In this episode Trent rebuts a documentary produced by the atheist Youtuber skydivephil that tries to refute the kalam cosmological argument for the existence of God. Part one focuses on the philosophical arguments for the beginning of the universe.
Welcome to the Counsel of Trent podcast, a production of Catholic Answers.
Trent Horn:
Hey everyone in today’s rebuttal, I’m going to look at the YouTube channel Skydivephil, and they have a whole documentary that criticizes the Kalam cosmological argument. Now this argument was popularized by the Protestant philosopher and theologian William Lane Craig, and it gets discussed a lot because it’s deceptively simple. It goes like this, whatever begins to exist has a cause for its existence. The universe began to exist, therefore the universe has a cause for its existence. Now this isn’t an argument for God strictly, you have to do an analysis of what the cause of the universe would be. And if it’s the cause of all space, time matter and energy, you would do an analysis showing it has divine properties. So in this video, this atheist who goes by the name Skydivephil, he actually does like a whole documentary where he interviews scientists and philosophers who critique the Kalam argument.
Trent Horn:
It’s got really slick production values. It looks great technically speaking, but ultimately I was disappointed because people like William Lane Craig, they have provided answers to the objections that are raised in this documentary, and a lot of those just simply aren’t included. Many of them can be found in the Blackwell Companion to Natural Theology, in that book Craig and a co-author James Sinclair they’ve written one of the best defenses of the Kalam argument in print, so I’ll be citing a lot from that. Okay, now with that being said though let’s take a look at Skydivephil’s criticism of the Kalam argument. And in this response I’m going to focus on the first half of this video that just deals with the Kalam and the philosophical arguments for the beginning of time. That’s what we’ll do here in part one.
Vidoe:
Creation stories of Pacific islanders tell us the world was made from a volcano. Other origin myths say the world came from water, but contemporary science tells us that the world evolved from a big bang. And the outdated view that this marks an absolute beginning has been used by religious philosophers most notably William Lane Craig to revive an old argument for God, known as the Kalam cosmological argument.
Trent Horn:
First, I feel like this introduction subtly tries to equate Christian philosophy that would show the universe had a beginning with ancient myths as if Craig’s argument is just a fancy version of a primitive myth, but you could easily do the same with atheism if you were uncharitable. You could equate atheism with a primitive myth about some kind of matter or causal force always existing. I’m not saying he’s trying to do that, but it could come off that way. Second in Craig’s original 1979 book, The Kalam Cosmological Argument, he doesn’t consider big bang cosmology to be the primary evidence for the beginning of the universe. His argument is mostly based just on philosophy and the impossibility of the infinite past. He says big bang cosmology empirically confirms his philosophical argument. So some of the science he relies on in the 1979 book, it’s a little outdated but as we’ll see Craig has kept up with developments in cosmology since that time.
Vidoe:
In this film we’ll hear why this argument fails from the very cosmologist quoted by Kalam supporters. And we’ll also hear from leading philosophers of mathematics, who will show why the concept of an infinite universe now being proposed by many physicists is perfectly coherent. And lastly we’ll see that if the universe did begin, it may not need a cause. The argument human is often expressed like this, whatever begins to exist has a cause, the universe began to exist. Therefore, the universe has a cause and that cause is taken to be God, let’s start at the beginning. Philosophers like Craig have argued that the past must be finite.
William 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.
Vidoe:
As we shall see contemporary mathematicians do not think infinity is contradictory.
Trent Horn:
And Craig doesn’t think infinity is contradictory either and is replied to atheist J.H. Sobel, Craig says we can have comparable infinite multiplicities in mathematics without admitting them into our ontology. Now this echoes other mathematicians who make a distinction between infinity existing in the abstract mathematical sense which is possible, and infinity existing in the concrete physical world, the concrete sense, which for actual infinities is not possible. I’ll give you some examples, according to the mathematicians Edward Kasner and James Newman they write, the infinite certainly does not exist in the same way that we say there are fish in the sea. The existence in the mathematical sense is wholly different from the existence of objects in the physical world. Likewise, the atheistic mathematician James Lindsay writes, infinity is an abstract concept made in existing only in the minds of those who can imagine it. Indeed, this is the mainstream interpretation of infinity among mathematicians.
Vidoe:
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.
Video:
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.
Trent Horn:
The universe could also be infinitely large in the sense that it’s forever expanding, and so it will grow in size forever, but overall this is a helpful distinction. Another way to put it is to note that there are an infinite number of points between you and the door of a room, but you can reach the door because the points get smaller and smaller as they’re potentially divided, this is a potential infinite. But if you had to walk across an actually infinite number of tiles that were the same size, you could never reach the door because that’s an actual infinite. As we continue you’ll see that while reality can make room for the potentially infinite, it can’t do the same for actually infinite collections of discreet things. And this forms the foundation for Craig’s objection that the past cannot be infinite.
Vidoe:
But in the 19th century Georg Cantor revolutionized the mathematics of the infinite.
Video:
What Cantor achieved was to treat infinity as a subject of mathematics itself.
Video:
It was a whole new branch of mathematics and it was of breathtaking ingenuity, showed incredible craftsmanship and creativity on Cantor’s part.
Vidoe:
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.
Video:
We can pair the even numbers up with all the numbers, all the counting numbers altogether. So two gets matched with one, four gets matched with two, six gets matched with three, eight gets matched with four, et cetera, et cetera.
Video:
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’d be half as many.
Video:
Well, okay so this just is counterintuitive and it’s counterintuitive because we’re used to dealing with finite sets and what we have to say in 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.
Trent Horn:
Craig and other defenders of the Kalam argument agree that when you deal with infinite sets there are unusual properties, but it’s all logically coherent. Here’s what Craig writes, “When it is alleged that an actual infinite cannot exist, the modality at issue is not strict logical possibility. Otherwise, the presumed strict logical consistency of axiomatic set theory would be enough to guarantee that the existence of an actual infinite is possible. Rather what is that issue here is so called metaphysical possibility, which has to do with some things being realizable or actualizable.” And here’s how Craig offered this reply in a debate with the atheistic physicist Lawrence Krauss who makes a similar objection, I’ll share Krauss’s argument and then Craig’s response.
Video:
The existence of infinity which he talked about which is self contradictory, is not self contradictory at all. Mathematicians know precisely how to deal with infinity do do physicist. It’s strange and very unappetizing and in fact you can sum things that look ridiculous. For example, if you sum the series one plus two plus three plus four plus five to six to infinity, what’s the answer? -112, you don’t like too bad.
Video:
He says that the universe doesn’t need to begin to exist because we know in mathematics how to deal with infinities, for example how to sum affinities. Well, of course in mathematics you can do that. Mathematics has certain conventions and rules that you use, but to prevent contradictions from occurring for example in trans finite arithmetic, the inverse operations of subtraction and division are prohibited because they lead the contradictions. But how you can slap the hand of the mathematician who tries to break the rules, if you’ve got say an infinite number of baseball cards you can’t stop for someone from giving away part of the cards. And so you will have contradictions when you translate it into reality. It may be possible on paper in the realm of mathematics, but it’s not possible in the realm of reality.
Trent Horn:
So Craig would agree that mathematics dealing with infinite sets it’s coherent even if it’s not familiar to us. The problem are the paradoxes that come up when you try to apply the infinite in specific cases in the real world, this point was made by the mathematician David Hilbert, we’ll talk about him a little later, but he said the role that remains for the infinite to play is solely that of an idea.
Video:
What do 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.
Video:
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.
Video:
So, 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 10 and he’s got as far as five, how many numbers has he got left to count? And he’s got five numbers left to count 6, 7, 8, 9, 10. But now imagine George is going to count all of the numbers, every single counting number and he’s got up as far as five, how many numbers has he got left account? He’s got infinitely many numbers still left account. What about when he gets to 10, how many numbers has he got left account? He’s still got infinitely many numbers left account. So his task isn’t going down over time, but when he’s counting any finite set his task is going down over time.
Trent Horn:
First, I find it interesting that people are willing to accept that our everyday intuitions can’t be applied to the infinite, but that’s not a reason to reject the existence of the infinite. But many of those same people try to apply every day intuition to God like to him being timeless or changeless, saying that well since we don’t understand what that’s like we have to reject God because it’s not like our normal experience. If we can accept that infinity is odd and it exists, why can’t we do the same for God? Second, Craig and other defenders of the Kalam argument they have no problem with things like Cantor’s principle of one to one correspondence. The problem rises only when you try to assert that three separate propositions relating to sets and infinity are all true. In logic and theism, the atheist Jordan Howard Sobel has said the Kalam argument it forces us to choose between three propositions, the first is Euclid’s principle is true or that a things parts are always smaller than the whole, part is smaller than a whole.
Trent Horn:
The second is Cantor’s principle or that a things part is not always smaller than the hole, if the two can be placed in one to one correspondence. We see this with infinite sets like how the even numbers that set is the same size as the natural numbers even though even numbers are a part of natural numbers. Now, one way to have both of these propositions to be true is if Cantor’s principle only refers to collections of abstract objects like sets, whereas collections of material objects always follow Euclid’s principle, the part is smaller than the whole, but then there’s the third proposition. There is a group of physical objects that contain an actually infinite number of members. Sobel says that not all of these three propositions can be true and that makes sense, because they’re physical objects they should follow Euclid’s principle, part is smaller than whole, but because their infinite in number they also follow Cantor’s principle.
Trent Horn:
So what do we do? Sobel’s solution is we just restrict Euclid’s principle. We say that we can’t apply it to actually infinite sets of physical objects. Of course, as operations and properties are extended from finite to transfinite cardinals, infinite numbers, some arithmetic principles are left confined to the finite, but as Craig notes Sobel hasn’t given us a reason why this is the choice we have to make. You could just as easily say Euclid and Cantor’s principles are both true, and that Euclid’s principle applies to every set of objects in the physical world, because there are no actually infinite sets of physical objects. If there were, you could perform the mathematical operations in accord with Euclid’s principle, that Sobel says you can’t perform. I mean who’s going to be there to stop you? Euclid? Sobel? Remember how Craig put it in his debate with Lawrence Krauss.
Video:
The inverse operations of subtraction and division are prohibited because they lead the contradictions. But while you can slap the hand of the mathematician who tries to break the rules, if you’ve got say an infinite number of baseball cards, you can’t stop from someone from giving away part of the cards. And so you will have contradictions when you translate it into reality, it may be possible on paper in the realm of mathematics, but it’s not possible in the realm of reality.
Trent Horn:
Rejecting actually infinite sets in the physical world, it avoids paradoxes and doesn’t create any paradoxes of its own. And the less paradoxical theory, it stands a much better chance of being the correct theory.
Vidoe:
One classic example that Craig has given to show infinity cannot exist is that of Hilbert’s infinite hotel.
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.
Vidoe:
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.
Video:
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 shuffle them all up right 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.
Trent Horn:
It’s important to note that the contradictions Craig says exist in Hilbert’s hotel are as we said earlier, they’re not logical contradictions. In mathematics involving infinite numbers or what some people call transfinite arithmetic, you can add finite numbers to infinite numbers or infinite numbers to other infinite numbers. Instead Craig is saying it’s metaphysically impossible, it’s not possible given the nature of reality for something like Hilbert’s hotel to exist. Here is Craig’s reply, as an illustrative embodiment of transfinite arithmetic based on the axiomatic set theory, Hilbert’s hotel will of necessity be as logically consistent as that system. Otherwise, it would be useless as an illustration, but it also vividly illustrates the absurd situations to which the real existence of an infinite multitude can lead. The absurdity is not merely practical and physical, it is ontologically absurd that a hotel exists which is completely full and yet can accommodate untold infinities of new guests just by moving people around.
Trent Horn:
So in this case [inaudible 00:19:41] the philosopher being interviewed has to evacuate the word full of all of its meaning in order to accommodate the absurd example of Hilbert’s hotel. But you could just as you easily and I would say preferably say it’s better to not allow the possibility of such a hotel or object in the first place than to change our understanding of the concept of full. In fact, since Hilbert’s hotel can accommodate an infinite number of guests, it is for all practical purposes both empty and full since it has the maximum number of rooms available which we would expect of an empty hotel, and every room is occupied which we’d expect of a full hotel. Since these contradictions are not logical in nature, you can’t logically prove they’re impossible like a married bachelor. Instead, it’s going to rest on your intuitions about what’s possible. Like how other things are metaphysically impossible, like an object that has color but no shape or shape but no size, or going back in time and killing your own grandfather.
Trent Horn:
And I would say that when we really think about the examples involving the infinite like Hilbert’s hotel, when we put them in reality we end up with something that seems to be more of an impossibility, like killing yourself through time travel which I’ll talk about later, than just a possible yet strange part of the real world.
Vidoe:
In Craig’s video, a contradiction is supposedly found by considering what happens when the guests leave the infinite hotel.
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.
Video:
The trouble that video is so below the threshold, the complaint in that clip… in particular the one that says that if there’re only three people left, then there’s still the same number of people who 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 [literally 00:22:25] ordered is such that what’s left is infinite. So no matter how far you go in fact, you are still leaving infinitely many elements ahead of you.
Video:
There’s a formal theory of arithmetic which is a characterized by the peano axioms. And that’s a language where you can express any sentence of arithmetic like seven plus three 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 three, 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.
Trent Horn:
Right, and this mirrors what Malpass said earlier in the documentary, but the problem with infinity doesn’t arise in discussions of the length of abstract finite sections of an infinite line. They arise when you subtract identical quantities from identical quantities in the real world which should always be the same answer, but in an infinite collection there’s an infinite possibility of answers. The philosopher Michael Huemer writes in his book Approaching Infinity, “The standard response to these problems is similar to the standard response to the set theoretic paradoxes prohibit the troublesome operations. Followers of Cantor counsel us to simply get you used to the fact that infinite numbers behave differently from finite numbers in certain respects.” But the problem is that if actually infinite collections could exist in the physical world, then these sets could in theory do actual things in the world, like be the subject of subtraction or division that no language is capable of describing which… but they’re able to do these things we can’t describe which seems counterintuitive.
Trent Horn:
Craig writes in his book Time and Eternity, that atheists can’t refute this problem by saying, “Well, this is just what we would expect if actual infinite sets existed.” Here’s what he writes, “But far from being the solution, this is precisely the problem because in infinite set theory Euclid’s Axiom is denied. One winds up with all sorts of absurdities such as Hilbert’s hotel when one tries to translate that theory into reality. The issue is not whether these consequences would result if actual infinities were to exist, we agree that they would. The question is whether such consequences are metaphysically possible.”
Vidoe:
One of the strange things that Cantor showed was there are infinities of different size. The first infinity is known as aleph-nought, the next largest is aleph-one and so on.
Video:
So there’s this infinite number which is called aleph-seven, and there’s also an infinite number which is called aleph-five, and we can add those. And if we add aleph-seven to aleph-five 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 little one. The smaller one is insignificant compared with the bigger one and aleph-seven plus aleph-five is just aleph-seven, aleph-seven just takes over and it’s as if the aleph-five wasn’t even there. So aleph-seven plus aleph-five is aleph-seven and similarly aleph-seven plus aleph-three is aleph-seven. If you add these smaller infinite numbers to aleph-seven you just get aleph-seven.
Video:
Now, suppose we tried to perform subtraction. Suppose we start with aleph-seven and ask what is it that you need to add to aleph-seven to get aleph-seven? Now, unfortunately there’s no clear answer to this because we saw that if we added aleph-three, that would just give us aleph-seven. If we added aleph-five that would give us aleph-seven, there’s no longer any such thing as the number that we need to add to aleph-seven to get aleph-seven. And this is an example of how subtraction just isn’t well defined in the infinite case. You could say the same about zero, that zero divided by zero isn’t defined. If anything divided by zero isn’t defined in normal arithmetic, but that doesn’t mean division is meaningless or that zero is contradictory.
Trent Horn:
First, a problem arises when you apply this to concrete objects, it’s hard to get away with saying things like one infinite amount swallows up another infinite amount as if it wasn’t there at all. When the amount really was there in the form of actual hotel guests who check in and still have to be accounted for. Second, Craig has addressed the objection that things like subtracting infinite numbers is only undefined and so it’s not impossible. In a 2011 debate with the philosopher Peter Millican, Millican raised a similar objection.
Speaker 10:
Infinity minus infinity apparently cannot be given a consistent result. This is true but absolutely nothing to worry about because all it means is that a certain equation infinity plus what equals infinity has more than one solution. And there’s absolutely nothing mysterious or contradictory about any of this. It’s the same reason why you can’t divide zero by zero.
Trent Horn:
And here is Craig’s reply to Millican.
Video:
Dr. Millican says that infinity minus infinity is not defined in transfinite arithmetic, there’s more than one solution to the equation. And that is precisely the problem when you try to translate this into the real world, you can slap the hand of the mathematician who tries to subtract infinity from infinity, but you can’t stop someone from taking away a certain number of coins. And the contradiction is that you have identical quantities, you subtract identical quantities and you come up with non-identical results and it needs to be understood infinity in this case is not that sideways lazy eight, its the number [inaudible 00:29:05] which is a number. It is the cardinal number of infinity and it would be identical minus identicals yields non identicals, and I submit in reality that’s absurd.
Video:
As for zero, I think zero is very problematic frankly. I mean suppose someone said there’s an elephant in the quad, and I said, “Well, I don’t see any elephant in the quad.” And he says, “Well, there is an elephant in the quad and its number is zero.” Well, I think that’s very problematic. I don’t think there is such a thing as zero, it means just the absence of something.
Trent Horn:
As Craig notes the problem lies not with arithmetic using zero or arithmetic using infinity, but the existence of actual infinities or an actual zero in the real world. Millican and [inaudible 00:29:54] their use of zero it doesn’t help here because you can just say that like actual infinities, zero does not exist in the real world. Zero is not a thing with no value, it’s a way to describe the absence of real things. For example with the natural numbers you can say, I have two books or I have books and their number is two. But while you can say I have zero books, it makes no sense to say I have books and their number is zero. Zero is very different. Zero and infinity have important roles in the world of mathematics. But when you try to instantiate them in the actual world as if they really existed, you get contradictions which reveals simply that these things, these mathematical concepts can’t have physical existence in the real world.
Vidoe:
As we saw earlier when presenting to a lay audience, Craig has claimed that the infinite is contradictory.
Video:
But mathematicians recognize that the existence of an actually infinite number of things leads to self contradictions.
