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portada mechanism, mentalism and metamathematics: an essay on finitism
Type
Physical Book
Author
Publisher
Year
2010
Language
English
Pages
285
Format
Paperback
Dimensions
22.9 x 15.2 x 1.6 cm
Weight
0.40 kg.
ISBN
904818357x
ISBN13
9789048183579
Categories

mechanism, mentalism and metamathematics: an essay on finitism

J. Webb (Author) · Springer · Paperback

mechanism, mentalism and metamathematics: an essay on finitism - Webb, J.

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Synopsis "mechanism, mentalism and metamathematics: an essay on finitism"

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.

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