How Train Cars and Set Theory Prove the Existence of God

Perhaps the strongest argument against atheism is the argument from contingency. In its barest form, it goes something like this:

A. All of reality, without exception, breaks down into one of two possible categories:
(1) that which is contingent, and (2) that which is non-contingent.

Let me explain what I mean by both the terms, “thing” and “contingent.” I mean “thing” in its broadest
possible sense: a physical object, a scientific law, whatever. If a thing requires something else to exist, it’s “contingent.”

Family Tree

You and I are radically contingent. Without our parents (and their parents, and their parents, all the way back), we wouldn’t exist. Even the slightest change: your great-great-great-great-great grandfather dies before meeting your great-great-great-great-great grandmother (or moves, or isn’t attracted to her, or marries someone else instead, etc., etc., etc.), and you don’t exist. But more than that, innumerous other factors had to line up just so: we had to live on a planet with all sorts of conditions making human life (and procreation possible), in just the right sort of universe, and so forth.

I’m not interested in debating here whether the coalescence of these factors was probable or improbable, mere chance or Grand Design.

My point is simpler: in order for you to exist, some other conditions much logically precede your existence. Your existence is logically dependent upon these other conditions. Therefore, if I know that a particular universe has you in it, I can deduce all sorts of other things about that universe: that it’s life-sustaining, contains (or contained) your parents, etc.

This is what we mean by a contingent reality. Under particular conditions, you come into existence. Had those conditions not been there, you wouldn’t.

All created things are in Category 1: they’re all contingent. They don’t arise necessarily. Sometimes this is stated as “everything that begins to exist has a cause.”

So all created things are contingent. But the opposite isn’t true: a thing could be infinitely old and still logically-contingent. So Category 1, as you might suspect, is enormous. It includes the entire universe.

B) You cannot simply have an infinite series of contingent causes;
an uncaused cause is logically necessary.

Contingent causes require something else to exist: that chain can’t simply go back forever. If A requires the existence of B, B requires the existence of C, and C requires the existence of A, you can’t posit A, B, or C as the cause of the existence of the set of A, B, and C.  A philosophy professor of mine gave me two helpful illustrations of this principle: one involving set theory, and one involving trains.

Let’s talk about set theory first. All causes can be divided into [Caused Causes] and [Uncaused Causes]. No matter how large the set of [Caused Causes] is, even infinitely large, it can’t cause itself. It needs an Uncaused Cause to begin. We tend to think of this temporally (that the uncaused cause exists prior to the caused cause), but this would be true even if the uncaused cause and caused cause(s) are both infinitely old.

That illustration is clean and simple, but it’s not for everyone. For that reason, he gave the illustration of trains. The picture below shows two cars - the car on the right is a locomotive, which has the engine; while the car on the left is an ordinary train car, which doesn’t:

If you’re at a railroad crossing and see an ordinary train car go by, you may be sure that it’s being pulled by a locomotive, even if you can’t see the front of the train. The car may be pulled by the locomotive directly, or by another train car or series of train cars which are themselves pulled along by a locomotive.

A train that was made up only of train cars, with no locomotive, could never move. It doesn’t matter if that locomotiveless-train was one car long, or a thousand, or a million, or infinite. Without something moving it, it won’t move an inch.

So it is with contingent realities: they are ultimately set in motion, so to speak, by what is necessary. It doesn’t matter if you have a single contingent reality, or a thousand, or an infinite number: they require the existence of a non-contingent reality.

By the way, this also explains why the atheist argument, “Who created God?” is philosophical nonsense. It’s like asking, “Well, if all train cars must be moved by a locomotive, who moves the locomotive?”

C) This necessary reality is what we call “God.”

At this point, we can say with certainty that Someone or Something necessary created the entire universe. We can say with absolute certainty that the entire universe – from every person to every particle to every scientific law – traces back to a common origin, some kind of Creator. This gives us a starting place to explore what sort of Creator we’re talking about. Here ends the proof.

It doesn’t immediately prove the truth of Catholicism (that’s known through a combination of reason and Divine self-revelation), but it does disprove the possibility of atheism. There’s simply no way to start with no uncaused causes, and end up with anything, be it physical laws or material realities or anything else.

P.S. What sort of Creator?

The proof might suggest that the universe has a Cause, but a wholly impersonal one. It turns out, using this proof, we can actually determine a whole lot about our Creator. You see, nothing can exist in an effect that doesn’t exist (at least in potency) in the sum total of the causes. You can’t put two and two together and get five. That whole notion violates basic causality.

And since all of the other causes derive from the same necessary cause, we can say that nothing can exist in the universe that doesn’t come from the Creator. So, for example, we exist in a universe that contains (and permits) personality and sentience. But the effects of personality and sentience can’t exist without the ultimate Cause possessing personality and sentience. So we know right away that we’re dealing with a personal God