On GödelWadsworth/Thomson Learning, 2000 - 74 páginas This brief text assists students in understanding Godel's philosophy and thinking so that they can more fully engage in useful, intelligent class dialogue and improve their understanding of course content. Part of the "Wadsworth Philosophers Series," (which will eventually consist of approximately 100 titles, each focusing on a single "thinker" from ancient times to the present), ON GODEL is written by a philosopher deeply versed in the philosophy of this key thinker. Like other books in the series, this concise book offers sufficient insight into the thinking of a notable philosopher better enabling students to engage in the reading and to discuss the material in class and on paper." |
Índice
Gödels Life and Personality | 6 |
Gödels Background | 19 |
Gödels Puzzling Inompleteness Proof | 29 |
Página de créditos | |
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actual world arithmetical propositions arithmetical statements arithmetical truth assumptions axiom of choice axiom system axiomatic set theory axioms of set basic Bertie Chapter concepts consistency proof continuum hypothesis deductive completeness defined descriptively complete developed diagonal lemma elementary arithmetic existence expressed falsifier Feferman first-order language formal provability foundations of mathematics Frege geometry Gödel number Gödel proved Gödel's actualism Gödel's completeness proof Gödel's first incompleteness Gödel's proof Gödel's result Gödelian sentence Hence higher-order logic Hilbert's program idea incompleteness result individuals instance intuition known Königsberg logic and mathematics logical truth logicians mathematical theories mathematicians means model theory model-theoretical natural numbers negation nonlogical notion number theory ordinary first-order logic philosophical Platonic play proof methods proof-theoretical quantifiers question received first-order logic recursive Robinson arithmetic role rules of inference second-order logic semantically complete sense set-theoretical shows Skolem functions speak standard interpretation system of elementary Tarski theorists thing true Turing machines unprovable