Antirealism and Falsity

Abstract

The ‘meaning is use’ approach to the theory of meaning, the approach we inherit through Dummett from Wittgenstein and which makes heavy use of natural deduction systems for the study of the meanings of logical words, has somehow to reconstruct proof-theoretically the properties of sentences and arguments that customarily are treated semantically by theorists of other schools. Another way of putting this idea is that the semantical properties of a language are the result of how it is employed socially. The main linguistic uses of the logical constants involve their roles in inferences, and Gentzen’s natural deduction systems have a strong philosophical claim to being the right codification of these uses, so this Wittgensteinian approach leads to concentration on natural deduction systems of logic for the study of the meanings of logical words. This approach to analysing semantical properties of language is seen, for instance, in Prawitz’s charge that Tarski’s analysis of validity is philosophically unenlightening [4, p. 67], cited in [2, p. 201]. The alternative is to hold an argument valid when it is provable subject to various structural constraints on the shape of the proof, i.e. when there is a canonical proof of the argument. Still, it is a mistake to think that this way of approaching questions of validity is not semantical in a broad sense. Semantical properties should be emergent properties, arising from the right constellation of proof-theoretical ones. On anyone’s account, validity has to have something to do with preserving truth (or ideal verifiability, or warranted assertibility or whatever truth-surrogate is active at the time). Likewise, if the meaning of the ampersand is fixed by its introduction and elimination rules, these must suffice to say when the conjunction is true or false, once the values of its conjuncts have been fixed.KeywordsClassical LogicIntuitionistic LogicDouble NegationLogical ConstantElimination RuleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.