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2 ideas
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. |
18166 | The loss of my Rule V seems to make foundations for arithmetic impossible [Frege] |
Full Idea: With the loss of my Rule V, not only the foundations of arithmetic, but also the sole possible foundations of arithmetic, seem to vanish. | |
From: Gottlob Frege (Letters to Russell [1902], 1902.06.22) | |
A reaction: Obviously he was stressed, but did he really mean that there could be no foundation for arithmetic, suggesting that the subject might vanish into thin air? |