Combining Texts

All the ideas for 'Set Theory', 'Ecce Homo' and 'fragments/reports'

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20 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
4424 A warlike philosopher challenges problems to single combat [Nietzsche]
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]
22. Metaethics / B. Value / 2. Values / i. Self-interest
2886 The distinction between egoistic and non-egoistic acts is absurd [Nietzsche]
22. Metaethics / C. The Good / 1. Goodness / i. Moral luck
4426 A bad result distorts one's judgement about the virtue of what one has done [Nietzsche]
23. Ethics / A. Egoism / 1. Ethical Egoism
3031 The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius]
23. Ethics / C. Virtue Theory / 3. Virtues / f. Compassion
4425 The overcoming of pity I count among the noble virtues [Nietzsche]
23. Ethics / F. Existentialism / 6. Authentic Self
20132 To become what you are you must have no self-awareness [Nietzsche]
23. Ethics / F. Existentialism / 8. Eternal Recurrence
20144 Eternal recurrence is the highest attainable affirmation [Nietzsche]
25. Social Practice / E. Policies / 5. Education / c. Teaching
2889 One repays a teacher badly if one remains only a pupil [Nietzsche]
28. God / C. Attitudes to God / 5. Atheism
2887 I am not an atheist because of reasoning or evidence, but because of instinct [Nietzsche]