Gödel and the Soul

For reasons that I’ll explain in a future post, I have realized that I left a major loose end hanging in my “Legends of the Fall” series.  I was planning out a post in my mind, and it occurred to me that at least one of the issues I need to deal with in order to write that post is long enough to deserve a post of its own.

C. S. Lewis, in Mere Christianity, I think, said that he came to believe in God before he came to a belief in the afterlife.  The latter came a few months later.  He does emphasize that this experience was his, and not necessarily universal.  For most of my life that I’ve been old enough to think about it, I’ve believed in both.  However, as I’ve become older and thought about it, I’d  have to say that while I still believe both, the belief in an afterlife–or more narrowly, the belief in a human soul–is more fundamental to me.  That is to say, losing belief in God would not affect my belief in an immaterial human soul.

The reason for this is direct experience, but it will need a little unpacking.  First, recall that the soul is truly immaterial.  That means it is not matter, nor even energy.  Star Trek style beings of “pure energy” are not equivalent to souls.  Energy, after all, following Einstein’s equation E=mc2, is interchangeable with matter.  The soul can’t be matter, so it can’t be energy, either.  For us, it is associated with our bodies, but of a different nature from them.

This puts us in a bit of a bind.  Everything we perceive through our senses–touch, sight, smell, hearing, proprioception, etc.–is intertwined with our bodies and the material cosmos.  Though there has never yet been a materialist account of the mind (and in my opinion never will be), it is still clear that the soul depends on the physical body and material brain for most of its functioning most of the time.  Were that not so, we’d never sleep, get drunk, feel dizzy, etc.  Furthermore, there are clear connections that can be observed between electrical activity in the brain and what a person is thinking or experiencing.  Thus, one might be challenged to present evidence that requires us to assume an immaterial soul.  The materialist, in short, might contend that even though we don’t yet have a full, materialist account of the mind–and even if we never have one–that’s not sufficient to make us assume a soul.  After all, what about our minds could not be explained, at least in principle, by natural forces, matter, and energy?

2 + 2 = 4, that’s what.

My background is in mathematics, and I’ve taught math most of my professional life.  I don’t claim to be a particularly outstanding mathematician–certainly not in a league with the greats–but I do have some small insight that I think is relevant here.

I believe I’ve discussed this before, in fact, but it bears repeating.  My most vivid recollections of doing math involve proofs.  Now, there are some proofs that are rather mundane, rather like skipping from stepping stone to stepping stone across a brook:  Step 1 leads to Step 2 leads to Step 3, and so on, until you have the proof, Q.E.D., end of story.  Remembering a proof that you’ve not had to do in a long time isn’t too interesting, either.  For example, unless I happen to be teaching trig, the proofs for the Law of Sines and the Law of Cosines aren’t at the front of my consciousness.  When I do teach that and have to show it on the board, I have to think a moment:  OK, yeah Step 1–then, let’s see, Step 2–OK, I remember now, etc.  What I have in mind is the resolution of difficult proofs.

I can think of several times working on a stubborn proof, turning it over and over in my mind, trying to see which way to go and heading up several blind alleys, sometimes putting it aside for awhile, then coming to the brink of giving up altogether.  Then, finally, when I least expected it, in one lightning like stroke, it was there!  The proof was perfectly clear!

Now if any math-oriented readers have had similar experiences, you know what I’m talking about.  I’ll try to describe it, however, although I keenly feel the limitations of language.  The strongest impression I have in such cases is of seeing (not literally with sight, but it’s the best word I can think of) the proof all at once in its entirety.  There is no perception of space or time–I’m not “seeing” the steps of the proof in my mind as if looking at a written paper; I’m not seeing the steps in order, one at a time.  Rather, I’m perceiving the entire thing all at once, knowing  how it works out.  From this instant, I would always have to write as quickly and in as much of a frenzy as I could to get it down before the vision faded.

In short, I had to “translate” the unitary perception into words written down in space over time.  It would be like being in a dark room with a window covered with a heavy drape; then when the drape is suddenly ripped off, seeing the beautiful garden outside in one instantaneous image.  Of course, if your eyes were dazzled by the bright light, it might be hard to make a drawing!  That’s the analogy–sometimes the initial insight would fade as I hastened to write the proof out, and I’d have to stop and concentrate to recover the vision so that I could finish.

This is why I’ve been somewhat sympathetic to Zen, once I first read of it, since the experiences I had of mathematical proof were not unlike the descriptions of kensho, though I wouldn’t be grandiose as to make too strong a connection.

Anyway, the strongest aspects of this perception of a proof in a flash of sudden insight were its objectivity and its transcendence.  Objective, in that, as Fox Mulder might say, the “truth was out there”.  In short, I never have the feeling that I’m just coming up with a good idea or making something up.  The proof is not made; it’s found.  In short, it exists outside my mind or any human mind.  It’s out there, waiting to be found, just as the other continents existed before any human ever set foot out of Africa.

Transcendent, in that the mathematical truth is not dependent on time and space.  This is clear:  2 + 2 = 4 is true regardless of what the objects you’re counting happen to be, or even if you have objects, or even whether objects even exist or not.  It’s also always true; the proof to a theorem, for example, is always and eternally accessible to anyone properly trained who exerts the effort to do so.  In short, mathematical truth exists objectively and independently of humanity, and outside of time and space.  This viewpoint is called mathematical Platonism, and I am an unabashed and unrepentant holder of this view.

Now this view is not the only view held by mathematicians far greater than I; and exactly what the status of mathematical truth is, is something that is definitely not uncontroversial.  However, many of the greats of mathematics, from Georg Cantor to the great Kurt Gödel, to say nothing of Pythagoras and of course Plato himself, were confirmed Platonists.  Gödel was particularly adamant as to the independent existence of mathematics.  He said that a mathematician finds mathematical truth through his intuition the same way a person sees an object with his vision.  He recommended sitting with eyes closed in a dim room as an especially good way to activate this intuition (though I’m sure different mathematicians  have their own means).

Well, if all this is indeed true of mathematics, it has many important corollaries.  If math is completely non-physical and totally transcends the material world, this implies that the human mind must, at least in part, be immaterial itself.  This necessarily follows:  after all, it’s difficult to see how a purely material thing–the brain–could perceive something immaterial.  It is true that some computer programs have been developed to help with proofs and find simpler ones; but it’s important to note that they all use data and beginning points programmed into them by humans with organic brains.  In short, the basics which humans could derive from the immaterial world of math were given to the machines, which then plug along iteratively and algorithmically .  The original insight had to be from humans.

Second, if the human mind is at least partly immaterial, it must not depend completely on the body.  This further implies at least the logical possibility, if not certainty, of the ability of the mind–or at least parts of it–to function without the body.  Thus, we have the basis for asserting the possibility of survival of the mind/soul after death, and even of hypothetical partial separation from the body (astral projection) during life.

In saying all this, we have asserted the possibility, the reasonableness, of the idea of a disembodied mind that can function independently of the material world.  If this is possible, then it logically follows that it must be possible for there to exist minds that have always been disembodied–what we usually call “angels” or “spirits”; and if this is so, there is no intrinsic bar to believing that one of these spirits is infinite–is in fact what we call God.

Now this is a lot of work to make the nature of mathematical proof do.  I am by  no means saying that my understanding of math compels any of this to be true.  All that I think I can demonstrate is that our minds are partially immaterial; that doesn’t even entail a necessity that they survive beyond death or can function without the body.  The rest is more out on a limb, admittedly.

However, once we’ve opened the door to the realm of the immaterial–the Immateria (as Alan Moore called it, in a different context)–with the key of math, we don’t necessarily need the key any more.  We have more space to play.  Many, especially positivists and materialists, want to reject even the possibility of a spiritual or non-physical realm a priori, on the grounds that only the material exists, or that “spiritual substances” are a contradiction in terms.  Given that we  have, IMO, demonstrated that the immaterial exists, we don’t have to worry about such claims.

