Combining Texts

All the ideas for 'Set Theory', 'The Concept of a Person' and 'What We Owe to Each Other'

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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]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / b. Scepticism of other minds
5662 Maybe induction could never prove the existence of something unobservable [Ayer]
16. Persons / B. Nature of the Self / 1. Self and Consciousness
5664 Consciousness must involve a subject, and only bodies identify subjects [Ayer]
16. Persons / B. Nature of the Self / 7. Self and Body / a. Self needs body
5668 People own conscious states because they are causally related to the identifying body [Ayer]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
5661 We identify experiences by their owners, so we can't define owners by their experiences [Ayer]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / a. Memory is Self
5665 Memory is the best proposal as what unites bundles of experiences [Ayer]
5666 Not all exerience can be remembered, as this would produce an infinite regress [Ayer]
16. Persons / D. Continuity of the Self / 6. Body sustains Self
5669 Personal identity can't just be relations of experiences, because the body is needed to identify them [Ayer]
23. Ethics / B. Contract Ethics / 9. Contractualism
20992 Right and wrong concerns what other people cannot reasonably reject [Scanlon]