 Although the second premise of the argument seems reasonable enough, the first premise is overly rigorous. In many cases, the chance of a premise being false is negligible, though not quite zero.  We might well rely on it simply because it isn’t worth the effort to formulate a more precise premise. For example, in choosing a path to walk home on a day when I am in no particular hurry, I might rely on the thought that the path I’m on is as good as any other--and I don’t bother to calculate the possibility that I’m wrong. Even in cases where I am, in fact, trying to be more careful, I’ll often have to rely on an uncertain belief at some point. Suppose I’m trying to decide whether to rely on the proposition that p but come to see that it is uncertain. So, I pull back to the claim that it is likely that p. But I may not be certain that it’s likely that p. If so, I can either pull back even further--to the proposition that it is likely that it is likely that p--or I can simply rely, albeit tentatively, on the proposition that p. In almost every case, the latter is the more natural course of action to take.