25 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] |
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] |
10709 | Priority is a modality, arising from collections and members [Potter] |
22167 | Our images of bodies are not produced by the bodies, but by our own minds [Augustine, by Aquinas] |
22117 | Our minds grasp reality by direct illumination (rather than abstraction from experience) [Augustine, by Matthews] |
7751 | Meaning needs an intention to induce a belief, and a recognition that this is the speaker's intention [Grice] |
7752 | Only the utterer's primary intention is relevant to the meaning [Grice] |
7753 | We judge linguistic intentions rather as we judge non-linguistic intentions, so they are alike [Grice] |
22118 | Augustine created the modern concept of the will [Augustine, by Matthews] |
4348 | Love, and do what you will [Augustine] |
7821 | Pagans produced three hundred definitions of the highest good [Augustine, by Grayling] |
22119 | Augustine said (unusually) that 'ought' does not imply 'can' [Augustine, by Matthews] |
22116 | Augustine identified Donatism, Pelagianism and Manicheism as the main heresies [Augustine, by Matthews] |
19338 | Augustine said evil does not really exist, and evil is a limitation in goodness [Augustine, by Perkins] |