12 ideas
| 18528 | The single imagined 'interval' between things only exists in the intellect [Auriol] |
| 472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
| 22511 | Some reasonings are stronger than we are [Philolaus] |
| 473 | There is no falsehood in harmony and number, only in irrational things [Philolaus] |
| 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] |
| 16589 | Prime matter lacks essence, but is only potentially and indeterminately a physical thing [Auriol] |
| 1497 | For Anaximenes nature is air, which takes different forms by rarefaction and condensation [Anaximenes, by Simplicius] |
| 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] |
| 16651 | God can do anything non-contradictory, as making straightness with no line, or lightness with no parts [Auriol] |