Volume 42, 1992
Criss-crossing a Philosophical Landscape
Wittgenstein, Anti-Realism and Mathematical Propositions
Wittgenstein is generally supposed to have abandoned in the 1930's a realistic conception of the meaning of mathematical propositions, founded on the idea of tmth-conditions which could in certain cases transcend any possibility of verification, for a realistic one, where the idea of truth-conditions is replaced by that of conditions of justification of assertability. It is argued that for Wittgenstein mathematical propositions, which are, as he says, "grammatical" propositions, have a meaning and a role which differ to a much greater degree from those of ordinary propositions than either platonistic realism or intuitionistic anti-realism would admit, and that is the tendency to assimilate the mathematical proposition to an ordinary descriptive proposition which confers on it an appearance of meaning independent of the possibility of proving it, and not, as Dummett would say, that it is a decision concerning the kind of meaning it has which gives it the status of a proposition describing a determinate objective reality.