24 ideas
9108 | From an impossibility anything follows [William of Ockham] |
9107 | A proposition is true if its subject and predicate stand for the same thing [William of Ockham] |
16300 | Ockham had an early axiomatic account of truth [William of Ockham, by Halbach] |
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] |
9106 | The word 'every' only signifies when added to a term such as 'man', referring to all men [William of Ockham] |
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] |
9113 | Just as unity is not a property of a single thing, so numbers are not properties of many things [William of Ockham] |
9110 | The words 'thing' and 'to be' assert the same idea, as a noun and as a verb [William of Ockham] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
15388 | Universals are single things, and only universal in what they signify [William of Ockham] |
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] |
9109 | If essence and existence were two things, one could exist without the other, which is impossible [William of Ockham] |
10709 | Priority is a modality, arising from collections and members [Potter] |
9105 | Some concepts for propositions exist only in the mind, and in no language [William of Ockham] |
1497 | For Anaximenes nature is air, which takes different forms by rarefaction and condensation [Anaximenes, by Simplicius] |