Harvard University Press, 1995 Cloth: 978-0-674-31942-4 | Paper: 978-0-674-31943-1 Library of Congress Classification QA8.6.F74 1995 Dewey Decimal Classification 510.1

ABOUT THIS BOOK | REVIEWS | TOC

ABOUT THIS BOOK

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.

REVIEWS

Scholarly, thorough, and well presented...This collection presents material that has important philosophical implications.
-- Gordon Baker Times Higher Education Supplement

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 Zentralblatt MATH

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.
-- Kenneth Manders, University of Pittsburgh

TABLE OF CONTENTS

Contents

Preface

Introduction

Demopoulos,
William

Appendix

Bell,
John L.

I.

The Intellectual Background to Frege's Logicism

1.

Kant, Bolzano and the Emergence of Logicism

Coffa,
Alberto

2.

Frege: The Last Logicist

Benacerraf,
Paul

3.

Frege and the Rigorization of Analysis

Demopoulos,
William

4.

Frege and Arbitrary Functions

Burgess,
John P.

5.

Frege: The Royal Road from Geometry

Wilson,
Mark

Postscript

II.

The Mathematical Content of Begriffsschrift and Grundlagen

6.

Reading the Begriffsschrift

Boolos,
George

7.

Frege's Theory of Number

Parsons,
Charles

Postscript

8.

The Consistency of Frege's Foundations of Arithmetic

Boolos,
George

9.

The Standard of Equality of Numbers

Boolos,
George

III.

Grundgesetze der Arithmetik

10.

The Development of Arithmetic in Frege's Grundgesetze der Arithmetik

Heck, Jr.,
Richard G.

Postscript

11.

Definition by Induction in Frege's Grundgesetze der Arithmetik

Heck, Jr.,
Richard G.

12.

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

Stein,
Howard

13.

Frege's Theory of Real Numbers

Simons,
Peter M.

14.

Frege's Theory of Real Numbers

Dummett,
Michael

15.

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

Neumann,
Peter M.

Adeleke,
S. A.

Dummett,
Michael

Postscript

16.

On the Consistency of the First-order Portion of Frege's Logical System

Harvard University Press, 1995 Cloth: 978-0-674-31942-4 Paper: 978-0-674-31943-1

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.

REVIEWS

Scholarly, thorough, and well presented...This collection presents material that has important philosophical implications.
-- Gordon Baker Times Higher Education Supplement

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 Zentralblatt MATH

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.
-- Kenneth Manders, University of Pittsburgh

TABLE OF CONTENTS

Contents

Preface

Introduction

Demopoulos,
William

Appendix

Bell,
John L.

I.

The Intellectual Background to Frege's Logicism

1.

Kant, Bolzano and the Emergence of Logicism

Coffa,
Alberto

2.

Frege: The Last Logicist

Benacerraf,
Paul

3.

Frege and the Rigorization of Analysis

Demopoulos,
William

4.

Frege and Arbitrary Functions

Burgess,
John P.

5.

Frege: The Royal Road from Geometry

Wilson,
Mark

Postscript

II.

The Mathematical Content of Begriffsschrift and Grundlagen

6.

Reading the Begriffsschrift

Boolos,
George

7.

Frege's Theory of Number

Parsons,
Charles

Postscript

8.

The Consistency of Frege's Foundations of Arithmetic

Boolos,
George

9.

The Standard of Equality of Numbers

Boolos,
George

III.

Grundgesetze der Arithmetik

10.

The Development of Arithmetic in Frege's Grundgesetze der Arithmetik

Heck, Jr.,
Richard G.

Postscript

11.

Definition by Induction in Frege's Grundgesetze der Arithmetik

Heck, Jr.,
Richard G.

12.

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

Stein,
Howard

13.

Frege's Theory of Real Numbers

Simons,
Peter M.

14.

Frege's Theory of Real Numbers

Dummett,
Michael

15.

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

Neumann,
Peter M.

Adeleke,
S. A.

Dummett,
Michael

Postscript

16.

On the Consistency of the First-order Portion of Frege's Logical System