Berka I 395
Truth/absolute truth/Hilbert: axioms and provable propositions are images of the thoughts which make up the method of the previous mathematics, but they are not themselves the absolute truths.
>
Axioms, >
Axiom systems, >
Axioms/Hilbert.
Def absolute truth/Hilbert: absolute truths are the insights provided by my proof theory with regard to the provability and consistency of the formula systems.
>
Proof theory/Hilbert.
Through this program, the truth of the axioms is already shown for our theory of proof
(1).
Berka I 486
Relative Truth/correctness in the domain/Tarski: the relative truth plays a much greater role than the (Hilbertian) concept of the absolute truth, which has so far been mentioned:
Definition correct statement in the domain a/Tarski: every statement in domain a is correct, which then (in the usual sense (s)> Putnam would choose spelling with asterisks)) would be true if we limit the scope of the individuals to the given class a.
That is, if we interpret the terms "individual" as "element of class a", "class of individuals" as "subclasses of class a", and so on.
Class Calculation: here you would have to interpret expressions, e.g. of the type "Πxp" as "for each subclass x of class a:p" and, e.g. "Ixy" as "the subclass x of the class a is contained in the subclass y of the class a".
Then we modify definition 22 and 23. As derived terms, we will introduce the concept of the statement, which in an individual domain with k elements is correct, and the assertion which is correct in each individual area
(2).
>
Truth/Tarski, >
Truth Definition/Tarski.
1. D. Hilbert: Die logischen Grundlagen der Mathematik, in: Mathematische Annalen 88 (1923), pp. 151-165.
2. A. Tarski: Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol 1, Lemberg 1935.
