Like several other contributions to The Puzzle of Existence, the essay by the late E. J. Lowe is devoted to the question whether there might have been nothing. Lowe calls the view that there might have been nothing ‘metaphysical nihilism,’ and he offers an argument against a certain version of it.
Lowe’s paper begins with some very helpful context-setting. In 1996, Peter van Inwagen had argued that there is a possible world which was ’empty’ in the sense of containing only abstract objects, and no concrete objects. However, according to van Inwagen, out of the infinitely many possible worlds, only one is the empty world, hence the probability that the empty world is actual is 0.
Van Inwagen’s argument was published together with a response by Lowe. In his article in Puzzle, Lowe summarizes his earlier argument as follows:
Some abstract objects exist necessarily, and so exist in every possible world. But all abstract objects depend on there being concrete objects – although not necessarily the same concrete objects in every possible world. Hence, concrete objects exist in every possible world, even if there is no necessary concrete being (182-183).
Lowe’s key examples of necessarily existing abstract objects were numbers, which he then thought were required to ground arithmetic truths. One important difficulty of Lowe’s understanding of the grounding of abstracta in concreta was that it required him to deny the existence of the null set and the number 0.
After 1996, two things happened: a number of objections to Lowe’s argument were raised, and (for reasons independent of those objections) Lowe stopped believing in numbers. The current paper reformulates the argument in a way that relies only on universals and ‘impure’ sets. Lowe’s argument is, essentially, that universals depend ontologically on their instances, and sets depend ontologically on their members, but there can be no cycles or regresses of ontological dependence, hence, if there are abstracta, there must be concreta. Lowe continues to reject the existence of the null set, and consequently of all ‘pure’ sets, on grounds that the null set cannot be properly grounded.
My key worry as I was reading the paper concerns a shift in Lowe’s characterization of van Inwagen’s position, against which he is supposed to be arguing. At the beginning of the paper, he describes van Inwagen as arguing for the existence of a world empty of concreta, but conceding that that world still contains abstracta (182). But later in the paper, Lowe characterizes van Inwagen as arguing that “there is an ’empty’ world in which there exist no concrete objects but abstract objects do exist” (187). At this point, Lowe makes it clear that he is no longer arguing that there must be concrete objects, but only that there can’t be abstracta without concreta. In other words, what was earlier a concession of van Inwagen’s has become part of van Inwagen’s thesis.
To his credit, Lowe explicitly addresses this worry in the very last paragraph of the paper. However, his response is concessive: he is indeed no longer arguing that there must be concreta. “Doesn’t that significantly reduce the metaphysical significance of the argument?” he asks rhetorically (194). I certainly think so. However, Lowe is certainly right that the fact that this argument is of lesser metaphysical significance than the argument he once tried to offer does not mean that the present argument is not interesting or significant. If Lowe is right about the ontological dependence of abstracta on concreta and the well-foundedness constraints on ontological dependence, there are wide-ranging metaphysical consequences.
(Cross-posted at blog.kennypearce.net.)