19 ideas
8000 | He who is ignorant of the history of philosophy is doomed to repeat it [Santayana, by MacIntyre] |
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] |
10245 | One geometry cannot be more true than another [Poincaré] |
14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
15923 | Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Poincaré, by Lavine] |
14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
10180 | Mathematicians do not study objects, but relations between objects [Poincaré] |
9916 | Convention, yes! Arbitrary, no! [Poincaré, by Putnam] |
18203 | Avoid non-predicative classifications and definitions [Poincaré] |
18521 | The criterion of existence is the possibility of action [Santayana] |
23060 | The good is not relative, but is rooted in facts about human needs [Santayana] |
15877 | The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré] |