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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Inessential Aristotle: Powers without Essences' and 'Contemporary Political Philosophy (1st edn)'

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53 ideas

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 / C. Powers and Dispositions / 1. Powers
Powers give explanations, without being necessary for some class membership [Chakravartty]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
9. Objects / D. Essence of Objects / 5. Essence as Kind
A kind essence is the necessary and sufficient properties for membership of a class [Chakravartty]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Cluster kinds are explained simply by sharing some properties, not by an 'essence' [Chakravartty]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
Explanation of causal phenomena concerns essential kinds - but also lack of them [Chakravartty]
16. Persons / E. Rejecting the Self / 2. Self as Social Construct
The 'Kantian' self steps back from commitment to its social situation [Kymlicka]
22. Metaethics / C. The Good / 1. Goodness / c. Right and good
Teleological theories give the good priority over concern for people [Kymlicka]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
Maybe the particularist moral thought of women is better than the impartial public thinking of men [Kymlicka]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
Utilitarianism is not a decision-procedure; choice of the best procedure is an open question [Kymlicka]
One view says start with equality, and infer equal weight to interests, and hence maximum utility [Kymlicka]
A second view says start with maximising the good, implying aggregation, and hence equality [Kymlicka]
24. Political Theory / A. Basis of a State / 2. Population / a. Human population
To maximise utility should we double the population, even if life somewhat deteriorates? [Kymlicka]
24. Political Theory / A. Basis of a State / 4. Original Position / c. Difference principle
The difference principles says we must subsidise the costs of other people's choices [Kymlicka]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
Social contract theories are usually rejected because there never was such a contract [Kymlicka]
24. Political Theory / D. Ideologies / 4. Social Utilitarianism
Utilitarianism is no longer a distinctive political position [Kymlicka]
The quest of the general good is partly undermined by people's past entitlements [Kymlicka]
We shouldn't endorse preferences which reject equality, and show prejudice and selfishness [Kymlicka]
Using utilitarian principles to make decisions encourages cold detachment from people [Kymlicka]
Utilitarianism is irrational if it tells you to trade in your rights and resources just for benefits [Kymlicka]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
Modern liberalism has added personal privacy to our personal social lives [Kymlicka]
24. Political Theory / D. Ideologies / 6. Liberalism / d. Liberal freedom
Liberalism tends to give priority to basic liberties [Kymlicka]
24. Political Theory / D. Ideologies / 6. Liberalism / g. Liberalism critique
Marxists say liberalism is unjust, because it allows exploitation in the sale of labour [Kymlicka]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
The 'Kantian' view of the self misses the way it is embedded or situated in society [Kymlicka]
Communitarians say we should pay more attention to our history [Kymlicka]
24. Political Theory / D. Ideologies / 7. Communitarianism / b. Against communitarianism
Communitarian states only encourage fairly orthodox ideas of the good life [Kymlicka]
25. Social Practice / A. Freedoms / 1. Slavery
If everyone owned himself, that would prevent slavery [Kymlicka]
25. Social Practice / A. Freedoms / 4. Free market
Libertarians like the free market, but they also think that the free market is just [Kymlicka]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
The most valuable liberties to us need not be the ones with the most freedom [Kymlicka]
25. Social Practice / A. Freedoms / 6. Political freedom
Ancient freedom was free participation in politics, not private independence of life [Kymlicka]
25. Social Practice / B. Equalities / 2. Political equality
Equal opportunities seems fair, because your fate is from your choices, not your circumstances [Kymlicka]
Equal opportunity arbitrarily worries about social circumstances, but ignores talents [Kymlicka]
25. Social Practice / B. Equalities / 3. Legal equality
Marxists say justice is unneeded in the truly good community [Kymlicka]
25. Social Practice / C. Rights / 1. Basis of Rights
The Lockean view of freedom depends on whether you had a right to what is restricted [Kymlicka]
25. Social Practice / D. Justice / 1. Basis of justice
Justice corrects social faults, but also expresses respect to individuals as ends [Kymlicka]
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
Some kinds, such as electrons, have essences, but 'cluster kinds' do not [Chakravartty]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Many causal laws do not refer to kinds, but only to properties [Chakravartty]