Combining Philosophers

All the ideas for Herodotus, John von Neumann and Antonio Gramsci

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18 ideas

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]
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]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
20937 The state should produce higher civilisations for all, in tune with the economic apparatus [Gramsci]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
20935 Eventually political parties lose touch with the class they represent, which is dangerous [Gramsci]
24. Political Theory / C. Ruling a State / 2. Leaders / a. Autocracy
20936 Caesarism emerges when two forces in society are paralysed in conflict [Gramsci]
24. Political Theory / C. Ruling a State / 2. Leaders / c. Despotism
20941 Totalitarian parties cut their members off from other cultural organisations [Gramsci]
24. Political Theory / C. Ruling a State / 3. Government / a. Government
20939 What is the function of a parliament? Does it even constitute a part of the State structure? [Gramsci]
24. Political Theory / D. Ideologies / 6. Liberalism / g. Liberalism critique
20938 Liberalism's weakness is its powerful rigid bureaucracy [Gramsci]
25. Social Practice / B. Equalities / 2. Political equality
20940 Perfect political equality requires economic equality [Gramsci]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
1513 The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus]