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Mechanism, Mentalism and Metamathematics

An Essay on Finitism

  • Judson Chambers Webb

Part of the Synthese Library book series (SYLI, volume 137)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Judson Chambers Webb
    Pages 1-32
  3. Judson Chambers Webb
    Pages 33-71
  4. Judson Chambers Webb
    Pages 72-174
  5. Judson Chambers Webb
    Pages 175-243
  6. Judson Chambers Webb
    Pages 244-247
  7. Back Matter
    Pages 248-285

About this book

Introduction

This book grew out of a graduate student paper [261] in which I set down some criticisms of J. R. Lucas' attempt to refute mechanism by means of G6del's theorem. I had made several such abortive attempts myself and had become familiar with their pitfalls, and especially with the double­ edged nature of incompleteness arguments. My original idea was to model the refutation of mechanism on the almost universally accepted G6delian refutation of Hilbert's formalism, but I kept getting stuck on questions of mathematical philosophy which I found myself having to beg. A thorough study of the foundational works of Hilbert and Bernays finally convinced me that I had all too naively and uncritically bought this refutation of formalism. I did indeed discover points of surprisingly close contact between formalism and mechanism, but also that it was possible to under­ mine certain strong arguments against these positions precisely by invok­ ing G6del's and related work. I also began to realize that the Church­ Turing thesis itself is the principal bastion protecting mechanism, and that G6del's work was perhaps the best thing that ever happened to both mechanism and formalism. I pushed these lines of argument in my dis­ sertation with the patient help of my readers, Raymond Nelson and Howard Stein. I would especially like to thank the latter for many valuable criticisms of my dissertation as well as some helpful suggestions for reor­ ganizing it in the direction of the present book.

Keywords

effectiveness formalism foundation idea mathematics model nature philosophy present subject

Authors and affiliations

  • Judson Chambers Webb
    • 1
  1. 1.Dept. of PhilosophyBoston UniversityBostonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-7653-6
  • Copyright Information Springer Science+Business Media B.V. 1980
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-8357-9
  • Online ISBN 978-94-015-7653-6
  • Buy this book on publisher's site