Wittgenstein on the Philosophy of Mathematics

My main area of concern is Wittgenstein's philosophy of mathematics, primarily as it is expressed in his Remarks On The Foundations of Mathematics . There is considerable controversy regarding the extent to which Wittgenstein understood the mathematical content of the views which he criticizes; among my primary aims will be an attempt to evaluate the degree to which he is faithful to the main theorems with which he deals. A number of approaches to the philosophy of mathematics will emerge in this examination of Wittgenstein's remarks, and I will be concerned to argue that these approaches can be effectively unified within the Wittgensteinian conception of a language-game; indeed, I shall argue that mathematics is most properly viewed as a collection of language-games; related to each other along the now familiar lines of "family resemblance"