Does This Fix the Kalam Cosmological Argument?

KEVIN HARRIS: Trent Horn is a Catholic philosopher and apologist who defended you and the kalam against the Skydive Phil videos (to which you also responded, by the way^[1]). Trent has a podcast called “Council of Trent” and in it he says your name, and he says that your and James Sinclair's work on the kalam in the Blackwell Companion to Natural Theology is one of the best ever. However, he does offer what he thinks strengthens the kalam in a recent video, and he also cites Andrew Loke's work on the kalam. So, Bill, before we watch these video segments, let me ask: Did any of these suggestions of Trent Horn catch you by surprise?

DR. CRAIG: Not really. These are fairly familiar objections in the literature, and I have responded to them. The only one that was new to me was near the end – that paper-passing paradox which bears all the vestiges of Alexander Pruss. Very, very clever. And I enjoyed what he had to say about that. We'll show that to our viewers later on. But I appreciate his support. My only correction would be that he continues to perpetrate this baffling misunderstanding that I'm arguing that the existence of an actually infinite number of things is logically contradictory — which is not what I'm arguing. I'm arguing that it's metaphysically impossible, but not that there is some sort of a strict logical contradiction in the notion of an actually infinite number of things.

KEVIN HARRIS: We're going to skip some of the introductory remarks in the video, but Trent does mention that the view of time you often refer to (he calls it presentism) is not as popular as other current views of time and is therefore a potential weakness in the kalam. Any thoughts on that?

DR. CRAIG: Well, in fact philosophers are fairly evenly divided on the nature of time. The question is whether time is tensed or tenseless. The key factor here would be whether you believe that temporal becoming is an objective feature of reality or merely a subjective illusion of human consciousness. I hold to the view that temporal becoming is real and objective. As I say, philosophers are pretty much evenly divided on this. When I was doing my work on God and time, it occurred to me that for every person who holds to the tenseless theory of time I could think of at least two philosophers or physicists who hold to the tensed theory of time and are of comparable stature in the scholarly community. So by no means is the presupposition or assumption of a tensed view of time, I think, a weakness. Fortunately, the view that I defend is admitted by everybody in the debate to be the common sense view of time – that temporal becoming is real and not just illusory. In any case, I think that the tensed view of time is true. I have written two volumes in defense of this view of time: The Tensed View of Time: A Critical Examination and The Tenseless Theory of Time: A Critical Examination. So anyone who wants to criticize the kalam cosmological argument on the basis of its philosophy of time has got to interact with those two volumes or his critique will be superficial.

KEVIN HARRIS: Let's go then to the first clip. Here Trent has introduced your use of Hilbert's Hotel as an illustration, but talks about other thought experiments that you use. Then he begins to make his case for revisions. Let's check out clip number one.

TRENT HORN: Craig also uses infinite libraries and infinite collections of baseball cards, but they all make the same point: actual infinites are contradictory so they can't exist in the real world. One problem though is that even if these arguments work, they only show an actual infinite number of objects (like a collection of hotel rooms) can't exist at the same time, not that actual infinites can't exist at all. For example, imagine a Hilbert room, that the room has always existed, and at the start of every minute a small iron pellet pops into existence and vanishes one second later. By the present moment, this room would have held an actually infinite number of pellets. Each pellet would correspond to a negative number in the past. But nothing seems absurd about the Hilbert room because the pellets never existed together at the same time. Past events aren't like rooms at Hilbert's Hotel that all stick around to contradict each other. They seem more like appearing and disappearing iron pellets in a Hilbert room that don't cause any contradictions because they're never together at the same time. So even if Hilbert's Hotel can't exist, that doesn't prove an infinite past can't exist because an infinite past is not an actual infinite collection of objects at a certain moment of time like a hotel.

KEVIN HARRIS: Let's just get right to it. Comment on what he says.

