@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} }