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. |
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according already analysis apply argument arithmetic assert Axiom believe calculus called choice claim classes clear concept consists construction contains corresponds criticisms defined definition described determine discussed distinction Dummett elementary propositions equations equivalent example Excluded Middle existence expression extension fact finite finitist Foundations Frege function give given hypothesis idea identity important induction infinite infinity interpretation introduced intuitionist language later limitations logical mathematics means method names natural numbers notation notion objects operation passage phenomenological Philosophical physical picture position possible precisely presented Principia Mathematica proof propositions proved quantifiers question Ramsey Ramsey’s reading reason rejection relation remarks result rule Russell Russell’s seems sense sequences signs similar simply speak statement strict symbolism theorem theory thing thought tion Tractatus Logico-Philosophicus true truth understand variable Weyl Wittgenstein writings