28 ideas
9065 | S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P) [Keefe/Smith] |
12456 | I aim to establish certainty for mathematical methods [Hilbert] |
12461 | We believe all mathematical problems are solvable [Hilbert] |
9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
12462 | Only the finite can bring certainty to the infinite [Hilbert] |
12455 | The idea of an infinite totality is an illusion [Hilbert] |
12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
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] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
22511 | Some reasonings are stronger than we are [Philolaus] |