15 ideas
| 13163 | Circles must be bounded, so cannot be infinite [Leibniz] |
| 10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
| 10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
| 10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
| 10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
| 472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
| 13162 | Sloth's Syllogism: either it can't happen, or it is inevitable without my effort [Leibniz] |
| 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] |
| 19339 | Evil is a negation of good, which arises from non-being [Leibniz] |
| 13164 | God only made sin possible because a much greater good can be derived from it [Leibniz] |