The compositionality solution
If we carefully notice the procedure through which the T-sentences are derived then we will see that the theory in question "must exhibit the semantic properties of the sentence as determined by the semantic properties of its lexical parts together with its syntactic structure."15 Moreover it is the theory that will arrive at the truth conditions of all the sentences of the language in this way. And it is then alone can we expect that the object language sentence embedded in the T-sentence will be correctly interpreted by the matching meta-language sentence. This is definitely a holistic constraint on the truth theory if it has to work as a meaning theory.
The moral is that we can have an extensional theory of meaning as long as we believe that the structural relations between formulas are respected while the derivations of the T-sentences are made. "The fact that each axiom of a truth theory has its impact upon an infinite number of T-sentences does indeed have the consequence that it is difficult for counterfeit theories to pass the test."16 Now a question arises: is compositionality really required to rule out the possibility of entailment of false sentences? If we are to say that the structural similarity between 'snow is white' and 'this is snow' is itself enough to ensure the truth of the sentence "'snow is white' is true iff snow is white" then we shall have to say, we have an a priori argument against the possibility of a non-compositional language. Fodor and Lepore have tried to come up with an explanation of such a non-compositional language which as they try to show may have expressions which will have determined truth-conditions.
| 15 | Ibid, p. 63. |
| 16 | McDowell, J. and Evans, G. (1976). Truth and Meaning. London: Oxford University Press, P.xv. |