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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]

01.1

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 alephnull 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
