Giuseppe Peano: a Revolutionary in Symbolic Logic?

  • Ivor Grattan-Guinness


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.


Mathematical Logic Traditional Theory Algebraic Logic Short Book Constituent Proposition 
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  1. 1.
    T.W. Hawkins (1970), 87–91.Google Scholar
  2. 4.
    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.Google Scholar
  3. 5.
    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).Google Scholar
  4. 6.
    Note by Peano in P.E.B. Jourdain (1912), 273.Google Scholar
  5. 9.
    G. Schubring (1996), 211–227.Google Scholar
  6. 10.
    U. Bottazzini (1985), 48–49.Google Scholar

Copyright information

© Springer-Verlag Italia 2011

Authors and Affiliations

  • Ivor Grattan-Guinness
    • 1
  1. 1.University of MiddlesexUK

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