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, 1995

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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 has been elicited by the discovery of the mathematical properties of Frege's contextual definition of number and of the 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 re-evaluation 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.

目次

  • Introduction, William Demopoulos
  • appendix, John L. Bell. Part 1 The intellectual background to Frege's logicism: Kant, Bolzano and the emergence of logicism, Alberto Coffa
  • Frege - the last logicist, Paul Benacerraf
  • Frege and the rigorization of analysis, William Demopoulos
  • Frege and arbitrary functions, John P. Burgess
  • Frege - the royal road from geometry - postscript, Mark Wilson. Part 2 The mathematical content of Begriffsschrift and Grundlageng: Reading the Begriffsschrift, Geoge Boolos
  • Frege's Theory of number - postscript, Charles parsons
  • The consistency of Frege's "Foundation of arithmetics", George Boolos
  • The standard of equality of numbers, George Boolos. Part 3 Grundgesetze der arithmetik: The development of arithmetic in Frege's "Grundgesetze der arithmetik - postscript, Richard G. Heck, Jr. Definition by induction in Frege's Grundgesetze der arithmetik, Richard G. Heck, Jr.
  • Eudoxus and Dedekind - on the ancient Greek theory of ratios and its relation to modern mathematics, Howard Stein
  • Frege's theory of real numbers, Peter M. Simons
  • Frege's theory of real number, Michael Dummett
  • On a question of Frege's about right-ordered groups, - postscript, Peter M. Newmann et al
  • On the consistency of the first-order portion of Frege's logical system, Terence Parsons
  • Fregean extensions of first-order theories, John L. Bell
  • Saving Frege from contradiction, George Boolos.

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