Naming the largest number: Exploring the boundary between mathematics and the philosophy of mathematics

TL;DR

This paper investigates the conceptual boundary between mathematics and philosophy regarding the largest number conceivable by humans, highlighting the limitations of current mathematical and philosophical approaches.

Contribution

It critically examines existing mathematical and philosophical formulations of the largest number, proposing a nuanced perspective on their interplay and limitations.

Findings

Mathematical approaches often miss the philosophical essence of the problem.

Philosophical formulations risk reducing the problem to purely philosophical debates.

The boundary between mathematics and philosophy is complex and not easily delineated.

Abstract

What is the largest number accessible to the human imagination? The question is neither entirely mathematical nor entirely philosophical. Mathematical formulations of the problem fall into two classes: those that fail to fully capture the spirit of the problem, and those that turn it back into a philosophical problem.