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|Thiel I 205
Ordinal numbers/Neumann/Thiel: Today, ordinal numbers are not only introduced differently than in Cantor and Dedekind, but are also defined differently.
John v. Neumann: Axiomatic construction of the set theory. In the foundation of logic certain formulas are recognized as "excellent formulas".
The rules allow us to form unreservedly new sentential connective-logical propositional schemas, in which we can recognize excellent ones and not a. But this does not provide us with a real overview of the sentences of the sentential connectives logic, nor a systematic insight into their connections.
We must distinguish between the logical framework and the sentences themselves in an axiomatic structure.
Axiomatization allows a potentially infinite set of sentences by representing them as a conclusion set from finitely many sentences.
|Neumann, John von
Philosophie und Mathematik Darmstadt 1995