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All the ideas for 'Structures and Structuralism in Phil of Maths', 'The Ethical Criticism of Art' and 'Creating Capabilities'

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43 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
Keep premises as weak as possible, to avoid controversial difficulties [Nussbaum]
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
Maybe literary assessment is evaluating the artist as a suitable friend [Gaut]
21. Aesthetics / B. Nature of Art / 2. Art as Form
Formalists say aesthetics concerns types of beauty, or unity, complexity and intensity [Gaut]
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
Good ethics counts towards aesthetic merit, and bad ethics counts against it [Gaut]
Good art does not necessarily improve people (any more than good advice does) [Gaut]
If we don't respond ethically in the way a work prescribes, that is an aesthetic failure [Gaut]
'Moralism' says all aesthetic merits are moral merits [Gaut]
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]