Wittgenstein's remarks on mathematics have not received the recogniยญ tion they deserve; they have for the most part been either ignored, or dismissed as unworthy of the author of the Tractatus and the I nvestigaยญ tions. This is unfortunate, I believe, and not at all fair, for these remarks are not only enjoyable reading, as even the harshest critics have conยญ ceded, but also a rich and genuine source of insight into the nature of mathematics. It is perhaps the fact that they are more suggestive than systematic which has put so many people off; there is nothing here of formal derivation and very little attempt even at sustained and organized argumentation. The remarks are fragmentary and often obscure, if one does not recognize the point at which they are directed. Nevertheless, there is much here that is good, and even a fairly systemยญ atic and coherent account of mathematics. What I have tried to do in the following pages is to reconstruct the system behind the often rather disconnected commentary, and to show that when the theory emerges, most of the harsh criticism which has been directed against these reยญ marks is seen to be without foundation. This is meant to be a symยญ pathetic account of Wittgenstein's views on mathematics, and I hope that it will at least contribute to a further reading and reassessment of his contributions to the philosophy of mathematics
CONTENT
I. Wittgenstein As Critic -- A. Platonism -- B. Intuitionism -- C. Formalism -- D. Empiricism -- E. Conventionalism -- F. Summary and Projection -- II. Wittgenstein as Creator -- A. Wittgenstein's Behavioral Theory of Inference -- B. The Role of Mathematics -- C. The theory as explanatory -- III. Critics of Wittgenstein -- A. Wittgenstein and Strict Finitism -- B. Wittgenstein and Objectivity -- C. Wittgenstein's Contributions -- Selected Bibliography
