20 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] |
8983 | If 'red' is vague, then membership of the set of red things is vague, so there is no set of red things [Sainsbury] |
8986 | We should abandon classifying by pigeon-holes, and classify around paradigms [Sainsbury] |
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] |
8982 | Vague concepts are concepts without boundaries [Sainsbury] |
8984 | If concepts are vague, people avoid boundaries, can't spot them, and don't want them [Sainsbury] |
8985 | Boundaryless concepts tend to come in pairs, such as child/adult, hot/cold [Sainsbury] |
13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
10709 | Priority is a modality, arising from collections and members [Potter] |
22110 | Demonstration provides depth of understanding and explanation (rather than foundations) [Kretzmann/Stump] |