Freges Philosophy Of Mathematics / Edition 1

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Overview

Widespread interest in Frege's general philosophical writings is, relatively speaking, a fairly recent phenomenon. But it is only very recently that his philosophy of mathematics has begun to attract the attention it now enjoys. This interest has been elicited by the discovery of the remarkable mathematical properties of Frege's contextual definition of number and of the unique character of his proposals for a theory of the real numbers.

This collection of essays addresses three main developments in recent work on Frege's philosophy of mathematics: the emerging interest in the intellectual background to his logicism; the rediscovery of Frege's theorem; and the reevaluation of the mathematical content of The Basic Laws of Arithmetic. Each essay attempts a sympathetic, if not uncritical, reconstruction, evaluation, or extension of a facet of Frege's theory of arithmetic. Together they form an accessible and authoritative introduction to aspects of Frege's thought that have, until now, been largely missed by the philosophical community.

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Editorial Reviews

Times Higher Education Supplement

Scholarly, thorough, and well presented...This collection presents material that has important philosophical implications.
— Gordon Baker

Zentralblatt MATH

This is clearly the best collection of articles on Frege's philosophy of mathematics in existence today. It is also (unlike many collections of articles that are published these days) practically very useful. It serves as an excellent introduction to what is the liveliest part of Frege scholarship today, and to what has become an important sub-field of contemporary philosophy of mathematics, namely the understanding and assessment of the logistic project.
— Leon Horsten

Times Higher Education Supplement - Gordon Baker
Scholarly, thorough, and well presented...This collection presents material that has important philosophical implications.
Zentralblatt MATH - Leon Horsten
This is clearly the best collection of articles on Frege's philosophy of mathematics in existence today. It is also (unlike many collections of articles that are published these days) practically very useful. It serves as an excellent introduction to what is the liveliest part of Frege scholarship today, and to what has become an important sub-field of contemporary philosophy of mathematics, namely the understanding and assessment of the logistic project.
Kenneth Manders
Distinctive, indeed, unique, in its concentration on the formal argument in Frege's work. There is no other secondary work in any form which engages the formal argument through the whole of Frege's project. These essays motivate the work, and locate it philosophically, rendering it independent of other secondary sources.
Zentralblatt MATH
This is clearly the best collection of articles on Frege's philosophy of mathematics in existence today. It is also (unlike many collections of articles that are published these days) practically very useful. It serves as an excellent introduction to what is the liveliest part of Frege scholarship today, and to what has become an important sub-field of contemporary philosophy of mathematics, namely the understanding and assessment of the logistic project.
— Leon Horsten
Times Higher Education Supplement
Scholarly, thorough, and well presented...This collection presents material that has important philosophical implications.
— Gordon Baker
Read More Show Less

Product Details

  • ISBN-13: 9780674319431
  • Publisher: Harvard University Press
  • Publication date: 3/25/1997
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 480
  • Product dimensions: 6.69 (w) x 9.61 (h) x 0.97 (d)

Meet the Author

William Demopoulos is Professor of Philosophy, University of Western Ontario.
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Table of Contents

Preface
Introduction 1
Appendix 21
1 Kant, Bolzano and the Emergence of Logicism 29
2 Frege: The Last Logicist 41
3 Frege and the Rigorization of Analysis 68
4 Frege and Arbitrary Functions 89
5 Frege: The Royal Road from Geometry 108
Postscript 149
6 Reading the Begriffsschrift 163
7 Frege's Theory of Number 182
Postscript 208
8 The Consistency of Frege's Foundations of Arithmetic 211
9 The Standard of Equality of Numbers 234
10 The Development of Arithmetic in Frege's Grundgesetze der Arithmetik 257
Postscript 288
11 Definition by Induction in Frege's Grundgesetze der Arithmetik 295
12 Eudoxus and Dedekind: On the Ancient Greek Theory of Ratios and its Relation to Modern Mathematics 334
13 Frege's Theory of Real Numbers 358
14 Frege's Theory of Real Numbers 386
15 On a Question of Frege's about Right-ordered Groups 405
Postscript 418
16 On the Consistency of the First-order Portion of Frege's Logical System 422
17 Fregean Extensions of First-order Theories 432
18 Saving Frege from Contradiction 438
Index of Frege's Writings 453
General Index 457
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