20 ideas
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] |
13010 | In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine] |
9002 | Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine] |
13681 | Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider] |
13829 | If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine] |
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] |
9003 | Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine] |
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] |
9004 | If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine] |
9006 | Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping [Quine] |
9001 | Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine] |
9005 | Examination of convention in the a priori begins to blur the distinction with empirical knowledge [Quine] |
1558 | Clearly the gods ignore human affairs, or they would have given us justice [Thrasymachus] |