28 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] |
| 8983 | If 'red' is vague, then membership of the set of red things is vague, so there is no set of red things [Sainsbury] |
| 8986 | We should abandon classifying by pigeon-holes, and classify around paradigms [Sainsbury] |
| 8982 | Vague concepts are concepts without boundaries [Sainsbury] |
| 8984 | If concepts are vague, people avoid boundaries, can't spot them, and don't want them [Sainsbury] |
| 8985 | Boundaryless concepts tend to come in pairs, such as child/adult, hot/cold [Sainsbury] |
| 3144 | Everything is what it is, and not another thing [Butler] |
| 21315 | A tree remains the same in the popular sense, but not in the strict philosophical sense [Butler] |
| 21317 | Despite consciousness fluctuating, we are aware that it belongs to one person [Butler] |
| 21313 | If consciousness of events makes our identity, then if we have forgotten them we didn't exist then [Butler] |
| 21314 | Consciousness presupposes personal identity, so it cannot constitute it [Butler] |
| 21318 | If the self changes, we have no responsibilities, and no interest in past or future [Butler] |
| 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] |
| 8066 | Butler exalts conscience, but it may be horribly misleading [Anscombe on Butler] |
| 10431 | Things are thought to have a function, even when they can't perform them [Sainsbury] |