Showing Mathematical Flies the Way Out of Foundational Bottles: The Later Wittgenstein as a Forerunner of Lakatos and the Philosophy of Mathematical Practice

Kriterion – Journal of Philosophy 36 (2):157-178 (2022)
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Abstract

This work explores the later Wittgenstein’s philosophy of mathematics in relation to Lakatos’ philosophy of mathematics and the philosophy of mathematical practice. I argue that, while the philosophy of mathematical practice typically identifies Lakatos as its earliest of predecessors, the later Wittgenstein already developed key ideas for this community a few decades before. However, for a variety of reasons, most of this work on philosophy of mathematics has gone relatively unnoticed. Some of these ideas and their significance as precursors for the philosophy of mathematical practice will be presented here, including a brief reconstruction of Lakatos’ considerations on Euler’s conjecture for polyhedra from the lens of late Wittgensteinian philosophy. Overall, this article aims to challenge the received view of the history of the philosophy of mathematical practice and inspire further work in this community drawing from Wittgenstein’s late philosophy.

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References found in this work

The unreasonable effectiveness of mathematics in the natural sciences.Eugene Wigner - 1960 - Communications in Pure and Applied Mathematics 13:1-14.
Mathematical Knowledge and the Interplay of Practices.José Ferreirós - 2015 - Princeton, USA: Princeton University Press.
Indispensability and Practice.Penelope Maddy - 1992 - Journal of Philosophy 89 (6):275.
Wittgenstein's philosophy of mathematics.Michael Dummett - 1959 - Philosophical Review 68 (3):324-348.

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