Combining Texts

All the ideas for 'A Structural Account of Mathematics', 'Paper of December 1676' and 'Mental Content'

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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 / 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]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Some explanations offer to explain a mystery by a greater mystery [Schulte]
17. Mind and Body / A. Mind-Body Dualism / 7. Zombies
It's impossible, but imagine a body carrying on normally, but with no mind [Leibniz]
18. Thought / C. Content / 1. Content
Phenomenal and representational character may have links, or even be united [Schulte]
Naturalistic accounts of content cannot rely on primitive mental or normative notions [Schulte]
Maybe we can explain mental content in terms of phenomenal properties [Schulte]
Naturalist accounts of representation must match the views of cognitive science [Schulte]
On the whole, referential content is seen as broad, and sense content as narrow [Schulte]
Naturalists must explain both representation, and what is represented [Schulte]
18. Thought / C. Content / 9. Conceptual Role Semantics
Conceptual role semantics says content is determined by cognitive role [Schulte]
18. Thought / C. Content / 10. Causal Semantics
Cause won't explain content, because one cause can produce several contents [Schulte]
18. Thought / C. Content / 11. Teleological Semantics
Teleosemantics explains content in terms of successful and unsuccessful functioning [Schulte]
Teleosemantic explanations say content is the causal result of naturally selected functions [Schulte]
18. Thought / C. Content / 12. Informational Semantics
Information theories say content is information, such as smoke making fire probable [Schulte]
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]