Euclidean Arithmetic: The Finitary Theory of Finite Sets

  • J.P. Mayberry
Part of the The Western Ontario Series in Philosophy of Science book series (WONS, volume 76)


There is a central fallacy that underlies all our thinking about the foundations of arithmetic. It is the conviction that the mere description of the natural numbers as the “successors of zero” (i.e., as what you get by starting at 0 and iterating the operation xx + 1) suffices, on its own, to characterise the order and arithmetical properties of those numbers absolutely. This is what leads us to suppose that the dots of ellipsis in


Natural Number Linear Ordering Global Function Arithmetical Function Definite Property 
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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Dept. of PhilosophyUniversity of BristolBristolEngland, UK

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