Full Idea
Hilbert proposed to circuvent the paradoxes by means of the doctrine (already proposed by Poincaré) that in mathematics consistency entails existence.
Gist of Idea
Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency
Source
report of David Hilbert (On the Concept of Number [1900], p.183) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 19 'Exist'
Book Reference
Potter,Michael: 'The Rise of Anaytic Philosophy 1879-1930' [Routledge 2020], p.129
A Reaction
Interesting. Hilbert's idea has struck me as weird, but it makes sense if its main motive is to block the paradoxes. Roughly, the idea is 'it exists if it isn't paradoxical'. A low bar for existence (but then it is only in mathematics!).