Combining Texts

All the ideas for 'Set Theory', 'Reference and Contingency' and 'Eight Theories of Ethics'

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27 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]
10. Modality / B. Possibility / 5. Contingency
14895 'Superficial' contingency: false in some world; 'Deep' contingency: no obvious verification [Evans, by Macią/Garcia-Carpentiro]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
11881 Rigid designators can be meaningful even if empty [Evans, by Mackie,P]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
6685 'Subjectivism' is an extension of relativism from the social group to the individual [Graham]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
6699 The chain of consequences may not be the same as the chain of responsibility [Graham]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
6698 Negative consequences are very hard (and possibly impossible) to assess [Graham]
22. Metaethics / C. The Good / 1. Goodness / i. Moral luck
6700 We can't criticise people because of unforeseeable consequences [Graham]
23. Ethics / A. Egoism / 1. Ethical Egoism
6704 Egoism submits to desires, but cannot help form them [Graham]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / h. Right feelings
6701 Rescue operations need spontaneous benevolence, not careful thought [Graham]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
6693 'What if everybody did that?' rather misses the point as an objection to cheating [Graham]
23. Ethics / F. Existentialism / 1. Existentialism
6691 It is more plausible to say people can choose between values, than that they can create them [Graham]
23. Ethics / F. Existentialism / 2. Nihilism
6688 Life is only absurd if you expected an explanation and none turns up [Graham]
23. Ethics / F. Existentialism / 5. Existence-Essence
6705 Existentialism may transcend our nature, unlike eudaimonism [Graham]
23. Ethics / F. Existentialism / 6. Authentic Self
6690 A standard problem for existentialism is the 'sincere Nazi' [Graham]
23. Ethics / F. Existentialism / 7. Existential Action
6689 The key to existentialism: the way you make choices is more important than what you choose [Graham]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
6706 The great religions are much more concerned with the religious life than with ethics [Graham]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
6709 Western religion saves us from death; Eastern religion saves us from immortality [Graham]