative adjectives. For degree adjectives, we can represent the relevant com parison class as a ' c ' subscript to a formula. For evaluative adjectives, we can represent the standard or criterion involved as an 's' subscript. Syntactically, context can be made explicit in 'hedges' which behave like sentence adverbials. The class of hedges is highly variable and hard to characterise syntacticall y . While I don ' t claim to offer a gram mar of hedges in the form of derivational and interpretive rules, the pairings of sentences and interpretations in ( 1 3 1 ) to ( 1 89) are consistent with m y claims and intuitively satisfying. ( 1 8 1)

John is tall. [tall •nohn)]c

( 1 82)

John is good. [good'nohn)]8

( 1 83)

Quang is a short Vietnamese. [short'(AQuang)]c &: Vietnamese' ( AQuang)

( 1 84)

Quang is a good com munist. [good'( �uang)], &: communist '(AQuang)

( 1 85)

For a Vietnamese, Quang i s tal l. [tall ' ( AQuang)] c

240

=

VIetnam ese

JS, vol. l , no.3


( 1 79)

EVALUATIVE A DJ F.CT:VES ( 1 86) John is short compared to a Watusi. [short'( "John)]c = w a t u s l ( 1 87) John is tall for a Pygmy and short for a Watusi. A x[ [tall '(x) c : P y g y & [short '(x)]c = w a t l ] ( "John) us m ( 1 88) In a sense, John is OK. 3s [ [OK '("John)]5 ] ( 1 89)

My car is g ood aesthetically but bad mechanically. A X [ [g oo d '(x)]s = a e s t h e t i c a l l y & [bad'(x)Js = m e c h a n i c a l l y ] (\my car)) ·

Examples ( 1 87) and ( 1 89) are extremely interesting in the light of the analysis proposed for other sentence adverbials. Hedges, just like sentence adverbs, must be applicable to individual adjectives within larger sentence structures.

Appendix The fact that sentence adverbs can modify attributive adjectives in isolation from the nouns those adjectives modify provides a strong argument against Montague's EFL treatment of adjectives. Adverbs like formerly and adjectives like former correspond to formula modif iers in logic. There exist syntactic constructions in which the argument of formerly is a formula wh1ch appears, in EFL, only as a product of the meaning postulates. In other words, in an EFL-like grammar, th(:� and . We can now state the first condition characteristic of the kind of transformations used in the identity test. This condition is purely syntactic. For a transformation T to be used in the identity test we would require as a minimum:

NEGATION, A MBIGUITY, AND THE IDENTITY TEST (ii)

the semantic correlate of T is defined for the grammatical history of a conjunction f(g(A), g(B)) if and only if the parallel occurrences of every expression in its com mon content have the same semantic value in that history.

The condition says in essence that we cannot equivocate over a deleted element. The requirement is natural enough and lies behind claims like Lakoff's that because ( 1 5) does not admit cross-readings, it is ambiguous. ( 1 5)

Selma likes visiting relatives and so does Sam.

I have chosen to state the condition semantically, in terms of a restriction governing cases in which the semantic correlate of the transformation is defined. From many of the examples given in the linguistic literature it is not clear that the relevant condition need be interpreted this way. In a sense, cross-readings of ( 1 5) and of other examples like Lakoff 's ( 1 6) and ( 1 7) are eliminated by the syntactic conditions (i) without mentioning semantic structure at all. ( 1 6) H arry was disturbed by the shooting of the hunters and so was A I . ( 1 7) The chickens are ready to eat and so are the children. As (i) is formulated, the syntactic structures of g(A) and g(B) fed into the transformation T in the form of the conjunction f(g(A), g(B)) must be structurally isomorphic except that where a tree headed by A appears in the first a tree headed by B appears in the second. Both conjuncts must be of the same part of speech, and it is not implausible to think that the various senses displayed in Lakoff ' s examples ( 1 5)-( 1 7) represent different parts of speech. Many ordinary uses of the test by linguists can be viewed as uncovering in this way what are really syntactic ambiguities. But the kind of ambiguity that interests Atlas and that we are trying to explain in metatheory is semantic, and we can construct other examples using more traditional sorts of lexical ambiguity that cannot plausibly be traced to switches in syntactic type. ( 1 8) Tony Benn is a radical and so is the square root of 2. ( 1 9) Ink goes in pens and so do pigs. It I S implausible to think that radical and pens here a r e s y n t ac tically ambiguous, falling into different parts of speech. Rather what is wrong is that there has been an equivocation. Literally the same syntactic entity has been used in two different senses. It is, moreover, a semantic constraint as formulated in (ii) that JS, vol. l , no.3

261


Her visiting relatives may mean the act of going to VISit relatives or the relatives who visit, but not both. Though the condition is plausible enough, a number of important points need to be made.

JOHN N . MARTIN

·

is appealed to in applications of the ambiguity test to negation in presupposition theory. Atlas suggests that in some examples negation may be part of the common content of a reduction, yet because cross readings of the reduced form are acceptable, the reduced sentences are not ambiguous. His example is (20), but I think ( 2 1 ) would do as well. (20) (2 1 )

The king of F rance is not w ise and the same (thing) goes for the queen of England. The king of France and the, queen of England are not wise.

It is important to see that just as in ( 1 8) and ( 1 9) the acceptability of (20) and ( 2 1 ) is not a syntactic matter resolvable by appeal to (i) alone. No one has questioned that the formation rules of English seem to use exactly the same syntax for the various sorts of negation. Rather the issue facing Atlas and ourselves, as we try to state a metatheory compatible w ith Atlas' prescriptions, is semantic. Given a single for mation rule for negation, should some uses be interpreted semantically by the semantic operation for exclusion negation and some by one for chotce negation? Believers of the ambiguity thesis say yes, doubters no. Thus to make sense of the debate over the ambiguity of negation and the use of the identity test to settle it, we must assume the seman tic condition ( ii). Now let us see exactly how (ii) bears on ambiguity in cases for which cross-readings are excluded. Ideally what we want to do is first define a conjunction reduction transformation as any transformation meeting conditions (i), (ii) and perhaps other conditions as well. We then need to define the notion of a reading, and prove some theorem like the following: If T is a conjunctive reduction transformation, then f(g(A), g(B)) is ambiguous if and only if there are some readings for f(g(A), g(B)) that are not readings for T(f(g(A), g(B))). As will emerge the readings open to the conjunction but closed to its reduction are what we have been calling informally the excluded 'cross-readings '· The theorem as stated is quite strong. It requires that the failure of some cross-readings is both a necessary and sufficient condition for ambiguity. Strictly spt:aking the so-called identity test for ambiguity requires only that it be a sufficient condition. What we do is hunt 262

JS, vol. l , no.3


One glosses the examples by explaining that the king of F rance is not w ise because there is no such person, and the Queen of England is not w ise because though existing she lacks the relevant properties. It does seem true that such a context can be convincingly described in which it is fair to say one could summarize the situation by either (20) or ( 2 1 ).

NEGATION , AMBIGU ITY, AND TH E IDENTITY TEST around for an example of a reduction that does have some excluded cross-readings and then conclude that the transformed sentence harbours an ambiguity. But Atlas' application of the test to presupposition theory requires the converse also. He generalizes from cases like (20) to the thesis that all cross-readings of the conjuctions involving negation also apply to their reductions. Then by appeal to the converse he can conclude that the conjunction is not ambiguous. Part of our task then is to see whether the properties of the transformations will support both directions of the principle.

(22) (23) (24) (25)

I saw a dog and a man. The search uncovered only a bug and a bat. A man's aggressive sexual behavior is correlated to testosteron levels and so IS a dog 's. The wings of the bat are covered by a thin memQrane and so are those of the bug.

But a technical and , from our viewpoint, a more interesting prelimi nary to evaluating either direction of the identity test is finding the right analysis of 'reading ' . This 1dea as 1t is used in linguistiC discussions is a bit slippery. On the one hand, genuinely ambiguous expressions are said to be so because they have more than one reading. In this usage, which I shall call intensiOnal, reading seems to mean something like meaning, sense, semantic representatiOn, or synonymous paraphrase. It IS what is represented in our foregoing theory by the idea of an expressions's semantic interpretation . Thus Zwicky and Sadock speak of (26) as having multiple 'unders.tandings ' . (26)

They saw her duck.

On the other hand, what makes some sentences vague, general, and non-specific 1s also that they have many readings. They differ from ambiguous expressions in that all of their readings also apply to their conjunctive reductions. Usmg essentially th1s idea of reading, Lakoff allows that Harry kicked Sam may be consistent with Harry ' s kicking Sam with the left foot or the right foot, and likewise Zwicky and Sadock explain that (27) may have as d1stinct understandings as both (28) and (29). 7

JS, vol. l , no.3

263


Before proceedmg further into theory, it is relevant to point out that the converse viewed as a generalizatiOn about language is not very accurate. It has some counter-examples. Both (22) and (23) admit cross-readings. In the f irst contained expressions are ambiguous between a wider class and its male subset, and in the second they are ambiguous between disjoint sets. But even by the identity test itself, the terms in question are ambiguous: there are cases, (24) and (25), m which cross-readings fail. In (24) both terms are limited to the male reading, and m (25) both stand for animals.

JOHN N . M ARTIN (27) (28) (29)

M y sister is a prominent composer. M y sister is the composer of "Concerto for Bassoon and Tympani". M y sister published a concerto last week.

· Now this sense of reading differs from the first in several important ways. First , this sort of reading is clearly not synonymous with the expression i t interprets and is something quite different from the tradi tional notions of an expression 's sense or intension. Harry ' s kicking Sam is not equivalent to his kicking with the left foot or to his kicking with the right. L ikewise (27) is not synonymous with either (28) or (29), and none of these entail any of the others.

Now the advantages and disadvantages of using possible worlds in semantic theory are well-known. Their attraction here is both general and specific. They can be used first of all to give concrete examples of languages and semantic interpretations as these notions have been defined in our general background theory. Indeed, i t would tell against these notions if they could not be seen as embracing the ordinary possible world semantics of logical theory. In these accounts semantic values or 'intensions' are set-theoretic constructions made up out of a postulated set of possible worlds. The sense of a sentence, for example, is a function that pairs a possible world with the truth-value of the sentence in that wqrld. How to define semantic operations on such intensions so as to generate well-defined semantic interpretations for simple formal languages is now well-known, and extensions of these methods to richer languages closer to natural speech is now also commonplace. It would be a strength of any account of the identity test to explain how it fits with these standard ideas. More specifically, the idea of possible world also provides a straight forward analysis of the second usage of reading. In this sense, which I shall call referential, a reading of a sentence is any possible world in which it is true. A sentence would then have more than one reading, and various other sentences would be partial specifications of it. Thus ( 1 6) and ( 1 7) help to specify a reading of ( 1 5) in that they could each be true in some world in which ( 1 5) is trut. All three might even be true together. It must be admitted at once that this notion of reading is rather trivial. Every sentence but a contradiction would have various 264

JS, vol. l , no. 3


It m ight be possible to explai_n this sense of 'understanding ', as Zwicky and Sadock suggest, as any state of affairs describable by the sentence. But in introducing states of affairs to semantic theory we would be adding a new theoretical concept that would itself need to be explained. Some recent formal work on facts or events might be used to this end. But there is a more obvious approach that does not introduce any more semantic entities than are regularly appealed to in intensional logic. We interpret state of affairs in the full-blooded sense of possible world. A possible world is, if you like, a total and complete state of affairs.

NEGATION, AMBIGUITY, AND THE IDENTITY TEST readings, and saying of a sentence that it is general, vague, or non specific because is has various readings is then to say not very much of interest. Most sentences, ambiguous or otherwise, would be general in this sense. It is not a very interesting idea. To be fair to those who use the notion, we should say that it is not given much weight; it is used for little more than as a means of contrasting the genuinely ambiguous from the merely general. But what is very interesting about the referential account is its ability to provide a simple and useful sense of 'reading'. Given the rather weak notion of referential reading, we can explain how the identity test establishes ambiguity. But before we do that let us backtrack to the intensional sense of ' reading' and investigate to what extent it is reconcilable with the identity test.

llleoce m

Proof

-In any language in which T is a conjunctive reduction and in which there are some intensional readings of f(g(A), g(B)) that are not also readings : of T(f(g(A), g(B))), the former expression contains an ambiguity. -Let T be as specified and let there be some reading for the conjunction that is not one for its transformation under T. The only reason a reading for the conjunction would not be the same as that of its T -transformation is that the semantic correlate of T is undefined for the semantic history of f(g(A), g(B)). But by (ii) it is undefined only if some expressions shared by g(A) and g(B) are ambiguous. B

This result also holds for the referential use of reading. Let a lan guage be said to have a possible world semantics if it assigns as a seman tic value to each sentence a function from possible worlds to truth values. We make no assumptions about the number of truth-values beyond the classical two values T and F, but require merely that the semantic operation corresponding to conjunction be normal in the many-valued sense: if both parts of a conjunction are assigned classical truth-values T or F, then the semantic operation ass1gns that value dictated by the classical truth-table for conjunction. We can now prove that lack of cross-readings in the referential sense marks ambiguity. Since th1s is essentially the use of 'reading' employed by linguists, the result is really a statement of the identity test. Theorem

Proof

(Tile Identity Test) - In any language with a possible world semantics, and in which T is a conjunctive reduction, and in which there is some referential reading of f(g(A), g(B)) that is not also a reading of T(f(g(A), g(B))), the former expression contains an ambiguity. -Assume the conditions. There is some world in which the conjunction is true but its T -reduction isn 't. Since the seman-

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For the time being let us call a conjwlCtive reduction any transforma tion meeting conditions (i) and (ii). Something like the identity test follows directly from the def initions.

JOHN N. MAR TIN tic correlate of T, if defined, is an identity mapping, the correlate of T must be undefined, and therefore, as in the last proof, g(A) and g(B) share ambiguous expressions. It is important to see, however , that the relevant converses of both theorems fail. Theor-em

Tileor"em

To the extent that these results fail to justify in our metatheory the converse of the identity test, they tend to undermine Atlas' argument. But they are in a sense too strong. What is established is just that acceptable cross-readings are consis tent with ambiguity when the ambiguity referred to is in those parts of the conjuncts which differ. All Atlas needs for his argument, however, is that acceptable cross-readings are inconsistent with ambiguity oc curring in those parts of the conjuncts which are the same. It is negation he wishes to argue is not ambiguous, and in all his examples negation is in the common content of the reduction. Within the contraints of our reconstructed metatheory, aren ' t acceptable cross-readings formallv 266

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Proof

-There are languages in which T is a conjunctive reduction and the conjunction contains some ambiguous expressions, yet every intensional reading of the conjunction is also a reading of the reduction. -There are languages with possible world semantics in which T is a conjunctive reduction and the conjunction contains some ambiguous expressions, yet every referential reading of the conjunctions is also a reading of the reduction. -To see why the firts result holds it suffices to note that the semantic correlate of T is always defined if and only if the intensional readings of the conjunction are always readings of the reduction. Moreover, according to (ii) it is always defmed if and only if all the common content of g(A) and g(B) is univocal. Languages are easily constructed that give the same interpretation to the com mon content but different interpretations to parts of A and B, by, for example, giving lexical items in the common content the same value, but items in A and B different values. In such languages the semantic correlate is always defined and hence all cross-readings are acceptable. Yet the expession contains ambiguities. Indeed with the right choice of f and g the conjunction itself can be made ambiguous. For the referential case observe first that every referential reading may hold of both the conjunction and the reduction, yet the semantic correlate of T might still be undefined for some values of the conjunction. We can nevertheless construct a language in which all cross-readings apply to both and the correlate of T is always defined. We may then proceed as In the intensional case.

NEGATION, A MBIGUITY, AND THE IDENTITY TEST

Theorem -In any lan guage in which T is a conjunctive reduction and

in which some expression in the common content of g(A) and g(B) is ambtguous, there is some intensional reading of f(g(A), g(B)) that is not a readmg of T(f(g(A), g(B))). Theorem -There is some language with posstble world semantics in which T is a conjunctive reduction and in which :;orne expres sion in the common content of g(A) and g (B) is ambiguous, yet every referential reading of f(g(A), g(B)) is also a readmg of T(f(g(A), g(B))).

Discussion could stop at this point if it were not for the fact that we may have under-represented conJunction reduction in an important way. It is common in the literature to impose additional condttions in the form of category constraints on the disparate parts, and it might seem posstble to obtain Atlas' converse if these additional assump tions are incorporated into the semantic theory. As I shall argue, I think such an approach fails, but it is interesting, especially in its need to clarify what sort of metatheory these category constraints presuppose. The condition in question requires that the disparate parts of the conjunction can be yoked in a reduced form only if they are originally of the same type. "Roughly", say Zwicky and Sadock, "to be eligible for reduction two conjoined clauses must be of the forms X--A--Y and X --B--Y, where A and B are constituents of the same type." Likewise, Chomsky posits "some general condition of the appl tcability of deletion operations such as the one that gives ( 3 1 ) from (3Q), a rather abstract condition that takes into account not only the structure to which the operation applies but also the history of derivation of this structure." 9

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inconsistent with ambiguity in the common content? The answer depends on the sense of reading. It is true that under the intensional notion all cross-readings apply if and only if the semantic correlate of the transformation is always defined. Hence by (ii) ambiguity in the common content entails that the correlate is undefined for some arguments and, therefore, that not all cross-readings apply. But under the referen tial sense of readmg this inference does not follow. It is compatible with that notion to have a language in which every world in which the conjunction is true is also a world in which the reduction is true, i.e., for all cross-readings to apply in this sense, yet the transformation 's correlate might also be undefined for some values. A trivial example can be constructed by defining a correlate that assigns to any proposition (function from worlds to truth-values) itself except in those cases in which the proposition is contradictory (assigns F to every wor ld) , and for these cases we let the correlate be undefmed. Then any world that satisfies the conjunction will also satisfy its reduction. Other more complex examples are also possible. We have in effect estabilshed two st mple results.

JOHN N . M A RTIN (30) (31)

I don ' t like John's cooking any more than Bill's cooking. I don ' t l ike John's cooking any more than Bill 's.

These conditions would allow the reduction only if cooking i n b o th con juncts was of the same type, both a general practice or an isolated act .

But the syntactic interpretation is not the most interesting, and the intentions of linguists in stating the condition are not always clear. Chomsky, like many others, posits a parallel between syntactic and semantic structures. Zwicky and Sadock are also typical in shifting from syntactic to semantic vocabulary in a manner justified by postu lating a vague correspondence. Moreover, it is clear that the syntactic interpretation will not help Atlas' argument. For the syntactic restric tion is already captured in the notion of a conjunctive reduction, and that idea does not y ield the implication from ambiguity to failure of cross-readings which Atlas needs. The semantic version is also interesting in itself. It would allow the possibility that two expressions of the same syntac tic type might belong to distinct semantic categor ies, and then require that reductions are meaningful only if the two disparate parts were of the same seman t ic category. Technically we would have to augment the specification of a language with what we may call (following Thomason and others) a sortal specification, some partitioning of possible semantic values for each part of speech, stipulated prior to the· definition of an interpre tation. Then in lieu of condition (ii) we would require: (iii)

the semantic correlate of T is def ined for the grammatical history of a conjunction f(g(A), g(B)) if and only if (a) the parallel occurrences of every expression in its common content have the same semantic value in that h istory, and (b) the interpretations of A and B in that history are of the same semantic category as defined in the sortal specification of the language.

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The idea behind the condition is itself somewhat ambiguous; the . notion of type involved may be construed as either syntactic or semantic. I think many of the examples used to il lustrate this condition in the literature do make sense when the type restriction is interpreted strict ly syntactically. Zwicky and Sadock's example in which reduction is allowed if both duck and swallow are verbs or both are nouns is a good case. L ikewise Chomsky seems to think that the differences in type of cooking w ill be exhibited in its various syntactic histories and that John 's cooking really does fall into two parts of speech. But if the condition is merely syntactic, it is essentially captured already in requirement (i). Formation functions are defined relative to parts of speech and in particular the operation g used in f(g(A), g (B)) is defined over a single part of speech. Therefore if g(A) and g(B) are defined, A and ·B are of the same syntactic type.

NEGATION , A M BIGUITY, AND T H E IDENTITY TEST This categorical restriction has been discussed in the philosophical literature under the topic of zeugma. 1 O Indeed , a zeugma may be defined as a conjunctive reduction that violates (b). It is granted by most that some such violation occurs, often with literary effect, but it is a matter of contention whether they are seriously deviant and if so how this deviance should be marked within semantic theory. First some examples. The f irst two are standardly given and the latter two are cited by Fowler: (32) (33) (34)

Most concede, I think, that such examples are grammatical. They differ on whether they are semantically deviant, and if so, how this deviance IS to be marked. Theories include classical accounts which admit that zeugmas contam category mistakes but argue that these should be represented as false in a classical two-valued semantics. On this v1ew, zeugmas are literally fa,lse. There are also various many valued approaches that conform better to the intention of (iii) and render zeugmas neither true nor false. .

The first point to make about the treatment of zeugma required in (iii) is that it is at odds with most for mal approaches. It is not really true that zeugmas are meaningless in formal accounts even though their deviance is marked. Whether th1s marking consists in assigning the classical truth-value false o r in assigning some more elaborate truth-value gap or non-classical value, the expression literally has an intenswn in the model theoretic sense. It is always interpreted by some function from poss1ble world to trut h-values, and the semantic operations generating interpretations of zeugmas would be defined for any argument. Another way to put this point is that the term 'meaningless' is itself ambiguous. It may mean that the semantic opera tions of the theory are really partial funct ions and that, though the interpretations of the parts are assigned, the whole has no semantic value because the appropriate semantic rule is undefined for those inputs. It is in this sense that (iii) ensures that zeugmas are meaningless. But the intensions assigning sentences non-classical values constitutes meaninglessness in a different sense. Such assignments usually assign set-theoretic meanings. Indeed there is an important techniCal reason why undefmed values for semantic operations are avoided. The usual theory of logical consequence is defined in terms of truth-values and presupposes that expressions always have intensions in the model theo retic sense. We may speculate that a theory of logical consequence for the surface forms represented in conjunctive reductions would be inappropriate or that it might somehow be managed even in the JS, vol. J , no.3

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(35)

She came in a flood of tears and a sedan chair. The room was not light but his fingers were. Half-clad stokers toasting in an atmosphere consisting of one part air to ten parts m ixed perspiration, coal dust, and profamty. Such frying, such barbecuing, and everyone dripping in a flood of sin and gravy.

