23 ideas
23449 | Interpreting a text is representing it as making sense [Morris,M] |
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] |
23484 | Bipolarity adds to Bivalence the capacity for both truth values [Morris,M] |
23494 | Conjunctive and disjunctive quantifiers are too specific, and are confined to the finite [Morris,M] |
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] |
23460 | To count, we must distinguish things, and have a series with successors in it [Morris,M] |
23451 | Counting needs to distinguish things, and also needs the concept of a successor in a series [Morris,M] |
23452 | Discriminating things for counting implies concepts of identity and distinctness [Morris,M] |
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] |
23491 | There must exist a general form of propositions, which are predictabe. It is: such and such is the case [Morris,M] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |