The Arché Papers on the Mathematics of Abstraction

Editors:

ISBN: 978-1-4020-4264-5 (Print) 978-1-4020-4265-2 (Online)

Table of contents (20 chapters)

  1. Front Matter

    Pages i-xxxvii

  2. The Philosophy and Mathematics of Hume’s Principle

    1. No Access

      Book Chapter

      Pages 3-15

      Is Hume’s Principle Analytic?

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      Book Chapter

      Pages 17-43

      Is Hume’s Principle Analytic?

    3. No Access

      Book Chapter

      Pages 45-60

      Frege, Neo-Logicism and Applied Mathematics

    4. No Access

      Book Chapter

      Pages 61-84

      Finitude and Hume’s Principle

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      Book Chapter

      Pages 85-93

      On Finite Hume

    6. No Access

      Book Chapter

      Pages 95-104

      Could Nothing Matter?

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      Book Chapter

      Pages 105-115

      On the Philosophical Interest of Frege Arithmetic

  3. The Logic of Abstraction

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      Book Chapter

      Pages 119-146

      “Neo-Logicist” Logic is not Epistemically Innocent

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      Book Chapter

      Pages 147-153

      Aristotelian Logic, Axioms, and Abstraction

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      Book Chapter

      Pages 155-172

      Frege’s Unofficial Arithmetic

  4. Abstraction and the Continuum

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      Book Chapter

      Pages 175-196

      Reals by Abstraction

    2. No Access

      Book Chapter

      Pages 197-218

      The State of the Economy: Neo-Logicism and Inflation

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      Book Chapter

      Pages 219-252

      Frege Meets Dedekind: A Neo-Logicist Treatment of Real Analysis

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      Book Chapter

      Pages 253-272

      Neo-Fregean Foundations for Real Analysis: Some Reflections on Frege’s Constraint

  5. Basic Law V and Set Theory

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      Book Chapter

      Pages 275-302

      New V, ZF, and Abstraction

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      Book Chapter

      Pages 303-329

      Well- and Non-Well-Founded Fregean Extensions

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      Book Chapter

      Pages 331-352

      Abstraction & Set Theory

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      Book Chapter

      Pages 353-382

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

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      Book Chapter

      Pages 383-420

      Neo-Fregeanism: An Embarrassment of Riches

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      Book Chapter

      Pages 421-454

      Iteration one More Time