17 ideas
14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
14240 | The empty set is something, not nothing! [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] |
17879 | Axiomatising set theory makes it all relative [Skolem] |
13536 | Skolem did not believe in the existence of uncountable sets [Skolem] |
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] |
17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
594 | Speusippus suggested underlying principles for every substance, and ended with a huge list [Speussipus, by Aristotle] |
2632 | Speusippus said things were governed by some animal force rather than the gods [Speussipus, by Cicero] |