G\'eom\'etrie et cognition; l'exemple du continu

TL;DR

This paper explores the distinction between truth and meaning in mathematics, proposing that perceptual neurophysiology underpins the foundational understanding of mathematical lines.

Contribution

It introduces a novel perspective linking neurophysiological findings to the foundational meaning of mathematical concepts, specifically the line.

Findings

Neurophysiological evidence supports the perceptual basis of the mathematical line.

A distinction between truth and meaning foundations in mathematics is proposed.

The perceptual system's role in mathematical understanding is emphasized.

Abstract

In this paper I propose the idea to establish a clear distinction between the foundations of truth and the foundations of meaning in Mathematics. I explore on the most basic example, the mathematical line, the possibility that the foundations of its meaning are provided by a protomathematical object resulting from the identification by our perceptual system of the visual line and the vestibular line, a point of view suggested by recent results of neurophysiology.