Wittgenstein, Finitism, and the Foundations of MathematicsMathieu 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. |
Contents
Logicism without Classes | 21 |
Arbitrary Functions | 48 |
Quantification and Finitism | 84 |
From TruthFunctional Logic to a Logic of Equations | 110 |
Philosophy and Logical Foundations | 147 |
The Continuum | 193 |
Strict Finitism | 213 |
| 237 | |
| 253 | |
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Common terms and phrases
according to Wittgenstein algorithm apply arithmetic assert Axiom of Choice Axiom of Infinity Borel Brouwer calculus choice sequences claim classes concept construction decimal Dedekind defined definition discussed Dummett elementary propositions ematics equations example Excluded Middle existence expression fact finite number Foundations of Mathematics Frascolla Frege functions in extension Gödel Goodstein Hilbert Hintikka hypothesis idea identity impredicativity infinite interpretation intuitionism intuitionist Kreisel Kronecker language Law of Excluded logical form math mathematical proposition means Michael Dummett negation notation notion objects operation passage phenomenological philosophy of mathematics physical Platonist Poincaré possible predicative prime numbers primitive recursive arithmetic Principia Mathematica propositional function quantifiers Ramsey Ramsey's real numbers recursive rejection result rule Russell Russell's Russellian Schlick and Waismann section 6.3 sense set theory Skolem statement strict finitism strict finitist symbolism tautology theorem tion Tractatus Logico Tractatus Logico-Philosophicus truth-functions variable Weyl Weyl's Wittgenstein's argument Wittgenstein's remarks