26 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] |
9470 | Modal logic is not an extensional language [Parsons,C] |
13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
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] |
9469 | Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C] |
9468 | On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C] |
6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
9932 | The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen] |
6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
9923 | We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen] |
17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
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] |
18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |
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] |
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] |
13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
9919 | The old debate classified representations as abstract, not entities [Burgess/Rosen] |
9922 | If space is really just a force-field, then it is a physical entity [Burgess/Rosen] |