25 ideas
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] |
14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [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] |
17743 | De Morgan introduced a 'universe of discourse', to replace Boole's universe of 'all things' [De Morgan, by Walicki] |
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] |
17000 | We might fix identities for small particulars, but it is utopian to hope for such things [Kripke] |
11868 | A different piece of wood could have been used for that table; constitution isn't identity [Wiggins on Kripke] |
17044 | A relation can clearly be reflexive, and identity is the smallest reflexive relation [Kripke] |
16999 | A vague identity may seem intransitive, and we might want to talk of 'counterparts' [Kripke] |
17058 | What many people consider merely physically necessary I consider completely necessary [Kripke] |
4970 | What is often held to be mere physical necessity is actually metaphysical necessity [Kripke] |
17059 | Unicorns are vague, so no actual or possible creature could count as a unicorn [Kripke] |
4950 | Possible worlds are useful in set theory, but can be very misleading elsewhere [Kripke] |
17003 | Kaplan's 'Dthat' is a useful operator for transforming a description into a rigid designation [Kripke] |
9221 | The best known objection to counterparts is Kripke's, that Humphrey doesn't care if his counterpart wins [Kripke, by Sider] |
17052 | The a priori analytic truths involving fixing of reference are contingent [Kripke] |
4969 | I regard the mind-body problem as wide open, and extremely confusing [Kripke] |
4956 | A description may fix a reference even when it is not true of its object [Kripke] |
17032 | Even if Gödel didn't produce his theorems, he's still called 'Gödel' [Kripke] |