1973 | Ontology and the Vicious Circle Principle |
p.283 | 18151 | Could we replace sets by the open sentences that define them? |
1990 | Constructibility and Mathematical Existence |
p.230 | 10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' |
p.231 | 10265 | Chihara's system is a variant of type theory, from which he can translate sentences |
p.239 | 8758 | We could talk of open sentences, instead of sets |
p.242 | 8759 | We can replace type theory with open sentences and a constructibility quantifier |
2004 | A Structural Account of Mathematics |
p.81 | 10192 | We can replace existence of sets with possibility of constructing token sentences |
01.1 | p.9 | 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects |
01.3 | p.16 | 9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them |
01.5 | p.24 | 9550 | We only know relational facts about the empty set, but nothing intrinsic |
01.5 | p.24 | 9549 | The set theorist cannot tell us what 'membership' is |
01.5 | p.25 | 9551 | What is special about Bill Clinton's unit set, in comparison with all the others? |
02.1 | p.33 | 9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced |
02.3 | p.43 | 9553 | Analytic geometry gave space a mathematical structure, which could then have axioms |
05.1 | p.79 | 9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum |
05.8 | p.133 | 9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? |
07.2 | p.174 | 9561 | The mathematics of relations is entirely covered by ordered pairs |
07.4 | p.192 | 9562 | In simple type theory there is a hierarchy of null sets |
07.5 | p.203 | 9563 | A pack of wolves doesn't cease when one member dies |
09.1 | p.236 | 9566 | No scientific explanation would collapse if mathematical objects were shown not to exist |
09.10 | p.277 | 9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' |
11.5 | p.336 | 9571 | ZFU refers to the physical world, when it talks of 'urelements' |
11.6 | p.343 | 9573 | The null set is a structural position which has no other position in membership relation |
11.6 | p.343 | 9572 | Realists about sets say there exists a null set in the real world, with no members |
App A | p.352 | 9574 | 'Gunk' is an individual possessing no parts that are atoms |