Combining Texts

All the ideas for 'fragments/reports', 'Creating Capabilities' and 'A Structural Account of Mathematics'

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37 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
Keep premises as weak as possible, to avoid controversial difficulties [Nussbaum]
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 / 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]
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
Storytelling is never neutral; some features of the world must be emphasised [Nussbaum]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
Particularism gives no guidance for the future [Nussbaum]
23. Ethics / C. Virtue Theory / 3. Virtues / f. Compassion
Compassion is unreliable, because it favours people close to us [Nussbaum]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
Social contracts assume equal powers among the participants [Nussbaum]
24. Political Theory / D. Ideologies / 4. Social Utilitarianism
We shouldn't focus on actual preferences, which may be distorted by injustices [Nussbaum]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
Liberalism does not need a comprehensive account of value [Nussbaum]
24. Political Theory / D. Ideologies / 12. Feminism
Women are often treated like children, and not respected for their choices [Nussbaum]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
Negative liberty is incoherent; all liberties, to do and to be, require the prevention of interference [Nussbaum]
25. Social Practice / A. Freedoms / 6. Political freedom
Political freedom is an incoherent project, because some freedoms limit other freedoms [Nussbaum]
25. Social Practice / C. Rights / 1. Basis of Rights
Political and civil rights are not separate from economic and social rights [Nussbaum]
25. Social Practice / D. Justice / 1. Basis of justice
Capabilities: Life, Health, Safety, Mental life, Love, Planning, Joining in, Nature, Play, Control [Nussbaum, by PG]
Justice requires that the ten main capabilities of people are reasonably enabled [Nussbaum]
Capabilities are grounded in bare humanity and agency; qualifying as rational is not needed [Nussbaum]
Rights are not just barriers against state interference; governments must affirm capabilities of citizens [Nussbaum]
25. Social Practice / E. Policies / 2. Religion in Society
Any establishment belief system is incompatible with full respect for all citizens [Nussbaum]
25. Social Practice / F. Life Issues / 6. Animal Rights
We should respect animals in the way that we respect the animal nature in humans [Nussbaum]
It may be no harm to kill an animal which cannot plan for its future [Nussbaum]
The Capabilities Approach sees animals as agents, not just as having feelings [Nussbaum]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]