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Mechanism, Mentalism and Metamathematics : An Essay on Finitism - J. Webb

Mechanism, Mentalism and Metamathematics

An Essay on Finitism

By: J. Webb

Hardcover

Published: 31st October 1980
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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.

I / Mechanism: Some Historical Notes.- II / Mind, Number, and the Infinite.- III / the Mental, the Finite, and the Formal.- IV / Effectiveness Mechanized.- Concluding Summary.- Index of Names.- Index of Subjects.

ISBN: 9789027710468
ISBN-10: 9027710465
Series: Synthese Library
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 285
Published: 31st October 1980
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 0.6