The problem of the foundations of mathematics in Wittgenstein

A major part of the studies on Wittgenstein's philosophy is related with his understanding of logic and language. There are also few studies on his understanding of religion, art and mind. However, studies on Wittgenstein's philosophy of mathematics are even less in number although Wittgenstein said that his chief contribution to philosophy was in the area of the philosophy of mathematics. In this dissertation, Wittgenstein's philosophical discourse in the first and second period of his philosophy was discussed in relation with the discussions of the philosophy of mathematics. There are two aspects of the study. First of these is to expose Wittgenstein's philosophy of mathematics in both periods. Second aspect of this study is to criticize Wittgenstein's philosophy of mathematics through our approach of the philosophy of mathematics. Main idea of this criticism is this; the mathematical framework that is structured through formal objects and formal relations in Tractatus, and finitistic mathematics that Wittgenstein adopted in his second period writings is insufficient to encompass the whole of mathematics.