Ideas from 'Must We Believe in Set Theory?' by George Boolos [1997], by Theme Structure
[found in 'Logic, Logic and Logic' by Boolos,George [Harvard 1999,0-674-53767-x]].
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4. Formal Logic / F. Set Theory ST / 1. Set Theory
10482
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The logic of ZF is classical first-order predicate logic with identity
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10492
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A few axioms of set theory 'force themselves on us', but most of them don't
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
10485
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Naïve sets are inconsistent: there is no set for things that do not belong to themselves
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10484
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The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10491
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Infinite natural numbers is as obvious as infinite sentences in English
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
10483
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Mathematics and science do not require very high orders of infinity
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10490
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Mathematics isn't surprising, given that we experience many objects as abstract
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8. Modes of Existence / D. Universals / 1. Universals
10488
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It is lunacy to think we only see ink-marks, and not word-types
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9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
10487
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I am a fan of abstract objects, and confident of their existence
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9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
10489
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We deal with abstract objects all the time: software, poems, mistakes, triangles..
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