Some Remarks on Wittgenstein’s Philosophy of Mathematics

摘要

Drawing mainly from the TractatusLogico-Philosophicus and his middle period writings, strategic issues andproblems arising from Wittgenstein’s philosophy of mathematics are discussed.Topics have been so chosen as to assist mediation between the perspective ofphilosophers and that of mathematicians on their developing discipline. Thereis consideration of rules within arithmetic and geometry and Wittgenstein’sdistinctive approach to number systems whether elementary or transfinite.Examples are presented to illuminate the relation between the meaning of anarithmetical generalisation or theorem and its proof. An attempt is made tomeet directly some of Wittgenstein’s critical comments on the mathematicaltreatment of infinity and irrational numbers.