The Kalam Argument, part 1

The Kalam argument for God’s existence, which was pioneered by John Philoponus (490-570), developed by Islamic philosophers such as al-Kindi and al-Ghazali, and championed in recent years by William Lane Craig (Craig 1979) and by me (Koons 2014), is an attempt to prove that the universe must have had a cause, a role which God seems best suited to fit. The argument typically takes the following form:
 
1. Whatever begins to exist must have a cause.
2. The universe began to exist, because time itself is bounded in the past.
Therefore, the universe had a cause.
 
The first premise has a great deal of intuitive appeal, and there are severe epistemological costs to countenancing the idea of uncaused origins. For instance, the skeptical scenario popularized by Bertrand Russell—How do we know that the universe didn’t simply appear 5 minutes ago?—would be a live possibility in the absence of an a priori causal principle similar to premise 1. So, let’s focus on premise 2.

The typical Kalam strategy for defending premise 2 is to argue that time past is not eternal, that is, that there is some finite temporal bound to all past events. Now, it is not immediately obvious that a finite bound to the past entails that the “universe” began to exist. First, it is not obvious that there is such a thing as the universe: perhaps the plurality of things that exist at a time t do not compose a single whole at t. We might try to avoid this composition question by modifying premise 2 into 2.1:
 
2.1 There is a time t such that everything existing at t began to exist at t, and nothing existed at any time prior to t.
 
In order to get the desired conclusion, we would also have to modify premise 1 as follows:
 
1.1 If some things xx began to exist at time t, then there must be some thing y or things yy not among the xx such that y (or the yy) caused the xx to begin to exist at t. (I am using double letters as plural variables, following George Boolos’s plural quantification (Boolos 1984). One should read ‘yy’ as ‘the y’s (plural)’.)
 
We will also have to rule out the possibility that the things coming into existence at the first moment of time might have been caused by things existing at later times:
 
3. If the yy cause the xx to exist at t, then the yy exist at t or at some time earlier than t or eternally.

Form 1.1, 2.1, and 3, we can reach the conclusion that something that exists eternally caused the beginning-to-exist of all the things that existed at the first moment of time (if there is such a first moment).
 
There is, however, a further lacuna to fill: from the fact that the past is finite in extent or duration, it does not follow that there is a first moment of time. For example, it could be that no event occurs 14 billion or more years ago, but for every length of time L years less than 14 billion years, there are events that occurred exactly L years ago. That is, there might be a finite bound on the past, with past moments that approach arbitrarily close to that boundary, but no moment that reaches it, i.e., no absolutely first moment. (Think of the set of positive real numbers, which approach arbitrarily close to zero without actually including it.)

Instead of looking for proof of the finitude of the past, we should look instead for support of what Alexander Pruss (2016) has called causal finitism. If we can show that every event has a finite causal history (i.e., no causal loops and no causal infinite regresses), then we can infer that there are uncaused events. If we can further assume that everything that begins to exist at a time must have a cause and that every non-eternal or fully temporal thing must have begun to exist at some time (because the past is finite), then we can conclude that all uncaused things must be eternal in nature (i.e., existing “outside” or “beyond” time itself). At that point, we might be able to show that such an eternal cause of temporal events must be relevantly godlike.
 
Here is a version of this Pruss-inspired argument:
 
P1. Every event has a finite causal history (no causal loops or infinite regresses).
P2. For everything that begins to exist (at some point in time), the event of its beginning to exist must have a cause.
P3. Every non-eternal thing began to exist at some point in time (since the past of each non-eternal thing is finite in length).
P4. If the yy cause the xx to begin to exist at t, then the yy exist at t or at some time earlier than t or eternally. [Premise 3 above]
Therefore, every non-eternal thing is ultimately caused to exist by some eternal (godlike) thing.

This proof assumes (in premise 3) that, for anything that begins to exist, there is a first moment of its existence. That seems pretty reasonable. In addition, one could probably derive this from causal finitism. Suppose, for contradiction, that some x has a finite past but no first moment of existence. Then it seems that there must an infinite regress of periods of x's existence, each caused by its predecessor, in contradiction to the principle of causal finitism.

But suppose one doesn't buy either of these moves. Then there would have to be a single initial period P of x's existence, a period which lacks a first instant. In that case, premises P2 and P4 (suitably modified) would entail that there must be some cause of x's beginning to exist, a cause that is either timeless or active at a time t that is prior to and adjacent to period P. And so the proof will go through.

The proof is pretty simple. Suppose x is some non-eternal thing. By P2 it begins to exist, and by P3 its beginning to exist must have a cause. By P4, this cause must either exist eternally or at the same or earlier time than that of the beginning of x's existence. If the cause is an eternal being, we're done. If the cause is a non-eternal being, then it must have a beginning of its existence. Premise P1 rules out an infinite regress of temporal causes. So, there must be an eternal cause.