Existence of God (part 9)

November 24, 2010     Time: 00:30:36


The Kalam Cosmological Argument continued.

Excursus: Natural Theology
§ II. Kalam Cosmological Argument
Lecture 4

We have been talking about the beginning of the universe, and I have shared with you two philosophical arguments that have been defended by the great medieval Muslim theologian al-Ghazali. They are the argument based on the impossibility of the existence of an actually infinite number of things and the argument based on the impossibility of forming an actually infinite collection by adding one member after another, one at a time.


Question: Do those philosophical arguments apply in our universe?

Answer: It would apply to all space-time realities. So if our universe is just a part of a big multiverse, it would apply to the multiverse as well. These philosophical arguments would even apply to God. There couldn’t be an infinite regress of events in God’s life either, which is why you get back to a timeless, changeless being in which there are no events occurring.

Question: Does this apply outside of space-time?

Answer: The first argument would apply outside of time. If you had, say, an actually infinite number of things that existed not in time but that were countable, the first of the two arguments would count against even that. The second argument would only count against things that are in time because it has to do with how a collection is formed by adding one member after another, and that implies change in time. So the first of the two arguments would apply to anything that exists, even if it is non-spatio-temporal. The second argument could apply to things that are not in space, like God himself, but it would only apply to things that involve time.

Question: Would the first argument apply against an infinite set?

Answer: If you are a Platonist – I see now where you are going with this – suppose you think that numbers really exist, that numbers are objects that exist independently of our minds out there. Then, yes, it would apply against that. It would show that you cannot have an actually infinite number of numbers. Fortunately, I don’t think we are forced to accept a Platonistic metaphysics, which thinks of numbers as sort of abstract objects existing independently of human cognition. You will remember right at the beginning of that argument, I talked about Cantor’s theory of infinite sets, and I suggested this is simply a universe of discourse that is governed by certain axioms and conventions, and they show us how to construct this universe of discourse to talk about infinity in a logically consistent way without contradicting ourselves. But that doesn’t mean that this universe actually exists anywhere. As my wife likes to say, just because you can draft it on paper doesn’t mean that it is actually in reality or descriptive of reality.

Followup: Unless you are an idealist?

Answer: Not an idealist – rather a Platonist. A Platonist is somebody who thinks that there are these abstract objects. And this would be consistent with there being a finite number of abstract objects, but not an infinite number. But if you are so deeply committed to Platonism that you don’t like the first argument then you still have the second argument.

Question: What actually limits the number system from being infinite?

Answer: This would be a good question. If you do think that numbers really exist independently of human minds, but that they are not infinite, then you would probably be some kind of a constructivist. You would think that numbers are constructed by adding 1. The way you get 3, is you add 1 to 2, and the way you get 4 is you add 1 to 3, and so forth. Numbers are therefore a sort of human construction, much the way fictional characters are, or musical works or novels. You could say that they exist, but they are just potentially infinite because you can keep on adding 1 and construct them in that way. That is not the route I go; I see no reason to go down that road. But if you did want to hold to a sort of marriage of Platonism and finitism, you would adopt a philosophy of mathematics which is called Constructivism or Intuitionism, which would think of numbers as constructs that are not discovered but rather constructed.1

First Scientific Confirmation

During the Middle Ages, people had no scientific evidence for the beginning of the universe. Al-Ghazali appealed to philosophical arguments in order to support the second premise. But in one of the most remarkable developments of modern science, there has emerged in the course of the 20th century pretty strong evidence that the universe is not eternal in the past but, in fact, had an absolute beginning.

All through history, people assumed that the universe as a whole was unchanging. Of course, things in the universe were moving about and changing in various ways, but the universe as a whole was just there, so to speak. This was also Albert Einstein’s assumption when he crafted the General Theory of Relativity, or his theory of gravity. In 1917, Einstein began to apply his theory of gravity to the universe as a whole. When he did so, he found that there was something terribly amiss. His equations predicted a universe which was either blowing up like a balloon or else collapsing in upon itself. Not knowing what to do with this problem, Einstein “solved” it by fudging his equations. He added a new term to his equations in order to enable the universe to walk this tight rope between exploding and imploding. But the Einsteinian universe was incredibly unstable. Even the transportation of matter from one part of the universe to another would upset the balance and cause the universe either to expand or to implode in upon itself.

