Monday, May 7, 2018

Heaven and materialism: The return of the swollen head problem

Plausibly, there is a maximum information density for human brains. This means that if internal mental states supervene on the information content of brains and there is infinite eternal life, then either:

  1. Our head grows without bound to accommodate a larger and larger brain, or

  2. Our brain remains bounded in size and either (a) eventually we settle down to a single unchanging internal mental state (including experiential state) which we maintain for eternity, or (b) we eternally move between a finite number of different internal mental states (including experiential states).

For if a brain remains bounded in size, there are only finitely many information states it can have, because of the maximum information density. Neither of options 2a and 2b is satisfactory, because mental (intellectual, emotional and volitive) growth is important to human flourishing, and a single unchanging internal mental state or eternal repetition does not fit with human flourishing.

Note, too, that on both options 2a and 2b, a human being in heaven will eventually be ignorant of how long she’s been there. On option 2b, she will eventually also be ignorant of whether it is the first time, the second time, or the billionth that she is experiencing a particular internal mental state. (I am distinguishing “internal mental states” from broad mental states that may have externalist semantics.) This, too, does not fit with the image of eternal flourishing.

This is, of course, a serious problem for the Christian materialist. I assume they won’t want to embrace the growing head option 1. Probably the best bet will be to say that in the afterlife, our physics and biology changes in such a way as to remove the information density limits from the brain. It is not clear, however, that we would still count as human beings after such a radical change in how our brains function.

The above is also a problem for any materialist or supervenientist who becomes convinced—as I think we all should be—that our full flourishing requires eternal life. For the flourishing of an entity cannot involve something that is contrary to the nature of a being of that sort. But if 2a and 2b are not compatible with our flourishing, and if 1 is contrary to our nature, then our flourishing would seem to involve something contrary to our human nature.

This is a variant of the argument here, but focused on mental states rather than on memory.


 James A. Gibson said...

Hi Alex. When you first presented this argument last year, I didn't feel the force of it. Now I do. But I think you will need to say more to make 2b unsatisfactory. So for example, you say that 2b (at least) is unsatisfactory because mental growth is important to human flourishing, and eternal repetition does not fit with flourishing. But in heaven, it is not obvious to me that the sort of changes that will occur in one's mental states (swapping some mental states for others) will undermine flourishing. I suppose that you think it would undermine flourishing because you think flourishing includes something like becoming better in some way, that it requires getting more and more mental states. I am not certain you think that though. But if you do, how would you motivate that? Heaven is supposed to have morally perfect persons; granted that does not imply static moral characters who do not grow in other ways. But in so far as heaven is thought of as a kind of ideal, one might doubt that the changes that occur need to be permanent, since the stuff that matters for being in heaven (moral perfection) remains. Let me suggest another way to run the argument against 2b. Consider your second objection to 2b that requires a human being to become ignorant of how long she's been there. I'll grant you that that belief, if true, has value, because truth has value. But if that belief is swapped out with another mental state, e.g., something about, say, how God's love for her is manifested in some significant experience, then on balance I see no problem with her losing her belief about how long she has been there. Now the problem with 2b becomes this: someone in heaven will eventually have enough such experiences that either one will run out of, say, "lower value" beliefs to replace, or one will have to replace beliefs that are of equal or greater value. And it is a bad thing for those of equal value, which may be crucial to one's flourishing from that time onward, to be replaced. So I think you can get this argument against 2b going for someone like me who initially thinks 2b isn't so bad.

Brian Cutter said...

A variant on (1) that doesn't require an ever-growing head is for our (ordinary 3-pound, meat-based) brains to become informationally integrated with an *external* computer of some kind, which can carry out an increasingly large share of our mental processing without creating strain on our necks. On this view, it's natural to think that our heavenly *minds* are part biological, part non-biological, with only the non-biological part getting bigger over time. This view *might* be incompatible with animalism (or at least the view that we are essentially animals), but it's probably compatible with materialism.

Alexander R Pruss said...


Yes, I am thinking that flourishing involves coming to better and better understand, or coming to feel new things, or improving morally, etc. Imagine that for eternity the person is cycling between just three conscious states: A, B and C. That just seems unsatisfactory. But it seems that *any* finite number is in the end also unsatisfactory. Eventually on 2b it will be correct for the person to say: "All that I will ever experience I have already experienced." This just doesn't seem like full human flourishing.

As for not knowing how long one's been in heaven, it's not just that ignorance is bad. It seems to be an important part of human life to have some sort of an estimate of how long that life has been going on. But eventually on 2b, that estimate has to take the form "more than N", for some large N. And that's a very poor estimate, once we've gone many orders of magnitude beyond N.


That's a very clever move. One worry I have is whether this is *human* flourishing, especially once the non-biological part of the constitution of the conscious states is many orders of magnitude greater than the biological part.

Also, as one of our grad students pointed out to me in regard to my earlier post, there is an issue with the speed of light limit.

It is intuitively difficult to see how one could have the unity of consciousness in a conscious state largely constituted by physical stuff that's light-years away. But maybe that is just the old problem of unity of consciousness for materialists, and it makes little difference whether the signals take years or nanoseconds?

 James A. Gibson said...

Thanks, Alex. Two things about that.

(1) What I tried to suggest is that you could run your argument without making claims, e.g., "It ... is an important part of human life to have some sort of an estimate of how long that life has been going on," a substantial part of your premises. It doesn't seem as important to me as it does to you. The good thing for your argument is that you don't have to settle that dispute with me, i mean, for the purposes of getting someone like me on board. I agree that there is some limited amount of space for beliefs to take up given materialism. (The move like Brian makes won't work, for even if there were a heavenly "cloud" (i.e. AWS, Azure) system, it would eventually require God to make "packets" of information stream at an instant across space, and that looks like a miracle (apologies to Pied Piper)... too many miracles. I considered the option that God increases the amount of absolute space we all take up in heaven but we all will fail to notice because the increases to us and the rest of creation are relatively proportional. That has the same problem as a divine cloud system.) But I also agree that human flourishing in heaven does involve growing in some way, e.g., increasing in our understanding of God, and that understanding will play a functional role in our distant future behavior. So at some point, too many significant beliefs will have to be swapped out. Notice that you don't have to say anything substantial about *which* beliefs are the important or valuable ones. You just need your audience to agree that the number of important beliefs will keep increasing and the head can store only so many, or one can function only so well given a head + external system.

(2) In your first paragraph, you say that "But it seems that *any* finite number is in the end also unsatisfactory." I would be worried about putting it that way. In the literature about whether heaven would be a good thing or not (I'm thinking of literature involving Bernard WIllams, John Fischer), you will sometimes see the claim that there is only a finite number of experiences. "Oh another sunset. Another glass of wine. Another thing to understand about God. How boring now. All that I will ever experience I have already experienced; just slight variations." I think that the argument you want to run about Christian materialism should not result in you having to take on substantial claims about this literature as well. The less commitments you have to taken on, the better.

Brian Cutter said...

Yeah, I was worried about the speed-of-light problems. Maybe a better thing for the materialist to say is that our union with God in heaven is such that the Divine Mind plays for us a role analogous to that of the external hard-drive/memory-store in my original proposal. (van Inwagen suggests something a bit similar about our prelapsarian union with God, e.g., his claim that union with God came with certain epistemic benefits that would help us avoid natural dangers.) There's a worry about losing individuality on this proposal, but maybe the worry isn't too troubling if we distinguish between stored memories (the non-conscious periphery of the mind) and the conscious core of our minds (which would still be in our biological brains).

Alexander R Pruss said...


Adding an infinite non-conscious storage to a mind that can only ever gain conscious access to a finite number of items to the storage (a total of a finite number of items; not just a finite number of items at a time) doesn't seem to me to help.

In fact, we can't even say that the items in the infinite storage are potentially accessible, for only a finite subset of the infinite set of items can be consciously synchronously experienced by a brain of bounded size.

Brian Cutter said...

My initial thought was that the brain might have access to each of an infinitely large number of items, even if it doesn't have access to any finite collection of items from the infinite memory storage (in just the way that my hand might have, for each marble m in an infinite collection of marbles, the potential to hold m, even if it doesn't have this potential with respect to all finite groups of marbles from the infinite collection). But on reflection, I guess that wouldn't work, because there's a crucial disanalogy between information and marbles. If a brain has finitely many (informationally distinct) possible states, then that puts a finite upper bound on the number of items it can have the potential to (individually) encode. Okay, I guess I'm convinced there's a real problem here for the Christian materialist, and probably the only way to solve it is to say that heavenly physics is very different from the physics of the present world (which comes with the problems you mention).

I think there might be an independent worry with the "different physics" move for the Christian materialist though. A materiaist like van Inwagen wants to say that our persistence into the afterlife requires physical continuity between our current bodies and our resurrection bodies. But it's not obvious that there could be physical continuity between my body as it is now and any body whose parts are governed by totally different physical laws. (Maybe you could keep the same particles, but radically change their causal powers all of a sudden, or gradually, or something like that. But that's hard to maintain if you think that the basic causal powers of, e.g., electrons are essential to them.)

Alexander R Pruss said...


I like your observation about problems with changes in physics being a problem for identity, though I think most materialists tend to have memory theories of identity.

I still think that the computer solution might work. In light of the considerations here, the computer would have to expand consciousness rather than just provide auxiliary storage. In other words, one would end up being a genuine human-machine hybrid rather than just a human with a large electronic assistant. It seems a bit unclear whether this would count as *human* fulfillment, though. It would be interesting if heaven ended up being a version of the singularity for Christian materialists. I suspect most Christian materialists would not be happy with the solution.

The speed of light limit is a problem, but I am still not convinced it's more of a problem than it already is for our brains. The problem is that we want to be able to constitute synchronic conscious states, but it's hard to do that out of ingredients that are light years apart. But the difference between light years and light picoseconds is merely quantitative. And the materialist has to say that the problem of components that are hundreds of light picoseconds apart is solvable, or else we don't have synchronic conscious states, which we plainly do.

Moreover, I think the problem presupposes the claim that a synchronic conscious state needs to be constituted by a synchronic physical state. But the materialist can, I think, deny that. Conscious states occur within "subjective time", and subjective time can come apart from objective time. A materialist is likely to think a computer could be conscious, but if we take a conscious computer and run its software at a different rate. Presumably, a computer whose size is light-years in diameter can do things in years that a brain whose components are hundreds of light picoseconds apart can do in hundreds of picoseconds. So it might be that eventually to have a conscious state that takes a second of subjective time might require 10^100 years of processing time. But given eternity, this isn't a problem.

There is, however, another human fulfillment issue. Embodiment matters. But if our mental processing is on the 10^100 year scale, that just doesn't fit well with the flourishing of our bodies. It seems that it is a part of human health that the mind can keep up with the body. Maybe this can solved by having what electronic engineers call different clock domains: maybe there would be a very slow 10^100 year scale conscious core (and getting slower all the time) that would be providing new conscious states very slowly, and a faster millisecond scale conscious core in charge of the body. I think this would make for a rather disunited human being, but it is the best I can think of.

There might also be some bandwidth and energy issues for computers of that physical size. Sending a signal over 10^100 light-years (handy that the universe can expand, isn't it?) is going to involve a lot of signal degradation.

How about this move? Maybe there just are constant miracles. So there are more and more computational modules, farther and father apart, and God miraculously and nearly instantaneously (with respect to some fixed reference frame) links them. There isn't any conceptual problem with faster than light communication (at least if it all happens past-to-future with respect to one fixed reference frame, so you can't generate causal loops). So God could miraculously arrange it. And since presumably most of what we would be thinking about would be God, it's not unfitting that there be constant miracles involved (after all, the traditional view of the beatific vision involves a miracle).

I still can't get away, though, from the idea that this isn't *human* fulfillment. Maybe the paper could be entitled: "Endless repetition, swollen heads or a miraculous singularity: A trilemma for Christian materialists".

Alexander R Pruss said...

By the way, another place head-swelling or miracles are needed is the avoiding of quantum glitches. Given infinite time, it's almost certain that at some point a fixed-size brain will quantum tunnel into a bunch of butterflies. I can think of two solutions:
1. God miraculously prevents this.
2. Redundancy in the brain increases as time goes on sufficiently quickly to make the probability of quantum glitch damage be small even over an infinite time. Such increase of redundancy requires head-swelling (or large computer-based backup systems).

