Mechanism, Mentalism and Metamathematics: An Essay on Finitism (1980) (Synthese Library #137)

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Synopsis
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.
Copyright:
1980

Book Details

Book Quality:
Publisher Quality
ISBN-13:
9789401576536
Related ISBNs:
9789027710468
Publisher:
Springer Netherlands
Date of Addition:
Copyrighted By:
Springer Science+Business Media Dordrecht
Adult content:
No
Language:
English
Has Image Descriptions:
No
Categories:
Nonfiction, Science, Health, Mind and Body, Philosophy
Submitted By:
Bookshare Staff
Usage Restrictions:
This is a copyrighted book.

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