Philosophy Lexicon of Arguments

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Consistency, philosophy, logic: 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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I 234
Consistency/Mates: can be doubly checked: a) semantically: by specifying an interpretation in which all axioms are true - b) syntactically: by showing without referring to an interpretation that there is no statement j such that both j and ~j can be derived from the axioms

Mate I
B. Mates
Elementare Logik Göttingen 1969

Mate II
B. Mates
0226509869 1981


> Counter arguments against Mates
> Counter arguments in relation to Consistency



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Ed. Martin Schulz, access date 2017-05-26