idea number gives full details.     |    back to list of philosophers     |     expand these ideas

Ideas of Charles Chihara, by Text

[American, fl. 1998, Professor at the University of California, at Berkeley.]

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