Philosophy Lexicon of Arguments

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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Thiel I 223
Widerspruchsfreiheit/maximal widerspruchsfrei/Thiel:
1920 bewies Post, dass, wenn man dem untersuchten Axiomensystem (bei ihm Principia Mathematica) einen nicht aus ihnen ableitbaren Satz hinzufügt, das erweiterte System widerspruchsvoll ist.
I 224
("Vollständigkeit als maximale Widerspruchsfreiheit").> maximal konsistent.

Chr. Thiel
Philosophie und Mathematik Darmstadt 1995

> Counter arguments in relation to Consistency

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Ed. Martin Schulz, access date 2017-05-27