12 ideas
| 16901 | The equivalent algebra model of geometry loses some essential spatial meaning [Burge] |
| 16902 | Peano arithmetic requires grasping 0 as a primitive number [Burge] |
| 472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
| 16892 | Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 473 | There is no falsehood in harmony and number, only in irrational things [Philolaus] |
| 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] |
| 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] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| 1787 | Philolaus was the first person to say the earth moves in a circle [Philolaus, by Diog. Laertius] |