PART ONE - WLC Responds to a Video Critiquing Him and the Kalam | Reasonable Faith Podcast

KEVIN HARRIS: Bill, there is a YouTube video, and it’s on you and the kalam cosmological argument. It’s called “Physicists & Philosophers reply to the Kalam Cosmological Argument featuring Penrose, Hawking, Guth.”[1] It is not only a long title, but it is a long video. Despite your confidence and your experience, this must have been a little intimidating with this kind of a lineup.

DR. CRAIG: Yes! When I first heard of this video with this stellar lineup of physicists and philosophers, I was very impressed. It looked like William Lane Craig against the world! But, when you actually dive into this video, I think you’ll find that there’s really a lot less than meets the eye. What you discover is that although the people being interviewed are great scholars, the people who produced this video are popularizers. And when they misrepresent the kalam argument to these scholars then the inevitable result will be criticisms aimed at a strawman, and that greatly diminishes the value of this video. As for the scientific material in the video, there is really nothing new here. It is just a rehash of old material that James Sinclair and I have already responded to in our published work. So the video really fails to advance the discussion. In the end, the video turns out to be somewhat less impressive than it at first appears.

KEVIN HARRIS: Due to the experts featured in this video and its popularity (it is up to around 52,000 views at this recording), we thought we would take the next several podcasts and give you a chance to respond. The video falls naturally into four sections. The first section is on the first philosophical argument for the beginning of the universe. The second section is on the second philosophical argument for the beginning of the universe. The third segment is on the scientific evidence for the beginning of the universe. And, finally, the fourth segment is on the need for a cause of the universe's beginning. Now, there's just no way that we can possibly respond to everything in the video so we're going to play a few representative clips and let you respond. And, by the way, Bill, will you be giving some more responses on the Question of the Week feature on the website to this?

DR. CRAIG: Yes. In our Question of the Week that is on the website every week I'll be doing four consecutive questions of the week responding to a transcript of this video covering exactly those four segments that you just mentioned. So it will not only be in video and audio on this podcast, but we'll have it also in print on the Question of the Week.

KEVIN HARRIS: ReasonableFaith.org. Outstanding. Let's begin a four-part series today based on these four sections. I have to say that I have noticed that a lot of our listeners and followers are responding to this, and they're doing a very good job all over social media, all over the Internet. Here's the beginning of the video. Here's how it begins.

NARRATOR: Let's start at the beginning. Philosophers like Craig have argued that the past must be finite.

WILLIAM LANE CRAIG: If the universe never began to exist that means that the number of past events in the history of the universe is infinite. But mathematicians recognize that the existence of an actually infinite number of things leads to self-contradictions.

DR. CRAIG: My studied position is that the existence of an actually infinite number of things is metaphysically impossible whether or not it's strictly logically impossible. Now this position requires us to understand the distinction between broad logical possibility and impossibility and strict logical possibility and impossibility. Something is strictly logically impossible if it involves a contradiction. But philosophers have come to recognize that there's a wide range of things which are plausibly metaphysically impossible even though they are strictly logically consistent. To give a few examples. “Gold has the atomic number three.” That statement doesn't involve any strict logical contradiction, but surely it's metaphysically impossible. If gold had the atomic number three it would be a different element. It wouldn't be gold. Or here's another one: “This desk could have been made of ice.” Now certainly we can imagine an ice desk that is in the same shape and size as my wooden desk, but it wouldn't be this desk. It seems that it's metaphysically necessary that this desk could not have been made of ice. Or here's another example: “Something has a size but not a shape.” There's no strict logical inconsistency in that, and yet surely it's metaphysically necessary that anything that has a size has a shape. Or another example: “Something can come into being from nothing.” There's no strict logical contradiction in asserting that, but I would say that if anything is metaphysically impossible it's surely that. Or here's my favorite example from Alvin Plantinga: “The prime minister is a prime number.” That is clearly metaphysically impossible and yet there's no strict logical contradiction in that. None of these things is strictly logically impossible and nevertheless plausibly they are metaphysically impossible. Some metaphysical impossibilities are also strictly logically impossible, but not all of them. My focus in the kalam argument is on situations that are metaphysically impossible even if they're not strictly logically impossible – things like a Hilbert's Hotel with an actually infinite number of rooms or Benardete's book with an actually infinite number of pages. If any of our viewers or listeners are interested in illustrations involving strict logical impossibilities, I want to recommend Alexander Pruss' recent book, Infinity, Causation and Paradox, in which he provides a plethora of illustrations showing that an actually infinite past would involve strict logical impossibilities. Let me just mention one of these that is very graphic and very accessible – the so-called grim reaper paradox. It goes like this. Imagine that you're alive at midnight but there is a grim reaper who will cut you down at one o'clock if you're still alive then. But there's a second grim reaper who will cut you down at 12:30 if you're still alive then. But then there's a third grim reaper who will cut you down at 12:15 if you're alive then, and so on at infinitum. The result of this is that it is logically impossible for you to live past midnight and yet you cannot be killed by any grim reaper because before any grim reaper could kill you you would already be dead. So this is a great illustration of how an actually infinite number of things leads to a strict logical impossibility.

KEVIN HARRIS: Thank you, Bill. I'll be getting no sleep tonight. [laughter] Continuing with the next excerpt. Adrian Moore appears in this clip. Let's go to that now.

NARRATOR: As we shall see, contemporary mathematicians do not think infinity is contradictory although it's true that philosophers of the past were troubled by it. But even they did not banish the concept. For example, Aristotle distinguished between different types of infinity.

ADRIAN MOORE: The distinction that he was drawing was between an infinity that's present all at once – all at some particular point in time – which is what he meant by an actual infinity contrasted with an infinity that is spread out over time which is what he called a potential infinity. So, for example, if space were infinitely big that would be an example of an actual infinity because the whole of space is there at any given point in time. On the other hand, if you imagine a clock endlessly ticking, the ticks might go on forever. But if they did that would be an example of a potential infinity.

DR. CRAIG: It’s a privilege to be interacting with Professor Moore. I have learned a great deal from him. One of the books in my personal library is his book, The Infinite, which I heartily recommend to anyone who's interested in the fascinating history of this challenging concept. Unfortunately here the narrator of the video begins to lead things off track. She says, “Contemporary mathematicians do not think infinity is contradictory.” But neither do I! I'm not claiming that the concept of the actual infinite is an inconsistent concept. Rather, I'm claiming that the instantiation of an actual infinite in reality is metaphysically impossible. So I follow Aristotle in thinking only potential infinites can exist in reality in contrast to actual infinites which are merely conceptual.

KEVIN HARRIS: Let's go to the next excerpt.

NARRATOR: But in the 19th century, Georg Cantor revolutionized the mathematics of the infinite.

DANIEL ISAACSON: What Cantor achieved was to treat infinity as a subject of mathematics itself.

ADRIAN MOORE: It was a whole new branch of mathematics, and it was of breathtaking ingenuity, showed incredible craftsmanship and creativity on Cantor’s part.

DR. CRAIG: Right! Cantor founded infinite set theory. It's important to understand that all of my arguments assume Cantorian set theory and ask whether that theory can be instantiated in reality. My claim is that that would result in situations that are plausibly metaphysically impossible.

KEVIN HARRIS: OK. Next clip.

NARRATOR: What Cantor showed was that an infinite set has a strange feature. We might call this the infinite property. That is, it can be put into a one-to-one correspondence with a subset of itself.

DR. CRAIG: Well, this is rather his definition of the actual infinite. This is not something that Cantor proved. He simply defined an actually infinite set to be a set which has a proper subset with the same number of members as the original set itself. Moreover, two sets are defined to have the same number of members if their members can be put into a one-to-one correspondence. This is all done by definition. Ironically, Cantorian set theory (which is called naive set theory) is, in fact, riddled with logical paradoxes. The way in which the mathematician solved this problem is by what's called axiomatization of set theory. That is to say, they simply adopt the axiom that there exists an infinite set, and as an axiom it cannot be proved nor does it enjoy any intuitive support. It is just a postulate that the mathematician makes. I don't challenge the internal consistency of Cantorian or infinite set theory given its axioms and definitions. My question rather is whether these actually infinite sets really can be instantiated in reality.

KEVIN HARRIS: Let's go to the next clip then that features Adrian Moore, and Alex Malpass makes a showing.

ADRIAN MOORE: We can pair the even numbers up with all the counting numbers all together. So two gets matched with one, four gets matched with two, six gets matched with three, eight gets matched with four, etc., etc.

ALEX MALPASS: So for instance you can show that there are just as many even numbers as there are counting numbers when intuition should tell you that there should be half as many.

ADRIAN MOORE: Well, OK, so this just is counterintuitive, and it's counterintuitive because we're used to dealing with finite sets. What we have to say is the case of finite sets just doesn't carry over to the case of infinite sets. But it doesn't follow that there's anything incoherent about what we say in the infinite case. It just follows that we have to start saying different things in the infinite case.

DR. CRAIG: Again, I’m not challenging the internal consistency of infinite set theory, given its definitions and axioms. The question rather is whether an actually infinite set of things can be instantiated in reality. Could there be, for example, an actually infinite number of baseballs?

KEVIN HARRIS: Here's the next clip.

DANIEL ISAACSON: What you get from most mathematicians, I would say almost all mathematicians, is an uncritical acceptance of infinity in the sense of actual infinity. That's what they need for doing the kind of mathematics that they do.

DR. CRAIG: Sure. There are a small number of intuitionist mathematicians who deny even the mathematical legitimacy of the actual infinite. But that's not the issue before us. I assume Cantorian infinite set theory in my arguments.

KEVIN HARRIS: Let's take a look at this next clip from Adrian Moore.

ADRIAN MOORE: So one of the first things that mathematicians come to appreciate is that infinite collections do have different properties from finite collections. Things that we absolutely take for granted in the finite case simply don't carry over to the infinite case. And if it's the finite case that is providing us with our basic intuitions then that means that some of the results about infinite sets are going to be counterintuitive. But that's just what you would expect. Why should the finite and the infinite be the same? As long as we're prepared for these differences, again the very worst that it will be is counterintuitive. It won't be contradictory. It won't be inconsistent.

DR. CRAIG: Again, at the risk of repeating myself, the claim is not that infinite set theory is self-contradictory or inconsistent. The question rather is whether the counterintuitive consequences of the real existence of an actually infinite number of things justifies skepticism about the metaphysical possibility of real actual infinites.

KEVIN HARRIS: Up next another clip from Alex Malpass.

ALEX MALPASS: One way to bring out the difference between the finite and the infinite is to think about somebody counting. So imagine George is counting to ten and he's got as far as five – how many numbers has he got left to count? He's got five numbers left to count – six, seven, eight, nine, ten. But now imagine George is going to count all of the numbers. Every single counting number. He's got up as far as five. How many numbers has he got left to count? He's got infinitely many numbers still left to count. What about when he gets to ten? How many numbers has he got left to count? He's still got infinitely many numbers left to count. So his task isn't going down over time but when he's counting a finite set his task is going down over time.

DR. CRAIG: OK. So turn the example around. Suppose George has been counting from eternity past. Is it really possible for someone to count down all the negative numbers one at a time ending at zero? That seems to be metaphysically impossible. And if you do think that that's possible then I would ask: Why didn't he finish yesterday? Why didn't George finish the day before that, or the day before that? At any point in the past he would already have had infinite time to finish his countdown, and therefore at any point in the past he should already be done. We should never find him counting. But that contradicts the assumption that he has been counting down from eternity. So I think this simply illustrates once more the metaphysical impossibility of the existence of an actually infinite past.

KEVIN HARRIS: This next clip includes an excerpt from our Zangmeister video on Hilbert's Hotel. They include that. Let's go to that now.

NARRATOR: One classic example that Craig has given to show infinity cannot exist is that of Hilbert's Infinite Hotel.

RF VIDEO: The mathematician David Hilbert illustrates the problem by imagining a hotel with an infinite number of rooms all of which are occupied. There's not a single vacancy. Every room in the infinite hotel is full. Now suppose a new guest shows up and asks for a room. The manager says, “Sure. No problem.” Then moves the guest who was in room number one to room number two, and the guest who was in room number two to room number three, and so on to infinity. As a result of this shuffling, room number one becomes vacant and the new guest happily checks in even though all the rooms were already full and nobody has checked out.

NARRATOR: It seems Craig is claiming infinity is problematic because the Hilbert Hotel is both full and able to admit new guests. But the problem may simply be the way “full” is being defined.

ALEX MALPASS: If what we mean by “full” is every room is occupied then that's true but it doesn't prohibit us being able to accommodate new guests because we can shuffle them all up in an infinite hotel. If what we mean by full is “can't accommodate new guests” then it's just false that it's full.

DR. CRAIG: Right! So do you think that it's really possible that an actual hotel could be full in the first sense (that is, every room is occupied by a flesh and blood person) and yet it could accommodate infinitely more guests just by moving people around? There's no logical contradiction involved in such a scenario, but is it really possible metaphysically?

KEVIN HARRIS: Here's our next excerpt.

NARRATOR: In Craig's video, a contradiction is supposedly found by considering what happens when the guests leave the infinite hotel.

RF VIDEO: Suppose all the guests in the odd numbered rooms check out. In that case, an infinite number of people have left the hotel. And yet there are no fewer people in the hotel. But suppose instead all the guests in rooms numbered four and above check out. In that case only three people are left. And yet exactly the same number of people left the hotel this time as when all the odd-numbered guests checked out. Thus we have a contradiction. We subtract identical quantities from identical quantities and get different answers.

DANIEL ISAACSON: The trouble . . . that video is so below threshold. The complaint in that clip – in particular the one that says that if there are only three people left then they're still the same number of people that have checked out as were there originally – that is a feature of infinity that has to be taken on board very importantly which is that any finite initial segment of an infinite set if it's linearly ordered is such that what's left is infinite. So no matter how far you go in fact you're still leaving infinitely many elements ahead of you.

DR. CRAIG: This is a solution? It simply restates in a confused way the counterintuitive consequences of the real existence of an actual infinite number of things. You can take away infinity from infinity and get any result from 0 to infinity.

KEVIN HARRIS: Another clip from Alex Malpass.

ALEX MALPASS: There's a formal theory of arithmetic which is characterized by the Peano axioms and that's a language where you can express any sentence of arithmetic – like 7 plus 3 equals 10 or something. But when it comes to this Cantorian transfinite arithmetic there's just no notion of subtraction. It's not well-defined to say infinity minus 3. That's not a sentence of either the Peano arithmetic or the Cantorian arithmetic. So while someone might say it informally, there's no formal language where that really makes any sense.

DR. CRAIG: Right. That's my point! Inverse operations like subtraction and division are prohibited mathematically for transfinite or infinite numbers. But you can't stop people from checking out of a hotel – bar the door and they'll jump out the windows!

KEVIN HARRIS: Here's the next clip. It features Adrian Moore.

NARRATOR: One of the strange things that Cantor showed was there are infinities of different size. The first infinity is known as aleph naught. The next largest is aleph one and so on.

ADRIAN MOORE: So there's this infinite number which is called aleph 7 and there's also an infinite number which is called aleph 5. We can add those. If we add aleph 7 to aleph 5 you might think that what we're going to get is aleph 12. But it doesn't work like that. The infinite case is different from the finite case. In fact what happens if you add two infinite numbers together is that the bigger one swallows up the littler one. The smaller one is insignificant compared with the bigger one. Aleph 7 plus aleph 5 is just aleph 7, aleph 7 just takes over and it's as if the aleph 5 wasn't even there. So aleph 7 plus aleph 5 is aleph 7. And similarly aleph 7 plus aleph 3 is aleph 7. If you add these smaller infinite numbers to aleph 7 you just get aleph 7. Now suppose we tried to perform a subtraction. Suppose we start with aleph 7 and ask what is it that you need to add to aleph 7 to get aleph 7? Now, unfortunately there's no clear answer to this because we saw that if we added aleph 3 that would just give us aleph 7. If we added aleph 5 that would give us aleph 7. There's no longer any such thing as the number that we need to add to aleph 7 to get aleph 7. This is an example of how subtraction just isn't well defined in the infinite case.

DR. CRAIG: The higher alephs only reinforce the suspicion that we're dealing here with a purely conceptual realm, not something that can exist in reality. Indeed, the real existence of a plurality of things that is numbered by one of these higher alephs is impossible because there wouldn't be enough space-time points to accommodate all of them. The number of points in continuous spacetime is aleph one, so any alephs higher than that (aleph two, aleph three, aleph four, aleph five) cannot exist in reality because there wouldn't be enough room for them. But in any case, this is all really quite beside the point because the kalam cosmological argument is concerned only with the least transfinite number, aleph null.

