Combining Texts

All the ideas for 'Against 'Ostrich Nominalism'', 'Reflections on Liberty and Social Oppression' and 'The Philosophy of Mathematics'

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20 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths and inference are characterized either syntactically or semantically [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
7. Existence / D. Theories of Reality / 3. Reality
Some think of reality as made of things; I prefer facts or states of affairs [Armstrong]
8. Modes of Existence / D. Universals / 1. Universals
Particulars and properties are distinguishable, but too close to speak of a relation [Armstrong]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Refusal to explain why different tokens are of the same type is to be an ostrich [Armstrong]
23. Ethics / A. Egoism / 1. Ethical Egoism
Morality would improve if people could pursue private interests [Weil]
24. Political Theory / C. Ruling a State / 1. Social Power
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
No central authority can initiate decentralisation [Weil]
24. Political Theory / C. Ruling a State / 4. Changing the State / c. Revolution
After a bloody revolution the group which already had the power comes to the fore [Weil]
24. Political Theory / D. Ideologies / 2. Anarchism
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
Only individual people of good will can achieve social progress [Weil]
24. Political Theory / D. Ideologies / 6. Liberalism / d. Liberal freedom
In the least evil societies people can think, control community life, and be autonomous [Weil]
24. Political Theory / D. Ideologies / 11. Capitalism
Marx showed that capitalist oppression, because of competition, is unstoppable [Weil]
25. Social Practice / A. Freedoms / 1. Slavery
The pleasure of completing tasks motivates just as well as the whip of slavery [Weil]
25. Social Practice / B. Equalities / 4. Economic equality
Inequality could easily be mitigated, if it were not for the struggle for power [Weil]