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Ideas for 'Realism in Mathematics', 'Higher-Order Logic' and 'On Platonism in Mathematics'

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3 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

10301

The axiom of choice is controversial, but it could be replaced [Shapiro]

4. Formal Logic / F. Set Theory ST / 7. Natural Sets

8755	Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

10304

Very few things in set theory remain valid in intuitionist mathematics [Bernays]