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
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We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
17843
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The idea of 'one' is the foundation of number [Aristotle]
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17850
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Each many is just ones, and is measured by the one [Aristotle]
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17851
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Number is plurality measured by unity [Aristotle]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
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9975
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Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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Mathematics studies abstracted relations, commensurability and proportion [Aristotle]
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