@misc{Lexicon of Arguments,
title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 28 Mar 2024},
author = {Hilbert,David},
subject = {Existence},
note = {Berka I 294
Existence/consistency/concept/Hilbert: if one assigns features to a concept which contradicts itself, I say: the concept does not exist mathematically.
>Consistency, >Contradictions.
FregeVsHilbert/(s): Frege would say the concept can exist, but there is no object for it.
>Concept/Frege, >Object/Frege, >Description levels,
>Levels/order.
Existence/number/Hilbert: the existence of a concept is proved if it can be shown that there are never contradictions in the application of a finite number of logical conclusions.
>Proofs, >Provability, >Finiteness, >Calculability.
This would prove the existence of a number or a function.
>Functions, >Numbers.
Berka I 294/295
Real numbers/existence/axioms/Hilbert: here, the consistency is a proof for the axioms and it is also the proof for the existence of the continuum(1).
>Real numbers.
1. D. Hilbert: Mathematische Probleme, in: Ders. Gesammelte Abhandlungen (1935), Vol. III, pp. 290-329 (gekürzter Nachdruck v. p. 299-301).},
note = {
Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 },
file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=410281}
url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=410281}
}