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Single Idea 10134

[filed under theme 6. Mathematics / C. Sources of Mathematics / 8. Finitism ]

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.

The 5 ideas with the same theme [true mathematics only concerns finite quantities]:

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]