  To see how this applies to the Problem of the Many, let's simplify the case a little bit so there are only two water droplets, w1 and w2, that are neither determinately part of the cloud nor determinately not a part of it. As well there is the core of the cloud, call it a. On an orthodox theory, there are four proto-clouds here, a, a + w1, a + w2 and a + w1 + w 2. On Hudson's theory the largest and the smallest proto-clouds still exist, but in the middle there is a quite different kind of object, which we'll call c. Let r1 be the region occupied by a and w1, and r2 the region occupied by a and w2. Then the following claims are all true according to Hudson: