Combining Texts

All the ideas for 'Taking Rights Seriously', 'Believing the Axioms I' and 'Grundlagen (Foundations of Theory of Manifolds)'

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16 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
15946 Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
13011 New axioms are being sought, to determine the size of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13013 The Axiom of Extensionality seems to be analytic [Maddy]
13014 Extensional sets are clearer, simpler, unique and expressive [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13021 The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy]
13022 Infinite sets are essential for giving an account of the real numbers [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13023 The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13024 Efforts to prove the Axiom of Choice have failed [Maddy]
13025 Modern views say the Choice set exists, even if it can't be constructed [Maddy]
13026 A large array of theorems depend on the Axiom of Choice [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
13019 The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13018 Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
15911 Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
23104 Dworkin believed we should promote equality, to increase autonomy [Dworkin, by Kekes]
25. Social Practice / B. Equalities / 1. Grounds of equality
23257 We can treat people as equals, or actually treat them equally [Dworkin, by Grayling]
18621 Treating people as equals is the one basic value of all plausible political theories [Dworkin, by Kymlicka]