JOHN N . MARTIN presence of partially defined semantic operations. But in doing so we should realize that w e 're taking a big step into unchart�d regions. As theories in formal semantics now stand, (iii) is actually implausible.

If A and B are ambiguous then their various meanings may be paired up m such a way that they fall together m different semantic categories. But thts idea is altogether too strong. Why couldn ' t all the meanings of two terms fall into the same sort? Let us turn to the converse. Does failure of cross-readings contmue to entail ambiguity as before? Assume that some cross-readings for the conjunction are closed to the reductton and that therefore the semantic correlate of T is undefined for some argument. Then by (iii) there is either an a mbiguity in the common content or a sortal violation. To derive the conclusion that there must then be an ambiguity in either of these cases, we need again a supplementary pr inciple, this time saying something like the following: Whenever the interpretations of A and B fall into different semantic categor ies, at least one expression in A or B is ambiguous. But this notion is even less plausible than the last. Why couldn 't A and B just be univocal lexical expressions of different sorts? This excursion into semantic category restricttons on conjunctive True, reduction has amounted in effect to a kind of elaborate reductio. there are some sorts of category constraints that make sense for conJunctive reduction, but these are syntactic and have already been captured in (i). 270

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A second point to make about (iii) is that even if It is accepted as it is, it needs buttressing to provide any links to ambiguity. Let us call a strengthened conjunctive reduction any transformation meeting conditions (i) and (iii). We may now ask whether the additional structure imposed in (iii) ensures Atlas' converse. Let us suppose that f(g(A), g(B)) contains an ambiguous expression. Given :hat the expression is in deep structure and therefore is no� syntactically ambiguous, this ambiguity must be traceable to ei ther some of the lexical expressions in the com mon content of g(A) and g(B) or to A and B themselves. To show that ambigutty entails failure of some cross-reading, what we must then be able to prove ts that ambiguity in any of these, together wtth (iii), entails that the semantic correlate of T is undefined. But (tii) as it stands only entails ambiguity if the source of the ambiguity is in the common content. Suppose the ambiguity is in A and B. To use (iii-b) we must be able to show that ambiguity in A and B entails a violation of sortal specification. We need some principle like the following:

NEGATION, AM B IGU ITY, AND THE IDENTITY TEST

It might seem that we could just do away with the referent1al sense and revert to readings as mtensions. But to do so would be to ignore an 1mportant heuristiC motivation. There is more to the referential idea than its use in the rather trivial defmition of a general expressiOn. Its attraction is methodological and epistemic. Intuitions about which situations make a sentence true are clearer, more positiv istically palpable than intuitions about proper analysis or definition. This is especially true of disputes about amb1gu1ty. It is not at all clear, to use a Quine 's example, whether hard has two definitions or just covers a range of quite disparate things. It IS precisely because intui tions about mtensions are unclear that the identity test is supposed to be useful. It removes inquiry from the real m of meanings to judge ments about truth and falsity. On th1s methodological preference, lingu1stic practice seems nght. Intuitions about truth are clearer than intu itions about how many senses an expression has, and Atlas' examples about negat1on are quite convincing. But it IS essential to this method that 'reading' be understood in the referent1al sense, and in this sense ambigu1ty is perfectly compatible with acceptable cross-readings. We may speculate that on some other analysis of reading, perhaps one somewhat in between the intensional and referential, the notion would support both d 1rect10ns of the identity test and serve to define generality. Atlas has actually raised this interesting possibility with me m conversation. One approach might be to take the Identif ication of reading with state of affairs more seriously, and to unpack reading m terms of various set-theoretic constructs of facts or events developed for other purposes in the logical literature. The reading of a sentence would then be any fact that if it obtained would make the sentence true. Whether facts could be defined sufficient to Atlas' purposes is, however, an open question. 1 1 JS, vol. l , no.3

27 1


The overall dialectic of the paper so far has not been simple. What we have been doing, in effect, is considering various elaborations of the theory behind the identity test. We would like to make 1t work, to make Atlas' converse work, and to maintain the referential notion of reading. Given the background assumptions I have adopted, we can conclude that the identity test itself with its referential usage of reading is justified, and that even with the intensional use of readmg, fa!lure of cross-readings marks ambiguity. We may also conclude that ambiguity entails failure of some cross-readings m the intensional, but not the referential sense. I suspect that 1t 1s the former entailment that Atlas may have in mind. If so, he is right insofar as I have justified it here. But it is wrong to assume the entailment for the referential notion of reading, as he does in the critique of presupposition. Both the identity test and Atlas' particular examples about negation are formulated in terms of the referential sense. These conclusions depend in part on the technical details of the background theory, and these no doubt are arbitrary in places and open to negotiation. But as far as I can see, no small change will alter the major crit1cal point.

JOHN N. M ARTIN Philosophy Department University of Cincinnati

Notes l would l ike to thank Jay A tlas and Merrie Bergmann for helpful discus sion of an earlier draft.

