Dretske on Closure of Knowledge and Its Rereading in Justification Logic

The K axiom in the logic of knowledge expresses this epistemological approach that knowledge is closed under known implications. For Dretske, for two reasons, the closure of knowledge cannot be tautology: first, the knowledge operator does not penetrate into some of the logical implications of our believed propositions; secondly, the conclusive reasons of belief in a proposition cannot be regarded as a conclusive for believing in the heavyweight implications of the proposition. Therefore, if we continue to insist on full adherence to the closure of knowledge, we will inevitably accept skepticism, and it is no way to exclude this epistemological principle and reject the axiom of K. But the abandonment of the closure of knowledge and, consequently, the rejection of the axiom of K would mean that all the modal logics that comprise this axiom cannot be suitable formal systems for the study of epistemological arguments. In this paper, we show that the logic of justification, as a modal logic, while satisfying Dretske’s views, can be a proper formal modal system for studying epistemological arguments.