Combining Texts

All the ideas for 'Set Theory', 'Epiphenomenal and supervenient causation' and 'Utilitarianism'

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29 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13030 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
13032 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
13033 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
13037 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
13038 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
13034 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
13039 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
13036 Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
13029 Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
13031 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
13040 Constructibility: V = L (all sets are constructible) [Kunen]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
3772 The will, in the beginning, is entirely produced by desire [Mill]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
3769 With early training, any absurdity or evil may be given the power of conscience [Mill]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
3767 Motive shows the worth of the agent, but not of the action [Mill]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
3771 Virtues only have value because they achieve some further end [Mill]
23. Ethics / D. Deontological Ethics / 2. Duty
3768 Orthodox morality is the only one which feels obligatory [Mill]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
3776 Utilitarianism only works if everybody has a totally equal right to happiness [Mill]
7202 The English believe in the task of annihilating evil for the victory of good [Nietzsche on Mill]
5935 Mill's qualities of pleasure is an admission that there are other good states of mind than pleasure [Ross on Mill]
3764 Actions are right if they promote pleasure, wrong if they promote pain [Mill]
23. Ethics / E. Utilitarianism / 2. Ideal of Pleasure
3766 Better to be Socrates dissatisfied than a fool satisfied [Mill]
3763 Ultimate goods such as pleasure can never be proved to be good [Mill]
3765 Only pleasure and freedom from pain are desirable as ends [Mill]
23. Ethics / E. Utilitarianism / 3. Motivation for Altruism
3770 General happiness is only desirable because individuals desire their own happiness [Mill]
23. Ethics / E. Utilitarianism / 5. Rule Utilitarianism
6697 Moral rules protecting human welfare are more vital than local maxims [Mill]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
3774 Rights are a matter of justice, not of benevolence [Mill]
3773 No individual has the right to receive our benevolence [Mill]
25. Social Practice / C. Rights / 1. Basis of Rights
3775 A right is a valid claim to society's protection [Mill]
26. Natural Theory / C. Causation / 8. Particular Causation / a. Observation of causation
3535 All observable causes are merely epiphenomena [Kim]