The Reason's Proper Study : Essays Towards a Neo-Fregean Philosophy of Mathematics

here, Bob Hale And Crispin Wright Assemble The Key Writings That Lead To Their Distinctive Neo-fregean Approach To 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 Program And The Contributions Made To It By The Various Papers; A Section Explaining Which Issues Most Require Further Attention; And Bibliographies Of References And Further Useful Sources. It Will Be Recognized As The Most Powerful Presentation Yet Of A Neo-fregean Program. 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. CONTENTS ORIGINS OF THE ESSAYS INTRODUCTION 1. Singular Terms (1) HALE 2. Singular Terms (2) HALE 3. Why Frege Does Not Deserve His Grain of Salt WRIGHT 4. Grundlagen #64 HALE 5. Implicit Definition and the A Priori HALE AND WRIGHT 6. Field and Fregean Platonism WRIGHT 7. Is Platonism Epistemologically Bankrupt? HALE 8. Dummett’s Critique of Wright’s Attempt to Resuscitate Frege HALE 9. Critical Notice of Michael Dummett’s Philosophy of Mathematics Frege WRIGHT 10. On the Harmless Impredicativity of N= (Hume’s Principle) WRIGHT 11. Response to Dummett WRIGHT 12. On the Philosophical Significance of Frege’s Theorem WRIGHT 13. Is Hume’s Principle Analytic? WRIGHT 14. To Bury Caesar... HALE and WRIGHT 15. Reals by Abstraction HALE POSTSCRIPT BIBLIOGRAPHY INDEX Addresses fundamental questions: What is mathematics about, and, How do we know it? This work features introduction, postscript, bibliographies, and an essay on a key problem. It offers a presentation of the controversial neo-Fregean view that mathematical knowledge may be based a priori on logic and definitional abstraction principles. There are two main ingredients in Frege's philosophy of mathematics-or more exactly, in his philosophy of Arithmetic (in his sense of 'Arithmetic', in which it covers both elementary number theory and analysis).