Some Non-Classical Approaches to the Branderburger-Keisler Paradox

TL;DR

This paper explores the Brandenburger-Keisler paradox using non-well-founded set theory and paraconsistent logic, revealing its persistence across different logical frameworks with distinct properties.

Contribution

It introduces non-classical logical frameworks to analyze the paradox, highlighting their effects on the paradox's properties and persistence.

Findings

The paradox persists in both frameworks for category theoretical reasons.

Different properties of the paradox are observed in each framework.

Abstract

In this paper, we discuss a well-known self-referential paradox in foundational game theory, the Brandenburger - Keisler paradox. We approach the paradox from two different perspectives: non-well-founded set theory and paraconsistent logic. We show that the paradox persists in both frameworks for category theoretical reasons, but, with different properties.