Mechanism, Mentalism and Metamathematics : An Essay on Finitism PDF
by J. Webb
Part of the Synthese Library series
Description
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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Download - Immediately Available
- Format:PDF
- Publisher:Springer Netherlands
- Publication Date:09/03/2013
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- ISBN:9789401576536
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Information
-
Download - Immediately Available
- Format:PDF
- Publisher:Springer Netherlands
- Publication Date:09/03/2013
- Category:
- ISBN:9789401576536
