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Evolutionary Foundations of Mathematics

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  • Tuncer, Ruhi

    ()
    (Galatasaray University Economic Research Center)

Abstract

We propose a simple cognitive model where qualitative and quantitative comparisons enable animals to identify objects, associate them with their properties held in memory and make naive inference. Simple notions like equivalence relations, order relations are used. We then show that such processes are at the root of human mathematical reasoning by showing that the elements of totally ordered sets satisfy the Peano axioms. The process through which children learn counting is then formalized. Finally association is modeled as a Markov process leading to a stationary distribution.

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Bibliographic Info

Paper provided by Galatasaray University Economic Research Center in its series GIAM Working Papers with number 11-3.

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Length: 22 pages
Date of creation: 03 Mar 2011
Date of revision: 03 Mar 2011
Handle: RePEc:ris:giamwp:2011_003

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Keywords: Cognitive system; equivalence relations; order relations; naive logic; Peano axioms; order precedes number; association; Markov chain;

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