Tautology, Barbers, Impredicativity and Self-Adjudication

This article discusses a tautological principle about self-adjudicating systems and applies it to a zero-player game called 'The Inaccessible Game'. It uses the barber paradox (Russell's paradox) to illustrate impredicative circularity and proposes a 'No Barber Principle' to avoid external adjudication. The author connects this to category theory, Lawvere's work, and the no-cloning condition, arguing for a foundational preference for von Neumann entropy over Shannon entropy. The article references a paper on arXiv and explores how prohibiting variable copying can prevent paradoxes in self-referential systems.