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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
Source
David Hilbert (On the Infinite [1925], p.186)
Book Ref
'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.
| 22930 | Lengths do not contain infinite parts; parts are created by acts of division [Aristotle, by Le Poidevin] |
| 18833 | A continuous line cannot be composed of indivisible points [Aristotle] |
| 19375 | The continuum is not divided like sand, but folded like paper [Leibniz, by Arthur,R] |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| 8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |