## Philosophy Lexicon 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._____________ 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. | |||

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Books on Amazon |
IX 209/10 Consistency/ML/Quine: we have been able to prove it twice as we have a simple model in finite sets - which does not apply if we once have added an axiom of infinity (UA) - consistency is questionable and more difficult and more urgent to prove. And the evidence is even less convincing - problem: the question of whether the methods themselves are consistent. _____________ 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. |
Q I W.V.O. Quine Wort und Gegenstand Stuttgart 1980 Q II W.V.O. Quine Theorien und Dinge Frankfurt 1985 Q III W.V.O. Quine Grundzüge der Logik Frankfurt 1978 Q IX W.V.O. Quine Mengenlehre und ihre Logik Wiesbaden 1967 Q V W.V.O. Quine Die Wurzeln der Referenz Frankfurt 1989 Q VI W.V.O. Quine Unterwegs zur Wahrheit Paderborn 1995 Q VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Q VIII W.V.O. Quine Bezeichnung und Referenz InZur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982 Q X W.V.O. Quine Philosophie der Logik Bamberg 2005 Q XII W.V.O. Quine Ontologische Relativität Frankfurt 2003 |

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Ed. Martin Schulz, access date 2017-09-22