Epistemic Horizons and the Foundations of Quantum Mechanics

TL;DR

This paper explores the fundamental limits on information gathering in quantum systems, proposing that paradoxical self-reference may explain epistemic horizons through a mathematical fixed-point theorem.

Contribution

It introduces a novel perspective linking self-reference paradoxes to quantum epistemic limits using category theory and fixed-point theorems.

Findings

Self-reference paradoxes may underpin quantum epistemic horizons

Fixed-point theorems provide a unifying framework for understanding information restrictions

The approach offers new insights into the foundations of quantum mechanics

Abstract

In-principle restrictions on the amount of information that can be gathered about a system have been proposed as a foundational principle in several recent reconstructions of the formalism of quantum mechanics. However, it seems unclear precisely why one should be thus restricted. We investigate the notion of paradoxical self-reference as a possible origin of such epistemic horizons by means of a fixed-point theorem in Cartesian closed categories due to F. W. Lawvere that illuminates and unifies the different perspectives on self-reference.