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

✍ Scribed by Mathieu Marion

• Publisher: Clarendon Press
• Year: 1999
• Tongue: English
• Leaves: 281
• Edition: 1
• Category: Library

✦ Synopsis

This pioneering book demonstrates the crucial importance of Wittgenstein's philosophy of mathematics to his philosophy as a whole. 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.

✦ Table of Contents

Contents
List of Abbreviations
1. Introduction: Wittgenstein's Anti-Platonism
2. Logicism without Classes
2.1. Operations and Arithmetic
2.2. Truth-Functions, Generality, and Infinity
2.3. Predicativity
3. Arbitrary Functions
3.1. Identity
3.2. Ramsey's Functions in Extension and the Axiom of Infinity
3.3. The Axiom of Choice and Numerical Equivalence
4. Quantification and Finitism
4.1. Weyl, Hilbert, and Ramsey
4.2. The New Logic of 1929
5. From Truth-Functional Logic to a Logic of Equations
5.1. Logical Form and Colour Exclusion
5.2. Assertions and Hypotheses
6. Philosophy and Logical Foundations
6.1. Intuitionism, Intentionality, Rules, and Decision Procedures
6.2. Excluded Middle and Existence
6.3. Formalism, Infinity, and Epistemic Limitations
7. The Continuum
7.1. Cauchy Sequences and the Diagonal Method
7.2. Choice Sequences and Dedekind Cuts
8. Strict Finitism
8.1. Dummett's Interpretation
8.2. Complexity
References
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
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W
Z