During the 1920s, the Russian mathematician Alexander Friedman and the Belgian astronomer Georges Lemaitre, by taking Einstein’s equations at face value, were able to craft, independently of each other, models of the universe which predicted an expanding universe. In 1929 the American astronomer Edwin Hubble, through tireless observations of the heavens at the Mount Wilson Observatory, made a remarkable discovery which verified Friedman and Lemaitre’s theory. He found that the light coming to us from distant galaxies appears to be redder than it should. This redshift in the light from distant galaxies was most plausibly explained by the fact that the light sources, the stars, are moving away from us, and therefore the light rays emanating from them are stretched so that they appear to be redder than if the objects were stationary. Wherever Hubble trained his telescope in the night sky, he discovered this redshift in the light from the distant galaxies. It appeared that we exist at the center, at the very heart, of a cosmic explosion and that everything else in the universe is flying away from us at fantastic speeds.

According to the Friedman-Lemaitre model, we are not really at the center of the universe. It just appears that way. Any observer associated with any galaxy would look out from his vantage point and see this redshift in the galaxies around him. So any observer will feel as though he were at the center of the expansion. The reason for this is that it is space itself that is expanding. The galaxies are actually at rest in space, but they move away from one another as space itself stretches and expands.2

To get a picture of this very difficult idea, imagine a balloon with buttons glued to the surface. The buttons are stuck in place. They are at rest with respect to the surface of the balloon. Nevertheless, as you blow up the balloon, the buttons will get farther and farther apart because the balloon is getting bigger and bigger. Because the surface of the balloon is stretching, the buttons will move away from each other in the sense that the distance between them increases, even though they are themselves at rest with respect to the surface of the balloon. Notice that there is no center to the balloon’s surface. Any observer located on one of these buttons will look out and see the other buttons receding from him, moving away from him. There is no center to the balloon’s surface. Someone might say, “But there is a center inside the balloon.” Ah, but then you are forgetting we are talking just about the surface of the balloon. Just the two-dimensional surface of the balloon has no center.

Those buttons are just like the galaxies in outer space. The two-dimensional surface of the balloon is the analogue to our three-dimensional space. The buttons represent the galaxies in space. The galaxies are actually at rest in space, but they move away from one another as space itself expands or stretches. Just as there is no center to the balloon’s surface, so there is no center to the universe.

Eventually, the Friedman-Lemaitre model came to be known as “the Big Bang Theory” of the origin of the universe. You can see by what I have said that that title, though catchy, is somewhat misleading. For to think of the expansion of the universe on the model of an explosion is misleading because we might think, then, that the galaxies are moving out from a central point into some pre-existing empty space. That would be a complete misunderstanding of the model. The model is not that the galaxies were once located at some central point and are now moving out into a pre-existing, empty space. The model is much more radical than that. The Big Bang did not occur at some point in a pre-existing space. Rather, it is space itself that is expanding. Again, you might say, “What about the point in the interior of the balloon? If the balloon shrinks down, wouldn’t it collapse down to that point?” Here, again, you are forgetting that the analogue to space is just the surface of the balloon. The balloon surface happens to be embedded in a third dimension, a higher dimension, so that there is depth as well as breadth and length. But on the Big Bang theory, our three-dimensional space is not embedded in some higher fourth dimension. So there just is nothing that corresponds to the space inside the balloon or outside the balloon. Our three-dimensional space is the analogue, or is like, the two-dimensional surface of the balloon, which has no center. Don’t be misled into thinking of the Big Bang as the explosion of a super-dense pellet which has been around from eternity and then a finite time ago suddenly blew up. That is not the theory!


Question: Regarding the Privileged Planet movie, it talked about our special location in our universe. Wouldn’t that go against the idea of centrality of our placement in the universe?

Answer: What that movie is talking about is our location as a planet in one of the spiral arms of our galaxy so that we can make visual observations of the universe rather than have the heavens be obscured.3 But that is just within our galaxy. What we are talking about with the Big Bang model is all of the galaxies and the galactic clusters, a much larger scale then just our location in our galaxy. Here we are abstracting to really, really big scales, where you think of the galaxies scattered all across the universe. And it is these galaxies and clusters of galaxies that are fleeing apart from one another at fantastic speeds. But within our Milky Way, our galaxy, things are hanging together in this spiral arm structure.

Question: How does this relate to the biblical perspective, as God described mankind’s creation and the Earth’s creation, in the grand scheme of things?

Answer: I think that what we have to say is that mankind is not the center of the universe in any sort of physical sense. But I don’t think that is ever taught in the Bible. No where does it suggest that we are physically located at the center of the universe. Rather the Bible presents human beings as the apex of creation, the crown of creation, in view of their being created in the image of God. That is what makes them special. That is independent of their size. You don’t have to be big to be morally worthy or to be intrinsically valuable. Human beings are intrinsically valuable because they are created in God’s image. In fact, biologists tell us that the human brain is the most complex structure in the entire universe. So the fact that we are dwarfed by the universe’s size doesn’t speak to our intrinsic worth or our importance in creation. It is not based on our size or location.

Question: So not a super dense pellet but a formerly non-existent, flat balloon?

Answer: I will say something more about that in a minute. What it would mean is that this geometry shrinks down to a boundary point before which it doesn’t exist. I will say something about that in just a minute. But you shouldn’t think of this pellet as existing in some big vacuum or big empty space, lying there from eternity, and then inexplicably blowing up a finite time ago. That is not the idea. It is time and space themselves that come into being at the beginning of the universe.

Question: How does this theory relate to Genesis 1:6: “Let there be an expanse in the midst of the waters, and let it separate the waters from the waters. God made the expanse, and separated the waters which were below the expanse from the waters which were above the expanse; and it was so. God called the expanse heaven.” Of course, we are told later that the stars themselves were placed within the expanse of the heavens. And so would you say that, if this theory is true, that that would mean that from the perspective of any planet, it would appear as though an expanse had been placed in the midst of the waters?

Answer: I am very loathe, very reluctant, to try to read modern science into the Bible and in particularly into Genesis 1. I think that is what’s called eisegesis – that is, you are reading into the text, you are reading between the lines – rather than exegesis, which is allowing the text to speak to us in the way that an ancient Hebrew writer would have thought and read about these things. So I respectfully disagree with my friend Hugh Ross, who would quote verses like that one, or Isaiah when it says, “He spread out the heavens,” and interpret this as a biblical prediction of the expansion of the universe. I think that rather, in its original context, what this ancient Hebrew writer was thinking of was of the heavens on the analogy of a tent that God has constructed, and you see the lights in the firmament, or in the expanse. But that is purely a phenomenal description; that is, it is a way things appear to us. We should not think that he is trying to give some sophisticated, astronomical theory.

Followup: Even if things are being described in phenomenological terms, wouldn’t you say that those terms still represent something, that they represent something in reality even though they may have been described from the perspective of the biblical writer?4

Answer: Fair enough, I think that is right. I would take Genesis 1:1: “In the beginning, God created the heavens and the Earth” to be a statement of the origin of the universe. That would be what we would call the Big Bang, that God created the Big Bang. And then in verse 2 it says, “and the Earth was without form and void.” There the focus has suddenly narrowed in a dramatic way to this planet. What is then described is how God transforms this planet from an uninhabitable waste to a place suitable for human beings to live and thrive. He creates an ecosystem in which they can flourish. So you are right; I think it does correlate. I am just reluctant to try to look at words like “expanse” and think of those in terms of, say, the expanding universe or try to read modern cosmology into those things. But I think you are quite right in saying this isn’t meant to be poetry; it does mean to describe real things.

Question: Since the Earth is the center of God’s creative purpose, but yet if we look at just the solar system from the Earth’s perspective, the solar system will seem very complicated. But we have to get out of our perspective to see where everything will fit together.

