We are finishing up the Cosmological Arguments with this series, this new series that's upon us. We are looking at the Kalam Cosmological Argument. We've just finished the Thomistic Cosmological Argument. I think I counted, we had seven lectures on that, and that cashes out to somewhere between 12 and 14 hours of lectures on just the Thomistic argument, going through the argument itself, and then looking at all of the objections to that argument. What that shows me is that the ontological argument and the Thomistic argument give us two things. First of all, they give us, in my opinion, the way I see it, undeniability with respect to God's existence. And that's true even if the universe has always been here. So if the universe is just, if we were to go in a time machine and go try to reach a first moment of time, we would never reach it, because the universe is just eternal. And this is an important point, I guess for one or two reasons. One, even if you demonstrated to my satisfaction that the universe is eternal, you wouldn't demonstrate to my satisfaction thereby that God doesn't exist. What would you demonstrate? Well, I do think you would demonstrate one thing. You would demonstrate that Christianity, Judaism, Islam, the Abrahamic religions are false. And the reason is because all three of those faiths insist that God brought the universe into existence from nothing. So in proving that the universe is eternal, you don't disprove God's existence, but you do disprove the Abrahamic religions, if that makes any sense. So you would still have a God much like the God described by the Abrahamic religions existing, but you wouldn't have a God who reveals himself through the Abrahamic traditions. Now, how did Thomas Aquinas deal with this? Because if you'll remember, he himself said that the universe cannot be proven to have had a beginning. So he argued that God exists on the assumption that the universe is eternal. In his day, In his day, there were individuals that were arguing the universe did not have a beginning. These were the people that followed Aristotle. Aristotelian philosophy starts on the assumption that the universe has always been here. And so what the Muslims and what some Christians, we would call them liberals, in Thomas' day, what they would do is they would take Aristotle's arguments and try to show that the universe has always existed. And so what Thomas did is he used reason to rebut those arguments. He would say you have to accept by faith that the universe is eternal, and what reason can do is reason can refute or rebut arguments that are thrown at the Christian doctrine or the biblical doctrine that the universe had an absolute origin. So that's how he handled it. That's how he reconciled his faith and his reason with respect to the origin of the universe. Several hundred years before Aquinas came on the scene, there were individuals arguing that you could actually use Aristotle against himself. You could actually demonstrate that the universe had a beginning. And so they offered philosophical arguments for that premise. And that's what we're gonna talk about today. What happened is a man by the name of John Philoponus, who is actually flourishing around the time that Muhammad is born and Muhammad is a little boy, a little prophet to be. He is arguing, he argues that the universe had a beginning. And there were Muslims that actually read his material. And they began to adapt and shape his arguments. And so they ended up creating a school of thought that we call the Kalam School of Thought. And the Kalam School, the most famous of these is Al-Ghazali. The Kalam School was a school of thought within Islam that argued for an absolute origin of the universe. John Philoponus was a Christian, then the Muslims came along and took his argument and developed it. And there were Christians after the Mutakallim had begun to flourish who took their argument and brought it back into Christianity. So Bonaventura, who was a contemporary of Aquinas, gave arguments to the effect that the universe had a beginning. Thomas Aquinas was aware of the Kalam argument. He rejected it. He thought it was unsound. But this argument has survived. You can actually see versions of it in Francis Turretin, the famous reformed theologian of the 17th century. But the person that has really made the argument, given sort of the strongest case for it, is the greatest living defender of Christianity today, and his name is William Lane Craig. Craig wrote his dissertation in the 70s entitled The Kalam Cosmological Argument. In fact, he's the individual that actually gave this argument its name. He wrote a really good book entitled The Cosmological Argument from Plato to Leibniz. And if you've been reading along with what I've written, you have seen this work cited several times. And it was Craig's work, more clearly than any that I've ever read, that distinguished very clearly between sort of the three types of cosmological arguments that are out there. The Leibnizian one, the Thomistic one, and the Kalam one. And we looked at the Leibnizian argument. We've also looked at the Thomistic one, and we've given a rigorous defense of it. And now we're about to look at the Kalam argument. And we're going to be following the work of William Lane Craig very closely. I'm giving you my own sort of adaptation to it, but it's clearly dependent upon his work. He's not the only one. We have people like G.J. Witrow and Pamela Hubby and others. Another really good presentation of this argument is found in J.P. Moreland's book, Scaling the Secular City. And you'll see all of these works cited in my footnotes. But let's start off here, kind of getting back to where we were, getting oriented to our flow of the argument, and it's the first paragraph. I'm just gonna read some of what I've written here. Thomas, and this is our man in the cave, remember Thomas? Poor guy. Thomas, by simply reflecting on the undeniable fact of his contingent existence, must come to the conclusion that a supreme reality exists. To be sure, merely reflecting on the contingent facts of our world cannot bring one to the conclusion that the universe began to exist. For all Thomas knows, the dark world around him, including the chains that bind him in the present, have always been around. Even so, he can know one thing for sure, namely his present existence is currently being sustained by the supreme reality. But what if Thomas were to get help from another quarter? What if those who held him in chains were to finally un-muffle his ears, remove the blindfold from his eyes, and un-gag him? What if they were to come to him with a light, maybe a torch, allow his eyes to get adjusted to the new sensations? show him his chains, unbind him, and for the first time in his memory, offer him pure water and a full meal. What if they were to teach him to speak and to walk? What if they were to show him drawings in the cave which told stories of other humans who lived long ago? What if they were to teach him about history and time? That is, that every life is composed of a succession of events in time. And when one moment in time has elapsed, it is gone forever. Could not Thomas begin to see that there was a first moment of time? Would he not then see another way of knowing the supreme reality? If this is so, then our man in the cave would not merely look upon the supreme being as his sustainer. He would realize that ultimate reality is also his creator. Now, if you think about it, these two arguments together give you the basic function, if I can speak this way, of God, of God with respect to creation. What is God? Well, if you define God in terms of his function, he is the creator and sustainer of the universe. And so these two arguments can argue for God's existence independently, the Thomistic one and the Kalam one. But if you put them together, you actually get the biblical description of how God relates to the universe. He brought it into existence and continues to hold it in existence moment by moment. So this argument is sound. we have a very powerful apologetic for God's existence, as well as a complement to the other argument for God's existence that we've already looked at. And so this is where the cosmological argument comes in. And I've already told you about William Lane Craig. And if you flip the page over, the basic argument for the beginning of the universe goes as follows. Everything that begins to exist has a cause of its existence. The universe began to exist, and therefore the universe has a cause of its existence. Another way to construe the argument is as a series of disjunctions about the universe, the existence of which is taken as a given. So we assume that there is a universe. By the way, is that a bad assumption? Is that safe, you think? That there is a universe? I think it's a pretty safe assumption. All right. Well, you only have two options. It either began to exist or it didn't. So that curlicue there in front of the word beginning is not beginning. So there's either a beginning or not a beginning. And if it had a beginning, it is either caused or not caused. And if it is caused, then the cause of its beginning is either personal or not personal. And so the flow of the argument is to try to argue for a personal transcendent cause of the universe. And again, if you were to ask the typical Abrahamic theist who is biblically informed, what are the two basic attributes of the biblical God that distinguishes him from all others? One is that God is personal, and one is that God is transcendent. And so you have a strong argument for God's existence here. So on page 273, we have my version of the Kalam cosmological argument. And you'll notice that at some point in the argument, it dovetails and looks a lot like the Thomistic one. Because what you end up doing is you end up proving the existence of a being who has the same attributes as the being proven in the Thomistic argument. So here's the argument. Whatever begins to exist requires a cause for its coming into existence. Premise two, or premise B, the universe began to exist. Therefore, the universe required a cause for its coming into existence. Now, let's say that we've proven that so far. We've established that. Naturalism is now destroyed. Because what you've proven is that there's something beyond the universe. You've proven that what Carl Sagan said is false. The cosmos is all there ever is, was, or will be. By showing that there's a cause of the universe, you're showing that there's something beyond the universe. I met with the president of the Albany Atheist Society several years ago. And for some reason, I had a really hard time convincing, you know, explaining that logic to him. He goes, well, how do you know it's beyond the universe? I said, because it's the cause of the universe. If it's the cause of the universe, then it has to be beyond the universe. I mean, isn't that clear? I don't know how else to say it. If the universe doesn't exist and there's a cause of the universe, And that brought the universe into existence. And obviously, there's something beyond the universe that's not the universe. Go ahead. Right, and we make actually this very explicit in the next couple of premises. So the next premise is the cause of the universe was not caused to come into existence, and the cause of the universe was not self-created or self-caused. Why? Because you can't exist before you exist. The cause of the universe is uncreated, therefore, or uncaused. And the uncaused cause of the universe is coming into existence. And notice what we have here. We have basically the same attributes of the God of the Kalam argument that we established with the God of the Thomistic argument. This cause is eternal, necessary, immutable, unlimited, independent, one, omnipresent, immaterial, omnipotent, omniscient, omnibenevolent, and personal. The uncaused cause greatly resembles the God of classical monotheism and therefore a God much like the one described by classical monotheism exists. Now of these arguments, excuse me, of these premises, which do you think is the most controversial? And let's not talk present day so much as historically. If I were to walk into Aristotle's Lyceum or Plato's Academy, which premise