The God Impossible

Is the existence of God logically impossible? I used to be suspicious of arguments that attempted to prove that, because they were usually so lame, and easily rebutted (although some stick, depending on which “God” you are talking about: see my discussion of this in Sense and Goodness without God IV.2.4, pp. 275-77; and for some serious, but not always successful, attempts at building these kinds of arguments, see the anthology The Impossibility of God; some other examples are cataloged at the Secular Web; but a very interesting example, quite pertinent to today’s post, is Evan Fales’ Divine Intervention: Metaphysical and Epistemological Puzzles). Yesterday I blogged an ontological argument for the necessary existence of our universe without God (Ex Nihilo Onus Merdae Fit), and I had to stay on point there (it was long enough as is), but in developing that argument over the years I had already been thinking about one implication of it: if an infinite selection of all logically possible universes exists, then many of them will contain gods, if gods are logically possible. Today I cover that angle.

Which God Was That Again?

To begin with, we can rule out the God of any monotheism, for the simple reason that if P1 is true (“in the beginning, there was absolutely nothing,” the key premise of the argument I developed in the previous post), then there are infinitely many more configurations with multiple gods than only one god. In fact, if we’re to ask about a true monotheistic God, such that no other gods exist at all (not even in other universes), then the probability that such a God will come into existence on P1 is infinitely close to zero. Because it’s infinitely improbable that of all the possible configurations, we’d get only one God out of all the universes whatever. Indeed, universes with many gods in them will vastly outnumber universes with only one god in them, even before we get to the possibility of no universes containing any gods except one of them. So you can’t rebuild monotheism on P1. At best you get polytheism. In universes we’re not in (because if we were in one, we’d have verified some gods in it by now).

And that’s even if God is logically possible to begin with. And lately I have suspected he is not. I have approached this question from two different directions in my random contemplation over the decades, and I see now they are approaching a common result, so here in one post I will discuss them both and how they reinforce the same conclusion. The first relates to yesterday’s post, and the general question of what sort of entities can logically exist (which connects to my published work on defining naturalism and the supernatural) and how likely they’d be if P1 there is true and we followed it here to the same conclusion reached there (that infinitely many universes exist, being a random selection of all possible universes). The second relates more specifically to our ability to conceive of disembodied minds (and disembodied mental powers even apart from minds) and whether that affords any evidence that such things must be logically possible (I conclude it does not, and that it may even prove the contrary).

From Boltzmann Brains to Boltzmann Gods

In my work on Defining the Supernatural I explored the difference between “natural entities” and “supernatural entities,” and demonstrated that the latter are ontologically basic mental entities, such that if no such things exist, then nothing supernatural exists. And if that’s the case, then all mental entities are not ontologically basic, but are instead reducible to interacting nonmental parts (like neurons, microcircuits, or what have you). And that being the case is what defines naturalism as a worldview. In my analysis I discussed the difference between supernatural gods and the kind of gods that could still exist if naturalism is true (skip to the section there called The Stoic and Epicurean Gods to see what those would be like). The latter would basically be animals, aliens, or computers, or mishmashes of all three, and most likely in a truly bizarre scifi way. There are infinitely many different kinds of gods like this that are logically possible even on presently known physics.

And that has to be acknowledged. Probability combined with the law of large numbers combined with the realities of cosmological scales of space and time entails some very weird things. Which are nevertheless certainly true. I’m not speaking of Nick Bostrom’s bizarre argument that we must be living in a simulated universe (Are you Living in a Simulation?), which doesn’t really work, because it requires accepting the extremely implausible premise that most civilizations will behave in the most horrifically immoral way imaginable, and for no practical reason whatever (in all good sense, by far almost all sims that anyone will ever generate will be games and paradises, not countless trillions of aimlessly tedious worlds with thousands of years of pointless wars, holocausts, plagues, and famines). Rather, I’m speaking of Boltzmann Brains.

If the universe were to slowly expand forever, even if it were to fade into a heat death of total equilibrium, even then, simply due to the laws of probability, the random bouncing around of matter and energy would inevitably assemble a working brain. Just by chance. It’s only a matter of time. Maybe once every trillion trillion years in any expanse of a trillion trillion light years. But inevitably. And in fact, it would happen again and again, forever. So when all is said and done, there will be infinitely many more Boltzmann brains created in this universe than evolved brains like ours. The downside, of course, is that by far nearly all these brains will immediately die in the icy vacuum of space (don’t worry, by far most of these won’t survive long enough to experience even one moment of consciousness). And they would almost never have any company.