Answer: I think you are right in saying there are different perspectives from which to look at it. But I would think that it is not so much a physical perspective as what I was saying in response earlier that you look at humanity from the perspective of its ethical and spiritual importance. It is in that sense that human beings are the crown of creation and the center of creation, in the sense that they are created in the image of God and, therefore, they are intrinsically valuable, so that God would send his Son to die for them. But our planet, considered from this sort of third-person, physical perspective, is this little speck of dust that is just lost in the Milky Way, and the Milky Way is just lost in this enormous universe. But that doesn’t say anything about the importance of human beings because importance, as I say, isn’t determined by size. That is the fallacy of some atheists or agnostics who, because we are so small, think that therefore we are insignificant. That is a fallacy based on thinking that significance is determined by how big something is.

As we trace this expansion back in time, in reverse, that means that everything gets closer and closer together. If our balloon had no minimum size but could just keep shrinking and shrinking, then eventually the distance between any two points that you pick on the balloon would shrink to zero. If it could just keep on shrinking, then eventually the distance between any two points on the surface of the balloon would shrink to zero. It would have, in effect, zero circumference, as it is measured.

According to the Friedman-Lemaitre model, that is what happens as you trace the expansion of space back in time. Eventually, the distance between any two points in space becomes zero, and you can’t get any closer than that. At that point you have reached the boundary of space and time. Space and time cannot be extended back any further than that. It is literally the beginning of space and time.

We could portray our expanding universe geometrically by means of a cone [see Figure 1].

Figure 1 - Conical Representation of Standard Model Space-Time. Space and time begin at the initial cosmological singularity, before which literally nothing exists.

If we let a disk represent the three dimensions of space [where the disk is a slice of the cone] (one dimension we have to suppress because it is on paper), with the vertical dimension being time, then as you trace the expansion of the universe back in time, the universe shrinks down to a point at which point the distance between any two points in space is zero.5 That marks the beginning of space and time [in Figure 1, this boundary point is labeled the “Initial cosmological singularity”].

What is significant about this is that the geometry of a cone is such that the cone can be extended indefinitely in one direction. You can keep adding to the cone going up, but in the other direction, a cone has a boundary point and cannot be extended any further. The cone can only be extended geometrically in the one direction. In the other direction it has a boundary point. Since that direction represents time, that means that at some time in the past, space began to exist. There is a boundary point before which nothing existed. What this implies, therefore, is that the past is finite and that time and space had a beginning.

Because space-time is the arena in which all matter and energy exist, this means that all matter and energy also came into being at this point. It is the beginning of the universe. Notice that there is simply nothing prior to the beginning of space and time. Let’s be philosophically careful, so we are not misled by words. When I say there is nothing prior to the beginning of space and time, I do not mean there is a prior state and it is a state of nothingness. What I mean is that, at the beginning point, it is false that there was anything prior to the universe. It is false that there is something prior to that point. That is what one means when one says there is nothing prior to the beginning.

The standard Big Bang model, as the Friedman-Lemaitre model came to be called, thus predicts an absolute beginning of the universe at some time in the finite past. If this model is correct, then we have amazing scientific confirmation of the second premise of the Kalam Cosmological Argument.


Question: Is there anything that theoretically prevents the cone from being an hourglass?

Answer: Yes. If this [the point of the cone] is what is called a singularity, then it represents a boundary point to space and time, and you cannot extend space-time through a singularity. A lot of the project of current cosmology is to try to get rid of this singularity at the very beginning, so as to extend the universe through. We can talk about that later on. But right now, insofar as we are talking about the standard model, the Friedman-Lemaitre model, it does feature a singularity and therefore has a boundary point and cannot be extended like an hourglass. That would be a different geometry than a cone geometry.

Question: What about the argument that the singularity simply results from a breakdown of the mathematics and because you are not actually at zero when you reach the singularity, you are at 10-43 second and there is still a fraction of time before the universe hits 0.

Answer: Actually, the singularity is at t=0. If the universe begins as the standard model has, it is at t=0. It is not prior to that.

What we need to discuss then is, “Is the standard model correct?” The standard model unequivocally predicts a beginning of the universe. The question is, is this model correct or, more accurately, more importantly, is it correct in predicting a beginning?6




1 5:13

2 10:04

3 15:07

4 20:00

5 25:28

6 Total Running Time: 30:35