Combining Philosophers

All the ideas for Dennis Whitcomb, Andr Gallois and Kenneth Kunen

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20 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
The devil was wise as an angel, and lost no knowledge when he rebelled [Whitcomb]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
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
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
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
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
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
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
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
Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
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
Constructibility: V = L (all sets are constructible) [Kunen]
8. Modes of Existence / A. Relations / 4. Formal Relations / b. Equivalence relation
An 'equivalence' relation is one which is reflexive, symmetric and transitive [Kunen]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
A CAR and its major PART can become identical, yet seem to have different properties [Gallois]
9. Objects / E. Objects over Time / 1. Objects over Time
Gallois hoped to clarify identity through time, but seems to make talk of it impossible [Hawley on Gallois]
If things change they become different - but then no one thing undergoes the change! [Gallois]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
4D: time is space-like; a thing is its history; past and future are real; or things extend in time [Gallois]
9. Objects / F. Identity among Objects / 3. Relative Identity
Gallois is committed to identity with respect to times, and denial of simple identity [Gallois, by Sider]
9. Objects / F. Identity among Objects / 6. Identity between Objects
Occasional Identity: two objects can be identical at one time, and different at others [Gallois, by Hawley]
If two things are equal, each side involves a necessity, so the equality is necessary [Gallois]