Wittgenstein on Cantor's Proof

In Gabriele Mras, Paul Weingartner & Bernhard Ritter, Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium. Berlin, Boston: De Gruyter. pp. 67-69 (2018)
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Abstract

Cantor’s proof that the reals are uncountable forms a central pillar in the edifices of higher order recursion theory and set theory. It also has important applications in model theory, and in the foundations of topology and analysis. Due partly to these factors, and to the simplicity and elegance of the proof, it has come to be accepted as part of the ABC’s of mathematics. But even if as an Archimedean point it supports tomes of mathematical theory, there is a question that demands clarification: What, exactly, does Cantor’s proof show? One of few places where this question is addressed is Appendix II of Wittgenstein’s Remarks on the Foundations of Mathematics. This essay is devoted to clarifying Wittgenstein’s remarks in that section.

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Chrysoula Gitsoulis
City College of New York (CUNY)

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