  A crucial part of the argument that the Problem of the Many is the argument that every oi is a cloud. If we can find a way to reject that step, then we the argument collapses. There are three obvious arguments for this premise, two of them presented explicitly by Unger, and the other by Geach. Two of the arguments seem to be faulty, and the third can be rejected if we adopt some familiar, though by no means universally endorsed, theories of vagueness. The first argument, due essentially to Geach, runs as follows. Geach's presentation did not involve clouds, but the principles are clearly stated in his version of the argument. (The argument shows that an ok is a cloud for arbitrary k, we can easily generalize to the claim that for every i, oi is a cloud.)