15 ideas
| 20771 | Six parts: dialectic, rhetoric, ethics, politics, physics, theology [Cleanthes, by Diog. Laertius] |
| 472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
| 19691 | Unlike knowledge, you can achieve understanding through luck [Grimm] |
| 19690 | 'Grasping' a structure seems to be modal, because we must anticipate its behaviour [Grimm] |
| 19692 | You may have 'weak' understanding, if by luck you can answer a set of 'why questions' [Grimm] |
| 6028 | Bodies interact with other bodies, and cuts cause pain, and shame causes blushing, so the soul is a body [Cleanthes, by Nemesius] |
| 20831 | The soul suffers when the body hurts, creates redness from shame, and pallor from fear [Cleanthes] |
| 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] |
| 5993 | The ascending scale of living creatures requires a perfect being [Cleanthes, by Tieleman] |