The Complete Cause

Believer: “Now the question is: under exactly what conditions does an existent bring a phenomenon into existence?

If we call the existent that brings phenomenon A into existence its cause, we can say that phenomenon A comes into existence when ‘its cause exists.’ In other words, once the complete and sufficient cause for a phenomenon exists, that phenomenon can no longer fail to come into existence.

Suppose that for a light bulb to turn on, we need a conducting wire and a sufficient, uninterrupted flow of electricity. If all of these are present, the bulb cannot fail to light up. If it still does not light up, then something else must also have been required.

In any case, if all the necessary and sufficient conditions for a phenomenon to come into existence are present, that phenomenon will come into existence. Likewise, when a phenomenon does come into existence, this means that its complete cause was present.”

Skeptic: “I have no problem with that. I understand that if I ever find that what I thought was the cause of a phenomenon fails to produce that phenomenon, I should not doubt the principle you just stated. The only thing I should doubt is whether what I had taken to be the complete cause of that phenomenon really was its complete cause. The mistake would have been mine: I had identified the cause incorrectly.

If the cause of a phenomenon exists, there can be nothing left to prevent the phenomenon from coming into existence. If something can still prevent it from coming into existence, then we can say that the complete cause of the phenomenon does not yet exist. Please continue.”

Believer: “Now, if the complete cause of a phenomenon is itself a phenomenon, then we must accept that it too requires a cause. In other words, the cause of one phenomenon is itself the effect of another cause.

Phenomenon A is the effect of phenomenon B; phenomenon B is the effect of phenomenon C; and so on. How far can this chain of causes and effects continue?”

Skeptic: “In which direction?”

Believer: “What do you mean?”

Skeptic: “If you mean toward the future, I would say that we cannot prove that it cannot continue forever. Every phenomenon may bring about another phenomenon. Every moment may be followed by another moment. I see no problem with this process continuing indefinitely.

But if you mean that this chain of causes and effects cannot extend eternally into the past and must necessarily have a beginning, then you will have to prove it.”

Refuting an Infinite Regress

Believer: “I’ll give you an argument to show that the chain of causes and effects cannot be beginningless and infinite.

At first, we do not know whether the set of phenomena that have successively brought one another into existence is finite or infinite. In other words, we do not know whether the number of members in this set is limited or unlimited.

If the chain of causes and effects has a beginning, then the set of causes and effects will be finite. If the chain has no beginning, then the set of causes and effects will be infinite.

Now suppose we remove ten members from the total set of causes and effects—that is, we remove the last ten phenomena. The resulting set will have ten fewer members than the original set, so it will be a smaller set.

If one set is smaller than another, then it cannot have infinitely many members. If we match the members of the two sets one by one, the reduced set will have fewer members, and that shows that it is limited. A set with infinitely many members has infinite size and cannot be smaller than another set. But our new set is smaller than the original one. Therefore, the original set must also be finite, with only ten more members than the reduced set.

And if the set of causes and effects is finite, that means it must have had a beginning1.”

The Skeptic thought for a moment, tapping the tip of his pen against the paper in front of him. Then he said:

Skeptic: “Your argument is entirely mathematical, and everything depends on the mathematical concepts of finite and infinite sets. I can show you that instead of removing ten members from a set, you can remove half of its members and the resulting set can still remain infinite.

Take the set of natural numbers:

1, 2, 3, 4, 5, ...

Now remove all the odd numbers. What remains is the set of even natural numbers:

2, 4, 6, 8, 10, ...

Although we would expect the second set to be half the size of the first, both still have infinitely many members.”

Believer: “But the set of natural numbers, or the set of even natural numbers, does not exist in the real world. I mean, these are only mathematical concepts. If we start counting real objects in the world using the natural numbers, we never reach a number called infinity. At every moment, only a finite number of objects have been counted, and we have reached some particular number.

Counting to infinity never actually happens. It never becomes complete in reality. But the chain of causes and effects has, in a sense, already been completed.”

Skeptic: “Listen, my friend... You made mathematics the basis of your argument. You can’t change the rules halfway through. You said that because a set with ten fewer members than another set must be finite, the larger set must also be finite, and therefore the number of phenomena must be finite.

But in mathematics and set theory, there is no problem with having two sets where one is a proper subset of the other and yet both are infinite. So either modify your argument, or give me a different one. In any case, this one was not convincing2.”

Believer: “Very well... Here is another argument.

Imagine a hall full of people. If you ask any person in the hall why he entered, he will answer: ‘Because that other person entered, so I followed him in.’ If you ask that other person why he entered, he will say: ‘Because a third person entered, so I entered after him.’”

Skeptic: “Just like the phenomena. If you ask any one of them why it came into existence, it would answer: ‘Because that other phenomenon, which was my cause, came into existence, so I came into existence too.’”

Believer: “Exactly. And you know that every person in the hall will give you the same kind of answer.

Now you know two things:

First, none of the people in the hall has been there eternally. Each of them entered the hall at some point.

Second, none of them was willing to enter unless someone else had already entered.

The conclusion is that, at some point, one person must have taken the first step and entered the hall without making his own entry dependent on someone else’s entry. In other words, the process of entering the hall must have started somewhere3.”

Skeptic: After a few minutes of silence, he said, “Although I feel that your argument should be correct, I think there is something wrong with it. I don’t understand why you want me to assume that the hall was empty at some point. It is true that every person in the hall entered it at some point and, before that, was not in the hall. But why should I accept that there must have been a time when the hall was completely empty?

It is true that the farther back we go, the fewer people there are in the hall. But why should we assume that we can go far enough back to reach an empty hall? What I mean is that if the number of people in the hall is infinite, then however far back we go, people will disappear from the hall one by one, but the hall will never become empty. That is precisely what follows from there being infinitely many people in the hall. We only need to suppose that their number is infinite. Then we will never reach a time when the hall was empty, while we can still accept that none of the people has been in the hall eternally.”

Believer: “This argument seems perfectly clear to me. I don’t think we should assume that the number of people in the hall is infinite, because whether their number is infinite or not is exactly what the argument is trying to determine. We should not include the very thing we are trying to discover among our assumptions. Whether the number of people in the hall is finite or infinite is something we are trying to find out, not something we can simply assume.”

Skeptic: “Your first two assumptions were correct. First, no individual person has been in the hall from the beginning. Second, each person’s entry depended on someone else entering. But these two assumptions can rule out an infinite number of people only if they contradict it. In other words, if we place your first two assumptions alongside a third assumption—‘the number of people in the hall is infinite’—only one side must be able to remain true: either the first two assumptions, or the third. Only then would we be forced to reject the third assumption.

Now, I do not take the statement that no individual person has been in the hall from the beginning to mean that the hall itself was once empty. Instead, I will assume that the number of people in the hall is infinite and that, however far back we go, we never reach a beginning. Let’s see what happens.

Under this assumption, for any person we choose, we can find a time when that person was not yet in the hall. But we will never reach a time when the hall was completely empty. Let me try the same thing with an infinite set, such as the set of natural numbers, and see whether it works.

Suppose we had an endless lifetime and began counting the natural numbers. There would be no particular number that we would not eventually reach. We know in advance that no individual number can claim that we will never reach it; every number can say that one day its turn to be counted will come. But does this mean that we will eventually finish counting all the natural numbers? Certainly not. We will never finish counting all of them, because the set of natural numbers is infinite.

In my example:

Reaching each individual natural number corresponds to reaching a time when a particular person was not yet in the hall and had not yet entered.

The order among the natural numbers corresponds to each person’s entry depending on another person’s entry. Just as each person in the hall says, ‘I would not have entered until that other person entered,’ each number can say, ‘I would not have been counted until the previous number had been counted.’

And the infinite number of members in the set of natural numbers corresponds to the infinite number of people in the hall.

So apparently, all three assumptions can exist together under certain conditions. Therefore, I cannot regard your argument as a proof.”

Believer: “Let’s continue this discussion next week. I need some more time to think and study.”

Skeptic: “All right. Next week, I’ll be waiting for you at a coffee shop. I’ll send you the address. It’s quieter there.”