would be the most controversial? Number two, I would agree, number two. You all agree number two? You're exactly right. Aristotle would not dispute premise A. He would say whatever begins to exist requires a cause, obviously. That's obvious, and Plato says this explicitly in his Timaeus, his little story of creation. He says it in so many words, and the atheist philosopher Lucretius, the Roman atheist, said, out of nothing, nothing comes, ex nihilo, nihil fit. If there was once absolutely nothing, then there wouldn't be anything here now. Now this is why the atheist believes in an eternal universe. He believes in an eternal universe precisely because he knows that something can't come out of nothing. Right? And so obviously the disputed premise in this argument is B, the universe began to exist. And so you'll notice that that's the first premise I defend. I defend the second premise first. Now, I could have put B as A, and just said the universe began to exist, and then said whatever begins to exist. But for aesthetic reasons, I just think it sounds better to put it this way. Whatever begins to exist has a cause, and then the universe began to exist, therefore it has a cause. But you could have reversed those premises. But the point I'm making is, since this is the controversial premise, This is the one we need to analyze. Now, it turns out that we have two types of arguments for the beginning of the universe, philosophical and scientific. And so what we're doing today and in the weeks to come is we're actually transitioning from a purely philosophical apologetic for theism into science apologetics. So this is the first time we're actually going to look at scientific evidence. Now, you guys tell me, what's the good thing about getting into science apologetics, and what's the bad thing about getting into science apologetics? I think the good thing is that's where a lot of folks We live in a scientistic culture. And so most people, I quote Bill Murray from Ghostbusters, back off, man, I'm a scientist. Remember that? That's one of my all-time favorite quotes in any movie. OK, so science is the end all, be all. For many people, it's the paradigm of rationality. So if you're not scientifically informed, you're just an ignoramus. And therefore, having an apologetic that is not scientifically informed is the height of stupidity in our culture, in the minds of many people. I've obviously illustrated to you how I don't think that our case for God's existence need depend on any scientific argument. So that's the first thing. We have a culture that is screaming out for this kind of information, and therefore, at least in terms of persuasive value, a lot of people are not going to trudge through the Thomistic argument. And they're darn sure not going to trudge through the ontological argument. But they may have truck with this argument, and I'll just go ahead and give you a little piece of my testimony. This is my first foot forward whenever I argue for God's existence with the average person on the street. He's like, you're waiting till now to present us with your first foot forward out on the street? Yes, because what is true logically and what you do academically is not necessarily what you do when you're just out on the street talking to people. In fact, when I was talking to this atheist at, you know, we were at the Harvest Moon eating, and when I was, yeah, great place. When we were having our dinner and talking about these issues, I don't think I once raised the issue of Thomas Aquinas' argument. I don't think I once raised the issue of the ontological argument. My first foot forward was this argument. Why? Because it's scientifically informed. Is there another good thing about the scientific apologetics? I mean, is there another good thing about bringing science into this equation and making our case for God's existence? I think so. People are going to be a lot more familiar with the scientific arguments than they will, like you said, the ontological arguments. Sure, yeah. Or the Thomistic arguments. You ask the average person that and they're not even going to know who or what it is. Sure, sure. But, you know, if you ask them questions about, you know, were the dinosaurs here first? How is the Bible historically accurate in light of all of this data that is out there? I think that in the information age you can find all the science you want. some of it true, some of it questionable. But I think one of the things I've always said is you have to talk to people where they're at, not necessarily where you're at. And to make those arguments. And then bring it to this one. Is it because it's centered so much on actual evidence that people I think so. So the good thing about science is that you have piles of evidence, of data, a collection of experiments, and all this material that's, in other words, that's available. That's kind of what Ben was saying. It's here. It's available. So it's something to grasp onto in thinking about these rational but philosophical A lot of people would look at the ontological argument and say, this is just a sheer abstraction. I'm persuaded by it, but I also recognize if I'm having a 15-minute conversation with somebody, do I really want to get into the concept of a greatest conceivable being? and start unpacking what that means, it's better to appeal to facts. My Greek professor, Dan Walsh, used to always say to us that an ounce of evidence is worth a pound of presumption. And with scientific arguments, you are appealing to facts, facts of our world. And this is going to therefore be the first hopefully not the last, concrete, genuinely concrete argument for God's existence. The contingency argument is concrete in the sense that you're appealing to a fact, namely that I am a contingent being. Right? And so it reasons from that fact to God's existence. But this is appealing to scientifically verifiable facts. We hope to show that the science demonstrates that the universe had a beginning. I'll say one more thing in favor of the science. I think science works, and I think science is a good way to arrive at the truth. I am not a scientist in the sense that I embrace Well, first of all, I'm not a scientist in the sense that I'm not a professional scientist. I don't have a degree in science. I didn't really do well in science classes in high school and college. I mean, I certainly didn't excel in them. And so I am a layman when it comes to science. But I fully embrace scientific evidence without embracing the philosophy of scientism. I wish scientism was not a word because the proper nomenclature to describe a person who embraces scientism is scientist. But we use that word for all kinds of people who don't embrace the philosophy of scientism. Y'all know what scientism is, right? It's the view that science is the sole paradigm of what it means to be rational. And so there are scientists out there and philosophers of science who not only think science is a great way of knowing the truth, but they think that it's the only way to know the truth. And therefore, all of the things that I've said in this course, from the beginning of Deltan Xiong to this moment, is irrelevant. Why? Because it's not scientifically informed. Now, The advantage that the domestic argument has over the argument as we're presenting it here is that the domestic argument is an argument I could have given to Aristotle. If you were to take me and transform me back in time, let me brush up on my Greek a little bit so I could talk to him. I could sit down with him and walk him through this argument and it would not be contingent upon, pardon the pun, it would not be dependent upon some modern scientifically verifiable fact to get through. Does that make sense? I can appeal to just him and his experience right where he is, and I don't have to worry about scientific information with the Thomistic argument. With this argument, I do. And that's good because we want a scientifically informed argument. But the disadvantage is that you, the person who's thinking through this argument, you're going to have to bone up on your scientific literacy. I mean, you're going to have to really become informed about what the scientists are saying. That's a challenge. And that's a good thing. But it's a challenge, nevertheless. You wanted to say something? I was going to say, in terms of what OK, you want to transition into a bad thing about? Well, I'm not sure if we've done good things yet or not. Well, my little point about going back and talking to Aristotle is that's an advantage that the domestic argument has over this one. The first bad thing about this argument, the first drawback to this argument, is that precisely because it is scientifically informed, the strength of the premise, the second premise on the universe's beginning, the strength of that premise is contingent upon the current status, the current consensus of scientists. So let's say, I mean, tomorrow they could discover something that totally debunks what we're establishing here today. In other words, scientific evidence is constantly changing. That's the nature of the game. And so all scientific conclusions are, in the nature of the case, rather provisional. You can say we've proven this scientifically, but for a scientist, that means that it's probable, not certain. It's more likely true than not, but not undeniable. And that's the first drawback of this approach. Yeah, go. And I think mine overlaps with yours a bit, which is that our science is defined by the limits of what humans currently understand and currently discover. Yes. I mean, science, taken from the Latin, literally just means knowledge. What we know is based on what we've been able to discern and observe thus far. Yes. confidence and boldness in people to say, oh, look how much we know. Conversely, if you look at it, you say, well, the fact that we have learned so much means that at different points in time when we've been confident that we know it all, we've been so very, very wrong. So what more will we know tomorrow than we know today? Exactly. Exactly. I agree with you 100%. Yes? You made the comment that scientism and those that look at that would totally So everything that you're doing, you seem to have a very similar parallel with making a process very clear with tests. So how is that not similar to science in a way? Because, I mean, the tests have been successful or they've failed. And in many cases, they've failed. Well, I appreciate that because I I think that, like let's say that you were talking to someone who embraced scientism and they had been patiently dealing with this, let's say that they had just been sitting in this course coming week in week out and engaging in these discussions. One thing I could do is say, picture what we've been doing up to this point, since you don't think that any of these arguments are of much value, picture what we've been doing up to this point as a testing of a hypothesis. And what we've been really looking at for the past six months is the coherency of it. I mean, it's extremely important that your hypothesis is internally coherent. And the idea that God exists and classical theism is true. Classical theism postulates a being of pure actuality who is infinite and personal. And we've been sort of testing that up to this point, testing its coherency. Now we're about to test it with facts. And scientists do that all the time with their hypotheses. The hypothesis first has to be internally consistent. And it has to be rational. It has to be something that could possibly explain the evidence before you. And that's an hypothesis. It doesn't translate into the realm of theory until you actually have it being something that explains the data better than all other competitors and actually makes future predictions about the way the world is going to work. Right? And then the next stage is law. We call this scientific theory now a law because it's just been proven beyond 99% or greater precision. So gravity is a law. The Big Bang is a theory. And I don't know. Something else. Go ahead. In science, in some of the studies that we did before, showed that it wasn't science embraced in philosophy. In other words, philosophy was sort of the mother of science. So to take science and compartmentalize and say we're going to have scientism and all the processes were still as one melting pot, right? Exactly. Yeah, I've explained in the past why I do not embrace scientism, and I guess it'll be good for me to review it right here. People like Lawrence Krauss or Is it DeGrasse Tyson? Neil DeGrasse Tyson. Neil DeGrasse Tyson. Are extremely bright gentlemen, great scientists, so on and so forth. But Einstein once said that the man of science is a poor philosopher. And they do, like Klaus does embrace scientism. That's his philosophy. And he's been pilloried for this. I mean, there have been people that have reviewed his work and they've pointed out to him just how flawed his understanding of philosophy is and how a good dose of philosophy would actually help his science. And it's precisely because of this, and it's what you're talking about. Every scientist that I've ever talked to, and this is way back in college, I had three of my roommates who were biology majors. And they hated the philosophy of science courses that they had to take. Why? Because they want to be in the lab doing the experiments. They don't want to be thinking about what is science, how does science work. They don't want to talk about all that stuff. They just want to do it. And that's commendable. They want to get out of their chairs Too many of us philosophers sit in our chairs all day. You need to get out and experience the sunshine and do your experiments and actually connect your ideas to real data. And that's commendable, what they want to do, but because they eschew the thinking part, the armchair part, which is an important first step, they don't understand the connections between philosophy and science. And as you just pointed out, philosophy is the mother of science. Without philosophy, there would have been no science. Philosophy asks the questions, and also philosophy sets up the presuppositions that make science possible. So for example, my belief that there's an external world cannot be proven scientifically. That's what science presupposes. My belief that the laws of logic connect with the data of experience cannot be proven scientifically. That's something I take to my scientific research. The idea that my senses are basically reliable. is, which is what science is absolutely, totally founded upon, that presupposition cannot be proven scientifically. Again, science presupposes that. Science presupposes an entire network of presuppositions that are philosophical in character, and therefore, on the face of it, scientism just cannot be a good and true philosophy. It's a bogus philosophy. That is not to say, of course, that science is bad. I'm promoting science, but it is to put science in its place. And I will say one more thing, and then we can get started on the actual argument. When we say that we're appealing to science in this argument, I don't want you to hear me wrong. I am not offering a scientific proof for God's existence. What I'm offering is a philosophical argument for God's existence that is scientifically informed. One of the premises in my argument for God's existence is informed by science. But that's not the same thing as saying that God's existence has been proven by science. Why? Because science, in the nature of the case studies, the natural. That's all it can do. It can't study anything beyond the natural because then that would be philosophy. That would not be science. And so science can only study the natural. So if you talk about anything beyond the natural, that's something that the scientists cannot comment on. This is why I'm not bothered by a scientist who doesn't really speculate all that much about the origin of the universe other than the fact that the universe had an origin. So if I run into a scientist who's never even given a thought as to what caused the universe, I'm perplexed on one level. I'm like, how can you not entertain the question, what caused the universe? But it doesn't bother me that in his peer-reviewed journal entry, he didn't really talk about God's existence. Why? Because he's a scientist, and all he can do is talk about the natural phenomena that he's describing. Does that make sense? But we're not just scientists. And the scientist is not just a scientist, he's a human. And so when he takes off his lab coat, and when he's not writing about explicitly scientific issues, I think it's very good to start asking about what are the implications of what you've discovered in the broader picture. And this is what the Kalam argument is trying to do. It's trying to show that there's something about these scientific discoveries that point us to something beyond the universe. Yes, but I guess I would have to say science is the study of causes within the universe, if you want to talk about that. Talk about it that way, yeah. Exactly. Well, yeah, to be more specific, it would be the, I guess the basis of science is that you observe natural phenomena, then you attempt to, by various hypotheses and testing, determine what the causes for those phenomena are. Right, yeah. If science is all about the study of natural phenomena, then how could you not be invested in trying to determine the cause of the arena for all those natural phenomena? Right. I would say this. Let's say that the scientific evidence pointed in favor of an eternal universe. Okay, let's entertain that. I would only have two arguments in my arsenal as far as traditional natural theology is concerned, right? I would have the domestic argument and the ontological argument. And I guess I couldn't blame the scientist so much for not asking the broader question in light of his research, because there would be nothing about his research that's pointing him in this direction. But as we're going to try to argue here, it's not that way. The scientific evidence is pointing us towards an origin of the universe, and that's why the question, where did the universe come from, screams out. In 1850, If I walk up to a scientist and say, where did the universe come from? The average scientist will say, well, it's just always been here. To ask where it came from begs the question. And he's right. If there's no evidence for an origin of the universe, then you're begging the question by saying, where did the universe come from? Right? But in 1950, things had changed. I will say one more thing. Yeah, go ahead. Yeah, well, the main negative about using science is that the scientific evidence could change tomorrow. So with this argument, you're not getting, yeah, so I guess maybe to finish my point about the negatives in using science in an argument, because the science can change, you're not getting certainty or undeniability in this argument. So this is not only the first scientifically informed argument for God's existence, it's the first argument we're looking at that does not give you undeniability, it does not give you certainty. Why? Because the strength of the second premise is dependent upon the evidence that we're giving for it, and since the evidence itself is probabilistic in character, you can't say you know the conclusion with certainty. I don't claim that for the domestic argument. For the domestic argument, I know absolutely, I know undeniably that I'm a contingent being. And from there, I just know that there's an uncaused cause sustaining me. Here, I don't know with absolute certainty the universe began to exist. And so I'm not gonna know the conclusion with absolute certainty. Now you'll remember at the end of Velton Chong, we had two basic tests for a worldview, combinationalism and then we had incontrovertibleism. And I use incontrovertibleism because combinationalism doesn't work. But I said having established our worldview in a broad sense, you can actually start using the combinational test. And so what I would say to those of you who are already theists, it's not so much that we're proving God's existence, it is that we're actually learning something new about God's existence through this argument. We're learning that God is not only our sustainer, but he's our creator. And it's perfectly legitimate within the context of a worldview to use probabilistic reasoning. So does the Kalam argument presuppose God's existence? Well, in a lot of ways it does, right? Okay, how we doing? And if the atheist gets mad at me there, I say, well, yeah, but your getting mad at me itself presupposes God's existence, because I have another thing called the transcendental argument that I can use. We have all kinds of arguments now that we're, remember I told you early on, this is like a snowball. And we're on something like our 10th argument right now. So we already have a lot of arguments in our arsenal. that we can just use whenever we see fit. It's kind of like you're being trained to be Green Berets. And you have arrows, you have grenades. You got a nuclear weapon with you, the transcendental argument. You have all kinds of weapons at your disposal that you can use in these encounters. And here's one more thing I'm going to say to you. We not only have scientific evidence of the origin of the universe, we have philosophical evidence. So remember I told you in 1850, if I were talking with them, I wouldn't have any scientific evidence for an origin of the universe? Well, I would have philosophical evidence. Now, this philosophical evidence was not greatly persuasive. But I will say, just as a piece of testimony, I've always been persuaded by these philosophical arguments. So you're going to have to be a little bit more patient with me. And we're not going to get into the science first. We're going to get into the philosophical arguments. And so what we're going to look at is two philosophical arguments for the origin of the universe. And then we're gonna look at the scientific evidence for the origin of the universe. And so this is gonna be where our philosophy transitions into science. Does that make sense? We're never gonna leave philosophy, obviously, but in terms of establishing the second premise, this is the first time you're gonna actually see scientific evidence, but not until after you see some philosophical evidence. So let's look at the philosophical arguments for the, origin of the universe or the beginning of the universe. And I'll read some of what I've written here. The basic arguments for the beginning of the cosmos have been with us at least since the day of John Philoponus, who seems to be the first philosopher to ever offer a serious philosophical critique of Aristotle's doctrine of an eternal universe. These arguments were then developed by several medieval thinkers, Muslim theologians like al-Ghazali and al-Kindi, Jewish theologians such as Sa'adiyya Gaon, and Christian theologians like Bonaventure and then later Francis Turretin. Although I will say that Turretin's development of the argument is not explicitly along these lines, it's very similar to it. A number of modern philosophers have developed the Klum argument, most notably G.J. Whitrow, Pamela Hubby, J.P. Moreland, but really the main person is William Lane Craig. I cannot underestimate or overstate what a, I cannot, what I meant to say is I cannot overstate what a treasure this man is for the Christian community at large. And I always get nervous when, I mean, I know conservative theologians have actually said that he's dangerous. I will never understand that this man is, He is an expert in so many fields of inquiry. He is a scholar of scholars. We're talking about a guy who has probably at this point 150 peer-reviewed journal entries. Peer-reviewed. Not to mention extremely dense scholarly tomes on all of these issues. So he's just, he's the greatest living defender of the Christian faith today. I don't think there, I just don't think that that's a deniable proposition. What is the significance of a peer-reviewed journal entry? I mean, I get it, it's peer-reviewed, but what is, I mean, what's better than just publishing a book through? If I write an essay and I have it published in Newsweek The editors at Newsweek obviously review it and determine whether it's relevant to whatever they're doing and they publish it. But that's not peer-reviewed. The editors at Newsweek are not experts in the field of inquiry that I'm maybe addressing. And so they themselves don't really have the training it takes to evaluate the arguments contained in the essay. A peer-reviewed journal entry would be a journal entry where the reviewers, they call them referees, the referee will determine whether these arguments, first of all, are even coherent, and second of all, are making a genuine contribution to a current discussion in philosophy, theology, or whatever it is you're talking about. And there are all kinds of rules you have to follow. So you may have at least one referee and probably two or more referees. And then what also happens is that if it's submitted in that peer-reviewed journal entry, other scholars are going to be reading it, and then they themselves are going to be responding to you. So to say that this essay is peer-reviewed means it's passed a major test academic inquiry and it's extremely important that the peer review process is maintained. I don't want to have any test that I call the most major because, you know, just because you do submit something in a peer-reviewed entry does not mean that you're right. It doesn't mean that it's not debatable. You know, everything that we're talking about is debatable. There are very few things out there that are not debatable. And you usually don't write peer-reviewed journal entries to defend those things because most people just take them for granted. I don't think I'd ever read, I don't think I'd bother reading an essay trying to prove to me that the universe exists. But I would read an essay arguing that the universe began to exist even though I've read, I don't know how many essays I've read on that topic up to this point. I just don't know. But I also know that we don't know that with absolute certainty. So I would be interested in reading a journal entry arguing that. I would also be interested in reading a journal entry arguing that the universe did not begin to exist. And the peer review process is also important because If you're reading a book and it's published by Oxford or Rutledge or Yale University Press or any other press where a peer review process has taken place. then you can at least know that you're getting a good informed idea as to how things are. And usually, even if you disagree with the conclusions of the book or the essay you're reading, you at least can walk away from it informed and you can actually take something with you. In other words, you'll benefit from it. So William Lane Craig has written things that I disagree with. in peer-reviewed journals, and I've walked away from it benefiting from it because it's been peer-reviewed, it's high-end scholarship. And therefore, beware of the book that's been published off of some press, and you're like, who is this publisher? Who are the people that read this? Who vetted this before it was published? If it's just some guy, and he publishes, and it's a self-publication, Okay, it still may be a great book, don't get me wrong, but your antennas have to go up. Did he submit this to another press? Did he get rejected? You know? Just because something is published in a high-end press, that doesn't mean that it's a good book. And just because something is self-published, doesn't mean it's a bad book. But as a general rule, you need to be wary of the person. Maybe this guy just couldn't get an audience and so he produced a masterpiece and it's self-published, right? Or maybe it's just not good at all. I know for a fact that if I'm reading something that's self-published, it may not be worth the paper it's written on. I know that that's a distinct possibility. If I read something from Oxford University Press, it still may not be that great of a work, but it's not going to be just a horrible piece of literature. It's kind of a guarantee. It's a guarantee that what I'm getting is a well-thought-out tome, however wrong it may be at the end of the day. And that's why that's important. All the Princeton University Press, all your major universities, when we think smart, we think Harvard, right? So anything coming out of Harvard University Press, we're going to say, OK, that at least has the stamp of scholarly credibility. Again, it could be wrong. I will say I have read books. from reputable publishers. And I'm like, how in the heck did this pass the review process? Because this is just not good. Anyway, moving on, William Lane Craig, I was praising him. And he is really the main person we're following, as I said before, in this argument. And here are the two philosophical arguments for the origin of the cosmos. and the two premises that we're going to be defending is this. First, it is impossible for an actually infinite number of things to exist. We're going to argue for that. And then second of all, even if an actually infinite number of things could exist, it is impossible to form such an infinite through successive addition. Okay. Now some of you are like, Okay, great. How is that relevant to anything? Well, we're going to try to explain that, but before you can really understand the relevance of what I just said, you have to know what an actual infinity is. What is an actual infinity? The problem arose long ago in the days of Zeno. And we have one person here who was with me as we went through all the worldviews. And we have Parmenides, right? And then his, His student was named Zeno. And so who's the Zeno fellow? Well, Zeno tried to prove what Parmenides had taught. He was picking up what Parmenides put down. Parmenides said that change is an illusion. Parmenides was a pantheist. And so he said, well, change is an illusion. Well, many of us look at that and we're like, that just can't be so, because look what I just did here. I moved from one place to another. I'm changing constantly right here. Well, what Zeno did is he actually created certain, or he noted certain paradoxes that exist, which he thought proved that change is an illusion. He said, pick any distance between two points. So how about the distance between me and that clock over there? Now, where do I have to arrive before I arrive at the clock? Halfway point. All right. You know where this is going? So where do I have to arrive before I get to that halfway point? halfway there, and then we're going to have to go halfway there, and halfway there, and halfway there, and halfway there. In other words, I can divide the division of points of movement is infinite. Now, it's impossible to traverse an infinite, right? Because if there's an infinite distance between me and the clock, I'm not going to reach the clock. There's an infinite distance between me and that clock. I just proved it through that process of division, right? So I can't get to the clock. But I do get to the clock, and that's why we call this a paradox. And so what is the resolution of the paradox if you're a Parmenidean? Well, it's all an illusion. The change is illusory. Trust the math. Right? Trust the rational process that we just used to stop trusting your experience. Follow Obi-Wan Kenobi to Luke Skywalker. Your senses can deceive you. Don't trust them. Right? That's a pantheistic way of thinking. Now, Aristotle comes along. And he pointed out that all you have to do to demonstrate or to get around these paradoxes is make a very simple distinction that arises from common sense. There's a distinction between a potential and an actual. Right? And so you'll remember when we did a critique of pantheism and we looked at the argument for pantheism, I introduced this notion between the distinction between potentialities and actualities right there. Things can differ in their potential. Also, in terms of motion or movement, I would never say there's an infinite distance between me and the clock. I would say there's a potentially infinite distance. is potentially divisible infinitely. But that doesn't mean that actually speaking, there's an infinite distance between me and the clock. And because there's a finite distance, an actually finite distance between me and the clock, I can move from here to there. And I think Aristotle's resolution works, right? But that raises the issue, that raises a point, doesn't it? What is, first of all, the real difference between a potentially infinite and an actual infinite? And can actual infinities exist? Those are the two questions we want to raise. And I, on page 274, give you another example of a potential infinite. The example between a potential infinite would be my father's grandchildren. So we could call a set, we could actually give a label to a set. Now, my sister has 12 children. And I have one, so my grandfather, I'm sorry, my father is the grandfather of 13 grandchildren. And so we can call the set, Edgar Campbell's grandchildren, and we can also refer to the subset of that, we could create a subset of Edgar Campbell's grandchildren, namely Edgar Campbell's granddaughters. Are y'all following me? So let's think about the set, Edgar Campbell's grandchildren, and then its subset, Edgar Campbell's granddaughters. So here's the set. Edgar, Willie, Marty, Norma, Daisy, Campbell, Henry, Evan, Gray, Ashburn, Rose, Martha, and Jane. Okay. The subset, Edgar Campbell's granddaughters, would be Marty, Norma, Daisy, Campbell, Rose, Martha, and Jane. Now, what do you notice about the subset and the relationship to the set? Obviously, they're names that are repeated. Is there a one-to-one correspondence between every member of the subset and the members of the set? Nope. Just by looking at it, you know that Marty corresponds to Edgar, Norma to Willie, Daisy to Marty, Campbell to Norma, Rose to Daisy, et cetera. But you don't have a corresponding member of the subset corresponding to every member of the set. That's actually a good example of a potential infinity. In other words, the subset of a potential infinity, or the subset of an actually finite number of things, is always going to be less than the number in the set. Does that make sense? This is real basic for all of you, right? Well, the other point is this. Can this set be added to? Can we add to the members of Edgar Campbell's grandchildren? Sure. In fact, when I first wrote this, I wrote a paper on this in seminary. And I think there were six grandchildren at the time. See? Now there are 13. So the set has actually grown in my lifetime, or since I've been writing this. So that's another example of a finite set. It's potentially infinite, to which my father once said, you got that right. It's like, good Lord, how many children will she have? She actually gave birth to 12 children, no twins. We got a football team with a spare on the bench. We got a basketball team with cheerleaders. So it's finite and has the potential to go on forever. If my sister were eternal, if I were eternal, if we were immortal, we could potentially just add to this set forever, right? So do y'all see what a finite set is, what a potential infinite looks like? Does that make sense? Now contrast, this is on page 275, contrast the two examples of the potential infinities that I just gave. One was Zeno's example of the infinite division, right? And the other example was Edgar Campbell's grandchildren. Contrast these two examples of potential infinities with an actual infinite. While there is only a potentially infinite distance between your house and the car you drive, imagine what it would be like if that distance was in fact actually infinite. It would be ridiculous to try to get to your car for every time you took a step in an attempt to reach your automobile, there would still be an infinite distance for you to walk. One step forward, two steps back. It's one step forward, two or three steps back, right? That's me. Can I ask you a question? Yeah, go ahead. I'm just understanding how it's potentially infinite when you take into consideration I understand, yeah. You've got to have some presumptions there. We're still in the conceptual realm a little bit. So I know that these arguments are still a little bit abstract. You and I both know that my sister or me, we cannot reproduce forever. So we're not even potentially able to reproduce forever. But we're just saying hypothetically, if we were immortal, we could just keep adding to the set. We could add to the set of Edgar Campbell's grandchildren. So, but y'all see, the