 Third, perdurantists who reject universalism seem committed to giving an account of the difference between collections of temporal parts which have a sum, and collections which do not. But such accounts seem to permit borderline cases, in which it’s not clear whether a certain collection has a sum. And borderline cases look like cases in which it is not clear whether a certain object (the sum of those parts) exists or not. And many find such vagueness in existence unacceptable. Objections to this argument turn on whether non-universalists really have to give such an account, and on whether vague existence really is unacceptable.