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15.3: Non-intersective adjectives

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    Our paradigm example of an adjective modifier has been the word yellow. As we have discussed a number of times, the phrase yellow submarine is compositional in a very straightforward way: its denotation set will be the intersection of the denotation sets ((yellow)) and ((submarine)) . This intersection corresponds to the set of all things in our universe of discourse which are both yellow and submarines.

    Adjectives that behave like yellow are referred to as intersective adjectives, because they obey the rule of interpretation formulated in Chapter 13: ((Adj N)) = ((Adj)) ∩ ((N)). Some examples of noun phrases involving other intersective adjectives are presented in (4).

    (4) a. Otacilio is a Brazilian poet.

    b. Marilyn was a blonde actress.

    c. Arnold is a carnivorous biped.

    Now the definition of intersection guarantees that if one of the sentences in (4) is true, then the individual named by the subject NP must be a member of both the denotation set of the head noun and the denotation set of the adjective modifier. This means that the inference in (5) will be valid.

    (5) Arnold is a carnivorous biped.
    Arnold is a mammal.

    Therefore, Arnold is a carnivorous mammal.

    However, there are other adjectives for which this pattern of inference will not be valid. Consider for example the syllogism in (6). It would be possible for a rational speaker of English to believe the two premises but not believe the conclusion, without being logically inconsistent. A similar example from The Wizard of Oz is presented in (7). Such examples force us to conclude that adjectives like typical are not intersective.2

    (6) Bill Clinton is a typical politician.
    Bill Clinton is a Baptist.

    ⁇Therefore, Bill Clinton is a typical Baptist. [not valid]

    (7) a. Dorothy: Oh — you’re a very bad man!
    Wizard: Oh, no, my dear. I — I’m a very good man. I’m just a very bad Wizard.

    b. Oz is a bad Wizard.
    Oz is a man.

    ⁇Therefore, Oz is a bad man. [not valid]

    Barbara Partee (1995) suggested the following illustration: imagine a situation in which all surgeons are also violinists. For example, suppose that a certain hospital wanted to put on a benefit concert, and all the staff members were assigned to play instruments according to their specialties: all the surgeons would play the violin, anesthesiologists the cello, nurses would play woodwinds, administrative staff the brass instruments, etc. Within this universe of discourse, the words surgeon and violinist have the same denotation sets; in other words, ((surgeon)) = ((violinist)) . However, the phrases skillful surgeon and skillful violinist do not necessarily have the same denotation sets, as seen by the failure of the following inference:

    (8) Francis is a skillful surgeon.
    Francis is a violinist.

    ⁇Therefore, Francis is a skillful violinist. [not valid]

    This example provides another instance in which two expressions having the same denotation (surgeon and violinist) are not mutually substitutable, keeping the truth conditions constant. Yet the meanings of phrases like typical politician and skillful surgeon are still compositional, because if we know what each word means we will be able to predict the meanings of the phrases. The trick is that with adjectives like these, as with propositional attitude verbs, we need to combine senses rather than denotations.

    We have seen that the meanings of adjectives like typical and skillful do not combine with meanings of the nouns they modify as the simple intersection of the two denotation sets. In other words, the rule of interpretation ((Adj N)) = ((Adj)) ∩ ((N)) does not hold for these adjectives. However, the following constraint on the denotation of the phrases does hold: ((Adj N)) ⊆ ((N)) . In other words, the denotation set of the phrase will be a subset of the denotation set of the head noun. This means that anyone who is a typical politician must be a politician; and anyone who is a skillful surgeon must be a surgeon. Adjectives that satisfy this constraint are referred to as subsective adjectives.3

    Subsective adjectives are intensional in the sense defined in §15.2: they combine with the senses, rather than the denotations, of the nouns they modify. One way of representing this is suggested in the following informal definition of skillful:

    (9) skillful combines with a common noun (N) to form a phrase which denotes a set of individuals. Any given individual within the universe of discourse will belong to the set of all “skillful Ns” just in case that individual belongs to the set of all Ns and is extremely good at the activity named by N.

