green numbers give 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
|
18151
|
Could we replace sets by the open sentences that define them? [Bostock]
|
|
1990
|
Constructibility and Mathematical Existence
|
|
|
p.230
|
10264
|
Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Shapiro]
|
|
|
p.231
|
10265
|
Chihara's system is a variant of type theory, from which he can translate sentences [Shapiro]
|
|
|
p.239
|
8758
|
We could talk of open sentences, instead of sets [Shapiro]
|
|
|
p.242
|
8759
|
We can replace type theory with open sentences and a constructibility quantifier [Shapiro]
|
|
2004
|
A Structural Account of Mathematics
|
|
|
p.81
|
10192
|
We can replace existence of sets with possibility of constructing token sentences [MacBride]
|
|
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
|
9549
|
The set theorist cannot tell us what 'membership' is
|
|
01.5
|
p.24
|
9550
|
We only know relational facts about the empty set, but nothing intrinsic
|
|
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
|
|
05.8
|
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
|