The Doctrine of Creation (part 9)October 26, 2008 Time: 00:29:43
Some of the arguments for Creation out of Nothing.
What we’ve been talking about is the doctrine of creation. We’ve been looking at arguments for creation. Last time we talked about the first philosophical argument for creation based on the impossibility of the existence of an actually infinite number of things. You will remember I argued there that the real existence of an actually infinite number of things is absurd. We gave the illustration of Hilbert’s Hotel to show the kind of situations that could result if you could have an actually infinite number of things. Then we pointed out, secondly, that a beginningless series of events in time would involve an actually infinite number of things, namely, an actually infinite number of past events. It follows from that that the series of past events cannot be beginningless. It must be finite. That means that the past does not go back forever; you come to a first event and a first uncaused cause, which is required by the first premise of the argument that whatever begins to exist has a cause [referring to the kalam cosmological argument].
Dr. Craig: I have not studied fractals myself. I am aware of what they are. I’ve seen articles on them. I haven’t studied them myself. What I would say is that I think, with respect to these, they are mathematical objects – fractals are. In that sense, they are not any different from, say, infinite sets or an infinite number of numbers or things of that sort. What I would simply say is that these things don’t have real existence. At best these have a kind of conceptual reality, but in actual physical reality fractals don’t exist because you get down to a minimal level when you encounter on the subatomic level these quanta of energy and space and time so that you can’t divide things any further in a practical way. These kinds of mathematical examples of the infinite I don’t think are troublesome. When I say an actually infinite number of things can’t exist, I am talking about things in reality, not just in the sort of mathematical realm which I think is really almost like a realm of fiction or an ideal or mental realm. That is a very good question.
The second argument that we want to go to is independent of the first one. Maybe you are not convinced by the first argument, and you think that there can be an actually infinite number of things. The second argument is based upon the impossibility of forming a collection of an actually infinite number of things by adding one member after another. We can present this argument also very simply.
1. A collection formed by adding one member after another cannot be actually infinite.
2. The series of past events is a collection formed by adding one member after another.
3. Therefore, the series of past events cannot be actually infinite.
This is a logically valid argument. That is to say, the conclusion (3) follows from the two premises by the rules of logic. The only question is, therefore, are the two premises true? If the two premises are true then the conclusion necessarily follows by the rules of logic. So are the two premises true?
The first one says that a collection formed by adding one member after another cannot be actually infinite. Sometimes this was called by the medieval philosophers “the impossibility of counting to infinity,” or other times it was called “the impossibility of traversing (or crossing) the infinite.” Think about it. No matter how high you count, you can never reach infinity because you can always add one more before you get there. You can never cross an infinite distance because you can always take one more step. So the idea of forming an infinite collection by adding one member at a time would seem to be impossible.
Somebody might say, Wait a minute! Maybe we can form an infinite collection by never beginning but ending at a certain point. That is to say, you form it by never having a starting point, just having always done it, and then you end at a certain point. In that way you form an infinite collection by adding one member after another. But when you think about it, this seems even more absurd and impossible than counting to infinity. If you can’t count to infinity, how can you count down from infinity? That would be like someone claiming to have counted down from all of the negative numbers: -3, -2, -1, 0! Phew! I finally finished. Such a task seems absurd. Before he can count any number there would always be another number he would have had to have counted first. Before he could count -2 he would have had to have counted -3. But before he could count that, he would have had to count -4. And so on and so forth. It seems like you are never able to count any number because there will always be an infinite number of numbers prior to that that you would have had to have counted first. Think about traversing the infinite. If you can’t cross the infinite by running in one direction, how could you have crossed it simply by running in the other direction? It doesn’t seem to make any sense.
When you think about it, indeed the formation of an actual infinite by adding one member after another does lead to all sorts of really bizarre sorts of paradoxes. Let me just mention one of these that Bertrand Russell mentions in one of his books. He mentions a character by the name of Tristram Shandy, who in the novel by Sterne writes his autobiography so slowly that it takes him a whole year to record the events of a single day. Tristram Shandy says, At this rate I’ll never finish my autobiography. Because every [day] of living generates another year of writing because he writes so slow it takes him a year to write the events of one day. So the longer he lives the more writing is accumulating. Russell says, Wait a minute! That conclusion doesn’t follow. If Tristram Shandy will live forever (if he were immortal) then the number of years that he will live and the number of days he will live are equal and therefore he should be able to write all of his autobiography even though the longer he writes the longer he falls behind. When you think about it, that is surely crazy – that seems perverse – because the longer Tristram Shady writes the farther behind he falls. For every year that he is writing, that means there has been 365 [days] of living, so the more he goes on the farther and farther behind he falls. Rather than approaching a state at which his autobiography would be finished, he would approach a state in which he would actually be infinitely far behind on his autobiography. The longer he goes on the farther behind he falls approaching a limit at which he would be infinitely far behind in his autobiography.
It occurred to me as I thought about this situation that Russell was describing, what if you turn it around? Turn the story around. What if Tristram Shandy has been writing his autobiography from eternity past? In that case he will have lived and written for an infinite number of years and an infinite number of days. But when you think about it, Tristram Shandy will have described an infinite number of past days. But where would those days be? Let’s let this be the present (in 2006) and here is 2005 and 2004 going back in time. If it takes him a whole year to write down the events of a single day, the most recent day he can have recorded if this is the present will be a day one year ago – right? He cannot have recorded a day yesterday or three weeks ago because it takes him a whole year to record a day. So the most recent recordable day that Tristram Shandy could write about would be a day one year ago. But now suppose he has been writing for two years? Where is the most recent recordable day? It can’t be here because he wants to record consecutive days of his life – right? He doesn’t want to jump around. He wants them to be consecutive days. That means that that day couldn’t be recorded by him – it is going to be a day after a day two years ago. So if he has been writing two years the most recent recorded day would be the day right after a day two years ago. Similarly, if he has been writing for three years then it would be a day two days after three years ago. And so on and so forth. The longer he has been writing, the more the days that he can have recorded recede into the past. What if Tristram Shandy has been writing for infinite years? Where will be the days that he has recorded? Well, they will recede to infinity. In other words, they will be days infinitely distant from the present. But then that raises the question: how can you traverse the distance between an infinitely distant past day and the present day? Technically, to put it the right way: how could a day that was once present have receded to an infinite distance in the past? It is impossible. When you go back in the past, no matter how far back you go, you will never find the most recently recordable day – it will already be a day that will be in the infinitely distance past. But given that it is impossible to traverse an infinite distance, it would be impossible for Tristram Shandy to have done such a thing.
What this shows, I think, is that this task that Tristram Shandy has invited to do – namely, to write his autobiography from eternity past at the rate of one day per year of writing – is impossible. But there is nothing impossible about writing your autobiography slowly. The task itself is not inherently paradoxical. It is a perfectly coherent task; namely, write your autobiography so slowly that it takes you a year to record the events of a day. So the impossibility doesn’t lie in the task itself. It must therefore lie in the idea of an infinite past – of trying to do this infinitely – which I think shows again the idea of an infinite past is absurd. You cannot have an infinite past which has been formed by adding one day at a time.
Now an even deeper paradox, I think, bursts to the surface. Let’s suppose that Tristram Shandy is writing the biography of some other immortal person that has lived for an infinite number of years so that there isn’t any problem about the days being infinitely distant. Let’s suppose that he finishes the biography of this person in the year 2006. The person has lived for an infinite number of years and Tristram Shandy finishes his biography in January 1, 2006. The reason he is able to do that is because he had an infinite number of years to record about this biography – writing at, say, the rate of one day a year or whatever. If Tristram Shandy is able to finish the biography of this immortal person by 2006, why didn’t he finish it by January 1, 2005? By then an infinite amount of time had already elapsed. Indeed, the same amount of time as had elapsed in 2006 – it is just infinite. Or why didn’t he finish it in 2004? Or 2003? Why didn’t he finish it ten trillion years ago? By then an infinite amount of time had already elapsed – the biography should have already been completed. What this seems to imply is that no matter how far you go back into the past, you would never find Tristram Shandy finishing the biography, because he would have already been done. But if at no point in the past do you find him finishing the biography then it isn’t true that he has been writing from eternity as the hypothesis supposes. Once again I think you see the absurdity that is involved in trying to form an actually infinite collection of things by adding one member after another.
These illustrations, I think, simply serve to bring out in a dramatic way the impossibility of forming an actually infinite collection of things by adding one member at a time. If an actual infinite could exist (contrary to the first argument we looked at) it would have to just exist all at once. Just – boom! – and there it is. But you could never form it by adding one member at a time and hoping to complete the collection in that way.
Dr. Craig: [laughter] I was thinking about having you give the argument from two weeks ago. Honestly, I am quite serious about this. This is not a lot to memorize. All of us, I think, are intelligent people. We can memorize this. Then if you get into a conversation and you say there are good reasons to think the universe began to exist, and they ask what are they, then grab a napkin and write this out on it and see what they say. I think it is a good witnessing tool to get people to thinking about the beginning of the universe and the need for a Creator. I am not giving a test, but I would encourage you to think about it in those terms. Say, I am going to memorize this and be ready to share it with somebody.
Dr. Craig: That’s a fair question. I used the example here of writing as my example of the things that are in the past. But let’s just use the motions of an atomic clock. OK? Let that be our standard event. We are going to pick a standard event which would be the ticks of an atomic clock that measures a very precise duration and that we all use to set our clocks by. The idea would be – can there be an actually infinite number of ticks of the atomic clock prior to today? The argument would be no because you could never form an actually infinite number of these events by one occurring after another.
Dr. Craig: In a deductive argument, if the premises are true and the logic is valid then the conclusion must follow. That is why I said for someone to reject (3) you can’t just say I don’t like it or That doesn’t seem right to me. You’ve got to say which premise is false. Unless you can do that logic obliges you by the rules of logic to agree with (3).
