In addition to the obvious stark ontological contrast between the two theories, they differ in two important ways in their implications for the philosophy of modality. First, if Lewis is right, then modal concepts can be defined in terms of paradigmatically non-modal concepts, since ‘world’ and all of Lewis's other technical terms can be defined using only ‘is spatiotemporally related to’, ‘is a part of’ and the vocabulary of set theory. For Kripke and Plantinga, however, modal concepts are sui generis, indefinable or having only definitions that appeal to other modal concepts. Secondly, Lewis's theory implies a kind of anti-realism concerning modality de re. This is because there is no one relation that is the counterpart relation—there are rather various ways or respects in which one could say that objects in two worlds “play the same role” in their respective worlds. Socrates, therefore, may well have non-human counterparts under one counterpart relation and no non-human counterparts under another. And the choice of a counterpart relation is a pragmatic or interest-relative choice. But on the KP theory, it is an entirely objective question whether Socrates fails to be human in some world in which he exists: the answer must be Yes or No and is independent of human choices and interests.