Which is how we know we aren’t Boltzmann brains. Because we aren’t just floating around alone in random space dust. Yes, there will also inevitably be a completely random assembly of a whole working earth and civilization and so on, but that will be vastly (and I mean vaaaaasssstlyy) rarer, and again even then we would see we were on a weird isolated earth floating around in a frozen dead universe. And yes, there will inevitably be a completely random assembly of a whole working universe out to a visible horizon fourteen billion light years away that just by accident happens to look like it’s undergoing an accelerating expansion, and look like it began by a Big Bang but didn’t, and people in that world will be fooled. But of all the worlds that look like that, almost none of them are like that. Rather, most worlds that look like that got there the hard way. And when I say most, if I were to attempt to show you the ratio of real to accidental worlds that look like that, you would be unable to conceive of the number I came up with. So the odds are as good as a hundred percent that we’re in one of those real worlds, and not one of the weirdo accidental ones that look exactly the same. Although, if P1 is false, then our world probably is the product of a Boltzmann Big Bang (see my comment in The End of Christianity, n. 31, p. 411). But it’s infinitely unlikely to be one of those accidentally deceptively assembled worlds.

Nevertheless, given infinite time, such worlds will exist. It’s a logically necessary truth. In fact, anything that has (and maintains) a stable nonzero probability of happening, will happen. Eventually. We can’t always be sure, though, what actually will maintain a stable nonzero probability of happening, and many things simply will not. Hitler will never be alive again. That probability is now zero. Because he’s dead. A copy of him might pop into existence some day, or some nearly identical sequence of events might produce someone nearly identical to him someday, but that would still be a different guy. And if universes don’t undergo eternal heat deaths, but collapse or explode on a regular basis (as ours is set to do), then there might never be a span of time enough to make a Boltzmann universe (although a Boltzmann brain, maybe). But even then, barring logical contradictions, even a sequence of short-lived universes might eventually make Boltzmann worlds. Ascertaining whether that will actually be impossible (and if possible, then it has a nonzero probability, and therefore will happen eventually) is a task perhaps beyond human ken.

But it doesn’t matter, because the point is, Boltzmann brains are an inevitability. In fact, because time will never end, there will be infinitely many of them. Boltzmann worlds, too. Which means Boltzmann gods are likewise inevitable…in fact, there will be (if there haven’t already been) infinitely many of them. What is a Boltzmann god? Think of a mind that is as near to perfection and power as could ever be physically made, a supermind, with a superbody, maybe even a body spanning and permeating a whole vast region of spacetime. The improbability of this is staggering. But remember, everything with a nonzero probability is going to happen, eventually. In fact, it’s going to happen infinitely many times. Only its relative frequency will be staggeringly low. Worlds without such lucky accidental gods will vastly (and I mean vaaaaasssstlyy) outnumber worlds with them. But the worlds lucky enough to get them will experience some pretty cool, or some pretty horrific, fates. In some, this god will be randomly evil and create civilizations just to torment them for fun (and let me reiterate: this may already have happened; in fact it may already be happening right now, in universes or regions of spacetime vastly beyond ours). In others, this god will be randomly awesome and create a paradise for his gentle children.

This will happen. It probably already has happened. It probably is happening as I type this. It’s a logically necessary truth. That’s weird. But there’s no escaping it. The only way this could ever be prevented is if time began, and were to end. Not the universe. Time itself. And not just time in our world, but in all worlds, all the spacetime continuums that exist beyond this one (if such there are). And there is no reason to believe that. Not only is there certainly no reason to expect time to end (there is no known physics on which it would–even the collapse of the universe will only create a ball of pressure so great that it will explode again into a new universe, with time still ticking; or seethe forever in a superdense state, time still ticking), but there is no reason even to expect that time ever began (we must assume it did if we grant P1, but if P1 is false…). Only Hawking’s nutshell model has time loop back in on itself at the Big Bang, and perhaps in an extremely unlikely scenario our universe may be one giant time loop somehow. But that’s just it: an extremely unlikely scenario.

