Combining Texts

All the ideas for 'works', 'fragments/reports' and 'A Structural Account of Mathematics'

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22 ideas

1. Philosophy / D. Nature of Philosophy / 4. Divisions of Philosophy
20771 Six parts: dialectic, rhetoric, ethics, politics, physics, theology [Cleanthes, by Diog. Laertius]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
9550 We only know relational facts about the empty set, but nothing intrinsic [Chihara]
9562 In simple type theory there is a hierarchy of null sets [Chihara]
9572 Realists about sets say there exists a null set in the real world, with no members [Chihara]
9573 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
9551 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
9549 The set theorist cannot tell us what 'membership' is [Chihara]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
9571 ZFU refers to the physical world, when it talks of 'urelements' [Chihara]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
9563 A pack of wolves doesn't cease when one member dies [Chihara]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
9561 The mathematics of relations is entirely covered by ordered pairs [Chihara]
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 [Chihara]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
9553 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
10192 We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
9559 If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara]
9566 No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
6028 Bodies interact with other bodies, and cuts cause pain, and shame causes blushing, so the soul is a body [Cleanthes, by Nemesius]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
20831 The soul suffers when the body hurts, creates redness from shame, and pallor from fear [Cleanthes]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
9568 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
9547 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
9574 'Gunk' is an individual possessing no parts that are atoms [Chihara]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
5993 The ascending scale of living creatures requires a perfect being [Cleanthes, by Tieleman]
28. God / C. Attitudes to God / 5. Atheism
3029 Stilpo said if Athena is a daughter of Zeus, then a statue is only the child of a sculptor, and so is not a god [Stilpo, by Diog. Laertius]