The Paradox of Hell and Justice

The instinct of many contemporary thinkers, Christian as well as non-Christian, has been to see an antinomy between two commitments:

  1. That God is altogether unimpeachably just, and
  2. That God allows some people to suffer for an everlasting eternity in hell

The trouble is that, given the classical Christian doctrine of hell, there are some people (precisely, the set of all those persons who are damned) who will be suffering in hell for an infinite everlasting period of time. However, since every sin is merely finite, it seems that it can only deserve a finite punishment. How, therefore, could a just God punish a person infinitely for a finite crime or set of finite crimes?

Unorthodox answers are increasingly near at hand, and have become (ever) so popular of late that it is almost a challenge to find anyone defending the classical orthodox doctrine of hell – only a minority of contemporary Christian thinkers have boldly defended the doctrine. The trend, however, has been towards some form of either universalism or annihilationism. Origen’s universalism has been transfigured into modern forms such as John Hick’s soul making theodicy, which he mistakenly christened an ‘Irenaean Theodicy’ (I refer the interested reader to the work of a past professor of mine, Dr. Mark S. M. Scott). It has also been the drumbeat to which emergent church leaders such as Rob Bell have been dancing.

The typical Anselmian answer to the challenge has been to say that an infinite punishment befits a crime of infinite gravity, such as is obstinately rejecting fellowship with God. This answer has left many contemporary Christians unpersuaded and unsatisfied. For example, some Christian philosophers like Chad A. McIntosh have suggested that the Anselmian response commits an equivocation between quantitative and qualitative senses of ‘infinity.’ As a very interesting aside, McIntosh has suggested that he can manage to maintain that the damned do receive a qualitatively and quantitatively infinite punishment in hell, even while maintaining universalism. He appeals to the idea that God can perform supertasks, and thus that God can actualize an infinite number of transpiring torments within a finite amount of time.

A supertask, for those who haven’t heard of such things, is defined by Jon Pérez Laraudogoitia in the Stanford Encyclopedia of Philosophy.

A supertask may be defined as an infinite sequence of actions or operations carried out in a finite interval of time. The terms ‘action’ and ‘operation’ must not be understood in their usual sense, which involves a human agent. Human agency may be involved but it is not necessary. To show this, let us see how actions can be characterised precisely without any references to man. We will assume that at each instant of time the state of the world relevant to a specific action can be described by a set S of sentences. Now an action or operation applied to a state of the world results in a change in that state, that is, in the set S corresponding to it. Consequently, an arbitrary action a will be defined (Allis and Koetsier 1995) as a change in the state of the world by which the latter changes from state S before the change to state a(S) after it. This means that an action has a beginning and an end, but does not entail that there is a finite lapse of time between them.

I note in passing that this would make Hell and Purgatory indistinguishable from each other, which seems absurd. For a simple reductio of this admittedly ingenious and provocative thesis, perhaps we can give the following sort of argument:

  1. If God can perform supertasks, then there is a logically possible world in which the Grim Reaper paradox occurs.
  2. However, there is no logically possible world in which the Grim Reaper paradox occurs.
  3. Therefore, God cannot perform supertasks.

The question of whether it is coherent to posit supertasks at all, however, is really tangential for my purposes here. What I am interested in demonstrating is that it is logically possible for a Christian philosopher and/or theologian to maintain both of the theses expressed at the outset in orthodox fashion. Let us say that 1&2 (the original 1&2, not the premises of the argument looming directly above) can be maintained just in case they are compossibles, which is to say that there is at least one logically possible world in which they are both true. Strictly speaking, of course, there is no obvious logical contradiction between 1&2 above, thus in terms of narrow logical possibility, they are obviously compatible. However, narrow logical possibility also commits one to saying that the counter-possible “if God is unjust then Hell cannot exist,” is ‘true.’ This is unsatisfying in both cases; we want more, and we should get it.

I will put forward four responses to the problem and argue that if even a single one of them is possible and resolves the apparent tension of maintaining 1&2, then it is possible to maintain the classical doctrine of hell without calling into question the nature of God as paradigmatically just. First, of course, I cannot help but rehearse the Anselmian answer and maintain that a crime of qualitatively infinite gravity also deserves a punishment of infinite gravity. I can then maintain that a punishment of qualitatively infinite gravity requires a sentence which is quantitatively (at least potentially) infinite. For something to be potentially infinite means simply, in the all too familiar words of Dr. William Lane Craig, “that infinity acts as the limit towards which something endlessly approaches.”

This answer isn’t likely to mollify the objector to the classical doctrine though. Presumably they have heard it before, and find it wanting. So then, I rehearse a second answer generally appealed to by Molinists. According to the Molinist there are subjunctive counterfactuals of libertarian-free creaturely acts. The Molinist can thus suggest that, for all we know, the set of all people in the actual world who are or will be in hell includes all and only people who will libertarian-freely continue to sin infinitely many times in hell, so as to incur upon themselves punishment upon punishment in endless succession. Notice that this suggestion is not to be confused with the suggestion that people in hell inevitably sin continuously – if it were inevitable it wouldn’t be categorically free.

There is a third very interesting solution posed by Dr. William Lane Craig, and I will simply provide it in his own words, from his debate with Ray Bradley, Can a Loving God Send People to Hell?

Finally, it’s possible that God would permit the damned to leave hell and go to heaven but that they freely refuse to do so. It is possible that persons in hell grow only more implacable in their hatred of God as time goes on. Rather than repent and ask God for forgiveness, they continue to curse Him and reject Him. God thus has no choice but to leave them where they are. In such a case, the door to hell is locked, as John Paul Sartre said, from the inside. The damned thus choose eternal separation from God. So, again, so as long as any of these scenarios is even possible, it invalidates the objection that God’s perfect justice is incompatible with everlasting separation from God.

This third solution sounds to me like a clever way to repackage the second solution, and so I’m inclined to think that those who find the second solution unacceptable will also find this third solution unacceptable.

There may yet be another, and perhaps even more attractive, solution to this problem. I would like to direct readers to a recent suggestion of Alexander Pruss’ according to which we distinguish between the objective time span which the damned spend in Hell, and their subjective perception of that time span. This is worked out in his post Another Model of Hell Worth Thinking About?.

Recall that the trouble for the person who sneers at the Anselmian answer that a crime of infinite gravity must be met with a punishment of infinite gravity is that the eternal punishment may be ‘infinite,’ but incurring an infinite amount of temporal punishment for sin is simply impossible, and thus such a punishment is absolutely incompatible with justice. Thus, the intuition seems to be that the temporal punishment for sin doesn’t fit the temporal crime. In light of this, Pruss’ model seems particularly attractive. According to this model, there is a distinction between objective and subjective lengths of time (for instance, just as when I experience a certain hour of the day whizzing by, somebody else may experience the same hour of the day as dragging on), and we can at least imagine that a person in hell may experience their first year in hell as having lasted about a year, and their second year in hell may subjectively feel like half a year, their third year may then subjectively feel like a quarter of a year, and so on, so that in principle a person could be in Hell for any amount of time objectively, and they would have subjectively experienced temporal pains only up to a certain much lower finite boundary towards which they are endlessly approaching. It acts as a finite boundary condition which is never subjectively arrived at, but is only ever and always approached.

One neat theological feature of this model, it seems to me, is the way it ties in nicely with the Catholic Church’s teaching about purgatory, or at least common opinion about purgatory. In his book Eschatology our emeritus pope, Benedict XVI, suggested that time in purgatory is perhaps best characterized as a kind of ‘existential’ time.

The transforming “moment” of this encounter cannot be quantified by the measurements of earthly time. It is, indeed, not eternal but a transition, and yet trying to qualify it as of “short” or “long” duration on the basis of temporal measurements derived from physics would be naïve and unproductive. The “temporal measure” of this encounter lies in the unsoundable depths of existence, in a passing-over where we are burned ere we are transformed. To measure such Existenzzeit, such an “existential time,” in terms of the time of this world would be to ignore the specificity of the human spirit in its simultaneous relationship with, and differentiation from, the world.[1]

The best way to make sense of Medieval talk of ‘time’ in purgatory is not to imagine that people in purgatory spend a literal set of days or hours there, but that they spend some existential equivalent to how much time it would have taken them to offer full reparation for their sins. Suppose, as a thought experiment, that there are two nearly identical logically possible worlds in which Tommy is on his death bed. Let’s imagine that in world W, Tommy rejects the Grace of God resolutely in his final moments, and let’s imagine that in W’, Tommy’ accepts the Grace of God. In world W’ we may say that Tommy’ will existentially experience 300 years of purgation. Why not think that in world W, Tommy will ‘existentially’ experience no more than 300 years of damnation, even though this latter is an eternal state (a state never to be succeeded)?

Moreover, to take another page from William Lane Craig, since there is no way for finite addition to result in an actually infinite sum, it seems to be a necessary truth that a person who experiences hell will only ever have experienced a finite amount of the pains and torments associated with hell. Their torment will always be, considered subjectively, merely potentially infinite, and never actually infinite. No person, therefore, can undergo an actually infinite number of subjective or existential ‘moments’ in the agony of dis-fellowship with God. Why not think, in addition, that there is some finite subjective or existential boundary condition to their suffering?

