Combining Texts

All the ideas for 'What is so bad about Contradictions?', 'Democracy in America (abr Renshaw)' and 'Russell's Mathematical Logic'

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25 ideas

2. Reason / B. Laws of Thought / 3. Non-Contradiction
9123 Someone standing in a doorway seems to be both in and not-in the room [Priest,G, by Sorensen]
2. Reason / D. Definition / 8. Impredicative Definition
10041 Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21716 In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
10035 Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10042 Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
10038 A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10046 The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10039 Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10043 Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
10045 Impredicative definitions are admitted into ordinary mathematics [Gödel]
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]