10 ideas
| 472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
| 19216 | Propositions (such as 'that dog is barking') only exist if their items exist [Williamson] |
| 7293 | It is legitimate to do harm if it is the unintended side-effect of an effort to achieve a good [Grayling] |
| 7292 | War must also have a good chance of success, and be waged with moderation [Grayling] |
| 1518 | Everything must involve numbers, or it couldn't be thought about or known [Philolaus] |
| 1519 | Harmony must pre-exist the cosmos, to bring the dissimilar sources together [Philolaus] |
| 473 | There is no falsehood in harmony and number, only in irrational things [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] |