13 ideas
| 472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
| 1554 | Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind] |
| 22511 | Some reasonings are stronger than we are [Philolaus] |
| 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] |
| 6011 | There is a remote first god (the Good), and a second god who organises the material world [Numenius, by O'Meara] |
| 1555 | People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus] |
| 1543 | He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus] |
| 535 | The gods are just personified human benefits [Prodicus] |