Although Craig has criticized the Leibnizian Cosmological Argument in a number of places, he offers a brief defense of it in The Rationality of Theism (Routledge, 2003, ed. Paul Copan and Paul Moser).
The Leibnizian cosmological argument depends on some version of the Principle of Sufficient Reason (PSR). The standard formulation of PSR can be expressed as follows:
(PSR) There is a sufficient reason for the existence of (a) every object, and (b) every state of affairs, either in terms of something else or in terms of its own nature.
A standard criticism of the argument is that PSR(b) is false.[1] Craig states the criticism 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." (p. 114)
Craig defends the argument against the criticism by eliminating PSR(b), and just relying on PSR(a) to get the conclusion of a necessarily existing object -- God -- as the explanation of the contingent universe.
However, this won't do. For as Peter van Inwagen points out[2], the conclusion can't be gotten with just PSR(a). For suppose there is an infinite, beginningless series of dependent beings[3], such that each being is explained in terms of another, 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 is explained by another contingent being. And if that's right, then PSR(a) is satisfied in such a scenario, and yet there is no need to appeal to a necessary being.
Now one might say that the series of contingent beings is itself a being, and so PSR(a) isn't satisfied without appeal to a necessary being. However, things aren't so easy. For ever since Christian philosopher Peter Van Inwagen wrote Material Beings[4], it's not so clear when, or even whether, two or more things compose another thing. Enter the material constitution debate. Thus, whether the collection of dependent beings is itself a being depends on which theory of material composition is true. A universalist (or "allist"), would say that any two or more objects is itself is an object. A nihilist (or "noneist") would say that no two objects compose an object -- there are only simples and their aggregates. Everyone else falls somewhere in between (the moderates). The problem is that every position on the matter has counterintuitive implications. Therefore, at the very least, it will require either a defense of a universalist account of material constitution, or a defense of a moderate account of material composition that allows the collection of dependent beings to count as a being (it should be noted that van Inwagen's own moderate account doesn't countenance the collection of dependent beings as itself a being). Needless to say, Craig has a lot more work to do in defending the Leibnizian cosmological argument against the criticism he raises here.
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[1] See for example, Peter van Inwagen's statement of the criticism in his text, Metaphysics (Westview Press).
[2] Ibid.
[3] Of course, Craig argues against the possibility of an actually infinite series such as this in his defenses of the kalam cosmological argument. But as I've argued in other posts (see Section 1.1.2 of my index, here), these arguments for a finite past have undercutting defeaters. But Wes Morriston has stated the problems with Craig's Kalam argument better than I can.
[4] van Inwagen, Peter. Material Beings (Cornell University Press, 1995).
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