Dictionary of Arguments

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Consistency, philosophy, logic: The expression of consistency is applied to systems or sets of statements. From a contradictory system any statement can be derived (see ex falso quodlibet). Therefore, contradictory systems are basically useless. It is characteristic of a consistent system that not every statement can be proved within it. See also systems, provability, proofs, calculus, consistency, theories, completeness, validity, expressiveness. Within a system, consistency may be demonstrated, but not beyond the boundaries of this system, since the use of the symbols and the set of possible objects are only defined for this system. Within mathematics, and only there applies that the mathematical objects, which are mentioned in consistent formulas, exist (Hilbert, Über das Unendliche, 1926). See also falsification, verification, existence, well-formed.

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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 Item    More concepts for author
Bigelow, John Consistency   Bigelow, John
Feyerabend, Paul Consistency   Feyerabend, Paul
Field, Hartry Consistency   Field, Hartry
Frege, Gottlob Consistency   Frege, Gottlob
Gödel, Kurt Consistency   Gödel, Kurt
Henkin, Leon Consistency   Henkin, Leon
Hilbert, David Consistency   Hilbert, David
Mates, Benson Consistency   Mates, Benson
Millikan, Ruth Consistency   Millikan, Ruth
Quine, Willard Van Orman Consistency   Quine, Willard Van Orman
Tarski, Alfred Consistency   Tarski, Alfred
Thiel, Christian Consistency   Thiel, Christian

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