27 ideas
9978 | Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait] |
9572 | Realists about sets say there exists a null set in the real world, with no members [Chihara] |
9986 | The null set was doubted, because numbering seemed to require 'units' [Tait] |
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] |
9984 | We can have a series with identical members [Tait] |
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] |
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] |
9981 | Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait] |
9982 | Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait] |
9985 | Abstraction may concern the individuation of the set itself, not its elements [Tait] |
9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
9972 | Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait] |
9980 | If abstraction produces power sets, their identity should imply identity of the originals [Tait] |
9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |