33 ideas
15457 | Interdefinition is useless by itself, but if we grasp one separately, we have them both [Lewis] |
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] |
17518 | Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers] |
17516 | If counting needs a sortal, what of things which fall under two sortals? [Ayers] |
17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
17520 | Events do not have natural boundaries, and we have to set them [Ayers] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
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] |
17519 | To express borderline cases of objects, you need the concept of an 'object' [Ayers] |
17511 | Recognising continuity is separate from sortals, and must precede their use [Ayers] |
17510 | Speakers need the very general category of a thing, if they are to think about it [Ayers] |
17522 | We use sortals to classify physical objects by the nature and origin of their unity [Ayers] |
17515 | Seeing caterpillar and moth as the same needs continuity, not identity of sortal concepts [Ayers] |
17517 | Could the same matter have more than one form or principle of unity? [Ayers] |
13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
17513 | If there are two objects, then 'that marble, man-shaped object' is ambiguous [Ayers] |
13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
17523 | Sortals basically apply to individuals [Ayers] |
17521 | You can't have the concept of a 'stage' if you lack the concept of an object [Ayers] |
17514 | Temporal 'parts' cannot be separated or rearranged [Ayers] |
17509 | Some say a 'covering concept' completes identity; others place the concept in the reference [Ayers] |
17512 | If diachronic identities need covering concepts, why not synchronic identities too? [Ayers] |
10709 | Priority is a modality, arising from collections and members [Potter] |