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Ideas for 'Parmenides', 'Grundgesetze der Arithmetik 2 (Basic Laws)' and 'Structuralism'

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4 ideas

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers

10553

A number is a class of classes of the same cardinality [Frege, by Dummett]

10020

Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

8921	Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism

8922	Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman]