Given that Hume argues that it is impossible to deduce the existence of a Deity from the existence of the world (for he says that causes cannot be determined from effects), miracles (including prophesy) are the only possible support he would conceivably allow for theistic religions.
Hume discusses everyday belief as often resulted from probability, where we believe an event that has occurred most often as being most likely, but that we also subtract the weighting of the less common event from that of the more common event. In the context of miracles, this means that a miraculous event should be labeled a miracle only where it would be even more unbelievable (by principles of probability) for it not to be. Hume mostly discusses miracles as testimony, in context of which he writes that when a person reports a marvellous event we (need to) balance our belief in their veracity against our belief that such events do not occur. Following this rule, only where it is considered, as a result of experience, less likely that the testimony is false than that a miracle occur should be believe in miracles.
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