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See especially Atlas ( 1 97 7) and Kempson ( 1 975: 99, 1 00). For an account of the history of the argument, see Atlas ( 1 978: 402, note 3). 2 Wilson ( 1 97 5) and Boer & L ycan ( 1 976). See also Martin ( 1 979). ' 3 There is · another sense in which an expression is ambiguous if there is some tree containing more than one occurrence of that expression and an interpretation for that tree that assigns different values to those occurrences. But given ambiguity in the first sense there are two trees each w ith the same maximal element assigned different semantic values. From these trees we can make up a larger one by feeding the two maximal elements as distinct occurrences into some formation function that takes this pair as arguments. Then the expres sion would be ambiguous in the second sense. Conversely, given ambigui ty in the second sense it is straightforward to break up the tree into two subtrees with the same sentence as maximal element but different interpretations. We may then define different interpretations over expressions, one that conforms to the interpretation relative to the first tree, and one to that relative to the second, and the expression is then ambiguous in the f irst sense. Note that if the expression is not in deep structure or cannot be repeated as part of the argument series of some formation operation, the implication from sense one to sense two fails. But the two notions are for practical purposes much the same, and l opt here for the former because it more closely conforms to usage in formal semantics and philosophy of language generally. 4 Chomsky ( 1 972: 32-35). 5 lakoff ( 1 970); Zwicky & Sadock ( 1 975); Atlas ( 1 977). 6 The observant reader may have noticed that the syntactic condition (i) doesn' t actually say anything about the shape or form of the simplification itself. In particular it doesn 't require that the common content be displayed in its previous form and that the disparate elements be yoked in some fashion with an 'and '. A complete account of conjunc tive reduction would indeed need these additional conditions howeve r they should really be spelled out. But for our purposes the actual shape of the resulting abbreviation is irrelevant, so l haven 't ventured t o mention it. Syntactically, conjunctive reduction is one of a large family of transformations that eliminate redundancies. Other sorts, for example, reduce 'Tom wants Tom to come ' to 'Toms wants to come', 'Tom is as large as Bill is' to 'Tom is as large as Bil l ' , and ' Tom looks like Bill looks' to 'Tom looks like Bill ' . Varieties of specific conjunction

N EGATION, AMBIGUITY, AND THE IDENTITY TEST

Refererx:es Atlas, J.D., 1 977: Negation, ambiguity, presupposition. Linguistics and Philosophy 1 ; 3 2 1 -336. Atlas, J.D., 1 9 78: On presupposing. Mind 8 7. Bergmann, M., 1 977: Logic and sortal incorrectness. Review of Metaphysics 31; 6 1 -79. Bierwisch, M. and H eidolph, K .E. (eds.), 1 970: Progress in Linguistics. Mouton, The Hague. Blackburn, W.K., unpublished: Ambiguity and non-specificity: a reply to Jay David Atlas. Department of Philosophy, University of Toronto. Boer, St. and Lycan, W.G., 1 976: The myth of semantic presupposition. Indiana University Linguistics Club. Bloomington Indiana. Proceedings of the Berkeley Channon, R., 1 975: Acceptable ambiguity. Linguistic Society I; 37- 6. Chomsky, N., 1 957: Syntactic Structures. ( Janua Linguarum 4). Mouton, The Hague. Chomsky, N., 1 972: Language and Mind. Harcourt, New York. Grinder, J. & Postal, P.M., 1 9 7 1 : Missing antecedents. Linguistic Inquiry 2; 269-3 1 2. Hankamer, J., 1 973: Unacceptable ambiguity. Linguistic Inquiry 4; 1 7-68. Linguistic Inquiry 2; Jackendoff, R., 1 97 1 : Gapping and related rules. 2 1 -35. =

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reductions including and-so-does constructions have been studied since the early days of transformational grammar. See Chomsky ( 1 957: 26- 27, 65-67). One imp ortant variety of conjunctive abbreviation is known as gapping, the deletion of centrally embedded (verbal) material, as in ' Mary catches fish and Tom butterflies'. See Ross ( 1 967). The syntac tic literature on the varieties of conjunctive reductions is qUJte large. Cf. Ross ( 1 970), Lakoff & Ross ( 1 970), Jackendoff ( 1 9 7 1 ), Grinder & Postal ( 1 97 1 ) , H ankamer ( 1 9 7 3) , Channon ( 1 97 5), Stillings ( 1 9 7 5), Neijt ( 1 978). It is interesting that all such reductions, conjunctive and otherwise, eliminate cross-readings and are probably governed by the sorts of semantic constraints discussed in this paper. Another interesting paper ciritical of Atlas, one which I came upon too late to discuss here, is Blackburn (unpublished). 7 Zwicky & Sadock ( 1 97 5), esp. p.3, note 9. 8 Note that even if g(A) and g(B) share some ambiguous expressions; any other whole they are parts of, like f(g(A), g(B)) and T(f(g(A), g(B))) , might well be unambiguous because semantic operations as defined are allowed to give different combmations of arguments the same value. 9 Zwicky & Sadock ( 1 975: 1 8); Chomsky ( 1 972: 33). 10 See Thomason ( 1 972); Martin ( 1 97 5a); Bergmann ( 1 977). 1 1 See for example Van F raassen ( 1 969); Martin ( 1 97 5b); Martin (in press).

JOHN N. M ARTIN

·

ical Linguistics.

·

Neijt, A., 1 978: Constraints on gapping. Chicago Linguistic Society 1 4; 307-3 1 5. Ross, J.R., 1 96 7: Constraints on Variables in Syntax. Dissertation M IT. Ross, J.R., 1970: Gapping and the order of constituents. In: Bierwisch & Heidolph (eds.); 249-259. Stillings, J.T., 1 975: The formulation of gapping in English as evidence Linguistic for variable types in syntactic transformations. Analysis 1 ; 247-274. Thomason, R., 1 972: A semantic theory of sortal incorrectness. Journal of Philosophical Logic 1; 209-258. Van Fraassen, B.C., 1 969: Facts and tautological entail ment. Journal of Philosophy 66; 4 77-487. W ilson, D., 1 97 5: Presupposition and Non-Troth-Conditional Semantics. Academic Press, London - New York. Zwicky, A.M. & Sadock, J.M., 1 975: Ambiguity tests and how to fail them. In: Kimball (ed.); 1 -36.

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Kempson, R . M ., 1 97 5: Presupposition and the Delimitation of Semantics. Cambridge University Press, Cambridge. Kimball, J.P. (ed .), 1 975: Syntax and Semantics I V. Academic Press, New York. Lakoff, G., 1 9 70: A note on vagueness and ambiguity. Linguistic Inquiry 1 ; 357-359. Lakoff , G., & Ross, J.R., 1 970: Two k inds of and. Linguistic Inquiry 1 ; 2 7 1 -272. Martin, J.N., 1 975a: A many-valued semantics for category mistakes. Synthese 31; 6 3-83. Martin, J .N ., 1 97 5b: Facts and the semantics of gerunds. Journal of Phil osophical Logic 4; 4 39-454. Martin, J.N., 1 979: Some misconceptions in the critique of semantic presupposition. Theoretical Linguistics 6; 235-282. Martin, J.N., in press: Facts and events as semantic constructs. Theoret-

DISJUNCTION

Stephen Read

Abstract

I . How many disjunctions are there? Even classically it has been common to distinguish exclusive from inclusive disjunction. More recently, w1th the development of the relevant logics, a distinction has been observed between (in both cases inclusive) extensional and intensional disJunctions. Formal calculi with the power of treatjng these connectives have been set up. showm g their logical behaviour and their interaction with other connectives. 1 (Of these calculi, I shall work for the purposes of this papaer in R, the calculus of relevant implication.) I wish here to consider whether such a distinction between two uses of or is present in everyday reasoning. For simply to be able formally to characterise a connective may have no relevance to our reasoning practice: consider, e.g., the many calculi for necessity (50.5, S l , 52, 54.2, t.ukasiewicz, K, etc.) which are most implausible as formal representations of any everyday notions. My question is whether one finds in natural reasoning these two different notions of disjunction. 2. Extensional inclusive disjunction, • v , may be formally characterised by: A f- A V B (Addition) '

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�

In relevant logics one can ormally distinguish two logical operators, symbolised as r A v B -, and A + B ! Addition holds for ' v ' and Dis junctive Syllogism for ' + ', but not vice versa. The question arises, whether this distinction between two different formal notions of disjunc tion can be found in natural reasoning. First it is necessary to rebut Quinean objections to any rival to classical logic, Grice 's claim that an intensional disjunction is not needed to e:rplain the everyday uses of or, and Kempson and Cormack's argument that there can be no ambiguity between putative readings one of which entails the other (for A + B f- A v B). Finally Jackson's use of assertibility-conditions to defend the thesis tha t r if A then B I is equivalent to r A :J B I is rejected, but the notion of robustness which he introduces is usefully adapted to show why Disjunctive Syllogism must fail for ' v '• Having cleared the ground in this way, two uses of or are considered which have in everyday reasoning the inferential properties of ' v ' and ' + ', thus de fending the relevantist claim that or is ambiguous.

5TEPHEN READ (A and

-+

C) &. (B

-+

CHI- (A v B)

-+

C ( Reasoning by Cases, and its converse)

� (A v B)-II- (� A &. � B)

(De Morgan)

(Here ' & ' is extensional conjunction, ' -+ ' is intensional (relevant) i mplication, and '--ll-' abbreviates two-way logical consequence - in R .) If we have available an intensional conjunction, 'x' (often written 'o' and called 'fusion'), we can characterise intensional disjunction '+ ' , in a similar way:

� (A + BH I- ( � A

X

� B)

C

(Disjunctive Syllogism) (Intensional Reaso11ing by Cases) ( IntensiOnal De Morgan)

We have also A + B --ll-- � A

-+

B.

3.

It is immediately apparent that one difference between 'V ' and ' + ' is that where 'v ' pairs w ith ' & ' , ' + ' pairs with ' x ' . But there is ;mother important feature: in R Addition actually fails for ' + ' , and Dis junct ive Syllogism ( DS) fails for 'v'; that IS, and

A v B, � A II B.

l:ldeed, in order to distinguish '+' from ' v ' , the consequence relation in relevant logic must deviate from that in classical logic. One can of course attempt a Quinean point here: that to " save the obvious" validity of DS, one must infer that in relevant logic the sense of · � · and 'v ' must be different: "Here is the deviant logician's predica ment: when he tries to deny the doctrine he changes the subject." (Quine 1 970: 8 1 ) But the classical paradigm, however obvious it may be to its proponents, is not thereby automatically correct: of course one can be w rong. about logic. Sheer logic is conclusive only m that, if correct, it I S necessarily so. It does not follow that all (classical) logical claims are true. G iven standard meanings to ·� ', ' v ' and ' 1- ' , it is denied m R that, e.g., DS is valid: the consequence relation has a different (smaller) extension. How then do we give standard meanings to ' � · , ' v ' and ' I- ' ? What is it that shows what is meant by, e.g., ' v '? If one is to challenge one conception of logical consequence by another, then one answer - the 216

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A + B, � A 1- B (A .... C) X (B .... CH I- (A + B) ....

DISJUNCTION wrong one - is not that all, but that enough of the logical relations in the one must be conserved in the other. And we do f ind that a good number of the i mportant classical relations of ' v ' are preserved in R (and E). We have A 1- A v B, B 1- A v B, and � A & - B 1- � (A v B). Thus the simple truth of A suffices for that of A v B (as does that of B), and the (extensional) conjunction of the falsity of both suffices for that o f r A v B -,.

