12 ideas
| 472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
| 14369 | Understanding is a precondition, comes in degrees, is active, and holistic - unlike explanation [Strevens] |
| 14365 | Scientific understanding is always the grasping of a correct explanation [Strevens] |
| 14368 | We may 'understand that' the cat is on the mat, but not at all 'understand why' it is there [Strevens] |
| 22511 | Some reasonings are stronger than we are [Philolaus] |
| 5996 | Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA] |
| 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] |