Frege's Philosophy of Mathematics

Frege's Philosophy of Mathematics

by William Demopoulos
     
 

ISBN-10: 0674319427

ISBN-13: 9780674319424

Pub. Date: 01/28/1994

Publisher: Harvard University Press

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

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.

Product Details

ISBN-13:
9780674319424
Publisher:
Harvard University Press
Publication date:
01/28/1994
Pages:
480
Product dimensions:
6.75(w) x 9.61(h) x 1.15(d)

Table of Contents

Preface

Introduction William Demopoulos

Appendix John L. Bell

1. The Intellectual Background to flege's Logicism

1. Kant, Bolzano and the Emergence of Logicism Alberto Coffa

2. Frege: The Last Logicist Paul Benacerraf

3. Frege and the Rigorization of Analysis William Demopoulos

4. Frege and Arbitrary Functions John P. Burgess

5. Frege: The Royal Road from Geometry Postscript Mark Wilson

2. The Mathematical Content of Begriffsschrift and Grundlagen

6. Reading the Begriffsschrift George Boolos

7. Frege's Theory of Number Postscript Charles Parsons

8. The Consistency of Frege's Foundations of Arithmetic George Boolos

9. The Standard of Equality of Numbers George Boolos

3. Grundgesetze der Arithmetik

10. The Development of Arithmetic in Frege's Grundgesetze der Arithmetik

Postscript Richard C. Heck, Jr.

11. Definition by Induction in Frege's Grundgesetze der Arithmetik, Richard C. Heck, Jr.

12. Eudoxus and Dedekind: On the Ancient Greek Theory of Ratios and its Relation to Modern Mathematics Howard Stein

13. Frege's Theory of Real Numbers Peter M. Simons

14. Frege's Theory of Real Numbers Michael Dummett

15. On a Question of Frege's about Right-ordered Groups

Postscript Peter M. Neumann, S. A. Adeleke and Michael Dumrnett

16. On the Consistency of the First-order Portion of Frege's Logical System Terence Parsons

17. Fregean Extensions of First-order Theories John L. Bell

18. Saving Frege from Contradiction George Boolos

Index of Frege's Writings

General Index

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