Combining Texts

All the ideas for 'plays (frags)', 'Believing the Axioms I' and 'Democracy in America (abr Renshaw)'

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27 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
13011 New axioms are being sought, to determine the size of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13014 Extensional sets are clearer, simpler, unique and expressive [Maddy]
13013 The Axiom of Extensionality seems to be analytic [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13021 The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy]
13022 Infinite sets are essential for giving an account of the real numbers [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13023 The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13024 Efforts to prove the Axiom of Choice have failed [Maddy]
13025 Modern views say the Choice set exists, even if it can't be constructed [Maddy]
13026 A large array of theorems depend on the Axiom of Choice [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
13019 The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13018 Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
10. Modality / C. Sources of Modality / 2. Necessity as Primitive
74 Even God could not undo what has been done [Agathon]
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
22673 Wherever there is a small community, the association of the people is natural [Tocqueville]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
22676 The people are just individuals, and only present themselves as united to foreigners [Tocqueville]
24. Political Theory / A. Basis of a State / 2. Population / b. State population
22679 Vast empires are bad for well-being and freedom, though they may promote glory [Tocqueville]
22680 People would be much happier and freer in small nations [Tocqueville]
24. Political Theory / B. Nature of a State / 3. Constitutions
22675 In American judges rule according to the Constitution, not the law [Tocqueville]
24. Political Theory / C. Ruling a State / 2. Leaders / b. Monarchy
22677 A monarchical family is always deeply concerned with the interests of the state [Tocqueville]
24. Political Theory / C. Ruling a State / 2. Leaders / c. Despotism
22683 Despots like to see their own regulations ignored, by themselves and their agents [Tocqueville]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
22669 Aristocracy is constituted by inherited landed property [Tocqueville]
24. Political Theory / C. Ruling a State / 4. Changing the State / a. Centralisation
22674 In Europe it is thought that local government is best handled centrally [Tocqueville]
24. Political Theory / D. Ideologies / 5. Democracy / b. Consultation
22678 An election, and its lead up time, are always a national crisis [Tocqueville]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
22682 Universal suffrage is no guarantee of wise choices [Tocqueville]
25. Social Practice / A. Freedoms / 1. Slavery
22670 Slavery undermines the morals and energy of a society [Tocqueville]
25. Social Practice / A. Freedoms / 3. Free speech
22681 The liberty of the press is more valuable for what it prevents than what it promotes [Tocqueville]
25. Social Practice / B. Equalities / 1. Grounds of equality
22672 It is admirable to elevate the humble to the level of the great, but the opposite is depraved [Tocqueville]
25. Social Practice / B. Equalities / 2. Political equality
22671 Equality can only be established by equal rights for all (or no rights for anyone) [Tocqueville]