Combining Texts

All the ideas for 'Set Theory', 'On the Law of War' and 'On Body and Force, Against the Cartesians'

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20 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]
14. Science / D. Explanation / 2. Types of Explanation / h. Explanations by function
13195 To explain a house we must describe its use, as well as its parts [Leibniz]
15. Nature of Minds / C. Capacities of Minds / 10. Conatus/Striving
13193 Active force is not just potential for action, since it involves a real effort or striving [Leibniz]
25. Social Practice / E. Policies / 1. War / a. Just wars
23569 The only just cause for a war is a wrong received [Vitoria]
23601 Leaders can only attack foreigners who have done wrong (as with their own subjects) [Vitoria]
25. Social Practice / E. Policies / 1. War / c. Combatants
23566 Princes should not justify a war to their subjects, and doing so would undermine the state [Vitoria]
25. Social Practice / E. Policies / 1. War / d. Non-combatants
23576 Sacking a city is lawful if it motivates the attacking troops [Vitoria]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
13194 God's laws would be meaningless without internal powers for following them [Leibniz]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
13196 All qualities of bodies reduce to forces [Leibniz]
13192 Power is passive force, which is mass, and active force, which is entelechy or form [Leibniz]