Full Idea
It is possible to use finitary reasoning to justify a significant part of infinitary mathematics.
Gist of Idea
Much infinite mathematics can still be justified finitely
Source
A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8)
Book Reference
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.219
A Reaction
This might save Hilbert's project, by gradually accepting into the fold all the parts which have been giving a finitist justification.