In this episode Trent sits down with Alex Malpass, one of the foremost critics of the kalam cosmological argument, to discuss objections Trent raised in his previous rebuttals of SkyDivePhil’s documentary on the argument.
Welcome to the Council of Trent podcast, a production of Catholic Answers.
Trent Horn:
Hey everyone. Welcome to the Council of Trent podcast. I’m your host Catholic Answer’s apologist and speaker Trent Horn. Recently I’ve been talking a lot about the Kalam cosmological argument and I’m excited for the guests I’m going to dialogue with today because he’s written a lot about the argument. He’s a critic of it, but a very thoughtful one. I think our exchange will be helpful to see things that we might agree about when it comes to the argument, where we disagree about, and help people to explore this very popular argument that’s very multifaceted, if you will. Without further ado, my guest today is Alex Malpass. He is a philosopher. I want to say, I should have your bio printed out, University of Bristol?
Alex Malpass:
Well, no, I did my PhD there. I worked there for a little bit.
Trent Horn:
Okay.
Alex Malpass:
I don’t currently work there.
Trent Horn:
Oh, okay, but I did connect. I was like, he has something with university of Bristol. You are a philosopher. You’ve published several papers on this and on another issues, but yeah. Feel free to tell people a little bit more about yourself.
Alex Malpass:
Well, that’s probably enough for this context. Yeah, I’m a normal person. I’m not some superstar philosophy guy or whatever. I always feel weird talking, giving a bio. I like discussing these things because it’s fun. I don’t take it super seriously in terms of like, finding the truth necessarily or, like pwnage, or some of these people get really into trying to humiliate their opponent by crushing them in debates or something. I don’t really tend to do it like that.
Trent Horn:
Well, I think that’s refreshing to hear. I think it’s hard. A lot of people, sometimes they’ll watch dialogues between two individual, especially on a tough issue and they’re just looking… I love you using the term pwnage which has to be spelled P-W-N-A-G-E… Which because someone, if they’re just hacking at their keyboard like a cave man will hit P instead of the O because they want to own somebody. You’re right. Now I do think that we want to come to the truth and we’ll see which views make sense to us, which don’t, but I think it’s always good for different views to have clash and to help people to understand.
Trent Horn:
Let’s jump into it then. We’re talking about the Kalam cosmological argument. If you’ve been checking out my channel, I’ve discussed it in the past few weeks, but just us as a refresher for everyone, the argument is whatever… Well, the argument was popularized by William Lane Craig, a Protestant philosopher in a 1979 book. Brought it out of relative obscurity, and now when you go on YouTube, you type in Kalam cosmological argument, like millions of videos of things on it. If anything, it gets a lot more treatment than a lot of the other cosmological arguments. I think, Alex, maybe you’ll agree with me, I think one reason I think that is because the argument is deceptively simple. That’s how I described it in a previous video. I don’t know if you would agree with that.
Alex Malpass:
Certainly. Yeah, yeah, absolutely.
Trent Horn:
Okay, so just to put it out there, whatever begins to exist is a cause. The universe began to exist, therefore the universe is a cause. A lot of people use this argument in support of the existence of God, so then what they would do next is if you can establish the universe as a cause you would do some kind of conceptual analysis of what the cause is to try to show that either by necessity or at least probability, it would have divine attributes or things like that. That would be our quick overview of the argument. I guess, would you agree with that kind of basic assessment of it? Summary?
Alex Malpass:
Yeah. I mean, it doesn’t really matter exactly whether you think that the Kalam is just the first bit of that or if the Kalam has two stages in it or something. Same argument regardless of where you draw that boundary. Yeah, so it’s basically trying to establish that the universe has a cause and then to show that the cause is like a personal creator deity kind of thing.
Trent Horn:
Then talking about the argument… I was thinking through my head how we would run through this. I would say that the two, well, I guess there’s three elements to it. One would be whether the argument is valid and then the other two would be the truths of the major premise and the minor premise. Whatever begins to exist is a cause and the universe began to exist. I think a lot of the discussion tends to focus around premise two, like how do we establish that the universe began to exist? Can we do that strictly speaking by reason alone? What does science tell us about this?
Trent Horn:
In this dialogue, I’m going to focus more on just the philosophy aspect. The question of mathematics, philosophy. Can reason tell us whether the universe began to exist or not. That is a question that has been pondered… The first person I know who kind of built up the argument a lot was a guy named John Philoponus in the sixth century. He was writing against the Aristotelians against the eternality of the world. He proposed the idea you could use reason to show it’s the universe must have a past that is finite. Then when you get into the middle ages, you get a branch.
Trent Horn:
What’s interesting here, and this is important for our listeners to know… that there are atheists who disagree with the Kalam argument, but there are also theists and Christians who disagree with it as well. My colleague Jimmy Akin is a fellow Catholic. He follows the tradition of St. Thomas Aquinas. He doesn’t think the argument works. I would be more in line with St. Bonaventure, who thought that it did work. Just so people know, you could be a good Catholic and not accept this argument, but I still think it’s a good argument.
Trent Horn:
All right, so when we deal with the premises, there’s different philosophical ways to defend the most controversial one, did the universe begin to exist? Let’s zoom out a little bit. Do you think the argument’s overall structure, though, that it’s valid? I mean that the structure itself, the argument is fine?
Alex Malpass:
Yeah, certainly the first bit of the argument, which is just two premises and the conclusion that the universe began to exist, is simple as it could be. In terms of logical form it’s effectively modus ponens. It’s P-O-N, not P-W-N, as you could attempt to write it.
Trent Horn:
Right.
Alex Malpass:
It’s not modus pwnage. Yeah, that’s as simple as it could be. There’s really no question about the validity of the argument. If the premises are true, the conclusion is true by logic.
Trent Horn:
That is helpful to hear because I’ve been writing about the argument and thinking a lot about it since my book Answering Atheism in 2013. I think some of my views are starting to evolve a little bit about how to approach it, but even in addressing the argument, both for the thoughtful critics and the less thoughtful, I have heard some people say that it begs the question that it assumes that there are things that don’t begin to exist, and the only thing that doesn’t begin to exist is God. Therefore the argument tries to sneak God into the premises. I don’t think that’s the case. If you think that by… What’s the law I’m looking for here, maybe excluded middle? That there are either going to be things that begin to exist and things that don’t begin to exist. The set of things that don’t begin to exist, that could be empty. It could be an empty set, but just the fact that the argument talks about that, it makes it possible there’s that kind of thing. It doesn’t mean that it’s begging the question. I don’t know if you’ve heard other people try to say the whole argument’s invalid.
Alex Malpass:
Well, and I can combat the question and be valid at the same time, a question begging isn’t a formal fallacy so it’s kind of separate issues. You could just go P therefore P. Obviously it’s valid, there’s no way the premises can be true and the conclusion is false, but it’s question begging because the premise is the conclusion. Those two things are not… Yeah, I don’t think the argument’s question begging anyway. It seems to me that these put straightforwardly, just everything that began to exist has a cause, the universe began to exist. Therefore, the universe has a cause. I mean that you could just write that in simple, like first order of logic and prove straightforwardly that it’s valid. I think there’s nothing to worry about there.
Trent Horn:
All right, well, let’s get into areas where people might have some worries then. The second premise, that the universe began to exist. There are different arguments that are put forward to try to show that the universe began to exist. William Lane Craig, since the 1970s, has offered two particular arguments. Then there are variations of those arguments that have developed a bit more recently. One of those, well… I guess the two that Craig argues is that it is impossible for an actual… The first one would be the argument from the impossibility of an actual infinite. The second one would be the impossibility of forming an actual infinite by successive edition.
Alex Malpass:
Yeah. The Hilbert’s Hotel argument and the successive edition argument. Yeah.
Trent Horn:
Right. What’s interesting is Craig purports to show that these are two independent arguments to try to establish the conclusion. Though, I think it is interesting that he… Now for me personally, as I’ve used the argument and studied and thought about it, I had found myself gravitating more to the success of edition argument than the actual infinite argument. I think we’ll see why as we discuss it a little bit more. What’s interesting is that if the first argument were successful, you wouldn’t actually need the second. If the first argument was successful beyond doubt. It’s very hard to get an argument that nobody can gain say, but if you can show actual infinites are impossible, you don’t really need anything else. It would seem.
Alex Malpass:
Yeah. That’s certainly right. From a dialectical point of view, anyway, if your opponent agrees with the first argument, then there’s certainly no need to press the second one. Yeah. They’re not independent in that sense, but I think they’re independent generally. I don’t think that they… Well, I think you can make the second one without making the first one. For instance, you could throw away the first one and still try and press the argument.
Trent Horn:
Right. Yeah, and that’s something that I think that in my work, in my older work especially, I’ve used more… probably I’ve altered a bit because you saw the debate that I had with Ben Watkins, for example, that was back in August. There I used a different formulation of the Kalam argument than I had used previously, like in my book Answering Atheism, because I think that it’s a stronger version of it, in coming to reflect more on it.
Trent Horn:
Let’s focus on the different ones. The first argument Craig offers for the finitude of the past is the impossibility of the actual infinite. Then it would go like this: an actual infinite cannot exist or cannot exist in reality. You might have to qualify what it means by cannot exist. An actual infinite cannot exist. A beginningless past is an actual infinite, therefore a beginningless past cannot exist, is what seems to be the first argument.
Trent Horn:
There are two important premises there. Well, one would be actual, infinite can exist. Second one is that the past is an actual infinite. I’m pretty confident of the first premise. The second one gives me a bit more trouble, when I think about it more. You’d agree that’s essentially the argument, the actual infinite argument? Actual infinites can’t exist, beginningless past is an actual infinite, therefore beginningless pasts can’t exist. That’s essentially the argument.
Alex Malpass:
That’s right. Yeah. A lot of Craig’s arguments have the same structure. A conditional premise, if something, then something else. Then second premise is the first thing, and then the conclusion is the second thing. Again, it’s just modus ponens again. That’s cool because it makes it super clear. It’s really easy for people to remember and see the logical structure. What’s going on is often these arguments are so simple that they’re just introductions to the discussion. They’re like a fulcrum around which you can start talking about the things that are really interesting. Why think that an actual infinite shouldn’t exist or-
Trent Horn:
Right. Yeah. It’s so hard now because I don’t want to bore you to tears, but I want to give it a nice-
Alex Malpass:
It’s educational.
Trent Horn:
Yeah. I want to give a nice incline to everybody because especially when we talk about infinity, it starts to spiral out of control and turn into an MC Escher, Dr. Strange type environment.
Alex Malpass:
Oh yes. Absolutely
Trent Horn:
All right, yeah, so that would be the first premise. Can an actual infinite exist. The arguments against the actual infinite, there are a variety of them that are offered. Most people will try to offer thought experiments of things that are actually infinite and then try to show there are contradictions or at least deeply counterintuitive things that happen if you have an actually infinite number of things. The most famous example that Craig offers would be Hilbert’s Hotel. If you had a hotel with an actually infinite number of rooms, each of which is occupied by a guest, what would transpire from that.
Trent Horn:
Now before I continue, I think it’s important for people to understand we’re using a term actual infinite that has a specific meaning to it. When most people think of infinity, they think of the sideways eight. I think it’s called the lemniscate, if I’m not mistaken. That sideways eight. That represents infinity in the sense of approaching a limit that would be never reached, such as the fact that a distance between two points can be potentially divided infinitely. That would be… We always do the midpoint, the quarter point, the one eighth point.
Trent Horn:
When we say actual infinite, what we’re talking about is a definite and complete set that is unlimited. Like the set of all natural numbers or the set of even numbers. It’s that existing that defenders of the argument find problematic. Is that correct?
Alex Malpass:
In the modern period, there’s a specific kind of mathematical way of explaining what we mean here. If you think about all of the counting numbers… 1, 2, 3, 4, blah, blah, blah. That’s obviously an endless number line that has no highest number in it. Keeps going forever.
Trent Horn:
Right.
Alex Malpass:
The kind of smallest version of infinity, the smallest actual infinity is just the number of numbers on that line. That’s how many numbers there are in the smallest infinity. It has a specific property that all infinite collections share, which is that you can… It’s this weird property, but it’s that you can show that some parts of that line, that shouldn’t be as big as the whole line, because it’s a part, are in fact the same size as the whole line.
Alex Malpass:
A classic example is take the even numbers like 2, 4, 6, 8, and match each even to a unique whole number. You match 2 with 1, 4 with 2, 6 with 3, and we keep doing… That’s a well defined operation. You could just imagine assigning the numbers in pairs like that. You can kind of see just straight away that you’re never going to run out of even numbers and you’re never going to run out counting numbers. You’d be able to assign each of them a unique partner to go with it.
Alex Malpass:
That’s enough already to show you that there’s the same amount of even numbers as there are whole numbers. There you go, you’ve got the property that infinite sets have. That’s the sort of most precise… That’s how mathematicians talk about actual infinities. It’s a bit different from back in the day, people like Aristotle would’ve talked about the distinction being whether or not some limitless thing is present all at once or whether it’s spread out over time. Like a clock ticking or something. If it just keeps ticking forever, at any one time it’s only ticking once. There’s only a finite amount of ticks present at any one point in time. If you look out over the whole of time, there’s infinitely many of them. That’s potential infinite as far as Aristotle is concerned.
Trent Horn:
Right.
Alex Malpass:
These terms get bandied about in lots of different ways. There’s a whole history of the infinite where you can see how the terms have you have changed at time.
Trent Horn:
Right.
Alex Malpass:
Yeah.
Trent Horn:
It seems like the defenders of the argument were saying that the actual infinite is impossible. I like to add the qualifier like, in concrete existence or physical existence, because I think a lot of people will say, well how can you say the actual infinite is impossible? We have infinite sets. We can do mathematical operations with them. There are a very small minority of mathematicians called Finitists who don’t believe in the actual infinite, but for most mathematicians, they say, well, no, clearly it does exist. We do math with it all the time.
Trent Horn:
I think Craig and others would say, well no, the problem becomes when you try to instantiate it in reality. Like with Hilbert’s Hotel. I guess this is a question where people are going to disagree about whether these kinds of things are plausible, whether you can have a hotel that is completely full and can always accommodate new guests because you just can shift them into rooms.
Trent Horn:
For example, take the guest in room one, move them to two, move two to three, three to four, and you do that forever. There’s ways you can do you that, that a hotel that’s completely occupied, you can always check in new guests. Problems with subtracting guests when normally with actual infinites or what are called transfinite numbers, normally subtraction with them is undefined. Craig says well, yeah, you’re not supposed to do that in the mathematical world. What happens if people check out of the hotel?
Trent Horn:
I think what people will do is they’ll place that… Hilbert’s Hotel is one example… with the problem of an infinite multitude. Then maybe we can talk about that for a bit, but there are other examples are brought up with problems of things like an infinite magnitude. What do you do with a three-dimensional shape that has an infinite number of parts? Can that exist in the physical world? You get puzzles with infinite magnitude versus multitude.
Trent Horn:
You’re not convinced that there is a problem with the actual infinite existing in reality, that it seems like we just get kind of counterintuitive results or it’s just kind of strange.
Alex Malpass:
I certainly don’t think that we’ve… Well, I mean, I don’t think there are any infinite magnitudes anywhere nearby. Maybe there’s black holes. I don’t know enough physics to give you a good answer about that. I’m not like a defender that there are actual infinites sort of all around the place or anything like that. I’m not really making the claim that they are actually present in the universe, existing or anything.
Alex Malpass:
What I think I see clearly is that some of the arguments that purport to show that there couldn’t be an actual infinite are not actually as convincing as they might seem when you first hear them. When you look under the bonnet and inspect the details, in my opinion, they don’t actually get you to the destination that was advertised. Maybe there are actual infinites, maybe there aren’t. Maybe they’re impossible, but these arguments don’t persuade me towards that. I’m being quite neutral in respect to like, what’s actually there.
Trent Horn:
Right. You’re against the claim that they’re not possible. You’re saying… Well, I don’t know if you’re saying that they are possible. You’re at least saying that they’re not impossible.
Alex Malpass:
Well, I’m saying these arguments are no good. That’s the simplest way to put it.
Trent Horn:
Yeah. Okay. What would you say is your problem with like the Hilbert’s Hotel example?
Alex Malpass:
Well, for one thing, when philosophers make arguments, you want to try and show that something’s impossible, what you want to do is try and show… There’s this basic form of argument in Western philosophy. You try and show that something that’s agreed upon, in present company ideally, contradicts something that follows from the thing that you’re talking about. That’s how you get to show that the thing you’re talking about couldn’t be that, it must be impossible. Contradictions are basically the bedrock thing that we agree on. It couldn’t be a contradiction if this thing was true, there would be, so that thing can’t be true. It’s kind of an argument by contradiction.
Trent Horn:
By contradiction, are you saying logical contradiction?
Alex Malpass:
I don’t know another type of contradiction. Well, I’m talking about proposition and its negation. That’s what a contradiction is. Well, I mean, contradiction is any sentence that’s false in virtue of its form. That’s a technical definition, but the most easy way of thinking about that, is a sentence which says P and not P. There’s no way that sentence could be true because it’s expressing one thing and it’s negation. That’s sort of what everybody means by contradiction.
Alex Malpass:
If we find that we are committed to some proposition P, whatever that is, and then some hypothesis is on the table and it turns out that if that hypothesis was true, then not P would also be true. Now we’ve got a choice. We either have to give up P or we give up our hypothesis. If we all agree that P is true, that’s one way of showing that the hypothesis is false.
Trent Horn:
Perhaps. Or we have to redefine what we mean by P, or qualify it. I Think with Hilbert’s Hotel, what people would point out, like a contradiction would be a hotel where every room is occupied. There’s a contradiction in a hotel that is full being able to accommodate new guests. It seems to make a contradiction about what it means to be full. That will center around, since full is not like a strict logical term… What you mean by that term. Some people will see that as contradictory and others won’t.
Alex Malpass:
Well, so let’s just pick a definition. Full means the hotel can’t admit any new guests. It’s a necessary condition. It’s not plausible to be both necessary and sufficient, but there’s got to be more to being full than not admitting new guests. If the hotel is full, then it can’t admit new guests. Let’s agree on that to begin with. Then it just seems like Hilbert’s Hotel isn’t full because it can admit new guests. There’s not a contradiction there. It’s not both full and not full. It’s just not full, if that’s the definition we’re using.
Trent Horn:
Right. Then I guess one person… You’d have to go backwards. What you would end up saying with a hotel that has a finite number of rooms, it can be full, but an infinite hotel can never truly be full.
Alex Malpass:
Yeah. It’s never full in that sense of full. That’s right.
Trent Horn:
What would be the other sense?
Alex Malpass:
Well, you could just say full means just that all of the rooms have a unique guest in, or something, but just not say anything about whether it can accept new guests. In that sense, it is full because by stipulation there’s somebody in each room.
Trent Horn:
Yeah. I think that… Well, let me answer that and then I might want to make a preface about talking about contradictions, since we’re going to be talking about contradictions and things like that. That how you understand the hotel, because I think for me that if a hotel, as we understand something to be a hotel, to be that kind of thing… If there is a guest in every room, then it follows from that, you cannot have any more guests in it. You’re right, it’ll go back to what you mean by full.
Trent Horn:
I think the other problem that we’ll have here, and this is something I’ve brought up before and I think you’ve discussed with William Lane Craig about, is the issue… We’re talking about contradictions about things like metaphysical possibility. Like is this the kind of thing that can happen in reality versus strict logical contradiction? The idea that can there be a married bachelor? That’s just can there be someone that is a bachelor and not bachelor at the same time? We see the contradiction staring us in the face.
Trent Horn:
There’s a lot of other cases it seems like where there’s not a strict logical contradiction, but we try to understand the nature of the thing as thing and reality, that we tease out a contradiction from it. I think a classic example, and I’m going to forget who… Maybe it was Hegel or Wittgenstein, talked about an object that has color, but does not have shape. It has the property of color, but it doesn’t have the property of shape. Or it has the property of shape, but it doesn’t have the property of size.
Trent Horn:
Someone might say, yeah, I don’t see the problem with an object that’s got color but it doesn’t have shape. Or it’s got a shape, but it doesn’t have any sort of size. The words don’t repel immediately like two negative magnets, but you start to think about it deeper, well, what would that thing be? You can’t wrap your head around it ever really existing. You see what I’m trying to think through?
Alex Malpass:
Yeah, I do, but… The way I see it is like this. What logical possibility means… Strict logical possibility is simply the things you can prove in a logical system, like propositional logic and this baby kind of introductory logic that you do when you study philosophy to begin with. Your first course in philosophy or do this baby logic. There are certain things you can just prove in that, that are both true. Some things are true in virtue of their form, their tautologies. Some things are false in virtue of their form, their contradictions. It’s such a straightforward language, you can very easily learn how to go through these proofs and decide whether a given formula is a contradiction of tautology or neither. It might be neither of those two. There’s ways of determining them.
Alex Malpass:
Logical possibility in its strictest sense, it’s just whether a sentence is false simply in virtue of its form, regardless of exactly what the topic is you’re talking about.
Trent Horn:
Right.
Alex Malpass:
That’s like logical possibility, but then you can increase the scope of the term logical possibility a bit by just thinking about well… Give me any old strict of propositions. If they’re consistent, then they’re logically possible. If they’re inconsistent then they’re logically impossible. That’s a helpful way of being able to use that term. Well, now if we start chucking in some truths that we take to be kind of axioms of, say physics or something, stuff about particles and the laws of physics and where things are and blah, blah, blah… You can start to just logically derive things about where they’re going to be in a few minutes or where they’re not going to be, because it would be breaking some of those laws or whatever.
Alex Malpass:
All we’re doing here is we’re just applying consistency to a moving set of assumptions. If you want to pile in stuff about what you know or what you can see, or what’s true according to our physical theories or whatever, then that’s fine. It builds a different set of truths that follow from that starting point. That seems to me, that metaphysical possibility is just that we take some truths or starting points that are not either physics or logic or to any other type of science or whatever, but other truths.
Trent Horn:
Right, because it sounds like we’re articulating three kinds of possibility here. Well actually, I can think of four kinds of possibility.
Alex Malpass:
There’s tons, yeah.
Trent Horn:
There’s technological. Yeah. There’s technological impossibility. We couldn’t get to the moon in 1868, but we could get there in 1968.
Alex Malpass:
Yeah.
Trent Horn:
Physical impossibility, just given the laws of physics you can’t go faster than the speed of light. Well, if the speed of light were different, we could. If technology were different, we could do these things. Physical impossibility, if the laws of physics were different, we could do these things. Once you get past there though, it’s like logical impossibility. If the laws of logic were different… it is controversial. Like what do we mean, there’s different logical forms and schemes and stuff like that.
Alex Malpass:
Of course. Yeah. Yeah.
Trent Horn:
Yeah, but in general we tend to think the laws of logic are not things that could be altered like the laws of physics. In general, we tend to think of that, at least in classical logic. I would say metaphysical possibility is an interesting one that it’s much closer to laws of logic than like the laws of physics. It seems to deal with truths related to the natures of things. It would seem to obtain in any possible world, even though it’s not just dealing with just the nature of the terms themselves.
Alex Malpass:
Well, but then the term possible world is one that admits of these very same degrees. It’s physically possible worlds, logically possible worlds, meta physically possible worlds. All we mean there is just a possible world is just one such collection of propositions that’s consistent according to… A physically possible world is a collection of propositions. It’s consistent and consistent with the laws of physics. It’s consistent itself, and it doesn’t violate any of the laws of physics. A technologically possible world is one that’s consistent and doesn’t violate any of our technological abilities or whatever. Always, in any of these grades, the measuring stick is consistency. That’s just, there’s only one type of consistency and it’s logical. It’s just, what are the assumptions that are built in to the set that we’re looking at? If we are constraining that set to just include what’s physical truths, the axioms of physics, then what you’re looking at is a physically possible world.
Alex Malpass:
That’s how I would suggest that you look at this because that’s how the philosophers in academia construct these things. The interesting distinction in fact is the one that has all of those types of possibility we were just thinking about, but then another type, which is ones that involve a subject. What’s epistemically possible because then you have to pick a person. What’s epistemically possible to me is everything that’s consistent with what I take myself to know. What’s epistemically possible for you might be different because you know different things than me, presumably. We will anchor a possible world around my own certain knowledge or what I can conceive of or whatever. There’s subjective modalities and objective modalities. Anyway, I’m saying in any case, consistency is the measuring stick that everybody uses here.
Trent Horn:
Right. But I would say that we’re using logic all the way through, but we’re asking for consistency. The most basic level is just logical consistency, but would you agree there is between… we’ll take physical. Between logical and physical, we’re looking for consistency, not with the laws of physics or the laws of logic, but some other kind of consistency.
Alex Malpass:
Well there’s-
Trent Horn:
Like that’s the nature of reality.
Alex Malpass:
Yeah. There’s a bit of a no man’s land between those two, because you can relatively well understood logical systems and relatively well understood physical systems… those are like lighthouses in the darkness where we know where we are when we’re there. But in between those…. I mean, if you take, for instance, Plantinga’s book The Nature of Necessity, literally on page one he starts off… Pretty much the first line of the book is him saying necessity’s really difficult to explain. He says with metaphysical necessity in particular, all you can do really is give a bunch of examples. He literally says “and hope for the best” because you’ve just got to hope that the reader kind of picks up on it. His examples are things like…
Alex Malpass:
Got to hope that the reader picks up on it, but he’s his examples are things like “no prime minister is a prime number;” “no one’s taller than himself,” blah, blah, blah. But there’s no rule that attaches to all these metaphysical truths. You just have to pick a bunch of metaphysical truths, hope that your opponent or your interlocutor agrees with you, and then you can crack on with deriving what follows from those things. But if you want to pick one of them and say an “actual infinite is metaphysically impossible,” well, logic’s not going to tell you that, because this is what we have to just plug in by hand to start before we can do any derivations. And there’s no guiding rule that says whether a proposition is in the metaphysically possible club or not. We have to give examples and hope for the best. So it’s a bit of a mess really. There’s no real theory of metaphysical possibility. Well, certainly not one that everybody agrees on.
Trent Horn:
And I think that’s going to explain… This is always is a big question in philosophy: why do reasonable people disagree? Or is it just the sense that there’s unreasonable people and they just haven’t quite figured it out yet? But I think one reason is when you get to some of these questions, that the verdict that we’re making on whether, let’s say, Hilbert’s Hotel is possible, it’s going to come down to a sense of intuition that you have. To give a parallel example that I’ve liked, and this may come up a little bit later when we get into some other of the paradoxes, is… Because you’re right, some metaphysical possibility, it seems like you’re right. No prime minister can be a prime number or things like that. Others… But yeah, what about the ones people disagree about? Like whether it’s possible to travel backwards in time, alter the past, and return to the same point in your own timeline. How do all those-
Alex Malpass:
Is it just a physical impossibility or is it a metaphysical impossibility? Very unclear, it seems to me.
Trent Horn:
That’s one I can think of. And another one that pops into my head dealing in philosophy of mind is the question “could there be a being that acts as if it’s conscious, even though it’s not conscious.” This would be a philosophical zombie or a “P zombie.” It’s always, when you read philosophical literature, you think you’re going to get something really exciting and it’s like “zombie,” oh actually it’s just… If I have time, maybe I’ll bring it up. On the phil paper survey, this is a survey for everyone doesn’t know philosophers, that was done in 2009 and I think in 2020, asking people what they thought about that. People were disagreeing about whether that was even metaphysically possible. Whether there could be a being who, it seems like they’re conscious, but there’s nothing going on upstairs really, they just automatically reply to things; whether you could even have something like that. And so reasonable people will disagree over those things. And I think people will disagree over the Hilbert’s Hotel.
Trent Horn:
I do have a question about Hilbert’s Hotel, because one of the arguments that Craig makes is about… The argument seems to go like this: in transfinite arithmetic, there are operations that are undefined. Like if you try to do subtraction, it’s kind of like dividing by zero. Undefined meaning there is no definite specific answer for the thing in question; if you subtract the even numbered guests from the Hilbert’s Hotel, an actual infinite number remain, if you subtract all of the guests greater than room three, three remain. In each case, you’re subtracting an actually infinite amount, but you’re getting different results. What is infinity minus infinity, to put it very basically. And the answer is, “well, it’s like what is zero divided by zero?” It’s not defined.
Trent Horn:
And Craig’s concern, and my concern would be, what if you had a real hotel and you perform these operations with real people? Suddenly you have something that when you read different textbooks saying things like this is a meaningless statement. It doesn’t correspond. It’s not defined. It’s very difficult for us to have undefined things that really exist in reality. I think it’s a concern people would have if you have an actual infinite multitude.
Alex Malpass:
Well, look, I think this is just nothing to worry about. Because what we’re talking about when we say it’s not defined and there’s no operation, blah, blah, blah, this is something to do with defining a formal system that characterizes the behavior of the concept. It’s a very technical issue. It’s not to say, so look, when you’ve got… If we just concern ourselves with just the normal counting numbers, there’s a kind of theory called arithmetic that everybody’s familiar with. Before they knew anything about theories or philosophy, they knew what arithmetic was and they were doing at school. But actually it’s also a formal theory, and there’s some operators: plus, minus, divide, multiply. And there’s a syntax, and everybody picks it up and it’s easy, and off you go. And you can say loads of stuff in that language.
Alex Malpass:
And you know, this is the language that Kurt Godel showed that there were unprovable propositions in his incompleteness theory, which was a famous logical result. But it was that very simple theory that he was talking about when he was saying that the incompleteness theorems. Now in that, there’s a plus and there’s also a minus. That’s cool. When you come to transfinite numbers, and this is a sort of system of mathematics that nobody had thought through properly until Cantor in the 19th century. So he’s this German mathematician… Austrian, whatever, European. And he was a tortured genius who ended up being… Nobody took him seriously in his lifetime. He died in an insane asylum. It was afterwards that people recognized the significance of this work. He was doing work on infinity. And he [crosstalk 00:41:35].
Trent Horn:
And then of course he ends up in an insane asylum because of that.
Alex Malpass:
Exactly, yeah. That’s what happens when you ponder infinity as hardcore as he did. Basically in the system that he showed, which is perfectly consistent, there’s not one unique answer when it comes to questions that look like the inverse of addition, which obviously in arithmetic is subtraction. So there’s a failure of uniqueness there. So in the interests of making the system complete and whole, and being able to give definite answers to all of the things you can do in the language, in that system, you just throw away the minus symbol. It just doesn’t have it. And that does sound… and then you go “but hold on a minute, throwing away a minus symbol, just like writing off a big chunk. I’m used to there being a minus sign in arithmetic, how come there isn’t one in this other system?”
Alex Malpass:
And we can talk about the technical reason for that. But I think what you’re interested in what’s the significance of that? Because surely I could get people to check out of Hilbert’s Hotel, and isn’t that the same as subtraction? So what’s going on? How can you forbid them from leaving the hotel? But nobody’s forbidding anybody from leaving anything. People can leave Hilbert’s Hotel, and what happens when they leave Hilbert’s Hotel is that the things that Craig is so famous for bringing out take place. So if everybody in room number three and greater leaves, then there’s only two people left, but if infinitely many people have left, but only two remain in that case. But if everyone in the even-numbered rooms leaves, infinitely many people leave, but there’s infinitely many people left still.
Alex Malpass:
So sometimes it looks like, start off with infinitely many, withdraw infinitely many, and you’ve got three. Then second time infinitely many withdraw, infinitely many, and you’ve got infinitely many left. So sometimes it’s three; sometimes it’s infinitely many. That’s the failure of uniqueness that I was talking about a moment ago. But look, just the thing you have to bear in mind is that that operation of people leaving the hotel, it needn’t correspond to a symbol in a formal theory. There isn’t going to be a kind of “operate sliding symbols around on a piece of paper.” It isn’t going to track that properly. But it doesn’t mean that there isn’t something definite going on in that case. And I just described to you a way of keeping track of what the outcome would be. And if I tell you in advance, the rule here is everyone in room number three and greater leaves, then you don’t have to worry about and how many people are left. You can figure it out in two seconds.
Alex Malpass:
So there is in a way kind of background theory that we’re applying here to know what the answer is to many of these questions. It’s just that it’s not Cantor’s theory, and what we’re doing isn’t subtraction. It’s taking a set, taking another set that’s exactly the copy of the first one, but without three of the members, the beginning, and just asking what’s left in this set? Now in normal arithmetic, that is subtraction, but in transfinite arithmetic, for technical reasons, that doesn’t give you a nice function that we can call subtraction. But it’s still a perfectly sensible thing you can look at and see what’s happening, analyze, and understand. So I’m just not worried about it. What would happen if Hilbert’s Hotel was real? Exactly what Craig describes, so what’s the problem? And I don’t see a problem with that.
Trent Horn:
Well, I think two problems come to my mind. One is the claim that you’re subtracting identical quantities. I know they’re different operations, but they’re still involving identical quantities, and you’re getting different results. Because it is interesting, when we talk about metaphysical possibility, it sounds like the word we’re using is “worry.” “If I go back and…” That seems to be the gauge we’re using a lot of these cases, “can I go back in time and kill myself?” One person says “I’m not very worried about that.” Another person says “I’m very, very worried.”
Trent Horn:
I think in a lot of these cases, that actually is the emotional regulator that we’re using. My worry arises, that’s one part, and number two, the sense that, “well, yes, this is something that we are not able to represent in the language of mathematics, but there’s nothing really wrong with it happening in the physical world.” Is there another example of something that we all kind of agree on, we can’t represent with a mathematical formula or language, yet we can do the operation, so to speak, in the real world. That in the mathematical world, you can’t do it with numerals, but in the physical world, you could do it with people or objects. I’m not familiar. It seems like that in the other cases that we have undefined things, they also don’t obtain in the physical world, if that makes sense.
Alex Malpass:
Well, what we’re doing is we’re basically having this conversation in a very informal version of set theory, because we are imagining a collection, or set, which is all the people in the hotel at 10:00. And then we’re imagining another set, which is all the people in the hotel after half of them have left at like half past 10. And we are doing some kind of comparison between those two sets, and we are determining that in one case, there’s only three people left in the second set. In the other case, there was infinitely many. So we are doing this in a language in a way, the kind of rough and ready version of set theory. It’s just not Cantorian transfinite arithmetic. It’s a different type of theory. This is why this is kind of boring, technical point. It doesn’t really have much significance. There’s a theory most people have never heard of which doesn’t have a symbol that they were expecting, but it doesn’t matter. It doesn’t mean anything interesting [crosstalk 00:47:44].
Trent Horn:
But this is important. It’s so funny, first we started with a gradual incline, and now we’ve gone up to about 60 degrees, which is fine because this is where… Why don’t people agree on the cosmological argument? It is going to get to these very… And this is true also, I think, with many other points in ethics, in metaphysics. You’re going to get to the “basement” or the nub of the disagreement. This happens a lot, I think, in ethics as well. I think it was Walter Sinnott Armstrong, well known ethicist, who one said “nearly all moral arguments eventually devolve to ‘and surely that is immoral,'” and you either see it or you don’t.
Trent Horn:
And I think we have something similar here with the metaphysical possibility, because when I think of things in mathematics that are either undefined or impossible, I think of subtracting infinity, dividing by zero… There are some puzzles, this might come up later as well, in geometry that are not defined, at least given certain kinds of planes versus other planes. But yeah, I would be more wor… I wouldn’t have as much of it… What is the guy from Mad Magazine, Alfred E. Newman, “let me worry.” I’m a bit more worried about its substantiation.
Alex Malpass:
What are you worried about? I still don’t really get it.
Trent Horn:
Well, I’m going back to what I said before. If I could find another example of something in mathematics that’s undefined, so we can’t do it with numerals or symbols, but we are able to do it with objects or people and just, we don’t have notation for it, that would put me more at ease. But it seems like with those kinds of things, we just recognize we can’t do it in math. It’s like math is the broader world, and the mathematical realm is broader and the physical world is narrower. Like if we can’t do it in the broader place, I see with these other examples, we can’t really do it in the physical world either. We have more freedom in the mathematical realm than here. There’s just more things to constrict us.
Alex Malpass:
Well, I don’t know whether this would be helpful or more confusing, but the incompleteness theorems that I was talking about before, what Godel is doing there, this was one of the most… Everyone talked about one of the most monumental discoveries in mathematical logic of all time. But what he showed, and he was just a nobody as well; he was a PhD student that no one had ever heard of, and then he proved this thing that everyone was amazed by. What he showed was that there are sentences in arithmetic. So there’s no using vocabulary, no more complicated than what we all learned at school, that can’t be proven to be true and can’t be proven to be false. They’re unprovable, yet they do have a truth value. They’re either true or false; you just can’t prove that.
Alex Malpass:
And that’s very counterintuitive because you think, well, hold on, what sort of sentence are you talking about? Because it makes you think, well, are you saying there’s some number of objects such that if you put them in front of me, I couldn’t do arithmetic operations on them. Two trees plus two trees is going to be four trees, right?You’re never going to show me a number of trees I can’t add together in principle. So what are you on about here, Godel? How could there be an arithmetic sentence that’s not provable? But there is; it’s just very complicated to go through the detail. Don’t ask me to do that. But you could just about manage to do it if you read the right book, or someone knowledgeable explains it to you, or maybe there’s some great YouTube a video out there that will do it.
Alex Malpass:
But don’t worry about arithmetic on the basis of that. It really has nothing… The world is exactly as it was before Godel did that. There’s no danger of the world’s collapsing it on itself, or you somehow counting three beans and two beans and getting 10 beans, or anything like that. It’s okay. There’s nothing to worry about. And here it’s just the same sort of thing. There’s some really esoteric bit of mathematics that’s not what we expected, but nothing about the real world follows from that. It just means that if the Hilbert’s Hotel was around, we’d still be able to count people out, we’d still be able to say all the things that Craig says about it. You just… Cantor’s theory of transfinite arithmetic still wouldn’t have this minus sign in it. It just wouldn’t be one of the symbols in that language.
Alex Malpass:
And I just can’t understand why anyone would worry about that. It doesn’t matter. Honestly, had you even heard of Cantor’s transfinite arithmetic before you heard of the Kalam? Cause most people haven’t, and then it’s just weird to worry about the lack of a certain symbol in a given formal system that they’d never heard about before. [crosstalk 00:52:42]
Trent Horn:
Right, most people aren’t concerned about the infinite because you don’t bump into it on the way to go get milk from the store, basically. It’s when, though, we start to think about it. And most people don’t think about what numbers are. They use them every day, but they don’t think about what a number is. They deal with numerals but not numbers. And then getting into the sticky weeds of, “I use these things. People made the numerals, but it doesn’t seem like anyone made the numbers.” And then you get into the deeper questions later. So I think that it’s fair, when we propose actual infinites or things like that could exist, trying to test them with our intuitions. And it’s just unfortunate because we can’t do physical experiments on the infinite or things like that. And it’s not within the realm of logic; it’s still within what you call the no man’s land of metaphysics. But I still want to get through the next three, but I think it is still helpful people to see the disagreement. We’ll see. This is our Hilbert’s discussion. Can it actually be infinitely long? Well, let’s go to… I think people could see where the metaphysical concern is there and then… [crosstalk 00:54:15].
