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The Search for Mathematical Roots, 1870-1940 by I. Grattan-Guinness

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8.6 PERIPHERALS: ITALY AND FRANCE

8.6.1 The occasional Italian survey. Italian interest faded during the 1910s as Peano switched interest steadily more to international languages, though we saw his work of 1913 in §8.2.4. But one lingering worry concerned the clash between Peano’s method of definition of cardinals by abstraction and Russell’s nominal definition by classes of classes (§6.5.2). Burali-Forti 1909a had proposed, as a third option, definitions of function(al)s of ordered pairs ‘(a;b)’ of ‘simple entities’ a and b, such as arithmetical operations on numbers, or (Russellian) classes of ordered pairs of integers. One of Peano’s minor followers, Eugenio Maccaferri (1870–1953), took up this idea to suggest that if members x and y of a ...

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