Regarding the HEAVEN vs HELL example, the confusion comes from the fact that the description of Heaven makes you imagine Heaven has more happy people than unhappy people.
But in fact, Heaven always had an equal number of happy and unhappy people to begin with. Our intuitions about finite quantities and geometries make us forget this.
In other words, Heaven should NOT sound great to you, you need to place more weight on the infinite number of suffering people in heaven and realize it is literally infinite!
As an analogy, imagine you had a wall which divided the universe into sides: one full of 10 happy people, and one full of 10 unhappy people.
You show an image of the happy side to Joe and offhandly mention the other people on the other side of the wall.
You show an image of the unhappy side to Joe and offhandly mention the other people on the other side of the wall.
You then ask Joe which is better, and he, being not so bright, says he prefers the happy universe you showed him. But both were the same universe! Joe just didn’t properly consider the other side of the wall.
Regarding the stated reasons to accept an actual infinite:
- I am not sure whether our best physics actually tells us that space is continuous, many QM researchers seem to think otherwise. But obviously I have no clue about QM, so there's probably no point discussing this
- Regarding the infinite future I basically agree with what Craig has said on this - roughly: There *are* no future events and for any time t in the future it will not be the case that at t there has been an infinite amount of events. So we have no counterexample.
Obviously you disagree that there are no future events, given that you lean towards B-theory, but if we have independent reasons to think infinities in conrete reality are impossible (as I think we do), then this seems to give us very good reason to reject any theory of time on which an infinite amount of events would be possible. So, if I were you, I would basically just Moorean shift this (If B-theory is right, then infinities may exist in concrete reality. But infinities can't exist in concrete reality. Therefore, B-theory is not right).
Thinking, instead, that the future HAS to be finite seems totally untenable to me - if I had to accept THAT, then I would just accept that infinities are possible. Surely we have more reason to think that the future can be infinite than to think that A-theory is false?!
The possibility of an infinite future only seems intuitive if A-Theory is true.
The problem is, a lot of the paradoxes arise once more if you accept the possibility of an infinite future. How should you value the pasadena game, for example? It seems like if you're willing to give up the possibility of actual infinite amounts of stuff, you should go all the way.
I also don't like the idea that you can't have an actual infinite. Seems like there are an actually infinite number of mathematical facts.
Finally, if I can't accept an infinite past or B-theory, I'll have to accept something in the vicinity of theism. But theism is obviously false :-P.
"The possibility of an infinite future only seems intuitive if A-Theory is true." - I disagree with that. Sure, I cannot literally *picture in my mind* what an infinite block universe would look like, but that seems irrelevant, I also can't picture a 1207-sided polygon.
I don't see at all why B-theory should make us think that there *has* to be a final moment in time (and tbh I'm not aware of any influential B-theorist who has ever defended the conditional "Necessarily, If B-theory is true, then the future is finite")
"Seems like there are an actually infinite number of mathematical facts." - I agree, but I specified that I am talking about concrete reality. That might seem ad hoc, but I don't think it is: all the good arguments against concrete infinities don't work with causally inert abstract objects imho
"Finally, if I can't accept an infinite past or B-theory, I'll have to accept something in the vicinity of theism. But theism is obviously false :-P."
I appreciate the honesty. I agree that if you think theism has an insanely low chance of being true and A-theory would imply that the Kalam succeeds, then this gives you good reason to accept the B-theory. But then again, imho if you have good reason to accept the B-theory, then you also have good reason to accept the possibility of infinities in concrete reality
To be more specific, if we're B-theorists then an infinite future being impossible is no weirder than an infinite space being impossible. And you have to believe that to avoid the paradoxes.
Even if I gave up B-theory and the possibility of an infinite past, I'd just accept that the universe began absent a cause. Doesn't seem to weird to me!
Again I don't agree that those are analogous. Imagine someone gets to the end of space and asks themselves "Why does space suddenly end here?", then "Because there is only a limited amount of matter in spacetime" seems like a perfectly good explanation (assuming relationalism about space, which is the most common view in the philosophy of space and time).
But now imagine that someone is at the last moment of time, would "This is the last moment of time because spacetime is limited in the later-than direction" really be a sensible explanation they could give? I don't think so. We would always ask the question how it could possibly be that the universe can *guarantee* that the future is finite, there needs to be some underlying mechanism that brings the end of the universe about (e.g. heat death). But that just seems like an incredibly strange mysterious force, similar to the mysterious force that would prevent you from killing your grandfather if time travel were possible. I don't see how the universe could possibly guarantee any such mechanism unless it's guided by reason.
Or do you think time just suddenly ends at some point, without any further reason whatsoever? Could it be that everything in the universe is perfectly harminous, yet from one minute to the next time suddenly ends, without any further explanation at all? That seems even more strange to me, then
I think there's probably some explanation of why time ends. I feel the force of the intuition, weakly, but it's not enough to overcome the ultmiate verdict. I think that a lot of puzzles--especially the pasadena one--reappear in the context of an infinite time.
You mentioned this but all of these seem like a problem for math and the philosophy of math, not ethics. We shouldn't reject Heaven>Hell OR the possibility of infinity, just because we couldn't use finite concepts on infinite sets on our first try. It honestly surprises me that milking paradoxes from the paradox machine is a somewhat-active research field. They don't tell us anything new! We gotta think harder about the nature of infinity and mathematical operations instead.
I don't think it solves anything and it is also very implausible. Say we have a 1% discount rate. This implies that Cleopatra getting a bit of welfare when she was alive is more important than saving the world today.
