A Note on Craig's Standard Reply to Mackie on the Kalam Cosmological Argument

Suppose one were to believe in the possibility of a beginningless past on the basis of the following inference:

1. Every finite subset of events in a beginningless past is traversable.
2. Therefore, the whole set of events in a beginningless past is traversable.

This is obviously a bad reason for that belief. For to infer (2) from (1) is to commit the fallacy of composition.

Interestingly, William Lane Craig attributes this fallacious inference to the late J.L. Mackie in reply to Mackie's criticism of the Kalam argument in the latter's The Miracle of Theism.[1] It's perhaps worth noting that Craig repeats this reply to Mackie's criticism in virtually all of his books and contributing chapters in which he defends the kalam cosmological argument. Furthermore, Mackie's is arguably the main criticism he raises to his argument in these writings.

I think Craig's characterization of Mackie's criticism of the kalam argument here is uncharitable at best, and mistaken at worst. In what follows, I'll attempt to point out where Craig goes wrong in this rejoinder to Mackie. But before I do so, I'll need to set things up with a brief discussion of the relevant part of the dialectic between Mackie and Craig.

Mackie's criticism is that, ". . .[i]t assumes that, even if past time were infinite, there would still have been a starting-point of time, but one infinitely remote, so that an actual infinity would have had to be traversed to reach the present from there. But to take the hypothesis of infinity seriously would be to suppose that there was no starting point, not even an infinitely remote one, and that from any specific point in past time there is only a finite stretch that needs to be traversed to reach the present." (The Miracle of Theism, p. 93).

Craig's offers two main points in his rejoinder. First, he says that it’s Mackie, and not the proponent of the kalam argument, who fails to take a beginningless past seriously. For the latter construes such a past as having no beginning at all – not even one infinitely distant from the present. But if so, then this makes the problem worse, not better. For then one couldn’t even get going to make progress in traversing an infinite set of events to reach the present moment.[2] Second, Mackie’s point that each event in a beginningless past is only finitely distant from the present is irrelevant. For the issue isn’t whether any finite segment of a beginningless past can be traversed to reach the present, but rather whether the whole infinite past can be so traversed. To think that a whole infinite set can be traversed because each finite segment can be traversed is to commit the fallacy of composition.[3]

What to make of this exchange? Mackie is correct, and Craig has misunderstood him -- or at least he has given Mackie's reply an uncharitable gloss. First, Mackie is correct to say that proponents of the kalam argument have misconstrued a beginningless traversal. For to say that the past is beginningless is to say that some infinite set of events or other has been traversed before every point in the past. But if so, then if a beginningless past is possible -- which is the very issue under dispute -- there can be no going from a state of not having traversed to having traversed an infinite series of events in a beginningless past. The only sort of scenario that involves a transition from a finite to an infinite traversal is one involving a beginning of the traversal at some point. And on the most charitable and forceful interpretation of Mackie's criticism, this is why he says that the proponent of the kalam argument conflates a beginningless past (i.e., {…, -3, -2, -1}) with a past that had a beginning an infinite amount of time ago (i.e., {1, 2, 3, …} or, say, {1, …-3, -2, -1}).

Second, in light of the previous point, we see why Craig is mistaken, or at least uncharitable, in saying that Mackie has committed the fallacy of composition. For on the more charitable and forceful construal of Mackie's reply, Mackie is not arguing that because every finite segment of a beginningless past is traversable, the whole infinite past traversable. Rather, he’s saying that if the past is beginningless -- which, again, is the very issue under dispute -- then an infinite set of events has already been traversed before every point of a beginningless past, and that is why there is only a finite set of subsequent events between that point and the present.[*]


[1] See, for example, "The Cosmological Argument", in Copan, Paul and Paul K. Moser, eds. The Rationality of Theism (Routledge, 2003, 124-135.
[2] Ibid.
[3] Ibid.
[*] An exposition of the standard criticisms of Craig's philosophical arguments against the existence and traversability of actual infinites can be found here.