Alex Malpass:
Well, can I say just one last thing about this before we move… I mean, did you want to leave Hilbert’s Hotel now? Because if so-
Trent Horn:
Well actually, I don’t mind throwing another example out there if you don’t mind. This is one that is not used as much, but I think it might actually… I’m surprised it’s not used as much, because I talked about infinite multitude, then there’s also the question of infinite magnitude. So suppose you had… I was reading this in Mark Nowacki’s book, The Kalam Cosmological Argument for God, the idea of something like a hyper-lump, something like a ball of clay that’s composed of an infinite number of smaller balls, so to speak. So with Hilbert’s Hotel, not only do we have an infinite multitude of people, could we have an object that has an infinite number of subset parts to it?
Trent Horn:
If we could talk about infinite sets, we could talk about some kind of an object like that in an abstract geometrical way, but it would seem… to have something like that in the real world, and we agree, we don’t think it exists in our world, but if there were such a world with such a thing in it. The problem… When I went back to metaphysical possibility, I am very certain that objects that have color have shape; objects that have shape have size. And it would also flow from that if an object exists, it must have some kind of definite shape. But if it had an infinite magnitude, I don’t see how it could have an infinite shape. And to me, we’re getting really close to that metaphysically impossible object that could exist. So there’s the multitude problem, and then there’d also be the magnitude problem. So I guess that’s another one.
Alex Malpass:
So often it’s easy to come up with an example of something that involves infinity that’s impossible, and then to conclude that it must be the infinity that’s to blame. And sometimes it will be something else that’s to blame instead, and we shouldn’t be too quick just to find any old story that involves infinity that’s impossible as evidence that infinity is impossible. That’s a kind of guilt by association or something. I could just cook up a story that was absurd and just drop in needlessly that the universe didn’t have a beginning or something, and then use that as evidence to suppose the universe must have had a beginning. So we’ve got to be careful here that we’ve definitely ruled out everything; couldn’t be anything else. So very, very tricky.
Alex Malpass:
I think I’d probably put these sorts of examples in that kind of case. But in particular, I suppose, I’m not sure that I agree that every object has to have a definite shape. I think things can have a vague shape. For instance, I think a cloud has a vague shape. I think if you zoomed in on me enough, you’d find out that I had a vague shape too, because I’m a bunch of particles or whatever. So I don’t know if I actually agree even that anything has a completely definite shape. Definite shapes are probably just those things that… Whatever you take abstract objects to be, whether they’re different from concrete things or whether they’re just things we imagine. A perfect triangle has a definite shape, but nothing in nature embodies that perfectly. So they’re all imperfect, and they’re probably all indefinite as well. So I guess maybe I would say there’s something wrong with that. We can blame that, maybe, instead.
Alex Malpass:
So now we have to wander off the beaten path here in trying to determine whether you could really settle that question. But unless you could, you wouldn’t have had a good counter-example to the infinite, because it’s only once we can settle that, that we can then come back to see whether the infinite really was the thing to blame. A lot of these are too complicated to provide good platforms of analysis for the question at hand.
Trent Horn:
Hmm. Well, I think with the question about definite shape, it reminds me a little bit… There’s two elements there. It almost reminds me of the Beard paradox or a Sorites type paradox. Where does something begin and… Well, Sorites is “when does a pile become a heap?” Beard is “I’m clean shaven; you have a beard. What’s the boundary between the two?” So you’re right; in abstract geometry, we’ve got the perfect triangle. There is no such thing like that in the world. But we can identify that certain things are triangular. Even if we zoomed in, it would be fuzzy and branchy maybe, we would still have that. But I think though that the example of something with infinite magnitude would go far beyond just something…. The fuzziness problem of a definite nature.
Trent Horn:
I think we’re getting closer. What do you think of… I’m going to say it’s Hegel; people can write in the comments if I’m wrong… That if a shape has the property of color, then it also needs to have the… Sorry, if something; I was begging the question there. If an object, a thing, has a property of having color, it would also need to have the property of having shape. Any way you conceive of something exemplifying color, it needs to have shape with it. That seems a metaphysical truth rather than a logical truth, but I can imagine someone saying, well, things could just be weird. There could be just shapeless colored objects. And they could still not be moved by that.
Alex Malpass:
Yeah. Like what about a gas? You have a colored gas, mustard gas, for instance, it’s a kind of greenish yellow. Does it have shape? Kind of? Really?
Trent Horn:
It may not have a shape.
Alex Malpass:
There was an example.
Trent Horn:
There’s a character like that in the Rick and Morty series actually. So that would take us far, far afield.
Alex Malpass:
But yeah, it just doesn’t strike me as necessary.
Trent Horn:
I mean, it’s not like we have a name for the shape, but it has a shape. Just like when you spill liquid on the ground, it has a shape, even though there’s no name for it.
Alex Malpass:
Well, but the thing about the gas and possibly also the water is that it’s not just that it’s very complicated shape, like some polygon with like a million angles in it or something, it’s just that there’s no real clear definition to it’s shape at all. There’s no one way of defining its boundary. There’s just loads of ways, almost infinitely many ways, maybe. So it’s more problematic than it just being a shape we haven’t named yet. It just doesn’t seem decidable, what shape it is. And think the easiest thing to do is to just say, it’s vague, doesn’t have any definite boundary to it. And a shape of anything is boundaries around some area. So that’s why vague things and shapes don’t really go together. But if anything’s vague, then there’s something without a definite shape. And there do seem to be good examples of vague things like clouds or gases, or even anything when you zoom in on it enough. So…
Trent Horn:
Right. Yeah. I think then, in the notion of something being definite, there can be a bit of approximation there. Otherwise I am concerned, and I think this can happen sometimes with these sorts of arguments, that in trying to deny what seemed to be these metaphysical truths, we might be purchasing more than we would prefer, like a thesis like neurological nihilism, which would be the idea that there are… And so for our listeners at home, for the $64,000 word, is the thesis that there are only fundamental particles that are arranged in different ways; sometimes very compactly, maybe loosely like a gas. And that if we start to deny these premises, my concern is that we’re going to start buying even more counterintuitive principles. We may not prefer to be at the philosophical purchase desk, if that makes sense.
Alex Malpass:
Yeah. Who knows where the fundamental level of things go, whether that even makes any sense or whatever, but what I’m doing, really, with these counter examples is I’m saying, look, it’s not clear that it if metaphysical possibility picks anything out. It’s supposed to be picking out things as they are, and if there’s any doubt about whether the example we’re talking about is fundamental, or if it’s at some level of approximation, which involves subjective decision making, then it’s not a good candidate for a metaphysical truth. We’re talking about concepts that are human made and have to be evaluated by humans, then they’re probably not metaphysical truths. That seems to be a clear way of drawing a dividing line.
Alex Malpass:
So what you want, if you want to go back to the prime minister and the prime number thing, it’s not about vagueness of the concept of prime minister there. I don’t know exactly why I can’t explain it very well, but it’s not like “does a cloud have a shape or something?” It’s very obvious that there couldn’t be a prime minister who is a prime number. So we must be talking about something independently of anybody’s particular way of then drawing the lines where concepts go or something. Everyone would agree on that one. So it’s at least a more plausible candidate for being a metaphysical truth. It’s not obviously dependent on us, using our minds to carve up reality. It’s at least potentially carving reality at the joints, which is what you’d want for a metaphysical truth. So all these other types of… There’s a massive cottage industry of people who cook up cool paradoxes of the infinite, and Graham Oppy’s got a book called-
Trent Horn:
Philosophical Perspectives on Infinity.
Alex Malpass:
There you go, that book. Exactly. And it’s got a dozen or two dozen search puzzles in one of the opening chapters. And he goes through explaining what’s going on with them, what he thinks about them or whatnot. And they’re all different. They’re all fun. And many of them, they bring up so many peripheral issues like the ones we’ve been talking about now, which is taking us off to something I had no anticipation we could have possibly been talking about that. But that’s the fun of the infinite [crosstalk 01:05:09].
Trent Horn:
And that’s what happens with this argument. Ironically enough, in geometry and mathematics, there are things called fractals, where you infinitely divide with shapes and more shapes appear, and you keep going with it. That kind of happens when you start talking about the Kalam argument. You start with what seems like a simple shape, and then you get to the edges and there’s more and more. And then it takes us-
Alex Malpass:
I like that. That’s nice.
Trent Horn:
And so it takes us to these fuzzy… To be honest, I think one of the big reasons that you’ll have disagreement about… And really, that’s where it’ll come down to, and it’s not just… I think some people might be tempted to want to say, if I’m a theist, you’re an… well, I don’t know if you use the term atheist or not, or non-theist or whatever; not a theist. Look at the theist, you can’t get this kind of agreement here. But I think in many other philosophical disciplines, we’re going to drive deeper and deeper and deeper into the fractal until we get to these fuzzy boundaries where we’re not sure which way is the right way to go, like with the contingency argument that starts obvious, and then it eventually gets to things like the principle of sufficient reason. And where you feel about that is a similar kind of fuzzy sort of thing, direction.
Alex Malpass:
Definitely.
Trent Horn:
Ethics, mind, things like that. What you brought up about Oppy I think is interesting, because he has Philosophical Perspectives on the Infinite. It’s a good book on that. Another philosopher, Alex Pruss, has a book called Infinity, Causation and Paradox. And so he does something very similar, where he will go through all of these different paradoxes of the infinite, and you take it all together. And I think that this may be the stronger argument going forward when we talk about Kalam or we talk about other things. I think a benefit… An advantage and a disadvantage. When you have Craig promoting the the Kalam, a lot of times it gets condensed into what he might say in a debate. That’s how a lot of people have come across this.
Alex Malpass:
[inaudible 01:07:34].
Trent Horn:
But you can make a stronger, more robust argument when you’re not giving a 15 minute opener or something. So when you’re trying to figure out, could an actual infinite exist, you might try to… Having one example is one way, but it seems like you could do what Oppy does or Pruss does, which is “all right, let’s put them all out on the table, all the different paradoxes we can think of, or at least…” Because there could be a thousand paradoxes, but they really just exemplify 40 or 50 principles. Because with the Kalam argument, you can come out Hilbert’s Hotel, Craig library, yada yada, a lot of them are just exemplifying the same principle, just with different illustrations.
Alex Malpass:
That’s right.
Trent Horn:
So what Pruss does is okay, we’ll put them all out there, and when you start to weigh them, a good explanation for these paradoxes of the infinite is to deny the existence of kinds of infinite, particular kinds of infinity. That helps us to explain all these paradoxes, versus another explanation might be, this is what we would expect. It’s just counterintuitive, but it’s not anything worth getting rid of. It seems like the stronger argument might be… Which is the more laborious argument… We put it all out a table and we weigh them like they’re on the fulcrum with the balance of understanding, if that makes sense.
Alex Malpass:
Yes. I mean, in a way I’m drawn to that type of analysis more. It seems to me it’s more grown up than trying to prove things black and white once and for all. It’s doing the evaluation, and that’s where the hard work really lies. But in a way it’s a weaker argument because it doesn’t really prove anything. What we’re doing is a kind of abductive case building here, where we’re trying to build a case for why this is the best explanation, effectively. So that’s one way that the grim reaper… gesturing towards proofs. So we’re talking about grim reaper arguments; this is slightly different, but still arguing for there being only finitely many past causes. So more or less the same thing as saying that time began at some point finitely far away in the past. And so there’s generally speaking-
PART 2 OF 4 ENDS [01:10:04]
Alex Malpass:
And so, there’s kind of generally speaking, there are people who take an axiomatic approach to this and try and prove using the Grim Reaper paradox that there couldn’t be an infinite past. And other people… Or sometimes proofs in certain places let’s say. We’ll talk as if what’s going on here is a kind of abductive case building exercise where the thesis of causal finitism. The thesis are there any finite, or any causes to it to any effect is the best explanation of some considerations but not proven definitively by them. So I like that approach. I think that’s certainly a grown up way of doing things. I mean, we can talk about that because I have a view that’s different to his, but I don’t know if you want to go into the details of that. But in general, I like that kind of abductive case building approach to these things.
Trent Horn:
Right. So like when it comes to the existence of God, there is offering a series of deductive arguments, something more like what William Lane Craig does. Or even like the Catholic philosopher, Edward Feser. And that’s something I’m partial to, but I do like a series of arguments. And then, there’d be something more inductive like Richard Swinburne, where you’re just analyzing what are the things in the world that are likely if there’s a God and things that are unlikely if there’s God.
Alex Malpass:
Sure.
Trent Horn:
And you try to tabulate them. So maybe you would be more a fan of that approach.
Alex Malpass:
Well, I think I’m advocating a third type of approach, which is sort of an abductive argument. So it’s trying to [crosstalk 01:11:33].
Trent Horn:
Best explanation.
Alex Malpass:
Best explanation. Exactly. Yeah. Yeah. So what’s going on with the Grim Reaper cases you might think is that, look, there’s all these versions of the Grim Reaper paradox. Your kind of version where people are passing each other notes or where they’re waiting to kill Fred. There’s a bunch of others. There’s dozens really. They play around the same theme, but you might wonder… You might want an explanation for why they don’t occur or why they’re impossible. And it’s not the same thing as providing a deductive proof that uses an assumption and derives a contradiction and blah, blah, blah.
