Combining Texts

All the ideas for 'works', 'Democracy in America (abr Renshaw)' and 'Maths as a Science of Patterns'

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24 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
6299 Axioms are often affirmed simply because they produce results which have been accepted [Resnik]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
6304 Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
13007 Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
6300 Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
6303 Sets are positions in patterns [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
6295 There are too many mathematical objects for them all to be mental or physical [Resnik]
6296 Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
6301 Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
6302 Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
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]