Frege's Philosophy of Mathematics
Published on 25. March 1997
Book
Paperback/Softback
480 pages
978-0-674-31943-1 (ISBN)
Description
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.
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 / Votes
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 PittsburghMore details
Language
English
Place of publication
Cambridge, Mass
United States
Target group
College/higher education
Professional and scholarly
Illustrations
3 line illustrations
Dimensions
Height: 235 mm
Width: 162 mm
Weight
626 gr
ISBN-13
978-0-674-31943-1 (9780674319431)
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Schweitzer Classification
Person
William Demopoulos (1943-2017), editor of Frege's Philosophy of Mathematics and author of Logicism and Its Philosophical Legacy, spent nearly four decades as Professor of Philosophy at the University of Western Ontario.
Content
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