KM §3 - Meaning and Structure

§3 Meaning and Structure (pp. 66-111)

Summary

3.1 Notions of structure

The first issue of the chapter is to sketch three possible structures for sentences made out of conjunctions and negations.Taking the case of sentences made out of the conjunction and, the three structures are:

Logical:
1. [and S1 S2] is true iff S1 is true and S2 is true.
Semantic:
1. [S1 and S2] is true iff S1 is true and S2 is true.
Syntactic:
1. [S1 [and S2]] is true iff S1 is true and S2 is true.

The challenge, then, is to find a way to choose among these alternatives.

3.1.1 Semantic structure and syntactic structure

One way is by assuming that structures converge across linguistic components. [What are the linguistic components?] There are three reasons for suspecting that structures might converge:

Representations in one component are used by another component, so they should not be wildly different.
It would make it easier to learn a language if representations used in one component were similar to those used in another component. In the best case, a child could learn the reprentational format of one componant just by learning that of another.
Even when we assume that representations across components are different, they share so many similarities that it looks like there is some pressure to make them conform to a single general pattern.

3.1.2 Semantic structure and logical structure

In contrast, linguistic structure, especially semantics, may not converge with logical structure. The main reason for suspecting such a divergence is that logicosemantic relations between sentences are not defined in the object language, but rather in the metalanguage.

3.2 Constraints on semantic rules

3.2.1 Strong compositionality

Strong compositionality hypothesis: R is a possible semantic rule for a human language only if R is strictly local [in scope] and purely interpretive [in contribution].

Now consider the two grammars that we have been assuming: