Existence of God (part 8)

October 19, 2010     Time: 00:26:22


The Kalam Cosmological Argument continued.

Excursus: Natural Theology
§ II. Kalam Cosmological Argument
Lecture 3

We have been talking whether or not an actually infinite number of things can exist. You remember the Muslim medieval theologian al-Ghazali argues for the creation of the universe and the existence of a Creator by saying that if the universe is beginningless, if the universe never began to exist, then there has been an infinite number of past events prior to today. But he argues an actually infinite number of things cannot exist – that leads to absurdities. That, therefore, implies that the number of past events must be merely finite, and therefore the series of past events doesn’t go back forever. There must have been a beginning. And given that whatever begins to exist has a cause, it would therefore follow that there is a transcendent cause of the universe that brought it into being.


Question: (inaudible)

Answer: The dates of when he lived? I do not know his birth date, but I think he died around 1111. He was a 12th century Persian who lived in what is modern day Iran.1

Second Philosophical Argument

Al-Ghazali has a second, independent argument for the beginning of the universe. If one wants to maintain that the universe is eternal in the past, he’ll have to refute, not only his first argument, but this second one as well because this is an independent argument. It doesn’t depend on the first one for its cogency.

This argument goes like this. Al-Ghazali says the series of past events, going back in time, has been formed by adding one member after another. The series of past events is like a series of dominoes falling one after another until the last domino, which is today, is reached. But, he says, no series which is formed by adding one member at a time, one after another, can ever be actually infinite because you cannot pass through an infinite number of things one member at a time.

Sometimes this is called the impossibility of counting to infinity. In the case of trying to count to infinity, it is very easy to see that, no matter how high you count, you will never reach infinity because there is always another number first that you would have to count before you would get to infinity. There is no finite number which, + 1, will land you at infinity. You can always count higher. So it is impossible to count to infinity.

But think about this – if you cannot count to infinity, how could you count down from infinity? This would be like someone’s claiming to have counted down all of the negative numbers: . . . , -3, -2, -1, ending at 0. This seems crazy – for somebody to say that you could count down all of the negative numbers, one at a time, ending at 0. Because before he could count -1, he would have to count -2; but before he could count -2, he would have to count -3; but before he could count -3, he would have to count -4, and so on, back and back. Before any number could be counted, an infinity of prior numbers would already have to have been counted first. So you just get driven back and back into the past, so that no number could ever be counted or reached. But then the final domino in this series could never fall, if an infinite number of prior dominoes had to fall first. So today could never be reached. But that is obviously absurd because here we are! We are at today; it has been reached. So this shows that the series of past events must be finite and have a beginning. That is the argument.2


Question: If there cannot be an infinite past, can there be an infinite future?

Answer: Remember we talked about this recently and said this depends upon your view of time. If you hold to the view of time which is often called the A-Theory (according to which the future does not exist; it is pure potentiality), then the future can be infinite in the sense that time can have a beginning and the series of future events can go on forever. It is potentially infinite. So it would be infinite in the sense we talked about: potential infinity. In this case it will never arrive at infinity; there will never be a future event that is the “infinitieth” event at which you will arrive. So, no, the future will not be infinite in that sense. It will be merely potentially infinite. From any point in time you pick, it will be a finite distance to the beginning, and the distance going forward will be finite but potentially infinite in the sense that infinity serves as a limit. If you adopt the B-Theory of time, according to which past, present, and future are all real and they are stretched out like a line, then, in that case, this argument would imply that time must have a beginning and an end because you couldn’t have an actually infinite amount of time.

Question: Which is more plausible, the A-Theory or B-Theory?

Answer: Well, al-Ghazali holds to an A-Theory of time. The people that hold to this argument hold to an A-Theory because they think that the way the past has been formed is not just by existing like a line, but rather it comes into being one event at a time, as one event occurs after another. And that is certainly the common sense view of time. This is the way we experience time, and I see no reason to think that that experience is illusory. I do not think we are suffering under some sort of gigantic delusion that temporal becoming is real, when in fact it is not. So I am a pretty ardent supporter of this so-called A-Theory of time which says that temporal becoming is a real and is an objective feature of reality. When we talked about divine eternity, we talked about this a little bit, too, and I pointed out there are certain theological problems with the B-Theory that the A-Theory doesn’t share. So look back at that section of the class when we talked about God’s attributes and His eternity. This will directly impinge on how we understand God’s relationship with time.

Question: Can you go over the B-Theory again?

Answer: The B-Theory says that the difference between past, present, and future is illusory in the sense that it is just a feature of human consciousness. For the people in the year 2000, 2000 is “now” and 2010 is “future.” But for the people in 2010, 2000 is “past” and 2010 is “now.” And for the people in 2050, both 2000 and 2010 are “past” and 2050 is “now.” So on this view what is past, present, or future is just a subjective point of view. It is very analogous to space when talking about what is “here.” There is no objective place that is “here.” It is just your subjective standpoint. If I were in Turkey, I would say Istanbul is “here;” but if I am in Atlanta, I would say Istanbul is “there” and Atlanta is “here.” But there isn’t any objective “here” or “there;” there are just these spatial locations. Similarly, B-Theorists would say all of the moments in time are just stretched out like a line, they are all equally real, and what you say is “now” is just the point where you are on the line, and the future is what is later than that, and the past is what’s earlier. There is no privileged “now.” Everybody thinks that his point is “now.” So it treats time very much like space. It thinks of time as just kind of there as a whole, like a spatial line, and what is “now,” or “present,” is very much like what is “here.” So there is a very close assimilation of time to space on this B-Theory.3

Question: With the B-Theory of time, if every time exists equally all at the same time. . .

Answer: Yeah, see, you can’t say “all at the same time” – your language trips you up. But, yes, they are all equally real and existent.

Followup: Exactly! O.K., so, does that mean I existed in 2000, and I am a different person, or am I the same person?

Answer: You are raising a very profound question about personal identity over time. What these B-Theorists, I think, have to say is that you are not a three-dimensional object that exists now. You are a four-dimensional object which is spread out through time. Sometimes this is called a space-time worm. You have temporal extension. What we see now is not really you. We see just a three-dimensional slice of you. You are actually stretched out through time, and we see just a slice of you right now. But that is not the same slice that exists, say, two hours from now – that is a different slice of you. The difficulty is, if that is true, that means you are not the same person that came in here a few minutes ago. You are somebody else. That slice is still back there, and you are someone else. So if we say that what we are seeing now is persons – in other words, you that I am seeing now are a person –, then it follows that no person endures over time. I said this creates theological problems – how can God judge the slice that exists at judgment day for the deeds done by some other slice earlier on in time? Why should he get the rap for what that earlier slice did? This is a really serious problem. If you say that, no, persons are not these three-dimensional slices, but rather the person is the whole four-dimensional worm, then that means that persons are not conscious, they don’t do anything, and they have no will. This is because that worm doesn’t have any self-consciousness; just the slices do. That is not what we mean by a person. So you have pulled a thread here in the fabric that really makes this B-Theory difficult to hold.

Question: I read a book by Brian Greene where he talks about how relativity theory creates a space-time “loaf,” and he brings up questions such as the idea of linking different times and how Newton’s absolute space doesn’t seem to work in modern theories.

Answer: What this is raising is the argument that many B-Theorists give, and that is relativity theory requires that we have this B-Theory of time – as you put it, a loaf that can be sliced up, which is the same as the worm metaphor, where you slice the loaf into different slices. What I would argue, and what I have argued in my written work, is a number of things. There can be a privileged reference frame in relativity theory – that is, a “preferred frame” – which does record the absolute time, and these other measurements of moving observers are simply due to the distortion of their instruments. Moving clocks run slow, measuring rods in motion shrink up, and therefore they do not detect the true time, which can only be given by someone who is at absolute rest. I think that interpretation of relativity theory is entirely adequate, and there are a number of physicists who hold to it. The other thing is to say that this whole debate is academic because the special theory of relativity is transcended by the general theory of relativity anyway. The special theory just deals with objects in uniform motion, but it doesn’t deal with accelerated motion or rotational motion. That is the general theory. And when you talk about the general theory of relativity, then what happens is that a preferred time, called cosmic time, does come suddenly into place. Cosmic time is the time that scientists use to measure the duration of the universe as a whole. When you hear scientists say that it has been about 13.7 billion years since the Big Bang, what they are talking about is cosmic time. That is the time that measures the duration of the universe. Fortunately for us, cosmic time coincides very nicely with Earth time. So our clocks do provide a very good measure of cosmic time. We can say it has been about 13.7 billion years since the Big Bang. Since this is a side track from the current discussion, let’s end it with that.4

Question: When you think of God being omnipresent in time, He is involved in the whole universe at any point in time. On the A-Theory, is it that He entered time so that there was a sequence of events? The God that was there before Jesus’ birth to the God at His point in death to the God today is omnipresent, and He didn’t change in the sense that He wouldn’t have in some way been a different entity. In other words, He is the same at each point in history. Yet He did take on a bodily form and enter time at that point.

Answer: That is the view that I defend. If you think back again to the section of the class when we did the attributes of God and we talked about God’s eternity, the view that I defended is that God existing alone without creation, without the universe, is timeless. And He creates the universe at the moment of the Big Bang, and in so doing He enters into time in order to have relationships with the creation that He has made. So the way I put it is that God is timeless without creation, and He is in time since the beginning of creation.

Followup: And this is consistent with the A-Theory?

Answer: That is consistent with the A-Theory because time would have a beginning, and we could go back to the first event of time. There is a finite number of events that takes you back to the first event, the first moment of time. Then beyond that – not before, but causally beyond that – would be God in His timeless eternity and He would be the Creator of time and space.