If we can so think, then we can so respond to the objector, and this response seems to hold a greater promise of satisfaction.


[1] Ratzinger, Joseph. “Eschatology: Death and Eternal Life, trans.” Michael Waldstein (Washington, DC: Catholic University of America Press, 1988): 230.

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4 thoughts on “The Paradox of Hell and Justice

  1. Pingback: Apologetics and Hell: A Possible Problem With the A-theory | Tyler Journeaux

  2. If you take the limit of the function “torment(objective time)”, it must asymptotically approach zero. No matter what the derivative of the function is, it must always trend negative. At some point, inevitably, the finite punishment (slope) will be reduced to insignificant amounts. Is such torment even meaningful? Let’s say Mao killed 50 million people and each life is worth 100 years. Under the eye-for-an-eye principle he is on the hook for 5 billion years of punishment. In eternity, that’s not a lot. In order to drag out the punishment over eternity, inevitably the slope of the curve will be so flat as to be nearly meaningless from a metaphysical standpoint. What does it mean for Mao to experience a subjective 5 nanoseconds of punishment in an objective year? You will get to the absurd case where Mao has served 4,999,999,999.9999 years of his punishment and just needs another eternity to finish that hour of punishment remaining.

    If the slope of the curve is too steep, the amount of punishment per objective time unit becomes so insignificant as to be nearly meaningless: It’s just delaying the punishment artificially, which is not just. If it is not steep enough, the punishment is paid off too quickly, leading to the absurd case of Mao. In eternity neither extreme can be avoided for long. The problem of whether or not it ever completes is beside the point: We can all agree that Mao essentially all-but paid off his debt by that point, whether it can complete or not. The additional punishment just ceases to be meaningful after a relatively short period of time.

    A few observations: First, the ‘time whizzes by’ analogy describes being distracted by other things and not noticing the passage of time. If that were the case then hell wouldn’t be so bad if you could postpone your punishment for another day while you pursue other things. Second, I don’t think that a comparison to purgatory is helpful either unless you are saying a stay in purgatory can be infinite. Third, there are two problems (not one) with a punishment that never completes in actuality: (1) Justice is not done because the debt is never paid; (2) Depriving someone a finite opportunity to pay the penalty for their finite debts effectively punishes the debt payer for not paying off the debt while they are paying it. Fourth, if the debt holder’s (e.g. one of the persons Mao killed) subjective time sense is faster than the debtor’s, it will appear to them that the debtor is not working towards paying off that debt. This is unjust. Fifth, mathematically speaking no matter what the finite debt, eventually all debtors will converge on the same amount of debt remaining. Thus all debts will eventually be treated equally, regardless of their original crime.

    Perhaps B-theory resolves some of these objections, but I’m not studied enough to make that judgment.

    • Thank you for your comments,

      These are some very interesting reactions you’ve provided, so I’d like to respond to them carefully and somewhat systematically.

      You write: “If you take the limit of the function “torment (objective time)”, it must asymptotically approach zero. No matter what the derivative of the function is, it must always trend negative. At some point, inevitably, the finite punishment (slope) will be reduced to insignificant amounts. Is such torment even meaningful?” I think it is, yes. Remember that, experientially speaking, the person in torment cannot tell the difference between their sentence being drawn out for longer periods of time, and their sentence not being drawn out. So experientially they are in a constant state. It seems unproblematic that objectively they are experiencing time pass extremely slowly relative to observers in heaven.

      “First, the ‘time whizzes by’ analogy describes being distracted by other things and not noticing the passage of time. If that were the case then hell wouldn’t be so bad if you could postpone your punishment for another day while you pursue other things.” The analogy has its limits; obviously I don’t mean that the perception of time’s slow crawl is the result of distractions in hell.

      “Second, I don’t think that a comparison to purgatory is helpful either unless you are saying a stay in purgatory can be infinite.” Purgatory cannot be infinite, of course, and so this is another respect in which analogies aren’t perfect, but I do fail to see how this disanalogy relevantly undercuts anything for which I have argued. Purgatory still insinuates a difference between the subjective experience of periods of time and the actual passage of time (read that without A-theoretic insinuations). At least it insinuates that there are experiences best expressed as ‘experientially taking up X amount of time’ which do not take up X amount of time. It also provides a sense of proportionality of temporal punishment which, it seems, should plausibly apply to the denizens of hell as well. Those are the respects in which I felt the analogy was relevant.
      You raise the concern, at one point, that one problem with the view I’ve proposed is that “Justice is not done because the debt is never paid.” Although it is true that at no time is the debt paid, if we are B-theorists of time this is not a problem because in objective fact the debt is paid in full, for the infinitely many times at which the debt is paid leave no debt left over to be paid, and each time is actual.

      “Depriving someone a finite opportunity to pay the penalty for their finite debts effectively punishes the debt payer for not paying off the debt while they are paying it.” So, Catholics typically distinguish between the temporal punishment for sin and the eternal punishment for sin. The eternal punishment is everlasting and categorical (i.e., eternal separation from communion with God), while the temporal punishment for sin is proportional to the moral crime of particular sins. What I’m proposing is that one can satisfy both on the model I’m recommending. If there were no legitimate distinction between temporal and eternal punishments for sin, then I might be inclined to agree with you… Though, to be honest, even there I find myself largely unmoved by this objection, for I cannot see that God would be at moral fault for punishing somebody everlastingly for a finite crime so long as the punishment befit the crime (which, in this case, it would).

      “The problem of whether or not it ever completes is beside the point: We can all agree that Mao essentially all-but paid off his debt by that point, whether it can complete or not. The additional punishment just ceases to be meaningful after a relatively short period of time.” So, it’s important to note that there is literally no ‘additional punishment’ here, nor is there any time at which Mao has only an infinitesimal amount of punishment left to satisfy.

      “If the debt holder’s (e.g. one of the persons Mao killed) subjective time sense is faster than the debtor’s, it will appear to them that the debtor is not working towards paying off that debt. This is unjust.” To my mind justice does not rely on the mollification of the victim of a wrong. Nevermind that if the victim is in heaven they may be assuaged regardless, it just doesn’t seem relevant (to me) whether the victim of a crime feels satisfied with the appropriate punishment.

      “Fifth, mathematically speaking no matter what the finite debt, eventually all debtors will converge on the same amount of debt remaining. Thus all debts will eventually be treated equally, regardless of their original crime.” Well, it doesn’t follow merely from convergence that they would at any time be treated equally, strictly speaking, but even if they were treated equally at some time or set of times, I don’t see that as a particularly powerful objection. It seems to me that it would do nothing to change the fact that justice is being dolled out correctly. If one person is in prison for 20 years for sexual assault, but another is in prison for 5 years for larceny, it may be true that they are both in prison under the same conditions at some time (for instance, if the person who committed sexual assault has 5 years left on her sentence the day her fellow felon begins her sentence for larceny, and we imagine that they are similarly situated in a myriad of other ways, it may begin to look like at some time they are living under the same conditions) – but so what? I don’t think anything interesting follows from that.

      These objections of yours are intriguing to me. If you don’t mind my inquiring, I’d like to ask what view you hold of the doctrine of hell[?].

      • “If you don’t mind my inquiring, I’d like to ask what view you hold of the doctrine of hell[?]”

        I don’t mind at all. I was raised Anabaptist, son of an Anabaptist minister. I don’t hold allegiance to any denomination or set of official doctrines. Mainstream denominations would label me a heretic, although I don’t know if God would. So there is that. I don’t fit into a traditional box, though I hold many traditional views. I’m concerned with truth seeing above all else. If you are curious about anything in particular, ask any time.

        So about hell. I object to the implied injustice of God allows some people to suffer for an everlasting eternity in hell and don’t find reasons 1 through 3 compelling, though much more could be said about them. I think rejecting A-theory and modifying the doctrine of hell (as you’ve done here) is required to make it palatable, however, the proposal is far from critically tested. It needs to be abused for a while, see if it holds up.

        Am I an annihilationist? Tentatively. It might be more accurate to say I have great reservations about the traditional doctrine. It makes the most sense (less contrived / less reliant on dogmatic claims) and despite your excellent defense of the alternative, I remain unconvinced. I’ll hold the annihilationist view for as long as it remains logical to do so. I don’t know where this will lead.

        The reality of hell is not predicated on my acceptance. I might be wrong but it wouldn’t change my faith either way. It does affect how I interact with others. This proposal may be a tool that I can use with unbelievers.

        The eternal punishment is everlasting and categorical….the temporal punishment for sin is proportional to the moral crime of particular sins

        The annihilationist says that the punishment is categorical and everlasting and cites scripture to show this. They also cite scripture to show that there is finite temporal punishment. Are you not, therefore, by even considering this viewpoint tacitly allowing the annihilationist interpretation of scripture? If so, then we are back at the stalemate decided by dogma and many of the points below are not as interesting.

        So, it’s important to note that there is literally no ‘additional punishment’ here, nor is there any time at which Mao has only an infinitesimal amount of punishment left to satisfy

        Please replace ‘additional’ with ‘remaining’ in my original comment. My mistake.

        I’m not convinced by your answer, but I need to know more. Now either you (1) don’t know what infinitesimal means; (2) you are suggesting that the eternal punishment isn’t really eternal, that is, there really is no such thing as the infinite, only the finite; or (3) you believe unequivocally that no non-zero quantity, no matter how small, of punishment can lack practical meaning. (or some combination of these things)

        There is something more fundamental here than just the subtle objection of ‘justice is never actually done’. What is the point of “The Lord Almighty will take vengeance on them….they shall weep in pain forever.”? If this isn’t either the traditional second commitment you referenced or hyperbole, then what is the purpose: what does it serve God to declare weeping in pain forever? Eternality of punishment, with a goal of finite degree, does not serve a meaningful explanatory purpose and is incompatible with the love, justice, and goodness of God. It replaces one strong moral objection (that God is cruel and unjust) with another somewhat weaker one (that he is petty).

        In the perspective of the damned the result is the same; it is the threat that is petty. If the actual degree of punishment is finite, why then did God state the eternality of pain, instead of just declaring annihilation? Or put another way, why not make the statement as finite as the degree of punishment? You can’t say it is because he wanted to emphasize the finality, because that’s just the annihilationist argument.

        justice does not rely on the mollification of the victim of a wrong. Nevermind that if the victim is in heaven they may be assuaged regardless, it just doesn’t seem relevant (to me) whether the victim of a crime feels satisfied with the appropriate punishment.

        If the victim is assuaged, shouldn’t that necessitate forgiveness of the debt? So, God eternally punishes to satisfy the need for vengeance, but nobody in heaven actually cares about vengeance? Also, are there not two victims, the person victimized, and God himself?

        “Is such torment even meaningful?” … It seems unproblematic that objectively they are experiencing time pass extremely slowly relative to observers in heaven.

        With the above in mind, if the residents of heaven don’t care and the person in torment does not notice, why is eternality meaningful? Or in terms of my original point, is the minuscule amount of remaining objective debt meaningful to (any?) observers. You can say “because God likes it that way” or “the Catholic Church said that’s how it is” or “not even God can’t terminate existence”, but these are…difficult. How else do I say this? Why would God make such a big deal about it in his scriptures if ‘at the end of the day’ it just appears arbitrary?

        I find myself largely unmoved by this objection, for I cannot see that God would be at moral fault for punishing somebody everlastingly for a finite crime so long as the punishment befit the crime (which, in this case, it would).

        You’ve nailed a fundamental issue. I might agree if the only consideration was punishment and punishing. Consider the fundamental nature of free will and existence: do we have a right to not exist or a right to unlimited existence? Those going to hell know, and are tormented by the fact, that the punishment is separation from God and an eternity of limited, but permanent existence. This is similar to, but lesser than, the moral objection against the traditional view: that punishment is separation from God and an eternity of unlimited, permanent existence.

        …even if they were treated equally at some time or set of times, I don’t see that as a particularly powerful objection….If one person is in prison for 20 years for sexual assault, but another is in prison for 5 years for larceny, it may be true that they are both in prison under the same conditions at some time…I don’t think anything interesting follows from that.

        Powerful? Perhaps not. I’m just critiquing the proposal and I might be making mistakes. The analogy highlights my objection. Unlike the real life situation, all eternal sentences begin at the same time, approach the same end, and converge on the same amount of time remaining until the difference between each is infinitesimal (all in terms of objective time).

        Let’s say we have observer G in non-subjective infinite objective time (“real time”). If G examines the amount of debt remaining for two subjective participants D and S, G will notice that the difference is infinitesimally small relative to the time left to complete it. So: (sentence(D) – sentence(S)) / ∞= 0 (or undefined). It is a meaningless distinction to make, just like the amount of time remaining for the individual: sentence(D) / ∞= 0 (or undefined).

        Next G says to his servant A, “write down the percentage of time served by D”, so A writes “0.99999999999….”, which is equal to 1. Therefore D’s time has been completely served, and yet time is not completed (and it’s meaningless to even suggest completing infinite time). Under B-theory all times are actual. You can’t avoid the paradoxes of infinity by having a separate subjective domain. What you’ve basically done is try to stretch the finite over top of the infinite, which mathematically-speaking, obligates you to accept these conditions.

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