18 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] |
15938 | Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett] |
17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
15939 | For intuitionists it is constructed proofs (which take time) which make statements true [Dummett] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
15990 | Every individual thing which exists has an essence, which is its internal constitution [Locke] |
10709 | Priority is a modality, arising from collections and members [Potter] |
15994 | If it is knowledge, it is certain; if it isn't certain, it isn't knowledge [Locke] |