more from Democritus

Single Idea 16146

[catalogued under 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units]

Full Idea

Democritus claimed that one substance could not be composed from two nor two from one. …The same will clearly go for number, on the popular assumption that number is a combination of units. Unless two is one, it cannot contain a unit in actuality.

Gist of Idea

Two can't be a self-contained unit, because it would need to be one to do that

Source

report of Democritus (fragments/reports [c.431 BCE]) by Aristotle - Metaphysics 1039a15

Book Reference

Aristotle: 'The Metaphysics', ed/tr. Lawson-Tancred,Hugh [Penguin 1998], p.218


A Reaction

Chrysippus followed this up the first part with the memorable example of Dion and Theon. The problem with the second part is that 2, 3 and 4 are three numbers, so they can count as meta-units.

Related Ideas

Idea 16058 Dion and Theon coexist, but Theon lacks a foot. If Dion loses a foot, he ousts Theon? [Chrysippus, by Philo of Alexandria]

Idea 16059 Change of matter doesn't destroy identity - in Dion and Theon change is a condition of identity [Chrysippus, by Long/Sedley]