Combining Texts

Ideas for 'Metaphysics', 'Persistence, Change and Explanation' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'

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7 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 / b. Greek arithmetic

17843

The idea of 'one' is the foundation of number [Aristotle]

17850

Each many is just ones, and is measured by the one [Aristotle]

17851

Number is plurality measured by unity [Aristotle]

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 / a. Structuralism

9793	Mathematics studies abstracted relations, commensurability and proportion [Aristotle]