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. The Reason's Proper Study 2 In Memory of 6 Preface and Acknowledgements 8 Contents 12 Origins of the Essays 14 Introduction 16 Part I Ontology and Abstraction Principles 44 1 Singular Terms (1) 46 2 Singular Terms (2) 63 3 Why Frege Does not Deserve His Grain of Salt99 87 4 Grundlagen 106 5 Implicit Definition and the A Priori 132 Part II Responses to Critics 166 6 Field and Fregean Platonism 168 7 Is Platonism Epistemologically Bankrupt? 184 8 Dummett's Critique of Wright's Attempt to Resuscitate Frege 204 9 Critical Notice of Michael Dummett's Frege: Philosophy of Mathematics 229 Part III Hume's Principle 242 10 On the Harmless Impredicativity of N= (Hume's Principle) 244 11 Response to Dummett 271 12 On the Philosophical Significance of Frege's Theorem 287 13 Is Hume's Principle Analytic? 322 Part IV On the Differentiation of Abstracts 348 14 To Bury Caesar . . . 350 Part V Beyond Number Theory 412 15 Reals by Abstraction 414 Postscript 436 Bibliography 452 Further Relevant Writings 459 Index 462 The,Reason's,Proper,Study Frege's analysis of language and the ontology that is based upon it-including, centrally, the argument which is at least implicit in Grundlagen for the existence of numbers as objects-presupposes the availability of criteria by means of which expressions functioning as proper names (in his broad sense-henceforth singular terms) may be recognized as such and distinguished from expressions of other kinds.