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© 1986

Hilbert’s Program

An Essay on Mathematical Instrumentalism

Book

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

  1. 1.Department of PhilosophyUniversity of Notre DameUSA

Bibliographic information

  • Book Title Hilbert’s Program
  • Book Subtitle An Essay on Mathematical Instrumentalism
  • Authors M. Detlefsen
  • Series Title Synthese Library
  • 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
  • Hardcover ISBN 978-90-277-2151-8
  • Softcover ISBN 978-90-481-8420-0
  • eBook ISBN 978-94-015-7731-1
  • Edition Number 1
  • Number of Pages XIV, 186
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Logic
    History of Mathematical Sciences
    Mathematical Logic and Foundations
  • Buy this book on publisher's site

Reviews

`The book is well written and recommended reading for everyone interested in the philosophical dimensions of technical results from foundations of mathematics and pure logic.'
S. Gottwald, Zentralblatt für Mathematik und ihre Grenzgebiete, Vol. 641.