Combining Texts

All the ideas for 'fragments/reports', 'A Structural Account of Mathematics' and 'Dispositions and Powers'

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34 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]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Humeans see properties as having no more essential features and relations than their distinctness [Friend/Kimpton-Nye, by PG]
Dispositions are what individuate properties, and they constitute their essence [Friend/Kimpton-Nye]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
Powers are properties which necessitate dispositions [Friend/Kimpton-Nye]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
Dispositional essentialism (unlike the grounding view) says only fundamental properties are powers [Friend/Kimpton-Nye]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
A power is a property which consists entirely of dispositions [Friend/Kimpton-Nye]
Powers are qualitative properties which fully ground dispositions [Friend/Kimpton-Nye]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
Dispositions have directed behaviour which occurs if triggered [Friend/Kimpton-Nye]
'Masked' dispositions fail to react because something intervenes [Friend/Kimpton-Nye]
A disposition is 'altered' when the stimulus reverses the disposition [Friend/Kimpton-Nye]
A disposition is 'mimicked' if a different cause produces that effect from that stimulus [Friend/Kimpton-Nye]
A 'trick' can look like a stimulus for a disposition which will happen without it [Friend/Kimpton-Nye]
Some dispositions manifest themselves without a stimulus [Friend/Kimpton-Nye]
We could analyse dispositions as 'possibilities', with no mention of a stimulus [Friend/Kimpton-Nye]
9. Objects / E. Objects over Time / 8. Continuity of Rivers
Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Dispositionalism says modality is in the powers of this world, not outsourced to possible worlds [Friend/Kimpton-Nye]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle]
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]
26. Natural Theory / D. Laws of Nature / 7. Strictness of Laws
Hume's Dictum says no connections are necessary - so mass and spacetime warping could separate [Friend/Kimpton-Nye]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]