more from David Hilbert

Single Idea 12457

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

Full Idea

A homogeneous continuum which admits of the sort of divisibility needed to realise the infinitely small is nowhere to be found in reality.

Gist of Idea

There is no continuum in reality to realise the infinitely small


David Hilbert (On the Infinite [1925], p.186)

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.186

A Reaction

He makes this remark as a response to Planck's new quantum theory (the year before the big works of Heisenberg and Schrödinger). Personally I don't see why infinities should depend on the physical world, since they are imaginary.