Some Remarks on Wittgenstein’s Philosophy of Mathematics - Open Journal of Philosophy

OJPP > Vol.10 No.1, February 2020

Some Remarks on Wittgenstein’s Philosophy of Mathematics ()

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DOI: 10.4236/ojpp.2020.101005 933 Downloads 3,365 Views

Author(s)

Richard Startup

Affiliation(s)

Honorary Research Fellow, Swansea University, Swansea, UK.

ABSTRACT

Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic issues and problems arising from Wittgenstein’s philosophy of mathematics are discussed. Topics have been so chosen as to assist mediation between the perspective of philosophers and that of mathematicians on their developing discipline. There is consideration of rules within arithmetic and geometry and Wittgenstein’s distinctive approach to number systems whether elementary or transfinite. Examples are presented to illuminate the relation between the meaning of an arithmetical generalisation or theorem and its proof. An attempt is made to meet directly some of Wittgenstein’s critical comments on the mathematical treatment of infinity and irrational numbers.

KEYWORDS

Wittgenstein, Philosophy of Mathematics, Rules, Number Systems, Theorem and Proof

Share and Cite:

Startup, R. (2020) Some Remarks on Wittgenstein’s Philosophy of Mathematics. Open Journal of Philosophy, 10, 45-65. doi: 10.4236/ojpp.2020.101005.

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