Trent Horn:
Right.
Alex Malpass:
It’s more a way of saying… So for instance, certain versions of those paradoxes involve things moving from one place to another. Right? Like you can think of a version of the Grim Reaper paradox where there’s a ball rolling along a plane.
Alex Malpass:
And there’s a mechanism set up such that where to get halfway along this plane, a barrier would be erected to prevent the ball moving any further. And also a quarter of the way down, there’s another barrier that would be erected were the ball to get that far, et cetera, cetera, cutting the distance. So there’s infinitely many. And they’re ever closer and closer together until you get to the point A, the beginning of the journey. Now the ball can’t get to the end of the path because were it to get halfway, a barrier would be erected that would prevent it from getting any further. Of course, it’s not going to get halfway, because if it was to get halfway, it would’ve had to have been a quarter of the way and blah, blah, blah. So it won’t get to the end, but also none of the barriers is going to be the one that prevents it from getting any further. Right? That’s super weird.
Trent Horn:
Right.
Alex Malpass:
So what’s going on there? So there’s loads of versions of that. So basically the same paradox. It’s the Grim Reaper.
Trent Horn:
Well let me offer just a summary of that. And kudos to everyone who’s with us so far.
Alex Malpass:
Is anyone still awake?
Trent Horn:
We’re going to keep going because it’s my podcast, and I can do what I want. There’s no mysterious force that will prevent me from talking more about this. It’s logically and metaphysically possible. So this is the other one. I feel bad we’re leapfrogging over… We managed to get through. Can there be an actual infinite? I had on my outline. Talk with Alex [Malpass 01:13:51]. Next, talk about successive addition. We’ll just talk about Grim Reaper because we’re already there. Maybe we’ll get back to the argument for successive addition.
Alex Malpass:
Sure.
Trent Horn:
So, this would be the idea that arguments… And there’s different people who have made them dealing with causal finitism saying, “All right, maybe you can have an infinite past because…” By the way, I didn’t get. I mentioned this a long time ago.
Trent Horn:
The thing that most concerns me about Craig’s argument is the idea that the… Because I feel pretty confident in my worry about an actual infinite existing in the physical world.
Trent Horn:
But I’m not as concerned about that because the past doesn’t all exist at one time. All my examples involve a [hyperlum 01:14:30], Hilbert’s Hotel. They’re all at one point in time. So like-
Alex Malpass:
Yeah.
Trent Horn:
So that’s where… And so like to find agreement with you, I think your criticisms of Craig’s… So you have done a lot of papers with Wes Morriston, another philosopher who’s done a bunch on this topic. That the problem with Craig’s argument is he wants to say, “All right, well look. There is an actual infinite past.” Beginningless past is actual infinite can’t exist. But if there’s an endless future, then that has an actually infinite number of events. So it can’t exist either unless you can find some kind of symmetry breaker that makes the past and the future different.
Trent Horn:
And so, I think Craig has tried to say, “Well, past events are different than future events because we can count them. They’ve happened.” And I’m very sympathetic to your counter reply to that, which is, “Well, we can count future events as well.” So it seems like that’s not much of a symmetry breaker to me. To me, the only hope of that particular argument to get off the ground would be if you could establish that past events cause the existence of something in the present, whatever that might be. And there’s different ways of going about it. There’s [Locke’s 01:15:58] argument where you could construct something over time, or an actual infinite exists now, or there are temporal marks, or that there are… That the past has caused, so to speak, something actually infinite now in some sort of way versus just the infinite past itself. So, I think that’s a successful reply to Craig, at least on that point. But I do think that-
Alex Malpass:
Did you like the symmetry argument then? Me and Wes’s symmetry argument. You like that?
Trent Horn:
I think it motivates people to look harder for the asymmetry. And I do think that there is an a… I was walking around the neighborhood because I had my kids this morning, and they were yelling and running at the playground. And I was just walking around the neighborhood, trying to clear my head. Trying to think like, “Well, I really do think the past and the future are…” Like I tried to think would it be like if they were truly symmetrical, and I had tried to envision what a world would be like if there was a present moment and then past and future events grew away from it at an equal rate. Like to me that would be-
Alex Malpass:
Yeah. That would be weird.
Trent Horn:
Right. But to me that would be like truly symmetrical. That either it’s like if somehow the past and future could grow away from the present moment. I don’t know. I have to… I’d love to think about it more about if that is even a metaphysically possible. Is it metaphysically possible? So logical contradiction. But it seems to me like when I look at… And I appreciate in your paper, making a distinction. And I think this is one that I and many others probably have missed when it comes to tenses because people will say, “Well, no. If you had a beginningless past, you have an actual infinite. But with future events, it’s a potential infinite because you never will count to infinity.” Good. I smuggled the successive addition argument in so we’re getting there.
Alex Malpass:
Cool.
Trent Horn:
And you raised the point. Well, there is a distinction between two types of tenses. The simple future, and perfect future, and the simple past, and the perfect past. So it is correct that in the future, there never… If you continue to count forever, there never will have been a moment when you counted an infinite number of numbers. But the question is more of the simple future. Will you count to infinity? And I’ll put that in very bold quotation marks, to infinity. And if you define it as well for every natural number in you will count that number. So the cardinality of all of the natural numbers you will count is actually infinite-
Alex Malpass:
That’s right.
Trent Horn:
… in that respect. And so, I think that is a fair point to bring up between like the simple past and the simple future. And though-
Alex Malpass:
And that distinction though, the important thing is that maps on perfectly to this potential infinite, actual infinite distinction too, because the… If you think about the number of numbers that I will have counted. Let’s suppose… Make it easy. Right? I say I count one number a minute. So at an even rate like that. How many numbers will I have counted in 10 minutes time? Obviously 10 numbers. So no matter how far forward into the future we go, like a million years into the future. I will still have only counted a finite number of numbers. But the number that I’m counting to is ever greater. Right? It’s always increasing. It’s increasing without limit, in fact.
Trent Horn:
Right.
Alex Malpass:
It’s approaching infinity, but it never actually gets to it. So it’s exactly what Craig means by a potential infinite. And that’s… Well if you say that’s what will have been counted.
Alex Malpass:
So at some point in the future, how many numbers have I already done at that point? That’s the future perfect counts. And so, that is exactly what he means by the-
Trent Horn:
Right.
Alex Malpass:
… potential infinite. But, and then all the point there is just instead of sort of zooming forwards and then looking back and seeing how many you’ve done, which I agree is only ever going to be potentially infinite. The point is simply just stand here, and just look out at all of the future events. How many of them are there if there’s no end to the future? That’s the answer to our question is infinitely many. Right? And actually infinitely many. Because you could assign each one a natural number. You’d have no natural numbers left over.
Trent Horn:
Right.
Alex Malpass:
So there you go. It’s just open and shut. So that seems to be black and white.
Trent Horn:
Well, it’s not necessarily black and white because the description hinges on a very precise use of grammar.
Alex Malpass:
Sure.
Trent Horn:
So it seems like you’re describing things like counting to infinity.
Alex Malpass:
Yeah. I don’t like that phrase because that phrase makes it sound like infinity is an ordinal number, and that’s not right.
Trent Horn:
Right.
Alex Malpass:
There’s no infinityith counting number. Right? There’s only finite counting numbers. But if you ask how many counting numbers there are? That’s not a finite number. It’s an infinite number. And that’s the sense. If you say counting to infinity, and you mean cardinality. How many numbers will you count? If you count now and never finish. The answer to that is infinitely many. But you’ve got to hear it properly as not meaning that at some point you will arrive at infinity, or a few unfinished. Great. I counted all the way to infinity.
Trent Horn:
Right. Right.
Alex Malpass:
So the phrase counting to infinity is kind of misleading because I’m not saying you can count to infinity-
Trent Horn:
Right.
Alex Malpass:
… in that ordinal sense just in the cardinal sense.
Trent Horn:
Right. Because somebody could make a similar argument like can you count to zero starting at zero? Well, if you just never count, then the cardinality of the set that you’re counting is zero. And so you’ve counted to zero. I’m like, “Well, I haven’t counted to zero. I just never started counting.” And it seems like, well it’s not that I counted to infinity. It’s just I never stopped counting.
Alex Malpass:
Yeah. That’s what I mean by counting to infinity.
Trent Horn:
Right. And so for people who are listening, wondering what the heck does that have to do with anything? Well, that goes back to the successive addition argument. To put it very simply in a way that’s easy to refute, but also easy to understand. It’s like the past couldn’t be infinite because that’d be like counting down from negative infinity when you can’t count up to positive infinity.
Alex Malpass:
Yes.
Trent Horn:
Now, of course, that’s a very simplistic way to put it. Liable to objection. There’s better ways to put it. I still see… I guess for me like the biggest asymmetry I still end up seeing between the two, which gives me more pause about things. When I was thinking about like past and future growing away is like from the perspective of the present moment in a beginningless past, there is no difference between the simple past and the past perfect. You can say there were an infinite number of events, and there have been an infinite number of events. They both-
Alex Malpass:
So, that’s not a distinction though. So to the past perfect is how many there were going to be. Right? So it’s a backwards look and then a forwards look as opposed to the forwards look and then a backwards look. Right? So they passed perfect tense. So imagine I’m counting down from 10 to zero, and I finish now. And I’m counting one number per minute. And I say, “Five minutes ago, how many numbers was I going to count?” I’m talking about the remaining five numbers that I still have left. So the answer to that question is five. Right? So, that’s how many I was going to count. That’s how it’s perfect. Because it’s like you go down the path, and then look back to where you started again. I suppose the future perfect is you start going up the line and then look back at the path you’ve traveled. So, that there’s an exact perfect mirror image past perfect tense. My PhD was intense logic. You might be able to pick that up.
Trent Horn:
Okay.
Alex Malpass:
So maybe trust me on this one, but I could definitely spell it out to you. I could draw you some pictures that would make it perfectly clear that there is in fact doesn’t… And look, but whilst there’s a tense, the tense isn’t perfectly symmetrical. I’m not saying that the past and the future are perfectly alike in every respect. I mean, quite happy with the idea that the past is fixed, and the future is open. For instance, I think there’s a modal asymmetry between them. I also think there’s an epistemological assymetry between them. I know things about the past like that it rained today in the sense that I can’t possibly know for sure whether it’s going to rain tomorrow in the same way.
Alex Malpass:
So there are obviously asymmetries between the past and the future. And I’m not saying that there aren’t any. All I’m saying is there’s an irrelevant asymmetry for this argument. Because all that’s going on is the original Hilbert’s Hotel argument was if the past was beginningless, then it would be actually infinite. But it couldn’t be an actual influence at the past as a beginning. And all we do in the paper is change the tenses of that argument to say, “If the future were endless, then it would be actually infinite. But it couldn’t be an actual infinite. So the future must have an end to it.”
Alex Malpass:
Now what all this going on there is it change of tense. So it’s not going to be appealing to anything epistemological, or modal, or anything that’s going to make any difference there. It’s just about tenses. So I do think that in terms of tenses, the past and the future are the same. They’re symmetrical with each other. But I’m not saying that some weird metaphysical thing, like the past and the future, both… Time travels in both directions or something weird like that. I certainly don’t think that. Right?
Trent Horn:
Right.
Alex Malpass:
But yeah. It’s a kind of dry academic point about the use of tenses is basically symmetrical with respect to the past and the future.
Trent Horn:
Yeah. But I think there’s also going to be a problem when you look at the asymmetry between the two for things like instantiation or actualization. I know you talk about this in one of your papers. But because when I think about a beginningless series of events that accumulate over time or a feature of successive addition, it is the case at every past moment there have… Well, at every future moment, there will be an actual-
Alex Malpass:
There you go.
Trent Horn:
… [occurrence 01:27:04] of future events.
Alex Malpass:
Right. Now you’re getting it.
Trent Horn:
Right. Right. But there are… Wait. So when I look at it… I guess the way I look at it is when I look at the particular moments in each element of the timeline. So, and in a beginning list series of events at every moment… Well, I guess like this idea of actualization or accumulation is helpful. So if I haven’t always been doing a task that endures through time in the past, then at every moment in the past, I’ve like amassed an actually infinite collection or something like that. Whereas in an end versus a beginningless task with an endless task at every moment, there is a finite collection. When you look at the principle of like actualization or accumulation, I think that’s the best avenue a person would have forward to try to find in a symmetry between the two.
Alex Malpass:
Okay. So good. So this is like Loche’s argument. Right? This is like imagine every day in the past someone built you a single hotel room and added it to an existing hotel.
Trent Horn:
Right. Or-
Alex Malpass:
And if the past was… Sorry.
Trent Horn:
Sorry. Go ahead.
Alex Malpass:
Well, I mean, the thought there is just if there was no beginning to that sequence, then there’d be infinitely many rooms on that hotel map is you’d been doing that task [crosstalk 01:28:46].
Trent Horn:
And now what makes it… Yeah. What makes it paradoxical is that at every past moment there weren’t actually an infinite number of rooms.
