display all the ideas for this combination of philosophers
3 ideas
| 16146 | Two can't be a self-contained unit, because it would need to be one to do that [Democritus, by Aristotle] |
| 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. | |
| From: report of Democritus (fragments/reports [c.431 BCE]) by Aristotle - Metaphysics 1039a15 | |
| 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. |
| 3907 | Could you be intellectually acquainted with numbers, but unable to count objects? [Scruton] |
| Full Idea: Could someone have a perfect intellectual acquaintance with numbers, but be incapable of counting a flock of sheep? | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 26.6) |
| 3908 | If maths contains unprovable truths, then maths cannot be reduced to a set of proofs [Scruton] |
| Full Idea: If there can be unprovable truths of mathematics, then mathematics cannot be reduced to the proofs whereby we construct it. | |
| From: Roger Scruton (Modern Philosophy:introduction and survey [1994], 26.7) |