Iterated Knowledge

Abstract

Abstract Omega knowledge is the strongest kind of knowledge. When you omega know something, you know it. You know that you know it. You possess every iteration of knowledge regarding it. This book is the first systematic treatment of omega knowledge. There are two existing theories of omega knowledge. On the one hand, skeptics say that we omega know hardly anything about the world: infinite iterations of knowledge would require infinitely reliable belief-forming methods. This book begins by arguing against the skeptics, by claiming that omega knowledge is a central concept in philosophy. The book argues that omega knowledge is required for rational assertion and action. For this reason, it is important to develop theories which allow us to have omega knowledge of ordinary claims about the world. The only existing theory that allows this is the KK principle, which says that you omega know everything that you know. But the KK principle faces a wide range of well-known counterexamples and theoretical challenges. The goal of this book is to open up new space in epistemology, by developing and critically comparing several new theories of omega knowledge. One of these theories says that you omega know everything that you know that you know. Another theory says that, whenever you know something, it is consistent with your knowledge that you omega know it. These theories avoid the classic challenges to the KK principle, while also making room for large amounts of omega knowledge. Along the way, the book gives treatments of justified belief, rational certainty, and normative requirements on assertion and action. The book ends by developing mathematical models of knowledge that carefully lay out the differing predictions of the various theories developed in the book.