Ideas from 'Believing the Axioms I' by Penelope Maddy [1988], by Theme Structure
[found in 'Journal of Symbolic Logic' (ed/tr -) [- ,]].
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expand these ideas
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
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13011
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New axioms are being sought, to determine the size of the continuum
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
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13014
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Extensional sets are clearer, simpler, unique and expressive
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13013
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The Axiom of Extensionality seems to be analytic
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
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13021
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The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics
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13022
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Infinite sets are essential for giving an account of the real numbers
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
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13023
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The Power Set Axiom is needed for, and supported by, accounts of the continuum
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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13024
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Efforts to prove the Axiom of Choice have failed
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13025
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Modern views say the Choice set exists, even if it can't be constructed
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13026
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A large array of theorems depend on the Axiom of Choice
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
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13019
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The Iterative Conception says everything appears at a stage, derived from the preceding appearances
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
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13018
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Limitation of Size is a vague intuition that over-large sets may generate paradoxes
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