20 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] |
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] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
8388 | Causation is either direct realism, Humean reduction, non-Humean reduction or theoretical realism [Tooley] |
8389 | Causation distinctions: reductionism/realism; Humean/non-Humean states; observable/non-observable [Tooley] |
8393 | We can only reduce the direction of causation to the direction of time if we are realist about the latter [Tooley] |
8390 | Causation is directly observable in pressure on one's body, and in willed action [Tooley] |
8392 | Probabilist laws are compatible with effects always or never happening [Tooley] |
8399 | The actual cause may not be the most efficacious one [Tooley] |
8391 | In counterfactual worlds there are laws with no instances, so laws aren't supervenient on actuality [Tooley] |
8394 | Explaining causation in terms of laws can't explain the direction of causation [Tooley] |
8398 | Causation is a concept of a relation the same in all worlds, so it can't be a physical process [Tooley] |