Alex Malpass:
Well, I don’t know if that makes a paradox. I think what the problem is supposed to be I thought the problem with that Loche’s trying to solve is, look you could say, “Look, the past doesn’t really exist.” Right? So it’s that there aren’t any past days now. They’re all in the past, aren’t they? So they’re done. So if you take a kind of a view on the ontology of the past, like you might just deny that, that exists. You might be a presentist like Craig. Only the present exists. Then-
Trent Horn:
Right.
Alex Malpass:
… Like the past isn’t really like Hilbert’s Hotel because it’s like a Hilbert’s Hotel where none of the rooms exist. Right? That’s not very problematic. And-
Trent Horn:
They only exist one moment at a time. Each room.
Alex Malpass:
Yeah.
Trent Horn:
They don’t endure.
Alex Malpass:
Yeah. There’s no actual infinite there as such. So it seems like if you want to draw the analogy with the infinite past and Hilbert’s Hotel, you kind of… To make it super clear, you should be committed to every one of those past days in some sense or another existing. They’re not present, of course. But they exist in some way. But Loche is like, “Look, let’s not get bogged down in all this ontology of time stuff. Let’s just think about an object that exists now in the present.” An infinite object now actually is Hilbert’s Hotel. Right? As long as some stuff has happened in the past, like somebody building a room every day. Then there’d be a Hilbert’s Hotel in the present. But so their thought goes. There couldn’t be a Hilbert’s Hotel in the present. Therefore the past couldn’t be infinite.
Alex Malpass:
So it’s not so much that… I mean, I think it’s very interesting that every previous day there would already had to be Hilbert’s Hotel. I think that’s true. But I don’t think that’s what makes it paradoxic. I think you’re supposed to see the existence of Hilbert’s Hotel in the present has literally just been contradictory to this metaphysical truth that they couldn’t be a Hilbert’s Hotel in the present. Right? Because such objects are absurd, and then therefore they couldn’t exist.
Alex Malpass:
And that’s how that’s supposed to be running. And, yes. I think that standardly, you would say “There’s an asymmetry here.” Because if somebody starts building a hotel now, and they keep adding a room one day at a time. No matter how long they do that for, they’re not going to have a Hilbert’s Hotel. And it’s very different to the beginning. So in some way the endless future is different to the beginningless past. Okay. So here’s what I think. Here’s one thing I wonder what you think about this? How about considering instead of a hotel room builder, a hotel room destroyer. Right? So imagine God… I mean, let’s suppose it’s possible that God could spend each past day creating out of nothing a hotel room. Let’s suppose that seems reasonably possible really. It doesn’t seem like it’s beyond his power to sort of pilfer a hotel room into existence.
Trent Horn:
Are you saying an enduring hotel room?
Alex Malpass:
Yes. That’s right. An enduring hotel room. So that-
Trent Horn:
An immortal hotel room. [inaudible 01:31:53]
Alex Malpass:
Yeah. He sustains it in existence after he creates it. So that such that today there’s a Hilbert’s Hotel. And that’s supposed to be Loche’s argument that shows the past couldn’t be beginningless. But now consider this. Surely it’s also possible that God could destroy a hotel room once a day and reduce it to nothingness entirely. Exact opposite of creating a hotel room out of nothingness. He could reduce a hotel room to nothingness. So it seems to me that those… That’s just as plausible as something that God could do.
Trent Horn:
Well, before we keep going. God could take a hotel room that exists and destroy it?
Alex Malpass:
Yeah.
Trent Horn:
Okay.
Alex Malpass:
And the exact opposite of what he did when he made it in the first place. So I think a builder could pull all of the bricks apart and put them back where he found them or something. And it seems like God could do whatever the opposite of building the hotel room was. But now ask yourself, could he do that every day throughout the endless future? What do you think?
Trent Horn:
Could he do… Wait. Are we starting at the present moment?
Alex Malpass:
Yes. So could he tomorrow destroy a hotel room?
Trent Horn:
Oh, sure. Could he destroy a hotel room every day into the future?
Alex Malpass:
Yeah.
Trent Horn:
Sure. But that would seem to assume that there is… Hilbert’s Hotel exists, and God could destroy each… one room a day for the rest of time.
Alex Malpass:
Right. Right. Exactly. So if for him to be able to… Obviously he could destroy one hotel room tomorrow. Doesn’t mean Hilbert’s Hotel exists today. Could just be one hotel room, and that’s it. Then he could destroy that. But for him to be able to keep destroying hotel rooms once per day forever, there’d have to be a Hilbert’s Hotel in the present. But aha. Second premise, Hilbert’s Hotel is impossible. Therefore God can’t destroy hotel rooms once a day for the rest of the endless future. Right? He lacks that capacity because there couldn’t be a Hilbert’s Hotel. That seems to be the sensible thing to say there.
Alex Malpass:
I mean, otherwise you could say maybe the future has an end. But that doesn’t… Probably don’t want to admit that either. The easiest thing to suppose is just because Hilbert’s Hotel is impossible. God couldn’t, in fact, destroy the unique hotel room every day for the rest of the future. That does seem to be the correct analysis. But then I think that’s exactly the analysis you should take to the past case too. I mean, if Hilbert’s Hotel is impossible, then it’s just not possible for God to have created a hotel room every day in the past for exactly the same reason.
Trent Horn:
Yeah. And I’d say I would have to give it some more thought. I’m just not sure if it is entirely symmetrical, what’s being proposed. Like for me, I agree that God could not like… And this is the first time I’ve heard this example. So let me stumble my way through it.
Alex Malpass:
Okay.
Trent Horn:
Yeah. It seems like to me, it is not the destruction that creates the problem in the future example. It’s just the existence of the hotel. But it is the construction in the beginningless past that gives us the problematic element and why it exists in the first place. It seems like the existence of the hotel is quite separate from the act of destruction versus the paradoxical element that’s involved. I think that’s like a first like-
Alex Malpass:
Yeah. I think some people have that same thought as well. I mean, that’s fair enough. So I like this example because it’s very different anyway. You were trying to say to me in the first place, “Oh, well the analogy, the symmetry would be you’re building a hotel rooms every day in the future. And I think actually if you wanted to be symmetrical, you should think of destroying in the future and building in the past.” Then you’ve got the proper mirror.
Trent Horn:
Well, I was thinking when I was reading… Yeah. When I was reading your paper, because I think one objection you raised is… Well, you’re going back to, what’s his name? Dretske, 1965, Count to Infinity paper.
Alex Malpass:
Well, this is about the accumulation argument then.
Trent Horn:
Right.
Alex Malpass:
Or successive addition, I guess I should say.
Trent Horn:
Right. Like, just because… The reason the destruction thing you were talking about, I was thinking about the counting each and every… Can you really count to infinity? It’s like, well, if you count each natural number, then you will have, then you will count… Not will have. You will count every natural number. Like the principle of each and every… Another concern that I have with these different kinds of thought experiments and trying to… When we’re trying to build our way out to see if endless futures, beginningless pasts. I think the thought experiments they do… We are more likely to end up with paradoxical results when we have an endless future series or beginningless past series that has a cause and effect relationship running completely through it versus counting. To me, it’s like if I said to you, “Alex, could there be a line of numbers that extend infinitely into the past?”
Trent Horn:
Well, it’s a number line? Sure. Yeah. And then, it’s like, now imagine each of those numbers was a year. Okay. Then we can have an infinite past. Or let’s just imagine there’s Fred. And there is a Fred at every number, and he recites the number he stands at. That-
Alex Malpass:
Sure.
Trent Horn:
… I guess for me, it’s like, well, the defender is saying, “Well, it’s quite possible for there to be a beginningless past.” Will propose examples. My concern sometimes is that what they propose is just kind of a dressed up version of a number line. Whereas what makes past, present, and future very different from the numbers on a number line are things like the causal relations that exist between them. Like number four exists independent of three. Three doesn’t cause four to exist. They just exist on the line.
Alex Malpass:
Okay.
Trent Horn:
So, I think that when I look at the examples… So like with building, accumulation, Grim Reapers, things like that. That’s where I think the problems start to arise. And to me, the problems begin to arise precisely when the scenario starts to be more like reality and how past, present, and future things interact. I don’t know if that makes sense.
Alex Malpass:
Yeah. I think what you’re saying is causation is asymmetric. And things in the past cause things in the present. Not things in the present causing things in the past.
Trent Horn:
Yeah. Because I am fascinated. I mean, I love when people try to come up with counter paradoxes. You think that’s bad? What about this? Like, that’s what you kind of do with Grim Reaper or like Grim Messenger. It’s like, ah, yes, but I feel so… There’s still some people who are with us, who are following all this, which is fine. That the Grim Reaper paradoxes… All of them seem to… Let me just explain. Give the basic, and then we’ll keep going. This idea that what if you stretch them into the past? I gave an example in my debate with Ben Watkins, like, “Let’s say somebody was building Hilbert’s Hotel one room at a time. And they write down… They’re given a blank sheet of paper. They’re given a sheet of paper from the guy who built the room before.” And I appreciate being complimented, by the way, in an email saying I was able to somehow bring Hilbert’s Hotel and causal finitism together in one example.
Alex Malpass:
Yeah. And Loche’s argument. All in one. Yeah. It was nice.
Trent Horn:
Yeah. Just put them all together. Like imagine we build Hilbert’s Hotel one year at a time. And the guys who are building it get a slip of paper from the guy before him saying, “It’s either got the room number, the previous room number, or it’s blank. If it’s blank, write your room number. If it has a number, pass it on.” And so, it’s supposed to go down the line, and it gets to the present. And the question is what number is on there? And well, it can’t be blank. But there is no natural number that could correspond to be on there.
Alex Malpass:
Yeah.
Trent Horn:
And so, that would be the paradoxes this has developed. I’m not smart enough, by the way, folks to come up with this stuff. I’m modifying an example from Robert Koons, who is a super smart Catholic philosopher, by the way. My job is just to take things that are out there and try to make them more fun and entertaining.
Alex Malpass:
But, of course it’s not Koons’… I mean, Koons wrote the version of the argument there. But it’s actually [Jose Benardete 01:40:37] who explored that in the first place.
Trent Horn:
Oh, is that a Benardete example?
Alex Malpass:
Yeah. Yeah. Yeah.
Trent Horn:
Yeah. Okay. So back-
Alex Malpass:
All of these Grim Reaper ones are his.
Trent Horn:
Yeah. Because this goes back to what was this like a 1964 book by Benardete on-
Alex Malpass:
Something like that. Certainly in the 60s. Yeah.
Trent Horn:
Yeah. Yeah. Yeah. On infinity and these different kinds of causal paradoxes that arise. And so here it’s like, well, we have an example I see of the causal chain moving through. And so, when you have with these examples, it’s like, you can’t do this. And there’s a lot of different examples, but there seems to be a basic rule. Like don’t do anything if and only if the previous member didn’t do anything or something like that.
Alex Malpass:
Yeah. That’s right. So it’s something like for each member. They have some property, call it P. And they have that property if and only if none of the previous ones have that property P. The property might be that they’ve written a number down, or that they’ve killed Fred, or that they’ve… The barrier that stopped the ball rolling or something.
Trent Horn:
Right.
Alex Malpass:
And they only do that if none of the previous ones have.
Trent Horn:
Yeah. So it’s refrain if and only if previous member has refrained is one element of it. And then the other element is, there is always a previous member. So-
Alex Malpass:
That’s right. There’s a beginningless sequence in some respect.
Trent Horn:
Yeah. Right. So there are… Yeah. I like the way of saying, if we’re talking about what previous members do, and there is always a previous member. Then it’s like, well, can we have both of these things? And I love… The paradoxes are okay. Yeah. But what if God instructs future angels to write down certain things in the future. And then, he… Fred can’t… He’s got to write down the number, and you just try to create a situation. Because it’s interesting because you have originally with Craig, I think it’s a lot easier with Craig’s version to try to deploy the symmetry argument. To show that Craig’s argument would mean that there can’t be an endless future if there cannot be a beginningless past. I think it becomes much more difficult with the causal finitism approach of trying to create examples. Normally what they all seem to rely on is a endless series of causal events. My arms sticking.
Trent Horn:
That’s why I got to put my arm out when I talk about it to keep my head straight. Stretching endlessly into the future. But the reason they have some kind of causal effect on some present thing like Fred writing down a number is because God uses his omniscience. And I’m just suspicious kind of, of this move that… It’s like that I don’t think it can be deployed against the future, because it’s almost like we’re trying to use omniscience to convert an endless future into a kind of past series of events that are given to Fred before he writes down. Whereas that natural intuition of the asymmetry, that past events cause future events. We keep the symmetry argument from being deployed in that way or at least as easily.
Alex Malpass:
Yeah. So I think I’m more sympathetic to the thought that these arguments don’t quite so easily point towards the future. Right? Like for a while I was thinking about whether there’s this like meta mirror principle where every argument that shows the past must have a beginning, can be equally turned into an argument that shows the future must have an end.
Trent Horn:
Right.
Alex Malpass:
But I’m less keen on that nowadays. And maybe these sorts of… I mean, it certainly becomes much less clear to me anyway with these. So I think the initial thought is like the reason causation is asymmetric. Right? So I can know stuff about the past. I can’t know stuff about the future. So any version of the paradox that involves me having to know about stuff like passing a note on. I can get passed a note by last year’s hotel room builder, but I can’t get passed a note by next year’s hotel room builder because he hasn’t got his note yet.
