Combining Texts

All the ideas for 'A Dictionary of Political Thought', 'Physiologia' and 'Set Theory'

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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]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16674 The quantity is just the matter, in that it has extended parts and is diffuse [Charleton]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
7590 Consequentialism emphasises value rather than obligation in morality [Scruton]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
7589 Altruism is either emotional (where your interests are mine) or moral (where they are reasons for me) [Scruton]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
7595 The idea of a right seems fairly basic; justice may be the disposition to accord rights to people [Scruton]
24. Political Theory / D. Ideologies / 3. Conservatism
7588 Allegiance is fundamental to the conservative view of society [Scruton]
24. Political Theory / D. Ideologies / 5. Democracy / f. Against democracy
7594 Democrats are committed to a belief and to its opposite, if the majority prefer the latter [Scruton]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
7593 Liberals focus on universal human freedom, natural rights, and tolerance [Scruton, by PG]
25. Social Practice / D. Justice / 2. The Law / d. Legal positivism
7592 For positivists law is a matter of form, for naturalists it is a matter of content [Scruton]
25. Social Practice / F. Life Issues / 3. Abortion
7587 The issue of abortion seems insoluble, because there is nothing with which to compare it [Scruton]