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|Berka I 405f
Conclusion/Entailment/Formal/Everyday Language/Tarski: the formal one 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: infinite - Solution: provability rather than actual evidence.
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.
Def of the logical conclusion has to do with the division into logical and extra-logical concepts - which is arbitrary.
_____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983
K. Berka/L. Kreiser
Logik Texte Berlin 1983