Combining Texts

All the ideas for 'Transworld Heir Lines', 'Anarchical Fallacies: on the Declaration of Rights' and 'Set Theory'

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19 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]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
11970 Logicians like their entities to exhibit a maximum degree of purity [Kaplan]
9. Objects / C. Structure of Objects / 7. Substratum
11969 Models nicely separate particulars from their clothing, and logicians often accept that metaphysically [Kaplan]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
11971 The simplest solution to transworld identification is to adopt bare particulars [Kaplan]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
11973 Unusual people may have no counterparts, or several [Kaplan]
11972 Essence is a transworld heir line, rather than a collection of properties [Kaplan]
19. Language / A. Nature of Meaning / 8. Synonymy
11967 Sentences might have the same sense when logically equivalent - or never have the same sense [Kaplan]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
20977 Natural rights are nonsense, and unspecified natural rights is nonsense on stilts [Bentham]
25. Social Practice / C. Rights / 1. Basis of Rights
21003 Only laws can produce real rights; rights from 'law of nature' are imaginary [Bentham]