A difficulty for Craig’s kalām cosmological argument?

Most versions of the cosmological argument, including those favored by Thomists, are not concerned with trying to show that the universe had a beginning.  The idea is rather that, whether or not the universe had a beginning, it could not remain in existence even for an instant were God not sustaining it in being.  The kalām cosmological argument, however, does try to show that the universe had a beginning.  Most famously associated with thinkers like Al-Ghazali, Bonaventure, and William Lane Craig, it was also famously rejected by Aquinas.  But it is defended by some contemporary Thomists (including David Oderberg).I’ve long been agnostic about it myself.  Among the reservations I have is one I briefly addressed in my article “Natural Theology Must Be Grounded in the Philosophy of Nature, Not in Natural Science” (which you can find in Neo-Scholastic Essays ).  I argued there that natural theology cannot get to the God of classical theism unless it brings into the picture something like the Aristotelian theory of actuality and potentiality.  But the kalām argument, at least as Craig presents it, makes no use of such Aristotelian notions.  (Which is not to say that it is entirely un-Aristotelian.  More on that presently.)

Another reservation I have is that the argument, at least as Craig presents it, in my view puts way too much emphasis on results in modern scientific cosmology.  As I have argued many times, the chief arguments for God’s existence rest not on empirical science but rather on deeper principles of metaphysics and philosophy of nature which cannot be overturned by – and indeed must be presupposed by – any possible empirical science.  Heavy emphasis on current physical theory thus threatens to muddy the waters and to give the false impression that cosmological arguments stand or fall with what the physicists happen to be saying this week.  (I have, of course, criticized contemporary design arguments on similar grounds.)
A third reservation – the one I will discuss here -- has to do with the question of whether one really can demonstrate that an infinitely old universe is metaphysically impossible, and in particular whether one can demonstrate that an accidentally ordered series of causes (as opposed to an essentially ordered series) cannot be infinite.  (This is, of course, the traditional bone of contention for Thomists.)  I am not convinced that this cannot be demonstrated.  But I’m not sure that Craig’s metaphysical arguments for that conclusion (e.g. the well-known appeals to Hilbert’s hotel and similar examples) work.
Recall that the basic kalām argument says:
1. Whatever begins to exist has a cause.
2. The universe began to exist.
3. So the universe has a cause.
That’s the easy part, and the main work in defending the argument involves (a) defending the second premise, and (b) showing that the cause of the universe must be a divine cause.  It is in defending the second premise that Craig appeals to examples like Hilbert’s hotel.
The basic idea of such arguments is this.  We can draw a distinction between an actual infinite and a merely potential infinite.  A potential infinite is a collection that is actually only finitely large, but can be added to without limit.  For example, suppose there are ten chairs in some particular room.  We could always add an eleventh, a twelfth, and so on, and (if we knock out some of the walls and expand the room) can in principle add any number of further chairs ad infinitum.  A potential infinite never is actually infinitely large, but can still always be added to in theory, as long as time and resources permit.  An actual infinite, by contrast, already is infinitely large.  An actually infinite collection of chairs, for example, would be one that already includes an infinite number of chairs, all at once and at the same time. 
This is a distinction Craig borrows from Aristotle, even if in other respects his argument is not particularly Aristotelian.  The use he makes of it is this.  The notion of a potential infinite is unproblematic, but the notion of an actual infinite is fraught with paradox.  For instance, if we imagine a hotel with an infinite number of rooms and an infinite number of guests checking in and checking out, we will, if we work out the implications, find them to be utterly bizarre.  So bizarre, in Craig’s view, that we should conclude that such a hotel could not possibly exist in reality.  (Those familiar with Craig’s argument will know how the details of examples like these go – I won’t rehearse them here.)  And this shows, Craig argues, that the idea of an actual infinite is in general very fishy.  There just can’t be an actually infinite collection of things.  Now, an infinitely old universe would constitute an actual infinite, Craig argues.  It would amount to an actually infinitely large collection of hours, days, years, or whatever other unit of time you pick.  Hence, since there cannot be an actual infinite of any sort, there cannot be an actual infinite of this particular sort.  So, the universe cannot be infinitely old. 
Now, one problem here is that it will not do to show merely that an actual infinite like the one described in the Hilbert’s hotel scenario is bizarre.  To show that something is bizarre does not suffice to show that it is impossible.  For that you need to show that it involves some outright contradiction or incoherence.  But perhaps that can indeed be shown.  That isn’t the issue I’m concerned with here.  So, for present purposes let’s concede for the sake of argument that scenarios like Hilbert’s hotel really are strictly metaphysically impossible.  The problem is this: How does this show that an infinitely old universe is impossible?  In particular, how does this show that there could not have been in the past an infinite series of hours, days, or years? 
The reason this is a problem is that Craig is a presentist.  That is to say, he thinks that it is present things and events alone that exist.  Past objects and events don’t exist anymore, and future objects and events don’t yet exist.  (This contrasts with theories of time like the “growing block” theory, which holds that past and present things and events exist, with the present being the growing edge of a block universe; and with the eternalist view that all things and events, whether past, present, or future, all equally exist.) 
Now, his commitment to presentism is not itself the problem; in fact I agree with Craig about that.  (I will have much more to say about that subject in forthcoming work.)  The problem is rather this.  If the present alone is real, then how can an infinite series of events in time count as an actual infinite?  Past moments of time are not actual; they no longer exist.  Hence an infinite series of past moments is not relevantly analogous to Hilbert’s hotel.  In the Hilbert’s hotel scenario, all of the hotel rooms in the infinite collection of rooms, all of the guests in the infinite collection of guests, etc. exist together all at once, at the same time.  But (for a presentist) past moments, and past things and events in general, no longer exist.  They don’t exist together, all at once and at the same time, because they don’t exist at all.  Hence there really is even prima facie (again, if one is a presentist) no such thing as an infinite collection of past moments of time, as there might at least prima facie be an infinite collection of rooms and guests.  So, an infinitely old universe scenario is simply not relevantly analogous to scenarios like Hilbert’s hotel – in which case, it seems Craig’s argument will fail even if it is conceded that an actual infinite is impossible.  For an infinitely old universe just wouldn’t be an actual infinite in the relevant sense.
To be sure, many naturalist critics of Craig would be reluctant to accept his presentism, in which case this sort of criticism wouldn’t be open to them.  But I think the difficulty indicates why Thomists have sometimes been wary of the kalāmargument.
So, that’s the “worry” (as analytic philosophes like to say).  Discuss.