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.
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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
Wheeler, Samuel J., "Wittgenstein on Miscalculation and the Foundations of Mathematics" (2022). Philosophy Faculty Publications. 98.