Epistemology versus Ontology

Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf

Editors:

ISBN: 978-94-007-4434-9 (Print) 978-94-007-4435-6 (Online)

Table of contents (17 chapters)

  1. Front Matter

    Pages i-xxvii

  2. PHILOSOPHY OF LOGIC AND MATHEMATICS

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-23

      Kant and Real Numbers

    3. No Access

      Book Chapter

      Pages 25-44

      Wittgenstein’s Diagonal Argument: A Variation on Cantor and Turing

    4. No Access

      Book Chapter

      Pages 45-67

      Truth and Proof in Intuitionism

    5. No Access

      Book Chapter

      Pages 69-85

      Real and Ideal in Constructive Mathematics

    6. No Access

      Book Chapter

      Pages 87-127

      In the Shadow of Incompleteness: Hilbert and Gentzen

    7. No Access

      Book Chapter

      Pages 129-138

      Evolution and Logic

    8. No Access

      Book Chapter

      Pages 139-159

      The “Middle Wittgenstein” and Modern Mathematics

    9. No Access

      Book Chapter

      Pages 161-180

      Primitive Recursive Arithmetic and Its Role in the Foundations of Arithmetic: Historical and Philosophical Reflections

  3. FOUNDATIONS

    1. Front Matter

      Pages 181-181

    2. No Access

      Book Chapter

      Pages 183-201

      Type Theory and Homotopy

    3. No Access

      Book Chapter

      Pages 203-213

      A Computational Interpretation of Forcing in Type Theory

    4. No Access

      Book Chapter

      Pages 215-241

      Program Testing and the Meaning Explanations of Intuitionistic Type Theory

    5. No Access

      Book Chapter

      Pages 243-263

      Normativity in Logic

    6. No Access

      Book Chapter

      Pages 265-279

      Constructivist Versus Structuralist Foundations

    7. No Access

      Book Chapter

      Pages 281-311

      Machine Translation and Type Theory

    8. No Access

      Book Chapter

      Pages 313-349

      Constructive Zermelo-Fraenkel Set Theory, Power Set, and the Calculus of Constructions

    9. No Access

      Book Chapter

      Pages 351-369

      Coalgebras as Types Determined by Their Elimination Rules

    10. No Access

      Book Chapter

      Pages 371-380

      Second Order Logic, Set Theory and Foundations of Mathematics

  4. Back Matter

    Pages 381-385