Combining Texts

All the ideas for 'Reference and Modality', 'The Decline of the West' and 'Set Theory'

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21 ideas

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
10928 Maybe we can quantify modally if the objects are intensional, but it seems unlikely [Quine]
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 / F. Referring in Logic / 1. Naming / b. Names as descriptive
10925 Failure of substitutivity shows that a personal name is not purely referential [Quine]
5. Theory of Logic / G. Quantification / 1. Quantification
10926 Quantifying into referentially opaque contexts often produces nonsense [Quine]
9. Objects / D. Essence of Objects / 15. Against Essentialism
10930 Quantification into modal contexts requires objects to have an essence [Quine]
10. Modality / A. Necessity / 4. De re / De dicto modality
14645 To be necessarily greater than 7 is not a trait of 7, but depends on how 7 is referred to [Quine]
10. Modality / A. Necessity / 11. Denial of Necessity
9201 Whether 9 is necessarily greater than 7 depends on how '9' is described [Quine, by Fine,K]
10927 Necessity only applies to objects if they are distinctively specified [Quine]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
9203 We can't quantify in modal contexts, because the modality depends on descriptions, not objects [Quine, by Fine,K]
24. Political Theory / B. Nature of a State / 5. Culture
20948 Human cultures are organisms which grow, and then fade and die [Spengler, by Bowie]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
10931 We can't say 'necessarily if x is in water then x dissolves' if we can't quantify modally [Quine]