Let’s consider a possible objection to this argument. Some critics have responded to this argument by saying that in an infinite past there is no event infinitely distant from the present. It is not as though you have to traverse the distance between an infinitely distant event in the past and today. Rather, there is no beginning point at all, not even an infinitely distant one. But every event in the past is only a finite amount of time from the present. You can give the analogy of the negative numbers. In the negative number series, there is no number that is minus infinity. But every number you pick is only a finite distance to zero. So whether you pick -10 or -1000000, there is only a finite distance to the present, or to zero, and that can be easily traversed. If the past is infinite, these critics say, there is no infinitely distant event from which you have to reach the present. From every point in the past, it is only a finite distance to the present, and therefore there is no problem.

It seems that this objection commits a logical fallacy, which is the fallacy of composition. What is that? The fallacy of composition is the fallacy of equating the property of a part of a thing to the whole thing. It is saying that because a thing’s parts have a certain property, therefore the whole thing has that property. For example, if would be like saying that because every little part of an elephant is light in weight, therefore the whole elephant is light in weight. That is obviously a fallacy. Every little piece of an elephant that you might pick might be light in weight, but that doesn’t imply that the elephant as a whole is light in weight. The fallacy of composition is ascribing the property of a part to the whole. That is fallacious reasoning.

What about the case in hand? Just because every finite part of the series can be crossed, or counted down, doesn’t mean that the whole infinite series can be crossed or counted down.5 These philosophers have committed an elementary logical fallacy. They think that because every part can be counted or traversed, therefore the whole can be counted or traversed. That commits the fallacy of composition. The question, after all, is not how can any finite part of the past be crossed to reach today; the question is how can the whole, infinite, beginningless past be crossed in order to reach today.

Let me share two more absurdities with the idea of an infinite past that al-Ghazali gave to round out this argument. Al-Ghazali tried to show that you cannot form an actually infinite past by adding one member at a time. But suppose it could be done. He gives this illustration. Let’s imagine that for every one orbit that Saturn goes around the Sun, Jupiter goes around two times as many. The longer they orbit, the farther and farther Saturn falls behind.6 If Saturn goes around two times, Jupiter has gone around four times, if Saturn goes around a million times, then Jupiter has gone around two million times. They are in a two-to-one ratio. The longer they orbit, the farther and farther Saturn falls behind. In fact, if they were to orbit forever, Saturn would approach a limit in which it would be infinitely far behind Jupiter. Now, says al-Ghazali, turn the story around. Let’s suppose that they have been orbiting the Sun from eternity past. Which one would have completed the most orbits? The answer is: the number of orbits is exactly equal – namely, infinity. They both have completed an infinite number of orbits. Don’t let somebody try to get out of this by saying infinity isn’t a number. Infinity is a number; it is the number of elements in the set {0, 1, 2, 3 . . .}. Infinity in modern mathematics is a number, and it would be the number of orbits completed by each of these planets. But yet that seems absurd because the longer they orbit, the farther Saturn falls behind. How are they now magically equal in virtue of the fact that they have been orbiting for an infinite amount of time from eternity past?

Here is another illustration al-Ghazali gives. Suppose we meet someone who claims to be counting down from eternity past and he is now finishing: . . . , -3, -2, -1, 0. Phew! He’s done with his infinite countdown. Al-Ghazali thinks, “Why did he finish his countdown today? Why didn’t he finish yesterday or the day before that or the day before that?” If he is counting at a rate of, say, one number per second, at any time in the past he has already had an infinite number of seconds to finish his countdown. So why did it take him so long until today to get through? He should have already finished. In fact, at any point in the past you pick, he already had infinite time to finish his countdown, so he should have already finished. But that means no matter how far back in time you go, you’d never find the man finishing his countdown. And that contradicts the hypothesis that he has been counting down from eternity, which again just shows the absurdity of trying to form an infinite past by adding one member after another.

These illustrations really underline al-Ghazali’s claim that, in the case of a series which is formed by adding one member after another, you cannot do this and have an actually infinite series. This is only possible with a finite series.7

I think those give us good grounds for, again, the second premise of the Kalam Cosmological Argument, that the universe began to exist. So now we have two philosophical arguments for the finitude of the past: one based on the impossibility of the existence of an actually infinite number of things and the other based on the impossibility of forming an infinite collection by adding one member after another (if it is actually infinite). So for both of these reasons, I think we have good grounds for thinking the second premise is true.

Next, we will look at the remarkable scientific evidence in support of this second premise that the universe began to exist. In the Middle Ages, al-Ghazali only had philosophical arguments. What has breathed new life into the Kalam Cosmological Argument is that we now have pretty strong astrophysical evidence that the universe is not eternal in the past, but had a beginning a finite time ago.8




1 He was born c. 1058, and he died in 1111.

2 5:04

3 10:12

4 15:20

5 20:09

6 Dr. Craig misspeaks here. The transcript corrects the mistake and has Saturn fall behind Jupiter, not the other way around.

7 24:57

8 Total Running Time: 26:21