Combining Texts

All the ideas for 'Causal Explanation', 'Mathematical Intuition' and 'A Structural Account of Mathematics'

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30 ideas

3. Truth / A. Truth Problems / 6. Verisimilitude
Verisimilitude has proved hard to analyse, and seems to have several components [Lewis]
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]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C]
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 / C. Powers and Dispositions / 3. Powers as Derived
A disposition needs a causal basis, a property in a certain causal role. Could the disposition be the property? [Lewis]
10. Modality / B. Possibility / 7. Chance
We can explain a chance event, but can never show why some other outcome did not occur [Lewis]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
Does a good explanation produce understanding? That claim is just empty [Lewis]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Science may well pursue generalised explanation, rather than laws [Lewis]
14. Science / D. Explanation / 2. Types of Explanation / f. Necessity in explanations
A good explanation is supposed to show that the event had to happen [Lewis]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
Lewis endorses the thesis that all explanation of singular events is causal explanation [Lewis, by Psillos]
To explain an event is to provide some information about its causal history [Lewis]
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 / C. Causation / 2. Types of cause
Explaining match lighting in general is like explaining one lighting of a match [Lewis]
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
Ways of carving causes may be natural, but never 'right' [Lewis]
We only pick 'the' cause for the purposes of some particular enquiry. [Lewis]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
Causal dependence is counterfactual dependence between events [Lewis]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]