Combining Philosophers

All the ideas for Anaxarchus, Cheryl Misak and Charles Chihara

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36 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
Modern pragmatism sees objectivity as possible, despite its gradual evolution [Misak]
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
Truth makes disagreements matter, or worth settling [Misak]
For pragmatists the loftiest idea of truth is just a feature of what remains forever assertible [Misak]
'True' is used for emphasis, clarity, assertion, comparison, objectivity, meaning, negation, consequence... [Misak]
'That's true' doesn't just refer back to a sentence, but implies sustained evidence for it [Misak]
Truth isn't a grand elusive property, if it is just the aim of our assertions and inquiries [Misak]
Truth is proper assertion, but that has varying standards [Misak]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Disquotation is bivalent [Misak]
Disquotations says truth is assertion, and assertion proclaims truth - but what is 'assertion'? [Misak]
Disquotationalism resembles a telephone directory [Misak]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflating the correspondence theory doesn't entail deflating all the other theories [Misak]
Deflationism isn't a theory of truth, but an account of its role in natural language [Misak]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
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]
Realists about sets say there exists a null set in the real world, with no members [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 / 4. Anti-realism
The anti-realism debate concerns whether indefeasibility is a plausible aim of inquiry [Misak]
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]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
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]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]