Counterpart theory (hereafter "CT"), as formulated by Lewis, requires that individuals exist in only one world. The standard account of possible worlds assumes that a modal statement about an individual (e.g., "it is possible that x is y") means that there is a possible world, W, where the individual x has the property y; in this case there is only one individual, x, at issue. On the contrary, counterpart theory supposes that this statement is really saying that there is a possible world, W, wherein exists an individual that is not x itself, but rather a distinct individual 'x' different from but nonetheless similar to x. So, when I state that I might have been a banker (rather than a philosopher) according to counterpart theory I am saying not that I exist in another possible world where I am a banker, but rather my counterpart does. Nevertheless, this statement about my counterpart is still held to ground the truth of the statement that I might have been a banker. The requirement that any individual exist in only one world is to avoid what Lewis termed the "problem of accidental intrinsics" which (he held) would require a single individual to both have and simultaneously not have particular properties.