Wittgenstein, Finitism, and the Foundations of Mathematics (Oxford Philosophical Monographs)

✍ Scribed by Mathieu Marion

• Publisher: Clarendon Press • Oxford
• Year: 1998
• Tongue: English
• Leaves: 282
• Series: Oxford Philosophical Monographs
• Edition: Second Edition
• Category: Library

✦ Synopsis

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 than on 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 a disjointed 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 also demonstrates that it has much to contribute to current debates about the foundations of mathematics.

✦ Table of Contents

Cover......Page 1
Title Page......Page 5
Preface......Page 9
Acknowledgements......Page 16
Contents......Page 19
List of Abbreviations......Page 21
1. Introduction: Wittgenstein’s Anti-Platonism......Page 23
2.1. Operations and Arithmetic......Page 43
2.2. Truth-Functions, Generality, and Infinity......Page 51
2.3. Predicativity......Page 60
3.1. Identity......Page 70
3.2. Ramsey's Functions in Extension and the Axiom of Infinity......Page 77
3.3. The Axiom of Choice and Numerical Equivalence......Page 94
4.1. Weyl, Hilbert, and Ramsey......Page 106
4.2. The New Logic of 1929......Page 116
5.1. Logical Form and Colour Exclusion......Page 132
5.2. Assertions and Hypotheses......Page 150
6.1. Intuitionism, Intentionality, Rules, and Decision Procedures......Page 169
6.2. Excluded Middle and Existence......Page 184
6.3. Formalism, Infinity, and Epistemic Limitations......Page 197
7.1. Cauchy Sequences and the Diagonal Method......Page 215
7.2. Choice Sequences and Dedekind Cuts......Page 224
8.1. Dummett's Interpretation......Page 235
8.2. Complexity......Page 250
References......Page 259
Index......Page 275