Dr. Craig: There certainly have been responses to it in the literature. I mention some of these in my books. I always try to interact with critics. Like in the chapter of Reasonable Faith. Let me see if I can remember. Here we go. This is a very common response to this. This response is offered, for example, by J. L. Mackie of Oxford University who was a very prominent atheist during his lifetime, and then more recently by John Howard Sobel who is a professor at the University of Toronto and has written a massive book on theism. Both of them say this. They say that there is no problem with forming an infinite number of past events by adding one member after another because from any point in the past you pick it is always a finite distance to the present. There is no event in the past that is infinitely distant from the present. From every point in the past you pick to the present moment there is always a finite distance and therefore there is no problem in traversing the infinite past. The problem with this objection – it seems to me is so obvious – is this commits what is called the fallacy of composition. The fallacy of composition is reasoning from the properties of a part to saying therefore it is the property of the whole. For example, because every part of an elephant is light in weight, therefore the elephant is light in weight. That commits the fallacy of composition. If you break up an elephant into little bitty bits, every piece of it is light in weight, therefore the whole elephant is light in weight. That is obviously fallacious. Similarly here, it is true every finite part of the past is only a finite distance to the present, and you can traverse any finite part of the past, but that doesn’t in any way imply that therefore the whole infinite past can be traversed. The question isn’t how can any finite part of the past be traversed. The question is how can the whole infinite past be traversed. To think that because every finite part of it can be traversed the whole can be traversed commits the fallacy of composition. It is just like reasoning that every part of the elephant is light therefore the whole elephant is light. That is, I think, the most common response to this argument. Yet, to me at least, it just seems obviously fallacious.
Dr. Craig: He asks, “How would this apply to an infinite God?” When we talk about the concept of actual infinity, we are talking about a quantitative concept. That is to say it is a mathematical concept having to do with a number of definite and discrete parts. But when we talk about God as infinite, we are not using this as a quantitative concept. God is not a collection made up of definite and discrete parts which are infinite in number. If you will, the infinity of God is a qualitative concept, not quantitative. When you think about it, what do we mean when we say God is infinite? What we mean is that God is necessary, perfectly holy, omnipotent, omniscient, omnipresent, eternal, self-existent. All of these superlative attributes that go to make up the infinity of God. None of those are quantitative concepts. The argument simply doesn’t apply to God. God is not a collection formed or is any kind of a collection really.
Dr. Craig: Actually, I think that is true. I think he has done a limited number of things in the sense that I don’t think God was doing anything prior to creation. We talked about this, I think, a couple of weeks ago. St. Augustine was asked the question, “What was God doing prior to creation?” He said, “We shouldn't tell the skeptic the answer is he was preparing hell for those that pry into mysteries.” Augustine said rather there isn’t any moment prior to creation because time begins at creation. So God beyond time isn’t doing anything in the sense of discrete acts that you can count and number. God is in a changeless, timeless state of perfection. He only begins to do things when time comes into existence at the moment of creation, and time is finite on the Christian view. It had a beginning.
Dr. Craig: That is right. People very often think of infinity in the future direction. But when it comes to questions like “Where did everything come from?”, “Why are we here?”, “Where did the universe come from?” there you are talking about the past and you have to face this question – did everything have a beginning or is the past infinite? What I’ve been trying to share with you are these arguments developed by these different medieval philosophers against the infinity of the past.
In response to what someone said a moment ago, I understand that many people don’t like these philosophical arguments; they are too abstract for them. But what is really amazing is that during the 20th century in a development totally unexpected by science there has emerged powerful empirical evidence for thinking that time and the universe had a beginning – that the universe actually came into existence around 14 billion years ago or so. Next week I am going to begin to share that.
By way of concluding today, let me just say a word about premise (2) – the series of past events is a collection formed by adding one member after another. I think this is fairly obvious. The past didn’t exist whole and entire as a kind of block. Rather, the past was formed by one event occurring on the heels of another. The past and time is something that has “becoming” to it. Therefore it is something that is formed by the addition of one member after another. Therefore it can be misleading sometimes when we talk about the regress of events. What regresses in time are our thoughts. As we think back starting in the present into the past, our thoughts regress back into the past, but the series of events is progressing in time in the sense that with each passing moment new events are added to the series of past events.
It seems to me that premise (2) is clearly true – the past is a collection formed by adding one member after another, and given that anything formed by adding one member after another cannot be infinite, it follows therefore that the series of past events cannot be actually infinite but that it must be finite and therefore there must be a first event and a beginning of the universe.
That is the second philosophical argument that I wanted to share with you. I think it is a sound argument; I think it is a good one. I am persuaded on the basis of both of these that the past is finite and the universe had a beginning.
Next week I want to share with you a little bit about the scientific evidence for the origin of the universe that I think is equally exciting.
 Total Running Time: 29:43 (Copyright © 2008 William Lane Craig)