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Full Idea
Maddy proposes that we can know (some) mind-independent mathematical truths through knowing about sets, and that we can obtain knowledge of sets through experience.
Gist of Idea
We know mind-independent mathematical truths through sets, which rest on experience
Source
report of Penelope Maddy (Realism in Mathematics [1990]) by Carrie Jenkins - Grounding Concepts 6.5
Book Ref
Jenkins,Carrie: 'Grounding Concepts' [OUP 2008], p.191
A Reaction
Maddy has since backed off from this, and now tries to merely defend 'objectivity' about sets (2011:114). My amateurish view is that she is overrating the importance of sets, which merely model mathematics. Look at category theory.
8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
10718 | A natural number is a property of sets [Maddy, by Oliver] |