TITLE:
Some Remarks on Wittgenstein’s Philosophy of Mathematics
AUTHORS:
Richard Startup
KEYWORDS:
Wittgenstein, Philosophy of Mathematics, Rules, Number Systems, Theorem and Proof
JOURNAL NAME:
Open Journal of Philosophy,
Vol.10 No.1,
January
3,
2020
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.