@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 29 Mar 2024}, author = {Tarski,Alfred}, subject = {Conditional}, note = {Berka I 405f Conclusion/Entailment/Formal/Everyday Language/Tarski: the formal conclusion does not coincide with the everyday language one. E.g. A0: 0 has the given property P A1: 1 has the given property P, etc. An: n has the given property P - with normal rules of inference it is impossible to prove the following proposition with this: A: Every natural number has the given property P - Solution: new rule of inference: infinite induction. Problem: infiniteness. Solution: provability rather than actual evidence. >Provability, >Proofs. Berka I 407 Inference/Entailment/Gödel: Problem: statements can be constructed that follow in the usual sense from the sentences of a theory, but which cannot be proven with the rules of inference. Berka I 409 Def Logical Conclusion/Tarski: the statement X logically follows from the statements of the class K iff. each model of class K is at the same time a model of the statement X. I 410 Def of the logical conclusion has to do with the division into logical and extra-logical concepts - which is arbitrary.(1) Cf. >Extensional language, >Extensions, >Extensionality, >Formalization, >Everyday language. 1. A.Tarski, „Über den Begriff der logischen Folgerung“, in: Actes du Congrès International de Philosophie Scientifique, Paris 1935, Bd. VII, ASI 394, Paris 1936, pp 1-11}, 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=239952} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=239952} }