Wittgenstein's Philosophy of Mathematics

Wittgenstein's Philosophy of Mathematics

by Pasquale Frascolla

Paperback(Reprint)

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Overview

Wittgenstein's role was vital in establishing mathematics as one of this century's principal areas of philosophic inquiry. In this book, the three phases of Wittgenstein's reflections on mathematics are viewed as a progressive whole, rather than as separate entities. Frascolla builds up a systematic construction of Wittgenstein's representation of the role of arithmetic in the theory of logical operations. He also presents a new interpretation of Wittgenstein's rule-following considerations - the 'community view of internal relations'.

Product Details

ISBN-13: 9780415861960
Publisher: Taylor & Francis
Publication date: 10/31/2013
Edition description: Reprint
Pages: 198
Product dimensions: 6.10(w) x 9.10(h) x 0.70(d)

Table of Contents

Preface Abbreviations I. The Philosophy of Arithmetic of the Tractatus 1. Preliminaries 2. Systematic Exposition 3. The "Knowledge" of Forms: Vision and Calculation 4. Foundations of Mathematics (I) II. Verificationism and its Limits. The Intermediate Phase (1929-'33) 1. Introduction 2. Finite Cardinal Numbers: the Arithmetic of Strokes 3. Mathematical Propositions 4. The Mathematical Infinite 4.1 Quantifiers in Mathematics 4.2 Recursive Arithmetic and Algebra 4.3 Real Numbers 4.4 Set Theory 5. Foundations of Mathematics (II) III. From Facts to Concepts. The Later Writings on Mathematics (1934-'44) 1. The Crisis of Verificationism: Rule-Following 2. Mathematical Proofs as Paradigms 3. The Problem of Strict Finitism 4. Wittgenstein's Quasi-Revisionism 4.1 Cantor's Diagonal Proof and Transfinite Cardinals 4.2 The Law of Excluded Middle 4.3 Consistency References

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