Economics Dictionary of ArgumentsHome
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| Satisfiability, logic: a statement can be satisfied if there is an interpretation (e.g. an insertion of constants instead of variables), in which the statement is true. E.g. tautologies are always satisfied, contradictions are never satisfied. See also tautology, contradiction, contingency, satisfaction, models, model theory._____________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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Alfred Tarski on Satisfiability - Dictionary of Arguments
Berka I 482 Satisfiability/Tarski: depends only on those terms of the sequence from which (with respect to their indices) correspond to the free variables of propositional functions. >Sequences/Tarski, >Propositional functions. In the case of a statement (without free variables) the satisfiability does not depend on the properties of the links. >Statements. Each infinite sequence of class satisfies a given true statement - (because it does not contain free variables). >Free variables, >Bound variables. False statement: satisfied by no sequence - variant: satisfiability by finite sequences: according to this view, only the empty sequence satisfies a true statement (because this one has no variables). Berka I 483 Satisfiability/sequences/statements/Tarski: (here: by finite sequences): E.g. the statement (not propositional function) L1U2l1,2. i.e. "PxlNPxllNIxlxll" according to Definition 22 (satisfiability) satisfies the propositional function L1,2 those and only those sequences f of classes for which f1 Being satisfied/satisfiability/Tarski: previously ambiguous because of relations of different linking numbers or between object and classes, or areas of different semantic categories - therefore actually an infinite number of different satisfiability-concepts - Problem: then no uniform method for construction of the concept of the true statement - solution: recourse to the class calculus: Satisfiability by succession of objects.(1) >Truth definition, >Truth theory, >Class calculus. 1. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol. 1, Lemberg 1935_____________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. |
Tarski I A. Tarski Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
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