Combining Philosophers
Ideas for Kretzmann/Stump, Protagoras and George Boolos
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8 ideas
4. Formal Logic / F. Set Theory ST / 1. Set Theory
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10482
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The logic of ZF is classical first-order predicate logic with identity [Boolos]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
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10492
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A few axioms of set theory 'force themselves on us', but most of them don't [Boolos]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
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18192
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Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
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7785
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The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
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10485
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Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
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10484
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The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
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13547
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Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter]
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4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
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10699
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Does a bowl of Cheerios contain all its sets and subsets? [Boolos]
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