|Existence, philosophy, logic: the fact that there is something to which properties can be attributed. That does not mean that something has to be given immediately or can be perceived by the senses. See also ontology, properties, predicates, existence statements, realism, quantification, ascription.|
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|Berka I 294
Existence/consistency/concept/Hilbert: If one assigns features to a concept which contradict themself, so I say: the concept does not exist mathematically.
FregeVsHilbert/(s): would say the concept can exist, but there is no object for it.
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.
This would prove the existence of a number or a function.
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.
K. Berka/L. Kreiser
Logik Texte Berlin 1983