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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.

Suggested Citation

  • Tuncer, Ruhi, 2011. "Evolutionary Foundations of Mathematics," GIAM Working Papers 11-3, Galatasaray University Economic Research Center, revised 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;
    All these keywords.

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