17 ideas
15970 | People generalise because it is easier to understand, and that is mistaken for deep philosophy [Feynman] |
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] |
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] |
17809 | Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel] |
17810 | The study of mathematical foundations needs new non-mathematical concepts [Kreisel] |
14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
9410 | Physical Laws are rhythms and patterns in nature, revealed by analysis [Feynman] |
18530 | Nobody understands quantum mechanics [Feynman] |
17707 | We should regard space as made up of many tiny pieces [Feynman, by Mares] |
17811 | The natural conception of points ducks the problem of naming or constructing each point [Kreisel] |