incompleteness
31Tarski's undefinability theorem — Tarski s undefinability theorem, stated and proved by Alfred Tarski in 1936, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics. Informally, the theorem states that arithmetical truth… …
32Logic — For other uses, see Logic (disambiguation). Philosophy …
33metalogic — /met euh loj ik/, n. the logical analysis of the fundamental concepts of logic. [1835 45; META + LOGIC] * * * Study of the syntax and the semantics of formal languages and formal systems. It is related to, but does not include, the formal… …
34mathematics, foundations of — Scientific inquiry into the nature of mathematical theories and the scope of mathematical methods. It began with Euclid s Elements as an inquiry into the logical and philosophical basis of mathematics in essence, whether the axioms of any system… …
35logic, history of — Introduction the history of the discipline from its origins among the ancient Greeks to the present time. Origins of logic in the West Precursors of ancient logic There was a medieval tradition according to which the Greek philosopher …
36Axiom — This article is about logical propositions. For other uses, see Axiom (disambiguation). In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self evident or to define and… …
37Gregory Chaitin — Born 1947 (1947) Chicago[1] Residence …
38Hilbert's second problem — In mathematics, Hilbert s second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that arithmetic of real numbers is consistent.In the 1930s, Kurt Gödel and Gerhard Gentzen proved results that cast new… …
39Hilbert's program — Hilbert s program, formulated by German mathematician David Hilbert in the 1920s, was to formalize all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent.Hilbert proposed that the… …
40Berry paradox — The Berry paradox is a self referential paradox arising from the expression the smallest possible integer not definable by a given number of words. Bertrand Russell, the first to discuss the paradox in print, attributed it to G. G. Berry, a… …
