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Single Idea 10116

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

Full Idea

Hilbert's project was to establish the consistency of classical mathematics using just finitary means, to convince all parties that no contradictions will follow from employing the infinitary notions and reasoning.

Gist of Idea

Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions

Source

report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6

Book Ref

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.156

A Reaction

This is the project which was badly torpedoed by Gödel's Second Incompleteness Theorem.

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]