Combining Texts

All the ideas for 'Believing the Axioms I', 'Beyond Individualism' and 'works'

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17 ideas

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]
19. Language / A. Nature of Meaning / 6. Meaning as Use
20949 Study the use of words, not their origins [Herder]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
7669 We cannot attain all the ideals of every culture, so there cannot be a perfect life [Herder, by Berlin]
24. Political Theory / C. Ruling a State / 4. Changing the State / c. Revolution
22258 Passion for progress is always short-lived [Sandel]
24. Political Theory / D. Ideologies / 3. Conservatism
22259 Conservatives are either individualistic, or communal [Sandel]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
7668 Herder invented the idea of being rooted in (or cut off from) a home or a group [Herder, by Berlin]
22260 Modern liberalism fails to articulate a vision of the common good [Sandel]