Combining Texts

Ideas for 'Philosophy of Mathematics', 'A World of Dispositions' 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 / 2. Proof in Mathematics

10885

Computer proofs don't provide explanations [Horsten]

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 / 6. Mathematics as Set Theory / a. Mathematics is set theory

10881

The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]