Gödel's theorem

Definition

That any formal-logic system (such as mathematics) contains propositions which cannot be proved to be true or false within that system. Therefore, no logical system can be complete or consistent in the sense of being able to provide proofs for all the axioms it is based on. This theorem scuttled the attempt by the UK mathematicians Alfred North Whitehead (1873-1956) and Bertrand Russell (1872-1970) to develop pure mathematics from a few logical principles, dismayed the scientists looking for a few axiomatic laws that logically explain all natural phenomenon, and refuted the notion that human mind is a mechanical (deterministic) system. Proved in 1931 by the Austrian-US mathematician and relativity researcher Kurt Gödel (1906-1978). Also called Gödel's incompleteness theorem.

单词	Gödel's theorem
释义	Gödel's theorem Definition That any formal-logic system (such as mathematics) contains propositions which cannot be proved to be true or false within that system. Therefore, no logical system can be complete or consistent in the sense of being able to provide proofs for all the axioms it is based on. This theorem scuttled the attempt by the UK mathematicians Alfred North Whitehead (1873-1956) and Bertrand Russell (1872-1970) to develop pure mathematics from a few logical principles, dismayed the scientists looking for a few axiomatic laws that logically explain all natural phenomenon, and refuted the notion that human mind is a mechanical (deterministic) system. Proved in 1931 by the Austrian-US mathematician and relativity researcher Kurt Gödel (1906-1978). Also called Gödel's incompleteness theorem.
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