We know from Scripture that God created the world a finite amount of time ago, but was that the only option he had? Could God have created a world with an infinite history?
Defenders of the Kalaam cosmological argument claim that he couldn’t have done so.
To show that, they would need to demonstrate that the idea of an infinite history involves a logical contradiction.
Some recent attempts to do this involve paradoxes that have been proposed by different authors.
Let’s look at a couple and see what we can learn.
The (Squished) Grim Reaper Paradox
The core of what has become known as the Grim Reaper paradox was proposed by Jose Bernardete, and the argument has taken different forms.
Here I’ll present a version that is close to the original. I’ll refer to it as the “squished” version for reasons that will become obvious.
Suppose that a guy named Fred is alive at 12:00 noon.
However, there are an infinite number of grim reapers waiting to kill him. For the sake of convenience, we will give the reapers names based on the negative numbers, with the last reaper being Reaper 0.
If Fred is still alive at 1 p.m., Reaper 0 will encounter him and kill him. However, before that, Reaper -1 will encounter Fred at 12:30 p.m. and kill him. Even before that, Reaper -2 will encounter Fred at 12:15 p.m. and kill him. But Reaper -3 will encounter him at 12:07:30 p.m., and so on, with each reaper set to encounter (and kill) Fred in half the remaining distance back to noon.
Which reaper will kill Fred?
The way the situation has been set up, we have a paradox. Reaper 0 should not kill Fred, because Fred should already have been killed by Reaper -1. But this reaper shouldn’t kill him either, because he should have been killed by Reaper -2. And Reaper -3 should have killed him before that, and so on.
It thus looks like Fred can’t possibly survive past 12:00 noon, but it’s impossible to name which reaper kills him. Paradox.
I called the above version “squished” because it squishes the infinite series of grim reapers into a single hour. But we don’t have to do it that way. We’ll see another version later.
The Problem with the Paradox
The resolution of this paradox is fairly straightforward. It has envisioned a situation where Fred begins alive and then will be killed by the first grim reaper he encounters.
The problem is that—if the series of grim reapers is infinite—then it must have no beginning.
To suppose that an infinite series of whole numbers has both a first and last member involves what I’ve called the First-and-Last Fallacy.
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- Infinite series can have no beginning ( . . . -3, -2, -1, 0)
- They can have no end (0, 1, 2, 3 . . .)
- Or they can lack both a beginning and an end ( . . . -3, -2, -1, 0, 1, 2, 3 . . . )
But if a series has both a beginning and an end, then it’s finite.
The series of reapers set to kill Fred has an end—Reaper 0—but if that’s the case, it cannot have a beginning.
This means that there is no first grim reaper that Fred encounters, just as there is no “first negative number.”
The idea of a first negative number involves a logical contradiction, and therefore the (Squished) Grim Reaper paradox is proposing a situation that cannot exist.
The (Spread-Out) Grim Reaper Paradox
To make the Grim Reaper Paradox more relevant to the Kalaam argument, some have proposed a new version that spreads out the grim reapers over an infinite history rather than squishing them into a single hour.
We can put the spread-out version like this:
Suppose that Fred has always been alive, all the way through an infinite past.
Suppose that there is an infinite series of grim reapers set to kill Fred, and they are set to kill him in sequence on New Year’s Day.
On New Year’s Day this year, Reaper 0 is set to kill him if he is still alive. But on New Year’s Day last year, Reaper -1 was set to kill him, and Reaper -2 the year before that, and so on.
Which reaper kills Fred?
Exactly the same paradox results. Each reaper should not be able to kill Fred because a previous reaper should already have done the dirty work.
But the problem is the same: The situation is set up so that the only reaper that could kill Fred is the first one in a beginningless series, and a beginningless series has no first element.
The spread-out version of the paradox thus has the same flaw that the original did: It proposes an entity that involves a logical contradiction and so can’t exist.
Application to the Kalaam Argument
Kalaam defenders use paradoxes like this in an attempt to undermine the idea of an infinite history.
For example, on the rhetorical level, the strategy can work like this:
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- They encourage their audience to imagine a set of circumstances that could exist and that don’t involve a logical contradiction (e.g., Fred exists, a grim reaper is scheduled to kill him at some time).
- They multiply the circumstance extending finitely into the past (suppose there are some other grim reapers who were also set to kill him previously).
- They extend this infinitely into the past, generating a contradiction.
- They point out this contradiction.
- Finally, they assert that, since the infinite extension into the past caused the contradiction, we must reject the idea of an infinite past.
This reasoning is mistaken, because it isn’t the infinite history that’s the problem. It’s the fact that you’ve proposed a first element in a beginningless series.
Consider the following scenario:
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- Suppose that some guy named Fred exists.
- Suppose that he existed last year.
- And the year before that.
- And that he’s always existed, with no beginning.
That involves an infinite history, but it doesn’t have a contradiction in it—because it does not propose a first element in a beginningless series.
It’s only when you introduce the latter that a contradiction occurs. So, it isn’t the infinite history that’s the problem but the impossible first element. Grim Reaper-like paradoxes thus are disguised forms of the First-and-Last Fallacy.
World Without End
Another way of seeing why the strategy used by Kalaam defenders is problematic is by flipping the arrow of time and considering a mirror image of the paradox that deals with the future:
Suppose that Fred is alive today and will remain alive as long as a grim reaper doesn’t kill him.
Suppose that there is an infinite series of grim reapers to kill him in the future and who we will name using the positive numbers, beginning with 0. Reaper 0 encounters Fred today, Reaper 1 encounters him tomorrow, Reaper 2 the day after, and so on.
But the reapers have agreed that the honor of killing Fred will go to the reaper with the highest number.
Which reaper kills Fred?
The way this scenario has been set up, the only reaper that can kill Fred is the last reaper.
But there can be no last reaper in a series that has no end, just as there can be no first reaper in a series that has no beginning.
The Future Reaper Paradox proposes the same kind of logically contradictory entity that the original paradoxes did.
And the problem is not the fact that the future is infinite in the scenario. The infinite future itself does not involve a contradiction, because it does not propose there being a last element in the series of days stretching into the future.
Indeed! From a Christian point of view, an infinite future is exactly what awaits us. The Christian faith teaches that God will give us endless life and there will be no day on which we pass out of existence. As a result, an orthodox Christian is committed to the idea of an infinite future.
It’s not the endlessness of the future that’s a problem in the above scenario, but the idea of that future containing a logically contradictory entity like the last member of an endless series of reapers.
In the same way, the idea of an infinite past is not a logical contradiction but the idea of a first reaper in a beginningless series.
The Underlying Assumptions
The paradoxes recently proposed in support of the Kalaam argument (and there are many) share a common set of assumptions:
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- Suppose some past scenario (P) that involves a first member.
- Suppose some past scenario (P’) that does not have a first member.
- Suppose that P and P’ are the same scenario.
By contrast, corresponding future-oriented paradoxes have these assumptions:
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- Suppose some future scenario (F) that involves a last member.
- Suppose some future scenario (F’) that does not have a last member.
- Suppose that F and F’ are the same scenario.
The way the paradoxes are fleshed out and expressed varies, and this can disguise the fact, but they all share the same set of assumptions.
As a result, they set up logical contradictions, but this does not tell us which of the premises must be rejected to diffuse the contradiction.
This is true of any such paradox. Consider the following geometrical one:
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- Suppose there is some closed geometrical shape (S) that has three sides.
- Suppose that there is some closed geometrical shape (S’) that has four sides.
- Suppose that S and S’ are the same shape.
This scenario sets up the idea of a four-sided triangle, which is logically impossible. But in resolving the paradox, we don’t have to reject any particular premise.
We could reject the idea that S (the three-sided shape) exists; we could reject the idea that (S’) the four-sided shape exists; or we could reject the idea that S and S’ are the same and then conclude that there must be two shapes. Each of these is a legitimate option.
As a result, when considering past- or future-oriented paradoxes, we don’t have to reject the idea of an infinite past or an infinite future, because neither of these concepts generates a logical contradiction on its own.
It is only when we introduce a logically contradictory entity into these scenarios—like the first member of a beginningless series or the last member in an endless series—that a paradox results.
Those are the entities that need to be rejected, and the recently proposed paradoxes do not disprove either the idea of an infinite past or an infinite future.
