@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 28 Mar 2024}, author = {Tarski,Alfred}, subject = {Consistency}, note = {Berka I 401 Consistency Proof/Gödel: a proof of consitency cannot be performed if the metalanguage does not contain higher type variables. >Metalanguage, >Levels, >Provability, cf. >Type theory. Undecidability: is eliminated when the examined theory (object language) is enriched with higher type variables. (1) >Object language. - - - Berka I 474f Consistency/Logical Form/Tarski: is present when - for any statement x: either x ~ε FL(X) or ~x ~ε FL(x). ((s) Either x is not an inference from the system or its negation is not an inference.) But: Completeness: accordingly: if - for any statement x either x ε FL(X) or ~x ε FL(X) ((s) if either any statement or its negation is an inference from the system). I 529 f Law of Contradiction/Tarski: "x ~ε contradiction or ~x ~ε contradiction". 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 law of contradiction. 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).(2) 1. A.Tarski, „Grundlegung der wissenschaftlichen Semantik“, in: Actes du Congrès International de Philosophie Scientifique, Paris 1935, VOl. III, ASI 390, Paris 1936, pp. 1-8 2. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol 1, Lemberg 1935}, note = { Tarski I A. Tarski Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=285017} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=285017} }