The reason's proper study : essays towards a neo-Fregean philosophy of mathematics

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The reason's proper study : essays towards a neo-Fregean philosophy of mathematics

Bob Hale and Crispin Wright

Clarendon Press , Oxford University Press, 2001

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注記

Includes bibliographical references (p. [437]-446) and index

内容説明・目次

内容説明

Bob Hale and Crispin Wright draw together here the key writings in which they have worked out their distinctive neo-Fregean approach to the philosophy of mathematics. The two main components in Frege's mathematical philosophy were his platonism and his logicism -- the claims, respectively, that mathematics is a body of knowledge about independently existing objects, and that this knowledge may be acquired on the basis of general logical laws and suitable definitions. The central thesis of this collection is that Frege was -- his own eventual recantation notwithstanding -- substantially right in both claims. Where neo-Fregeanism principally differs from Frege is in taking a more optimistic view of the kind of contextual explanation (proceeding via what are now commonly called abstraction principles) of the fundamental concepts of arithmetic and analysis which Frege considered and rejected. On this basis, neo-Fregeanism promises defensible and attractive answers to some of the most important ontological and epistemological questions in the philosophy of mathematics. In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the programme and the contributions made to it by the various papers; a postscript explaining which issues most require further attention; and bibliographies both of references and of further useful sources. The Reason's Proper Study will be recognized as the most powerful presentation yet of the neo-Fregean programme; it will prove indispensable reading not just to philosophers of mathematics but to all who are interested in the fundamental metaphysical and epistemological issues on which the programme impinges.

目次

  • Origins of the Essays
  • Introduction
  • I. ONTOLOGY AND ABSTRACTION PRINCIPLES
  • 1. Singular Terms (1)
  • 2. Singular Terms (2)
  • 3. Why Frege Does Not Deserve His Grain of Salt: A Note on the Paradox of 'The Concept Horse' and the Ascription of Bedeutungen to Predicates
  • 4. Grundlagen 64
  • 5. Implicit Definition and the A Priori
  • II. RESPONSES TO CRITICS
  • 6. Field and Fregean Platonism
  • 7. Is Platonism Epistemologically Bankrupt?
  • 8. Dummett's Critique of Wright's Attempt to Resuscitate Frege
  • 9. Crispin Wright: Critical Notice of Michael Dummett's Frege: Philosophy of
  • MATHEMATICS
  • III. HUME'S PRINCIPLE
  • 10. On the Harmless Impredicativity of Hume's Principle
  • 11. Response to Dummett
  • 12. On the Philosophical Significance of Frege's Theorem
  • 13. Is Hume's Principle Analytic?
  • IV. ON THE DIFFERENTIATION OF ABSTRACTA
  • 14. To Bury Caesar..
  • V. BEYOND NUMBER-THEORY
  • 15. Reals by Abstraction
  • Postscript: Eighteen Problems
  • Bibliography
  • Bibliography of further relevant writings
  • Index

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