|Interpretation: A) making statements about other statements, whereby the new statements of the vocabulary make use of the original statements and possibly introduce new vocabulary. If no new vocabulary is introduced, new information can be obtained by changing the syntactic elements.|
B) In logic, the insertion of values (objects) instead of the constants or free variables.
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Interpretation/logic/Mates: an interpretation assigns: individual constants: individuals - one-digit predicates: properties (classes of individuals) - two-digit predicates: relations - statement letter: truth values - truth values come into play when the logical constants are interpreted.
Truth values: may change when we pass from one interpretation to another, without the form of the statement being changed - the terms "true" and "valid" refer to all interpretations of a particular type.
A statement is always true in relation to an interpretation.
Interpretation/QL/Mates: if quantifiers have to be considered, we need a helping concept. We need two interpretations I and I"- b: is an individual constant - then b-variant - the interpretations then differ at the most in what they assign to b ("at most to b-th place").
Then has the substitution y"(namely y a/b) a specific truth value at every interpretation.
Complete interpretation: not desirable because we also examine statements, where not names for all individual constants are available - e.g. real numbers.
Interpretation/translation/truth/intention/artificial language/Mates. Problem: The interpretation also has a "manner of being given". E.g. "2" as the "smallest prime" or "only even prime number" - translation: not unambigiuous - solution. helping concept: "predicate of the German language" - Problem: no systematic rules - meaning/everyday language: depends on the context.
Interpretation specifies truth conditions (WB) fixed - truth condition: Then here in German. - With that it will give every statement a meaning.
Interpretation/logic/Mates. would there be a complete I, then scheme: (W) X is only true if and only then at I when p - although the truth conditions are in German.
Elementare Logik Göttingen 1969