KEVIN HARRIS: In this next clip the narrator introduces you again, Bill.

NARRATOR: As we saw earlier, when presenting to a lay audience Craig has claimed that the infinite is contradictory.

WILLIAM LANE CRAIG: But mathematicians recognize that the existence of an actually infinite number of things leads to self-contradictions.

DR. CRAIG: Yes. That is a shortcut to communicate these extraordinarily difficult concepts to laymen. Some, but not all, metaphysically impossible situations involve logical contradictions.

KEVIN HARRIS: Next clip.

NARRATOR: But when talking to philosophers, a different claim is made.

WILLIAM LANE CRAIG: Now Alex is certainly right that when we appeal to these absurdities we are not talking about logical contradictions or incoherences. Jose Benardete in his book on infinity says that there's no logical contradiction involved in these monstrosities but you have only to look at them in their concrete reality to see that this is metaphysically impossible.

DR. CRAIG: Right. Illustrations like Hilbert's Hotel and Benardete's book may not be strictly logically impossible, but I think they are metaphysically impossible. Other paradoxes, like Pruss’ grim reaper paradox, however, do involve logical contradictions.

KEVIN HARRIS: Another clip from Alex Malpass.

ALEX MALPASS: In contrast to other notions of possibility, metaphysical possibility is far less clear what the definition of that is supposed to be. And many of us are dubious that just simply pointing that something seems absurd is enough to forbid it from existing in reality. Philosophers have to be a lot bolder than that. A lot more open-minded.

DR. CRAIG: Fair enough. The boundaries of the metaphysically impossible are unclear since they may not involve logical inconsistencies. For example, is it metaphysically possible that gold might have had a different atomic number than 79? Or that your desk could have been made of ice? Intuitions may differ. But most philosophers would say that these logically consistent scenarios are nonetheless metaphysically impossible. Similarly, given the counterintuitive consequences of the real existence of an actually infinite number of things I think that skepticism about their metaphysical possibility is surely justified.

KEVIN HARRIS: Up next, a clip from Daniel Isaacson.

DANIEL ISAACSON: A hotel case is so basic that that's no place for anybody to dig in their heels against infinity. Even if you only accept potential infinity, the Hilbert Hotel and those results about it are completely incontrovertible.

DR. CRAIG: A strange response. He must mean merely that Hilbert's Hotel is a good illustration of the existence of an actually infinite number of things. Well, of course it is. We should expect that David Hilbert, perhaps the greatest mathematician of the 20th century, knew how to illustrate accurately the actual infinite. His hotel is not merely potentially infinite.

KEVIN HARRIS: Here's another clip from Dr. Alex Malpass.

ALEX MALPASS: The examples that are supposed to be problematic always involve admitting new guests, shuffling guests from one room to the other. And if we imagine a hotel where the doors were sealed and nobody could move from one room to the other it's hard to think of a similar example that could bring out anything that looked absurd about it. It would just be a hotel with infinitely many rooms in. And if that's right, it does lead you to wonder whether the problem is the infinity involved or whether it's the manipulation of those infinite elements that's the problem. And that's helpful because it's plausible to suppose that what's done is done and you can't change that. The past is fixed and unchangeable. So that if the past is supposed to be like an infinite hotel then it's more like one where the guests can't shuffle around than one where they're free to move to different rooms. It's just impossible that yesterday didn't happen given that it has happened.

DR. CRAIG: This reply is bizarre. We can use any concrete reality to illustrate the existence of an actually infinite number of things, for example: baseballs, coins, stars, people. There is nothing about the absurdity involved in Hilbert’s Hotel that hinges upon the illustrations involving a hotel with rooms and doors.

KEVIN HARRIS: We’re out of time. Let’s pick it up right there. On the next podcast we will be talking about the second philosophical argument for the kalam cosmological argument. That’s coming up on the next podcast right here.[2]

[1] https://www.youtube.com/watch?v=pGKe6YzHiME (accessed February 14, 2022).

[2] Total Running Time: 30:11 (Copyright © 2022 William Lane Craig)