As part of his wider critique of the credibility of miraculous testimony, Hume also offers a rather curious argument as to the mutual detriment of conflicting testimony for the miracles of contrary religious worldviews. Scholarship on this aspect of Hume’s reasoning has debated whether or not the considerations are to be understood as essentially probabilistic, and as to whether or not a probabilistic interpretation of the argument is logically valid. The consensus would appear to offer a positive answer to the (...) first question and a negative answer to the second. In this paper I expose a deeper fallacy in Hume’s reasoning that undermines both probabilistic and non-probabilistic readings. My critique is closely based upon analogous considerations in the philosophy of science, and the equally intriguing issue as to the epistemological relevance of conflicting scientific theories throughout the history of science. (shrink)