Some conceptions of logic claim that they are universal. By contrast, I assume that the applications of any logic are central to its conception, so that it has to comprise a hierarchy of its metalogics, metametalogics, …, indefinitely extended but never capped off with some universal logic. I also advocate for the distinction between parts and moments of a multitude as key to this conception, and I query the assumption that set theory provides the most general means of handling collections of objects.