25 ideas
1597 | Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales] |
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] |
12184 | Logical necessity overrules all other necessities [McFetridge] |
15083 | The fundamental case of logical necessity is the valid conclusion of an inference [McFetridge, by Hale] |
15084 | In the McFetridge view, logical necessity means a consequent must be true if the antecedent is [McFetridge, by Hale] |
12180 | Logical necessity requires that a valid argument be necessary [McFetridge] |
12181 | Traditionally, logical necessity is the strongest, and entails any other necessities [McFetridge] |
12183 | It is only logical necessity if there is absolutely no sense in which it could be false [McFetridge] |
12192 | The mark of logical necessity is deduction from any suppositions whatever [McFetridge] |
12182 | We assert epistemic possibility without commitment to logical possibility [McFetridge] |
12187 | Objectual modal realists believe in possible worlds; non-objectual ones rest it on the actual world [McFetridge] |
3013 | Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius] |
12186 | Modal realists hold that necessities and possibilities are part of the totality of facts [McFetridge] |
1494 | Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle] |
1713 | Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle] |
1742 | Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius] |