A Review of Wittgenstein's View on Finitism in Mathematical Philosophy

The concept of infinity in mathematics was one of the main points of difference between the four schools of philosophy of mathematics in the early decades of twentieth century and it is really interesting to review this puzzling concept from a historical perspective. Four schools, Platonism, Formalism, Logicism, and Intuitionism tried to have an acceptable justification on the ontological aspect of infinite numbers and sets but it does not seem that any of them succeeded in their mission. Among these schools, Wittgenstein followed his own unique way and with his Socratic Method criticized all of them. Most commentators and critics believe that Wittgenstein had a finitistic account in the last period of his philosophical work. However, this essay by referring to his lectures on foundation of mathematics, Cambridge 1939, challenged their views and came up with Wittgenstein's criticism of finitistic account.