28 ideas
5438 | Hermeneutics of tradition is sympathetic, hermeneutics of suspicion is hostile [Ricoeur, by Mautner] |
9065 | S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P) [Keefe/Smith] |
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] |
14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [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] |
9064 | Objects such as a cloud or Mount Everest seem to have fuzzy boundaries in nature [Keefe/Smith] |
9044 | If someone is borderline tall, no further information is likely to resolve the question [Keefe/Smith] |
9048 | The simplest approach, that vagueness is just ignorance, retains classical logic and semantics [Keefe/Smith] |
9055 | The epistemic view of vagueness must explain why we don't know the predicate boundary [Keefe/Smith] |
9049 | Supervaluationism keeps true-or-false where precision can be produced, but not otherwise [Keefe/Smith] |
9056 | Vague statements lack truth value if attempts to make them precise fail [Keefe/Smith] |
9058 | Some of the principles of classical logic still fail with supervaluationism [Keefe/Smith] |
9059 | The semantics of supervaluation (e.g. disjunction and quantification) is not classical [Keefe/Smith] |
9060 | Supervaluation misunderstands vagueness, treating it as a failure to make things precise [Keefe/Smith] |
9050 | A third truth-value at borderlines might be 'indeterminate', or a value somewhere between 0 and 1 [Keefe/Smith] |
9061 | People can't be placed in a precise order according to how 'nice' they are [Keefe/Smith] |
9062 | If truth-values for vagueness range from 0 to 1, there must be someone who is 'completely tall' [Keefe/Smith] |
9063 | How do we decide if my coat is red to degree 0.322 or 0.321? [Keefe/Smith] |
9045 | Vague predicates involve uncertain properties, uncertain objects, and paradoxes of gradual change [Keefe/Smith] |
9047 | Many vague predicates are multi-dimensional; 'big' involves height and volume; heaps include arrangement [Keefe/Smith] |
9053 | If there is a precise borderline area, that is not a case of vagueness [Keefe/Smith] |