29 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] |
23651 | Universals are not objects of sense and cannot be imagined - but can be conceived [Reid] |
23650 | Only individuals exist [Reid] |
23649 | No one thinks two sheets possess a single whiteness, but all agree they are both white [Reid] |
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] |
11874 | Real identity admits of no degrees [Reid] |
10709 | Priority is a modality, arising from collections and members [Potter] |
23029 | Knowledge is secured by the relations between its parts, through differences and identities [Green,TH, by Muirhead] |
23652 | We must first conceive things before we can consider them [Reid] |
23648 | First we notice and name attributes ('abstracting'); then we notice that subjects share them ('generalising') [Reid] |
23046 | States only have full authority if they heed the claims of human fellowship [Green,TH] |
23051 | Equality also implies liberty, because equality must be of opportunity as well as possessions [Green,TH] |
23028 | The highest political efforts express our deeper social spirit [Green,TH, by Muirhead] |
23054 | Communism is wrong because it restricts the freedom of individuals to contribute to the community [Green,TH, by Muirhead] |
23047 | Original common ownership is securing private property, not denying it [Green,TH, by Muirhead] |
23042 | National spirit only exists in the individuals who embody it [Green,TH, by Muirhead] |
23048 | The ground of property ownership is not force but the power to use it for social ends [Green,TH, by Muirhead] |
23049 | Property is needed by all citizens, to empower them to achieve social goods [Green,TH] |