Wittgenstein and the Turning Point in the Philosophy of Mathematics

Preface


List of Abbreviations

1. Wittgenstein's Turning-Point


1. Philosophy's Debt to Schlick
2. Sceptical Confusions about Rule-following
3. Dispersing the Clouds of Epistemological Confusion

2. The Strains in the Realist/Anti-realist Framework


1. Wittgenstein's Verificationism
2. Wittgenstein's 'Conversion"
3. The Objectivity of Mathematical Knowledge

3. The Nature of Proof


1. The Burden of Proof
2. Observing the Law of Excluded Middle
3. Mathematical 'Stimuli'

4. Surveyability


1. The Bounds of Perspicuity
2. 'Probabilistic Proofs'
3. The Appel-Haken Solution of the Four-Colour Problem

5. The Perils of Prose


1. The Nature of Infinity
2. Coming to Grips with the Irrational
3. 'Prose': The Meeting-point Between Mathematics and Philosophy

6. Consistency


1. Hilbert's Programme
2. Mathematical Totems and Tabus
3. The Application of an 'Inconsistent System'

7. The Recovery of Certainty


1. The Foundations of the Foundations of Mathematics
2. Equations are Rules of Syntax
3. Unconventional Conventionalism

8. Freedom and Necessity


1. Discovering, Creating, Inventing
2. Anarchy versus Autonomy
3. The Interrelatedness of Mathematical Truths

Bibliography


Index