Wittgenstein, Finitism, and the Foundations of Mathematics

Mathieu Marion offers a careful, historically informed study of Wittgenstein's philosophy of mathematics. This area of his work has frequently been undervalued by Wittgenstein specialists and by philosophers of mathematics alike; but the surprising fact that he wrote more on this subject thanon any other indicates its centrality in his thought. Marion traces the development of Wittgenstein's thinking in the context of the mathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in adisjointed and incomplete way. In particular, he illuminates the work of the neglected 'transitional period' between the Tractatus and the Investigations. Marion shows that study of Wittgenstein's writings on mathematics is essential to a proper understanding of his philosophy; and he alsodemonstrates that it has much to contribute to current debates about the foundations of mathematics.

'Marion's book is an important contribution to the small but growing body of literature on Wittgenstein's philosophy of mathematics. Its value lies especially in the advance it makes over previous work in situating Wittgenstein's philosophy of mathematics not only in its philosophical, butalso its mathematical context ... a welcome addition to the literature.'Mark A.Joseph

'fine historical study ... Marion tells an interesting and convinving story. He carefully identifies both the continuities and the discontinuities in the evolution of Wittgenstein's ideas, and makes good sense of each ... Marion's book is certainly to be recommended both for its exegesis and,through its compelling presentation of these ideas, for its contribution to the philosophy of mathematics.'A W Moore, Studia Logica