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

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.

Origins of the Essays, Introduction,. Part 1: Ontology and Abstraction Principles. 1: Bob Hale: Singular Terms (1), 2: Bob Hale: Singular Terms (2), 3: Crispin Wright: 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: Bob Hale: Grundlagen 64, 5: Bob Hale and Crispin Wright: Implicit Definition and the A Priori,. Part 2: Responses to Critics. 6: Crispin Wright: Field and Fregean Platonism, 7: Bob Hale: Is Platonism Epistemologically Bankrupt?, 8: Bob Hale: Dummett's Critique of Wright's Attempt to Resuscitate Frege, 9: Crispin Wright: Critical Notice of Michael Dummett's Frege: Philosophy of Mathematics,. Part 3: Hume.s Principle, 10: Crispin Wright: On the Harmless Impredicativity of Hume's Principle, 11: Crispin Wright: Response to Dummett, 12: Crispin Wright: On the Philosophical Significance of Frege's Theorem, 13: Crispin Wright: Is Hume's Principle Analytic?,. Part 4: On the Differentiation of Abstracta. 14: Bob Hale and Crispin Wright: To Bury Caesar.,. Part 5: Beyond Number.theory, 15: Bob Hale: Reals by Abstraction, Postscript: Eighteen Problems, Bibliography, Bibliography of further relevant writings, Index