Regarding the HEAVEN vs HELL example, the confusion comes from the fact that the description of Heaven makes you imagine Heaven has more happy people than unhappy people.
But in fact, Heaven always had an equal number of happy and unhappy people to begin with. Our intuitions about finite quantities and geometries make us forget this.
In other words, Heaven should NOT sound great to you, you need to place more weight on the infinite number of suffering people in heaven and realize it is literally infinite!
As an analogy, imagine you had a wall which divided the universe into sides: one full of 10 happy people, and one full of 10 unhappy people.
You show an image of the happy side to Joe and offhandly mention the other people on the other side of the wall.
You show an image of the unhappy side to Joe and offhandly mention the other people on the other side of the wall.
You then ask Joe which is better, and he, being not so bright, says he prefers the happy universe you showed him. But both were the same universe! Joe just didn’t properly consider the other side of the wall.
Nice article.
Regarding the stated reasons to accept an actual infinite:
- I am not sure whether our best physics actually tells us that space is continuous, many QM researchers seem to think otherwise. But obviously I have no clue about QM, so there's probably no point discussing this
- Regarding the infinite future I basically agree with what Craig has said on this - roughly: There *are* no future events and for any time t in the future it will not be the case that at t there has been an infinite amount of events. So we have no counterexample.
Obviously you disagree that there are no future events, given that you lean towards B-theory, but if we have independent reasons to think infinities in conrete reality are impossible (as I think we do), then this seems to give us very good reason to reject any theory of time on which an infinite amount of events would be possible. So, if I were you, I would basically just Moorean shift this (If B-theory is right, then infinities may exist in concrete reality. But infinities can't exist in concrete reality. Therefore, B-theory is not right).
Thinking, instead, that the future HAS to be finite seems totally untenable to me - if I had to accept THAT, then I would just accept that infinities are possible. Surely we have more reason to think that the future can be infinite than to think that A-theory is false?!
The possibility of an infinite future only seems intuitive if A-Theory is true.
The problem is, a lot of the paradoxes arise once more if you accept the possibility of an infinite future. How should you value the pasadena game, for example? It seems like if you're willing to give up the possibility of actual infinite amounts of stuff, you should go all the way.
I also don't like the idea that you can't have an actual infinite. Seems like there are an actually infinite number of mathematical facts.
Finally, if I can't accept an infinite past or B-theory, I'll have to accept something in the vicinity of theism. But theism is obviously false :-P.
"The possibility of an infinite future only seems intuitive if A-Theory is true." - I disagree with that. Sure, I cannot literally *picture in my mind* what an infinite block universe would look like, but that seems irrelevant, I also can't picture a 1207-sided polygon.
I don't see at all why B-theory should make us think that there *has* to be a final moment in time (and tbh I'm not aware of any influential B-theorist who has ever defended the conditional "Necessarily, If B-theory is true, then the future is finite")
"Seems like there are an actually infinite number of mathematical facts." - I agree, but I specified that I am talking about concrete reality. That might seem ad hoc, but I don't think it is: all the good arguments against concrete infinities don't work with causally inert abstract objects imho
"Finally, if I can't accept an infinite past or B-theory, I'll have to accept something in the vicinity of theism. But theism is obviously false :-P."
I appreciate the honesty. I agree that if you think theism has an insanely low chance of being true and A-theory would imply that the Kalam succeeds, then this gives you good reason to accept the B-theory. But then again, imho if you have good reason to accept the B-theory, then you also have good reason to accept the possibility of infinities in concrete reality
To be more specific, if we're B-theorists then an infinite future being impossible is no weirder than an infinite space being impossible. And you have to believe that to avoid the paradoxes.
Even if I gave up B-theory and the possibility of an infinite past, I'd just accept that the universe began absent a cause. Doesn't seem to weird to me!
Again I don't agree that those are analogous. Imagine someone gets to the end of space and asks themselves "Why does space suddenly end here?", then "Because there is only a limited amount of matter in spacetime" seems like a perfectly good explanation (assuming relationalism about space, which is the most common view in the philosophy of space and time).
But now imagine that someone is at the last moment of time, would "This is the last moment of time because spacetime is limited in the later-than direction" really be a sensible explanation they could give? I don't think so. We would always ask the question how it could possibly be that the universe can *guarantee* that the future is finite, there needs to be some underlying mechanism that brings the end of the universe about (e.g. heat death). But that just seems like an incredibly strange mysterious force, similar to the mysterious force that would prevent you from killing your grandfather if time travel were possible. I don't see how the universe could possibly guarantee any such mechanism unless it's guided by reason.
Or do you think time just suddenly ends at some point, without any further reason whatsoever? Could it be that everything in the universe is perfectly harminous, yet from one minute to the next time suddenly ends, without any further explanation at all? That seems even more strange to me, then
I think there's probably some explanation of why time ends. I feel the force of the intuition, weakly, but it's not enough to overcome the ultmiate verdict. I think that a lot of puzzles--especially the pasadena one--reappear in the context of an infinite time.
Fair enough!
You mentioned this but all of these seem like a problem for math and the philosophy of math, not ethics. We shouldn't reject Heaven>Hell OR the possibility of infinity, just because we couldn't use finite concepts on infinite sets on our first try. It honestly surprises me that milking paradoxes from the paradox machine is a somewhat-active research field. They don't tell us anything new! We gotta think harder about the nature of infinity and mathematical operations instead.
Have you written about temporal discounting anywhere? While it’s not going to solve every problem in infinite ethics, it might help with some.
I don't think it solves anything and it is also very implausible. Say we have a 1% discount rate. This implies that Cleopatra getting a bit of welfare when she was alive is more important than saving the world today.