Wittgenstein's Philosophy of Mathematics / Edition 1

by V.H. Klenk

Overview

Wittgenstein's remarks on mathematics have not received the recognition they deserve; they have for the most part been either ignored, or dismissed as unworthy of the author of the Tractatus and the I nvestiga­ 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 con­ 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 system­ 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 re­ marks is seen to be without foundation. This is meant to be a sym­ 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.

Product Details

ISBN-13:	9789024718429
Publisher:	Springer Netherlands
Publication date:	09/30/1976
Edition description:	Softcover reprint of the original 1st ed. 1976
Pages:	128
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

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.- 1. Mathematics as a Technique.- 2. Inference and Behavior.- 3. Agreement.- 4. Convention and Compulsion.- B. The Role of Mathematics.- 1. Mathematics and Empirical Language.- 2. Concept-Formation.- 3. Concept-Formation and Compulsion.- 4. Wittgenstein’s Earlier Theory.- C. The theory as explanatory.- III. Critics of Wittgenstein.- A. Wittgenstein and Strict Finitism.- 1. Wittgenstein and Non-finitary Mathematics.- 2. Wittgenstein and Meta-mathematics.- 3. Wittgenstein and Elementary Mathematics.- B. Wittgenstein and Objectivity.- C. Wittgenstein’s Contributions.- Selected Bibliography.