31 ideas
| 9572 | Realists about sets say there exists a null set in the real world, with no members [Chihara] |
| 9550 | We only know relational facts about the empty set, but nothing intrinsic [Chihara] |
| 9562 | In simple type theory there is a hierarchy of null sets [Chihara] |
| 9573 | The null set is a structural position which has no other position in membership relation [Chihara] |
| 9551 | What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara] |
| 9549 | The set theorist cannot tell us what 'membership' is [Chihara] |
| 9571 | ZFU refers to the physical world, when it talks of 'urelements' [Chihara] |
| 9563 | A pack of wolves doesn't cease when one member dies [Chihara] |
| 9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
| 9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara] |
| 9553 | Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara] |
| 23026 | We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz] |
| 10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
| 9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara] |
| 9566 | No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara] |
| 13189 | A necessary feature (such as air for humans) is not therefore part of the essence [Leibniz] |
| 19432 | Intelligible truth is independent of any external things or experiences [Leibniz] |
| 20298 | The traditional a priori is justified without experience; post-Quine it became unrevisable by experience [Rey] |
| 19430 | We know objects by perceptions, but their qualities don't reveal what it is we are perceiving [Leibniz] |
| 19431 | There is nothing in the understanding but experiences, plus the understanding itself, and the understander [Leibniz] |
| 9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
| 20300 | Externalist synonymy is there being a correct link to the same external phenomena [Rey] |
| 9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
| 20294 | 'Married' does not 'contain' its symmetry, nor 'bigger than' its transitivity [Rey] |
| 20293 | Analytic judgements can't be explained by contradiction, since that is what is assumed [Rey] |
| 20297 | Analytic statements are undeniable (because of meaning), rather than unrevisable [Rey] |
| 20301 | The meaning properties of a term are those which explain how the term is typically used [Rey] |
| 20302 | An intrinsic language faculty may fix what is meaningful (as well as grammatical) [Rey] |
| 20303 | Research throws doubts on the claimed intuitions which support analyticity [Rey] |
| 20299 | If we claim direct insight to what is analytic, how do we know it is not sub-consciously empirical? [Rey] |
| 9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |