Thursday, September 17, 2009

The Impossibility of an Infinite Regress - Causal and Temporal

Thomas rejects the possibility of an essentially-ordered infinite regress of causes. This, however, does not entail the impossibility of an eternal (re: infinitely-old) universe. Imagine a watch that has endured infinite time. If there is no spring, then no matter how many gears there are (even infinitely-many), none of them will be able to move. Likewise, if there is no First Mover, then there can be no intermediate movers. But since it is obvious that intermediate movers exist, it follows necessarily that a First Mover exists.

Bonaventure goes further than this. Not only does he reject the possibility of an infinite regress of essentially-ordered causes, but he also maintains that an infinite regress of temporal events is impossible. William Lane Craig and Mark Nowacki summarize Bonaventure's argument like this:

1. The temporal series of events is a collection formed by successive addition.
2. No collection formed by successive addition can be an actual infinite.
3. Therefore, the temporal series of events cannot be an actual infinite.

(1) assumes the common-sense theory of time, the so-called "dynamic theory", which posits each successive moment of time as an addition to the previous moment. Only the present, under this view, is actually real. The past has been actualized, but no longer exists; the future, however, is merely potential.

(2) is fairly easy to grasp once we reflect on the nature of infinity. No matter how long time has elapsed, it is always and indefinitely possible to add another moment before arriving at infinity. "Infinity", in this respect, is really just a limit. Craig considers the future to be potentially infinite, since although it will continue forever, it will always be finite.

Some have objected to (2), saying that an actual infinite can be formed by successive addition if there was never a beginning to the addition. This would be like someone claiming to have counted down from infinity and end in 0, which is quite strange, regardless of whether the objection is accepted or not. In response, Craig asks rhetorically, "why has the present arrived today, and not yesterday, or at any time in the finite past?" This question is especially pertinent, since assuming the universe's past is infinite, the same amount of time has elapsed before AD 1000 as it has before AD 2000. Why, then, did AD 2000 arrive at the time it did, and not before?

Thomas' objection to Bonaventure's argument is that while the past may not be actually infinite, it may be potentially infinite (and therefore, without beginning). The way to understand this is by conceiving of any time at all in the past. Any time you choose will have a finite interval between then and the present, so any moment in the past can be traversed until we arrive at today.

There are two ways of responding to this. First of all, Thomas' objection (with all due respect to the Angelic Doctor) commits a composition fallacy. The fact that each finite moment of the past can be traversed does not imply that the whole infinite set of past events can be traversed. Even if it could, we still have to reconcile this with the AD 1000-2000 paradox). Secondly, and perhaps more to the point, the past cannot be potentially infinite for the simple reason that every moment of the past has been actualized, and nothing actualized is merely potential. Time travels forward, and not backwards. As a result, a moment of the past T1 cannot be preceded by T2 with T2's being added to T1 via successive addition.

It appears to me, then, that both Thomas' argument for a First Mover and Bonaventure's argument for a Creator are both sound. Of course, the causal premises of each proof have to be defended, but one need only appeal to ex nihilo nihil fit (out of nothing comes nothing) to support them.