Anti-Realism and Anti-Revisionism in Wittgenstein’s Philosophy of Mathematics

Grazer Philosophische Studien 97 (3):451-474 (2020)
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Abstract

Since the publication of the Remarks on the Foundations of Mathematics, Wittgenstein’s interpreters have endeavored to reconcile his general constructivist/anti-realist attitude towards mathematics with his confessed anti-revisionary philosophy. In this article, the author revisits the issue and presents a solution. The basic idea consists in exploring the fact that the so-called “non-constructive results” could be interpreted so that they do not appear non-constructive at all. The author substantiates this solution by showing how the translation of mathematical results, given by the possibility of translation between logics, can be seen as a tool for partially implementing the solution Wittgenstein had in mind.

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Anderson Nakano
Pontifícia Universidade Católica de São Paulo

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References found in this work

The logical basis of metaphysics.Michael Dummett - 1991 - Cambridge: Harvard University Press.
Remarks on the foundations of mathematics.Ludwig Wittgenstein - 1956 - Oxford [Eng.]: Blackwell. Edited by G. E. M. Anscombe, Rush Rhees & G. H. von Wright.
Remarks on the Foundations of Mathematics.Ludwig Wittgenstein - 1956 - Oxford: Macmillan. Edited by G. E. M. Anscombe, Rush Rhees & G. H. von Wright.
Philosophical grammar.Ludwig Wittgenstein - 1974 - Oxford [Eng.]: Blackwell. Edited by Rush Rhees.
Philosophical remarks.Ludwig Wittgenstein - 1975 - Chicago: University of Chicago Press. Edited by Rush Rhees.

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