Ideas of Charles Chihara, by Theme

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

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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set

9572	Realists about sets say there exists a null set in the real world, with no members

9550	We only know relational facts about the empty set, but nothing intrinsic

9562	In simple type theory there is a hierarchy of null sets

9573	The null set is a structural position which has no other position in membership relation

4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets

9551	What is special about Bill Clinton's unit set, in comparison with all the others?

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing

9549	The set theorist cannot tell us what 'membership' is

4. Formal Logic / F. Set Theory ST / 7. Natural Sets

9571	ZFU refers to the physical world, when it talks of 'urelements'

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

18151

Could we replace sets by the open sentences that define them? [Bostock]

8758	We could talk of open sentences, instead of sets [Shapiro]

9563	A pack of wolves doesn't cease when one member dies

5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic

9561	The mathematics of relations is entirely covered by ordered pairs

5. Theory of Logic / K. Features of Logics / 2. Consistency

9552	Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry

9553	Analytic geometry gave space a mathematical structure, which could then have axioms

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism

10192

We can replace existence of sets with possibility of constructing token sentences [MacBride]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory

10265

Chihara's system is a variant of type theory, from which he can translate sentences [Shapiro]

8759	We can replace type theory with open sentences and a constructibility quantifier [Shapiro]

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism

10264

Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Shapiro]

7. Existence / D. Theories of Reality / 10. Ontological Commitment / e. Ontological commitment problems

9559	If a successful theory confirms mathematics, presumably a failed theory disconfirms it?

9566	No scientific explanation would collapse if mathematical objects were shown not to exist

18. Thought / E. Abstraction / 7. Abstracta by Equivalence

9568	I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes'

19. Language / B. Reference / 3. Direct Reference / b. Causal reference

9547	Mathematical entities are causally inert, so the causal theory of reference won't work for them

27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter

9574	'Gunk' is an individual possessing no parts that are atoms