at different moments (see the counterpart relation, below). An opposing view is that any object in time is made up of temporal parts or is perduring. Lewis' view on possible worlds is sometimes called modal realism. The basics The possibilities that CT is supposed to describe are “ways a world might be” (Lewis 1986:86) or more exactly: (1) absolutely every way that a world could possibly be is a way that some world is, and (2) absolutely every way that a part of a world could possibly be is a way that some part of some world is. (Lewis 1986:86.) Add also the following “principle of recombination,” which Lewis describes this way: “patching together parts of different possible worlds yields another possible world […]. can coexist with anything else, […] provided they occupy distinct spatiotemporal positions.” (Lewis 1986:87-88). But these possibilities should be restricted by CT. The counterpart relation The counterpart relation (hereafter C-relation) differs from the notion of identity. Identity is a reflexive, symmetric, and transitive relation. The counterpart relation is only a similarity relation; it needn’t be transitive or symmetric. The C-relation is also known as genidentity (Carnap 1967), I-relation (Lewis 1983), and the unity relation (Perry 1975). If identity is shared between objects in different possible worlds then the same object can be said to exist in different possible worlds (a trans-world object, that is, a series of objects sharing a single identity). Parthood relation An important part of the way Lewis’s worlds deliver possibilities is the use of the parthood relation. This gives some neat formal machinery, mereology. This is an axiomatic system that uses formal logic to describe the relationship between parts and wholes, and between parts within a whole. Especially important, and most reasonable, according to Lewis, is the strongest form that accepts the existence of mereological sums or the thesis of unrestricted mereological composition (Lewis 1986:211-213). The formal theory As a formal theory, counterpart theory can be used to translate sentences into modal quantificational logic. Sentences that seem to be quantifying over possible individuals should be translated into CT. (Explicit primitives and axioms have not yet been stated for the temporal or spatial use of CT.) Let CT be stated in quantificational logic and contain the following primitives: ( is a possible world) ( is in possible world ) ( is actual) ( is a counterpart of ) We have the following axioms