Full Idea
Just as in the limit processes of the infinitesimal calculus, the infinitely large and small proved to be a mere figure of speech, so too we must realise that the infinite in the sense of an infinite totality, used in deductive methods, is an illusion.
Gist of Idea
The idea of an infinite totality is an illusion
Source
David Hilbert (On the Infinite [1925], p.184)
Book Reference
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.184
A Reaction
This is a very authoritative rearguard action. I no longer think the dispute matters much, it being just a dispute over a proposed new meaning for the word 'number'.