Philosophy Dictionary of Arguments  
 
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, wellformed. _____________ 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  
Mischel, Walter  Consistency  Mischel, Walter  
Quine, Willard Van Orman  Consistency  Quine, Willard Van Orman  
Tarski, Alfred  Consistency  Tarski, Alfred  
Thiel, Christian  Consistency  Thiel, Christian  