Trent Horn:
Right.
Alex Malpass:
So, because causation runs in one direction. It is an obvious thing that gets in the way of making a future tense version of that argument. But I think that sort of seductive thought was, “Well, God sometimes reveals things about-
PART 3 OF 4 ENDS [01:45:04]
Alex Malpass:
Sort of seductive thought was, “Well, God sometimes reveals things about the future in the Bible.” According to some theists, that He has the ability to know the future, and that allows you to, as long as you can come up with a story where He goes along with it, that He could tell people enough stuff about the future that you come up with a version of this paradox that overcomes that asymmetry that’s intrinsic to causation.
Alex Malpass:
But I suppose the reason I’m less keen on these days is just because I think it just ends up grounding out in stuff about theology, which is, I find, just all open season on someone’s going to have that version of God, right? And then you start carving, well, I suppose if you think this about God, then this argument doesn’t make any difference to you. But we are targeting these people who hold this specific view. And I just sort of… I guess I lose interest. I’m a philosopher, not a theologian, I suppose. And I’m doing theology now, not philosophy anymore. So it sort of seems like it would be handy to bring in God’s omniscience, but for me, it takes the clarity out of the analysis. So yeah, they’re fun, but they’re not serious, I think.
Trent Horn:
Yeah, because it adds a big step-up in the argument. Whereas the idea of what tries to be intuitive about the paper passer example or the Grim Reapers… And the Grim Reaper, by the way, if people aren’t as familiar with that one, would be… I think anyone who’s stuck around this long doesn’t… maybe, maybe they still know, is that there is a being, a reaper. Imagine… He’s the Grim Reaper, right? He’s got the scythe. He’ll chop your head off. There’s one who will kill… And there’s Fred. Fred has been alive forever, beginningless past. Doesn’t seem counterintuitive, right? Or it doesn’t seem impossible right off the bat. But there’s a Reaper who will kill Fred if he’s still alive at year 1 BC, or before present moment, BPM, 2 BPM, 3 BPM, 4 BPM. There’s a Grim Reaper at every past moment who would kill Fred.
Trent Horn:
So Fred can’t be alive today, but there’s nobody who could kill him, because once again, they are programmed to kill Fred if and only if a previous one has not killed him, and so it stretches back. And I think the… What’s the word I’m looking for here? The attractiveness of the Grim Reaper stretched out into the past, or the paper passer, this idea of what we’re trying to do is, well, could there be an infinite past? It’s like, “All right, well, let’s make that world in our minds, infinite past.” If that really is a world, though, let’s populate it and see what happens in it. In philosophy talk, this is, now we get into what are called patchwork principles. “All right, well, what could really happen here?” We can have these reapers or these paper passers. And it’s like, if they can pass papers and chop heads off here, here, here, here, and here, seems like we can keep extending that. But if we extend it all the way, not all the way to, but if we extend it within the [crosstalk 01:48:01] into the beginning…
Trent Horn:
Yeah, we fill the past. We get the contradictions. And then if you try to do any move like that in the future, it doesn’t… Because it’s attractive to say it’s paradoxical in the past, because it’s just all these little steps that are taken over and over and over again. Not like, we do all these little, little steps in the future of angels who are giving instructions. And then God transforms that knowledge into present knowledge, and Fred does something. It’s like, “Wait, we took a big step-up here that gums up the works.”
Trent Horn:
But I think an objection you’ve raised, and this is something… I get payoff for talking about… Something else I mentioned will be salient here… is the problem, and I think with these other examples you brought up is, well, just because you have a problem with the infinite doesn’t mean the infinite is the problem. There’s a bumper sticker slogan you can use.
Alex Malpass:
Yeah. Nice.
Trent Horn:
Yeah, just because you have a problem in the infinite doesn’t mean the infinite is the problem, or you don’t have a problem with the infinite. Maybe it’s just the case that you could have an infinite past, but you can’t have Grim Reapers doing this stuff. You can’t have paper passers, and so…
Alex Malpass:
Can’t fill the past with them. You could have some finite number of them, any finite number in fact, but not all of them.
Trent Horn:
Right. Yeah, and so in the literature, and I think the first time I found a reference to this. This is called the Unsatisfiable Pair Diagnosis. What was his name, Shackel? I think there was a guy in 2005 who… Okay, yeah. That’s the furthest back, I found at least this term being used to describe [crosstalk 01:49:40].
Alex Malpass:
But, I mean, you can see it in a couple of papers by [Ablo 01:49:42] and I would argue you can see it in a paper from, 64, by 64, or maybe even earlier by Arthur Prior, but nobody… The term Unsatisfiable Pair Diagnosis is Shackel’s.
Trent Horn:
Yeah.
Alex Malpass:
Yeah.
Trent Horn:
Yeah, and so that would be… The idea here is that… And the point we’re getting, by the way, to find common ground with you, I think you and others have lodged serious criticisms of Craig’s argument. I think there might be ways around it if you really double down on the theory of time or the growing block view, which is something that I’m kind of partial towards, but I don’t have a fully fleshed out view of it myself.
Trent Horn:
But anywho, I think it’s moving in an impetus to have things like Locke’s argument or Causal Finitism to really focus especially on the causation element as being a big difference between past and future. So the idea with the Unsatisfiable Pair Diagnosis is, just because you can create a world, and you can populate it, don’t think the world is the problem. You’re populating might be the problem. So there’s a world where John is taller than Steve. In a parallel universe, people don’t always understand possible worlds, a parallel universe where Steve is taller than John. They can both exist in their worlds, but you can’t have a world where both of them are, a world where John is taller than Steve and Steve is taller than John, and they’re both in the same world.
Trent Horn:
It’s a logical contradiction, so it’s an unsatisfiable pair. The problem is not the world I made. So the idea is like, if there’s a Minotaur in one world and a Centaur in another world, I could have a world with a Minotaur and Centaur, doesn’t seem to be problematic there, but there do seem to these cases where it’s an unsatisfiable pair. And so the question becomes, is this a case where the Grim Reapers or the paper passers going into the past, is it the infinite past that is giving us grief, or is it just these particular members that we have populated with the past?
Trent Horn:
And when I think about this… This kind of gets us back to the defining problem with the actual [inaudible 01:52:05] we discussed earlier. Well, this is kind of the reverse of your problem with metaphysical impossibility. It’s almost like the mirror problem with it, in that there’s some cases of metaphysical impossibility seem real clear, like prime minister is not a prime number. Others, not as clear. There seem to be cases where the Unsatisfiable Pair is very clear. John and Steve, Steve and John. It’s almost logical there. But then there’s other cases where I’m not quite sure that it is an Unsatisfiable Pair, it doesn’t seem… It doesn’t smack us in the face right away, like John and Steve, John taller than Steve, Steve taller than John, of Grim Reapers forever and… or, sorry, the Unsatisfiable Pair is refrained if and only if there’s no previous member. There is always a previous member, is basically [crosstalk 01:52:54].
Alex Malpass:
Yeah, it doesn’t seem like that’s a contradiction on its face. That’s Shackel’s whole point is that what’s going on is that people can almost by accident, find themselves describing a scenario, not noticing that they have in fact committed to two propositions, both of which can’t be true together. And then come to the end of the description and think that they have to jettison one of the assumptions. But that’s not, I mean in a way you do have to jettison one of the assumptions, they can’t both literally be true in the same place. But the thought is just if you’ve contradicted yourself, you haven’t described a possible world at all because possible a consistent set of propositions. So if what you’ve done is tell a story that inadvertently smuggles in a contradiction, then that’s not actually a possibility at all. So it’s only by doing the logical analysis, quite clearly, that you can get to that situation of seeing it just as easily as when you see the taller than example.
Trent Horn:
Yeah, and I think the reply to that, the reply would be is that the case that this pair is really contradictory of one another and we just had to dig deeper to find it or that these things aren’t contradictory, but the world as it exists will lend themselves to that. So I would agree with you that the pair refrain from an [inaudible 01:54:31] paper passing, killing Fred, if there’s no previous member, there’s always, and there’s always a previous member. If the pair propositionally boiled down to there in a pos… There is a first member of a Causal Chain and there is no first member of a Causal Chain. That’s like the Steven John. It’s like, okay, you’ve got an Unsatisfiable there…But I don’t think it…
Alex Malpass:
Well, look, I think everybody agrees really, is it Pruss, Koons they also agree that this is an Unsatisfiable Pair because you need it to show the inconsistency. So nobody’s arguing that these are not [crosstalk 01:55:13].
Trent Horn:
I guess the question is which thing do we say can actually happen.
Alex Malpass:
That’s right, yeah. They want to say that you… The most sensible thing to do, and then this is not logical, but this is like extra logical kind of arguing about which premise we should get rid of the sensible thing to do the best thing to do or whatever is to get rid of the assumption that there could have been a beginningless sequence of events. I think that’s guilt by association because there’s perfectly innocent. Even though that’s a logically contradictory beginning the sequence of events, there are other beginning, the sequence of events, so they’re innocent of that logical contradiction. Ones where everybody passes everyone else a note that says, I love you or whatever, nothing wrong there. Right? This some sort of nice, cozy, perfectly logically, consistent world, even if it’s got no beginning and to rule that out, just because there’s some naughty, logically inconsistent world just seems to me a faux part, right?
Alex Malpass:
So you’re just doing something wrong there, especially if there are other options on the table. And it strikes me that there is another option on the table because well, the idea that one can always recombine individually possible things into using a Patchwork Principle, into some third setting where both of the individually possible things are present together. That principle seems to me that it’s not an enviable law of, I don’t know, metaphysics, or it’s really the epistemology of modalities where that comes from this very obscure area. And nobody can prove to me that that’s an exception to this rule and there are other… Everybody thinks really everybody thinks that there are exceptions to this. David Lewis is famous for coining this term, although I’m sure it goes back earlier than him, but no sooner. As he said, the principle in his book, The Plurality of Worlds, then he immediately qualified it and said, “well, of course, you can’t have”, he said, you could have a dragon and a unicorn each individually possible.
Alex Malpass:
That means you must have a third world where there’s both of them together. And he said, but of course they couldn’t be completely overlapping with each other. Because what does it mean for a dragon and a unicorn to occupy exactly the same space as each other, that doesn’t really make any sense. Right? So there has to be some kind of restrictions to this. It can’t just be any old combination of patches pasted into each other. So, and everybody has their exceptions. Causal Finitism itself is a restriction on which things can be copy and pasted in to the same world with each other. Right? Also proofs quite explicitly thinks God’s Omni, benevolence is a restriction on the perpetuate principle too. So it’s not like there aren’t restrictions on this, right. Everybody thinks there are. And the argument only works if you forget that and try and pretend as if there aren’t any restrictions.
Trent Horn:
And I think though, right, but I think the way that it would work here, it goes back to what I was saying about, could there be a beginningless past and there’s like a Causal Thread running through it. Because even if you have the example of like passing a note, I love you. And it arrives at the present. Doesn’t seem to be problematic, but then it’s.
Alex Malpass:
That cause of sequence.
Trent Horn:
Yeah. But then it’s like, well let’s say we have an infinite past and there’s always a thread at negative four, sorry, negative 1, 2, 3, 4. And they count or recite the number or they write down something. It still seems to me it’s getting us closer to more like the number line I was thinking of before. That there’s nothing, I guess maybe it’s lacking, things that are like transformative or things like that. But I see what you’re saying. But if we go to the Unsatisfiable Pair, we all agree… refrain, we call the Bernadette rule is another one people talk about, so refrain if, and only if no previous member Reaper swipes paper passer passes… The Bernadette rule. And there’s always a previous member. I think those who would defend Causal Finitism would say, I just have a lot more going for me to accept the Bernadette Rule, than the idea that there is always a previous member. So I think that’s one way of looking at it.
Alex Malpass:
Well That doesn’t seem very principled.
Trent Horn:
Go ahead I had another thought, but…
Alex Malpass:
Okay, so we’ll come back to your further thought, but it seems to me, you can have…you can satisfy that Bernadette Rule for any number, any finite number of instances, for any end, but not for infinitely many. So I don’t know where you…how you are training your intuitions here. So, so carefully that it can pick up distinction. But seems to me, even if you did have a strong intuition, it’s probably going to be satisfied in the range of cases I’m allowing. You can have any number of Grim Reapers you like any finite number, a million, a billion, a trillion, however many you want, surely you…are you trying to tell me that your intuitions are so finely tuned, that that’s not enough to satisfy and [inaudible 02:00:31] a strong, clear, distinct intuition that you have to also have infinitely many possible?
