Inexact Knowledge without Improbable Knowing

Abstract

In a series of recent papers, Timothy Williamson has argued for the surprising conclusion that there are cases in which you know a proposition in spite of its being overwhelmingly improbable given what you know that you know it. His argument relies on certain formal models of our imprecise knowledge of the values of perceptible and measurable magnitudes. This paper suggests an alternative class of models that do not predict this sort of improbable knowing. I show that such models are motivated by independently plausible principles in the epistemology of perception, the epistemology of estimation, and concerning the connection between knowledge and justified belief.