Combining Texts

All the ideas for 'fragments/reports', 'The Ultimate Constituents of Matter' and 'Set Theory'

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21 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]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
7548 Classes, grouped by a convenient property, are logical constructions [Russell]
7. Existence / D. Theories of Reality / 4. Anti-realism
7545 Visible things are physical and external, but only exist when viewed [Russell]
12. Knowledge Sources / B. Perception / 4. Sense Data / b. Nature of sense-data
7553 Sense-data are purely physical [Russell]
7549 If my body literally lost its mind, the object seen when I see a flash would still exist [Russell]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
7546 A man is a succession of momentary men, bound by continuity and causation [Russell]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
7550 We could probably, in principle, infer minds from brains, and brains from minds [Russell]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
7551 Matter is a logical construction [Russell]
7547 Matter requires a division into time-corpuscles as well as space-corpuscles [Russell]
27. Natural Reality / C. Space / 2. Space
7552 Six dimensions are needed for a particular, three within its own space, and three to locate that space [Russell]