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All the ideas for 'Set Theory', 'The Moral Problem' and 'Liberalism: the basics'

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58 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 / 4. Axioms for Sets / b. Axiom of Extensionality I
Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
Constructibility: V = L (all sets are constructible) [Kunen]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Capturing all the common sense facts about rationality is almost impossible [Smith,M]
20. Action / C. Motives for Action / 1. Acting on Desires
Goals need desires, and so only desires can motivate us [Smith,M]
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]
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]
24. Political Theory / A. Basis of a State / 4. Original Position / a. Original position
Rawls's theory cannot justify liberalism, since it presupposes free and equal participants [Charvet]
24. Political Theory / A. Basis of a State / 4. Original Position / b. Veil of ignorance
People with strong prior beliefs would have nothing to do with a veil of ignorance [Charvet]
24. Political Theory / D. Ideologies / 3. Conservatism
Societies need shared values, so conservatism is right if rational discussion of values is impossible [Charvet]
24. Political Theory / D. Ideologies / 4. Social Utilitarianism
The universalism of utilitarianism implies a world state [Charvet]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
Liberals value freedom and equality, but the society itself must decide on its values [Charvet]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
Modern libertarian societies still provide education and some housing [Charvet]
Liberalism needs people to either have equal autonomy, or everyone to have enough autonomy [Charvet]
Kant places a higher value on the universal rational will than on the people asserting it [Charvet]
24. Political Theory / D. Ideologies / 6. Liberalism / c. Liberal equality
Liberalism asserts maximum freedom, but that must be equal for all participants [Charvet]
Egalitarian liberals prefer equality (either of input or outcome) to liberty [Charvet]
24. Political Theory / D. Ideologies / 6. Liberalism / e. Liberal community
Liberals promote community and well-being - because all good societies need them [Charvet]
24. Political Theory / D. Ideologies / 6. Liberalism / f. Multiculturalism
Identity multiculturalism emerges from communitarianism, preferring community to humanity [Charvet]
24. Political Theory / D. Ideologies / 7. Communitarianism / b. Against communitarianism
For communitarians it seems that you must accept the culture you are born into [Charvet]
24. Political Theory / D. Ideologies / 9. Communism
Give by ability and receive by need, rather than a free labour market [Charvet]
25. Social Practice / A. Freedoms / 3. Free speech
Allowing defamatory speech is against society's interests, by blurring which people are trustworthy [Charvet]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
'Freedom from' is an empty idea, if the freedom is not from impediments to my desires [Charvet]
Positive freedom can lead to coercion, if you are forced to do what you chose to do [Charvet]
First level autonomy is application of personal values; second level is criticising them [Charvet]
25. Social Practice / B. Equalities / 1. Grounds of equality
Mere equality, as in two trees being the same height, has no value at all [Charvet]
25. Social Practice / B. Equalities / 4. Economic equality
Inequalities are worse if they seem to be your fault, rather than social facts [Charvet]
Money allows unlimited inequalities, and we obviously all agree to money [Charvet]
25. Social Practice / D. Justice / 2. The Law / b. Rule of law
The rule of law is mainly to restrict governments [Charvet]
The 1689 Bill of Rights denied the monarch new courts, or the right to sit as judge [Charvet]
From 1701 only parliament could remove judges, whose decisions could not be discussed [Charvet]
Justice superior to the rule of law is claimed on behalf of the workers, or the will of the nation [Charvet]
The rule of law mainly benefits those with property and liberties [Charvet]
25. Social Practice / E. Policies / 3. Welfare provision
Welfare is needed if citizens are to accept the obligations of a liberal state [Charvet]