17 ideas
| 472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
| 23029 | Knowledge is secured by the relations between its parts, through differences and identities [Green,TH, by Muirhead] |
| 467 | A virtue is a combination of intelligence, strength and luck [Ion] |
| 23046 | States only have full authority if they heed the claims of human fellowship [Green,TH] |
| 23051 | Equality also implies liberty, because equality must be of opportunity as well as possessions [Green,TH] |
| 23028 | The highest political efforts express our deeper social spirit [Green,TH, by Muirhead] |
| 23054 | Communism is wrong because it restricts the freedom of individuals to contribute to the community [Green,TH, by Muirhead] |
| 23047 | Original common ownership is securing private property, not denying it [Green,TH, by Muirhead] |
| 23042 | National spirit only exists in the individuals who embody it [Green,TH, by Muirhead] |
| 23048 | The ground of property ownership is not force but the power to use it for social ends [Green,TH, by Muirhead] |
| 23049 | Property is needed by all citizens, to empower them to achieve social goods [Green,TH] |
| 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] |