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Ideas for 'Are there propositions?', 'Grundgesetze der Arithmetik 1 (Basic Laws)' and 'The Concept of Logical Consequence'

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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]
     Full Idea: If 'number' is the referent of a numerical symbol, a real number is the same as a ratio of quantities. ...A length can have to another length the same ratio as a mass to another mass.
     From: Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], III.1.73), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's'
     A reaction: This is part of a critique of Cantor and the Cauchy series approach. Interesting that Frege, who is in the platonist camp, is keen to connect the real numbers with natural phenomena. He is always keen to keep touch with the application of mathematics.