actual infinite, if there's an actual infinite distance between me and the clock or me and my car that I drive or whatever, I can't get to the car. Are y'all following that? Also, whereas the members of a potentially infinite set do not have a one-to-one correspondence with the members of a subset, the set Edgar Campbell's grandchildren is always going to be greater than the subset, Edgar Campbell's granddaughters. The members of an actually infinite set do. For example, compare a set containing all natural numbers with a subset containing all even numbers. You know, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 4, 6, 8, 10, 12, et cetera. The notice that the subset of natural numbers that are even you can create a one-to-one correspondence between the subset and its set. Does that make sense? Well, if you look at set B, set B says 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and then the dot, dot, dot means we could just stretch that out forever. In the subset B, that's the subset of all the even numbers. So 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. And you can stretch that out forever. So the members of the subset are equal to the members of the set. Because they're both infinite. Because they're both infinite. So in other words, one of the characteristics of an actual infinite is that its subset is equal to the set. Why? Because they're both actually infinite. All right, J.P. Moreland has given us three distinctives that characterize actual infinities. He says this, first, an actual infinity is a timeless totality which neither increases nor decreases in the number of members it contains. A proper subset or part of an actual infinite can be put in one-to-one correspondence with or be made equal to that actual infinite. This can contrast with a finite set where the whole is always greater than any of its proper parts. In addition, one can add or subtract many members from an actual infinite set and not change the number of the members of that set. So I have a question. Do you all know what an actual infinity is? You get this. As well as I can. I think so. OK. Here's my first argument for the origin of the universe. And it's based on the idea that it is impossible for an actually infinite number of things to exist. What we're going to argue is that actual infinities do not exist in reality. Okay? Here's the argument. An actual infinite cannot exist. The second premise is an infinite temporal regress of events is an actual infinite. Therefore, an infinite temporal regress of events cannot exist. Now, if the universe has always existed, then that means that there has been an infinite number of events that have existed. And infinite temporal regressive events have transpired. But we just said that actual infinities can exist. And therefore, if actual infinities cannot exist, the universe cannot consist of an actually infinite temporal regressive events. All right. Right. Well, here we go. So, an actual infinite cannot exist. That's the first premise, right? So you're ready for this? At the risk of being too repetitive, And I'm going to try to nail this home before we actually look at the arguments. At the risk of being too repetitive, we need to make sure that we understand what we are arguing against. We are suggesting that actual infinities cannot exist. We are not suggesting that potential infinities cannot exist, nor are we arguing against the existence of an indefinite collection or set of things. Craig and Sinclair write the following, they explain the difference. An infinite set then is one that is such that the whole set has the same number of members as a proper subset. In contrast to this, a finite set is a set that is such that if n is a positive integer, the set has n members. Because set theory does not utilize the notion of potential infinity, a set containing a potentially infinite number of members is impossible. Such a collection would be one in which the membership is not definite in number, but may be increased without limit. It would be best to describe as and indefinite. The crucial difference between an indefinite set, sorry, the crucial difference between an infinite set and an indefinite collection would be that the former is conceived as a determinant whole actually possessing an infinite number of members, while the latter never actually attains infinity, although it increases perpetually. We have then three types of collection that we must keep conceptually distinct, finite, infinite, and indefinite. So to give an example, a finite set would be the number of cars outside in the parking lot. It's just a finite number of cars. An indefinite set would be Edgar Campbell's grandchildren, because that set can increase, right? Okay. By the way, you can, you can increase the number of cars out in the parking lot right now. Right. But we're talking about like right now, but the set of the granddaughters, there's something about that set that is, that could potentially increase. So it's indefinite. And then we have an actually infinite number of things like all the positive numbers that's actually infinite. Okay. And that cannot increase at all. It's just a completed totality in which the part is equal to the whole. If actual infinities cannot exist, then there are only a finite number of things in the universe. What about what you just mentioned, numbers? Well, do numbers exist? That would be a question that we'll raise at some point. Well, it seems, though, to me that we're talking about what exists at a point in time. Right now, there's X number of cars out there in the parking lot. Right. Tomorrow there are going to be more cars out there in the parking lot. That's true. But in any given case, if I say, if I talk about the number of cars currently in the parking lot, there's something about that set that would just be finite. If I say the number of Edgar Campbell's grandchildren, there's something about that set that we have to call indefinite. It's a finite set, of course, but it does inherently have the potential of increasing forever. It assumes a point in the present versus a time in the future. Right, there you go. That's fair to say. All right, 277. By exist, we mean to be instantiated in the mind-independent world. Are there, in the words of Craig and Sinclair, extra-theoretical correlates to the terms used in our mathematical theories? Let's just keep going and see if we can explain ourselves as we go along. As far as the actual infinite is concerned, our answer is no. However, as Craig and St. Clair go on to say, our point here is not to deny the mathematical existence of the actual infinite. This is the point that I want you to get, Nathan, in light of your question. What about numbers? The point here is not to deny the mathematical existence of actual infinities. In other words, we grant, with most mathematicians today, that the actual infinite is mathematically legitimate. It exists as a coherent idea in the mind. However, there is nothing actually infinite in the extramental world. Here's what Craig and Sinclair say. For many thinkers, a commitment to the mathematical legitimacy of some notion does not bring with it a commitment to the existence of the relevant entity in the non-mathematical sense. For formalist defenders of the actual infinite, such as Hilbert, mere logical consistency was sufficient for existence in the mathematical sense. At the same time, Hilbert denied the actual infinite is anywhere instantiated in reality. We're on page 277. Clearly, for such thinkers, there is a distinction or differentiation between mathematical existence and existence in the everyday sense of the word. We are not here endorsing two modes of existence, but simply alerting readers to the equivocal way in which existence is often used in mathematical discussions, lest the denial of existence of the actual infinite be misunderstood to be a denial of the mathematical legitimacy of the actual infinite. A modern defender of the Kalam argument, Amouddou Kaleem, might deny the mathematical legitimacy of the actual infinite in favor of intuitionistic or constructivist views of mathematics, but he need not. Now, what is he getting at there? There are some people who believe that numbers do not actually exist at all, and they are called intuitionists, for example. That's fine. But the point is that even if you affirm infinities, numbers as real and infinities as legitimate constructs in the mind, that does not mean that actual infinities actually exist in the real world. That's the point. So are y'all getting that firmly in your heads? Here's why this is important. I'm conceding the logical possibility of actual infinities existing. And therefore, if a person's gonna critique my argument, or the Kalam argument of Craig and Sinclair and others, if you're gonna critique this argument, you have to make sure you understand that just by proving the logical consistency of an idea, in this case the actual infinite, that doesn't mean you've fairly critiqued my argument. Does that make sense? Because I'm already conceding that this is a logically consistent idea. I mean, a lot of times what will happen is you'll get on YouTube and you'll see these atheists who will kind of be waving their hands at the Klum argument. Title of videos such as the stupidity of the Klum argument, the Klum argument easily refuted. And they rarely even get to this point, this depth of the argument, right? They're rarely even discussing the argument at this depth. But when they do, they think that they've defended the actual infinite by simply showing that it's logically consistent. And I'm saying, once again, that I am conceding the logical consistency of an actual infinite. What I'm saying is that actual infinities cannot exist in the real world. In other words, what we're saying is that actual infinities are metaphysically impossible, even though they're logically possible. Now, because I'm giving not a logical argument against the actual infinity, but a metaphysical one, that's what makes this argument probabilistic in character. You can always opt out by saying, well, as long as it's logically consistent, it could still be true, and therefore you've not absolutely proven your point. Well, I agree that I've not absolutely proven my point. See how I'm conceding this all the way up at the front? I'm letting you know. I'm giving a probabilistic argument for the beginning of the universe. In this case, this is a philosophical argument, and it's metaphysical in character. And I understand, as Craig and Sinclair say here, A metaphysical argument is a woolier notion. I like that term. It's wooly. It's not as clean and crisp as a logical issue. Right? If I were giving you a purely logical argument to the effect that actual opinions couldn't exist, then that means that I would be giving an argument that cannot be assailed by the critic. Does that make sense? All right. So let's go to page 278. What are these arguments against the actual infinity? Why think that actual infinities can't exist? Well, I want you to consider, as a first-off idea, the infinite library. Imagine that there's a library with an actually infinite number of books, like the one in Game of Thrones, which I don't know about because I guess I haven't caught up with the series. And let's just be a little bit arbitrary and say that every single book in this library is either black or red. We may not be surprised if we found that the number of red books equals the number of black books. But what if you were told that the number of red books equals the number of black books plus the number of red books? An absurd statement such as this would be true in a world where actual infinities exist. That's the nature of the actual infinite. The parts are equal to the whole. Right? And what we're arguing here is that your experience is teaching you that that just can't be. But if you affirm the actual existence of an actually infinite number of things, then you run into an absurdity like that, that the number of red books equals the number of black books plus the number of red books. Imagine further that each book in the library has a number printed on its spine. This would mean that every possible numeral would be exhausted in an attempt to number these books. But this would render any attempt to add to the number of books in this particular library impossible, for all possible numerals already exist on the spines of the books. Such a scenario surely contradicts what we observe in the real world, since after all, everything we observe can be added to and numbered. You could just prove the existence of numbers. Possibly. I would prove the existence of numbers if there were an actually infinite number of things in the real world. But that would contradict our experience of the real world. Why? Because we know that books and libraries can be added to. Here's a way to add to the library, right? You might say, no, every single book, conceivable book is written and it's in this library. Oh really? I could go, I could pick 500 books in this library, pull one page out of each book, put them together, put a cover on that and add to the book, to the library. So it's impossible for me to imagine how I couldn't in the real world, add to the number of books in the library. What about, like in astrology, stars, galaxies, is there the same sense of things being added to, taken away? Clearly there's still, and we don't know if it's infinite or not, but clearly there's still more stars, more galaxies. Well, we're about to get into astronomy, but I will say that my short answer is that the universe has been measured. and therefore it is finite. In fact, I'll give you a little anecdote. Well, I'll give you an anecdote. Hugh Ross, who I've given great praise, and you're a big fan of J. Warner Wallace. In his book, God's Crime Scene, he appeals to Ross a lot. By the way, you may be interested to know, I have a Twitter account, but I never use it. I just basically get on there to see what Kanye or somebody, what they're saying. But Jay Warner Wallace is following me. And I was like, I don't know why. I read Cold Case Christianity, but I have not read God's Crimes. OK. Yeah, so I just thought it was funny that he was following me. So I followed it back. But that's probably a good thing. I'm following you back, Jay Warner. If you're going to follow me, and I'm not contributing to Twitter at all, then I'll follow you. But if you assume, for example, that actual infinities exist, and you would assume that the universe is infinite, then you would say, well, then the number of stars is a completed totality to which none can be added. because you've exhausted the number of stars that could be, because there's an actually infinite number of stars. But in our experience, we see stars coming into existence. See, and that's why, this is why Hugh Ross launched his ministry, going back to my point about him. In the 1980s, he was already convinced that God existed and so on, and one of the reasons was that the evidence for the origin of the universe. But once the universe was measured, he believed he could start an apologetic organization that could prove God's existence to our generation that is so caught up in scientific reasoning. And so he started Reasons to Believe for that very reason. It was instigated by the measurements of the universe. So if we can measure the universe, then we know the universe is finite. And if we know the universe is finite, we know it had a beginning. That's just one more way of saying that. But let's get back to the philosophy. Here's another illustration of how absurd, metaphysically absurd, actual infinities are. And this is my favorite one. This is really fun to think about. Hilbert's Hotel. Have y'all ever heard of Hilbert's Hotel? It's a fun hotel to go to. This is the brainchild of David Hilbert, who was a respected mathematician. And he says, suppose that there exists a hotel with a finite number of rooms. Imagine also that every room in the hotel is occupied. Of course, this state of affairs is not difficult to imagine, since many of us have encountered it from time to time. When a guest walks into a hotel room with no vacancy, he is told, sorry, all the rooms are full. And that is the end of the story. But now imagine that a hotel exists with an actually infinite number of rooms. And suppose again that all the rooms are occupied. What is a guest told when he walks into Hilbert's hotel and asks for accommodations? Does the proprietor say, sorry, all the rooms are full? Maybe that's his prerogative. But, and here's the key point, the proprietor is under no obligation to say this to a potential client. Why would he? There is money to be made from this potential customer. Why sure, we've got lots of room in my hotel, says the manager. How can he truthfully say such a thing? Because there is lots of room in Hilbert's hotel. Even when all the rooms are occupied, for all the proprietor has to do to accommodate his guests is move the person in room one to room two, the person in room two to room three, the person in room three to room four, et cetera. And once this is done, room one is now available for his new guest. The reason you're resisting this is because your experience tells you that's absurd. That's the point. Well, they're constantly moving. It's not a hotel. It's just an elevator. Right. But see, if a hotel like this existed, though, this would have to be the case. You could shift them all to another room, and here's the room. You can walk in. But you'd just be opening one door and then going into the next. And it's a constant movement of people, infinite. Oh, it wouldn't need to be a constant movement of people, it would just be... But as people come in to the hotel, you have... Oh, yeah, yeah, they would be shifting over, yeah. But again, all this could happen if actual infinities could exist. Well, that's really a good example of a child's question about heaven, you know. Right. How are you going to get everybody in there? Well, there you go. Now notice, before this new guest checked in, all the rooms were full. And notice also that there were an infinite number of people occupying this hotel before the new guest arrived. And once the new guest checks in, a name has been added to the register. But there are no more people in the hotel than there were before. The number before and after he arrived was infinite. Does this not seem a little counterintuitive? A new guest is checked into the hotel, but the number remains the same. However, strange things are constantly afoot at Hilbert's Hotel. For suppose an infinity of new guests arrive and ask for accommodations. Of course, says the proprietor, who then moves the person in room 1 to 2, the person in room 2 to 4, the person in room 3 to 6, the person in room 4 to 8, the person in room 5 to 10. Any number multiplied by 2 is an even number, right? And so he could literally have an infinite number of people come into his hotel, and he would have plenty of room for them. He'd just make that shift, and they would all come in and have a room available for them. But they're never in a room. They're always moving. That's my point. It's the clock all over again. Well, the point I'm making is that if such a hotel did exist in the real world, then it may be the case that they're not always moving. The reason we're having a hard time with this is because it is so counterintuitive and contrary to our experience. But it would be a great business to have, right? I mean, you would be a trillionaire in four days. But is he getting paid anymore? Because the number of people is not increasing, right? But the number of monies that he has is infinite. Well, the problem is... And he's adding... Does he need any more guests? And he's adding... Well, he's adding money to his cash account. But the problem is... Even though his money is already infinite. He can't ever stop it. He's working all the time. He can't ever stop it. It's worthless. Notice again that even when we add an infinite number of guests to the hotel, the number of occupants in the hotel has not increased one bit. In fact, the proprietor could repeat this process infinitely many times, and yet there would never be a single person more in the hotel than before. If this is not a contradiction, it's at least enough to give us all intellectual constipation. But things get stranger still in this very odd hotel. For what if the person in room one checks out of the hotel? Is there not one less person in Hilbert's Hotel than there was before? No. According to infinite set theory, the same number of people remains despite the subtraction of a guest. Imagine guests 1, 3, 5, 7, 9 on out to infinity check out, in which case an infinite number of guests have left the hotel. Given such a scenario, the number of people in the hotel remains the same. But suppose the proprietor of the hotel does not like an infinite number of rooms empty, that might not look good for business, right? He can easily solve this problem by moving the guests in even-numbered rooms into rooms half their respective numbers. For example, move the guest in room 100 to 50, the guest in 50 to 25, the guest in room 12 to 6, and so on and so forth. In which case, the half vacant hotel becomes full again. Indeed, the proprietor need not wait for a person to walk into the lobby before adding guests to his register, for he can double the occupants of the hotel with guests he already has. For example, what if there are an infinite number of rooms, each having one guest per room? Well, if the manager wants to double the number of guests in his hotel, all he has to do is carry out his dividing procedure by placing those in even-numbered rooms into rooms half their respective numbers, again, by moving guests, for example, in room 10 to 5, 8 to 4, 6 to 3, and so on, and then do it again, and then have one guest per odd-numbered room move next door into the higher even-numbered room. When he does this, Hilbert's Hotel will have two people in each room. of its actually infinite accommodations. Some might think that these kinds of maneuvers would ensure an infinity of hotel guests in the room. Not true. For we can imagine every guest in rooms four on out to infinity, right? Checking out. In that case, an infinite number of members have left the hotel and the names on the register in rooms one, two, and three have been reduced to three. And hence, the infinite has been converted to the finite. And nevertheless, the same number of guests had checked out as when all the guests in the odd number of rooms checked out. In short, infinity minus infinity equals contradictory results. In other words, Hilbert's hotel is absurd. But if an actual infinite were metaphysically possible, then such a hotel would be metaphysically possible. It follows that the real existence of an actual infinite is not metaphysically possible. As Craig has written elsewhere, some of the most eager enthusiasts of the system of transfinite arithmetic are only too ready to agree that these theories have no relation in the real world. To illustrate the point, he quotes David Hilbert. who said this, and he's the guy that came up with Hilbert's Hotel. He said, the infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought. A remarkable harmony between the world of being and the world of thought. The role that remains for the infinite to play is solely that of an idea. If one means by an idea in Kant's terminology, a concept of reason which transcends all experience and which completes the concrete as a totality, that of an idea which we may unhesitatingly trust within the framework erected by our theory. Or again, in Craig's words, our case against the existence of the actual infinite says nothing about the use of the idea of the infinite in conceptual mathematical systems. You can play with this all you want, That's fine, but don't think that such a thing could possibly exist in the real world. All right, before I take another step, do y'all have any questions about this? Yeah. I would say so. In the real world, I would say so. Anything that you can measure is, by definition, finite. Time is the thing that comes to mind. I would say time had a beginning. And that's really tied to the universe. Right. And we'll talk about it when we get to the science. We're done, and I know you can tell. How are we doing? Is this fun? We just made the point that in mathematics you can play around with infinites even if they don't