Given that we now know the mind to be part of the Immateria, it seem reasonable to respect the fairly consistent beliefs, especially those that are experientially based (through meditation, etc.), of most of humanity in the most wildly different cultures and religions through the ages, that the human soul can, in fact, operate without a body and does, in fact survive spiritual death.  I think we can also assent to the other very common assertions of the existence of disembodied minds–angels, or whatever name you wish to use for them.  Demonstration of God is another matter, which I don’t want to get into here, but at least the concept of God as spirit is found to be sound from our reasoning, so belief in Him can’t be rejected on that ground.

Therefore, I assert that regardless of my opinions of God, that it is reasonable to assume the existence of a human soul that survives death and that can function without the human body.

I hesitate quite to say that I know this, as opposed to “strongly believe”, since the intuitions which I’ve spoken of can be so blurry and so fleeting.  Also, following Descartes, I’d have to say that probably the only thing one can perfectly prove is one’s own thinking, though that way lies solipsistic madness. Still, I think I’d say that the reality of the Immateria and of human souls is to me 99.999999999999999999999999999+% certain.

Gödel thought all this, too.  While not a conventional church-goer (he was, in fact, unconventional in many ways), he had no doubt of the existence of God or the soul, and was very devout in his own way.

Thus, I am confident in saying that whatever else I might believe religiously, my belief in the soul and its persistence after death are not affected by my other beliefs.  Even if I were to lose faith in Catholicism or in Christianity altogether–which I don’t anticipate–I would not seem humans as just “plains apes” or “talking monkeys”.  The human soul and the special status it gives humankind isn’t something that would have to be reformulated or dropped as a belief.

Part of the series Legends of the Fall.

Posted on 09/07/2012, in mathematics, metaphysics, philosophy and tagged , , , , , . Bookmark the permalink. 8 Comments.

  1. Hearsay.

    Anyway, so far as you intuitively experience ‘spirit’ — There is no way to fit that into a materialist frame. So it only makes sense to fit the material into a spiritual frame.

    As we inhabit a coherence, not a chaos — ‘Spirit’, ‘the One’, etc is not far from that.

    There are plenty of materialist explanations of ‘the mind’ as an external phenomenom. What gets me is the fact that materialists, with a straight face, can claim that this explains the ongoing experience of their own minds from inside…

    Mathematics, alas! Though it is certainly objectively true, independent of material circumstance — George Lakoff does a pretty good job of grounding it as a structure of metaphors based on common, elementary concrete experiences. Which is, after all, exactly the way we naturally try to explain it to nonmathematicians, via examples. The only thing that puzzles me about this — why normies have so much trouble with metaphor!

    • I’d agree with you that explaining mind from the outside still doesn’t explain it from the inside. In short, no one has yet explained qualia. I use mathematics since it is something I’m personally acquainted with, and because many would tend to view it as more objective.

      I’m aware of Lakoff’s book, and I actually disagree with it rather strongly. Math is instantiated and experienced in the concrete, but that’s not where it comes from. Of course. that’s a long-standing area of debate in the philosophy of math, anyway.

      • As a poet (and hedge-mathematician) I find the notion that we do our serious thinking via metaphor — not just appealing, but accurate.

        The difficulty of explaining these simple metaphors to people who don’t get it — does look like a serious flaw, especially since what Lakoff is proposing isn’t so much ‘a theory of what mathematics IS’ as ‘a theory of how people manage to think mathematically, to see our conclusions as ‘objectively given’ — see mathematical objects as one big abstractive level above the particular phenomena we explain mathematically.

        Of course a relation is one level of abstraction up from the whatevers we’re relating by it….

        If you see the constraints of mathematics as elements of God’s nature… and they do exhibit that implacable sort of necessity… then the details of how human beings come to recognize their truth may be a small side-issue.

        But then a truly amazing amount of stuff turns out to have ‘The Way Things Have To Be’ status. Boggling!

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