Abstract
Semantic indefiniteness appears in all areas of the lexicon. However, one part of speech is especially well-suited for an initial analysis of the phenomenon: the adjective. Examples with adjectives can demonstrate many different aspects of semantic indefiniteness; and they do so rather directly and clearly, because they are usually found to be “unmixed”, whereas other parts of speech, such as common nouns, are complicated by other semantic phenomena that present problems of their own (see Ch. 4.4 below). Moreover, indefiniteness manifests itself in a large, uniform portion of the adjective lexicon more clearly than anywhere else. I would like to begin the discussion with this type of examples: the “degree adjectives”.
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References
This heading quotes the title of Kamp (1975). As a counterpoint to Montague (1970), the article develops a semantic theory based on the example of degree adjectives; the fundamentals of the precisification semantic approach suggested here are related to this theory.
Kamp (1975) also argues that it is impossible to integrate a semantic treatment of the comparative into the framework of Montague’s analysis.
A semantic approach to the attributive adjective on the basis of the predicative form is shown in Pinkal (1980). Kamp (1975) and Klein (1980) also give analyses based on the predicative use [MP: Bierwisch/Lang (1989) give a detailed account of a wide variety of data in the field of relative adjectives]. — Since I am only concerned about the semantics of adjectives insofar as they allow statements about the semantics of indefinite expressions in general, I will spare the details.
The article also contains a comprehensive survey of the “hedge expressions” of English.
The most important consequence — namely that a truth-functional interpretation of the connectives of propositional logic is not possible — is discussed at length in 5.7.
The alternatives divided by a slash in (10) do not always lead to the same result: a can be “intensionally more precise” than β(i.e. it can lead to a restriction of the indefinite domain under certain conceivable states of the world), without consequences for the extension of the expression in the real world; and vice versa: a can extensionally precisify expression βand at that same “deprecisify” it under certain conceivable states. Since I restrict myself to extensions here, I will not go into the differences any further. (Cf. Fine 1975)
— as long as fast is accepted as a vague expression (cf. Ch. 4.1 p. 76). As the discussion in 4.4 will show, the principle must be modified for vague expressions. But that does not falsify it.
In fact, there is a certain tradition for such a confusion. Russell (1923) can be mentioned as an older example from philosophy; more recent cases in linguistics are Lakoff (1970) and Kempson (1977).
Because of the dispositional character of clever, the dimension of time has no effect in (e).
In such cases, remnants of vagueness remain in the comparative of these expressions; cf. Quine (1960), p. 127.
Referential and non-referential adjectives together form the class of restrictive predicates (which constrain the denotation of their head noun) as opposed to the non-restrictive adjectives. The latter form a small, rather wild and non-uniform group of words that are different from the remainder of the adjectives in almost every respect. What they have in common with the other adjectives is their applicability in the attributive use. But they do not allow predicative use, and just for that reason require a special treatment. Examples are prospective, prior, potential, supposed, putative, alleged, fake. Their common characteristic is of a negative nature: they are not restrictive. An alleged frog need not be a frog, and a fake frog cannot be one (but is probably a degenerate toad or a clown in a costume). The entire spectrum of modal and attitude semantics, as well as some other phenomena, is reflected in this small group of adjectives. For this reason, I leave non-restrictive adjectives out of consideration here and in the following.
It normally makes use of classes or predicates of comparison, yielding threshold values in a second step — cf. Pinkal (1980).
This does not mean that further investigations into the role of context and contextual givens must be excluded. Nor does anything prevent an attempt to extend precisification semantics to a full semantics of context. In section 6.2, I will specify an “interface” to context theory in the formal description of precisification semantics.
I refer to Eikmeyer/Rieser (1983) and Kindt (1983), who deal with the social aspect of context theory with respect to vagueness phenomena. Eikmeyer and Rieser invoke Putnam’s theory of the “linguistic division of labor” (cf. Putnam 1975). On a more abstract level, Kindt investigates possible interactive adaptations of different contexts and interpretations.
The context semantics of Cresswell (1973) also falls under this category. Although he works with “context properties”, a kind of partially defined contexts, it is a prerequisite for evaluation that the complete set of properties relevant to a given utterance are available.
For example, there are two types of NP’s in sentence (h) that I do not want to deal with here: the tubercle bacillus is a generic NP (more specifically: an NP in generic use); it refers to a kind and not to an individual object. the discoverer of the tubercle bacillus has a functor-argument structure. The classical presupposition analysis of definite descriptions is based on expressions of this special form (cf. example (s) in Chapter 1.2), and its plausibility depends on expressions of this type.
An informal suggestion of this kind was made in Lewis (1979); a formal semantic analysis is carried out in Pinkal (1979).
The “naturalness” of this dialogue may resemble that of sample texts from experimental dialogue systems. The problem in such systems and in this example is that the individual steps of the identification process are made explicit. In natural communication, much of this is achieved by other means, beneath the threshold of verbalisation.
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Pinkal, M. (1995). The Phenomenon of Precisification. In: Pinkal, M. (eds) Logic and Lexicon. Studies in Linguistics and Philosophy, vol 56. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8445-6_4
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