27 ideas
10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
13044 | Infinity: There is at least one limit level [Potter] |
10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
16235 | Persistence conditions cannot contradict, so there must be a 'dominant sortal' [Burke,M, by Hawley] |
14753 | The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider] |
16072 | 'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman] |
13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
14751 | Tib goes out of existence when the tail is lost, because Tib was never the 'cat' [Burke,M, by Sider] |
16071 | Sculpting a lump of clay destroys one object, and replaces it with another one [Burke,M, by Wasserman] |
16234 | Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley] |
13278 | Maybe the clay becomes a different lump when it becomes a statue [Burke,M, by Koslicki] |
14750 | Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider] |
13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
14637 | Only individuals have essences, so numbers (as a higher type based on classes) lack them [McMichael] |
14636 | Essences are the interesting necessary properties resulting from a thing's own peculiar nature [McMichael] |
14640 | Maybe essential properties have to be intrinsic, as well as necessary? [McMichael] |
14638 | Essentialism is false, because it implies the existence of necessary singular propositions [McMichael] |
10709 | Priority is a modality, arising from collections and members [Potter] |
14639 | Individuals enter into laws only through their general qualities and relations [McMichael] |