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Ideas for 'The Roots of Reference', 'Grundgesetze der Arithmetik 1 (Basic Laws)' and 'Contextualism Defended (and reply)'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

18252

Real numbers are ratios of quantities, such as lengths or masses [Frege]

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 / C. Sources of Mathematics / 6. Logicism / a. Early logicism

18165

My Basic Law V is a law of pure logic [Frege]