Combining Texts

All the ideas for 'fragments/reports', 'The Philosophy of Mathematics' and 'Procedural republic and unencumbered self'

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14 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]
23. Ethics / D. Deontological Ethics / 2. Duty
Kant's moral law has no foundation - because that would undermine its priority [Sandel]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
Modern liberal rights in democracies protect individuals against the majority [Sandel]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
Liberals say rights always come first, and justice is neutral on social values [Sandel]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
Liberal justice means the withdrawal of the self, as transcendental or as unencumbered [Sandel]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Liberalism concerns rights, and communitarianism concerns the common good [Sandel, by Avineri/De-Shalit]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]