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All the ideas for 'Necessary Existents', 'A Structural Account of Mathematics' and 'The Moral Problem'

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38 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
Analysis aims to express the full set of platitudes surrounding a given concept [Smith,M]
2. Reason / D. Definition / 1. Definitions
Defining a set of things by paradigms doesn't pin them down enough [Smith,M]
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]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Capturing all the common sense facts about rationality is almost impossible [Smith,M]
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]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]
20. Action / C. Motives for Action / 1. Acting on Desires
A pure desire could be criticised if it were based on a false belief [Smith,M]
A person can have a desire without feeling it [Smith,M]
In the Humean account, desires are not true/false, or subject to any rational criticism [Smith,M]
Subjects may be fallible about the desires which explain their actions [Smith,M]
Humeans (unlike their opponents) say that desires and judgements can separate [Smith,M]
If first- and second-order desires conflict, harmony does not require the second-order to win [Smith,M]
Objective reasons to act might be the systematic desires of a fully rational person [Smith,M]
Goals need desires, and so only desires can motivate us [Smith,M]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
Motivating reasons are psychological, while normative reasons are external [Smith,M]
Humeans take maximising desire satisfaction as the normative reasons for actions [Smith,M]
We cannot expect even fully rational people to converge on having the same desires for action [Smith,M]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / h. Against ethics
'Externalists' say moral judgements are not reasons, and maybe not even motives [Smith,M]
A person could make a moral judgement without being in any way motivated by it [Smith,M]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
Moral internalism says a judgement of rightness is thereby motivating [Smith,M]
'Rationalism' says the rightness of an action is a reason to perform it [Smith,M]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
Expressivists count attitudes as 'moral' if they concern features of things, rather than their mere existence [Smith,M]
22. Metaethics / B. Value / 1. Nature of Value / a. Nature of value
Is valuing something a matter of believing or a matter of desiring? [Smith,M]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]