become infinite. part of the real world. In mathematics, you can still do this all day. So I think there's a, we were taught in school that the universe was infinite. Right. We're told that all the time, but most, I mean, the average astronomer doesn't believe that. Right. And I guess that goes back to my question about being able to measure something and that in itself making it finite. because it has a starting point and an ending point, even in time. Sure. You know, we think of it in such big numbers in millions of years or billions of years, believe the science, and somewhere it's going to have an end. Right. And take the billions of years as a real measure. Billion is not a metaphor for an infinite time. I mean they they it's it's it's a real finite limit on Right We're so engulfed by the magnitude of the universe because it is it's 14 billion light-years across That means if you traveled at the speed of light from one end to the other You would it would take you 14 billion years to do that Okay So that's a big, big universe. But a big, big universe is still a finite universe. So let's look at some objections to our arguments against the actual infinite. I'm not going to, well, I guess I need to walk you through this because this is an important point. So you'll notice that this is not our usual procedure. When we give the Kalam argument, I'm not waiting for another chapter to go through the objections. I'm gonna give you the objections as we go along. Because there are a lot of people that are gonna stop you and go, wait a minute. Well, let's look at some objections against the actual infinite. First, the first objection is that actual infinities can exist because we use them all the time in mathematics. The very fact that there is such a thing as the infinite mathematical set theory dispels all the puzzles used to show the actual infinities are not real. As a point out, that's not a good objection. To illustrate why this is so, consider the fact that there are three logically consistent geometries, Euclidean, Lobachevskian, and Riemannian. Each of these are logically consistent in themselves, but inconsistent with one another, so they can't all be true. Hence, as J.P. Moreland notes, one simply cannot move from the mathematical to the real without further argument or evidence. Moreland also asks us to consider the fact that there are three schools of thought concerning the nature of numbers, nominalism, intuitionalism, and then Platonism. Nominalists insist that numbers do not exist independently of the minds that entertain them. Mathematical systems are merely internally consistent, formal languages generated by a formation of rules, and mathematical systems have no ontological implications, that is, they have no implications about the way the world is. Intuitionists insist that math is about concepts going on in the minds of mathematicians, and that it's a mathematical object that exists only to the extent that it can be constructed in the mind. Intuitionists deny the existence of an actual infinite, since no one can actually construct such a set in the mind. The third school of thought, one which Moreland himself favors, is the Platonist or Realist school. Now, this is the school of thought that says that numbers really do exist. And you say, well, hey, if you're a Platonist, you have to think that actual infinities exist. Well, Moreland doesn't think actual infinities exist, and yet he's a Platonist. Here's what he says, he says, this school holds that mathematical entities really exist in the world. For example, mathematical realists hold that numbers exist. Some say there are substances and some properties and still others call them sets. It is only the Platonists in mathematics who believes that there are straightforward ontological implications from mathematical theories. But even a Platonist could deny the existence of an actual infinite. He could be a Platonist about finite sets, but deny Platonism about infinite sets if he were persuaded by the puzzles raised against the infinite sets. Therefore, the mere presence of a mathematics of infinite sets does little to show that an actual infinite really exists in the world. This follows only if one is a Platonist of a certain sort. So this objection does little to counter the puzzles raised against the actual infinite. Thoughts about that first objection? Go ahead. I think it goes back to what we said about an actual vote as a potential infinite. If somebody tried to convince me that actual infinites exist, I'd simply say, OK, go up to the dry erase board or the chalkboard and write me an infinite number. when you can't do it because you've never stopped. It's the hotel all over it. Sure. Yeah, and any attempt to do that would illustrate more of a potential infinite than an actual infinite. Well, here's the second objection. The puzzles against an actual infinite existing in the real world are illegitimate. In finite sets, the whole must be greater than the parts. But in infinite sets, the part can be equal to the whole. All the puzzles really do, when all is said and done, is fault infinite sets for not being what they never intended to be. Finite sets. And here's my response to that. First, it needs to be pointed out again that the critic of the actual infinite is not criticizing the use of actual infinities in mathematics. He is simply saying that actual infinities cannot exist in the real world. And second of all, and this is Moreland. He says, there do not seem to be sufficient independent reasons for accepting an actual infinite with its unusual properties. As has been pointed out, the mere presence of the mathematics of infinity is insufficient. And I know of no other reason which sufficiently justifies acceptance of infinite sets. Further, the lack of justification becomes more troublesome when we realize that terms like part, add, or subtract are being used in such an odd way in connection with the actual infinite that this usage should be rejected because it lacks sufficient justification. How can something still be a part of a whole if it equals that whole? How can members be added to or subtracted from a set without increasing or decreasing its members? Sense can be made out of the concept of an actual infinite. That's another point that's made. You can make sense out of these concepts. Richard Sorobji has tried to show how terms like add, subtract, and part make sense when applied to actual infinities. His whole argument rests on a distinction between besides and beyond. Imagine two lines extending from the present moment to the infinitely distant past. One line possesses an actually infinite number of years, the other possesses an actually infinite number of days. The line possessing the infinite number of days, reasons Sarabji, is not longer than, it does not stick out beyond the line containing years, since neither line has a far end. the lines are equal. Nevertheless, the line containing an actual infinite number of days will contain more members than the line with an actual infinite number of years. The days line contains more members besides the years line, but not more members beyond the years line. Moreland has responded to Saurabhji this way, There are two problems with Sirabji's suggestion. First, I cannot conceive of a line extending an actual infinite distance without an end. Asserting the existence of such a line is begging the question here, since it is precisely such a state of affairs that is being debated. Second, suppose that the two... By the way, I want to take a second to comment on this. Both sides of this debate have a case to make, and they bear a burden of proof. We've been conceding the eternality of the universe for the sake of discussion up to this point. Now we're raising a question about it. But you've got to remember that it's not, you can't just assume that the universe is eternal. You've got to actually make a case for that. And it seems like people like Swarabji are just saying, the eternality of the universe is our given, and it's up to you to prove otherwise. No, the eternality of the universe is a possibility, and it's up to you to prove that it's eternal, and it's up to me to prove that it's not eternal. We both bear the equal burden of proof here. So don't, I mean, that's one of the problems I have with what he's saying. But second of all, suppose that the two lines with one with an infinite number of days and one with years really did exist side-by-side, then it would be possible to divide the lines into equal segments and pair them up one-to-one. Each year segment on the second line would be placed side-by-side with a day segment on the first line. In other words, Saurabhji doesn't appreciate the fact that the division of days and years is analogous to the division of numbers and then the subset of even numbers. Right? But even though the subset of even numbers is a subset of, even though the subset of numbers, the even numbers, is a subset, you can still line them up one-to-one correspondence. Well, if you have an infinite number of days lined up with an infinite number of years, you could still line them up in one-to-one correspondence. It doesn't matter that days are a division of years. Does that make sense to all of you? It says each year segment on the second line would be placed side by side with a day segment on the first line, but how could this be? There would be 365 more day segments than year segments. Furthermore, if one added a year to the second line, then this would amount to adding one segment to the line, but then one would have to add 365 more segments to the first line. How could it be that one line would not extend beyond the other in such a situation? Denying that the lines have ends simply begs the question. In other words, what Moreland is saying is that in the real world, there are always going to be more days than years. Why? Because the year is composed of 365 days. So you're always going to have more on one line than the other. But if you're talking about actual infinities, you wouldn't have that. which contradicts the way the world really is. And again, we're not talking about the logical nature of this, we're talking about the experiential nature of this. This contradicts the way the world really is. Sraubji does not really clarify, says Moreland, the notion of an actual infinite. He merely asserts its existence by setting up the example the way he does. But the problematic puzzles appear all over again. It would seem then that none of the objections removes remove the force of the puzzles that have been raised against the actual infinite. It does not seem that an actual infinite could exist, but since a beginningless series of events is an actual infinite, then a beginningless series of events is impossible. The universe must have had a beginning." Well, here's another objection. Despite the incoherencies, an actual infinity is still metaphysically possible. We're not really sure how to word this objection, which is really not a single objection to the argument, but a family of objections. Defenders of the actual infinite, at the end of the day, feel that all we have given is a prejudice against the infinite. But why can't they simply insist that, in the words of Graham Oppie, these allegedly absurd situations are just precisely what one would expect if there were physical infinities? But Craig and Sinclair say this in response to Oppie. Oppie's objection does nothing to prove that the envisioned situations are not absurd, but only serves to reiterate, in effect, that if an actual infinite could exist in reality, then there could be a Hilbert's Hotel, which is not a dispute. The problem cases would, after all, not be problematic if the alleged consequences would not ensue. Rather, the question is whether these consequences really are absurd. But then there's a rejoinder. J.H. Sobel has given an objection to the Kalam argument that is similar to Oppie's. He says that our thought experiments bring into conflict two seemingly innocuous ideas. Namely, first, there are not more things in a multitude M than there are in a multitude M prime. if there is a one-to-one correspondence of their members. And second of all, there are more things in M than there are