My previous criticism of (i) was that merely factually necessary beings are sufficient to satisfy a plausible version of PSR. Here my criticism shall be that a plausible version of PSR can be satisfied without appeal to necessary beings of any sort -- i.e., it can be satisfied merely in terms of continent, dependent beings. This sort of criticism goes back to Hume, of course, but William Lane Craig has tried to circumvent Hume's criticism in recent years. Therefore, as with the previous two posts on this topic, I'll use some of his work on the topic as my foil.
Perhaps the first thing that stands out about Craig’s version of PSR is that it’s a bit weaker than standard versions. Thus, a standard formulation of PSR can be expressed as follows:
(PSRs) There is an explanation for (a) the existence of every being, and for (b) the obtaining of every state of affairs.
A standard criticism of PSRs is that clause (b) seems false, i.e., it seems that not all states of affairs can have an explanation. Craig states the standard criticism of PSRs tersely: "There cannot be an explanation of why there are any contingent states of affairs at all; for if such an explanation is contingent, then it, too, must have a further explanation, whereas if it is necessary, then the states of affairs explained by it must also be necessary." In response to this criticism, Craig attempts to salvage a version of PSR by eliminating PSR(b), and just relying on PSR(a), i.e., by restricting the range of things needing an explanation to objects alone. He expresses his resultant version of PSR as:
(PSRc) Every existing thing has an explanation for its existence, either in terms of the necessity of its own nature or in terms of an external cause.
Craig then deploys (PSRc) as premise (1) of his version of the Leibnizian cosmological argument to infer that a contingent universe requires an explanation in terms of a necessarily existent God. Craig expresses his version of the argument as follows:
1. Every existing thing has an explanation of its existence, either in terms of the necessity of its own nature or in terms of an external cause.
2. If the universe has an explanation of its existence, that explanation is God.
3. The universe is an existing thing.
4. Therefore, the universe has an explanation of its existence.
5. Therefore, the explanation of the existence of the universe is God.
The argument is clearly valid. Furthermore, (4) follows from (1) and (3), and (5) follows from (2) and (4). That leaves (1), (2) and (3). Why should we accept them?
For the purposes of this post, I'm granting the truth of Craig's version of PSR, viz., his (1) above. Troubles arise, however, with (2) and (3). For Craig's use of 'the universe' is ambiguous in these premises. On the one hand, it might mean 'our universe', i.e., the (roughly) 13.7 billion year old entity that began with our Big Bang. But if this is Craig's intended referent of the term, then while (3) seems true, it's less than clear that (2) is true. To see this, suppose there is a beginningless series of contingent universes such that each such being is explained in terms of its predecessor, as follows:
. . .C --> B --> A
In this series, A is explained by B, B is explained by C, and so on. But if so, then each contingent being in the series (including our universe) is explained by another contingent being. And if that's right, then PSRc is satisfied in such a scenario without an appeal to a necessarily existent God, in which case premise (2) is undercut.
On the other hand, by 'the universe' Craig might mean 'all physical reality'. But if this is Craig's intended referent of the term, then whatever the merits of (2), it's not at all clear that (3) is true. For it's epistemically possible that there is more (perhaps much more) to physical reality than our universe. So, for example, our scenario above involving a beginningless series of contingent universes is such a possibility. But at least since the publication of Peter van Inwagen's Material Beings, it has become extremely unclear when – or even whether – two or more things compose a further thing. And if that’s right, then a fortiori it is controversial that all physical reality is a thing. Thus, whether the collection of all contingent things is itself a thing depends on which theory of material composition is correct. Universalists about material composition say that any two or more things is itself a thing. At the other end of the spectrum, nihilists about material composition say that no two things compose a thing -- there are only “simples” (or part-less beings) and their aggregates. Finally, moderates are those who fall somewhere in between universalists and nihilists, allowing that two or more things sometimes compose a thing, depending on whether they stand in a certain special relation to one another. So, for example, Peter van Inwagen’s moderate account entails that two or more things compose a new thing just in case they function together in such a way that their activities constitute a life. For a moderate like van Inwagen, then, there are just two sorts of things: simples and living beings.
The problem this debate poses for Craig's argument is that each position has significant problems, in addition to their own set of strengths, and it's not clear how one should weigh each of these in determining which theory is correct. It therefore seems that an adequate defense of (3) would require a widely persuasive defense of a position in the material composition debate that entails that the universe (i.e., all physical reality) is itself a thing. Now universalism entails that the universe is itself a thing, while nihilism entails that it is not, and it's at least conceivable that a moderate position could be developed that is more plausible than universalism and nihilism, and which entails that all physical reality is itself a thing. So an adequate defense of (3) would seem to require a defense of either a universalist account of material composition or a defense of a moderate account that meets the desiderata mentioned above. Unfortunately, though, Craig has yet to offer such a defense.