Natural Gods or Supernatural Gods?

So Boltzmann gods are almost certainly an inevitability. Just immensely rarer than Boltzmann brains. Maybe even rarer than Boltzmann worlds, although many must surely be easier to randomly construct. They would be like the many different kinds of naturalistic gods I started talking about. Infinitely many configurations even under known physics would produce all kinds of gods of different sizes, powers, characters, of all degrees of intelligence and knowledge. These would in effect be alien gods, gods with bodies (however ephemeral or bizarre those bodies might be), gods with limitations. But they would be capable of anything gods of yore were, from immortality and superpowers, to intelligently creating universes and working scientific wonders (miracles, for all intents and purposes: see Clarke’s Third Law).

That’s what would distinguish them from just any Boltzmann brain, the ability to do those things; that’s what would classify them as accidental gods, and not just accidental people. And they need not even be accidental: we ourselves might one day create gods like this; we may even one day become gods like this. Barring an extremely unlikely disaster, a million years from now we will have the technology to accomplish either. And we are unlikely to be the only ones in this universe able to do this. In fact, in all probability, someone has done it already (statistically, we must have gotten started billions of years later than many civilizations in the cosmos). It’s just that, odds are, they are probably a billion galaxies away. And their gods, being physical beings with all the limitations that entails, won’t be able even to know we exist, much less communicate with us or lend us a hand.

Which is why many people don’t really allow these sorts of beings to be called “gods.” That is, this is not what people mean when they ask whether God exists, or insist that He does. Not even polytheists mean their gods to be distant aliens, accidental or manufactured. So the real question is not whether “gods” exist somewhere, in this or any of the universes that exist if P1 is true, but whether supernatural gods exist. Gods that don’t have the limitations and flaws of physical creatures. Gods that can be everywhere in the universe at once. Gods that aren’t slowed by the speed of light or weakened by the laws of thermodynamics. Invisible Gods that created our universe and hear our thoughts and meddle in our affairs, for good or ill. Gods that have constructed awesome heavenly places for us to go live in after we die (or horrific eternal prisons, as the case may be). Those kinds of Gods.

Certainly, if the question is, “If P1 is true, doesn’t that entail that there will be countless universes with all kinds of naturalistic gods in them, some accidental, some manufactured?” then the answer is “Yes.” Not only is that inevitably the case across any infinite array of purely naturalistic universes, but it’s inevitably the case in our own universe, where eventually there will indeed be Boltzmann brains, and far more rarely, but just as inevitably, Boltzmann gods; and sooner than either, gods of our own or alien manufacture. But what about supernatural gods? What about God?

The Probability of Supernatural Gods

As for monotheism, as I already pointed out, even if a supernatural One True God is logically possible (and as I’ll get to in a moment, I suspect it is not), then if P1 is true, the probability that this God exists is still infinitely close to zero: because infinitely many gods are possible, but God is here being defined as the one and only, and of all possible combinations of gods that could exist (in this universe alone, much less across all the infinite universes there would be), that only one would be selected to exist bears odds of many infinities to one against. It’s pretty much the most improbable thing humanly conceivable. In fact, it must necessarily have a probability of zero now, for the simple reason that once other gods exist, it becomes logically impossible for there ever to be one and only one God. So if all the infinite multiverses born of the original nothingness did not at that singular moment produce one and only one God over all of them (and him the most marvelous and perfect of all the singular gods there could have been), then that ship has sailed.

Since we observe there to be no such God in our universe, we know that no such God came to be. Therefore, none ever can come to be. But if you let go of your dogmatic and emotional need to “believe” in that extremely improbable God, and instead just clinically examine what possible gods are left, there could one day perhaps be a really supremely awesome “supernatural” Boltzmann God (or may even already be countless many of them, scattered across other universes we’re not in). If supernatural gods are logically possible. So that’s the question. But before we answer that, let’s explore the logical consequences of assuming that such gods are logically possible.

