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Mathematical Intuitionism and Intersubjectivity

A Critical Exposition of Arguments for Intuitionism

  • Book
  • © 1999

Overview

Authors:
  1. Tomasz Placek
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Part of the book series: Synthese Library (SYLI, volume 279)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    • Tomasz Placek
    Pages 1-16

  3. Brouwer’s Philosophy

    • Tomasz Placek
    Pages 17-102

  4. Heyting’s Arguments

    • Tomasz Placek
    Pages 103-146

  5. Dummett’s Case for Intuitionism

    • Tomasz Placek
    Pages 147-193

  6. Conclusions

    • Tomasz Placek
    Pages 194-196

  7. Back Matter

    Pages 197-220
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Keywords

About this book

In 1907 Luitzen Egbertus Jan Brouwer defended his doctoral dissertation on the foundations of mathematics and with this event the modem version of mathematical intuitionism came into being. Brouwer attacked the main currents of the philosophy of mathematics: the formalists and the Platonists. In tum, both these schools began viewing intuitionism as the most harmful party among all known philosophies of mathematics. That was the origin of the now-90-year-old debate over intuitionism. As both sides have appealed in their arguments to philosophical propositions, the discussions have attracted the attention of philosophers as well. One might ask here what role a philosopher can play in controversies over mathematical intuitionism. Can he reasonably enter into disputes among mathematicians? I believe that these disputes call for intervention by a philo­ sopher. The three best-known arguments for intuitionism, those of Brouwer, Heyting and Dummett, are based on ontological and epistemological claims, or appeal to theses that properly belong to a theory of meaning. Those lines of argument should be investigated in order to find what their assumptions are, whether intuitionistic consequences really follow from those assumptions, and finally, whether the premises are sound and not absurd. The intention of this book is thus to consider seriously the arguments of mathematicians, even if philosophy was not their main field of interest. There is little sense in disputing whether what mathematicians said about the objectivity and reality of mathematical facts belongs to philosophy, or not.

Bibliographic Information

  • Book Title: Mathematical Intuitionism and Intersubjectivity

  • Book Subtitle: A Critical Exposition of Arguments for Intuitionism

  • Authors: Tomasz Placek

  • Series Title: Synthese Library

  • DOI: https://doi.org/10.1007/978-94-015-9315-1

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1999

  • Hardcover ISBN: 978-0-7923-5630-1Published: 30 June 1999

  • Softcover ISBN: 978-90-481-5187-5Published: 06 December 2010

  • eBook ISBN: 978-94-015-9315-1Published: 09 March 2013

  • Series ISSN: 0166-6991

  • Series E-ISSN: 2542-8292

  • Edition Number: 1

  • Number of Pages: XII, 220

  • Topics: Philosophy of Science, History of Mathematical Sciences, Logic, Mathematical Logic and Foundations, Epistemology

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