16 ideas
| 10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
| 10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
| 10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
| 10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
| 10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
| 10626 | Objects just are what singular terms refer to [Hale/Wright] |
| 472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
| 10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
| 10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |
| 5996 | Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA] |
| 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] |