As I’ve noted, naturalistic Boltzmann gods will exist, but will be so extremely complex and improbable we will almost certainly never meet one (the only naturalistic gods we are likely to encounter are those we build ourselves). And those that exist across the multiverse, created spontaneously by the instantaneous transformation of the original nothingness, will be extraordinarily rare (and that’s an understatement). But what about supernatural gods? Obviously, by definition, you can’t randomly assemble those out of nonmental parts. How would one come to exist by accident then? They could only come to exist by the random assembly of irreducibly mental properties, supernatural “parts” as it were, and since we have no known physics of that, we can’t really run calculations for it (in the way we can, for example, in statistical mechanics).

However, we can approach something like a conceptual analog. Note that even a supernatural God is vastly complex in its constituent parts. Any mind must necessarily be, much more so a mind with powers beyond those of mere thought. Theists will insist that God is somehow simple in the sense of having no parts, or all his parts logically entailing each other and therefore inseparable, and so on and so forth, but that’s all just handwaving. Sound proofs are always wanting. There is no conceptual basis for thinking that any mind “must necessarily” be omnipotent or omniscient in any sense, or for thinking that any supernatural spirit “must necessarily” be omnipotent or omniscient in any sense, or that any creative intelligence must be, either. Certainly lesser deities, lesser spirits, lesser supernatural minds are logically possible. Therefore a God could be a lesser being. If we are to randomly produce a God from among all logically possible Gods (as P1 would entail we do, if supernatural gods are logically possible), then we will certainly not get an omni God of any sort. We will get a God of some lesser knowledge, intelligence, virtue, and power than the best we could logically get.

Thus most Gods will be lesser deities. Few to none will be anywhere near omni. But how many will there be, in terms of per-universe frequency, say? First of all, most universes with gods in them, will have vast numbers of gods in them (the number of logically possible universes with many gods is infinitely greater than the number with single gods in them). So already, universes with just one god in them, will not only in all probability have a lesser god, but such universes will be extraordinarily rare (and that’s a ridiculous understatement). Polytheistic worlds will be vastly more common. But secondly, a randomly produced supernatural god will not be much more probable than a natural Boltzmann god. The only thing in their favor is that, unlike natural Boltzmann gods, they won’t need a lot of superstructure to operate (e.g. no digestive system or equivalent, for example), and thus require a lot fewer parts. However, even natural Boltzmann brains do not require much superstructure relative to the complexity required of their brain to begin with. That is, almost all their improbability derives from the vast complexity of the brain itself (such as is required to generate a mind), in comparison with which the complexity of their bodies is trivial or incidental.

And that complexity will have to be shared by a supernatural mind, in two respects: (1) of all the possible combinations of mental contents and properties and their infinite degrees, godlike assemblies will be extremely few, relative to all the combinations that fall short of godlike; and (2) even mundane minds require vast complexity of organization, to produce a reliable system of beliefs and memories and of processing perceptions and contemplations. For example, to keep distinct the 500 or so faces our own brains are capable of memorizing, and correctly connect those faces to large systems of correct information about each face, and not get these connections all crossed up and confused, requires an extremely complex arrangement of neurons and synapses, any rearrangement of which would create confusion and error and literally eliminate information. A supernatural mind must also keep all this information inside it and also keep all these connections correctly linked up, which also requires a structure no less complex.

That structure might not be made of “stuff,” it might somehow be made of dreams or rainbows or bare supernatural brute facts or whatever, but the structure must still exist. Because of all the ways to connect up a supernatural mind, vastly more of them will be connected up all wrong, than will be connected up all right–much less connected up right for a superhuman scale of information and information processing. When picking random supernatural minds, most of them (by far) are going to be babbling lunatics or even completely nonfunctional spirits. After getting past those, of what remains, most (by far) will not be godlike. And after getting past those, of what remains, most (by far) will be truly minor gods. And after getting past those, of what remains, most (by far) will be merely mediocre gods. And so on. The number of gods who will be anything close to what Christians would want to worship, for example, is going to be infinitely fewer by comparison. In other words, the probability of any universe getting such a God in it is going to be well near infinity to one against. Even if the supernatural is logically possible.

So Is the Supernatural Logically Possible?