' v ' is a rigid designator whose reference is fixed by a rigid descrip tion: it is that truth-function which has truth-line TTTF. Then in R and E one is claiming that OS fails for that connective: that a particular possibili ty for that connective is actual. • v ' is an extensional disjunction for which Addition holds and OS fails. '+' is an intensional disjunction for which Addition fails and OS holds. 4. Disjunctive Syllogism is certainly a very common form of argument, and therefore an understanding of ' + ' has a large part to play ir. exploring the logic of natural language. From ( I ) Every student studies e ither Latin or Logic, one can infer that if a student chooses not to read Latin he or she enrols in Logic. Addition clearly fails for such a use. The Lewis argu ment, from r A & � AI via r (A or B) &� A I , by Addition, to B, by OS, reveals the unacceptable consequence of combining Addition and OS in one connective. Accepting OS for r A or B-, shows that its sense is I r if not-A then B ; the above regulation is, we saw, tantamount to (2)

lf

any student does not study Latin, he or she studies Logic.

But the truth of (2) is not a necessary condition of every student 's studying Latin (or for that matter, Logic), i.e., A does not entail r if not-A then B , . 3 What is more puzzling is whether any uses of or in English exhibit the JS, voi. J , no. 3

277


The trouble with this, shall we say Fregean, view is that it seems not to permit radical disagreements over the conception of logical consequence, just as its analogue for names does not per m i t considera tion of radically different histories. This thought may lead us to claim that the connectives are rigid designators, or at least can be used rigidly. z That is, that whatever one supposes true of the connectives, it i s the connective3 themselves which one supposes it of. Just as one may suppose that N ixon was innocent of Watergate, and supposes this of Nixon himself, not any counterpart of him, so too one can suppose that ' v ' and ·� ' do not satisfy Disjunctive Syllogism, and suppose this of ' v ' and ·� ' themselves, not of any counterparts of them, simply by stipulation: one stipulates that it is Nixon, and 'v ' and '� ', which are being considered.

STEPHEN READ logical behaviour the role ' v ' has on the conflation less, natural uses

of ' v ' . This may seem a surpnsmg doubt considering played in classical logic. But classical logic has rested of these two different d isjunctions. There are, nonethe of ' v ' . Here is one:

(3) You qual ify for a grant if either you are over 65 or you earn less than $2000 a year. We have here a disjunctive condition - a condit ional with a disjunctive antecedent; and one can satisfy the condition by satisfying either disjunt - so Addition holds for it. Secondly, it is equivalent to

where the conjunctions admits Simplif ication, and so is extensional. Hence this use of or IS extensional. 5. Paul Grice ( 1 978) has aq�ued against there being two such senses, intensional and extensional, of or. However, his arguments depend on two prejudicial assumpt ions about the relation between the senses which do not apply to ' + ' and ' v '. He takes the two putative senses to be: (I) the 'weak ' sense given in ' v ; and (Ii) the 'strong' sense such that I A or B I contains two components, first the assertion of IA v B I , and secondly the assertion of a non-truthfunctional reason for acceptmg IA v B I. '

Now it is certainly true (at least in R and E) that I A + B I entails v B I ; but it does not follow that there is some identifiable claim or condition P such that I A + B I is equivalent to I (A v B) & P I , but not to P alone. (This is worthy of remark since many detractors, and I even some proponents �of relevant logic have supposed that IA -+ B ' means 1 (A => B) & Q 1 for some condition Q such as A and B are mutually relevant'. But relevance is not identif iable (m general) separate ly from the existence of an impl ication relation from A to B . If A really does imply B then what greater reason can we have for clai ming that A is relevant to B? IA

Further, the account of the sense of r A + Bl need not make reference to I A v B I . A + B is true j ust when if A is not true then B IS true. (Ct. the classical truth-condition, that IA => B I is true j ust when either A is not true or B is true - using the extensional sense of or!) This truth condition is contained implicitly in the claim that DS holds for ' + ' given the analytic condition that Modus Ponens holds for if. 11f A then B-; is the material mode expression of the formal mode claim that B follows from A, 1 if A then, necessarily, B 1 is the material mode expres sion of the formal mode claim that A entails B.) Grice 's arguments are two: first , that the putative strong sense has 278

JS, vol. l , no.3


(4) If you are over 65 you qualify for a grant and if you earn less than $2000 a year you qualify for a grant.

DISJUNCTION restrictet application, whereas the weak sense is universal. This sugges tion results from classical blinkering. Certainly the classical Weltan schauung has led us to believe that many l!Ses of or a r e e x t ens ional for it has claimed that all are. But I am arguing that the intensional sense is a common one. The weak sense occurs in such restricted area!> as the antecedents of conditionals. Thus Grice's first argument cannot even get started. The same happens with the second argument. It depends on the use of the extra condition P, which i tself involves the weak sense, to characterise the strong sense, urging us that this should lead us to look for a way - a conversational way - of explicating the stcong sense as derivative from the weak. But we have seen that the strong sense does not depend on the weak iri this way.

If this argu ment were sound, then my claim that I A or B I (also) ex would be wrong, hibits an ambiguity b�tween I A + B I and IA v B 1 for, as I said, lA + B ! entails I A v B I . However, it is not sound. J agree with Kempson and Cormack that being true in a var !ety of different circumstances is not a mark of ambiguity. All sentences are true in a vari�ty of c i rcumstances: e.g., Someone is com ing down the road is true whether it is a man or a woman, whether it is Fred or Charlie or Alice; and Fred is com ing down the road is true regardless of whether it is raining or not, and so on. The ability to construct, for any sentence S, further sentences P, Q, R etc. which further charac terise different sorts of circumstance in all of which S is true, so that S is equivalent to some disjur.cticn P or Q or R or ... , d o e s not �how that S is ambiguou5. :ndeed, the point this drives home is that ambigu i ty in a sentence is not a mat ter of its having a disjunctive truth-co:-�di tion. (Kempson and Cormack appear to recognise this on "an amb!guous expre:;sion cannot be characterised by a sing!? p. 263 "in the d:sjur.ctive set oi p.:>ss1biEties" - only to forget it on p. 264 face of this :!VIdence [against the assumpt1on c.f no ambigui ty], one �isht

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