Epistemic Logic, Monotonicity, and the Halbach–Welch Rapprochement Strategy

Abstract

Predicate approaches to modality have been a topic of increased interest in recent intensional logic. Halbach and Welch (Mind 118(469):71–100, 2009) have proposed a new formal technique to reduce the necessity predicate to an operator, demonstrating that predicate and operator methods are ultimately compatible. This article concerns the question of whether Halbach and Welch’s approach can provide a uniform formal treatment for intensionality. I show that the monotonicity constraint in Halbach and Welch’s proof for necessity fails for almost all possible-worlds theories of knowledge. The nonmonotonicity results demonstrate that the most obvious way of emulating Halbach and Welch’s rapprochement of the predicate and operator fails in the epistemic setting.