truth-condition. There are several other kinds of a b ilitie s that Dummett might have mentioned. Consider a speaker's a b ility to pursue correctly the practices of evidentially evaluating assertions. Even Dummett should concede that a speaker could come to understand the truth-conditions, however construed, of sentences through recognizing the conditions which warrant, to different degrees, assertions of the sentences and the conditions which warrant, to different degrees, with drawals of the assertions. An a n ti-re a lis t like Dummett might wish to
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add the following reservation to this claim: when the truth-conditions of sentences are construed classically and not constructively one could not 1 earn the classical conception of truth through acquiring the practices of tentative assertion and subsequent withdrawal; rather that conception
12
of truth would govern the practices. On a re a lis t understanding of these practices of evidential evaluation, a grasp of the classical truth- condition of a sentence would be a grasp of the condition which determines what counts as good evidence and what counts as damaging evidence for the assertion of the sentence. Nonetheless, regardless of whether the truth-condition receives a classical or constructivist interpretation,
i t is undeniable that a speaker could manifest his understanding of the truth-condition of a sentence by a correct pursuit of the practice of evidential evaluation.
An even more glaring omission by Dummett is his fa ilu re to mention the a b ility of speakers to recognize arguments as valid and invalid. I t is clear that there is no better kind of a b ility to examine in connexion with tests of a speaker's knowledge ofssentence's truth-condition than his a b ility to discern the v a lid ity of an argument which contains the sentence as assumption, premiss, or conclusion. The reason for this is fam iliar: an argument is valid when and only when the truth of the assump tions and premisses necessitates the truth of the conclusion. Consequently, a recognition of the v a lid ity of the argument requires an understanding of the conditions under which the assumptions, premisses, and conclusions are true. Moreover, by determining whether a speaker accepts classically valid or only in tu itio n is tic a lly valid arguments i t is possible to settle
12. For this point see the exchange between Strawson and Wright: P.F. Strawson, 'Scruton and Wright on Anti-Realism E tc', Proceedings of the Aristotelian Society, vol LXXVII, p .16; Crispin Wright, 'Strawson lOn Anti-Realism', Synthèse, XL(1979), p.296
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whether he is interpreting the truth-conditions of the relevant sentences classically or in tu itio n is tic a lly .
I t is unclear why Dummett should have chosen not to mention these a b ilitie s , possessed by speakers, to follow the rules of evidential evaluation and to judge whether arguments are valid or not. (I shall call these a b ilitie s evidential and inferential a b ilitie s respectively.) At any rate, they do not lend much support, as we shall see, to his criticisms of a re a lis t theory of meaning which assumes the principle of bivalence.
&3 An Argument against Realism
Now Dummett places the whole weight of his attack on realism on certain arguments about the form which a theory of meaning should take. From §1 i t is clear that Dummett identifies realism with the thesis that
knowing the meaning of a sentence consists in knowing the conditions under which i t is true or false, where the notions of truth and fa ls ity obey the classical principle of bivalence. What is important about this identification is the restriction of truth and fa ls ity by the principle of bivalence, rather than the equation of meaning with truth- conditions. In fact Dummett envisages the possibility of a theory of meaning in terms of the conditions for a sentence's being true or false;
the only difference is that he understands the notions of truth and fa ls ity in tu itio n is tic a lly .
The arguments against realism revolve around what Dummett calls undecidable sentences:
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The d iffic u lty arises because natural language is fu ll of sentences which are not effectively decidable, ones for which there exists no effective procedure for determining whether or not their truth- conditions are f u l f i l l e d . . . Many features of natural language
contribute to the formation of sentences not in principle decidable: the use of quantification over an in fin ite or unsurveyable domain (e.g. over all future times); the use of the subjunctive conditional, or of expressions explainable by means of i t ; the possibility of referring to regions of space-time in principle inaccessible to us. ('Theory of Meaning I T , p.81)
An undecidable sentence, then, is simply one such that no effective procedure is available to us for finding out whether i t is true or false
The passage above does not te ll us the kind of effective procedure which is available in the case of decidable sentences but not in the case of undecidable ones. In mathematics, an effective procedure would be an algorithm lik e m ultiplication, addition, etc. But what are the analogues of these computation procedures in the case of non-mathematical decidable sentences? There is good evidence to show that Dummett
believes that the only effective procedure we have in the case of non- mathematical sentences is observation. (See ‘Theory of Meaning I I ' , pp.98-99; Elements, pp.378-379) So, in short, a non-mathematical sentence is undecidable for Dummett because we cannot observe i t to be true or false. This view entails that all past-tense sentences, a ll counterfactuals, and a ll sentences quantified over an in fin ite domain are undecidable. But note that although a sentence may be
undecidable i t need not remain undecided: some non-effective method of