Peano and the Foundations of Arithmetic

  • Gabriele Lolli


At the end of the 1880s two episodes occurred in rapid succession which formed the bases of what we call the foundations of arithmetic: the publication in 1888 of Was sind und was sollen die Zahlen by Richard Dedekind and in 1889 of Arithmetices Principia, nova methodo exposita by Giuseppe Peano. This work was to give Peano lasting fame, in that he had for the first time expounded the axioms for the system of natural numbers; from that time on they were linked to his name, and from the English “Peano Arithmetic” were known by the acronym PA.


Natural Number Peano Arithmetic Associative Property Logical Axiom Inferential Method 
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  1. 1.
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  2. 2.
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    Pieri (1906d), 203.Google Scholar
  53. 70.
    Replacing it with II below, he has to modify an axiom on the classes used by Burali-Forti, which Whitehead had pointed out as erroneous, and Poincaré (1908), 209, had derided.Google Scholar
  54. 71.
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Copyright information

© Springer-Verlag Italia 2011

Authors and Affiliations

  • Gabriele Lolli
    • 1
  1. 1.Scuola Normale Superiore of PisaItaly

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