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Ideas for 'Logic (Encyclopedia I)', 'Frege philosophy of mathematics' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'

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5 ideas

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics

18271

We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]

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

10623

Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]

9975	Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique

9829	The identity of a number may be fixed by something outside structure - by counting [Dummett]

9828	Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]