FUNCIONALIDAD

A recursive Semantics in terms of truth, but not necessarily in the form of a truth-theory

Parameters

describing factors involved in speakers' actual judge­ ments about v a lid ity

explain

A speaker's semantic competence consisting in

A probability calculus

Parameters

describing factors involved in speakers' actual judge­ ments about evidential support

inferential a b ilitie s which issue in judgements about whether arguments are valid

explain evidential a b ilitie swhich issue in judgements about whether sentences are well supported

-64“

Such a theory, even in its most schematic formulation, is to ta lly 'different from Dummett's. The difference does not just reduce to a difference over the phenomena which the theory of meaning must account for: Dummett has verbal and recognitional a b ilitie s while I have evidential and inferent­ ial a b ilitie s . In acknowledging the need for idealization in theory- construction, the theory sketched above lacks any equivalent to Dummett's theory of sense, which connects theory with phenomena in a piecemeal

fashion. In acknowledging the modular structure of semantic competence, i t posits, in contrast with Dummett's theory, different theoretical

17 representations for the different constitutive a b ilitie s .

I t is significant to observe that this conception of the theory of meaning does not fa ll into either category of modest or full-blooded theory.

I t is not a full-blooded theory: i t does not contain a description of how a speaker's im plicit knowledge of the sentences of the theory is manifested. But such a theory is not modest either. I t conveys more information than the facts which a speaker knows when he knows the meanings of the sentences of a language: i t provides an explanation of the way in which a speaker, on individual occasions, exercises

the a b ilitie s constituting his semantic competence.

17. For a discussion of the modular structure of linguistic competence,

from which I have learnt much, see Noam Chomsky, Rules and Representations op. c i t . , pp.40-46, 60-61, 89«90.

-65-

CHAPTER THREE VERIFICATIONÎSM AND LOGIC

In this chapter I shall discuss the way in which Dummett thinks that his argument against realism necessitates a repudiation of classical logic in

favour of in tu itio n is tic logic. In

Si

against real ism. In §2 I shall present Dummett's distinction between demonstrations and canonical proofs and his more general distinction between direct and

indirect verifications. In § 3 I shall consider the way in which Dummett attempts to characterize mathematical truth and general truth in terms of

these distinctions. In §4 I shall discuss a problem which confronts a verification is theory of meaning of the kind Dummett espouses and show that there is a flaw

in Dummett's argument that a v e rific a tio n is t theory of meaning leads to a rejection of classical logic.

§1 Dummett's Arguments against the Appeal to Inferential A b ilities

Dummett identifies realism with the thesis that a speaker's understanding of the sentences of a language should be analyzed in terms of the notions of classical truth and fa ls ity . Dummett's argument against realism, so conceived, relies heavily on using Wittgenstein's dictum that meaning should be exhaustively manifestable in use as a constraint on the theory of meaning, that is , the theory of what a speaker knows in understanding the sentences of the language. Wittgenstein's dictum is used as a constraint on the theory of meaning in the sense that i t restricts the concept of truth to be employed in the recursive specification of sentences' truth-conditions.

—6 6 —

None of the objections I lodged against Dummett's argument in the last chapter was intended to involve a denial of Wittgenstein's dictum. One objection, lodged in §5 of the last chapter, was that a sophisticated adherence to the principle, which makes due concession to the amount of idealization involved in constructing a systematic and explanatory theory of meaning, does not require that sentences of the theory be connected in a piecemeal fashion with practical linguistic a b ilitie s . An ea rlier objection, lodged in §2, was that i f speakers' inferential a b ilitie s

are included as part of the use in which speakers' understanding of sentences can be manifested, then there are no grounds for denying, even given the application of Wittgenstein's dictum as a s tric t constraint on the theory of meaning in the way that Dummett intends, that speakers can manifest th eir knowledge of the conditions for the classical truth and fa ls ity of sentences.

This last objection is an obvious one to make. Therefore, we should expect Dummett to have some response to i t . There are, in fa ct, two lines of argument in Dummett's work which can be seen as responses to this objection. One line of argument is this:

This answer[ involving the appeal to inferential a b ilitie s ] is thin. -, It. is undoubtedly the case that i f we have a grasp of some conception

of truth for mathematical statements with respect to which the principle of bivalence holds, then the laws of classical logic are valid;

but i t is hardly plausible that the mere propensity to reason in