Gödel's theorem


Gödel's theorem
Gödel's theorem
n.
either of two theorems published by the mathematician Kurt Gödel in 1931 that prove all mathematical systems are incomplete in that their truth or consistency can only be proved using a system of a higher order: also called Gödel's proof or Gödel's incompleteness theorem

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Principle of the foundations of mathematics.

One of the most important discoveries of 20th-century mathematics, it states the impossibility of defining a complete system of axioms that is also consistent (does not give rise to contradictions). Any formal system (e.g., a computer program or a set of mathematical rules and axioms) powerful enough to generate meaningful statements can generate statements that are true but that cannot be proven or derived within the system. As a consequence, mathematics cannot be placed on an entirely rigorous basis. Named for Kurt Godel, who published his proof in 1931, it immediately had consequences for philosophy (particularly logic) and other areas. Its ramifications continue to be debated.

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Universalium. 2010.

Look at other dictionaries:

  • Gödel's theorem — n. either of two theorems published by the mathematician Kurt Gödel in 1931 that prove all mathematical systems are incomplete in that their truth or consistency can only be proved using a system of a higher order: also called Gödel s proof or… …   English World dictionary

  • Gödel's theorem — may refer to: *Gödel s incompleteness theorems *Gödel s completeness theorem …   Wikipedia

  • gödel's theorem — noun also gödel s incompleteness theorem ˈgœ̅dəlz Usage: usually capitalized G Etymology: after Kurt Gödel died 1978 American mathematician : a theorem in advanced logic: in any logical system as complex or more complex than the arithmetic of the …   Useful english dictionary

  • Gödel's theorem(s) — Gödel s first incompleteness theorem states that for any consistent logical system S able to express arithmetic there must exist sentences that are true in the standard interpretation of S, but not provable. Moreover, if S is omega consistent… …   Philosophy dictionary

  • Godel's theorem — noun Etymology: Kurt Gödel died 1978 American mathematician Date: 1933 a theorem in advanced logic: in any logical system as complex as or more complex than the arithmetic of the integers there can always be found either a statement which can be… …   New Collegiate Dictionary

  • Godel’s Theorem — all branches of mathematics are based on propositions that can’t be proved within that branch (named for mathematician Kurt Godel) …   Eponyms, nicknames, and geographical games

  • Gödel's theorem — /ˈgɜdəlz θɪərəm/ (say gerduhlz thearruhm) noun the proposition that in a formal axiomatic system, such as logic or mathematics, it is impossible to prove consistency without using methods beyond those of the system itself. {from Kurt Gödel,… …   Australian English dictionary

  • Gödel's theorem(s) — …   Philosophy dictionary

  • Gödel's incompleteness theorems — In mathematical logic, Gödel s incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest. The theorems are of… …   Wikipedia

  • Gödel, Kurt — born April 28, 1906, Brünn, Austria Hungary died Jan. 14, 1978, Princeton, N.J., U.S. Austrian born U.S. mathematician and logician. He began his career on the faculty of the University of Vienna, where he produced his groundbreaking proof (see… …   Universalium


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