A Mathematical Approach to the Plato's Problem

TL;DR

This paper introduces a mathematical model inspired by Plato's Allegory of the Cave, aiming to simulate the problem of knowledge acquisition and perception as described in ancient philosophy.

Contribution

It formulates a novel mathematical framework to represent the philosophical problem posed by Plato, bridging classical thought with formal modeling.

Findings

A new mathematical model of Plato's Allegory of the Cave

Insights into perception and knowledge through formal simulation

Potential applications in understanding cognitive processes

Abstract

Maybe the first inverse problem presented in the history of the occidental thought is described in the book Republic, written by Plato. The problem is posed in the Book VII in a text known as the Allegory of the Cave. That text motivated us to formulate a simple mathematical model that simulates, in a sense, the situation of the persons described in that problem.