 Chisholm (1967) arrives at his role-switching world by a series of steps. Thus his argument appears to rely on the combination of the transitivity of identity (across possible worlds) with the assumption that a succession of small changes can add up to a big change. And ‘Chisholm’s Paradox’ (as it is called) is sometimes regarded as relying crucially on these assumptions, suggesting that it has the form of a sorites paradox (the type of paradox that generates, from apparently impeccable assumptions, such absurd conclusions as that a man with a million hairs on his head is bald). (See, for example, Forbes 1985, Ch. 7.)