Trent Horn:
No, Craig does not simply say the infinite is contradictory. Even in a debate like the one with Christopher Hitchens which is where this clip is from, where you have very little time to speak. Craig takes care to say that only a specific kind of infinity is contradictory.
Video:
The existence of an actually infinite number of things leads to self contradictions.
Vidoe:
But when talking to philosophers a different claim is made.
Video:
Now, Alex is certainly right that when we appeal to these absurdities we are not talking about logical contradictions or incoherence. Jose [Benardt 00:31:38] 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.
Trent Horn:
It’s not a different claim, in the second clip Craig is teasing out what he means by impossible or contradictory. He’s saying that he’s referring to as we said before metaphysical impossibility or contradiction, rather than logical impossibility or contradiction. That is what Craig means in the statement from the Hitchen’s debate, because he uses the phrase an actually infinite number of things. So this is not a case of Craig contradicting himself or pulling the wool over his audience’s eyes, what is explicit in the dialogue with Malpass is implicit in his debate with Hitchens, and Craig would be prepared to defend it if Hitchens objected to it. But Hitchens in that debate he didn’t even make a half-hearted attempt to try to refute the Kalam argument for God.
Video:
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 at something seems absurd is enough to forbid it from existing, in reality [inaudible 00:33:03] have to be a lot bolder than that and a lot more open minded.
Video:
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.
Trent Horn:
Here I think that Isaacson, the mathematician being quoted has misunderstood Craig. He might think Craig’s appeal to Hilbert’s hotel means that Craig denies the concept of infinity. This might be why he talks about someone who only believe in the potential infinite rather than the actual infinite. Now there are mathematicians who reject the infinite, but they’re a very small minority. One of them Doron Zeilberger, he proudly calls himself a math heretic, but Craig is not one of these mathematical finitist, one who would deny the infinite and say that only the finite exists. He writes finitism would too radically truncate mathematics to be acceptable to most mathematicians. And he says that his thought experiments are “Employed on behalf of metaphysical not mathematical finitism.” Now Craig himself is a nominalist, he doesn’t believe any abstract objects whether they’re finite or infinite actually exists, but that’s a discussion for another time. Rather, the point is that once again I feel like I’m infinitely repeating this. Craig affirms the actual infinite can exist abstractly in the realm of mathematics, but not in the physical world.
Trent Horn:
[inaudible 00:34:46] to the mathematician that Craig quotes in the dialogue with Alex Malpass, he makes the same judgment writing this, viewed in abstracto there’s no logical contradiction involved in any of these enormities, but we have only to confront them in [concreto 00:35:01] for their outrageous absurdity to strike us full in the face.
Video:
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 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… I mean 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 then one way they’re free to move to different rooms. I mean it’s just impossible that yesterday didn’t happen given that it has happened.
Trent Horn:
First, it seems like Malpass is conceding a little bit on the example. He doesn’t just bluntly say well manipulating the infinite is an impossible, so what’s the big deal. Instead, this is what I think Malpass is saying in this clip. It’s not the existence of an infinite hotel that is impossible, it’s just doing certain things in an infinite hotel that’s problematic, like adding or subtracting guests. But here’s what I find unsatisfying about this kind of response. This would be like saying changing the past is impossible which as we see Malpass agrees, but you could still travel back in time, you could travel in the past, you just couldn’t change anything. But what if you really had an infinite hotel or you really had a time machine, it seems like under Malpass’s view, in order for the paradoxes to not happen there’d have to be like some kind of mysterious force that would just keep the doors of the hotel closed or would always cause your gun to jam when you tried to go back in time and kill your younger self.
Trent Horn:
Now other philosophers have argued that the high number of coincidences that are needed to make time travel possible, actually counts as strong evidence saying that it’s impossible to do any kind of time travel into the past. Likewise, the philosopher Alex Pruss has said there is something strange about saying infinite things or in Pruss’s case infinite causal chains could exist, but there be some mysterious force that prevents paradoxes from occurring. This view it almost seems to [inaudible 00:37:39] a kind of God that exists that would protect the world from paradoxes of the infinite, instead of just saying the infinite can’t exist because that fact could be used later to prove God actually does exist.
Vidoe:
Another example given to try and refute infinity are the orbits of Jupiter and Saturn.
Video:
Supposed that for every one orbit Saturn completes around the sun, Jupiter completes two. The longer they orbit the further Saturn falls behind. Now, what of these two planets have always been orbiting the sun from eternity pass, which has completed the most orbit? Strangely enough the number of their orbits is exactly the same, infinity, but that seems absurd for the longer they orbit the greater the difference becomes.
Video:
If they were all this orbiting, then there is no notion of one being… at any given point having gone twice as many times as the other, that just doesn’t make sense.
Video:
The hypothesis is not that they start orbiting at some point in time and that they’ve done zero orbits at that point. But if the hypothesis is that they’ve always been orbiting, then it’s just the case that they’ve both always done infinitely many orbits. There’s no sense in which you draw a graph that they start a zero and then diverge away from each other, and then one of them catches up or something. They’re just both always having done infinitely many.
Trent Horn:
This was St Bonaventure’s objection to the past being infinite. And I agree though it’s not the strongest counter example, but we can take the observation that an infinite process into the past is always infinite, and show that the past itself can’t be infinite. One example I gave was from my debate with Ben Watkins and that would be the following, right? Imagine that the rooms in Hilbert’s hotel were constructed one room per year for all eternity passed. Each construction worker receives a piece of paper from the worker who built the previous year’s room. If the paper is blank, the worker writes the number of the room he just built on it. But if the paper already has a room number on it, then the worker passes that piece of paper along to the worker constructing next year’s room. Now here’s the question, what number is written on the paper given to the worker who was building this year’s room?
Trent Horn:
There has to be some number written on the paper because if the paper were blank, he would just write his own room number that he built in this year. But the paper it couldn’t have been blank, because the construction worker who built the room the year before him, well, he would’ve written his room number on it but then that he wouldn’t have written his room number on it, it wouldn’t be blank, he’d get the number from the previous year. If this goes back forever into the past we’re going to have a paradox. A piece of paper arrives in the present and it must have some room number on it, but it can’t have any particular room number on it, we have a paradox.
Trent Horn:
Now this particular example is based on one offered by the philosopher Robert Koons, but other paradoxes have been offered of infinite causal chains by people like Alex Pruss in his book, Infinity Causation and Paradox. And in that at book he argues that when you take all the paradoxes together, that result from allowing the infinite to exist in the physical world, you get a strong case that what they all have in common is not doing something illicit with an infinite quantity, but just the mere fact that an infinite quantity or causal chain exists in the physical world, so that the infinite causal chain or infinite history or infinite set, that is what must be impossible in all the scenarios and therefore an actually infinite set or actually infinite past causal series can’t exist.
Vidoe:
Infinity is accepted by mathematicians.
Trent Horn:
Most mathematicians but not all. Intuitionism is a school of mathematics, a very small school that treats every infinite as a potential infinity. It denies the actual infinite, but more importantly infinity is also so accepted by William Lane Craig, just not an infinite set existing in the physical world. Now this is me repeating this clarification, I felt like I’ve said this in infinite amount of times, now this would be infinity plus one saying it.
Vidoe:
So what about physicists?
Speaker 11:
So in regards to infinity and physics, the only that we have is an observer cannot measure an infinite number because infinity is not a number, things that are observable cannot be infinite but things like the entire volume of a space or the entire duration of time can be infinite as long as an observer cannot measure them.
Speaker 12:
Roger, why don’t you start with the absurdity of a Hilbert hotel, that you can’t-
Speaker 11:
It’s not an absurdity, it’s just what happens if you have infinity. I mean that was the major thing that Cantor had showed you can talk about infinity in a serious way, and you deduce very powerful results from talking about infinity in the right way. You have to be careful when you talk about infinity, but yes if you’re careful talking about infinity is perfectly reasonable. So I can’t see a general statement about infinity is not physics.
Speaker 12:
I think what Roger’s probably thinking is what I would think is that there’s certainly a well defined mathematical description that one can imagine, where’s some function that’s defined for all time that describes what’s happening at all time. Maybe a [wave 00:43:23] function that evolves with time and is defined for all time. And how did we get to now question really just doesn’t arise at the time [inaudible 00:43:35] that we call now, the way function says that certain things are happening. And if that’s an accurate description, that’s what’s happening. Well, it doesn’t have to start at the beginning at minus infinity and go through all the times to get to now, one is just here now.
Trent Horn:
The problem here is that physics often includes things in models that don’t correspond to the actual world. For example, consciousness can’t be represented in the equations of physics, but you and I are clearly conscious beings. So we need to be careful about relying on physics to tell us what can or can’t exist in the physical world, because some things exist that can’t be modeled and we should be careful when people say some things can exist, merely because they are in the models of physicists. For example, physicists might use things like imaginary numbers which are the square root of a negative number in their formulas. But that doesn’t mean you could have an imaginary number of things in the real world. In his book, A Brief History of Times, Stephen Hawking described how you could use imaginary numbers as time coordinates in order to get imaginary times, in order to solve the equations of physics.
Trent Horn:
Now, while the models may use these numbers, Hawking admits, “We may regard our use of imaginary time and Euclidian space time as merely a mathematical device or trick to calculate answers about real space time.” In a book he co-author with Roger Penrose called the Nature of Space and Time, Hawking admitted, I take the positivist viewpoint that a physical theory is just a mathematical model and that it is meaningless to ask whether it corresponds to reality. So since physics is really applied math and we agree the infinite can exist in the realm of mathematics, the fact that you can use the infinite in physics equations it doesn’t show the infinite can really exist in the physical world because the equations and models that are used in physics, they don’t necessarily directly correspond to the way the world really is. And many physicists even like Hawking will say they don’t care that it doesn’t.
Vidoe:
Craig claims that the infinite past is impossible because one can’t reach infinity by success of edition, which is true if you only have a finite amount of time, but what if you have an infinite amount of time, could you count all the numbers then?
Video:
Yes, if you are counting forever, if you’re never finishing.
Trent Horn:
This misstates Craig’s argument from successive edition. So here’s how he put the argument in a 2005 debate with the philosopher Austin [Daicy 00:46:21].
Video:
A collection formed by adding one member after another cannot be actually infinite. The series of past events is a collection formed by adding one member after another, therefore the series of past events cannot be actually infinite.
Trent Horn:
Craig’s argument is not about reaching infinity in a certain amount of time. It’s about the fact that time itself which is a temporal series of events forms by successive addition, one time, at least that’s true under the view of time Craig defense called presentism, the view that only the present exists. If time forms in this way then time itself it could never be infinite, because you could never form a finite temporal series and form it one at a time and change it from being finite to infinite.
Video:
There is a sense in which you can count them all and it’s the following sense. Given any individual counting number however big, a million, a billion, a trillion, you’ll eventually get there. It doesn’t mean that you ever will reach the point that you can stop and say done it, I’ve now finished. I’ve counted all the infinite numbers, that never happens. However far into the future you go, you’ve still got infinitely many numbers still to count. So, no this isn’t a task that [inaudible 00:47:48] but we didn’t claim that it did. The claim was only that you can count infinitely many numbers in an infinite amount of time.
Video:
Okay, so sometimes the problem is supposed to be that we can’t transition from the finite to the infinite, after all if we’ve got something finite and we add a finite amount to it then the results going to be finite. So no matter how many times we do that we’re never going to break out from the finite to the infinite. The problem is not so much that that’s false and it seems to me that that’s true, it’s just that the hypothesis of the past having no beginning is such that it’s always been infinite. It’s never been any point in the past where there’d only ever been finitely many so there’s no need for a transition.
Video:
So, you never get to the end of this process, you never get to the last biggest counting number, this is a sequence. The sequence of counting numbers is a sequence without an end, but that’s perfectly acceptable, that makes perfectly good sentence. The fact that you can’t get to the end is indicative of the fact that there is no end.
Trent Horn:
Let’s return to Craig’s argument. He says the following premise one, a collection formed by successive edition cannot be an actual infinite. Number two, the temporal series of events is a collection formed by successive edition, and three therefore the temporal series of events cannot be an actual infinite. Now, as we saw in this clip Malpass agrees with premise one where that you can never add enough to a finite collection in order to make it an infinite collection, it’s impossible. So the documentary he rejects premise two, or that the past is formed by success of edition one event at a time. But it only rejects this premise by just assuming the past did not form by successive edition of temporal events, without making an argument for that assumption and it doesn’t engage Craig’s defenses of premise two arguing for this.
Trent Horn:
And what Adrian Moore one of the people being interviewed says about an endless future, it’s compatible with the Kalam argument because under Craig’s view an endless future would be a potential infinite that can exist. It’s potentially infinite so it can exist, whereas the past is an actual infinite that cannot exist. That’s because if you start at zero and begin counting, you will count a potentially infinite number of numbers. Now we know this because at any point you pick along the counting process into the future, you’ll always be counting a finite number. You’re never going to be counting a trans finite number like aleph-seven, and Craig doesn’t deny this he writes, the only sense in which there will be an infinite number of events in the future is that the series of events will go toward infinity as a limit. But that is the concept of a potential infinite, not an actual infinite.
Trent Horn:
So there’s nothing contradictory about an endless future though that will be challenged a little bit later here in the documentary, but Craig’s assertion is that a beginningless past that’s not like an endless future. A beginningless past is an actually infinite temporal series of events and this kind of collection can’t be formed by successive edition. So under this view the future and the past are very different.
Vidoe:
Suppose we agree the infinite is impossible. What does that mean for the infinite future? Supporters of the Kalam are generally committed to this idea, not just because religious text seemed to promise it, but also because some alleged that our lives have no meaning without it.
Speaker 13:
That on a naturalistic worldview, everything is ultimately destined to destruction in the heat death of the universe. Our moral lives become vacuous because they don’t have that kind of cosmic significance.
Speaker 14:
I still need to have you explain that for me better, because again it seems to me it’s one thing to say it lacks eternal cosmic everlasting significance, it’s another thing to say it lacks significance. In fact, to give one of your examples you talked about… again, I can’t remember the source of this quote, but the torturers, was it Nazi tortures, right?
Speaker 13:
Yeah.
Speaker 14:
You say if theism isn’t true, then it doesn’t really matter. This strikes me as… I’m sorry, I’m sure it’s going to sound rude, but it strikes me as an outrageous thing to suggest, it doesn’t really matter. Surely it matters to the torture victims whether they’re being tortured. What doesn’t that this makes some cosmic difference to the eternal significance of the universe for it to matter whether a human being is tortured, it matters to them, it matters to their family, it matters to us. So again how do you move from the lack of eternal significance to the thought that if it doesn’t have eternal significance, it can’t have any significance?
Speaker 13:
Because the victim that obviously matters to him in the sense that he’s in pain and agony, but ultimately it doesn’t matter that he was ever in pain and in an agony. The whole thing just degenerates into utter meaninglessness and insignificance.
Vidoe:
It’s hard to see how someone can claim that infinity is incoherent and then state that our lives are meaningless unless they are eternal.
Trent Horn:
Actually, infinite collections are incoherent but our lives have the fullest meaning when we see they don’t end. And as I’ve shown an endless future is a potential infinite that’s possible rather than an impossible actual infinite in reality. Now I’m not going to defend Craig’s argument about the meaning of life because it’s not directly related to what we’re talking about, which is the Kalam argument. However, I think what Craig seems to be getting at is that ultimately our lives lose meaning if everything fades away into dust as time passes. Now, as I said I’m not going to go in depth into that argument, there are objections that can be raised to it. What’s more important are claims that the Kalam argument would show an infinite future is impossible, which contradicts nearly all theology that Christians hold.
Vidoe:
After all the infinite future seems to have remarkably similar properties to an infinite hotel.
Video:
If you think about the number of events in the future as like equivalent to the number of guests in the hotel, and then as time passes we are removing an event from the future and putting it in the present. And we can ask how many events are there left in the future? It’s the same number of events in the future as there were before that event entered the present. So even though we’ve taken one away, we’ve got the same number left, and that’s exactly the same property. It’s adding one guest and having the same number of guests after adding it in. So if one of them is problematic, so is the other.
Video:
If the idea of infinity is putting pressure on the idea of an infinite past, then it’s going to put equal pressure on the idea of an infinite future. There’s no clear asymmetry there that means that one of those is problematic in a way in which the other isn’t.
Trent Horn:
Asymmetry would mean there is something that gives us a good reason to say the past can be treated in a different way than the future. And I think you can show there is such a asymmetry. One of the chief complaints against Craig’s argument is that even if an actual infinite is impossible and infinite past is not an actual infinite, so it’s not a problem. What makes Hilbert’s hotel paradoxical is that all the guests exist at the same time. But if each hotel room, let’s say it only appeared for one second and then disappeared before a new hotel room reappeared, then this happened for all eternity. At any given moment you wouldn’t have an actual infinite you just have one hotel room, and that would better seem to correspond to Craig’s view of time which is called presentism, that says only the present moment exists.
Trent Horn:
And if only the present exists then an actually infinite past never exists, so there’s no problem. Frankly, I’m surprised the documentary didn’t lean more into this objection to Craig’s argument, because it’s a strong one. So you could use this reply against Malpass objection, you can say, look what you’re saying about all these future events, trying to put them together to make a paradox well the future events don’t exist or at least they don’t all exist at the same time for one of these paradoxes to happen. You can talk about them, but they’re not all together at the same time so there’s no problem. But now there seems to be a problem if we were refute Malpass’s objection in this way about an infinite future aren’t we refuting Craig’s argument because all of the infinite past moments don’t exist together at the same time.
Trent Horn:
Now Craig has several ways of addressing this objection, but one approach I like actually comes from another philosopher Andrew Locke, and here’s what he asked us to do to show the past and the future are different and how this objection… this reply would diffuse Malpass’s objection but still show that an infinite pass is impossible. Here’s what Locke asks us to imagine. Suppose Hilbert’s hotel is constructed at the rate of one room every year and each room is equipped with a device that creates an immortal guest who checks in, kind of like my example of building the hotel over time with the paper passers. Now, if this process happened across the span of an infinite past, then in the present moment there would be a hotel with an actually infinite number of rooms each of which is occupied, and paradoxically actually every moment in the past there would be a hotel with an infinite number of rooms, just like when I gave the counting example with the blocks stacked as the tower, just as like every moment in the past you’d have an infinitely high tower which doesn’t make sense.
Trent Horn:
You would have a hotel with an infinite number of rooms if the rooms were built one room one year at a time, and you would have that with an infinite past, it would be actually infinite at every moment in the past but if you built one room at a time starting in the present going to an endless future, you would only have a finite hotel just like you would have a finite collection of counting blocks. So then we can take all of this and use it to create Locke’s version of the Kalam argument, it would go like this. If an infinite past is metaphysically possible, then Hilbert’s hotel is metaphysically possible. Hilbert’s hotel is not metaphysically possible, therefore an infinite past is not metaphysically possible. Okay? Now, a few things about this argument. First, it doesn’t require us to say past itself is an actual infinite.
Trent Horn:
It only commits us to the view that in an infinite past, you could have impossible states of affairs like Hilbert’s hotel. We’re not saying the past is a contradiction, but that the past… an infinite past entails contradictions, and so there cannot be an infinite past. And as I said before you can’t apply this to an endless future because if you kept building in an endless future, you would always have a finite hotel and no finite collection as Malpass says in the documentary can ever become an infinite collection. Whereas if you had always been building in the past, you actually would’ve always had an infinite hotel paradoxically enough. So now we have an asymmetry that shows an endless future is possible, but a beginningless past is impossible.
Vidoe:
Craig’s response to this problem is to suggest that an infinite past would be actual, but the infinite future would only be potential.
Video:
It seems to me that this rests on a mistake because Craig instead of focusing on the question, how many future events will there be if the future is endless, to which the answer is infinitely many. Craig instead switches to how many future events will have been, and that it’s true is always finite and increasing over time and approaching infinity but never getting there. But it’s problem is that those two things are compatible with each other, and for one thing it’s changing the subject if you say how many events will there be, and to answer in terms of how many events there will have been it’s changing the subject, but also they’re both true. I mean even though there will have been finitely many events, it’s also true that there will be infinitely many events in the infinite future, those two are not incompatible with each other.
Trent Horn:
I believe we can still identify an asymmetry between a beginningless past and an endless future that gets around the problem of identifying things via a different tensed language. So as we saw on the block and Locke’s version of Hilbert’s hotel, the endless collection of future events is completely formed by successive edition. But the beginningless collection of past events is not completely formed by successive edition. You might be able to add members to an already infinite collection and form it by success of edition that way, but there will have always been an infinite that previously existed, that we know could not have been formed by successive edition. Now this is a point actually that Craig brought up in his dialogue with Jimmy Akin on the Kalam argument.
Video:
When I speak of forming an infinite collection I mean completing an infinite collection, and the series of past events is completed in the present event. And so we can talk about two ways of completing a collection by successive edition, one would be by starting at a point and never ending, the other way would be by never starting but ending at a point. And it seems to me that that second way is even more inconceivable than the first way. How could anyone successively enumerate all of the negative numbers consecutively ending at zero? To me that seems like an inconceivable task and I’m certain it’s true that if you just give someone say all of the negative numbers up to negative five, then he can complete the collection from negative five down to zero, but that’s not the issue. The entire series needs to be formed or completed by successive edition, and that to me seems inconceivable, meta physically impossible.
Trent Horn:
So, in this case we can still identify an asymmetry to treat the past differently than the future, so that future events are potentially infinite but past events that are beginningless, they are actually infinite and an actually infinite past or a beginningless past would be impossible because if one could exist, you could have meta physically impossible situations like Hilbert’s hotel.
Vidoe:
The infinite future is not the only infinity supporters of the Kalam tend to embrace. They’ve also claimed that the Big Bang singularity proves beginning of time.
Video:
Rise at a state of infinite density at some point in the finite past. This state represents a singularity at which space time curvature, along with temperature, pressure and density becomes infinite. It therefore constitutes an edge or boundary to space time itself.
Video:
The argument by Lane Craig that the fact that there’s… that the infinite past is impossible and therefore that conception of the universe is untenable, is incompatible with their claim that there is a singular point at which the universe originates, because the properties of that singularity are entirely infinite.
Video:
Precisely what a singularity is as John Barrow has forcefully emphasized is something that involves a kind of actual infinity, for physical reasons involves a kind of actual infinity. And this is precisely what these very same thinkers said that they were suspicious of. So to put it very bluntly and very crudely, are they trying to have their cake and eat it, accepting an actual infinity in one context while trying to dismiss it and being suspicious of it in another context.
Trent Horn:
First, when people describe the singularity as being infinite, that doesn’t mean the singularity is an actually infinite collection of distinct objects like what we have with Hilbert’s hotel. Instead, the singularity is infinite in the sense that the density of the entire universe is compressed into a point of zero volume beyond any calculation. The late atheistic philosopher Quentin Smith described it this way, here’s what he writes. If the universe is finite and the Big Bang singularity a single point, then at the first instant the entire mass of the universe is compressed into a space with zero volume. The density of the point is N over zero, where N is the extremely high but finite number of kilograms of mass in the universe. Since it is impermissible to divide by zero, the ratio of mass to unit volume has no meaningful and measurable value and in this sense is infinite. In the article from John Barrow, Barrow wasn’t talking about the singularity at the beginning of the Big Bang, but the hypothesized singularity that’s in every black hole.
Trent Horn:
But here’s what he goes on to say in that article, people’s attitudes to these infinities differ, cosmologists who come from particle physics and are interested in what string theory has to say about the beginning of the universe would tend to the view that these infinities are not real, that they are just an artifact of the unfinished character of our theory. And here is John Barrow himself cautioning about the use of the word infinite with something like singularities.
John Barrow:
Well, in generalistic cosmology we know the long history of singularities, how do we characterize them? Why it’s not wise perhaps to characterize them primarily in terms of infinities in any physical quantity, but in terms of [inaudible 01:06:57] incompleteness. And then to try to prove theorems that show that infinities of a particular well defined sort may accompany those incomplete [inaudible 01:07:08]
Trent Horn:
So, we have good reason to believe that singularities aren’t examples of impossible actually infinite sets, but even if the singularity were an actual infinite just like Hilbert’s hotel, that’s not a problem for Craig because the Kalam argument does not rely on the universe beginning from a singularity. And in fact while the talk of a singularity was commonplace among cosmologists several decades ago, astrophysicists like Ethan Siegel say the proposal is about 40 years out of date. In his article there was no Big Bang singularity, Siegel says that what we’ve observed in the background radiation of the universe shows the universe it never reached the really high temperatures we would expect if it came out of a state of infinite density. He also says that the evidence for an inflationary universe… We’ll talk about that in part two, would show that it must have come from a finite part of space time.
Trent Horn:
So, as I said inflationary universes that’ll come up later, I’m not going to go into that now, instead I just want to note that Craig acknowledges the existence of other models of the origin of the observable universe that don’t include a singularity. But he claims that they “Feature an absolute beginning of the universe, even if the universe does not come into being at a singular point.” So nothing about the singularity can be used to refute the Kalam argument.
Vidoe:
Mathematicians do not think infinity is contradictory. What may be contradictory is claiming that infinity is both a contradiction and not a contradiction. Claiming that the infinite past is incoherent when the infinite future is embraced, and claiming that at the beginning of time is confirmed by the Big Bang singularity which itself involves infinities.
Trent Horn:
Since these are all Straw man assumptions that I’ve already addressed, nothing more needs to really be said.
Vidoe:
A further problem for the Kalam argument is that it assumes an eternal universe would’ve had to traverse infinite time in order to get to a unique now, but in relativity there is no such notion, time is relative. In order to tackle this Craig appeals to what is known as the Neil Lorentzian interpretation of relativity, which does restore a unique sense of now.
Trent Horn:
So I don’t think this next section is very helpful for the documentary’s argument because it’s easy for the viewer to get confused, as it would assume one knows the difference between things like general relativity and special relativity or what the Neil Lorentzian interpretation of special relativity is. So let’s watch the section and I’ll show why it doesn’t refute Craig’s argument.
Video:
Discovery with Copernicus is that the earth is not the center of the universe. Well, but you can always rethink the earth… you can imagine that you can add a center, nobody prevents you for doing that, you just complicate life for yourself, and it’s the same for special activity. You can add a preferable reference frame, it’s not visible, it’s not detectable, but you think it’s there, that’s the new Lorentzian [inaudible 01:10:28] What do we gain? The only thing we gain is that we can do the new physics with old mindset, but I think we should adapt our intuition to the new physics not adapt new physics to our intuition, right? When we discover this round, that’s up that up, that’s down, but if you’re in Sydney it’s the other way around. [inaudible 01:10:56]
Video:
I mean you have to adapt your intuition of adapt down to the discovery not the other way around Physicists are not particularly keen about new Lorentzian individual special activity. And in sense that when you go to general relativity, have a neo-lorentzian interpretation is much harder because in special activity you just pick a frame and you… in general relativity there is no global frame too. I think everything in physics [inaudible 01:11:29] there is no preferred time slice, there’s no preferred time.
Vidoe:
Craig has suggested there is a universal clock that gives us a unique, that is cosmological time, the time since the Big Bang.
Video:
Cosmic time is the same for every hypothetical observer in the universe, regardless of his state of motion. In other words, cosmic time is a kind of reinstatement of Newton’s absolute time.
Video:
Well, cosmological time is a fake. Why? Because matter, gravity is lost time so inside the galaxy clock goes slower than outside. Point is there are many different clocks in the universe which they don’t agree with one another, and there are many times in the universe which don’t agree with one another. The idea of the cosmological time is just one arbitrary definition of an average, but I can give a different definition of [inaudible 01:12:29]
Trent Horn:
All right, so this objection is basically that Craig assumes there was an absolute measurable amount of time from the Big Bang, but this seems to be denied by relativity theory. Relativity theory shows that local clocks, they run at different speeds. Like when you get near a black hole, time can go faster or slower. This has shown really well in the movie Inter-stellar, by the way definitely see it if you haven’t watched it yet, but scientists can still calculate the amount of time that has passed since the Big Bang, about 13.7 billion years. So, that’s not really the problem, instead the objection is about Craig’s view of time or presentism because he holds that there would be an absolute present moment, one present that is the same for all observers. But relativity theory says there are things like the relativity of simultaneity which is a fancy way of saying there’s no unique present moment for everyone that might be confusing. Check out some videos on YouTube, they’ve described this in more detail, but this rough description should be good for us right now.
Trent Horn:
So Craig’s view seems to imply there is one absolute present moment. Relativity theory says there is no such thing, but this doesn’t refute the Kalam argument for several reasons. For example, you could just adopt another view of time that’s compatible with the Kalam argument and is more friendly to relativity theory. In a podcast I did a while ago, I talked about my preference for the growing block view of time, which says the present and the past are real and time is like a growing block of existence. George Ellis, he’s one of the world’s leading experts on relativity theory.
Trent Horn:
He even coauthored The Large Scale Structure of Space Time with Stephen Hawking, he endorses this view of time so it’s not like a fringe theory thing, it’s minority but it’s not fringe. Or you could defend presentism but just reject how special relativity is applied in this case. The Catholic philosopher Ed Fraser points this out, he writes the most that special relativity rules out is a privileged reference frame that is empirically detectable, but that makes the notion of a privileged reference frame objectionable only if one assumes verification is… or some other brand of scientism, which are philosophical position rather than anything required by the physics and positions which I argue we already have ample reason to reject whatever we think of special relativity. So this just might say that the Kalam and the presentism it’s not compatible with the equations that are used in special relativity theory, but not with reality itself because we’ve already seen that the equations in physics, the models in physics don’t necessarily describe reality as it actually is.
Trent Horn:
Finally, this objection won’t work against versions of the Kalam argument like Andrew Locke’s I discussed earlier that show the infinite past is impossible just because it allows for meta physically I situations or Alex [inaudible 01:15:34] arguments, which show that no effect can be generated by an infinitely long causal chain. All right, so that concludes part one of my review of Skydivephil’s documentary on the Kalam cosmological argument. Next week, I’m going to discuss the second half of his documentary where he moves from the philosophical arguments for the finite past to talking about the Kalam first present… first premise, which is whatever begins to exist has a cause, and the scientific evidence for the beginning of the universe from astrophysics and cosmology. And by the way if you like this video don’t forget to like it, subscribe and definitely support us at trenthornpodcast.com so we can keep making great content like this.
Trent Horn:
Thank you guys so much and hey I hope you have a very blessed day, come back next week for part two of our reply of Skydivephil’s anti-kalam cosmological argument documentary. Thank you guys, hope you have a blessed day.
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