27 ideas
17082 | Paradox: why do you analyse if you know it, and how do you analyse if you don't? [Ruben] |
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] |
9572 | Realists about sets say there exists a null set in the real world, with no members [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] |
13827 | Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz] |
9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
13826 | Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz] |
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] |
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] |
17087 | The 'symmetry thesis' says explanation and prediction only differ pragmatically [Ruben] |
17081 | Usually explanations just involve giving information, with no reference to the act of explanation [Ruben] |
17092 | An explanation needs the world to have an appropriate structure [Ruben] |
17090 | Most explanations are just sentences, not arguments [Ruben] |
17094 | The causal theory of explanation neglects determinations which are not causal [Ruben] |
17088 | Reducing one science to another is often said to be the perfect explanation [Ruben] |
17089 | Facts explain facts, but only if they are conceptualised or named appropriately [Ruben] |
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] |