Alex Malpass:
I just, I kind of, I’m not going to say I don’t believe you, but I just, I don’t have any intuitions that are anywhere near as finely tuned as that in metaphysics. That’s crazy. I’ve intuitions that if this thing is actual, then it’s possible. Basic intuitions like that. But I certainly don’t, I can’t carve up abstract [inaudible 02:00:55] space with my intuitions and feel confident about it in that sort of way that you’d need here. So here’s a kind of Lewisian tactic as well to say, look, I can’t…your intuitions might not be satisfied necessarily the way you’re stating them, but here’s an offering, right? Here’s a scenario that’s so close to what you claim is required for your intuitions to be satisfied that it’s implausible, that you really do have an intuition that’s tracking a different circumstance from the one that’s available in the range of cases that I’m allowing. So this is not necessarily kind of, [inaudible 02:01:29] say maybe a diffusing reply to what you’ve said. I’m not telling you that you’re wrong, but I’m kicking up dust in the face of that approach. And it seems to me it’s going to be very difficult for these-
Trent Horn:
This is how philosophers fight with each other.
Alex Malpass:
It is true, yeah.
Trent Horn:
Now you’re a philosopher. I’m just doing it as a hobby as in trying to…
Alex Malpass:
Well, me too, but like that’s the tactic here, it just makes it very difficult for you. Sometimes I’m a keen chess player, but often chess grounds out in a draw. And what will happen is one player will just pick a tactic that they’re not going to win, but it’s very difficult for the other person to win either. And it just turns into a draw and it’s perfectly reasonable for professional chess players to do that. And that’s kind of what I’m doing here. I just think that it’s going to be very hard for you to rely on your intuitions here and make any headway.
Trent Horn:
Well, I think the problem where, where people will go is when they try to, extend these causal elements into a beginningless pass, reapers, paper passers, a question that will rise. This is an objection that Pruss is leveled is, well, if you could have an infinite past but you can’t have these things happen in it. Why can’t they happen? What’s preventing that from happening? And so, see you are the chess player, like, ah, he’s moved the pond where I want it to be no…
Alex Malpass:
Queens down a bit. You’re playing and I know this line very well.
Trent Horn:
Yeah, so what is preventing that from, from happening? And that would be, what’s called the mysterious forces objection. The ideas like, seems like it could have the reapers stretch out in time. Or even if you had an infinite number of them spatially around thread with the same Bernadette rule, it’s like, why don’t they strike? Why can’t they write? What prevents that from happening? And to me, the analogy I like in reference to that is like, we discussed earlier about the possibility of time travel into the past. I apologize, I’m looking out my window, because a utility man came to our house, but my wife will talk to him. It’s fine. We can’t break away from this. We’re almost there, we can’t break away that, the problem is the time travel example.
Trent Horn:
It’s like, well, some people, one school of thought is you can’t go… Travel’s impossible because you would create paradoxes that are bad news bearers. The other school of thought like with David Lewis and others says, well yeah, you could have time travel in the past return to the same point in the timeline, you just won’t be able to change anything. You can have that, you just can’t have a world. It’s an unsatisfiable pair if you have time travel as possible and I killed my grandfather. That’s unsatisfiable pair, you just can’t have that. You could have time travel, you just can’t have the other thing. But I’m like, well what would stop me from pulling the trigger? And this is like the Novikov consistency principle and this kind of stuff. Well, something just will you’ll slip on a banana peel, you’ll kill the wrong guy. That seems to import… mysterious things seems to import more to keep it going that it adds cost of a hypothesis it seems like.
Alex Malpass:
Yeah. Right. [inaudible 02:04:46] the piling up the coincidences, the gun jams, you slip on a banana skin, blah blah, blah.
Trent Horn:
And that’s why when I look and the philosophers disagree, but that’s why I really side with those who would say the number of coincidences you would need for time travel in the past week possible, they would say it’s just easier to say… Not just that it’s easy, but that it’s just parsimonious or whatever there you don’t in… It’s less costly and it’s perfectly rational and makes more sense, so you just can’t go back and then you don’t get these paradoxes and the casual finitist try to incorporate that into the infinite past that similar move, it seems like.
Alex Malpass:
Okay, so that’s right. So you get people like Lewis who say that time traveling in the past is possible because you won’t kill your grandfather no matter what you try, it’s not going to happen. And then you get people like [inaudible 02:05:34] who’s the guy who says that overwhelming balance of coincidences makes it too implausible to think that that could happen. Whatever…
Trent Horn:
I was reading a philosophy book on time, I don’t think it was him it was another guy, but I mean there’s two camps.
Alex Malpass:
Sure, yeah there’s two camps anyway. And so fine. So I do think there’s a passing similarity to the time travel case. Let’s just point out that dissimilarity is that if there’s a contradiction, it’s not actually formally derivable in the same way as a Bernadette case it’s the time travel case, it showed me the formal model where someone’s actually drive the contradiction properly. And then we… I’ll change my tune here, but I’ve never actually seen that and I’m not sure that it’s there and the literatures of hand wavy to some extent.
Trent Horn:
That there is a paradox that arises if you like kill your younger self or grandfather?
Alex Malpass:
Yeah, I mean intuitively it’s paradoxical, right? But in order to derive that properly, you have to pile in a load of stuff about how the time travel is working. And I don’t know that anyone’s got any of that mechanism cashed out properly. So it offers the promise of a contradiction, but you can’t quite get that. It’s not up to the standards of a [inaudible 02:06:50] Whereas in the Bernadette cases it is because much simpler and there are, Koons’s paper has an example of one such derivation Shackels paper does too. This paper by Luna and Erasmus, it was out in 2020. That also has a very good, clear up to the standards of a [inaudible 02:07:08] showing how that Bernadette case comes out. So there’s a dissimilarity there too. The time travel case, which is intrinsically more hand wavy than the Bernadette case. So…
Trent Horn:
Do you mean the contradiction? Because it seems like in the Bernadette case, we have a paper that is not blank, but has no number, Fred can’t live, but he can’t die. It’s not as clear cut a contradiction. If you go back and kill your grandfather, return to the same point in the timeline, then you will never existed to travel in the past.
Alex Malpass:
I think that intuitively just as good as each other. But I think that if you try to really write it down into the standards of a mathematical deduction, you’d find it really hard to spell out everything you needed to in the time travel case to reach that level of rigor where it’s not difficult in the Bernadette case. Because this number of assumptions is way easier.
Trent Horn:
We might be able to say just not to worry that we can conclude it is a paradox, even though we lack symbols and note notation to describe it…
Alex Malpass:
Yeah, yeah, yeah. I’m not saying it’s not a paradox because I can’t write it down. I’m just saying that there’s a passing similarity to it, but it’s important to note that there’s a dissimilarity to the cases as well. And here’s an analogy I preferred than the time travel one because to me it’s easier and there’s a mathematical aspect of this too. But so there’s this puzzle that made Euler famous about crossing the seven bridges of Königsberg without doubling back on yourself. Right? So it was like an open puzzle at the time. And he invented a field of graph theory to show that it wasn’t what he invented graph theory field of topology to show that it wasn’t possible. It wasn’t mathematically impossible for anybody to cross over that all of their seven bridges without doubling back on themselves.
Alex Malpass:
And it leads to this notion of an Eulerian circuit and blah, blah, blah, blah, blah. So there is a town or Königsberg is a real place and you can go there and it’s really got seven bridges and maybe it’s got more now, but at least at the time it had seven bridges. And you can imagine trying to do the experiment. Now what’s going to happen when you do the experiment. My dog just waking up in the background.
Trent Horn:
That’s all right.
Alex Malpass:
What’s going to happen. Right. What’s not going to happen is a contradiction happens, right? You’re not going to usher in Pi and [inaudible 02:09:39] Pi for any proposition. It might be that you slip on a banana skin or that you fall into the river or something like that. But all I can tell you what will happen is something consistent will happen, because it would just be a normal day with you wandering around bridges and eventually going home, not having succeeded.
Alex Malpass:
I can’t tell exactly what will happen, but something consistent will happen. And, and yet no strange force, it needs to be invoked here. It’s just, it’s mathematically topologically impossible for you to have completed the circuit you were trying to do, but not because topology suddenly has some causal influence on your path across a bridge one day, but just because that’s not something you can do. And the same exact thing happens here. You can derive a contradiction from the assumptions. So that’s why it’s not going to happen. I mean, you don’t need to appeal to anything else as in like, it’s just easier to see than the time travel one, which brings in all this extra stuff about the philosophy of time, how would I travel back, blah, blah, blah, blah, blah. It’s just, you could literally go… you physically could go to Königsberg tomorrow.
Alex Malpass:
You could buy the ticket, you could go there and you could try this experiment. And we both know you’re not going to succeed it. And we both wouldn’t appeal to mathematics having some causal force that influenced you there. And I think that if you agree with me about that, I don’t understand why you think a causal force is required to explain why there couldn’t be a beginningless past filled with reapers embodying that property you were talking about before. I mean, the reason there couldn’t be is because it’s contradiction and that’s it. No need to appeal to a magical force preventing from taking place.
Trent Horn:
I think that the… I just think the example still has like these relevant, the Königsberg bridge. My understanding is you have… It’s two banks, two islands, seven bridges. Can you cross all of the bridges once without doubling back on yourself without crossing another bridge again? What seems to me here is that the task that is being proposed seems relevantly different from asking if Grim Reapers can continue into the past or even like the time travel example, because in those previous cases it seems like, I’m on the threshold of a paradox happening, but something keeps it from happening. Whereas in Königsberg I’m not really worried about anything paradoxical occurring or anything like that. That asking me to cross all seven bridges without doubling back is kind of like asking me to square the circle or draw a square circle.
Trent Horn:
I’m not able to do that versus in the other cases where like, I don’t know, this is philosophically imprecise, like I’m standing on the threshold of paradox. I don’t think it’s a case where it’s like, I can cross a certain number of bridges and then I’ll just slip on the banana peel and not cross the paradoxical bridge. It’s like, you have to follow the rules. Like when I imagine it… I’ve thought of this before. I wonder if you took the Königsberg bridge and you put it on a toroid. Cause this is similar, I remember when I was in the seventh grade, there was the utility problem. There was three power plants and three houses and you have to get the electricity water and sewered each house without crossing the lines.
Trent Horn:
And it’s like, how do you do that? And then I told the teacher, I’ll just do this. And I drew the lines and folded the paper over and taped it to like… And I think that actually is I look up now and I’m like, oh, I think that actually was kind of like the solution. So it’s like in Königsberg, I’m like, well, I could do that if I just picked up the city and I folded it into a toroid and what you would say is, well, no that you can’t, that’s not part of the rules of the thing. So that’s my first shock at it as being, being too distinct, I don’t know.
Alex Malpass:
So I’m going to have to go in a minute because it’s half past ten here. And I’ve got to…
Trent Horn:
And I am going to be in so much trouble, my wife’s like you were supposed to talk to this guy. Okay, well…
Alex Malpass:
But look, let me just reply very quickly.
Trent Horn:
Let’s have the last word.
Alex Malpass:
Oh, we can’t both have the final word that would be possible. But look, I think you said that you feel like you’re on the threshold of the… realizing the Grim Reaper idea and that makes it different from being in Königsberg where you’re never really on the threshold of finishing that task or something. But I don’t think that’s right, because for each reaper to… there’s traveling forwards through time in a normal way. It can’t ever be that you get to some point in time and if only the next guy did something, then the paradoxical scenario would’ve been realized because for the paradox to be in that situation here for each reaper, there’s already infinitely more reapers that have just gone right, in the past. So for it to have been paradoxical is, there’s already, you have had to have had infinitely many that didn’t pass on the note when they should have done or something like, it’s always too late for whatever the next guy does to be the thing that causes the paradox to appear.
Alex Malpass:
It’s always already too late. So you’re never on a threshold, right? It’s always the case that the infinite past already has infinitely many things and it’s already back paradoxical. So there’s no threshold, it’s just like with the hotel room builder example, there’s already infinitely many rooms even. So if God took a nap yesterday, didn’t build his room yesterday. Doesn’t make any difference there’s already infinitely many rooms, right? He’s never on the threshold of building the hotel. It’s always already built. So that’s what, just wanted to point out there that I don’t think that’s a difference between the two cases. It’s not the case that in the Grim Reaper one you’re on a threshold, there’s no threshold.
Trent Horn:
I’m in trouble, I think he left. I’m supposed to talk to him.
Alex Malpass:
Okay, well let’s call this…
Trent Horn:
After the utility guy and catch him or something.
Trent Horn:
Ah he’s gone. no, it’s fine. Alex, it was a real treat to talk with you about this.
Alex Malpass:
No problem.
Trent Horn:
Where can people learn more about your work?
Alex Malpass:
I don’t know. They’ll have to…they’ll be lucky if they spot me somewhere.
Trent Horn:
I thought you had a little blog or website
Alex Malpass:
Ah, yeah. I haven’t written the blog for a while, but I used to write the blog, but I’m thinking about writing papers more these days. I’m playing chess more than doing philosophy these days. So you’re more likely to find me on chess.com than on my blog. Much more likely.
Trent Horn:
Maybe people can chat about the Königsberg bridge with Alex, while they play a game of chess. You never know. So thank you so much, sir and yeah. Once again yeah, thanks for being on the show today.
Alex Malpass:
Cool, thanks for having me.
Trent Horn:
Alrighty. And thank you guys for watching and for listening and if you guys have suggestions for other thoughtful critics of the arguments for natural theology or whatever it might be leave them in the comments below. We’d love to invite other people on to have these kinds of robust discussions. So thank you guys. And I hope you have a blessed day.
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