Richard Gale and Alexander Pruss have advanced an interesting update on the traditional Cosmological Argument for the existence of God.[i] This argument begins with some definitions.
A possible world is a “maximal, compossible conjunction of abstract propositions. It is maximal in that, for every proposition p, either p is a conjunct in this conjunction or its negation, not-p, is, and it is compossible in that it is conceptually or logically possible that all of the conjuncts be true.”[ii]
The Big Conjunctive Fact for a possible world consists of the conjunction of all of the propositions that would be true if that world were the actual world. Some of these are necessarily true. But the Big Conjunctive Fact of each possible world also contains propositions that are contingently true- true in some possible worlds and not in others. Each possible world contains a unique conjunction of contingent propositions. Gale-Pruss refer to this as the Big Conjunctive Contingent Fact, or BCCF. It is the BCCF of a world that individuates that world, distinguishing it from all other possible worlds. Let p be the BCCF of the actual world.
Is there an explanation for p- an explanation for why this particular set of contingent facts is the case, rather than not?
At this point the defender of a traditional Cosmological Argument would introduce the Principle of Sufficient Reason:
For every proposition, p, if p is true, then there is a proposition, q, that explains p.
But it may not be reasonable to expect the skeptic to accept this principle. In its stead, Gale-Pruss offer a weaker form of the Principle of Sufficient Reason:
For any proposition, p, if p is true, then it is possible that there exists a proposition, q, such that q explains p.
Unlike traditional cosmological arguments, Gale-Pruss’ argument does not require us to assume that there actually is an explanation for p. It only needs to be possible that there is such an explanation. Gale-Pruss assert that it is: There is some possible world, W1, in which p is true, and in W1, some proposition q is true, and q explains p.
Now, are W1 and the actual world the same world? Gale-Pruss insist that they are. For p is the Big Conjunctive Contingent Fact of the actual world; p is true in W1, and the BCCF of a given world is what individuates it. Therefore, there is some proposition q that is true in the actual world and explains p, the BCCF of the actual world. Now, what sort of explanation is it?
According to Gale-Pruss there are only two kinds of explanation: Scientific, and personal. Personal explanations are explanations in terms of the intentions of some person. But q cannot be a scientific explanation. A scientific explanation “must contain some law-like proposition, as well as a proposition reporting a state of affairs at some time.”[iii] But these are contingent propositions, and therefore members of p. Yet they purport to explain p, as well as each proposition contained within p, which means they would explain themselves, and this is impossible.
Therefore q must be a personal explanation. Now what sort of person does q invoke? It cannot be a contingently existing being, since a proposition asserting the existence of a contingently existing being would be part of p and once again, q would explain itself. So q explains p, the Big Conjunctive Contingent Fact of the actual world, by reference to the intentional action of a necessary being. The proposition q, then, asserts something like this:
“There exists a necessary being who intentionally creates the world.” [iv]
Gale-Pruss treat q as though it is not one of the member-conjuncts of p. This is well motivated. For one thing, if q were contained within p, the Big Conjunctive Contingent Fact of the actual world, then q would be part of the very state of affairs that it hopes to explain. But worse than this, to define p as the BCCF of the actual world, and then to presume that q is contained within p, is to presume at the outset that the actual world is explained by the intentions of a necessary being, and this is what the argument seeks to prove.
And yet, as Gale-Pruss acknowledge, q is a contingent proposition,[v] and so prima facie, one would think that for any possible world, either it, or its negation, is a member-conjunct of that world’s Big Conjunctive Contingent Fact.[vi] But let us set this observation aside and follow Gale-Pruss in treating q as though it is not contained within p.
Since q is a contingent proposition, there are possible worlds in which it is not true. That means that in addition to W1, which contains p and in which p is explained by q, there is another possible world, W2, which contains p, and in which p is not explained by q, because it is not true in W2 that there is a necessary being who intentionally creates that world. As it turns out, if a Big Conjunctive Contingent Fact does not contain either q, or its negation, then pace Gale and Pruss, it does not individuate a possible world.
This means that a world’s containing p does not imply that it is identical with the actual world. Gale and Pruss are not entitled to infer, from the fact that p is true in W1, that W1 is identical with the actual world, since p is true in W2 as well.
The actual world is identical with one of these worlds, W1 or W2, but the Gale-Pruss argument leaves us with no reason to prefer one over the other. Since they hoped to prove that the existence of the actual world is explained by the intentions of a necessary being, and they can do this only if they can show that the actual world is identical with W1 rather than W2, Gale and Pruss’ argument fails.
Department of Philosophy
[i] “A New Cosmological Argument,” Richard M. Gale and Alexander R. Pruss; Religious Studies, vol 35, Number 4 (Dec 1999), pp. 461-476
[ii] “A New Cosmological Argument,” p. 461. For a more detailed explanation of the notion of a possible world, see https://plato.stanford.edu/entries/possible-worlds/.
[iii] Ibid. p 465
[iv] Gale-Pruss realize that they have not proven the existence of the God of Western theism, since they have not proven that this being is omniscient, omnipotent, and benevolent. They require only that God be powerful enough to create the actual world. But they think- and I agree- that their more limited conclusion is still an interesting one.
[v] In fact they argue for this claim on p. 466ff
[vi] It seems likely that Gale-Pruss are thinking of q as having some kind of special status that sets it apart from ordinary contingent facts. Perhaps they wish to say that it is a supernatural fact, because it reports the intentions of a necessary being. (On p. 468 they claim that a necessary being is a supernatural one.) In this case p is really the Big Conjunctive Contingent Natural Fact. I do not have space to pursue this suggestion here, which does not, in any case, seem to affect my analysis.