Evolutionary Foundations of Mathematics

TL;DR

This paper presents a cognitive model illustrating how animals' comparison processes underpin the development of human mathematical reasoning, including the formalization of counting and the foundations of number systems.

Contribution

It introduces a simple cognitive framework connecting animal comparison behaviors to the formal structure of mathematics, including Peano axioms and counting learning.

Findings

Ordered set elements satisfy Peano axioms.

Children's counting process is formalized.

Association modeled as a Markov process with stationary distribution.

Abstract

We propose a simple cognitive model where qualitative and quantitative com- parisons enable animals to identify objects, associate them with their properties held in memory and make naive inference. Simple notions like equivalence re- lations, 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.