Combining Texts

All the ideas for 'Letters to Paul Pellison-Fontinier', 'Set Theory' and 'Why Constitution is not Identity'

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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]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
16078 Clay is intrinsically and atomically the same as statue (and that lacks 'modal properties') [Rudder Baker]
16077 The clay is not a statue - it borrows that property from the statue it constitutes [Rudder Baker]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
16080 Is it possible for two things that are identical to become two separate things? [Rudder Baker]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
16076 Constitution is not identity, as consideration of essential predicates shows [Rudder Baker]
16081 The constitution view gives a unified account of the relation of persons/bodies, statues/bronze etc [Rudder Baker]
16082 Statues essentially have relational properties lacked by lumps [Rudder Baker]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
12719 Clearly, force is that from which action follows, when unimpeded [Leibniz]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
12720 Time doesn't exist, since its parts don't coexist [Leibniz]