7.13—
Compositionality and the Conventionality of Syntax

Thus far we have shown systematic disregard for one feature of CTM which is in some ways quite important—namely, that it is supposed to support semantic compositionality. The representations envisioned by Fodor and other advocates of CTM, after all, are not all lexical primitives; the vast majority of them are made up of a large number of primitives combined with the help of syntactically based compositional rules. The semantic properties of complex representations are explained by (a ) the semantic properties of their atomic constituents, in combination with (b ) the compositional rules by which those constituents are combined.

Now this feature of CTM leaves the theory no better off with respect to the objections already raised: if the "semantic properties" are of the conventional or intentional kind, the fact that compositionality is thrown in does not rescue the theory from circularity or regress. Any taint of semantic convention or intention is enough to scuttle the whole project. But the appeal to compositionality does introduce a further problem: according to the analysis of symbols in chapter 4, syntax, as well as semantics, is conventional in nature, and hence there is a second kind of conventionality involved in CTM for the complex representations, assuming that CTM's advocates mean by "syntax" what one normally means when speaking of the syntactic properties of symbols.

The problem might be looked at in the following way. In order for there to be compositionality, it is not enough to have assignments of interpretations to primitive elements and rules governing legal concatenations of symbols. That is, it is not enough to assign "Lincoln" to A and "Douglas" to B and say that there is a legal schema for expressions 'x -&-y ' into which A and B may be substituted. There must, additionally, be a rule that will further determine that 'A & B ' counts as meaning "Lin-

coln and Douglas" and not, say, "Lincoln, Douglas" (a list), "Lincoln is greater than Douglas," or "Lincoln or Douglas." Semantic compositionality requires a notion of syntax that consists in more than rules for legal concatenation—it requires a notion of syntax that delivers complex semantic values. (It is worth noting that most of the time when we speak of syntactic categories we speak of them in ways that have some semantic overtones: for example, "count noun," "dependent clause," "conjunction symbol," or even "Boolean operator.")

But this is quite problematic if we try to move from natural languages (where conventions are a commonplace) to an inner language of thought, where conventions are an embarrassment. For the only way we have of generating complex symbolic meanings from atomic meanings is through syntactically based combinatorial rules, and the only such rules we have are conventional rules. But if the meanings of mental states are dependent upon syntactic convention, the old problems about semantic conventions reassert themselves at a different level: in brief, (1) the actual existence of such conventions is extremely dubious, (2) their existence is in fact irrelevant to the meanings of our mental states, and (3) positing such conventions would lead to a regress of mental states.

This problem with the conventionality of syntax, moreover, in some ways poses a problem for CTM more fundamental than that posed by the conventionality of semiotic-semantic properties. As we shall see in the next chapter, one might try to rescue CTM by developing a notion of "semantic properties" for representations that is not convention- or intention-dependent. Some would say we already have such notions. It is far less clear, however, that we do have or could have an account of compositionality that was not ultimately based upon conventions, and hence this objection will recur for the versions of CTM to be explored in chapters 8 and 9.