25 ideas
9921 | 'True' is only occasionally useful, as in 'everything Fermat believed was true' [Burgess/Rosen] |
9924 | Modal logic gives an account of metalogical possibility, not metaphysical possibility [Burgess/Rosen] |
13451 | The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano] |
8956 | What is a singleton set, if a set is meant to be a collection of objects? [Szabó] |
13452 | Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano] |
9933 | The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set [Burgess/Rosen] |
9928 | Mereology implies that acceptance of entities entails acceptance of conglomerates [Burgess/Rosen] |
9926 | A relation is either a set of sets of sets, or a set of sets [Burgess/Rosen] |
13449 | We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano] |
13450 | Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano] |
13453 | Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano] |
9932 | The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen] |
9923 | We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen] |
9925 | Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen] |
9934 | Number words became nouns around the time of Plato [Burgess/Rosen] |
9918 | Abstract/concrete is a distinction of kind, not degree [Burgess/Rosen] |
9929 | Much of what science says about concrete entities is 'abstraction-laden' [Burgess/Rosen] |
8953 | Abstract entities don't depend on their concrete entities ...but maybe on the totality of concrete things [Szabó] |
9927 | Mathematics has ascended to higher and higher levels of abstraction [Burgess/Rosen] |
9930 | Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas [Burgess/Rosen] |
8954 | Geometrical circles cannot identify a circular paint patch, presumably because they lack something [Szabó] |
9919 | The old debate classified representations as abstract, not entities [Burgess/Rosen] |
8955 | Abstractions are imperceptible, non-causal, and non-spatiotemporal (the third explaining the others) [Szabó] |
13448 | The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano] |
9922 | If space is really just a force-field, then it is a physical entity [Burgess/Rosen] |