more from Penelope Maddy

### Single Idea 18184

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory]

Full Idea

The set theory axioms developed in producing foundations for mathematics also have strong consequences for existing fields, and produce a theory that is immensely fruitful in its own right.

Gist of Idea

Making set theory foundational to mathematics leads to very fruitful axioms

Source

Penelope Maddy (Naturalism in Mathematics [1997], I.2)

Book Reference

Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.26

A Reaction

[compressed] Second of Maddy's three benefits of set theory. This benefit is more questionable than the first, because the axioms may be invented because of their nice fruit, instead of their accurate account of foundations.

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Set theory brings mathematics into one arena, where interrelations become clearer **[Maddy]**

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Unified set theory gives a final court of appeal for mathematics **[Maddy]**

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ZFC could contain a contradiction, and it can never prove its own consistency **[MacLane]**