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

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

10492

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. Naïve logical sets

10485

Naïve 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

10484

The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite

10491

Infinite natural numbers is as obvious as infinite sentences in English

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities

10483

Mathematics and science do not require very high orders of infinity

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

10490

Mathematics isn't surprising, given that we experience many objects as abstract

8. Modes of Existence / D. Universals / 1. Universals

10488

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

10487

I am a fan of abstract objects, and confident of their existence

9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta

10489

We deal with abstract objects all the time: software, poems, mistakes, triangles..