26 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] |
23623 | Predicativism says only predicated sets exist [Hossack] |
23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
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] |
23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |
9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara] |
23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
9553 | Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara] |
23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
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] |
16755 | The possible Aristotelian view that forms are real and active principles is clearly wrong [Fine,K, by Pasnau] |
9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |