Lexicon 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 Consequently a sequence f satsfies the function L2 ~ (L1,2) only then if every sequence g, which differs from f at most on 2nd spot, the function ~ (L1,2) satisfies, thus the formula: g1 Berka I 505
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