Philosophy Dictionary of ArgumentsHome
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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.
_____________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 |
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Hartry Field on Goedel - Dictionary of Arguments
II 347 Godel sentence/Field: is true only if unprovable, if proved, it is not true. >Provability, >Proofs, >Goedel, cf. >Completeness, >Incompleteness._____________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. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich, Aldershot 1994 |
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Ed. Martin Schulz, access date 2024-04-19