Combining Texts

All the ideas for 'Community and Citizenship', 'Reference and Necessity' and 'A Structural Account of Mathematics'

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


30 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
A pack of wolves doesn't cease when one member dies [Chihara]
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 / F. Referring in Logic / 1. Naming / c. Names as referential
To understand a name (unlike a description) picking the thing out is sufficient? [Stalnaker]
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]
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 / C. Structure of Objects / 7. Substratum
Possible worlds allow separating all the properties, without hitting a bare particular [Stalnaker]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
If it might be true, it might be true in particular ways, and possible worlds describe such ways [Stalnaker]
Possible worlds are ontologically neutral, but a commitment to possibilities remains [Stalnaker]
Possible worlds allow discussion of modality without controversial modal auxiliaries [Stalnaker]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
Kripke's possible worlds are methodological, not metaphysical [Stalnaker]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
Rigid designation seems to presuppose that differing worlds contain the same individuals [Stalnaker]
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 / A. Nature of Meaning / 1. Meaning
If you don't know what you say you can't mean it; what people say usually fits what they mean [Stalnaker]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
In the use of a name, many individuals are causally involved, but they aren't all the referent [Stalnaker]
Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara]
19. Language / C. Assigning Meanings / 2. Semantics
'Descriptive' semantics gives a system for a language; 'foundational' semantics give underlying facts [Stalnaker]
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
To understand an utterance, you must understand what the world would be like if it is true [Stalnaker]
24. Political Theory / B. Nature of a State / 4. Citizenship
Citizenship involves a group of mutually supporting rights, which create community and equality [Miller,D]
24. Political Theory / D. Ideologies / 14. Nationalism
Socialists reject nationality as a false source of identity [Miller,D]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]