Combining Texts

All the ideas for 'Set Theory', 'Treatise 2: Virtue or Moral Good' and 'Fath and Love, or the King and Queen'

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26 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 / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
6248 Reason is too slow and doubtful to guide all actions, which need external and moral senses [Hutcheson]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
6238 We approve of actions by a superior moral sense [Hutcheson]
6239 We dislike a traitor, even if they give us great benefit [Hutcheson]
6240 The moral sense is not an innate idea, but an ability to approve or disapprove in a disinterested way [Hutcheson]
6242 We cannot choose our moral feelings, otherwise bribery could affect them [Hutcheson]
6247 Everyone feels uneasy when seeing others in pain, unless the others are evil [Hutcheson]
22. Metaethics / B. Value / 2. Values / f. Altruism
6244 Human nature seems incapable of universal malice, except what results from self-love [Hutcheson]
22. Metaethics / B. Value / 2. Values / i. Self-interest
6243 As death approaches, why do we still care about family, friends or country? [Hutcheson]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
6246 My action is not made good by a good effect, if I did not foresee and intend it [Hutcheson]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
6241 Contempt of danger is just madness if it is not in some worthy cause [Hutcheson]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
6245 That action is best, which procures the greatest happiness for the greatest number [Hutcheson]
24. Political Theory / C. Ruling a State / 2. Leaders / b. Monarchy
19589 The whole point of a monarch is that we accept them as a higher-born, ideal person [Novalis]
25. Social Practice / C. Rights / 1. Basis of Rights
6251 The loss of perfect rights causes misery, but the loss of imperfect rights reduces social good [Hutcheson]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
6250 We say God is good if we think everything he does aims at the happiness of his creatures [Hutcheson]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
6249 If goodness is constituted by God's will, it is a tautology to say God's will is good [Hutcheson]