Gödel's proof

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Gödel's proof

[′gərd·əlz ′prüf]
(mathematics)
Any formal arithmetical system is incomplete in the sense that, given any consistent set of arithmetical axioms, there are true statements in the resulting arithmetical system that cannot be derived from these axioms.
References in periodicals archive ?
Their work called 'Formalization, Mechanization and Automation of Godel's Proof of God's Existence' state that his ontological proof of God has been analysed for the first time with an unprecedented degree of detail and formality with the help of higher-order theorem proves.
Godel's proof emerged from deep insights into the self-referential nature of mathematical statements.
Self-reference, feedback loops, paradoxes and Godel's proof all play central roles in the view of consciousness articulated by Douglas Hofstadter in his 2007 book I Am a Strange Loop.
Godel's proof showed that math is "incomplete"; it contains truths that can't be proven.
His main goal was to demonstrate the independence of the hypothesis, but in order to keep the course as self-contained as possible, he included background material in logic and axiomatic set theory as well as Godel's proof of the consistency of the hypothesis.
If applicable to law (a significant contingency indeed), Godel's proof indicates unavoidable judicial susceptibility to inconsistency, since abstinence from adjudication of formally undecidable cases is impractical.
29) His program was soon to be shattered by Godel's proof.
32) Godel's proof shattered the possibility of complete and consistent axiomatization.
Proposition VI of Godel's proof asserts that any formal system sufficiently complex to support arithmetic (36) must contain statements that are either internally "undecidable"--statements that cannot be proved or disproved within the system--or provably inconsistent.
Feferman presents two claims to support his contention that Godel's proof cannot demonstrate that science must remain incomplete.
Nagel and Newman first published the book Godel's Proof in 1958, bringing the intricacies and importance of this great work to a larger audience.