The Reason's Proper Study
Essays towards a Neo-Fregean Philosophy of Mathematics
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Product details:
- Publisher OUP Oxford
- Date of Publication 13 November 2003
- ISBN 9780199266326
- Binding Paperback
- No. of pages472 pages
- Size 233x157x22 mm
- Weight 673 g
- Language English 0
Categories
Short description:
Bob Hale and Crispin Wright draw together here the key writings in which they have worked out their distinctive approach to the fundamental questions: what is mathematics about, and how do we know it? The volume features much new material: introduction, postscript, bibliographies, and a new essay on a key problem. The Reason's Proper Study is the strongest presentation yet of the controversial neo-Fregean view that mathematical knowledge may be based a priori on logic and definitional abstraction principles. It will prove indispensable reading not just to philosophers of mathematics but to all who are interested in the fundamental metaphysical and epistemological issues which the programme raises.
MoreLong description:
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.
Table of Contents:
Origins of the Essays
Introduction
I. Ontology and Abstraction Principles
Singular Terms (1)
Singular Terms (2)
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
Grundlagen 64
Implicit Definition and the A Priori
II. Responses to Critics
Field and Fregean Platonism
Is Platonism Epistemologically Bankrupt?
Dummett's Critique of Wright's Attempt to Resuscitate Frege
Critical Notice of Michael Dummett's Frege: Philosophy of Mathematics
III. Hume's Principle
On the Harmless Impredicativity of Hume's Principle
Response to Dummett
On the Philosophical Significance of Frege's Theorem
Is Hume's Principle Analytic?
IV. On the Differentiation of Abstracta
To Bury Caesar...
V. Beyond Number-theory
Reals by Abstraction
Postscript: Eighteen Problems
Bibliography
Bibliography of further relevant writings
Index
