Combining Philosophers
Ideas for Edmund Husserl, Penelope Maddy and Volker Halbach
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21 ideas
4. Formal Logic / F. Set Theory ST / 1. Set Theory
15657
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To prove the consistency of set theory, we must go beyond set theory [Halbach]
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16309
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Every attempt at formal rigour uses some set theory [Halbach]
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4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
18194
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'Forcing' can produce new models of ZFC from old models [Maddy]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
18195
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A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy]
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13011
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New axioms are being sought, to determine the size of the continuum [Maddy]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13013
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The Axiom of Extensionality seems to be analytic [Maddy]
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13014
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Extensional sets are clearer, simpler, unique and expressive [Maddy]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13021
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The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy]
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13022
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Infinite sets are essential for giving an account of the real numbers [Maddy]
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18191
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Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13023
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The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
18193
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The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13024
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Efforts to prove the Axiom of Choice have failed [Maddy]
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13025
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Modern views say the Choice set exists, even if it can't be constructed [Maddy]
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13026
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A large array of theorems depend on the Axiom of Choice [Maddy]
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17610
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The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
18169
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Axiom of Reducibility: propositional functions are extensionally predicative [Maddy]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
13019
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The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13018
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Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
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4. Formal Logic / F. Set Theory ST / 7. Natural Sets
17824
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The master science is physical objects divided into sets [Maddy]
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8755
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Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
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