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Kurt Gödel: Kurt Gödel (1906 – 1978) was a logician, mathematician, and philosopher. He is best known for his incompleteness theorems, which show that within any axiomatic system powerful enough to express basic arithmetic, there will always be statements that can neither be proven nor disproven within that system. Major works are "On Formally Undecidable Propositions of Principia Mathematica and Related Systems" (1931), "Consistency-Proof for the Generally Covariant Gravitational Field Equations" (1939), "What is Cantor's Continuum Problem?" (1947), "Russell's Mathematical Logic" (1951), "On Undecidable Propositions of Formal Mathematical Systems" (1956). See also Incompleteness, Completeness, Proofs, Provability.
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Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

 
Author Concept Summary/Quotes Sources

Benson Mates on Goedel - Dictionary of Arguments

I 289
Goedel/Mates: main result: Goedel showed by the incompleteness theorem that one can not identify mathematical truth with derivability from a particular system of axioms.
>K. Gödel
, >Incompleteness/Gödel, >Mathematical truth, >Validity, >Derivation, >Derivability, >Axioms, >Axiom systems.

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Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Mate I
B. Mates
Elementare Logik Göttingen 1969

Mate II
B. Mates
Skeptical Essays Chicago 1981


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> Counter arguments in relation to Goedel

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