 Lewis’s argument here might be expanded as follows: Consider any putative problem about the conditions under which a thing x is identical with a thing y. There are only two cases: either (i) x is identical with y, or (ii) x is not identical with y. Consider case (i). In this case the putative problem is about the conditions under which x is identical with itself. But there cannot be any such problem, because it is a conceptual truth that everything is identical with itself, and so x is identical with itself under all conditions. To ask for the conditions under which something is identical with itself is like asking ‘Under what conditions is one thing one thing, and not two things?’ There can be no informative answer because necessarily, if something is one thing then it is one thing, and not two things, and nothing more can be said. Now consider case (ii). The putative problem is now about the conditions under which a thing x is identical with a different thing y. But there cannot be any such problem, because it is a conceptual truth that one thing and a different thing are not identical, and so there are no conditions under which x and y are identical. To ask for the conditions under which one thing and a different thing are identical is like asking ‘Under what conditions are two things one thing, and not two things?’ There can be no informative answer because necessarily, if two things are two things, then they are two things, and not one thing, and nothing more can be said. And so, whether case (i) or case (ii) holds, there can be no problem about the conditions under which a thing x is identical with a thing y.