Single Idea 12462

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite]

Full Idea

Operating with the infinite can be made certain only by the finitary.

Gist of Idea

Only the finite can bring certainty to the infinite

Source

David Hilbert (On the Infinite [1925], p.201)

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.201


A Reaction

See 'Compactness' for one aspect of this claim. I think Hilbert was fighting a rearguard action, and his idea now has few followers.