 Independently of his counterpart theory, Lewis’s definition of a possible object has some peculiar consequences, given that existence in general is understood as bearing of the part-of relation to the whole that constitutes the domain of discourse. Take any two possible worlds w1 and w2. Lewis wants to assert that both w1 and w2 exist in some sense. So for the assertion to be true, it must be true relative to a domain of discourse which contains as a sub-domain some whole of which both w1 and w2 are part. Not both are part of a single possible world or of its part. The smallest whole of which they both are part is the (mereological) sum of w1 and w2. So, some domain D containing such a sum as a sub-domain must count as an acceptable domain of discourse for the evaluation of an existence claim. Consider a proper part p1 of w1 and a proper part p2 of w2. Let Gerry be the sum of p1 and p2. Then it is true to say that Gerry exists when the domain of discourse is D. So, there is a sense in which Gerry exists. In fact it is the same sense in which w1 and w2 exist. But Gerry is not a possible object, according to Lewis’s conception, for Gerry does not have all of its parts at a single possible world. This is peculiar. Gerry is an object which exists in the same sense in which possible worlds exist but Gerry is not a possible object. Since—as sanctioned by the universality of mereological summation, which Lewis accepts—Gerry is an object, Gerry is an impossible object. But there is nothing impossible about Gerry any more than there is about the sum of w1 and w2. Perhaps the sum of w1 and w2 is an impossible object, too. But this idea flouts the initially plausible principle of recombination for possibility of objects, which says that if x is a possible object and y is a possible object independent of x, then the totality consisting exactly of x and y is a possible object. Defenders of Lewis’s theory may take this to mean that the principle of recombination, despite its initial plausibility, is to be rejected. There is another unexpected consequence of Lewis’s theory. If the sum of w1 and w2 is an impossible object, then the sum of all possible worlds is an impossible object, for the former is part of the latter and no impossible object is part of a possible object. But this makes the domain in which all possible worlds reside, or “logical space”, an impossible object. This appears unwelcome. Lewis does consider an alternative conception of a possible object, which says that a possible object is an object every part of which exists at some possible world or other (Lewis 1986: 211). This allows a possible object to have parts at different possible worlds. Lewis, who accepts the universality of mereological summation, does not deny that possible objects in this sense are as real as possible objects in his preferred sense. He however dismisses them as unimportant on the ground that we do not normally name them, speak of them, or quantify over them. But given that sets of possible worlds and sets of possible objects figure in important philosophical discussions concerning the identity of propositions and properties, these sets seem important. If the sum of the members of an important set is important, then Lewis’s dismissal appears hasty. Again, defenders of Lewis may stand this line of reasoning on its head and conclude that the sum of the members of an important set is not always important.