Combining Philosophers

All the ideas for W Wimsatt/W Beardsley, Michael Burke and Charles Chihara

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36 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Realists about sets say there exists a null set in the real world, with no members [Chihara]
We only know relational facts about the empty set, but nothing intrinsic [Chihara]
In simple type theory there is a hierarchy of null sets [Chihara]
The null set is a structural position which has no other position in membership relation [Chihara]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
The set theorist cannot tell us what 'membership' is [Chihara]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
ZFU refers to the physical world, when it talks of 'urelements' [Chihara]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Could we replace sets by the open sentences that define them? [Chihara, by Bostock]
A pack of wolves doesn't cease when one member dies [Chihara]
We could talk of open sentences, instead of sets [Chihara, by Shapiro]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
The mathematics of relations is entirely covered by ordered pairs [Chihara]
5. Theory of Logic / K. Features of Logics / 2. Consistency
Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro]
We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara]
No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
Persistence conditions cannot contradict, so there must be a 'dominant sortal' [Burke,M, by Hawley]
The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
Tib goes out of existence when the tail is lost, because Tib was never the 'cat' [Burke,M, by Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
Sculpting a lump of clay destroys one object, and replaces it with another one [Burke,M, by Wasserman]
Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley]
Maybe the clay becomes a different lump when it becomes a statue [Burke,M, by Koslicki]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara]
21. Aesthetics / C. Artistic Issues / 1. Artistic Intentions
Intentions either succeed or fail, so external evidence for them is always irrelevant [Wimsatt/Beardsley, by Davies,S]
The author's intentions are irrelevant to the judgement of a work's success [Wimsatt/Beardsley]
Poetry, unlike messages, can be successful without communicating intentions [Wimsatt/Beardsley]
The thoughts of a poem should be imputed to the dramatic speaker, and hardly at all to the poet [Wimsatt/Beardsley]
The intentional fallacy is a romantic one [Wimsatt/Beardsley]
Biography can reveal meanings and dramatic character, as well as possible intentions [Wimsatt/Beardsley]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]