A Counterfactual Cosmological Argument

Consider the xxs such that (i) for all x such that x is one of the xxs, x is a contingent object, and (ii) for all x such that x is a contingent object, x is one of the xxs; that is, consider the contingent objects. Call them 'the ccs'. In this post I will offer an argument for the following thesis:
The Dependency of the Contingents (DC): There is an x such that x is concrete, x is not one of the ccs, and the ccs depend on x,
where
Dependency (D): Necessarily, for all xxs and for all yys, the xxs depend on the yys iff if it were the case that it is not the case that the yys exist, then it would be the case that it is not the case that the xxs exist.

The argument in favor of DC is simple:
1. For all xxs, if the xxs are contingent, then there is an x such that x is concrete, x is not one of the xxs, and the xxs depend on x.
2. If the ccs are contingent, then there is an x such that x is concrete, x is not one of the ccs, and the ccs depend on x. [From (1) by existential instantiation]
3. The ccs are contingent. [By our stipulations regarding the reference of 'the ccs'.]
Conclusion: Therefore, there is an x such that x is concrete, x is not one of the ccs, and the ccs depend on x.

The argument is valid. Premise (3) is clearly true and premise (2) is merely a subconclusion. The only controversial premise, then, is premise (1). Do we have any reason to believe (1)? Indeed we do. We have much evidence for (1). For instance, we know of many contingent objects x that there is a y such that y is concrete, y is distinct from x, and x depends on y. But then for any xxs such that x is one of the xxs and y is not one of the xxs, the xxs depend on y.

So we have good (if weak) inductive reason to believe premise (1). In addition (so far as I can see), we have no good reason to deny that premise. Therefore, we have good (if weak) reason to believe DC. This is not to say that we are justified in believing DC. Our evidence is weak, after all, perhaps too weak to justify a belief in DC. However, we certainly have evidence to believe it, and no evidence against it.

What is the import of this conclusion? One important point to note is how weak DC is. Consider Mary and I. Necessarily, if it is not the case that I exist, then it is not the case that Mary and I exist. So, if there is something such that I depend on it, then Mary and I depend on that very same thing. This point holds in general; that is, for all x, y, and xxs, if x is one of the xxs and x depends on y, then the xxs depend on y. Therefore, if there is something x such that x is concrete, x is not one of the ccs, and one of the ccs depends on x, then DC is true.

There is one important fact about this thing whose existence is claimed by DC; namely, that it is a necessary existent. This follows from the fact that it is not one of the ccs, among which are all of the contingent objects. So, if DC is true, then there is a necessarily existing concrete object such that the ccs depend on it (albeit perhaps in the very weak sense outlined in the previous paragraph).

Now it is not very surprising that if there is a necessarily existing concrete object O, then the ccs depend on it. For as we have stipulated, the ccs depend on O iff if it were the case that it is not the case that O exists, then it would be the case that it is not the case that the ccs exist. Given that O is necessarily existing, however, the antecedent of the counterfactual conditional:
If it were the case that it is not the case that O exists, then it would be the case that it is not the case that the ccs exist.
is false and so (given the standard Stalnaker-Lewis truth-conditions for counterfactuals) the whole conditional is vacuously true. Perhaps what is really surprising about the argument, then, is that it gives us reason (if only weak reason) to believe that there is a necessarily existing concrete object.

In conclusion, this counterfactual cosmological argument for DC has little theological import, despite the fact that an English gloss of its conclusion ("There's a necessarily existing concrete thing on which all contingent things depend") makes it sound like it does. We non-theists need not be worried.

[This post was inspired by an interestingly different argument offered in Hawthorne and Cortens (1993), "The Principle of Necessary Reason". Although I disagree with H&C's conclusions, I highly recommend their paper.]