Abstract
In this paper I consider Peano’s main mathematical concerns in the 1880s, and the relations between them. I shall propose that he had a sort of magical moment that led him to create his mathematical logic, but also that he was obscure, or at least unclear, about one of the major attendant changes in thought. The material covered is summarised historically in Grattan-Guinness (2000, especially chs. 2, 4 and 5), and treated in more detail in various works cited there.
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References
T.W. Hawkins (1970), 87–91.
The English translation of the book on Grassmann renders at one point Peano’s ‘nullo’ (G. Peano 1888a, 18) as ‘the empty set’ (L.C. Kannenberg 2000, 14), which is surely far too Cantorian. Note also ‘nulla’ as ‘empty’ at G. Peano (1888a), L.C. Kannenberg (2000), 2.
Peano’s own copy of the arithmetic book contains many annotations, but none relates to this point (C.S. Roero 2002, Peano’s file 1889a+). Borga notes the change in theory of collections, but he does not bring out its significance (M. Borga 1985, 26).
Note by Peano in P.E.B. Jourdain (1912), 273.
G. Schubring (1996), 211–227.
U. Bottazzini (1985), 48–49.
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© 2011 Springer-Verlag Italia
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Grattan-Guinness, I. (2011). Giuseppe Peano: a Revolutionary in Symbolic Logic?. In: Skof, F. (eds) Giuseppe Peano between Mathematics and Logic. Springer, Milano. https://doi.org/10.1007/978-88-470-1836-5_7
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DOI: https://doi.org/10.1007/978-88-470-1836-5_7
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