Nebraska Academy of Sciences
Date of this Version
1982
Citation
Transactions of the Nebraska Academy of Sciences, vol. 5 (1978)
Abstract
In Wittgenstein's speculation the transition from the philosophical point of view expressed in the Tractatus logico-philosophicus to the later development of his thought, as it is reflected in the Philosophical investigations and On certainty, is relevant also to his conception of mathematics.
In particular, while in the Tractatus, mathematics is not given an account of its own, independent of the account which is given to logic, the Remarks on the foundations of mathematics seems to offer sufficient evidence for the belief that, in the late stage of Wittgenstein's speculation, the analysis of the foundations of mathematics received an explicit treatment on its own.
This discussion is concerned with the attempt to illustrate the transformation which occurred in Wittgenstein's way of conceiving mathematics; that is to say, with the passage from the original idea of mathematics as a discipline, on a par with logic itself, reflecting the unmodifiable, and therefore necessary, features of the logical structure of the world, to the more "intuitionistic" conception of mathematics, as a constructive activity, leading to merely conventional truths.
The different connotations of the notion of "truth," in relation to these two different conceptions of mathematics, are also considered.
Comments
Copyright by the author.