DR. CRAIG: Oh, well, there's nothing about the simultaneous existence of the objects that is necessary for the absurdities. All that is necessary is that the objects are definite and discreet and can be counted and so add up to an actually infinite collection. Whether they exist simultaneously or not is as irrelevant as the color of the hotel or whether it's built out of bricks or concrete and mortar. There is an actually infinite number of iron pellets that have been produced in his thought experiment. We can do the same sort of thought experiments with them that we do with the hotel. If we consider all of the odd numbered pellets, for example, there are just as many odd-numbered pellets as there are in the whole collection of odd plus even numbered pellets. So it doesn't matter that they don't all exist simultaneously. In any case, what you can say is that suppose the pellets don't disappear? Suppose the pellets just pile up outside the hotel? By now, how many pellets will be out there? Well, there will be an actually infinite number of coexisting pellets. So this objection, I think, is not a serious objection to the impossibility of an actually infinite number of past events.

KEVIN HARRIS: Here's clip number two where Trent introduces the so-called symmetry objection. Let's go to that.

TRENT HORN: Another problem with Craig's argument is the symmetry objection. Basically if a beginningless past can't exist because it contains an actually infinite number of past events then an endless future can't exist either because it also contains an actually infinite number of future events. This objection has been made by philosophers like Wes Morriston and Alex Malpass. They show there is a symmetry between the arguments for a finite past and the arguments for a finite future. Even if you can prove the past must have a beginning, that same argument could be used to show the future must have an end, which isn't good for Christians who believe that heaven will be an endless existence with God. Craig's standard reply is that an endless future only has a potentially infinite number of events while a beginningless past has an actual infinite number of past events. The past will always have had an infinite number of past days, but the future approaches infinity as a limit and never reaches it. But Malpass has pointed out that Craig makes a mistake here in tenses. In an endless future there will never be a day number infinity. That's true. But the total number of days going forever forward on a timeline is the same as the total number of days going forever backward on a timeline: infinite. This is true even if there is no single moment in the future when someone notices an infinite number of days has elapsed. So Craig's argument faces a calamity. First, a beginningless past may not be an impossible actual infinite because past events don't all exist together at the same time. A beginningless past is infinite, but it's not an actual infinite collection of things. Second, any argument to show the past must have a beginning (because if it didn't it would be an impossible actual infinite) could be used to show the future must have an end so that it's not an actual infinite either. So how do we escape these objections? I believe that Craig was on the right track in arguing that the past cannot be infinite or beginningless because this leads to contradictions. Where he errs is that it is not the infinite past itself that is the contradiction or the thing that can't exist. An infinite past is not impossible in the same way an infinite hotel is impossible. Instead, an infinite past is impossible because it allows things like infinite hotels to exist that are impossible. The difference is subtle but important.

KEVIN HARRIS: The symmetry objection. I'm trying to understand several things here. How a timeline fits in the objection, and this subtle distinction that he's trying to make.

DR. CRAIG: Notice that he says that Malpass and Morriston show there is a symmetry between past and future. That's not true. That is exactly what they do not do. They simply assert that the past and the future are perfectly symmetrical. Here I think your philosophy of time becomes absolutely critical. On a tensed theory of time, according to which temporal becoming is real, future events in no sense exist. There are no events later than the present. The only events that actually exist are those that have transpired up until the present moment. So if the past is beginningless there will have occurred an actually infinite number of events prior to the present. But if the future is endless then the series of events will simply be potentially infinite. It would just keep growing and growing and growing but at no point will you have more than a finite number of events. Now, Malpass and Morriston say that there will be an actually infinite number of events. And that's, again, simply not true. There will never be an actually infinite number of events. The series of events will always be finite and always increasing. This asymmetry, I think, between the past and the future shows that the symmetry objection fails. Even though the past cannot be beginningless, that does not show that the future cannot be endless. Neither the past nor the future is actually infinite, but if the future is potentially infinite in that the series of events is potentially infinite then there's no problem in denying a beginningless past but affirming an endless future.

