25 ideas
15927 | Definition just needs negation, known variables, conjunction, disjunction, substitution and quantification [Weyl, by Lavine] |
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] |
18151 | Could we replace sets by the open sentences that define them? [Chihara, by Bostock] |
9563 | A pack of wolves doesn't cease when one member dies [Chihara] |
8758 | We could talk of open sentences, instead of sets [Chihara, by Shapiro] |
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] |
10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
10265 | Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro] |
8759 | We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro] |
10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro] |
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] |
9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
8638 | Thomae's idea of abstract from peculiarities gives a general concept, and leaves the peculiarities [Frege on Thomae] |
9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
10246 | The limit of science is isomorphism of theories, with essences a matter of indifference [Weyl] |
9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |