12 ideas
| 15457 | Interdefinition is useless by itself, but if we grasp one separately, we have them both [Lewis] |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| 15400 | We must avoid circularity between what is intrinsic and what is natural [Lewis, by Cameron] |
| 15458 | A property is 'intrinsic' iff it can never differ between duplicates [Lewis] |
| 15459 | Ellipsoidal stars seem to have an intrinsic property which depends on other objects [Lewis] |
| 13165 | Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus] |
| 9569 | The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus] |