Wittgenstein's Philosophy of Mathematics

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Wittgenstein played a vital role in establishing mathematics as one of this century's principal areas of philosophic inquiry. In this book, Pasquale Frascolla examines the three phases of Wittgenstein's reflections on mathematics, considering them as a progressive whole rather than as separate entities. Frascolla discusses the development of Wittgenstein's views on mathematics from the Tractatus up to 1944. He looks at the presentation of arithmetic in the theory of logical operations, the presence of a strong verificationist orientation and the rule-following considerations in Wittgenstein's writings. Frascolla identifies a unifying key--a ``quasi-formalism''--to the development of Wittgenstein's reflections on mathematics.
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Product Details

  • ISBN-13: 9780415024839
  • Publisher: Taylor & Francis
  • Publication date: 10/24/1994
  • Edition description: ANN
  • Pages: 200
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.56 (d)

Table of Contents

1 The Philosophy of Arithmetic of the Tractatus 1
Preliminaries 1
Systematic exposition 8
The "knowledge" of forms: vision and calculation 23
Foundations of mathematics I 33
2 Verificationism and its Limits: The intermediate phase 1929-33 42
Introduction 42
Finite cardinal numbers: the arithmetic of strokes 44
Mathematical propositions 54
The mathematical infinite 72
Foundations of mathematics II 99
3 From Facts to Concepts: The later writings on mathematics 1934-44 111
The crisis of verificationism: rule-following 111
Mathematical proofs as paradigms 128
The problem of strict finitism 142
Wittgenstein's quasi-revisionism 157
Notes 174
References 185
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