Lexicon of Arguments

 

I 72
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.
>Individual constants, >Individuals, >Properties, >Predicates, >Relations, >Truth values, >Constants.
I 73
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.
>Truth, >Validity, >Universal validity, >Proofs, >Provability.
I 74
A statement is always true in relation to an interpretation.
I 78
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").
I 81
Then has the substitution y"(namely y a/b) a specific truth value at every interpretation.
>Inserting.
I 83
Complete interpretation: not desirable because we also examine statements, where not names for all individual constants are available - e.g. real numbers.
>Real numbers, >"Not enough names".
I 91
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.
>Sense, >Everyday language.
I 92
Interpretation specifies truth conditions (WB) fixed - truth condition: Then here in German. - With that it will give every statement a meaning.
>Truth conditions, >Translation, >Translation indeterminacy.
I 93
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.