more from Penelope Maddy

Single Idea 17823

[catalogued under 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism]

Full Idea

The popular challenges to platonism in philosophy of mathematics are epistemological (how are we able to interact with these objects in appropriate ways) and ontological (if numbers are sets, which sets are they).

Gist of Idea

If mathematical objects exist, how can we know them, and which objects are they?


Penelope Maddy (Sets and Numbers [1981], I)

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.345

A Reaction

These objections refer to Benacerraf's two famous papers - 1965 for the ontology, and 1973 for the epistemology. Though he relied too much on causal accounts of knowledge in 1973, I'm with him all the way.

Related Idea

Idea 17826 Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy]