Combining Texts

All the ideas for 'Unconscious Cerebral Initiative', 'Essays on Intellectual Powers 3: Memory' and 'Set Theory'

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29 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 / E. Objects over Time / 1. Objects over Time
1350 Continuity is needed for existence, otherwise we would say a thing existed after it ceased to exist [Reid]
9. Objects / E. Objects over Time / 13. No Identity over Time
21322 We treat slowly changing things as identical for the sake of economy in language [Reid]
9. Objects / F. Identity among Objects / 1. Concept of Identity
21320 Identity is familiar to common sense, but very hard to define [Reid]
1367 Identity can only be affirmed of things which have a continued existence [Reid]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
23644 Without memory we could have no concept of duration [Reid]
23643 We all trust our distinct memories (but not our distinct imaginings) [Reid]
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
1356 A person is a unity, and doesn't come in degrees [Reid]
16. Persons / A. Concept of a Person / 2. Persons as Responsible
1359 Personal identity is the basis of all rights, obligations and responsibility [Reid]
16. Persons / A. Concept of a Person / 3. Persons as Reasoners
21319 I can hardly care about rational consequence if it wasn't me conceiving the antecedent [Reid]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / a. Memory is Self
21323 The identity of a thief is only known by similarity, but memory gives certainty in our own case [Reid]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / c. Inadequacy of mental continuity
21321 Memory reveals my past identity - but so does testimony of other witnesses [Reid]
21324 If consciousness is transferable 20 persons can be 1; forgetting implies 1 can be 20 [Reid]
21325 Boy same as young man, young man same as old man, old man not boy, if forgotten! [Reid]
21327 If a stolen horse is identified by similitude, its identity is not therefore merely similitude [Reid]
1366 If consciousness is personal identity, it is continually changing [Reid]
16. Persons / D. Continuity of the Self / 7. Self and Thinking
1352 Thoughts change continually, but the self doesn't [Reid]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
7861 Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau]
6660 Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe]