16 ideas
| 17833 | The first-order ZF axiomatisation is highly non-categorical [Hallett,M] |
| 17834 | Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M] |
| 17837 | Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M] |
| 17836 | The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M] |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| 472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
| 22511 | Some reasonings are stronger than we are [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] |
| 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] |