Combining Texts

All the ideas for 'Set Theory', 'Conceptions of Truth' and 'Naming and Necessity notes and addenda'

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26 ideas

2. Reason / D. Definition / 12. Paraphrase
18491 The idea of 'making' can be mere conceptual explanation (like 'because') [Künne]
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]
9. Objects / A. Existence of Objects / 5. Simples
17000 We might fix identities for small particulars, but it is utopian to hope for such things [Kripke]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
11868 A different piece of wood could have been used for that table; constitution isn't identity [Wiggins on Kripke]
9. Objects / F. Identity among Objects / 5. Self-Identity
17044 A relation can clearly be reflexive, and identity is the smallest reflexive relation [Kripke]
9. Objects / F. Identity among Objects / 9. Sameness
16999 A vague identity may seem intransitive, and we might want to talk of 'counterparts' [Kripke]
10. Modality / A. Necessity / 7. Natural Necessity
17058 What many people consider merely physically necessary I consider completely necessary [Kripke]
4970 What is often held to be mere physical necessity is actually metaphysical necessity [Kripke]
10. Modality / B. Possibility / 1. Possibility
17059 Unicorns are vague, so no actual or possible creature could count as a unicorn [Kripke]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
4950 Possible worlds are useful in set theory, but can be very misleading elsewhere [Kripke]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
17003 Kaplan's 'Dthat' is a useful operator for transforming a description into a rigid designation [Kripke]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
9221 The best known objection to counterparts is Kripke's, that Humphrey doesn't care if his counterpart wins [Kripke, by Sider]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
17052 The a priori analytic truths involving fixing of reference are contingent [Kripke]
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
4969 I regard the mind-body problem as wide open, and extremely confusing [Kripke]
19. Language / B. Reference / 3. Direct Reference / c. Social reference
4956 A description may fix a reference even when it is not true of its object [Kripke]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
17032 Even if Gödel didn't produce his theorems, he's still called 'Gödel' [Kripke]