KEVIN HARRIS: This kept me up last night. I'm picturing something symmetrical. If an artist draws a picture of a bottle, he'll draw a vertical line that serves as the middle of a bottle, and in order for it to be symmetrical it has to be equal on both sides when he draws the bottle. Equal on both sides of the line. So I'm wondering where the middle of the timeline would be. Where's the midpoint on the eternal timeline that facilitates its being symmetrical?

DR. CRAIG: Well, in the case of the series of temporal events, the endpoint is constantly changing with the present moment, and therefore there is no fixed midpoint between the beginning and the present moment where the series comes to an end. The midpoint will be constantly changing as more and more events are added to the series.

KEVIN HARRIS: I will sleep better tonight. Thank you. In this next clip, Trent brings up time travel. Clip number three.

TRENT HORN: To make an analogy, imagine you want to show time travel into the past is impossible. You don't have to show the act of time travel is like a square circle. I mean, you can imagine going into the past being there for one nanosecond then returning to the present without causing any paradoxes. But you can't imagine a square circle. Likewise a critic of the kalam argument might say you can imagine every previous day having a previous day before that, and there's no contradiction that arises from that simple thought. In fact, the philosopher Arif Ahmed said something like that in his 2005 debate with Craig:

ARIF AHMED: That doesn't mean the notion of infinity is contradictory. It certainly doesn't mean the universe had to have a beginning. It's very easy to refute this part of Dr Craig's position. It could be true that before every event that took place there was another one. That makes perfectly good sense. And if it were true, there's no first event. There's nothing for God to cause. Let me repeat that. Every event follows another one. I hope Dr. Craig can tell us later on tonight which of those five words he doesn't understand.

TRENT HORN: But something can be impossible even if it seems possible at first. Time travel movies make it seem like you could go into the past and remain on the same timeline and return to the present. But if you stop to think about it, this can't happen. If you could be in the past for a nanosecond, could you be there for one second? How about 60 seconds? If you can displace the air in the past, could you displace other molecules? Could a gun that you brought displace air and then human tissue when you use it to kill your grandfather? If you could travel into the past and remain on the same timeline, what would stop you from doing something impossible like killing your grandfather before he met your grandmother? If you did that, you would never be born and then you would never go back in time to kill your grandfather, thus causing the famous grandfather paradox. That's why some philosophers say the best way to avoid these kinds of paradoxes is just to say that time travel into the past is impossible. We can make a similar move to strengthen the kalam argument. An infinite past is impossible not because the infinite past itself is impossible but because an infinite past would allow impossible things to happen. The argument could be formulated like this. (1) If the past were infinite, then contradictions would be possible. (2) Contradictions are not possible. (3) Therefore, the past is not infinite.

KEVIN HARRIS: The grandfather paradox. There's been a version of that in almost every popular time travel movie.

DR. CRAIG: Unfortunately, we're back here to square circles and contradictions which is not the kalam cosmological argument. I agree with Trent that the paradoxes of time travel do make huge problems for the metaphysical possibility of time travel. But time travel is metaphysically impossible for a much more fundamental reason, and that is once again related to the objectivity of temporal becoming and the tensed view of time. Namely, when the time traveler suddenly appears in the present, ask yourself: Where did he come from? Future events do not exist. There is no time machine from which the time traveler could have pulled the levers and entered our present moment. At the time that the time traveler appears in the present, he and the future time machine are nothing – they are unreal. Therefore, time travel on a tensed theory of time would involve something coming into being from nothing. Therefore, I think time travel is metaphysically impossible because of the tensed theory of time. As I say, the kalam cosmological argument as I defended is predicated upon such a tensed theory of time, and we've seen how that ruins the asymmetry objection as well.

KEVIN HARRIS: Next Trent brings up the effects of an infinite past versus the past events themselves. Clip number four.

TRENT HORN: In order to bring out the impossible effects of an infinite past, the philosopher Andrew Loke asks us to imagine a Hilbert's Hotel that is built at the rate of one room every year and that each room is equipped with a device that creates an immortal guest who then checks into the hotel. Oh, and if you think the whole Hilbert's Hotel thing is silly, it doesn't say anything about whether the past can be infinite, we can change the example to make it more realistic and boring. You could do something like imagining an indestructible iron pellet pops into existence once every 10 to the 500 years (that's a one followed by 500 zeros). In that amount of time you'd think anything could happen. Right? And if the past were infinite then in the present moment there would have been an infinite number of 1 in 10 to the 500 segments of time. And so in the present there would be an actual infinite number of indestructible iron pellets. But back to hotel rooms. They're more interesting to talk about. Under this view the objection that past events don't exist at the same time evaporates. We can point out that it's possible for the effects of all these past events to exist at the same time in the present even though the past events themselves never existed together in this way. By focusing on the effects of an infinite past, this answers the objection that an infinite past is not an actual infinite collection. The past itself may not be, but it can result in an actual infinite collection just as time travel can result in things like the grandfather paradox. To prevent both paradoxes it's best to conclude that the past cannot be infinite and you can't travel to the past from the present. Loke's modified version of Hilbert's Hotel preserves the essence of Craig's claims about the impossibility of an infinite past, but it escapes common objections to it by focusing on the impossible effects of the past rather than the past itself being impossible.

KEVIN HARRIS: We're getting to the crux of his podcast here. That is, the effects versus the events.

DR. CRAIG: Yes. In fact, Thomas Aquinas gave a very similar illustration to Trent's illustration of the iron pellets piling up. Thomas Aquinas talked about a blacksmith working from eternity past, and he periodically breaks his hammers as he's pounding in his blacksmith shop. Aquinas asks: If the smith has been working from eternity past, how many broken hammers will there be in the present? Well, there will be an actually infinite number of broken hammers. So this is very familiar to discussions of the kalam cosmological argument. There's no reason to have things disappear in the past. They can pile up in the present, and that makes it very clear that we're dealing with an actually infinite number of things.

KEVIN HARRIS: In this next clip Trent returns to the symmetry objection. Let's go to clip number five.

TRENT HORN: Next, by comparing the effects of an infinite past to the effects of an infinite future, we can avoid the symmetry objection. Even if the past, present, and future are all equally real, there is still a difference between the past and the future. Present effects exist because of past causes, not future causes. For example, if you started today and built one room of Hilbert's Hotel every year into an endless future, there would never be a time when an impossible Hilbert's Hotel exists. The Hotel would always have a finite number of rooms. This captures the essence of Craig's objection that an endless future is potentially infinite. It is potentially infinite if each moment involves actualizing something as part of a collection, like incrementally building a hotel. But paradoxically, if Hilbert's Hotel had been incrementally constructed in the same manner every year from an infinite past then at every point in the past there would be an infinite number of rooms that cannot exist, just as at every moment in an infinite past there are an infinite number of moments that precede every past moment. The symmetry is broken when we see that in classical causation, causation flows in one direction – from the past into the future.

KEVIN HARRIS: Does that answer it?

DR. CRAIG: I think here Trent is approaching very closely to my symmetry breaker between the past and the future; namely, the past is actualized whereas the future is purely potential. If someone has been building a hotel at the rate of one room per year then by the present moment there will be an actually infinite number of rooms in the hotel. But if he starts in the present building a hotel at one room per year, there will never be an actually infinite number of rooms. Instead you will just have a potentially infinite hotel that is at every point finite and always growing. Now, unfortunately what Trent says is, “Give up this tensed theory of time. Regard the past, present, and future as all equally real.” The difficulty is if you do that then why couldn't you have backward causation? When you look at those who defend the metaphysical possibility of backward causation and time travel they inevitably presuppose this tenseless view of time according to which past, present, and future are equally real and therefore future events can be causes of present events. And on the tenseless theory of time, Malpass and Morriston will still say there will be an actually infinite number of rooms if the future is endless. So I don't think that Trent is taking the right course here in appealing to a tenseless theory of time to try to escape the objection.

