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Title: Collected Works: Publications 1938-1974 by Kurt Godel, Solomon Feferman, Stephen C. Kleene, Gregory H. Moore, John W., Jr. Dawson, Robert M. Solovay, Jean Van Heijenoort ISBN: 0-19-514721-9 Publisher: Oxford University Press Pub. Date: March, 2001 Format: Paperback Volumes: 1 List Price(USD): $34.95 |
Average Customer Rating: 4 (1 review)
Rating: 4
Summary: Excellent material that fits lots of class uses
Comment: A summary of his statement on p. 125 on "Russell's Mathematical Logic" describes the "vicious circle principle: forbids a certain kind of circularity which is made responsible for the paradoxes. The fallacy in these, so it is contended, consists in the circumstance that one defines (or tacitly assumes) totalities, whose existence would entail the existence of certain new elements of the same totality, namely elements definable only in terms of the whole totality." This led to the formulation of a principle which says that "no totality can contain members definable only in terms of this totality, or members involving or presupposing this totality." (The vicious circle principle). (Also a "not applying to itself principle to keep the vicious circle principle from applying to itself p. 126
In describing Russell's theory of types he says, "The paradoxes are avoided by the theory of simple types which is combined with the theory of simple orders - a "ramified hierarchy""
Godel argues that the vicious circle principle is false rather than that classical mathematics is false.
p. 202 "A remark about the relationship between relativity theory and idealistic philosophy (1949a) (Note that this view supports my usual presentations in class on this!)
"The argument runs as follows: Change becomes possible only through the lapse of time. The existence of an objective lapse of time 4, however, means (or, at least, is equivalent to the fact) that reality consists of an infinity of layers of "now"
p. 203 which come into existence successively. But, if simultaneity is something relative in the sense just explained, reality cannot be split up into such layers in an objectively determined way. Each observer has his own set of "nows", and none of these various systems of layers can claim the prerogative of representing the objective lapse of time. 5"
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Title: Collected Works: Unpublished Essays & Lectures by Kurt Godel, Solomon Feferman, John W., Jr. Dawson, Warren Goldfarb, Charles Parsons, R. Solovay ISBN: 0195147227 Publisher: Oxford University Press Pub. Date: May, 2001 List Price(USD): $34.95 |
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Title: A Shorter Model Theory by Wilfrid Hodges ISBN: 0521587131 Publisher: Cambridge University Press Pub. Date: 10 April, 1997 List Price(USD): $47.00 |
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Title: The Search for Mathematical Roots, 1870-1940 by I. Grattan-Guinness ISBN: 069105858X Publisher: Princeton Univ Pr Pub. Date: 15 January, 2001 List Price(USD): $55.00 |
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Title: Logic, Logic, and Logic by George Boolos, Richard Jeffrey ISBN: 067453767X Publisher: Harvard Univ Pr Pub. Date: October, 1999 List Price(USD): $25.50 |
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Title: Contributions to the Founding of the Theory of Transfinite Numbers by Georg Cantor ISBN: 0486600459 Publisher: Dover Pubns Pub. Date: 01 June, 1955 List Price(USD): $9.95 |
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