Recently Richard Gale and Alexander Pruss (1999) advanced a modal version of the cosmological argument that rests on the weak PSR (for every true contingent proposition, it possible that there is an explanation for that proposition) and Modal Axiom S5 (if it is possible that it is necessary that p, then it is necessary that p). They phrase the argument in terms of contingent and necessary propositions. A contingent proposition is one that is both possibly true and possibly false (i.e., true in some worlds and false in others); a necessarily true proposition is true in every possible world. In its simplest form, the argument is (1) if it is possible that it is necessary that a supernatural being of some sort exists, then it is necessary that a supernatural being of that sort exists. Since (2) it is possible that it is necessary that a supernatural being of some sort exists, (3) it is necessary that this being exists. The being Gale has in mind is a very powerful and intelligent designer-creator, not the all perfect God of Anselm, for this perfect God who would exist in all possible worlds would be incompatible with the existence of gratuitous and horrendous evils to be found in some of those possible worlds.
If one grants Axiom S5, the critical premise in the argument is the second, and Gale and Pruss proceed to defend it. They begin with the notion of a Big Conjunctive Fact (BCF), which is the totality of propositions that would be true of any possible world, were it actualized. Since all possible worlds would have the same necessary propositions, they are differentiated by their Big Conjunctive Contingent Fact (BCCF), which would contain different contingent propositions. In place of what Gale terms the strong PSR, which affirms that the actual world's BCCF has an explanation, Gale suggests a weaker PSR that he thinks would be acceptable to a critic of the cosmological argument — applied here, that it is possible that any BCCF has an explanation, that is, that there is some proposition q that explains the BCCF. So there is a possible world that contains p (the BCCF of the actual world), among whose propositions are q and the proposition that q explains p. Since this possible world ultimately is the actual world, the actual world contains p, q, and the proposition that q explains p. The explanation of the BCCF cannot be scientific, for such would be in terms of law-like propositions and statements about the actual world at a given time, which would be contingent and hence part of the BCCF. Hence, q provides a personal explanation of the BCCF in terms of the intentional action of some agent. The explanation cannot be that of a contingent being, for it would be part of the BCCF. Hence, the explanation is the intentional action (which would be contingent) of a necessary being who freely brings it about that the world exists. Gale concludes that though this necessary being exists in every possible world, this tells little about its power, goodness, and other qualities. To make this being palatable to theists, he offers that the argument be supplemented by other arguments, such as the teleological arguments, to suggest that the necessary being is the kind of being that satisfies theistic requirements.
Graham Oppy (2000) argues that suppose p1 is the BCF of some possible world, and p1 has no explanation. Then, given r (namely, that p1 has no explanation) there is a conjunctive fact p1 and r. Since by hypothesis the conjunctive fact p1 and r is true in some world, on Gale's account it is true in the actual world. Then by the weak PSR there is a world in which this conjunction of p1 andr possibly has an explanation. If there is an explanation for the conjunction of p1 and r, there is an explanation for p1. Thus, we have the contradiction that p1 both has and does not have an explanation, which is absurd. Hence, no world exists where the BCCF lacks an explanation, which is the strong principle of sufficient reason that Gale allegedly circumvented. Since accepting the weak PSR would commit the nontheist to the strong PSR and ultimately to a necessary being, the nontheist has no motivation to accept the weak PSR.
Gale and Pruss (2002) subsequently concede that their weak PSR does entail the strong PSR, but they contend that there still is no reason not to proceed with the weak PSR, which they think the nontheist would accept. The only grounds for rejecting it, they claim, is that it leads to a theistic conclusion, which is not an independent reason for rejecting it. Oppy, however, maintains that there is a modus tolens reason to reject it, since there are other grounds for thinking that theism is false.
Jerome Gellman has argued that the Gale/Pruss conclusion to a being that is not necessarily omnipotent also fails; this being is essentially omnipotent and, if omnipotence entails omniscience, is essentially omniscient. This too Gale and Pruss concede, which means that the necessary being they conclude to is not significantly different from that arrived at by the traditional cosmological argument that appeals to the PSR.
Finally, there is doubt that Gale's rejection of the traditional cosmological argument on the grounds that the necessary being could not be necessarily good is well grounded. Gale argues that since there are possible worlds with gratuitous or horrendous evils, and since God as necessary would exist in these worlds, God cannot be necessarily good. The problem here is that if indeed there is this incompatibility between a perfectly good necessary being (God) and gratuitous evils or even absolutely horrendous evils, then it would follow that such worlds would not be possible worlds, for they would contain a contradiction. In all possible worlds where a perfectly good God as a necessary being would exist, there would be a justificatory morally sufficient reason for the evils that would exist, or at least, given the existence of gratuitous evils, for the possibility of the existence of such evils (Reichenbach, Evil and a Good God, 38–39).