Non-Transitive Self-Knowledge: Luminosity via Modal μ-Automata

This essay provides a novel account of iterated epistemic states. The essay argues that states of epistemic determinacy might be secured by countenancing self-knowledge on the model of fixed points in monadic second-order modal logic, i.e. the modal μ-calculus. Despite the epistemic indeterminacy witnessed by the invalidation of modal axiom 4 in the sorites paradox -- i.e. the KK principle: $\square$$\phi$ $\rightarrow$ $\square$$\square$$\phi$ -- an epistemic interpretation of the Kripke functors of a μ-automaton permits the iterations of the transition functions to entrain a principled means by which to account for necessary conditions on self-knowledge.