more from David Hilbert

Single Idea 12455

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite]

Full Idea

Just as in the limit processes of the infinitesimal calculus, the infinitely large and small proved to be a mere figure of speech, so too we must realise that the infinite in the sense of an infinite totality, used in deductive methods, is an illusion.

Gist of Idea

The idea of an infinite totality is an illusion


David Hilbert (On the Infinite [1925], p.184)

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.184

A Reaction

This is a very authoritative rearguard action. I no longer think the dispute matters much, it being just a dispute over a proposed new meaning for the word 'number'.