in M prime if M is a proper sub-multitude of M. We cannot have both of these principles along with three prime and infinite multitude exists. Sobel insists that all one needs to do to avoid the Kalam argument is embrace one and three. In short, actual infinities can exist after all. Now let's unpack that. Look at the first line. There are not more things in a multitude M than there are in a multitude M prime if there is a one-to-one correspondence of their members. So imagine all the natural numbers and then all the even numbers, right? So that's one. Two, There are more things in M than there are in M prime if M is a proper sub-multitude of M. So think here of Edgar Campbell's grandchildren and the granddaughters. We cannot have both of these principles along with an infinite multitude exist. So what does Sobel do? Let's just accept one and three and give up two. Now my question to all of you is this, what's wrong with what Sobel has said? Assuming you understand what he said. It looks like it centers around a one-to-one correspondence. Has he shown us that we should accept three? No. All he's shown us is that one and three are consistent. But he's not shown us that we should accept that an infinite multitude exists. It again highlights the difference between the logical and the metaphysical. Right. That's all he's done here. So I'm not going to read the big block quote I have of Craig and Sinclair. I'll leave you guys to do that. But that's basically what they're getting at. You can't just arbitrarily say, oh, one and three are consistent, so I'm going to accept three. Yeah, we know that that's consistent. The question is, because of the puzzles that we've raised, you don't want to accept three. And so, accept one and two, and not three. Go ahead. Right. Yeah, I think that We're dealing with atheists here who, of course, they don't have any truck with any of the other arguments we've considered. And they are desperately wanting to make sure that the only things that exist are natural entities. And they will accept anything, no matter how absurd it may be experientially. They'll accept anything. And we're going to talk about quantum mechanics eventually, right? But they'll pull out those kinds of those kinds of things, those kinds of considerations, to say, well, our universe is just stranger than you thought it was. And look at all this stuff going on here. So why not embrace the actual infinite? I mean, in other words, they would just hand wave here and say, you're just expressing a prejudice. But is that not in and of itself an unscientific approach to Yes, this is a very good point that you're making, and it really always baffles me, that experience should be prejudicial, shouldn't it? I mean, if I experience something, then shouldn't I cling on to what that experience implies until something better comes along? I mean, if you're going to be scientific. We could talk about what is unreasonable and what is formally illogical. The actual infinity is absurd in the sense that it's just unreasonable, but it's not strictly illogical. And logical, you've got to remember this, logical possibilities come cheap. There are all kinds of things that are logically possible. I mean, unicorns are logically possible, but no one takes seriously the claim that they exist. Well, I have better reason to reject the actual infinity, the idea that an actually infinite number of things exists. I have a better reason to reject that than unicorns. I mean, for all I know, there's some planet somewhere with a unicorn on it, right? But here's what I also am really convinced of, that where there may be a unicorn on some planet somewhere, there is no actual infinite anywhere to be found in reality. We're almost done here. I'm going to read over or look over page 287 to 288. And then I'll tell you what we're going to talk about next week. But let's go ahead and finish out the point here. We've looked at what four objections and even some rejoinders. And I point out on page 287 that we might say in passing that some atheistic scholars fail to see the implications of what they admit to be true. This came to me when I was reading Nicholas Everett's book, The Non-Existence of God. He's an atheist scholar. And here's what he says. Everett says this, Craig has unfairly loaded the dice in his illustration of the infinite library. Remember that library containing an infinite number of books? Apparently that's found in Hilbert's Hotel, that different line. And this is a stupid joke. All right, how so? How has he loaded the dice? Everett says, of course, we know antecedently that no library contains infinitely many books because we know that books take a finite time to write. And there have only been finitely many people in the history of the universe who have written a book. So of course, there have only ever been finitely many books in the universe. But this is a fact about books. and the conditions of their production. It tells us nothing about the infinity. A few lines later, Everett insists that Craig's thought experiments have no force as an objection to the very idea of an infinite collection, while recognizing that Craig's library, and other examples I add, like Hilbert's hotel, have an intuitive appeal from a logical point of view, they have no force. Of course, it is Everett who has missed the point in his remarks, for as we have seen, Craig never intended to prove the logical impossibility of the actual infinite. For as he states, if that were his intention, then it would be impossible to come up with the thought experiments. Think about that. You can't come up with the thought experiments about the implications of Hilbert's Hotel if you didn't grant their logical possibility in the first place. So you're missing the point when you say they're logically possible. Craig's point then is to show the metaphysical impossibility of the actual infinite, not its logical impossibility. Also, whenever it insists that, of course, no library in the real world can contain an actually infinite number of books, since after all, every book in the real world takes finite time to write, he is making our point for us. Indeed, an actual infinite is only an idea of the mind. It can never be true of anything or group of things in the real world. You see that point? Well, of course you can't have an infinite library of an infinite number of books, because in the real world, books take time to write, and they're only a finite number of people. Exactly, Dr. Everett, exactly. Of course you can't have a Hilbert's Hotel in the real world, because hotels only have finite amount of rooms. You don't even have an infinite number of people on the earth. There's no point in having, exactly. Precisely, you can't have an infinite number of things in the real world. That just illustrates the point. Now given the fact that we've established A, that it's metaphysically absurd to say that infinities can't exist, we have good reason to accept premise A, and so we move on to premise B. And here's premise B. If the universe never had a beginning, then an infinite number of events have transpired up until the present moment. Indeed, if the universe is eternal, then if we were to take a time machine into the past, we could never witness a first moment of the universe's history. For every moment of time we reach, there is yet another prior moment before it, and one before that one, and then another before it, and so on. ad infinitum. The question before us is this, did the universe have an absolute beginning of its existence? If we say yes, then we've established a major premise of the Kalam argument, the universe began to exist. If we say no, then we must conclude that the universe is eternal, and hence the number of past moments in our universe's history is actually infinite. Y'all see that? If the number of, I'm sorry for cutting you off, but if the universe never had a beginning, then the number of past events in our universe's history is actually infinite. But actual infinities can't exist. And so, the universe has to have had a beginning. Just to go through the logic one more time. Actual infinities can't exist, but an infinite temporal regressive events is an actual infinite. An infinite temporal regressive events just is an eternally existing universe. And therefore, the universe is not actually infinite and there are not an actually infinite number of past events, the universe must have had a beginning. Now I'm going to stop right there. We'll field a few questions and then we're about to get into the issue of the nature of time. Are you an A theorist or are you a B theorist? That's the issue that we'll cover next week. So what is your question? Yeah, now you're addressing the issue of traversing the infinite, and that's the second philosophical argument for the beginning of the universe. That argument presupposes that actual infinities are metaphysically possible. So there are two philosophical arguments. And again, one of the reasons I'm going through the objections the way I am is because we're making sure that we're concentrating on one argument at a time. Because what happens is when you talk to unbelievers, they start throwing all these things out at you. So what you have to do is you have to step back and say, OK, you're arguing against something else, and that's not my point. Okay, so the first philosophical argument tries to show that actual infinities are impossible, metaphysically impossible. The second philosophical argument is going to show that even if we granted the metaphysical possibility of actual infinities, we know that our universe is not eternal. All right, so one argues against the possibility of actual infinities, and one presupposes their possibility, but says that even so, our universe just isn't that. And so the countdown and all that stuff applies to that version of the philosophical argument. Yes? So even as we are taking this time to argue against actual infinities within the physical world, Very good. That's one of the objections I address in the chapter. But that's one of the first things that comes up, so I'll go ahead and address it. So very good. And just to kind of prolong the objection, and I know that some of you are anxious to go. But to prolong the objection, I saw a YouTube video where a young lady held up two signs. And it was basically just an easy reputation of Craig, if I remember this correctly. She held up two signs. Actual infinities cannot exist. God is actually infinite. And then of course, ergo, God can't exist. QED, done, over with. God is knocked out. Now obviously, you have to make a distinction between what you mean by actual infinities. There's an actually infinite number of things, and we're saying that is impossible. We're arguing against actually infinite quantities, but we're not arguing against something that is qualitatively infinite. And from the beginning of our worldview study, we made a distinction between the pantheist who says that God is quantitatively infinite, God is everything, and the theist who says that God is qualitatively infinite, meaning you can't place limits on God's attributes. So God can be, you know, the number one is quantitatively finite. And the set of all numbers is quantitatively infinite, right? But you can't translate that into quality. And so you have to ask something else about quality. Now, there's certain attributes that a number might have if it exists that has a certain quality about it, like it's eternal. It's immaterial. That's qualitative. Those are qualitative descriptions about numbers. But the number itself is a quantity. I don't know, does that answer your? He's everywhere, but not everything. Okay, these are very good questions. We'll unpack it when we get to the God proven in the argument, but my short answer is that he's everywhere but not everything. And remember also we're talking about a being who is simple, and therefore it's not like God's one attribute exists here on Earth and one exists in Alpha Centauri. All of what God is exists in, with, and through everything, and therefore you cannot break God up into parts. So there are no quantities in God in that sense that are broken up into parts. All right, I think that that is a good place to close.