Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson (2006) present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, rest upon significant assumptions – amongst them a relatively strong structural assumption to the effect that the underlying probability space is both finite and uniform. In this paper, I will show that something very like Douven and Williamson’s argument can in fact survive with much weaker structural assumptions – and, in particular, can apply to infinite probability spaces
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