    [selectional restriction: skillful combines with nouns that denote the actor of a volitional activity.]

    Certain types of adjectives turn out to be neither intersective nor subsective. Some examples are presented in (10).

    (10) a. former Member of Parliament
    b. alleged terrorist

    The adjective former is not subsective because a former Member of Parliament is no longer a Member of Parliament; so any person who can be referred to as a “former Member of Parliament” will not belong to the denotation set of Member of Parliament. This also proves that former is not intersective. Moreover, it is not clear that the adjective former even has a denotation set; how could we identify the set of all “former” things? Similarly, an alleged terrorist may or may not actually be a terrorist; we can’t be sure whether or not such a person will belong to the denotation set of terrorist. This means that alleged is not subsective. And once again, the adjective by itself doesn’t seem to have a denotation set; it would have to be the set of all “alleged” things, whatever that might mean. So alleged cannot be intersective either.

    How do we calculate the denotation of phrases like those in (10)? Although they cannot be defined as a simple intersection, the phrases are still compositional; knowing what each word means allows us to predict the meanings of the phrases. The trick is that with adjectives like these, as with propositional attitude verbs, we need to combine senses rather than denotations. In other words, these adjectives are intensional: they combine with the senses of the nouns they modify. Informal definitions of former and alleged are suggested in (11):

    (11) a. former combines with a common noun (N) to form a phrase which denotes a set of individuals. Any given individual within the universe of discourse will belong to the set of all “former Ns” just in case that individual has belonged to the set of all Ns at some time in the past, but no longer does.

    b. alleged combines with a common noun (N) to form a phrase which denotes a set of individuals. Any given individual (x) within the universe of discourse will belong to the set of all “alleged Ns” just in case there is some other individual who claims that x belongs to the set of all Ns.

    The adjective former has the interesting property that a “former N” cannot be a member of the denotation set JNK. In other words, denotation sets of phrases containing the word former are subject to the following constraint: ((Adj N)) ∩ ((N)) = ⌀. Adjectives that satisfy this constraint are referred to as privative adjectives. Other privative adjectives include: counterfeit, spurious, imaginary, fictitious, fake, would-be, wannabe, past, fabricated (in one sense). Some prefixes have similar semantics, e.g. ex-, pseudo-, non-.

    As we have seen, the adjective alleged is not subsective; but it is not privative either, because an alleged terrorist may or may not belong to the denotation set of terrorist. We can refer to this type of adjectives as non-subsective. Other non-subsective adjectives include: potential, possible, arguable, likely, predicted, putative, questionable.

    At first glance, many common adjectives like big, old, etc. seem to be intensional as well. Partee (1995) discusses the invalid inference in (12), which seems to indicate that adjectives like tall are non-intersective. The crucial point is that a height which is considered tall for a 14-year-old boy would probably not be considered tall for an adult who plays on a basketball team. This variability in the standard of tallness could lead us to conclude that tall does not define a denotation set on its own but combines with the sense of the head noun that it modifies, in much the same way as typical and skillful.

    (12) Win is a tall 14-year-old.
    Win is a basketball player.

    ⁇Therefore, Win is a tall basketball player. [not valid]

    However, Siegel (1976) argues that words like tall, old, etc. are in fact intersective; but they are also context-dependent and vague. The boundaries of their denotation sets are determined by context, including (but not limited to) the specific head noun which they modify. Once the boundary is determined, then the denotation set of the adjective can be identified, and the denotation set of the NP can be defined by simple intersection.

    One piece of evidence supporting this analysis is the fact that a variety of contextual factors may contribute to determining the boundaries, and not just the meaning of the head noun. Partee notes that the standard of tallness which would apply in (13a) is probably much shorter than the standard which would apply in (13b), even though the same head noun is being modified in both examples.

    (13) a. My two-year-old son built a really tall snowman yesterday.
    b. The fraternity brothers built a really tall snowman last weekend.

