Grim Reapers and the Infinite Past

One of the modern arguments for God’s existence is the Kalam Cosmological Argument (see my outline of it here); one of that argument’s two premises is that the universe began to exist. While I covered several reasons to accept that premise in my original post, my favorite reason for it was, unfortunately, too lengthy to include. Having finished the introductory outline of a case for Christianity, I now devote my first “random” post to this reason.

It’s called the Grim Reaper Paradox, and its application to the Kalam is due to the work of philosophers Rob Koons and Alexander Pruss. In order to understand it, though, we’ve first got to talk about the general logical tool known as “proof by contradiction.” The basic idea is that we don’t have to judge ideas as isolated points; we can judge the plausibility of an idea by the plausibility of its implications as well. If an idea has ridiculous implications, we shouldn’t believe it. The proof by contradiction is simply an extreme case of this reasoning; it is absolutely impossible for a contradiction to exist in reality, so if an idea implies a contradiction, that idea is necessarily false. (Fun fact: the simplest way to prove that 2 is irrational is a proof by contradiction.)

Returning to the Kalam Cosmological Argument, our goal is to show that the universe began to exist. Now either it began to exist or it didn’t (it’s “past-eternal”); therefore, one way to show that it began to exist is to assume that it didn’t and derive a contradiction. This is precisely what the Grim Reaper Paradox does. It goes like this:

Assume that our universe is past-eternal. Using conventional dating, we can number every year – this is 2019, there was a year 20, a year 2000 BC, and a year 20000000 BC. Since the universe is past-eternal, there is a BC year associated with every natural number. Now suppose there is also a past-eternal man named Fred. Unfortunately for him, there are infinitely many Grim Reapers out to kill him. There is one Grim Reaper for every natural number, and it is the duty of Grim Reaper number n to kill Fred during the year n BC.

  1. For any natural number n, Fred is either dead or alive at the end of n+1 BC.
  2. If he is dead, he remains dead, and is dead at the end of n BC.
  3. If he is alive, the nth Grim Reaper kills him, and he is dead at the end of n BC.
  4. Either way, Fred will be dead at the end of n BC for any natural number n.
  5. As a special case, we know that Fred is dead at the end of 1 BC.
  6. Because Fred is dead, some Grim Reaper must have killed him; since every Grim Reaper has a number, the one that killed him must have a number. Let’s call it Grim Reaper k, where k is a natural number.
  7. The fact that Grim Reaper k killed Fred means that he was alive after k+1 BC, but since k+1 is a natural number, this contradicts 4.

So we achieved our goal! We assumed that the universe was past-eternal and derived a contradiction; it follows that the universe cannot be past-eternal, i.e. it began to exist. Furthermore, it seems to me that each step of the argument is completely logically unassailable; the only way to avoid it is to say that the contradiction resulted from some other questionable assumption. In the interest of telling a good story, we did make a few such assumptions (e.g. the existence of a past-eternal man and the existence of an infinite number of Grim Reapers). But we can now trim these out to show that the contradiction remains even when the story is more boring.

We can easily replace the infinity of Grim Reapers with a single Grim Reaper who checks every year to see if Fred is dead; the contradiction is then derived in that there is a year in which Fred both was and was not dead. To replace our past-eternal man, there can instead be a past-eternal sheet of paper that each Grim Reaper is to sign during his year if it isn’t already signed. Alternatively, each Grim Reaper can supernaturally add a proton or a planet to the (past-eternal) universe if another Grim Reaper has not already done so. So these peripheral assumptions can be reduced to quite modest ones without damaging the essence of the contradiction; it would seem that the source of the problem really is the assumption of the past-eternal universe. If that’s right, we can be confident that the universe began to exist even apart from the abundance of scientific evidence we have for the same conclusion. In the face of these two lines of evidence, the traditional atheistic view of the universe as eternal no longer holds water. The inescapable beginning of the cosmos is something that any view of reality must explain; I expect that my atheist friends will have a lot more difficulty with that than me.

General Theism (Part 2): The Kalam Cosmological Argument

We’ll be starting our “debate” on General Theism with the affirmative side; what are some reasons we ought to believe that God exists (or at least that He plausibly might exist)? Before I begin, I’ll note that there are innumerably many reasons why theists actually believe that God exists and I’ll readily concede that many of them aren’t good; however, the existence of bad arguments for a thing doesn’t imply that there aren’t also good ones. I’ll also note that I’m not claiming to know with certainty that God exists – I don’t even know with certainty that my apartment exists. My contention is merely that these arguments, taken together, make it more plausible that God exists than that He doesn’t.

The first argument in my cumulative case is called the Kalam Cosmological Argument. My presentation of it will be closely based on the work of Dr. William Lane Craig, an excellent philosopher/theologian/apologist who’s defended this argument in great depth. (He’s also the founder of Reasonable Faith, of which we are a chapter.) I’ll be giving a very light version of the argument aimed at comprehension; if you’re interested in a heavier treatment of it, you can check out Dr. Craig’s work at reasonablefaith.org.

The argument runs like this:

  1. Everything that begins to exist has a cause.
  2. The universe began to exist.
  3. Therefore, the universe has a cause.

This is a deductive argument, meaning that it has a set of premises (statements 1 & 2) which together imply a conclusion (statement 3). You cannot rationally believe that 1 and 2 are true but 3 is false. Hence, all the defender of this argument needs to do is defend the truth of its two premises.

So why believe premise 1, which states that everything that begins to exist has a cause? A few reasons can be given in support of this pretty intuitive principle. For starters, we observe no exceptions to this rule in the collective scientific and day-to-day experience of humanity, so it’s reasonable to inductively infer that the principle holds in general (rather than that things do begin to exist without causes, but coincidentally only when our back is turned). Furthermore, suppose for a moment that something (say, a universe) could causelessly begin to exist; what’s stopping a universe from causelessly beginning to exist in front of me right now? (Or now? Or now?) It seems that someone who rejects this premise would have to say “nothing” – there is absolutely no reason why a universe couldn’t appear in front of me right now and incinerate me in the second Big Bang. It seems extremely implausible that universes can causelessly begin to exist but have, for no reason whatsoever, only done so once.

What about premise 2 – why believe that the universe began to exist? (Note that by “the universe,” I’m referring to all space, time, matter, and energy – this is a relatively standard definition.) We have good reason, both philosophically and scientifically, for thinking that it did. Philosophically, an infinite number of past events is absurd, since we’d have had to traverse an actually infinite amount of time to reach the present. (Think of why it’s impossible for someone to count from negative infinity to 0.) It would seem that there must be finitely many past days (for instance) – but this implies an absolute beginning. Scientifically, the Big Bang model explains what we see about the universe far better than any competing model, and it implies an absolute beginning of the universe (after which the model is named) about 13.8 billion years ago. One would have to reject both of these streams of evidence in order to deny this premise.

So if the first two premises turn out to be true, it follows logically that the universe has a cause. But nothing can cause itself (since it’d have to exist prior to its own existence), so if the universe (which is all space, time, matter, and energy) had a cause, that cause would have to be spaceless, timeless, and immaterial. We even have reason to suspect that it’s personal, but that requires heavier thinking than I want to do in this introductory post – if you’re curious, check out Dr. Craig’s treatment of the argument. But even without pressing for personality, the conclusion that the universe has a transcendent cause should help make the existence of God more plausible.

As I stated up front, I’m not claiming that this argument gives us certainty that God exists, and I don’t even require that it gives us a high degree of confidence that He does. I’ll be making a cumulative case for God’s existence, so we’ll be examining several different lines of evidence; even if no one of them is strong enough to demonstrate God’s existence on its own, I claim that they succeed when taken together. But even before seeing those other arguments, the Kalam should make you pause and think – are you willing to deny either premise in order to escape the conclusion, and if so, why? Be sure to share you thoughts and comments below!