Volume 341 2009

Logicism, Intuitionism, and Formalism

What has Become of Them?

ISBN: 978-1-4020-8925-1 (Print) 978-1-4020-8926-8 (Online)

Table of contents (20 chapters)

  1. Front Matter

    Pages I-XII

  2. Introduction: The Three Foundational Programmes

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 1-23

      Introduction: The Three Foundational Programmes

  3. Logicism and Neo-Logicism

    1. Front Matter

      Pages 25-25

    2. No Access

      Book Chapter

      Pages 27-46

      Protocol Sentences for Lite Logicism

    3. No Access

      Book Chapter

      Pages 47-68

      Frege’s Context Principle and Reference to Natural Numbers

    4. No Access

      Book Chapter

      Pages 69-90

      The Measure of Scottish Neo-Logicism

    5. No Access

      Book Chapter

      Pages 91-125

      Natural Logicism via the Logic of Orderly Pairing

  4. Intuitionism and Constructive Mathematics

    1. Front Matter

      Pages 127-127

    2. No Access

      Book Chapter

      Pages 129-151

      A Constructive Version of the Lusin Separation Theorem

    3. No Access

      Book Chapter

      Pages 153-166

      Dini’s Theorem in the Light of Reverse Mathematics

    4. No Access

      Book Chapter

      Pages 167-187

      Journey into Apartness Space

    5. No Access

      Book Chapter

      Pages 189-207

      Relativization of Real Numbers to a Universe

    6. No Access

      Book Chapter

      Pages 209-219

      100 Years of Zermelo’s Axiom of Choice: What was the Problem with It?

    7. No Access

      Book Chapter

      Pages 221-236

      Intuitionism and the Anti-Justification of Bivalence

    8. No Access

      Book Chapter

      Pages 237-253

      From Intuitionistic to Point-Free Topology: On the Foundation of Homotopy Theory

    9. No Access

      Book Chapter

      Pages 255-275

      Program Extraction in Constructive Analysis

    10. No Access

      Book Chapter

      Pages 277-299

      Brouwer’s Approximate Fixed-Point Theorem is Equivalent to Brouwer’s Fan Theorem

  5. Formalism

    1. Front Matter

      Pages 301-301

    2. No Access

      Book Chapter

      Pages 303-355

      “Gödel’s Modernism: On Set-Theoretic Incompleteness,” Revisited

    3. No Access

      Book Chapter

      Pages 357-396

      Tarski’s Practice and Philosophy: Between Formalism and Pragmatism

    4. No Access

      Book Chapter

      Pages 397-433

      The Constructive Hilbert Program and the Limits of Martin-Löf Type Theory

    5. No Access

      Book Chapter

      Pages 435-448

      Categories, Structures, and the Frege-Hilbert Controversy: The Status of Meta-mathematics

    6. No Access

      Book Chapter

      Pages 449-483

      Beyond Hilbert’s Reach?

    7. No Access

      Book Chapter

      Pages 485-503

      Hilbert and the Problem of Clarifying the Infinite

  6. Back Matter

    Pages 505-512