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

    The Reason's Proper Study by Hale, Bob; Wright, Crispin;

    Essays towards a Neo-Fregean Philosophy of Mathematics

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    A termék adatai:

    • Kiadó OUP Oxford
    • Megjelenés dátuma 2003. november 13.

    • ISBN 9780199266326
    • Kötéstípus Puhakötés
    • Terjedelem472 oldal
    • Méret 233x157x22 mm
    • Súly 673 g
    • Nyelv angol
    • 0

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    Rövid leírás:

    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.

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    Hosszú leírás:

    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.

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    Tartalomjegyzék:

    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

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