Combining Texts

All the ideas for 'Counterfactual Dependence and Time's Arrow', 'Set Theory' and 'The Good State'

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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]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
23262 Experience, sympathy and history are sensible grounds for laying claim to rights [Grayling]
24. Political Theory / C. Ruling a State / 1. Social Power
23263 Politics is driven by power cliques [Grayling]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
23255 It is essential for democracy that voting is free and well informed [Grayling]
23254 Democracies should require a supermajority for major questions [Grayling]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
23260 A cap on time of service would restrict party control and career ambitions [Grayling]
24. Political Theory / D. Ideologies / 5. Democracy / e. Democratic minorities
23253 Majority decisions are only acceptable if the minority interests are not vital [Grayling]
25. Social Practice / B. Equalities / 1. Grounds of equality
23256 Liberty and equality cannot be reconciled [Grayling]
25. Social Practice / D. Justice / 1. Basis of justice
23258 The very concept of democracy entails a need for justice [Grayling]
25. Social Practice / D. Justice / 2. The Law / a. Legal system
23259 There should be separate legislative, executive and judicial institutions [Grayling]
26. Natural Theory / C. Causation / 5. Direction of causation
8433 There are few traces of an event before it happens, but many afterwards [Lewis, by Horwich]