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Type of bind: Paperback
Dewey Decimal Number: 510
EAN num: 9780195147216
ISBN number: 0195147219
Label: Oxford University Press, USA
Manufacturer: Oxford University Press, USA
Quantity: 1
Page Count: 432
Printing Date: June 21, 2001
Publishing house: Oxford University Press, USA
Sale Popularity Level: 776164
Studio: Oxford University Press, USA
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Kurt Godel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computation theory, as well as for the strong individuality of his writings on the philosophy of mathematics. Less well-known is his discovery of unusual cosmological models for Einstein's equations, permitting 'time-travel' into the past.
This second volume of a comprehensive edition of Godel's works collects together all his publications from 1938 to 1974. Together with Volume I (Publications 1929-1936), it makes available for the very first time in a single source all of his previously published work. Continuing the format established in the earlier volume, the present text includes introductory notes that provide extensive explanatory and historical commentary on each of the papers, a facing English translation of the one German original, and a complete bibliography. Succeeding volumes are to contain unpublished manuscripts, lectures, correspondence, and extracts from the notebooks.
Collected Works is designed to be accessible and useful to as wide an audience as possible without sacrificing scientific or historical accuracy. The only complete edition available in English, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science. These volumes will also interest scientists and all others who wish to be acquainted with one of the great minds of the twentieth century.
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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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