12 ideas
| 472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
| 4871 | A thing is free if it acts only by the necessity of its own nature [Spinoza] |
| 20416 | By 1790 aestheticians were mainly trying to explain individual artistic genius [Kemp] |
| 20417 | Expression can be either necessary for art, or sufficient for art (or even both) [Kemp] |
| 20419 | We don't already know what to express, and then seek means of expressing it [Kemp] |
| 20418 | The horror expressed in some works of art could equallly be expressed by other means [Kemp] |
| 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] |