Combining Texts

All the ideas for 'fragments/reports', 'Reflections on Liberty and Social Oppression' and 'Russell's Mathematical Logic'

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22 ideas

2. Reason / C. Styles of Reason / 1. Dialectic
20768 Like spiderswebs, dialectical arguments are clever but useless [Ariston, by Diog. Laertius]
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]
23. Ethics / A. Egoism / 1. Ethical Egoism
23865 Morality would improve if people could pursue private interests [Weil]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
3049 The chief good is indifference to what lies midway between virtue and vice [Ariston, by Diog. Laertius]
23. Ethics / D. Deontological Ethics / 1. Deontology
3549 Ariston says rules are useless for the virtuous and the non-virtuous [Ariston, by Annas]
24. Political Theory / C. Ruling a State / 1. Social Power
23866 In oppressive societies the scope of actual control is extended by a religion of power [Weil]
24. Political Theory / C. Ruling a State / 4. Changing the State / a. Centralisation
23871 No central authority can initiate decentralisation [Weil]
24. Political Theory / C. Ruling a State / 4. Changing the State / c. Revolution
23867 After a bloody revolution the group which already had the power comes to the fore [Weil]
24. Political Theory / D. Ideologies / 2. Anarchism
23870 Decentralisation is only possible by co-operation between strong and weak - which is absurd [Weil]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
23863 Only individual people of good will can achieve social progress [Weil]
24. Political Theory / D. Ideologies / 6. Liberalism / d. Liberal freedom
23869 In the least evil societies people can think, control community life, and be autonomous [Weil]
24. Political Theory / D. Ideologies / 11. Capitalism
23861 Marx showed that capitalist oppression, because of competition, is unstoppable [Weil]
25. Social Practice / A. Freedoms / 1. Slavery
23868 The pleasure of completing tasks motivates just as well as the whip of slavery [Weil]
25. Social Practice / B. Equalities / 4. Economic equality
23864 Inequality could easily be mitigated, if it were not for the struggle for power [Weil]