KEVIN HARRIS: Trent offers another improvement on the kalam involving the causal chain. Let's check out that clip number six.

TRENT HORN: Another way to improve Craig's argument would be to say that if the past were infinite then it could be possible for there to be an infinitely long causal chain. But philosophers like Rob Coons and Alex Pruss have shown that causal chains cannot be infinite. If they were infinite they, too, would yield contradictions. Imagine if instead of just reciting numbers for all eternity, our eternal counter wrote each negative number down on a separate sheet of paper God made for him in that moment. In the present moment when his countdown is finished there will be an actual infinite number of papers each with a different negative number on it. This would be similar to Loke's example involving Hilbert's Hotel and how an infinite past creates an actual infinite collection. And, like Hilbert's Hotel, you can modify the example to make it more mundane. The point is just to show that a certain kind of causal sequence that requires every member to act only when a previous member acts but also has no first member always causes a contradiction. But let's change the example slightly. Each person in the line receives a piece of paper from the person on their left. If the paper is blank, they write their name on it. If the paper already has a name on it, they then pass the paper on to the next person. Eventually the paper reaches Mr. Zero. Now, here's the question: What number is written on the paper Mr. Zero received? There has to be some number written on the paper because if it were blank then Mr. Negative One would have written his name on the paper. But the paper could not have been blank when Mr. Negative One got it because Mr. Negative Two would have written his name on the paper, and so on. We end up with a piece of paper that arrives in the present that must have some number on it but it cannot have any particular number written on it, which of course leads to a contradiction. But it seems that you can have causal chains where each member pauses until another one acts. The impossible element we should reject then is the claim that there could ever be no first member, but then we have to reject an infinite past because it would contain causal chains without first members or infinite chains. So once again we're back to the modified kalam argument. It would go like this. (1) If the past were infinite then contradictions like infinite causal chains would be possible. (2) Contradictions like infinite causal chains are not possible. (3) Therefore, the past is not infinite.

KEVIN HARRIS: We've talked about various illustrations and thought experiments. What about the causal chain?

DR. CRAIG: This is the paper-passing paradox that I referred to at the beginning of our discussion. I think this is a wonderful illustration that I'd never heard before, but it is of the same type as the more well-known Grim Reaper Paradox which imagines a series of grim reapers each of whom will swing his scythe and strike you dead if you're not already dead by then. It turns out that you can be neither dead nor alive, just as here the piece of paper can neither be blank nor have any number on it. I think these are great illustrations that show the absurdity of an actually infinite temporal regress of events.

KEVIN HARRIS: We have one more clip, and this is a compilation of how Trent started and ended this particular podcast. Let's go to it.

TRENT HORN: One of the people who helped me convert from deism (belief in a generic creator God) to Christianity was the Protestant philosopher and theologian William Lane Craig. He's also been a role model to me for how to do apologetics because Craig embodies the rare combination of someone who is well-read in philosophy, science, history, theology, can communicate those ideas in a winsome way, and defend them in a debate by being quick on his feet. I do want to thank William Lane Craig for all the work that he has done in this area, how he's modeled to present this argument with those who disagree with him, and personally all the work that he has done for me to lead me to faith in Christ and model for me how to be a good Christian apologist.

KEVIN HARRIS: Quite a compliment there, Bill! In conclusion, will you sum up these revisions that Trent has offered?

DR. CRAIG: Yes. What Trent says is that we should focus on the way in which an infinite regress of past events would imply the possibility of a simultaneously existing, actually infinite number of things today. He also wants to say that the past and the future are in some way asymmetrical so that the impossibility of a beginningless past does not imply the impossibility of an endless future.^[2]