    She adds (1995: 331):

    Further evidence that there is a difference between truly non-intersective subsective adjectives like skillful and intersective but vague and contextdependent adjectives like tall was noted by Siegel (1976): the former occur with as-phrases, as in skillful as a surgeon, whereas the latter take forphrases to indicate comparison class: tall for an East coast mountain.

    Bolinger (1967) noted that some adjectives are ambiguous between an intersective and a (non-intersective) subsective sense; examples are presented in (14–16).4 The fact that the (b) sentences can have a non-contradictory interpretation shows that this is a true lexical ambiguity; contrast #Arnold is a carnivorous biped, but he is not carnivorous.

    (14) a. Marya is a beautiful dancer. (Siegel 1976)
    intersective: Marya is beautiful and a dancer.
    subsective: Marya dances beautifully.
    b. Marya is not beautiful, but she is a beautiful dancer.

    (15) a. Floyd is an old friend.
    intersective: Floyd is old and a friend.
    subsective: Floyd has been a friend for a long time.
    b. Floyd is an old friend, but he is not old.

    (16) a. He is a poor liar. (cf. Bolinger 1967)
    intersective: Floyd is poor and a liar.
    subsective: Floyd is not skillful in telling lies.
    b. He is a poor liar, but he is not poor.

    Thus far we have only considered adjectives which occur as modifiers within a noun phrase; but many adjectives can also function as clausal predicates, as illustrated in (17). In order to be used as a predicate in this way, the adjective must have a denotation set. Since all intersective adjectives must have a denotation set, they can generally (with a few idiosyncratic exceptions) be used as predicates, as seen in (18).

    (17) John is happy/sick/rich/Australian.

    (18) a. Otacilio is a Brazilian poet; therefore he is Brazilian.
    b. Marilyn was a blonde actress; therefore she was blonde.
    c. Arnold is a carnivorous biped; therefore he is carnivorous.

    When an adjective which is ambiguous between an intersective and a subsective sense is used as a predicate, generally speaking only the intersective sense is available (19). So, for example, (19c) is most naturally interpreted as a pun which makes a somewhat cynical commentary on the way of the world.

    (19) a. # Marya is a beautiful dancer; therefore she is beautiful.
    b. # Floyd is an old friend; therefore he is old.
    c. He is a poor liar; therefore he is poor.

    We have already noted that the adjectives former and alleged don’t seem to have a denotation set. As predicted, these adjectives cannot be used as predicates, and the same is true for many other non-subsective adjectives as well (20a). However, given the right context, some non-subsective adjectives can be used as predicates (20b, c). In such cases it appears that information from the context must be used in order to construct the relevant denotation set. In addition, cases like (20c) may require a kind of coercion to create a new sense of the word money, one which refers to things that look like money. As Partee points out, similar issues arise with phrases like stone lion and chocolate bunny.

    (20) a. * That terrorist is former/alleged/potential/…
    b. His illness is imaginary.
    c. This money is counterfeit.

    The main conclusion to be drawn from this brief introduction to the semantics of adjectives is that compositionality cannot always be demonstrated by looking only at denotations. All of the adjectives that we have discussed turned out to be compositional in their semantic contributions; but we have seen several classes of adjectives whose semantic contributions cannot be defined in terms of simple set intersection. These adjectives are said to be intensional, because their meanings must combine with the sense (intension) of the head nouns being modified.


    2 This is also true for bad in the sense Oz intended in the phrase bad Wizard; but bad is a tricky word, and the various senses probably do not all belong to the same semantic type. Of course the polysemy is also part of the problem with the invalid inference in (7).

    3 Of course, all intersective adjectives are subsective as well; but since the term “intersective” makes a stronger claim, saying that a certain adjective is subsective will trigger an implicature that it is not intersective, by the maxim of Quantity.

    4 Examples adapted from Morzycki (2015: ch. 2). The adjective bad mentioned above is probably also ambiguous in this way.


    This page titled 15.3: Non-intersective adjectives is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Paul Kroeger (Language Library Press) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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