Arithmetic and ontology : : a non-realist philosophy of arithmetic / / Philip Hugly and Charles Sayward ; edited by Pieranna Garavaso.

• Superior document: Poznań studies in the philosophy of the sciences and the humanities, Monographs-in-debate v. 90.
• Author: Hugly, Philip.
• TeilnehmendeR: Sayward, Charles.; Garavaso, Pieranna.
• Place / Publishing House: Amsterdam : : Rodopi,, 2006.
• Year of Publication: 2006
• Language: English
• Series: Poznań Studies in the Philosophy of the Sciences and the Humanities 90.
• Physical Description: 1 online resource (393 pages).
• Notes: Includes commentaries by Colin Cheyne, Sanford Shieh, and Jean Paul Van Bendegen and replies by the authors to the commentaries.; Includes index.

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, id est, 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, id est, 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.

Table of Contents

Preliminary Material / Philip Hugly , Charles Sayward and Pieranna Garavaso -- ACKNOWLEDGMENTS / Philip Hugly , Charles Sayward and Pieranna Garavaso -- EDITOR’S INTRODUCTION / Philip Hugly , Charles Sayward and Pieranna Garavaso -- ARITHMETIC AND ONTOLOGY: A NON-REALIST PHILOSOPHY OF ARITHMETIC -- ANALYTICAL TABLE OF CONTENTS / Philip Hugly , Charles Sayward and Pieranna Garavaso -- INTRODUCTION / Philip Hugly , Charles Sayward and Pieranna Garavaso -- NOTES TO GRUNDLAGEN / Philip Hugly , Charles Sayward and Pieranna Garavaso -- OBJECTIVISM AND REALISM IN FREGE’S PHILOSOPHY OF ARITHMETIC / Philip Hugly , Charles Sayward and Pieranna Garavaso -- THE PEANO AXIOMS / Philip Hugly , Charles Sayward and Pieranna Garavaso -- EXISTENCE, NUMBER, AND REALISM / Philip Hugly , Charles Sayward and Pieranna Garavaso -- ARITHMETIC AND NECESSITY / Philip Hugly , Charles Sayward and Pieranna Garavaso -- ARITHMETIC AND RULES / Philip Hugly , Charles Sayward and Pieranna Garavaso -- THESIS ONE / Philip Hugly , Charles Sayward and Pieranna Garavaso -- THESIS TWO / Philip Hugly , Charles Sayward and Pieranna Garavaso -- THESIS THREE / Philip Hugly , Charles Sayward and Pieranna Garavaso -- REFERENCES / Philip Hugly , Charles Sayward and Pieranna Garavaso -- NUMBERS, REFERENCE, AND ABSTRACTION / Colin Cheyne -- WHAT IS NON-REALISM ABOUT ARITHMETIC? / Sanford Shieh -- NON-REALISM, NOMINALISM AND STRICT FINITISM THE SHEER COMPLEXITY OF IT ALL / Jean Paul Van Bendegem -- REPLIES TO COMMENTARIES -- ABOUT THE CONTRIBUTORS / Philip Hugly , Charles Sayward and Pieranna Garavaso -- INDEX / Philip Hugly , Charles Sayward and Pieranna Garavaso -- POZNAŃ STUDIES / Philip Hugly , Charles Sayward and Pieranna Garavaso.