Combining Texts

All the ideas for 'Necessary Existents', 'The Ultimate Constituents of Matter' and 'A Structural Account of Mathematics'

expand these ideas     |    start again     |     specify just one area for these texts

27 ideas

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 [Chihara]
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]
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
7548 Classes, grouped by a convenient property, are logical constructions [Russell]
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 / 4. Anti-realism
7545 Visible things are physical and external, but only exist when viewed [Russell]
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]
12. Knowledge Sources / B. Perception / 4. Sense Data / b. Nature of sense-data
7553 Sense-data are purely physical [Russell]
7549 If my body literally lost its mind, the object seen when I see a flash would still exist [Russell]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
7546 A man is a succession of momentary men, bound by continuity and causation [Russell]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
7550 We could probably, in principle, infer minds from brains, and brains from minds [Russell]
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]
19. Language / D. Propositions / 3. Concrete Propositions
19216 Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
7551 Matter is a logical construction [Russell]
7547 Matter requires a division into time-corpuscles as well as space-corpuscles [Russell]
9574 'Gunk' is an individual possessing no parts that are atoms [Chihara]
27. Natural Reality / C. Space / 2. Space
7552 Six dimensions are needed for a particular, three within its own space, and three to locate that space [Russell]