Does Mathematics Need Foundations?

Wagner, Roy

doi:10.1007/978-3-030-15655-8_17

Cited by 5 publications

(1 citation statement)

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“…Some of these differences are too nuanced to be exposed here. For instance, while the later Wittgenstein's philosophy of mathematics has usually been characterized as antifoundationalist (Floyd 2021, p. 1;Grève and Mühlhölzer 2014;Rodych 1999), some suggesting this trait carries over from his middle phase (Rodych 2018), it has also been proposed that it is plurifoundationalist, while Lakatos deserves the anti-foundationalism label instead (Wagner 2019).…”

Section: Wittgenstein's Late Philosophy Ofmentioning

confidence: 99%

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

Pérez-Escobar

2022

KRITERION – Journal of Philosophy

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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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Section: Wittgenstein's Late Philosophy Ofmentioning

confidence: 99%