No grammar of a language is complete without an account of how its speakers understand its sentences constructed by themselves and others. The ultimate goal of any semantic theory is to construct a model of the native speaker’s knowledge of meaning, or semantic competence. A fundamental
task dictated by this goal is to formulate the general principles that bring into correspondence (units of) syntactic structure with (units of) semantic structure.
Since basically any theory of meaning in natural language seeks to establish, among other things, the principles that map units of syntactic structure onto units of meaning, it is crucial that an adequate model of the native speaker’s knowledge of meaning account for the way locutions of varying complexity identify the semantic or ontological entities to which they correspond.
In set-theoretic terms, to identify an entity presupposes a set in which that entity is a member and implies distinguishing this member from any and all other members of the same set. From this it follows that the identification of an element in a set implies the contrasts that distinguish the particular element from all other members of that set. The set itself will be identified by the property or properties that are shared by all its members.
Assuming a theory of language (in the spirit of Chomsky 1981, and Jackendoff 1983, 1990), which has a level of mental representation beyond LF, at which linguistic expressions are “paired with entities of mental representation” (cf. Chomsky 1981:324), one way to bring units of syntactic structure into correspondence with units of semantic structure is to view elements of semantic structure as set theoretical entities. A relation that holds between a linguistic expression and the semantic entity to which it corresponds may then be regarded as identification. Thus, a linguistic expression identifies the semantic entity, or set of entities, with which it is brought into correspondence by the principles of semantic theory.
Another important and well-motivated assumption that will be adopted in the present work has to do with the nature of the language faculty of humans. Given that linguistic competence is embedded in a system of other cognitive capacities, “it is reasonable to suppose that the design of language should facilitate the perceptual [and interpretational] strategies that are used by the hearer” (cf. Chomsky and Lasnik 1977:434, and see also Jackendoff 1983 for the development of a very similar conclusion).
We may proceed on the reasonable assumption that sentences describe eventualities, that is, they correspond to eventualities in a domain D of semantic entities at the level CS of Conceptual Structure, where linguistic expressions are paired with units of mental representation.
Further, we may regard eventualities as set-theoretic entities, that is, elements in sets. Given these assumptions, we may say that to describe a particular eventuality is to identify it in a relevant set of eventualities in the domain D of CS. Since a particular eventuality Ei a sentence describes is
identified through the contrasts that hold between Ei and all other eventualities in the relevant set R, sentences must contain some information with regard to the relevant set R, a subset of which they identify.
Since any individual entity may be regarded as a set with only one member, that is a unit set, we can always conveniently refer to the target of identification as a set, which may have one or more than one member. In set-theoretic terms, to identify a subset A of entities (with one or more than one member) presupposes a set R of which the target of identification is a subset, and it implies distinguishing the member or members of this subset A from any and all other members of R. From this it follows that the identification of A in R implies the contrasts between each element of A and all other members of R, that is, members in the complement set CA of A with respect to R. The relevant set R itself will be designated by the property or properties that are shared by all its members.
In conceptual terms, the successful identification of a subset A of entities in a relevant set R presupposes the recognition of the relevant set R a subset A of which is identified, and entails the recognition of contrasts between the elements in A and the elements in the complement set CA of the subset A with respect to the relevant set R.
If the elements of semantic structure to which linguistic expressions correspond are viewed as set-theoretical entities, it is clear that the understanding of implied contrasts between the member(s) of a subset of a relevant set of semantic entities and all other members of the relevant set is vital for the understanding of the meaning of linguistic expressions. Given that the understanding of implied contrasts presupposes the recognition of a relevant set a subset of which is being identified, it follows that the proper designation of the relevant set is crucial.
It is reasonable to conclude, then, that the understanding of implicit contrasts is an important part of understanding the meaning of sentences because implied contrasts simply are an important aspect of the meaning of sentences.
In general, to understand the meaning of a sentence is to understand, among other things, the implied contrasts that are expressed at various levels of syntactic and semantic structure. A sentence either implies (a) a contrast directly between the proposition it expresses and the negation of that proposition, or (b) a contrast between the proposition it expresses and a set of (potential) conflicting propositions.
One is prompted to ask: How do sentences express all this? Relevant sets and contrasts in those sets are rarely spelled out explicitly. Rather, relevant sets and contrasts in those sets are implied. Even though such
implications are hardly ever made explicit, we clearly understand them, or if we do not, we desire that they be spelled out.
To capture this aspect of the meaning of sentences, we will say that they evoke, or introduce, relevant sets. A relevant set R is designated by the property or properties that all its members have in common, and a sentence may somehow indicate what these properties are. The relevant set R a sentence evokes is therefore characteristic of the kind of implied contrasts it expresses, and, in general, it is characteristic of the meaning of the sentence.