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Truth, Proof and Infinity

A Theory of Constructive Reasoning

  • Book
  • © 1998

Overview

Authors:
  1. Peter Fletcher

    1. Department of Mathematics, Keele University, UK

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Part of the book series: Synthese Library (SYLI, volume 276)

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Table of contents (49 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Philosophical Foundations

    1. Introduction and Statement of the Problem

      • Peter Fletcher
      Pages 1-12

    2. What’s Wrong with Set Theory?

      • Peter Fletcher
      Pages 13-23

    3. What’s Wrong with Infinite Quantifiers?

      • Peter Fletcher
      Pages 24-40

    4. Abstraction and Idealisation

      • Peter Fletcher
      Pages 41-50

    5. What are Constructions?

      • Peter Fletcher
      Pages 51-69

    6. Truth and Proof of Logical Formulae

      • Peter Fletcher
      Pages 70-76

    7. The Need for a Theory of Constructions

      • Peter Fletcher
      Pages 77-81

    8. Theories of Constructions

      • Peter Fletcher
      Pages 82-97

    9. Hilbert’s Formalism

      • Peter Fletcher
      Pages 98-116

    10. Open-Endedness

      • Peter Fletcher
      Pages 117-127

    11. Analysis

      • Peter Fletcher
      Pages 128-139

  3. The Theory of Constructions

    1. Introduction to Part II

      • Peter Fletcher
      Pages 140-141

    2. Design of the Term Language

      • Peter Fletcher
      Pages 142-149

    3. The Term Language

      • Peter Fletcher
      Pages 150-161

    4. From the Term Language to the Expanded Term Language

      • Peter Fletcher
      Pages 162-198

    5. The Expanded Term Language

      • Peter Fletcher
      Pages 199-208

    6. The Protological Sequent Calculus

      • Peter Fletcher
      Pages 209-211

    7. Commentary on the Protological Axioms and Rules

      • Peter Fletcher
      Pages 212-215

    8. From Protologic to Expanded Protologic

      • Peter Fletcher
      Pages 216-230
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Keywords

About this book

Constructive mathematics is based on the thesis that the meaning of a mathematical formula is given, not by its truth-conditions, but in terms of what constructions count as a proof of it. However, the meaning of the terms `construction' and `proof' has never been adequately explained (although Kriesel, Goodman and Martin-Löf have attempted axiomatisations). This monograph develops precise (though not wholly formal) definitions of construction and proof, and describes the algorithmic substructure underlying intuitionistic logic. Interpretations of Heyting arithmetic and constructive analysis are given.
The philosophical basis of constructivism is explored thoroughly in Part I. The author seeks to answer objections from platonists and to reconcile his position with the central insights of Hilbert's formalism and logic.
Audience: Philosophers of mathematics and logicians, both academic and graduate students, particularly those interested in Brouwer and Hilbert; theoretical computer scientists interested in the foundations of functional programming languages and program correctness calculi.

Authors and Affiliations

  • Department of Mathematics, Keele University, UK

    Peter Fletcher

Bibliographic Information

  • Book Title: Truth, Proof and Infinity

  • Book Subtitle: A Theory of Constructive Reasoning

  • Authors: Peter Fletcher

  • Series Title: Synthese Library

  • DOI: https://doi.org/10.1007/978-94-017-3616-9

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media B.V. 1998

  • Hardcover ISBN: 978-0-7923-5262-4Published: 31 October 1998

  • Softcover ISBN: 978-90-481-5105-9Published: 07 December 2010

  • eBook ISBN: 978-94-017-3616-9Published: 29 June 2013

  • Series ISSN: 0166-6991

  • Series E-ISSN: 2542-8292

  • Edition Number: 1

  • Number of Pages: X, 470

  • Topics: Logic, Mathematical Logic and Foundations, Theory of Computation, Philosophy of Science

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