Christoph Jäger has argued that Dretske’s information-based account of knowledge is committed to both knowledge and information closure under known entailment. However, in a reply to Jäger, Dretske defended his view on the basis of a discrepancy between the relation of information and the relation of logical implication. This paper shares Jäger’s criticism that Dretske’s externalist notion of information implies closure, but provides an analysis based on different grounds. By means of a distinction between two perspectives, the mathematical perspective and (...) the epistemological perspective, I present, in the former, a notion of logical implication that is compatible with the notion of information in the mathematical theory of information, and I show how, in the latter, Dretske’s logical reading of the closure principle is incompatible with his information-theoretic epistemological framework. (shrink)