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Full Idea
No continuum can be composed of indivisibles: e.g. a line cannot be composed of points, the line being continuous and the points indivisibles.
Clarification
An 'indivisible' is an 'atom'
Gist of Idea
A continuous line cannot be composed of indivisible points
Source
Aristotle (Physics [c.337 BCE], 231a23), quoted by Ian Rumfitt - The Boundary Stones of Thought 7.4
Book Ref
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.210
A Reaction
Rumfitt observes that ' the basic problem is to say what the ultimate parts of a continuum are, of they are not points'. Early modern philosophers had lots of proposals.
| 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] |