18 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] |
10429 | It is best to say that a name designates iff there is something for it to designate [Sainsbury] |
10425 | Definite descriptions may not be referring expressions, since they can fail to refer [Sainsbury] |
10438 | Definite descriptions are usually rigid in subject, but not in predicate, position [Sainsbury] |
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] |
579 | Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle] |
578 | Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle] |
10432 | A new usage of a name could arise from a mistaken baptism of nothing [Sainsbury] |
10434 | Even a quantifier like 'someone' can be used referentially [Sainsbury] |
10431 | Things are thought to have a function, even when they can't perform them [Sainsbury] |