Frege's philosophy of mathematics

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書誌事項

Frege's philosophy of mathematics

edited by William Demopoulos

Harvard University Press, 1997

  • : pbk

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注記

Includes bibliographical references and indexes

内容説明・目次

内容説明

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.

目次

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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