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  • Arithmetic and Ontology: A Non-Realist Philosophy of Arithmetic. Edited by Pieranna Garavaso

    Arithmetic and Ontology by Hugly, Philip; Sayward, Charles; Garavaso, Pieranna;

    A Non-Realist Philosophy of Arithmetic. Edited by Pieranna Garavaso

    Series: Poznań Studies in the Philosophy of the Sciences and the Humanities; 90;

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      • Publisher's listprice EUR 117.00
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    Product details:

    • Publisher BRILL
    • Date of Publication 1 January 2006

    • ISBN 9789042020474
    • Binding Hardback
    • No. of pages393 pages
    • Size 230x155 mm
    • Weight 788 g
    • Language English
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    Short description:

    This volume documents a lively exchange between five philosophers of mathematics. It also introduces a new voice in one central debate in the philosophy of mathematics. Non-realism, i.e., the view supported by Hugly and Sayward in their monograph, is an original position distinct from the widely known realism and anti-realism. Non-realism is characterized by the rejection of a central assumption shared by many realists and anti-realists, i.e., the assumption that mathematical statements purport to refer to objects. The defense of their main argument for the thesis that arithmetic lacks ontology brings the authors to discuss also the controversial contrast between pure and empirical arithmetical discourse. Colin Cheyne, Sanford Shieh, and Jean Paul Van Bendegem, each coming from a different perspective, test the genuine originality of non-realism and raise objections to it. Novel interpretations of well-known arguments, e.g., the indispensability argument, and historical views, e.g. Frege, are interwoven with the development of the authors? account. The discussion of the often neglected views of Wittgenstein and Prior provide an interesting and much needed contribution to the current debate in the philosophy of mathematics.

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    Long description:

    This volume documents a lively exchange between five philosophers of mathematics. It also introduces a new voice in one central debate in the philosophy of mathematics. Non-realism, i.e., the view supported by Hugly and Sayward in their monograph, is an original position distinct from the widely known realism and anti-realism. Non-realism is characterized by the rejection of a central assumption shared by many realists and anti-realists, i.e., the assumption that mathematical statements purport to refer to objects. The defense of their main argument for the thesis that arithmetic lacks ontology brings the authors to discuss also the controversial contrast between pure and empirical arithmetical discourse. Colin Cheyne, Sanford Shieh, and Jean Paul Van Bendegem, each coming from a different perspective, test the genuine originality of non-realism and raise objections to it. Novel interpretations of well-known arguments, e.g., the indispensability argument, and historical views, e.g. Frege, are interwoven with the development of the authors? account. The discussion of the often neglected views of Wittgenstein and Prior provide an interesting and much needed contribution to the current debate in the philosophy of mathematics.

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    Table of Contents:

    Acknowledgments
    Editor?s Introduction
    Philip HUGLY and Charles SAYWARD: Arithmetic and Ontology a Non
    -Realist Philosophy of Arithmetic
    Preface
    Analytical
    Chapter 1. Introduction
    Part One: Beginning with Frege
    Chapter 2. Notes to Grundlagen
    Chapter 3. Objectivism and Realism in Frege?s Philosophy of Arithmetic
    Part Two: Arithmetic and Non
    -Realism

    Chapter 4. The Peano Axioms
    Chapter 5. Existence, Number, and Realism
    Part Three: Necessity and Rules
    Chapter 6. Arithmetic and Necessity
    Chapter 7. Arithmetic and Rules
    Part Four: The Three Theses
    Chapter 8. Thesis One
    Chapter 9. Thesis Two
    Chapter 10. Thesis Three
    References
    Commentaries
    Colin Cheyne, Numbers, Reference, and Abstraction
    Sanford Shieh, What Is Non
    -Realism about Arithmetic?
    Jean Paul Van Bendegem, Non
    -Realism, Nominalism and Strict Fi
    -nitism. The Sheer Complexity of It All

    Replies to Commentaries
    Philip Hugly and Charles Sayward, Replies to Commentaries
    About the Contributors
    Index

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