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