Lexicon of Arguments

 

Berka I 405f
Conclusion/Entailment/Formal/Everyday Language/Tarski: the formal conclusion does not coincide with the everyday language one.
E.g.
A0: 0 has the given property P
A1: 1 has the given property P, etc.
An: n has the given property P -
with normal rules of inference it is impossible to prove the following proposition with this:
A: Every natural number has the given property P - Solution: new rule of inference: infinite induction.
Problem: infiniteness.
Solution: provability rather than actual evidence.
>Provability, >Proofs.
Berka I 407
Inference/Entailment/Gödel: Problem: statements can be constructed that follow in the usual sense from the sentences of a theory, but which cannot be proven with the rules of inference.
Berka I 409
Def Logical Conclusion/Tarski: the statement X logically follows from the statements of the class K iff. each model of class K is at the same time a model of the statement X.
I 410
Def of the logical conclusion has to do with the division into logical and extra-logical concepts - which is arbitrary.⁽¹⁾
Cf. >Extensional language, >Extensions, >Extensionality, >Formalization, >Everyday language.


1. A.Tarski, „Über den Begriff der logischen Folgerung“, in: Actes du Congrès International de Philosophie Scientifique, Paris 1935, Bd. VII, ASI 394, Paris 1936, pp 1-11