Ideas of Geoffrey Hellman, by Theme

[American, fl. 1989, Professor at the University of Minnesota. An active concert pianist.]

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6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / a. Structuralism
Structuralism is now common, studying relations, with no regard for what the objects might be
6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / c. Nominalist structuralism
Modal structuralism says mathematics studies possible structures, which may or may not be actualised
Statements of pure mathematics are elliptical for a sort of modal conditional
Modal structuralism can only judge possibility by 'possible' models
Maybe mathematical objects only have structural roles, and no intrinsic nature