Combining Texts

All the ideas for 'works', 'The Limits of Abstraction' and 'A Structural Account of Mathematics'

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32 ideas

2. Reason / D. Definition / 3. Types of Definition
'Creative definitions' do not presuppose the existence of the objects defined [Fine,K]
Implicit definitions must be satisfiable, creative definitions introduce things, contextual definitions build on things [Fine,K, by Cook/Ebert]
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 / A. Nature of Existence / 4. Abstract Existence
Abstracts cannot be identified with sets [Fine,K]
Points in Euclidean space are abstract objects, but not introduced by abstraction [Fine,K]
Postulationism says avoid abstract objects by giving procedures that produce truth [Fine,K]
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]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
Freud treats the unconscious as intentional and hence mental [Freud, by Searle]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
Freud and others have shown that we don't know our own beliefs, feelings, motive and attitudes [Freud, by Shoemaker]
18. Thought / A. Modes of Thought / 3. Emotions / a. Nature of emotions
Freud said passions are pressures of some flowing hydraulic quantity [Freud, by Solomon]
18. Thought / E. Abstraction / 1. Abstract Thought
Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Fine,K, by Cook/Ebert]
18. Thought / E. Abstraction / 2. Abstracta by Selection
Many different kinds of mathematical objects can be regarded as forms of abstraction [Fine,K]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
We can abstract from concepts (e.g. to number) and from objects (e.g. to direction) [Fine,K]
Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Fine,K, by Cook/Ebert]
Abstractionism can be regarded as an alternative to set theory [Fine,K]
An object is the abstract of a concept with respect to a relation on concepts [Fine,K]
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]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Freud is pessimistic about human nature; it is ambivalent motive and fantasy, rather than reason [Freud, by Murdoch]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]