This is something Christian dualists face as well. But perhaps supposing miracles in the brain is less troubling to dualists.

Brian Cutter said...

Interesting points. I think the worry about the mind getting increasingly out of step with the body is basically fatal for the giant-consciousness-supporting-external-computer model (w/o superluminal signals).

It seems like pretty much all the serious options for the Christian materialist fall into two camps: (i) infinite repetition (let's understand the single-unchanging-mental-state model as a limiting case of infinite repetition), and (ii) Novel physics. Under (ii) we would have various specific models, including: (ii-a) Our mental lives are housed inside normal-sized heads, but novel physics allows our brains to have indefinitely many informationally distinct states. (ii-b) Our mental lives (including our conscious lives) are supported in part by an external computer, which stays in step with the body by way of superluminal signals (you could describe this as "constant miracles," but if the miracles are regular enough, it starts to just sound like novel physics). (ii-c) Our mental lives stay within our heads, but our heads get increasingly large. This probably shouldn't be called a "serious" option, but in any case, it would also require novel physics. For instance, it will eventually require superluminal signals for the same reason as (ii-b) (in order to keep the mind in step with the body), and will almost certainly require other changes in physics, e.g. to prevent the head from collapsing under its own gravity, and to prevent the head from crushing the rest of the body.

The problems for type-(i) models (i.e. infinite-repetition models) are pretty clear, I think. As for type-(ii) models, these are only problematic to the extent that being largely or wholly constituted by matter governed by novel physics is incompatible with properly *human* flourishing (or with being human being at all). There seems to be something to this idea, but then again, even a dualist might have reasons for accepting a novel-physics picture. In particular, it seems like the social/interpersonal dimension of human flourishing requires that we have a body whose states can adequately express or communicate the contents of our minds. So, if our bodies have a finite and fixed number of informationally distinct states while our minds get increasingly capacious, then eventually our bodies will be woefully expressively inadequate vis-a-vis our minds. This seems like a weirdly disunified state of being---sort of like if you kept your present mental capacities but your behavioral abilities were limited to wiggling your pinky---and one where our bodies start to seem like pointless appendages. (A novel-physics picture is also arguably suggested by the new testament, e.g. 1 Cor 15.)

Alexander R Pruss said...


Your worry for the dualist is really interesting, but there are infinitely many things that are sayable or writeable by a human being. So even without novel physics, there need be no repetition of what a human being says. Of course, this could mean that the discourses get longer without bound. But that's not so crazy, if our mental faculties are sufficiently sophisticated. (This would require a pretty strong dualism, though, in that the processing of the long discourses would need to go beyond the information capacity of the brain.)

Another issue--inspired by Kierkegaard's discussion of repetition--is that one can have the same physical states with meaningfully deeper mental states. Suppose Mary really loves the Mass. She attends Mass every Sunday, always with the same priest. Suppose the priest re-runs the homilies and hymnody in sync with the re-run of the Mass readings. Mary always kneels and sings in the same way. But each time the three year cycle of Mass readings comes around, she understands the readings more deeply. Her gestures and words come to mean more. Her first "Amen" on Pentacost at age 73 sounds relevantly just like at age 24, but there is much more meaning in it, as it is suffused with memories of the 15 "Amens" in between, and her greater depth of reflection.

And we can imagine this communally. As people grow in deeper experience, the same words can come to have deeper shared meaning for them. We can imagine greeting the same person every day in heaven and exchanging the same simple "Jesus Christ be praised" greeting and "For ever and ever, Amen" response, but the words coming to mean more and more every day, with deeper and deeper shared meaning. In fact, even without changes in meaning per se, there is a difference in perlocutionary force in a greeting when one says it the first time to one's beloved, when one says it the tenth time, and when one says it the thousandth time, simply from the fact that these are the first, tenth and thousandth times, respectively, as long as one has some sort of a vague recollection of how many times one has said it.

Think of how spirituality is tied to physical routine in monasticism. The physical activities are similar from day to day, and even more similar from year to year. And they are very important. But the spiritual life nourished by the physical routine is, hopefully, growing in riches.