附註:Includes bibliographical references (page 125) and index.
The problem of consistency -- Absolute proofs of consistency -- The systematic codification of formal logic -- An example of a successful absolute proof of consistency -- The idea of mapping and its use in mathematics -- Gödel's proofs -- A Gödel numbering -- The arithmetization of meta-mathematics -- The heart of Gödel's argument -- Concluding reflections -- Appendix: Notes -- Brief bibliography -- Index.
摘要:"In 1931 Kurt Godel disrupted some of the fundamental assumptions underlying mathematics and logic with the publication of his revolutionary paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." Ironically, few mathematicians of the time were able to understand the young scholar's complex proof, and the full importance of this work was largely overlooked for many years. Godel was at last recognized by his peers and presented with the first Albert Einstein Award in 1951 for achievement in the natural sciences - the highest honor of its kind in the United States. The award committee, which included Albert Einstein and J. Robert Oppenheimer, described his work as "one of the greatest contributions to the sciences in recent times."" "In Godel's Proof, Ernest Nagel and James Newman provide a readable and non-technical explanation for both scholars and non-specialists of the main ideas and broad implications of Godel's discovery. First published in 1958 and in print continuously in ten languages, this highly popular, seminal work offers every educated person with an interest in mathematics, logic, and philosophy the opportunity to understand a previously difficult and inaccessible subject."--Jacket.
