Combining Texts

All the ideas for 'Logological Fragments II', 'The Idea of Overlapping Consensus' and 'Believing the Axioms I'

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17 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / c. Philosophy as generalisation
19588 The highest aim of philosophy is to combine all philosophies into a unity [Novalis]
19598 Philosophy relies on our whole system of learning, and can thus never be complete [Novalis]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / d. Philosophy as puzzles
19586 Philosophers feed on problems, hoping they are digestible, and spiced with paradox [Novalis]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
19587 Philosophy aims to produce a priori an absolute and artistic world system [Novalis]
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]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
19597 Logic (the theory of relations) should be applied to mathematics [Novalis]
24. Political Theory / D. Ideologies / 7. Communitarianism / b. Against communitarianism
23420 In a pluralist society we can't expect a community united around one conception of the good [Rawls]