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Moreland offers one more argument against beginningless traversals -- one he says was suggested to him by Dallas Willard (his mentor at USC). After a brief discussion of the nature of causal sequences, and how any given event depends on the actualization of every event in the causal sequence that led up to it, he expresses the argument as follows:
"...the present moment has as its ultimate chain of causal antecedents the entire history of the cosmos. If any past event has not already been actualized, then the present moment could not have occurred. This means that the past is actual and contains a specifiable, determinate number of events. This chain of events must have had a first member. Without a first member, there could be no second, third, or nth member in the chain where the nth member is the present event. But an infinite succession of past events would not have a determinate number of members nor would it have a first member. So if the past is actually infinite, the prese…
Moreland offers an Aristotelian solution to one of Zeno's paradoxes as the basis of an argument against a beginningless past. Moreland sets up Zeno's Dichotomy paradox as follows:
"...Consider a runner who begins at some point A and who wishes to reach the midpoint between A and B. But before he can reach this midpoint, he must reach the midpoint of the midpoint. In order to move from any point to any other point, a runner must traverse an infinite number of points and this is impossible. Thus, [concludes Zeno] motion is an illusion."
Moreland then argues that a structurally identical paradox applies to the hypothesis of a beginningless universe: he argues that if the past were beginningless, then the prospects of traversing all the events of the past to reach the present moment would be like those of Zeno's runner on the assumption that his task involved the traversal of an actual infinite: one couldn't even begin such a task, much less finish it.
Wes Morriston's latest paper, "What if God Commanded Something Terrible? A Worry for Divine-Command Meta-Ethics (Religious Studies 45 (2009), pp. 249-67), is now available at his department webpage. Here is the link.
It's worth mentioning that, along the way, Morriston critiques Robert Adams' version of divine command theory in his Finite and Infinite Goods, which is arguably the most sophisticated version of the theory.
"...suppose a person were to think backward through the series of events in the past...Now he will either come to a beginning or he will not. If he comes to a beginning, then the universe obviously had a beginning. But if he never could, even in principle, reach a first moment, then this means that it would be impossible to start with the present and run backward through all the events in the history of the cosmos...But since events really move in the other direction, this is equivalent to admitting that if there was no beginning, the past could have never been exhaustively traversed to reach the present. Counting to infinity through the series 1, 2, 3, ... involves the same number of steps as does counting down from infinity to zero through the series -5, -4, -3, -2, -1, 0. In fact this second series may be even more difficult to traverse than the first. Apart from the fact that …
"It is impossible to count to infinity. For if one counts forever and ever, he will still be, at every moment, in a place where he can always specify the number he is currently counting. Furthermore, he can always add one more member to what he has counted and thereby increase the series by one. A series formed by successive addition is a potential infinite. Such a series can increase forever without limit, but it will always be finite. This means that the past must have been finite. For the present moment is the last member of the series of past events formed by successive addition. And since one cannot reach infinity one at a time, then if the past was actually infinite, the present moment could not have been reached. For to come to the present moment, an actual infinite would have to have been crossed." (p. 29, my copy. Italics added)
Virtually all his arguments against the traversability of actual infinites presuppose that any traversal must have a beginning. In other words, he just blatantly begs the question against the possibility of a beginningless past. At least Craig offers arguments against the possibility of beginningless traversals, viz., his "immortal counter" reductio and his variation on the Tristram Shandy Paradox (which, unfortunately, have been decisively critiqued by (e.g.) Wes Morriston -- here, for example). I hope to discuss Moreland's arguments in detail some time soon.
UPDATE: Here is a link to a detailed discussion of Moreland's arguments against the traversability of a beginningless past.