To sum up the criticism expressed above: the expression, 'the universe' is ambiguous in (2) and (3) of Craig's Leibnizian cosmological argument. Either (a) it means 'our universe' or (b) it means 'all physical reality'. If (a), then (3) is undercut. For it leaves open the possibility that our contingent universe is explained in terms of an infinite regress of universes (or in any case of contingent beings), where each is the cause of its successor. And if (b), then (2) is undercut. For it's extremely controversial among those who specialize in the material composition debate whether the universe (i.e., all physical reality) is a thing. And in any case, it's not at all clear that it's the sort of entity that requires an explanation. Either way, Craig's argument appears to contain at least one dubious premise.
Craig has offered two main responses to the objections raised above. His first response is to argue that we can tell that the universe is a thing independently of an argument on behalf of a particular account of material composition. For here we can appeal to our intuitions, which indicate that the universe is, in fact, a thing -- or at least it was a thing, during the earliest stages of its existence: “ . . . the universe is obviously an existing thing (especially evident in its very early stages when its density was so extreme), possessing many unique properties such as a certain density, pressure, temperature, space-time curvature, and so on . . .” In this way, Craig defends the standard reply that the collection of all contingent beings or things in the series is (or at least was) itself a being, in which case PSRc requires an explanation of the universe in terms of a necessary being.
His second response is to argue that the material composition debate can be sidestepped altogether, on the grounds that whether the universe is properly considered a thing or not, it is nonetheless the sort of entity that requires a cause or explanation: "I do not mean to pronounce here on ontological debates about what constitutes an object, but merely to claim that the universe is just as much a thing as are other familiar entities which we recognize to have causes, such as chairs, mountains, planets, and stars.”
What to make of these responses? Now I’m inclined to agree with Craig that, at least in its earliest stages, our universe was a single existing thing, or at least the sort of entity that requires a cause or explanation in terms of one or more or other things. However, it’s not clear how this helps to answer the criticism raised above. For absent an independent argument that our universe is co-extensive with all physical reality, it’s epistemically possible that our universe is properly explained in terms of temporally prior processes involving other universes (or in any case, other natural contingent entities), and so on back ad infinitum. To answer the criticism above, therefore, it looks as though Craig will need to provide a reason for thinking that a collection of beings of the latter sort (i.e., a beginningless series of contingent universes) is itself a contingent being – or at least the sort of entity that requires a cause or explanation.
Unfortunately, the reasons we’ve looked at from his writings don’t look plausible when applied to the latter sort of case. For unlike our universe during its earliest stages, it’s just not clear that a beginningless series of contingent universes is itself a thing, or even (thing or not) an entity that requires a cause or explanation. It therefore looks as though the material composition debate cannot be sidestepped so easily after all.
In short, it looks as though Craig has more work to do in defending the Leibnizian cosmological argument against the criticisms raised here. Absent such a defense, even those who accept his version of PSR are left without a good reason for thinking there is a metaphysically or factually necessary being.
 This formulation is equivalent to that stated in Rowe, William. Philosophy of Religion: An Introduction, 4th ed. (Wadsworth, 2006), pp. 23.
 Craig, “The Cosmological Argument”, p. 114. Cf. Rowe, William. The Cosmological Argument (Fordham University Press, 1998), pp. 103-111; Van Inwagen, Metaphysics, 2nd edition (Westview, 2002), pp. 119-122.
 Cf. Craig, “The Cosmological Argument”, in Copan, Paul and Paul K. Moser, eds. The Rationality of Theism (Routledge, 2003), p. 114; Reasonable Faith, 3rd edition (Crossway, 2008), p. 106.
 Cf. Craig, “The Cosmological Argument”, p. 114-116, esp. p. 114; Reasonable Faith, 3rd edition (Crossway, 2008), pp. 106-111, esp. p. 106. Craig notes his indebtedness to Stephen T. Davis for his formulation of the argument. Cf. Davis, “The Cosmological Argument and the Epistemic Status of Belief in God”, Philosophia Christi 1:1 (New Series) (1999), pp. 5-15.
 The following criticism is based on Peter van Inwagen's. See, for example, van Inwagen, Metaphysics, 2nd ed. (Westview, 2002), pp. 126-128.
 Craig is of course known for his arguments against the existence and traversability of actual infinites in relation to his defense of the kalam cosmological argument. Discussion of those arguments is beyond the scope of this post. However, I've discussed virtually all of Craig's (and Moreland's) arguments on this score on other occasions (e.g., here and here). I refer the interested reader to those posts.
 Cornell University Press, 1995.
 Cf. Material Beings.
 For an overview of the range of positions and their strengths and weaknesses, see (e.g.) Markosian, Ned. “Restricted Composition”, in Hawthorne, John, Theodore Sider, and Dean Zimmerman (eds.), Contemporary Debates in Metaphysics (Basil Blackwell), 2007, pp. 341-364.
 “The Cosmological Argument”, p. 115,
 Ibid., p. 130, fn. 6.