Carnal Reason

I ran across a version of the Kalam cosmological argument at a site called Stand to Reason. This argument has the curious flavor of Zeno’s arguments against the possibility of motion, and is every bit as persuasive. The version presented at STR got my attention, for reasons I will make clear.

STR’s exposition is a bit long-winded, so I present an outline of the Kalam argument as given by Philosophy of Religion.info.

(1) Everything that has a beginning of its existence has a cause of its existence.
(2) The universe has a beginning of its existence.
Therefore:
(3) The universe has a cause of its existence.
(4) If the universe has a cause of its existence then that cause is God.
Therefore:
(5) God exists.

It is part (2) that is concerns us here. The argument is that either the universe has always existed, and is hence infinitely old, or it is only finitely old. Stipulated. The next step is to argue that the universe cannot be infinitely old because there is some mathematical difficulty with the concept of infinity. Before considering the argument as presented at STR, I turn again to the more lucid (albeit weak) explanations at Philosophy of Religion.info. PoR offers three alleged mathematical difficulties. The first is silly, the second is more interesting but I shall not bother with it now. It is the third I quote, because it is the same argument STR uses, succinctly stated.

If I were to set out on a journey to an infinitely distant point in space, it would not just take me a long time to get there; rather, I would never get there. No matter how long I had been walking for, a part of the journey would still remain. I would never arrive at my destination. Infinite space cannot be traversed.

Similarly, if I were to start counting to infinity, it would not just take me a long time to get there; rather, I would never get there. No matter how long I had been counting for, I would still only have counted to a finite number. It is impossible to traverse the infinite set of numbers between zero and infinity.

This also applies to the past. If the past were infinite, then it would not just take a long time to the present to arrive; rather, the present would never arrive. No matter how much time had passed, we would still be working through the infinite past. It is impossible to traverse an infinite period of time.

Clearly, though, the present has arrived, the past has been traversed. The past, therefore, cannot be infinite, but must rather be finite. The universe has a beginning. This is the third mathematical argument for the second premise of the kalam cosmological argument.

Here is how to traverse an infinite distance in a finite time, every moment traveling at finite speed. The trick is to keep accelerating. Say you travel the first foot in 1/2 second. Pick up the pace; travel the second foot in 1/4 second, the third foot in 1/8 second, … the n-th foot in 1/(2^n) second. Your speed is always finite, but you will traverse an infinite distance in one second.

If you find this hard to imagine, consider the alternative. Suppose someone claims the hypothetical traveler covers only a finite distance. Then there must be some upper bound B (measured feet) which exceeds the distance he traversed. Assuming B is an integer, a simple computation shows that the traveler reached B at time (2^B - 1)/(2^B). If B is not an integer, round it up. Since there is no upper bound on the distance traversed, the traveler must have covered an infinite distance. Granted, this is not physically feasible, but it is mathematically simple.

With this bit of background in place, I present STR’s version of the Kalam argument.

This point in time we call “now” is actually future with reference to all of the past. We agreed you cannot get to any infinite point in the future by adding as events one to another. Therefore, this present moment in time can’t represent an actual infinite number of events added one to another proceeding from the past. Time has proceeded forward from the past as one event is added onto another to get us to today. But we know that whenever you pause in the count as we’ve done today, that you can’t have an infinite number of events. Which means that there is no infinite number of events that goes backward from this point in time, only a finite number of events. Here’s another way of putting it. If you can’t get into the infinite future from a fixed reference point (the present) by adding consecutive events one by one, you cannot get into the infinite past by subtracting consecutive events, one by one, from a fixed reference point (the present). If you can’t transverse the distance in one direction (present to infinite past), you can’t transverse it in the other direction (infinite past to present). This means that if the universe consisted of an infinite series of events in time, you could never arrive at this present moment. Philosopher Dallas Willard puts it this way: “As in a line of dominoes, if there is an infinite number of dominoes that must fall before domino x is struck, it will never be struck. The line of fallings will never get to it.” ( Does God Exist–The Great Debate , p. 203-204) In other words, there would have to be an infinite number of events completed before you could get to the domino before you. But you can never complete an infinite number of events. An infinite series is innumerable by definition, so you can’t treat it as if it were a number you could ever arrive at. This means the universe is not eternal.

So why did this catch my eye? Here is the punchline. STR, having supposedly established that it is impossible for anything to have always existed, continues with

The universe has not existed forever and ever with no beginning. The universe, in fact, had a beginning. If it had a beginning, if the universe came into being, and it’s not eternal, then something must have caused it that didn’t have a beginning itself. The universe had a Beginner, some infinite, self-existent, uncaused, non- contingent Someone who started it all.

There you have it. Actual infinities are impossible, ergo the universe cannot be eternal, ergo an actually infinite God exists. And presumably always has. I am reminded of the unexpected elephant.

Posted on October 30th, 2006 by pwyll
Filed under: religion