2004 | Set Theory and Its Philosophy |
Intro 1 | p.4 | 10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning |
01.1 | p.8 | 10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional |
01.2 | p.13 | 10704 | We can formalize second-order formation rules, but not inference rules |
02.1 | p.22 | 13041 | Collections have fixed members, but fusions can be carved in innumerable ways |
02.1 | p.23 | 10707 | Mereology elides the distinction between the cards in a pack and the suits |
03.2 | p.37 | 10708 | Nowadays we derive our conception of collections from the dependence between them |
03.3 | p.39 | 10709 | Priority is a modality, arising from collections and members |
03.3 | p.40 | 13042 | If dependence is well-founded, with no infinite backward chains, this implies substances |
03.6 | p.43 | 10711 | Russell's paradox means we cannot assume that every property is collectivizing |
03.8 | p.51 | 10712 | If set theory didn't found mathematics, it is still needed to count infinite sets |
04.3 | p.59 | 10713 | Usually the only reason given for accepting the empty set is convenience |
04.7 | p.65 | 13043 | A relation is a set consisting entirely of ordered pairs |
04.9 | p.68 | 13044 | Infinity: There is at least one limit level |
05.2 | p.92 | 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms |
13.5 | p.227 | 13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects |