Creationists may have bitten their own head off with their idea of specified complexity. Because there is a case to be made that if specified complexity can exist, the supernatural cannot. The creationist William Dembski famously contrived the concept of “specified complexity,” as a distinct category of mere complexity, early this century. Many criticisms (some fatal) have taken this out of contention as a useful pathway to design arguments. But outside its epistemic application, the ontological category remains valid: there is a difference between mere complexity, and specified complexity. And that difference matters.

Explaining the Difference

A large sea of completely random events can be extremely complex, because it is large (the more options, the more complex) and less bounded by limitations (the fewer limitations, the more options); but it will remain quite simple to model and thus in no need of explaining its structure by any other mechanism than random chance acting on a simple set of fixed rules. For instance, I can double the number of cards held in a hand at poker (from five to ten), and thus greatly increase the complexity of a drawn hand, yet the hand drawn is still determined completely at random. As anyone who has experience playing Pinochle can attest, there are many more possible hands in a ten card hard than in a five card hand. You can have hands that are quite complex indeed. But all we need to explain that, is to state how many cards are in a deck, how many will be drawn, and that they are randomized upon drawing. Those three statements, explain all observed complexity in every hand ever drawn. No convoluted theory about card-selecting demons is needed to explain the ensuing complexity of hands that will be observed.

Dembski’s goal was to identify that there are things that are not random like poker hands, yet are also complex. The basic obvious point is that certain things are so complex, that random chance is not a good hypothesis to explain how they arose or why they continue (like, if you kept drawing flushes, no matter how hard you tried to randomize the deck each time). Which is why we then start proposing other hypotheses (e.g. a card shark is rigging the deck); and in the sciences, we’ve developed tools for testing those hypotheses to see which is most likely the cause of the observed complexity (e.g. ruling out the card shark).

At some point, we would even have to concede magic is involved, were it so.

For instance, if we ruled out every hypothesis we can think of for the weird “every hand draws flush” phenomenon, yet someone present says they are controlling it with magic—and we can control for that, by having them “turn on and off” the magic for us; and having them show the effect in a wide variety of circumstances, particularly ones it is extremely unlikely they could rig or control any other way, e.g. like at several different tables at several different casinos, with no prep time—then magic would, alas, become the most probable explanation of the effect. Science would then start studying that magic, like it does any other power or force in the universe. And soon we’d have peer reviewed sorcerology journals, and the whole shebang. It’s the fact that this never happens that forms the empirical argument against the supernatural.

But there may be a logical argument against the supernatural. I’ve argued this before, in The God Impossible. There I make the point that we can trace the outline of an empirical argument for the logical impossibility of the supernatural. An actual formal proof may be too complex for us to discern presently (the formal proof of Fermat’s Last Theorem alone is 129 pages long and took centuries of hundreds of dedicated researchers to develop). But that doesn’t mean there isn’t one. Here I will get even more specific, and trace out what one such formal proof might look like, in very general terms. Whether anyone can ever develop it further remains to be seen.

Getting From There to Intelligent Design

Of course Dembski meant by specified complexity something even more specific: if a highly complex but orderly outcome (like “every hand draws a flush”) could be caused by fixed natural laws (some dumb mechanism), then it no longer qualified as specified complexity (though the assembly of those laws could be, but that was then a separate question). Because in that case, the outcome only has complexity owing to the abundance of materials the mechanism works on (the number of cards in the deck; the number of cards in the hand). The outcome can still be modeled very simply: you have some randomness perhaps, plus some simple rules that just always apply (e.g. the number of each kind of card, the number of cards, and the size of the hand, are all just fixed facts governing the outcome; none of those facts are, themselves, intelligent agents).

In the end, since when governed by fixed laws, the outcome is then not at all improbable, you no longer need posit design. The genius of Darwin was discovering just such a process (combining some simple fixed laws with random chance) for all of biology. Ooops. No more need of a designer. This has annoyed Christians for over a hundred and fifty years now. But alas, stymied, they moved to cosmology instead, the last frontier. Or tried finding things in biology Darwin’s process couldn’t explain, like irreducible complexity—although they failed. But though they keep failing on the facts, Dembski at least tried to give Christians the methodological machinery to succeed, should they ever actually find an example. (We’re still waiting for one. As likely to arrive as Godot.)

Thus, Dembski tried to bootstrap this ontological concept into an empirical test: if you see complexity, and can rule out randomness (e.g. when random chance to produce that complexity is highly improbable) and fixed order (e.g. no dumb set of fixed rules can produce it), the only remaining hypothesis with any probability is intelligent design (e.g. some form of intelligent information processor; which itself could still be fully explained as the combination of randomness and fixed order, so Dembski admitted that getting from “design” to “supernatural designer” required additional arguments). As many then pointed out, this isn’t how empirical reasoning, much less science, actually works. But I’m not going to get into that today. It’s not necessary here. Here, I’m only interested in the ontological category of specified complexity: a thing that is (a) complex and (b) not that way randomly or inevitably.

Why We Think the Supernatural Is Possible

As I’ve explained in Defining the Supernatural (and later in an article for Free Inquiry), in practice pretty much everyone means by “the supernatural,” phenomena that evince specified complexity without a reductive mechanism (see also my follow-up discussions in Defining the Supernatural vs. Logical Positivism and Epistemology without Insurmountable Regress).

The way I defined it in the past was more colloquial, something like “mental phenomena that cannot be reduced to nonmental phenomena.” Everything someone says is supernatural, is something satisfying that definition. Because any time something mental is fully explained by a system of nonmental parts, everyone agrees it is natural, not supernatural. In my original blog article I gave many different kinds of examples, from love potions to gods. In each case, we can describe a potion that everyone agrees isn’t magic, and a god everyone agrees is really just a space alien; and the difference is always whether the thing in question (the effects of the potion; the powers of the god) can be reduced entirely to a system of nonmental entities (nanobot flotillas; superhuman neurology), or not.

We can then easily explain why we ever think the supernatural exists, as simply an inevitable cognitive error. We can observe a mind think, or a car roll uphill, without seeing the engine inside actually bringing about the effect (the person’s brain; the car’s motor). So we can conceive of a mind thinking without a brain, and a car rolling uphill without an engine. But that’s an error. In fact, neither is possible: minds can’t exist without brains, nor can cars roll uphill without some complicated machine bringing that about. It is our inability to see the mechanism, and our seeing instead only a cause and an effect (without all the intervening messy system of causes—the neurons and blood vessels, the gears and pistons—linking the one to the other), that leads us to imagine the supernatural: a disembodied mind; a magical car. We don’t see the hidden mechanism; so we think we don’t need the hidden mechanism. But that’s a fallacy.

And that’s what the supernatural actually ends up being in everyone’s mind:

Activity without mechanism. Complexity without components.

And there’s the rub.

Activity without mechanism, actually logically entails complexity without components. They are just translations of the same phrase, synonymous. But…isn’t complexity without components by definition a logical contradiction?

Why We Should Think the Supernatural Is Impossible

Consider a god’s mind. A god has to know things (store information), and think things (process information). But there is a difference between correct and incorrect information, present and absent information; between conflation and distinction. A god has to be able to distinguish one person’s face, from another; and correctly connect each face, with other information about the corresponding person, like that Joe’s face goes with Joe’s job in sales and wife of eleven years, and Mark’s face goes with Mark’s service in the military and husband of eleven years. That information could be connected up differently—wires crossed, and Joe’s face gets incorrectly linked to Mark’s husband, producing the false information that Joe has a husband, and so on. And notice how many different ways connections can be crossed up: the more information, the more different connections are possible. And most of them (in fact, all but one of them; out of effectively infinitely many) will be false.

And that’s just for the one part of a mind: stored information. The other part, information processing, is the same: it can be connected up correctly (only ever producing logically valid conclusions from the premises available, namely the stored information; and always producing all such conclusions possible), or, in some degree or other, incorrectly (sometimes producing logically invalid conclusions; and sometimes not producing possible conclusions, e.g. for want of time or processing power). And indeed there are infinitely many “incorrect” processor arrangements (in which some part is flawed or limited), and only one possible “correct” one (in the sense of forming all possible valid conclusions; rather than only some, or some invalid, or both). A processor can get conflated and jumbled up, and thus produce some invalid conclusions, or prevent obtaining some available conclusions. Its “circuitry” (the rules by which it processes information, and how much) can be perfect or imperfect.

What becomes apparent here is that both are manifestations of, by Dembski’s own logic, specified complexity. You can’t get a sound mind by random chance (all the information, all in the right connected order), or indeed any mind (how would you roll a die on a table, and get “knowledge of Joe’s face”? … on Boltzmann brains as the exception, indeed, see my discussion in The God Impossible). And what set of dumb fixed laws would do it? We actually do know the answer—evolution by natural selection can do this. And did. But of course, it can’t get the perfect result (both our information and our processor are always limited and flawed), nor even would it getting that result satisfy what Dembski really wants: a supernatural god. An embodied, naturally evolved superbeing, is still just a space alien. Not a god. And if there are no fixed set of laws “prior to and outside of” god that can produce the correct mind, how then does his mind exist?

That’s not the argument I’m going to make here. Though it is a time-tested one. If everything with specified complexity needs a designer, who designed god? Theists never have any coherent answer to this. They just handwave with some vague insistence that some ontological argument will sort out the problem and explain why God’s perfect mind is a logically necessary outcome of simply being God. But when we ask them to produce that argument, all we get is fallacious bullshit (see my discussion, for example, in Bayesian Counter-Apologetics and Plantinga’s Two Dozen or So Arguments). Hence the problem remains. God’s complexity is vast. Where did it come from? Explaining one complex thing (e.g. the observed universe) by just pulling out of your ass a wholly unevidenced and merely proposed even more complex thing, is going backwards in the explanation department. It only makes the observed facts (the universe) less likely, not more so. As explanations go, that’s just a failure.

But I have in mind another problem with all this. One you might not have thought about yet. The question I am concerned about here is not causal (the “how it got that way”), but ontological: what forms the components and keeps them separate, so they don’t get mixed and conflated? How do you have complexity without parts? It seems inherently impossible, a direct logical contradiction, to say something is complex and has no distinct parts. It is also a direct logical contradiction to say God has a perfect mind and is not complex. Because a perfect mind has the most specified complexity possible: of all the infinitely many “less perfect” arrangements of information and circuitry, only one is perfect. This requires God’s mind to be not only extraordinarily specified (of all the minds he logically could have, he has that specific one) but also extraordinarily complex.

This is as opposed to, for example, the mind of a worm, which is vastly simpler. It would be illogical to say God’s mind is simpler than a worm’s, or a vegetable’s. Obviously it’s vastly more complex than either. Otherwise, he would’t be a god. He’d just be a dumb force or something, as unintelligent and ignorant as a worm or a cabbage. But if God is extraordinarily complex (owing to the vast specified complexity of his mind), he must have parts. Knowledge of Joe’s face has to be separate from knowledge of Mark’s face. Otherwise, by definition, God could not tell the difference between them.

Likewise all other information, which constitutes, by definition, maintaining distinctions between things. And distinctions entail component separation. You can’t distinguish one face from another, if you can’t keep them separate; and you can’t keep them separate if there is no difference between them; and if they are the same one part (and thus not distinct parts), there would be no difference between them. It does not help to say they are “inseparable” and therefore “all the same part” (though how knowledge of two distinct faces would constitute a single inseparable thing escapes me), because that’s a non sequitur. Parts being inseparable, does not even make each of them the same thing, much less the same part.

This seems to me a much more serious problem than the causal one (how God just luckily happened to get his perfect mind, though that’s a pretty serious problem in its own right). This isn’t solved by theologians’ attempts to claim God’s knowledge (etc.) follows necessarily from his other properties (like his omnipotence), or anything else akin. That would only solve the causal problem. Not the ontological one. It also doesn’t work, since no such demonstration has ever been produced (e.g. that a god exists who even could have that kind of omnipotence, much less actually does; or that even having it, would in fact produce the requisite mind). But theists like making things up for which they have no evidence and pretending that is “evidence.” But no. Even if that did work, we still have the ontological problem. How does God have that complexity? Not how did he get it; but how does it stick around. How does it obtain at all. (Many of these problems have been noted before.)

Even if God uses his “omnipotence” (how is that manifest again? [sound of crickets]) to “keep his mind intact” by continually reassembling it over and over again in every micro-moment of time, that still doesn’t explain how he assembles it at all. Even in any micro-moment, what keep’s Joe’s face separate from Mark’s face? What keeps God’s mental circuit’s logical operations in the right order, so as not to flip a modus ponens into an affirming the consequent? We can diagram the logical operations and their order and arrangement that make the difference between modus ponens and affirming the consequent; but a diagram of a thought mechanism, doesn’t think. And in any case, even a diagram requires physical materials (e.g. ink on paper), with parts. The more so an actual working mechanism, that successfully runs a modus ponens operation instead of something else.

It seems self-evident that if nothing exists to separate Joe’s face from Mark’s face, their faces cannot be distinguished. They will simply blend together, and there will be no way to tell them apart. So some thing must exist to keep them apart. Also, to connect them together (if, e.g. Joe and Mark are friends; as opposed to enemies; or relatives; or co-workers; or just don’t know each other). The information has to be stored in some material. That material need not be conventional matter. It could be stored as some distinguishable structure in light, or a twist in spacetime, or made out of ectoplasm, or something. But it has to be something. Otherwise, information cannot be stored in any way that allows distinctions to be made. Nor can a mind process information in any way that allows correct vs. incorrect inference procedures to be run on that information. How could it, if we can’t keep distinct even the various possible procedures or relations? And without a circuit stamped in some material, there is no way to keep distinct even the various possible procedures and relations.

In short, quite simply, God’s mind appears to be logically impossible.

And this extends to all of the supernatural. Because God is just an extreme case of the supernatural. Every other case is the same: by proposing a property or effect can obtain without parts composing and driving it, all claims of the supernatural claim complexity without enough parts, which is a logical contradiction. Few parts, means no complexity. Yet the observed phenomenon, is complex.

For example, for a car to magically roll uphill, you need a certain specified complexity (improbable, sustained, directed movement of a mass), without an underlying mechanism to cause it (like the machinery of an internal combustion engine). All the “parts” you need to get the result (some gravity-defying, entropy-reversing, direction-maintaining machinery) are removed from the system. Yet the result remains. That’s a logical contradiction. You have a mental phenomenon (intelligent motion: the car just “magically” knows which direction to go and just “magically” wills itself to go there), which is way more complex than we think, yet with no nonmental machinery bringing it about (no information processor to get the direction right and the forces generated and pointed the right way). The outcome requires more parts (the information processor and physical driver) than are claimed.

This inconsistency, between how simple we think a phenomenon is, and how complex it actually is, is a routine error in human cognition. We’ve run into this repeatedly in AI development: try programming a car to roll up a hill (staying on the road; pushing against gravity). It’s far more complex a program than you probably assumed. I mean, it seems so simple. Car, direction, roll. Just three words. Surely the simplest thing ever! Nope. It’s actually very complicated. Even in a simulation, like a computer game, where you totally control all the laws of physics, and can literally just make a car roll uphill by simply saying that it does, the code—even the most efficient code logically possible—is really incredibly complicated. It’s not just three words. Even if you wrote an operating system that could do it with three words, that would just conceal the complexity in the operating system. Try coding “car, roll uphill” with just the words “car, roll uphill,” without any underlying operating system (much less physical processors and memory chips). Nothing will happen. Because it can’t.

We intuitively take this as an empirical fact. “It can’t,” because we tried, and observed computers don’t just obey words we type into them; you have to program the computers to (in some sense) know what those words mean, etc., so it takes a hell of a lot more words; likewise the rest of the world: we simply observe that telling the world to behave a certain way, has no effect. But really, I strongly suspect, it’s a logically necessary fact. It is simply logically impossible to have a computer without an information processor; and you can’t get any purportedly supernatural effect, without an information processor. Because you need some mechanism that translates commands and descriptions, into effects (that translates the symbols “car, roll uphill” into a car actually rolling uphill; even a simulated car rolling up a digital hill). And you can’t get a specified complex effect (a car “knowing” what direction to roll, and “knowing” to overcome the forces that would normally prevent it, and how), without information processing (such as: an engine and steering system).

This is true everywhere. Because all worlds are just computers. Whether simulated or real, all any universe is, by definition, is just an information processor and a system of information. We call the processor “the laws and constants of physics” and the information “facts.” But it’s still just a computer. It is no more logical to expect the universe to manifest supernatural phenomena, than it is to expect a computer to obey commands with no operating system—much less to expect a computer to “know” what operating system to run, when it has no physical circuitry or memory to store and manifest that system. If it has no structure, it can never “know” the difference between that operating system and any other. It can’t make any distinctions. And yet making distinctions, is required for intelligent action. Or indeed any nonrandom action at all.

As with all supernatural phenomena, so with God: we think we can have disembodied minds (and powers and everything else), because we can imagine all the required shape and structure and forces and distinctions existing without a material substrate; but we can only imagine that with a brain: a material substrate. It is thus an illusion, and a fallacy, to conclude that things we can imagine on a physical processor, can exist without a physical processor. This illusion comes from not knowing (or forgetting) that we are doing all this imagining on a physical processor; that we need it, to imagine anything at all. This was the point I already, and more extensively, explored in The God Impossible. But it should seem even more obvious now. Since a material appears to be needed to manifest structure and maintain distinctions, indeed even to imagine structure and the maintaining of distinctions, maybe God is impossible.

Complexity Logically Entails Components

So you probably can’t even conceivably have a mind without a physical structure to realize and distinguish its needed components—its individual and distinct pieces of knowledge and their correct relations, including procedures of reasoning and inference. But you certainly can’t have a mind that is simple, in any relevant sense. A mind must necessarily be complex; else it could not know or think anything. As I noted, it is logically contradictory to claim even a human mind, much less a God’s mind, is simpler than a worm’s, or even a cabbage (and cabbages, especially their information processing system, are pretty complex). Obviously, it’s vastly more complex. That’s what makes it a human or a God. And not a worm or a cabbage. This is a problem for theologians like Edward Feser who need God to be the simplest thing possible. But alas, that’s impossible.

Spacetime can be the simplest thing possible. Because you don’t change spacetime by taking any of it away or changing how much of it there is. You can thereby change what shapes it takes, what things it manifests, but spacetime itself doesn’t change its properties. Each bit of it, keeps the same properties. And remains spacetime, and not something else. In fact, you can’t break it up into any further components. There is nothing “out of which” spacetime is made. Other than just spacetime. Everything else—particles, matter and energy, shaped regions of spacetime—and all the structures these can combine into, like planets and people and brains and computers, is not fundamental. It is a product of the substrate of spacetime. You can break them up, remove components, and they cease being what they are, and become something else.

And this means minds, also, cannot be the substrate of the universe. They can only ever be a product of it. Because minds have specified complexity. Which means you can take parts of them away (remove information, remove connections between pieces of information, remove inference steps from reasoning circuits; and replace them with different ones), and they become something else. God, less smart and knowledgeable, becomes just a space alien. Remove enough parts from God’s mind, and he’s just a human being; indeed he could end up being identical to any one of us. Or dumber. Because remove even more, and God becomes identical to a worm. Remove even more, and God becomes identical to a cabbage. Feser would insist that this is impossible because all of God’s knowledge is logically entailed by…something or other. But he never produces any evidence or valid argument that that’s so.

Richard Dawkins is credited with making something akin to this same argument. Though he’s not the most careful of thinkers. There is an attempt at responding to it in his form in The Routledge Handbook of Contemporary Philosophy of Religion edited by Graham Oppy, but it mostly just takes advantage of Dawkins, for want of being a practiced philosopher, being his own straw man. This is in Ch. 4, “New Atheist Approaches to Religion,” by Trent Dougherty and Logan Paul Gage, in a section called “Dawkins on why there almost certainly is no God,” pp. 54-61. This illustrates how hard it is to actually escape the conclusion of God’s enormous specified complexity—and thus possession of components, as complexity as a concept logically entails.

There they claim it is not obvious that God’s mind would be more complex than the known universe, for example. But it is obvious. Because the contrary is actually logically impossible. It is a well-known law of computer science that the simplest computation for simulating a system, is the system itself (see Labyrinths of Reason on this point). In other words, it requires a more complex computer to simulate a world, than the world simulated. Simply because you have to have all the complexity of that world, plus the added complexity of the infrastructure of simulating it. As in God’s case, not only must God’s mind contain all true information about the universe, which is logically necessarily identical in complexity to the universe thus known, but his mind will also contain all true information about all other possible universes. This he needs in order to decide which is the best universe to make, and the best actions to take to maintain it (which knowledge, requires comparing one choice with all others, so as to discover the best). But even if he didn’t know any of that (a fact that would substantially diminish his divinity), his mind must contain all true information about himself. Thus, his mind cannot avoid being more complex than the universe…which for its entire existence and operation requires no added information about gods.

Dougherty and Gage absurdly think they can refute this by jotting down on a piece of paper “God knows everything” and thereby prove God is simpler than “everything” (they ask us to start our list of “everything” with aardvarks). This is phenomenally stupid. Obviously the word “everything” is just an artificial code that’s hiding a vast complex of things…starting with aardvarks. You can’t claim God is simple because the word “everything” is simple. That word may be one word, of only ten letters. But its kolmogorov complexity is vast. Try describing an information system that contains “everything” and you’ll start to see the problem. Even if you can come up with a simpler algorithm that, when run to completion, would produce “everything” (aardvarks and all)—though good luck with that—you still end up with a complex result. Where are you going to store all that information? Not in anything simple. You can’t fit “everything” into 128 megabytes of RAM. But moreover, you then have to admit the universe is itself already governed by such an algorithm. And it is necessarily simpler than any mind could ever be.

That’s right. Think it through. In no way was “make aardvarks” coded into the fundamental physics of the universe—ever, much less at the start of the unfolding of the program (which we call The Big Bang). A vastly simpler set of rules (only the most fundamental laws and constants of physics) unfolded inevitably into aardvarks (and everything else). Indeed, it may be as simple as a single point of space-time with no properties at all—no laws and no constants—other than what is logically necessary. But even if not. The set of code describing the core laws and constants of physics, is necessarily smaller than any set of code describing a mind capable of knowing that universe code. Because again: the mind has to have all the added complexity (of being a mind, and not a mindless universe) on top of the information known (the code for the unfolding the universe, which itself is obviously not conscious of itself, or anything). Thus, even if you can come up with a simpler algorithm by which God knows everything, it must still be more complex than the thing known: the algorithm that would by itself produce everything, without God. “But you need God to write that algorithm!” Yeah. Exactly. Which requires more complexity in God, than could possibly be in that algorithm. See the problem?

And complexity logically entails components, the parts that make the complexity. In any mind, a part can be removed, or changed, and it becomes a different mind, but still a mind. Remove the right parts, or enough parts, and it ceases even to be a mind. Though cabbages have complex information processing systems, we do not generally say they have minds. Because their processors are so simple, they don’t even have a central nervous system (or in fact even a nervous system); they accordingly are not producing any coherent form of cognition, much less knowledge or right reason. Take even more parts away, and you don’t even have a cabbage anymore. You have mulch. Eventually, just a box of rocks. Quite the opposite of “things that have minds.” So it cannot be claimed God is simple. He must necessarily be vastly complex; indeed, by logically necessary fact, he must be more complex than the known universe. And he must have parts, components. Lest it would be logically impossible for him to be complex.

And how does one have components, which require being kept distinct from each other and properly arranged, without a material substrate to keep them in place, and keep them apart? Much less connected and arranged in just the right way—as is required to make the difference between a cabbage and a person: which is entirely and solely a function of how the components are arranged.

Conclusion

God has extraordinary specified complexity. Specified complexity without parts is logically impossible. And parts without a material or substance to keep them separate from each other, and connected in the right way, is probably logically impossible. And the same goes for every other claim of the supernatural. As to be supernatural, means in every case (from magic potions to ghosts) to have complexity, without parts—to have a specified complexity in action or property, that reduces to no simple components explaining it, but just “is,” without any further explanation. This is asserting something has the complexity, without any actual complexity. A logical contradiction. And thus, a logical impossibility. This is in no way a deductive or formal proof of the conclusion. Not as yet. It’s just the outline of an argument that someone probably could formalize someday. It’s hard to imagine any coherent way to avoid it. And that is evidence for the impossibility. We have reason to believe it’s logically impossible; without yet knowing for sure that it is.