Combining Philosophers

All the ideas for Verity Harte, John von Neumann and Alexis de Tocqueville

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32 ideas

2. Reason / F. Fallacies / 7. Ad Hominem
15842 An ad hominem refutation is reasonable, if it uses the opponent's assumptions [Harte,V]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
3340 Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
15943 Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
3355 Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA]
4. Formal Logic / G. Formal Mereology / 1. Mereology
15841 Mereology began as a nominalist revolt against the commitments of set theory [Harte,V]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
13489 Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
22716 Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]
12336 A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
18179 For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
18180 Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
15925 Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13672 All the axioms for mathematics presuppose set theory [Neumann]
7. Existence / B. Change in Existence / 1. Nature of Change
15858 Traditionally, the four elements are just what persists through change [Harte,V]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
15848 Mereology treats constitution as a criterion of identity, as shown in the axiom of extensionality [Harte,V]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
15837 What exactly is a 'sum', and what exactly is 'composition'? [Harte,V]
15839 If something is 'more than' the sum of its parts, is the extra thing another part, or not? [Harte,V]
15838 The problem with the term 'sum' is that it is singular [Harte,V]
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]