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Ideas of Charles Chihara, by Text
[American, fl. 1998, Professor at the University of California, at Berkeley.]
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1973
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Ontology and the Vicious Circle Principle
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p.283
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18151
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Could we replace sets by the open sentences that define them? [Bostock]
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1990
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Constructibility and Mathematical Existence
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p.230
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10264
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Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Shapiro]
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p.231
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10265
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Chihara's system is a variant of type theory, from which he can translate sentences [Shapiro]
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p.239
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8758
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We could talk of open sentences, instead of sets [Shapiro]
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p.242
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8759
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We can replace type theory with open sentences and a constructibility quantifier [Shapiro]
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2004
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A Structural Account of Mathematics
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p.81
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10192
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We can replace existence of sets with possibility of constructing token sentences [MacBride]
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01.3
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p.16
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9547
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Mathematical entities are causally inert, so the causal theory of reference won't work for them
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01.5
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p.24
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9549
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The set theorist cannot tell us what 'membership' is
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01.5
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p.24
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9550
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We only know relational facts about the empty set, but nothing intrinsic
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01.5
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p.25
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9551
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What is special about Bill Clinton's unit set, in comparison with all the others?
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02.1
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p.33
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9552
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Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced
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02.3
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p.43
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9553
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Analytic geometry gave space a mathematical structure, which could then have axioms
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05.8
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p.133
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9559
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If a successful theory confirms mathematics, presumably a failed theory disconfirms it?
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07.2
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p.174
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9561
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The mathematics of relations is entirely covered by ordered pairs
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07.4
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p.192
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9562
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In simple type theory there is a hierarchy of null sets
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07.5
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p.203
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9563
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A pack of wolves doesn't cease when one member dies
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09.1
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p.236
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9566
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No scientific explanation would collapse if mathematical objects were shown not to exist
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09.10
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p.277
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9568
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I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes'
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11.5
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p.336
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9571
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ZFU refers to the physical world, when it talks of 'urelements'
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11.6
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p.343
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9572
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Realists about sets say there exists a null set in the real world, with no members
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11.6
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p.343
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9573
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The null set is a structural position which has no other position in membership relation
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App A
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p.352
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9574
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'Gunk' is an individual possessing no parts that are atoms
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