28 ideas
| 10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
| 9065 | S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P) [Keefe/Smith] |
| 21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
| 10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
| 10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
| 10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
| 10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
| 10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
| 10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
| 10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
| 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] |
| 22040 | Freedom is produced by the activity of the mind, and is not intrinsically given [Hegel] |
| 22039 | Geist is distinct from nature, not as a substance, but because of its normativity [Hegel, by Pinkard] |