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Ideas for 'Universal Prescriptivism', 'Letters to Russell' and 'Practical Necessity'

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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
18253 I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege]
     Full Idea: You need a double transition, from cardinal numbes (Anzahlen) to the rational numbers, and from the latter to the real numbers generally. I wish to go straight from the cardinal numbers to the real numbers as ratios of quantities.
     From: Gottlob Frege (Letters to Russell [1902], 1903.05.21), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's'
     A reaction: Note that Frege's real numbers are not quantities, but ratios of quantities. In this way the same real number can refer to lengths, masses, intensities etc.