24 ideas
14240 | The empty set is something, not nothing! [Oliver/Smiley] |
14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
14637 | Only individuals have essences, so numbers (as a higher type based on classes) lack them [McMichael] |
14636 | Essences are the interesting necessary properties resulting from a thing's own peculiar nature [McMichael] |
14640 | Maybe essential properties have to be intrinsic, as well as necessary? [McMichael] |
14638 | Essentialism is false, because it implies the existence of necessary singular propositions [McMichael] |
19712 | Maybe there is plain 'animal' knowledge, and clearly justified 'reflective' knowledge [Vahid] |
19703 | Epistemic is normally marked out from moral or pragmatic justifications by its truth-goal [Vahid] |
19705 | 'Mentalist' internalism seems to miss the main point, if it might not involve an agent's access [Vahid] |
19706 | Strong access internalism needs actual awareness; weak versions need possibility of access [Vahid] |
19707 | Maybe we need access to our justification, and also to know why it justifies [Vahid] |
19709 | Internalism in epistemology over-emphasises deliberation about beliefs [Vahid] |
19704 | Externalism may imply that identical mental states might go with different justifications [Vahid] |
19710 | With a counterfactual account of the causal theory, we get knowledge as tracking or sensitive to truth [Vahid] |
19711 | Externalism makes the acquisition of knowledge too easy? [Vahid] |
14639 | Individuals enter into laws only through their general qualities and relations [McMichael] |