Combining Texts

All the ideas for 'Set Theory', 'The Courtier and the Heretic' and 'Introduction to the Philosophy of History'

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20 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / d. Nineteenth century philosophy
20109 Hegel inserted society and history between the God-world, man-nature, man-being binary pairs [Hegel, by Safranski]
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]
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
23274 World history has no room for happiness [Hegel]
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
23275 The state of nature is one of untamed brutality [Hegel]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
23276 The soul of the people is an organisation of its members which produces an essential unity [Hegel]
24. Political Theory / D. Ideologies / 6. Liberalism / g. Liberalism critique
23272 The human race matters, and individuals have little importance [Hegel]
24. Political Theory / D. Ideologies / 10. Theocracy
7825 The politics of Leibniz was the reunification of Christianity [Stewart,M]
24. Political Theory / D. Ideologies / 14. Nationalism
23273 In a good state the goal of the citizens and of the whole state are united [Hegel]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
23271 The goal of the world is Spirit's consciousness and enactment of freedom [Hegel]
25. Social Practice / E. Policies / 5. Education / d. Study of history
23270 We should all agree that there is reason in history [Hegel]