32 ideas
| 22270 | Frege changed philosophy by extending logic's ability to check the grounds of thinking [Potter on Frege] |
| 8939 | We should not describe human laws of thought, but how to correctly track truth [Frege, by Fisher] |
| 4971 | I don't use 'subject' and 'predicate' in my way of representing a judgement [Frege] |
| 17745 | For Frege, 'All A's are B's' means that the concept A implies the concept B [Frege, by Walicki] |
| 14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
| 14240 | The empty set is something, not nothing! [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] |
| 7728 | Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing) [Frege, by Weiner] |
| 16881 | The laws of logic are boundless, so we want the few whose power contains the others [Frege] |
| 7622 | In 1879 Frege developed second order logic [Frege, by Putnam] |
| 7729 | Frege replaced Aristotle's subject/predicate form with function/argument form [Frege, by Weiner] |
| 9950 | A quantifier is a second-level predicate (which explains how it contributes to truth-conditions) [Frege, by George/Velleman] |
| 9991 | For Frege the variable ranges over all objects [Frege, by Tait] |
| 10536 | Frege's domain for variables is all objects, but modern interpretations first fix the domain [Dummett on Frege] |
| 7730 | Frege introduced quantifiers for generality [Frege, by Weiner] |
| 7742 | Frege reduced most quantifiers to 'everything' combined with 'not' [Frege, by McCullogh] |
| 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] |
| 13824 | Proof theory began with Frege's definition of derivability [Frege, by Prawitz] |
| 13609 | Frege produced axioms for logic, though that does not now seem the natural basis for logic [Frege, by Kaplan] |
| 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] |
| 17855 | It may be possible to define induction in terms of the ancestral relation [Frege, by Wright,C] |
| 14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
| 10607 | Frege's logic has a hierarchy of object, property, property-of-property etc. [Frege, by Smith,P] |
| 11008 | Existence is not a first-order property, but the instantiation of a property [Frege, by Read] |
| 22280 | Frege's account was top-down and decompositional, not bottom-up and compositional [Frege, by Potter] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| 7741 | The predicate 'exists' is actually a natural language expression for a quantifier [Frege, by Weiner] |