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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 Ref
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.
18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |
10114 | Bounded quantification is originally finitary, as conjunctions and disjunctions [George/Velleman] |
10134 | Much infinite mathematics can still be justified finitely [George/Velleman] |