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.

The liar’s paradox is a simple yet harrowing problem that has plagued logicians and philosophers who study natural language. It is an uncommon sentence, and perhaps a largely useless one outside of artificially-created circumstances. However, it threatens to undo any naivelyconstructed theory of natural language semantics, if the theory does not take the paradox into account. Indeed, many well-...

This paper proposes a new framework to solve the surprise examination paradox. I survey preliminary the main contributions to the literature related to the paradox. I introduce then a distinction between a monist and a dichotomic analysis of the paradox. With the help of a matrix notation, I also present a dichotomy that leads to distinguish two basically and structurally different notions of s...

There are three distinct questions associated with Simpson’s paradox. (i) Why or in what sense is Simpson’s paradox a paradox? (ii) What is the proper analysis of the paradox? (iii) How one should proceed when confronted with a typical case of the paradox?We propose a “formal” answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding...