Combining Texts

All the ideas for 'Set Theory', 'The Principles of Science' and 'Essays on Active Powers 1: Active power'

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22 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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8628 I hold that algebra and number are developments of logic [Jevons]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
23664 Powers are quite distinct and simple, and so cannot be defined [Reid]
23669 Thinkers say that matter has intrinsic powers, but is also passive and acted upon [Reid]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
23666 It is obvious that there could not be a power without a subject which possesses it [Reid]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / e. Cause of consciousness
23665 Consciousness is the power of mind to know itself, and minds are grounded in powers [Reid]
16. Persons / F. Free Will / 4. For Free Will
23668 Our own nature attributes free determinations to our own will [Reid]
20. Action / B. Preliminaries of Action / 2. Willed Action / c. Agent causation
20051 Reid said that agent causation is a unique type of causation [Reid, by Stout,R]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
8383 Day and night are constantly conjoined, but they don't cause one another [Reid, by Crane]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
23667 Regular events don't imply a cause, without an innate conviction of universal causation [Reid]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
23670 Scientists don't know the cause of magnetism, and only discover its regulations [Reid]
23671 Laws are rules for effects, but these need a cause; rules of navigation don't navigate [Reid]