## Philosophy Dictionary of ArgumentsHome | |||

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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. | |||

Author | Concept | Summary/Quotes | Sources |
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Christian Thiel on Consistency - Dictionary of Arguments Thiel I 223 Consistency/Maximum Consistency/Thiel: In 1920 Post proved that if one adds to the axiom system examined (in his case Principia Mathematica) a proposition that cannot be derived from them, the extended system is contradictory. I 224 ("completeness as maximum consistency") > maximum consistency. _____________ 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. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |

> Counter arguments against **Thiel**

> Counter arguments in relation to **Consistency ...**

Ed. Martin Schulz, access date 2022-09-25