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Hilbert’s Program

An Essay on Mathematical Instrumentalism

  • Michael Detlefsen

Part of the Synthese Library book series (SYLI, volume 182)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Michael Detlefsen
    Pages 45-76
  3. Michael Detlefsen
    Pages 77-92
  4. Michael Detlefsen
    Pages 93-141
  5. Back Matter
    Pages 161-186

About this book

Introduction

Hilbert's Program was founded on a concern for the phenomenon of paradox in mathematics. To Hilbert, the paradoxes, which are at once both absurd and irresistible, revealed a deep philosophical truth: namely, that there is a discrepancy between the laws accord­ ing to which the mind of homo mathematicus works, and the laws governing objective mathematical fact. Mathematical epistemology is, therefore, to be seen as a struggle between a mind that naturally works in one way and a reality that works in another. Knowledge occurs when the two cooperate. Conceived in this way, there are two basic alternatives for mathematical epistemology: a skeptical position which maintains either that mind and reality seldom or never come to agreement, or that we have no very reliable way of telling when they do; and a non-skeptical position which holds that there is significant agree­ ment between mind and reality, and that their potential discrepan­ cies can be detected, avoided, and thus kept in check. Of these two, Hilbert clearly embraced the latter, and proposed a program designed to vindicate the epistemological riches represented by our natural, if non-literal, ways of thinking. Brouwer, on the other hand, opted for a position closer (in Hilbert's opinion) to that of the skeptic. Having decided that epistemological purity could come only through sacrifice, he turned his back on his classical heritage to accept a higher calling.

Keywords

design epistemology knowledge mathematics mind opera truth

Authors and affiliations

  • Michael Detlefsen
    • 1
  1. 1.Department of PhilosophyUniversity of Notre DameUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-7731-1
  • Copyright Information Springer Science+Business Media B.V. 1986
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-8420-0
  • Online ISBN 978-94-015-7731-1
  • Buy this book on publisher's site