16 ideas
13451 | The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano] |
13452 | Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano] |
13449 | We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano] |
13450 | Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano] |
13453 | Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano] |
17813 | Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP] |
17812 | Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP] |
472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
13448 | The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano] |
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] |