@misc{Lexicon of Arguments,
title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 29 Mar 2024},
author = {Neumann,John von},
subject = {Ordinal Numbers},
note = {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.
>Numbers.
John v. Neumann: Axiomatic construction of the set theory. In the foundation of logic certain formulas are recognized as "excellent formulas".
>Axioms, >Axiom systems, >Set theory, >Sets.
I 206
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.
>Logic, >Statements.
I 207
Axiomatization allows a potentially infinite set of sentences by representing them as a conclusion set from finitely many sentences.
>Axiomatization, cf. >Are there infinitely many possible sentences?/Researchgate.},
note = { NeumJ I J. v. Neumann The Computer and the Brain New Haven 2012
T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 },
file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=808149}
url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=808149}
}