Thursday, January 30, 2014

Another model of hell worth thinking about?

Suppose that objectively, hell lasts forever. But while the first objective year of hell is experienced subjectively as a year long, the second objective year "goes by faster" as we say, and only takes half a year, the the third objective year "goes by even faster" and only takes a quarter of a year, and so on. Thus, while the damned will always exist and always be suffering, they will only experience two years' worth of suffering over that objectively eternal suffering.

Now the difficult question is whether this is an orthodox view of hell. When Jesus talks about the suffering being everlasting, is he talking of subjective or objective time? We certainly wouldn't find the analogous view of heaven satisfactory. But heaven and hell aren't exact parallels: in heaven one is with God, and the absence of God is not much of a parallel to God.

Now, without affirming the model, it can still be of some use in apologetics. For suppose a non-Christian objects that nobody deserves an everlasting hell. One answer is Anselm's: an infinite crime deserves infinite punishment and some crimes against an infinite being are infinite. But given the above model or the alternate model here, one can say that an everlasting hell could involve only a finite amount of suffering. So one can say: if someone is damned, then either she committed a crime that deserves infinite punishment or her total suffering is finite. Since both options are compatible with everlasting hell, in neither case does the objection to an everlasting hell go through. And one can give this disjunctive answer while strongly inclined to think that the Anselmian infinite crime model of hell is superior, as long as the alternate model is not a heresy (if it is, I will of course withdraw it).


Unknown said...

I really like the idea of this account, but I'm not sure if it solves the problem that people typically have with hell. I take the problem to be that hell seems unjust. A finite crime cannot deserve an infinite punishment. On your account, though, there is still an infinite punishment for a finite crime (Presumably, the point of your account is to show how this is possible. Otherwise, it doesn't really seem preferable to Anselm's. You seem to agree with this when you say that on your model "one can say that an everlasting hell could involve only a finite amount of suffering".) The difference on your model is that the infinite punishment is only objectively implemented, and not subjectively. But this doesn't seem to solve the question of justice. It still seems unjust to implement an objective infinite punishment for a finite crime.

This is especially clear if one accepts the distinction between internal and external harm. An external harm might be construed as one that does not involve subjective awareness on the part of the one harmed (e.g. as when a man's wife is cheating on him even though he isn't aware of this). An internal harm, on the other hand, is one that does involve subjective awareness (e.g. as when someone punches me in the stomach for no good reason while I'm fully conscious). This distinction seems analogous to your distinction between objective and subjective suffering/punishment.
Now, even if one accepts that internal harms are greater than external harms (e.g. it seems plausible to think that a husband who is aware of his wife cheating is harmed more than one who is not aware of it), it doesn't change the fact that they are both harms. Likewise, one might think that subjective punishment is more important than objective punishment, but it is still hard to see what could justify an infinite objective punishment for a finite crime.

Neil Bates said...
This comment has been removed by the author.
Neil Bates said...

Putting aside the theology, this idea of mapping finite to infinite time (or vice versa) is intrinsically fascinating. Note that we can e.g. do the opposite of your drawing out a subjectively finite time across eternity: compress infinity into a finite space via the transformation x' = x/sqrt(1 + x^2) etc. That compresses all reals into the interval between -1 and one. So imagine that is "time" in some other universe, and they go through eternity but we keep on going "after" that is over! It seems absurd but it's a valid mapping. Conversely, we could be the ones "mapped" into a finite stretch of someone else's time (and/or space.) Reality is relative.

The slowing of time for the hell-dweller is reminiscent of falling into a black hole - from outsider perspective it "takes forever" but the faller finds a finite time to hit the singularity. (Note - BH research is a bit unsettled now due to various controversies and challenges involving QM.)

You can also make extended number systems out of such practices.

Alexander R Pruss said...


That's a cool objection. I was thinking that only the suffering would be the punishment, but you may be right that there is an external harm here to be considered.

But I am not quite clear on what the external harm is. Is it the deprivation of proper human perceptual function as your functioning slows down year to year? The first year, you have normal human perceptual function, but the second you've lost half of your function (you notice half as much of time's passage), the third you've lost 3/4 of it, and so on. The total loss is infinite. But if you count loss like this, then that would mean that on annihilationism we should say that the punishment is infinite, too, because the person who is annihilated has been deprived of an infinite amount of future function. So annihilationism faces the same problem.

But not every deprivation is a harm. Only deprivation of a due good is a harm. The annihilationist might say that eternal life is not a due good for humans, and so while there is infinite deprivation as compared to the heavenly alternative, it's not an infinite loss. Maybe the person who defends the view I suggested could say that eternal non-decreasing perceptual function is not a due good for humans? So at least one could say that this account has no more trouble than annihilationism in this regard, and fits better with Scripture and Christian tradition.

Maybe one could also make the following case. The decrease in functioning due to the slowing down of subjective time may actually be a good thing to wicked person, as it ensures that she only commits a finite number of sins over eternity.

Alexander R Pruss said...


I've wondered: Would it be better to have an afterlife whose days are of order type omega+omega (i.e., like a second copy of the natural numbers following a copy of the natural numbers) rather than an afterlife whose days are of order type omega (i.e., like the natural numbers)?

But I think there is a serious problem with the omega+omega scenario, in that I am sceptical whether a single event can have an infinite causal chain (for Grim Reaper reasons). But the first event in the second omega would have an infinite causal chain (though not with a reverse of the usual order type for a causal chain).

Unknown said...

I'm not sure if that's the sort of external harm I had in mind. But I'm also not positive that I'm fully understanding your model. Let me suggest a case that seems to me to be parallel to it, and try to point to what I think the external harm would be.

Suppose that someone commits a series of terrible, but finite crimes. As punishment, the individual is placed in a cell where he will be unendingly beaten continually by someone (the punisher). The individual will also be hooked up to a machine that gradually slows down his cognitive faculties so that for the first objective year he will subjectively experience the beating as a year long, the second objective year he will subjectively experience it as half a year long, the third objective year he will subjectively experience it as a quarter of a year long, etc. So from his first-person subjective perspective, the punishment only lasts a finite amount of time. From the punisher's third-person objective perspective, however, the punishment is unending. Objectively, then, the punishment is infinite, even though the crimes were finite.

My intuitions tell me that the harm rests in the fact that he is being punished far more than he deserves for his wrong action. Even though he may subjectively perceive that he is receiving exactly how much punishment he deserves, he is in fact (from the third-person objective perspective) receiving an unjust amount of punishment. So the harm is not in some privation per se, as if he is missing something that ought to be there, but rather the harm is in the fact that something excessive has been added, namely, the additional objective punishment that goes beyond what he deserves.

Neil Bates said...

Alexander: your question does bring up a paradox. Instead of asking what do outsiders see if someone has their infinity compressed, let's imagine that the target of compression is not an ordinary human but a presumptively logically possible being. She has miraculous powers of "utter" immortality and unlimited memory for events.

She is subjected to time compression of the kind I noted, as well as having her history all recorded on an equally ideal continuous medium. (Not a "material world" here.) But after it "finishes" for us, she is still "there"! (ie, does not vanish into thin air.) We ask her, "what was it like?" She answers "well, it was an eternity! Yeah I was there through it all. Pick a date in my time, any date whatsoever, and I'll tell you about it." So I pick 10^10000 years etc and no matter what it is, she can come up with some event that I can in principle check with a super-microscope to examine the compressed record.

Everything matches up, but isn't it odd, that she can go through a subjective eternity and still have an "after" to experience being asked questions! I mean, imagine being her and waiting and waiting on and on ... and so the final debriefing should never happen! Is this a good paradox? I'm (we?) can write it up somewhere if it's original.

Walker: it seems to me that "punishment" is fundamentally about what the recipient experiences, altho others are also trying to show disapproval etc. So the punishment is effectively "finite" in these draw-out cases, despite what the punishers can see or define.

Alexander R Pruss said...

Pain is only as bad as you feel it. A pain that feels like it's only half an hour long is about half as bad as a pain that feels an hour long at the same intensity, even if they have objectively the same length.

I think that to make your case be like mine, imagine that the blows get slower and slower. So maybe in the first day there are 100 blows. In the second there are only 50. And so on. (Eventually, a blow might last two days.) And perceptions slow down, so that the slower blow feels subjectively just like the faster one would. Then there will only be a total of 200 blows. They will take eternity, but each blow contributes the same finite total amount of pain, no matter how long the blow takes.

Alexander R Pruss said...


It is quite weird, and fun to think about, but I don't know what exactly it shows.

And it seems like we can imagine being subjectively in her position after the first compressed infinity. You have infinitely many vivid apparent memories--whichever subjective year number you turn your memory to, you seem to vividly remember events then. You don't remember them all at once, but one at a time. No paradox, just a very strange epistemic position.

It seems to me that it would feel kind of like all those events happened to a stranger. One would feel infinitely distant--and subjectively one would be--from each of them.

Anonymous said...

Note: objections notwithstanding, couldn't we also add the apologetic note that people subjectively experience pain in hell to the degree to which they incur temporal punishment as distinguished from eternal punishment? Thus were Susie to be saved through purgatory, the suffering she would need to endure in purgatory corresponds to the amount of subjectively experienced pain in hell she would have experienced had she not been saved (mutatis mutandis).

Austin said...

Maybe I'm being nitpicky here (or perhaps wrong), but I don't know if your mathematics work out. Isn't the summation of the harmonic series divergent as opposed to converging to 2 ( This would mean that one would still subjectively experience an infinity in hell, right?

Either way, I'm sure we could pick some different model that actually does converge. It's an interesting idea to which I'll have to give more thought.

Unknown said...

Ah, now I think I understand. I was missing the point that both the subjective experience and the objective reality slow down. I think my objection would only work if only the subjective experience was slowed down while the objective reality remained "normal".

Alexander R Pruss said...


It's not a harmonic series. I say: The first year feels like a year; the second like a half; the third like a quarter; .... That's 1+1/2+1/4+..., i.e., powers of 1/2.

Phil said...

power series

Unknown said...

I don't see how <2 years can be experienced eternally or why you would assume the experience would "feel" twice as short each year, or why you would assume there is no 2nd death or that the wages of sin is not death or that one shall not perish without Christ.