12 ideas
| 17462 | A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt] |
| 17461 | Some 'how many?' answers are not predications of a concept, like 'how many gallons?' [Rumfitt] |
| 18933 | Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius] |
| 472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
| 5864 | Destroy seriousness with laughter, and laughter with seriousness [Gorgias] |
| 9866 | Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato] |
| 473 | There is no falsehood in harmony and number, only in irrational things [Philolaus] |
| 1519 | Harmony must pre-exist the cosmos, to bring the dissimilar sources together [Philolaus] |
| 1518 | Everything must involve numbers, or it couldn't be thought about or known [Philolaus] |
| 469 | Existing things, and hence the Cosmos, are a mixture of the Limited and the Unlimited [Philolaus] |
| 476 | Self-created numbers make the universe stable [Philolaus] |
| 1787 | Philolaus was the first person to say the earth moves in a circle [Philolaus, by Diog. Laertius] |