30 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] |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
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] |
16665 | There are entities, and then positive 'modes', modifying aspects outside the thing's essence [Suárez] |
16666 | A mode determines the state and character of a quantity, without adding to it [Suárez] |
16667 | Substances are incomplete unless they have modes [Suárez, by Pasnau] |
17007 | Forms must rule over faculties and accidents, and are the source of action and unity [Suárez] |
16780 | Partial forms of leaf and fruit are united in the whole form of the tree [Suárez] |
16758 | The best support for substantial forms is the co-ordinated unity of a natural being [Suárez] |
16743 | We can get at the essential nature of 'quantity' by knowing bulk and extension [Suárez] |
16742 | We only know essences through non-essential features, esp. those closest to the essence [Suárez] |
22143 | Identity does not exclude possible or imagined difference [Suárez, by Boulter] |
22146 | Minor Real distinction: B needs A, but A doesn't need B [Suárez, by Boulter] |
22145 | Major Real distinction: A and B have independent existences [Suárez, by Boulter] |
22144 | Real Essential distinction: A and B are of different natural kinds [Suárez, by Boulter] |
22147 | Conceptual/Mental distinction: one thing can be conceived of in two different ways [Suárez, by Boulter] |
22148 | Modal distinction: A isn't B or its property, but still needs B [Suárez, by Boulter] |
22149 | Scholastics assess possibility by what has actually happened in reality [Suárez, by Boulter] |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
16682 | Other things could occupy the same location as an angel [Suárez] |