Combining Texts

All the ideas for 'fragments/reports', 'The Central Questions of Philosophy' and 'Set Theory'

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25 ideas

2. Reason / E. Argument / 3. Analogy
5331 You can't infer that because you have a hidden birth-mark, everybody else does [Ayer]
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]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
2611 It is currently held that quantifying over something implies belief in its existence [Ayer]
9. Objects / D. Essence of Objects / 3. Individual Essences
16520 We see properties necessary for a kind (in the definition), but not for an individual [Ayer]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
2613 The theory of other minds has no rival [Ayer]
5328 Originally I combined a mentalistic view of introspection with a behaviouristic view of other minds [Ayer]
5330 Physicalism undercuts the other mind problem, by equating experience with 'public' brain events [Ayer]
16. Persons / B. Nature of the Self / 5. Self as Associations
5326 Qualia must be united by a subject, because they lead to concepts and judgements [Ayer]
5325 Is something an 'experience' because it relates to other experiences, or because it relates to a subject? [Ayer]
16. Persons / B. Nature of the Self / 7. Self and Body / a. Self needs body
5324 Bodily identity and memory work together to establish personal identity [Ayer]
16. Persons / C. Self-Awareness / 2. Knowing the Self
5322 Self-consciousness is not basic, because experiences are not instrinsically marked with ownership [Ayer]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / c. Inadequacy of mental continuity
5327 Temporal gaps in the consciousness of a spirit could not be bridged by memories [Ayer]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
5329 Why shouldn't we say brain depends on mind? Better explanation! [Ayer]
19. Language / D. Propositions / 6. Propositions Critique
2610 Talk of propositions is just shorthand for talking about equivalent sentences [Ayer]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]