The Threshold Problem, the Cluster Account, and the Significance of Knowledge

Abstract

The threshold problem is the task of adequately answering the question: “Where does the threshold lie between knowledge and lack thereof?” I start this paper by articulating two conditions for solving it. The first is that the threshold be neither too high nor too low; the second is that the threshold accommodate the significance of knowledge. In addition to explaining these conditions, I also argue that it is plausible that they can be met. Next, I argue that many popular accounts of knowledge cannot meet them. In particular, I lay out a number of problems that standard accounts of knowledge face in trying to meet these conditions. Finally, near the end of this paper, I argue that there is one sort of account that seems to evade these problems. This sort of account, which is called a cluster account of knowledge, says that knowledge is to be accounted for in terms of truth, belief and a cluster of epistemic properties and also that knowledge doesn't require having all members of the cluster, but merely some subset.

Reductive Views of Knowledge and the Small Difference Principle

“… 6 The same goes for extant fallibilist solutions to the threshold challenge. Consider, for instance, Immerman (2020)’s cluster account, on which there is a large cluster of properties such that none are individually necessary or sufficient for turning one’s belief into knowledge (lack of one property can be made up for by having another), but if one’s belief instantiates sufficiently many of them, one knows that . Importantly, if just one of the properties in the cluster is gradable, my challenge arises for the cluster view.…”