We know that although no horse in a given horse race necessarily will be the winner, it is, nevertheless, necessary that some horse in the race will be the winner. (1975, 164)
It turns out that dispositionalists cannot plausibly appeal to this possibility as a way of avoiding a necessary being. Here's why: either causal history is infinite, or it is not. If it is not, then the dispositionalist has very good reason to affirm the existence of a (set of) necessary being(s); see e.g. Vance (2014), Vetter (2015), and Kimpton-Nye (2021). So the dispositionalist who wishes to avoid a necessary being should assume that causal history is infinite. But, as it turns out, this strategy will not work either.
Let S be the plurality of all actually-existing contingent concrete things. (If nothing is necessary, then S will include all actually-existing concrete things.) Suppose that the cosmological arguer asks for an explanation of why the beings in S exist, and the critic gives the aforementioned reply that it is necessary for some contingent things to exist. But note that on a naturalistic dispositionalism, "every possible world contains some natural thing that actually exists... necessarily, every world contains some stretch of our actual natural past" (Leftow 2017, 326). This means that the critic's reply commits them to claiming that it is necessary for at least some of the beings in S to exist.
Is this reply at all plausible? I think not; after all, every being in S is contingent, and so fails to exist in some possible world. But it seems obvious that if x could fail to exist, and if y could fail to exist, then both x and y could jointly fail to exist; otherwise, we would have to suppose that x's nonexistence somehow forces y to exist, which seems implausible. As Vetter puts it, "the possibility, for each contingent object, that it does not exist, together with what we might call a principle of independence—that the non-existence of contingent objects can never force other contingent object into existence—yields the global possibility that none of the actual contingent objects exist" (2015, 275).
A further problem is that while the critic might claim that it is necessary for some of the beings in S to exist, there can be no particular beings in S which exist necessarily. This should be obvious merely from the fact that, as stipulated, S is the plurality of all actual contingent things; however, the point becomes more interesting when put in terms of branching causal histories. Recall that, as Leftow points out, the theory under consideration entails that "every world contains some stretch of our actual natural past" (2017, 326), which, given an infinite past-eternal universe, "would be an infinite stretch" (ibid., 326). However, this would not be the same stretch of our actual past; rather, different possible worlds would share different stretches of the actual past. To make the problem clearer: if causal history is infinite, then for any causal node n, there is an earlier node n-1. But this entails that there is no single node n which is part of the shared history of all possible worlds. Hence, the aforementioned critic of the cosmological argument must claim that it is a necessary truth that all possible worlds share a stretch of causal history with the actual world, but not any particular stretch. This does not seem like a very good explanation of the entire causal series.
It is also worth noting that the naturalist dispositionalist is committed to claiming that "there could not have been other natural laws... [nor] could there have been a different total amount of mass-energy" (Leftow 2017, 325). Their view will also threaten modal collapse, since "If [this] theory is true and determinism is true, the actual world is the only possible world: there are no chancy causes, so there are no branches off the tree of actual history" (ibid., 326). Thus, on this view "we should take modal Spinozism precisely as seriously as we take determinism" (ibid., 326).
The upshot is that the dispositionalist must either admit that there is a (set of) necessary being(s), or else claim that it is a necessary truth that some actually-existing contingent things exist. Given that this latter claim seems extremely unlikely (if not flat-out nonsensical), entailing as it does many implausible consequences, it appears that the dispositionalist has strong reason to accept the existence of a (set of) necessary being(s).
