The Origins of Cyberspace collection described as lots 1-255 will first be offered as a single lot, subject to a reserve price. If this price is not reached, the collection will be immediately offered as individual lots as described in the catalogue as lots 1-255.
GÖDEL, Kurt. "On undecidable propositions of formal mathematical systems." N.d. [ca. mid-1930s-1940s].
Details
GÖDEL, Kurt. "On undecidable propositions of formal mathematical systems." N.d. [ca. mid-1930s-1940s].
4o. [1], 29 [2]ff. 3. Unbound typescript copy, on paper with an English watermark. In black binder. Provenance: Richard Bevan Braithwaite, author of the preface to the first English translation of Gödel's proof (1962).
In the spring of 1934, in a series of lectures delivered at Princeton's Institute for Advanced Study, Gödel addressed the problem of decidability in mathematics--the third of Hilbert's three questions posed in 1928. It was in these lectures that Gödel introduced the notion of general recursiveness, which Church showed, in his paper of 1936 to be equivalent to his own concept of \Kl\k-definability; furthermore, he also showed that both his and Gödel's concepts were precise explanations of the informal notion of effective calculability. Interestingly, Gödel did not accept Church's thesis until after reading Alan Turing's paper on computable numbers which analyzed the notion of computability in terms of abstract computing machines, and showed that it was equivalent to -definability and general recursiveness. "These notions became fundamental for the enormously important subject of recursion theory. They also provided the key theoretical concepts for modern general-purpose digital computers, as realized by von Neumann and Turing in the 1940s" (Feferman 1986, 18).
The text of Gödel's 1934 lectures was supplied from notes taken at the lectures by Stephen C. Kleene and J. B. Rosser, which were "put out in installments to the persons who had requested them. After the lectures were finished, the whole set of the notes, supplemented by two pages of 'Notes and errata,' was approved by Gödel" (Kleene 1986, 338). The complete notes were originally published in mimeograph; our typescript is a copy made for R. B. Braithwaite, who may have been unable to obtain one of the original mimeographed copies. The lectures first appeared in book form in The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions, ed. Martin Davis (1965). OOC 307.
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In the spring of 1934, in a series of lectures delivered at Princeton's Institute for Advanced Study, Gödel addressed the problem of decidability in mathematics--the third of Hilbert's three questions posed in 1928. It was in these lectures that Gödel introduced the notion of general recursiveness, which Church showed, in his paper of 1936 to be equivalent to his own concept of \Kl\k-definability; furthermore, he also showed that both his and Gödel's concepts were precise explanations of the informal notion of effective calculability. Interestingly, Gödel did not accept Church's thesis until after reading Alan Turing's paper on computable numbers which analyzed the notion of computability in terms of abstract computing machines, and showed that it was equivalent to -definability and general recursiveness. "These notions became fundamental for the enormously important subject of recursion theory. They also provided the key theoretical concepts for modern general-purpose digital computers, as realized by von Neumann and Turing in the 1940s" (Feferman 1986, 18).
The text of Gödel's 1934 lectures was supplied from notes taken at the lectures by Stephen C. Kleene and J. B. Rosser, which were "put out in installments to the persons who had requested them. After the lectures were finished, the whole set of the notes, supplemented by two pages of 'Notes and errata,' was approved by Gödel" (Kleene 1986, 338). The complete notes were originally published in mimeograph; our typescript is a copy made for R. B. Braithwaite, who may have been unable to obtain one of the original mimeographed copies. The lectures first appeared in book form in The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions, ed. Martin Davis (1965). OOC 307.
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