Document Type

Article

Publication Date

2022

DOI

10.1111/phin.12379

Publication Title

Philosophical Investigations

Volume

46

Issue

4

Pages

480-495

Abstract

In Remarks on the Foundations of Mathematics, Wittgenstein notes that he has 'not yet made the role of miscalculating clear' and that 'the role of the proposition: "I must have miscalculated"...is really the key to an understanding of the "foundations" of mathematics.' In this paper, I hope to get clear on how this is the case. First, I will explain Wittgenstein's understanding of a 'foundation' for mathematics. Then, by showing how the proposition 'I must have miscalculated' differentiates mathematics from the physical sciences, we will see how this proposition is the key to understanding the foundations of mathematics.

Rights

© 2022 The Author.

This is an open access article under the terms of the Creative Commons Attribution 4.0 International License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Original Publication Citation

Wheeler, S. J. (2023). Wittgenstein on miscalculation and the foundations of mathematics. Philosophical Investigations, 46(4), 480-495. https://doi.org/10.1111/phin.12379

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