 Concerning the first sort of worry, one could of course construe every restricted composition principle as a biconditional expressing both a sufficient and a necessary condition for the existence of an upper bound, or a sum, of a given pair or set of entities. But then the question of how such conditions should be construed becomes crucial, on pain of turning a weak sufficient condition into an exceedingly strong requirement. For example, with regard to (P.11ξ) we have mentioned the idea of construing ‘ξ’ as ‘O’, the rationale being that mereological overlap establishes an important connection between what may count as two distinct parts of a larger (integral) whole. However, as a necessary condition overlap is obviously too stringent. The top half of my body and the bottom half do not overlap, yet they do form an integral whole. The topological relation of contact, i.e., overlap or abut, might be a better candidate. Yet even that would be too stringent. We may have misgivings about the existence of scattered entities consisting of totally disconnected parts, such as my umbrella and your left shoe or, worse, the head of this trout and the body of that turkey (Lewis 1991: 7–8). Yet in other cases it appears perfectly natural to countenance wholes that are composed of two or more disconnected entities: a bikini, a token of the lowercase letter ‘i’, my copy of The Encyclopedia of Philosophy (R. Cartwright 1975; Chisholm 1987)—indeed any garden-variety material object, insofar as it turns out to be a swarm of spatially isolated elementary particles (van Inwagen 1990). Similarly for some events, such as Dante's writing of Inferno versus the sum of Sebastian's stroll in Bologna and Caesar's crossing of Rubicon (see Thomson 1977: 53f). More generally, intuition and common sense suggest that some mereological composites exist, not all; yet the question of which composites exist seems to be up for grabs. Consider a series of almost identical mereological aggregates that begins with a case where composition appears to obtain (e.g., the sum of all body cells that currently make up my body, the relative distance among any two neighboring ones being less than 1 nanometer) and ends in a case where composition would seem not to obtain (e.g., the sum of all body cells that currently make up my body, after their relative distance has been increased to 1 kilometer). Where should we draw the line? In other words—and to limit ourselves to (P.15ψ,i)—what value of n would mark a change of truth-value in the soritical sequence generated by the schema