12 ideas
| 472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
| 23633 | Many truths seem obvious, and point to universal agreement - which is what we find [Reid] |
| 23630 | Only philosophers treat ideas as objects [Reid] |
| 23629 | The ambiguity of words impedes the advancement of knowledge [Reid] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 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] |
| 23632 | Similar effects come from similar causes, and causes are only what are sufficient for the effects [Reid] |
| 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] |