Combining Texts
Ideas for
'27: Book of Daniel', 'Must We Believe in Set Theory?' and 'Introduction to Zermelo's 1930 paper'
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7 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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17833
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The first-order ZF axiomatisation is highly non-categorical [Hallett,M]
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17834
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Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M]
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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 / 7. Natural Sets
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17837
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Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]
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