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This article is concerned with a statistical proposal due to James R. Beebe for how to solve the generality problem for process reliabilism. The proposal is highlighted by Alvin I. Goldman as an interesting candidate solution. However, Goldman raises the worry that the proposal may not always yield a determinate result. We address this worry by proving a dilemma: either the statistical approach does not yield a determinate result or it leads to trivialization, i.e. reliability collapses into truth (and anti-reliability into falsehood). Various strategies for avoiding this predicament are considered, including revising the statistical rule or restricting its application to natural kinds. All amendments are seen to have serious problems of their own. We conclude that reliabilists need to look elsewhere for a convincing solution to the generality problem

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In this paper, we propose a new theory of rationality defeat. We propose that defeaters are indicators of ignorance, evidence that we’re not in a position to know some target proposition. When the evidence that we’re not in a position to know is sufficiently strong and the probability that we can know is too low, it is not rational to believe. We think that this account retains all the virtues of the more familiar approaches that characterize defeat in terms of its connection to reasons to believe or to confirmation but provides a better approach to higher-order defeat. We also think that a strength of this proposal is that it can be embedded into a larger normative framework. On our account the no-defeater condition is redundant. We can extract our theory of defeat from our theory of what makes it rational to believe—it is rational to believe when it is sufficiently probable that our belief would be knowledge. Thus, our view can provide a monistic account of defeat, one that gives a unifying explanation of the toxicity of different defeaters that is grounded in a framework that either recognizes knowledge as the norm of belief or identifies knowledge as the fundamental epistemic good that full belief can realize.