12 ideas
| 472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
| 23111 | If we say that freedom depends on rationality, the irrational actions are not free [Sidgwick] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 23059 | Self-interest is not rational, if the self is just a succession of memories and behaviour [Sidgwick, by Gray] |
| 4129 | It is self-evident (from the point of view of the Universe) that no individual has more importance than another [Sidgwick] |
| 20588 | Sidwick argues for utilitarian institutions, rather than actions [Sidgwick, by Tuckness/Wolf] |
| 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] |
| 473 | There is no falsehood in harmony and number, only in irrational things [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] |