15 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] |
8447 | In 'Etna is higher than Vesuvius' the whole of Etna, including all the lava, can't be the reference [Frege] |
8448 | Any object can have many different names, each with a distinct sense [Frege] |
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] |
8446 | We understand new propositions by constructing their sense from the words [Frege] |
8449 | Senses can't be subjective, because propositions would be private, and disagreement impossible [Frege] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |