Combining Texts

All the ideas for 'fragments/reports', 'A Structural Account of Mathematics' and 'Some Remarks on Essentialism'

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23 ideas

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]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
13952 Essentialism says some of a thing's properties are necessary, and could not be absent [Cartwright,R]
9. Objects / D. Essence of Objects / 14. Knowledge of Essences
13954 The difficulty in essentialism is deciding the grounds for rating an attribute as essential [Cartwright,R]
9. Objects / D. Essence of Objects / 15. Against Essentialism
13955 Essentialism is said to be unintelligible, because relative, if necessary truths are all analytic [Cartwright,R]
9. Objects / F. Identity among Objects / 3. Relative Identity
13953 An act of ostension doesn't seem to need a 'sort' of thing, even of a very broad kind [Cartwright,R]
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]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
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]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]