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The Arché Papers on the Mathematics of Abstraction

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  • © 2007

Overview

Editors:
  1. Roy T. Cook
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  • Comprises a survey of the philosophical and technical work being done at Arché: The AHRB Centre for the Philosophy of Logic, Language, Mathematics, and Mind at the University of St Andrews
  • Provides an overview of the Neo-Fregean position in philosophy of mathematics
  • Collects together hard to find material on Neo-Fregean set theory and real analysis
  • Contains papers by distinguished philosophers of mathematics, including George Boolos, William Demopoulos, Bob Hale, Richard Heck, Crispin Wright, Stewart Shapiro, and rising stars such as Roy T. Cook, Agustin Rayo, and Gabriel Uzquiano
  • Contains a preface by Crispin Wright

Part of the book series: The Western Ontario Series in Philosophy of Science (WONS, volume 71)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xxxvii
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  2. The Philosophy and Mathematics of Hume’s Principle

    1. Is Hume’s Principle Analytic?

      • George Boolos
      Pages 3-15

    2. Is Hume’s Principle Analytic?

      • Crispin Wright
      Pages 17-43

    3. Frege, Neo-Logicism and Applied Mathematics

      • Peter Clark
      Pages 45-60

    4. Finitude and Hume’s Principle

      • Richard G. Heck Jr
      Pages 61-84

    5. On Finite Hume

      • Fraser MacBride
      Pages 85-93

    6. Could Nothing Matter?

      • Fraser MacBride
      Pages 95-104

    7. On the Philosophical Interest of Frege Arithmetic

      • William Demopoulos
      Pages 105-115

  3. The Logic of Abstraction

    1. “Neo-Logicist” Logic is not Epistemically Innocent

      • Stewart Shapiro, Alan Weir
      Pages 119-146

    2. Aristotelian Logic, Axioms, and Abstraction

      • Roy T. Cook
      Pages 147-153

    3. Frege’s Unofficial Arithmetic

      • A. Rayo
      Pages 155-172

  5. Basic Law V and Set Theory

    1. New V, ZF, and Abstraction

      • Stewart Shapiro, Alan Weir
      Pages 275-302

    2. Well- and Non-Well-Founded Fregean Extensions

      • Ignacio Jané, Gabriel Uzquiano
      Pages 303-329

    3. Abstraction & Set Theory

      • Bob Hale
      Pages 331-352

    4. Prolegomenon to Any Future Neo-Logicist Set Theory: Abstraction and Indefinite Extensibility

      • Stewart Shapiro
      Pages 353-382

    5. Neo-Fregeanism: An Embarrassment of Riches

      • A. Weir
      Pages 383-420
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About this book

InSeptember2000theArchéCentrelauncheda ve-yearresearchprojecten- tled the Logical and Metaphysical Foundations of Classical Mathematics. Its goal was to study the prospects, philosophical and technical, for abstractionist foundations for the classical mathematical theories of the natural, real and complex numbers and standard set theory. Funding was provided by the then Arts and Humanities Research Board (now the Arts and Humanities Research Council) for the appointment of full-time postdoctoral research fellows and PhD students to collaborate with more senior colleagues in the project, and at the same time the British Academy awarded the Centre additional resources to establish an International Network of scholars to be associated with the work. This was the beginning of the serial ‘Abstraction workshops’ of which the Centre had staged no less than eleven by December 2006. We gra- fully acknowledge the generous support of the Academy and Council, sine qua non. The project seminars and Network meetings generated—and continue to generate—a large number of leading-edge research papers on all aspects of the project agenda. The present volume is the rst of what we hope will be a number of anthologies of these researches. With two exceptions,—the contribution by the late George Boolos and the co-authored paper by Gabriel Uzquiano and Ignacio Jané,—the papers that Roy Cook has collected in the present volume are all authored by sometime members of the project team or of the British Academy Network.

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