## 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. | |||

Author | Item | Excerpt | Meta data |
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Books on Amazon |
Berka I 401 Consistency Proof/Gödel: cannot be performed if the meta language does not contain higher type variables - Undecidability: is eliminated when the examined theory (OS) is enriched with higher type variables Berka I 474f Consistency/Logical Form/Tarski: is present when - for any statement x - either x e FL(X) or ~x e FL(X). (sic) - (s) either x is not an inference from the system or its negation is not an inference - but: completeness/complete: accordingly: if - for any statement x - either x e FL(X) or ~x e FL(X) - (s) if either any statement or its negation is an inference from the system) I 529 f Law of Contradiction/Tarski: "x ~e contradiction or ~x ~e contradiction" - Point: we cannot make any generalization from the class of these statement functions! The generalization of these statement functions would itself be a (general) statement, namely the of the SvW - Problem: infinite logical product that cannot be derived with normal methods of inference. I 531 Solution: "rule of infinite induction" - (differs from all other rules of inference by infinitist character) |
Tarsk I A. Tarski Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983 Brk I K. Berka/L. Kreiser Logik Texte Berlin 1983 |

> Counter arguments against **Tarski**

> Counter arguments in relation to **Consistency**

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Ed. Martin Schulz, access date 2017-05-24