Doing without absences
An old puzzle: The average mother has 3.4 children. Yet the average mother does not exist. So how can she have children? An old solution: She doesn't. "The average mother has 3.4 children" is to be understood as "the number of children divided by the number of mothers is 3.4". So "average mother" is not a genuine predicate, but rather a meaningless part of numerical predicates like "the average mother has ... children".
If this solution is correct, it is meaningless to say that average mothers exist, that some of them influence others, and that all of them are distinct. Which indeed it is.
David Lewis, in "Void and Object" and "Causation as Influence", applies that solution to absences. Absence of food causes death, yet there is no such thing as absence of food. So how can it cause death? It doesn't. When an absence of food occurs, what really happens is just that there is no food around. Hence Lewis: "the proposition that an absence occurs is a perfectly good negative existential proposition" [influence, p.195].
If you think, as I thought until yesterday, that it should not be too difficult to rephrase Lewis' (new) theory of causation using only perfectly good negative existentials instead of talk about absences, please go ahead and try it! (And let me know the result.) You'll find a lot of statements saying that absences exist, that some of them influence others, and that all of them are distinct.