more from David Hilbert

Single Idea 12460

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

Full Idea

To preserve the simple formal rules of ordinary Aristotelian logic, we must supplement the finitary statements with ideal statements.

Gist of Idea

We extend finite statements with ideal ones, in order to preserve our logic


David Hilbert (On the Infinite [1925], p.195)

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.195

A Reaction

I find very appealing the picture of mathematics as rooted in the physical world, and then gradually extended by a series of 'idealisations', which should perhaps be thought of as fictions.