Still, if P1 is true, then it would still be the case that, in a broad sense, naturalism must be false, because supernatural things will inevitably exist, in some universes somewhere. If naturalism is true at all, it would only be true of our universe. But therein lies our first clue that the supernatural might in fact be logically impossible: the fact that we don’t observe anything supernatural operating in this universe. If it were in any way common for supernatural things to exist, certainly if they were as common as nonsupernatural things (and given P2, which is entailed by P1, why wouldn’t they be?), then our universe should be full of supernatural things, or at least have enough of them for many to have been scientifically confirmed by now. It would be extremely unlikely that we “just by chance” ended up in a completely supernatural-free universe (and no anthropic principle entails we would, either). Which in turn would entail that a supernatural god is impossible. Because if the supernatural is impossible, so are supernatural gods.

This is not a proof, however. There are extremely improbable ways that the supernatural could still exist and we would just happen never to have seen any. So at best this is evidence for the logical impossibility of the supernatural. Unless, of course, P1 is false. Then perhaps the supernatural is logically possible but just happens never to have become actual, owing to something (?) that prevents it. Although even then it would have to be possible to create supernatural things in this or some other universe. Because what it is to be a possible thing is to be a potential thing. That a triangle made of freshly severed dinosaur heads is “logically possible” means that any region of spacetime can (in principle) be configured to produce it. In fact, that very reconfiguration is what it means to be a triangle made of freshly severed dinosaur heads: it’s what the sentence “there is a triangle made of freshly severed dinosaur heads” means, such that if we didn’t know (at least in outline) what configuration of spacetime would make that statement true, then we literally wouldn’t know what that statement meant. (See Sense and Goodness without God II.2-III, pp. 27-208.)

So how exactly would we reconfigure spacetime to produce a supernatural property? That question is meaningless, because the supernatural by definition is not reducible to configurations of spacetime (it’s irreducible mental stuff, not spacetime stuff). So in what sense is the supernatural ever a “potential” property of anything in spacetime, much less of spacetime itself? I confess I cannot conceive of how it ever could be. But that again is not a proof, because many things we cannot conceive of are nevertheless true. Our inability to conceive of something only demonstrates our ignorance–which ignorance can be produced either by something not being possible or by our simply not knowing what makes it possible.

Maybe the supernatural is prohibited from existing by the laws of physics, which laws, if we could change them, would allow the supernatural again. I don’t know (I doubt it). But the point is, if P1 is false, then so is P2. So then the supernatural no longer has the same probability as the natural, and might even have a probability of zero, if something just happens to always have existed that prevents it from existing, something that does not necessarily exist, but just always has for no reason (the way God is supposed to always have existed for no reason). Although I confess that P1 is so surprisingly successful and simple an explanation for all that we observe (as I proved yesterday), I almost think it would be amazing if it wasn’t true. And anyway, I still have to ask whether the supernatural is logically possible. Since if P1 is true, then the truth of naturalism, in the grand scheme, requires the supernatural not merely to be nonexistent, but to be logically impossible. Because otherwise, the supernatural necessarily exists. Somewhere. Even if it’s not around here.

But again, that there isn’t any around here is clue number one that the supernatural is logically impossible after all.

On the Conceivability of Disembodied Minds

Although it’s obvious that an inability to conceive of something in no way proves it is impossible, I used to think that if something was conceivable, it must be logically possible (this is a working assumption evident, for example, in my 2004 critique of Reppert’s Argument from Reason). I now know there is one major flaw in that assumption, discussing which is how I shall end today’s meditation on the possibility of God.

First, it must be noted that many things (in fact, countlessly many things) are logically impossible that we do not know and at present cannot know are such (likewise things which are logically necessary). This is often overlooked, as it is assumed that if something is logically impossible, that fact should be obvious. But consider as an example Fermat’s Last Theorem, which simply states “no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than two.” Now, this statement was either necessarily false, or necessarily true. Thus, we either had a logically necessary truth, or a logical impossibility. Yet no one could prove which it was, for almost four hundred years. Only very recently did anyone prove that it was, after all, true (and therefore logically necessary). In fact, since it’s a statement declaring something to be logically impossible, by proving it’s true we had discovered something that is logically impossible. Many attempts had been made to prove this statement, which convinced people for a short time but were found upon further examination to be invalid or unsound (thus we can fool ourselves into believing something is logically possible or impossible, even when it isn’t). Finally, the proof that finally proved valid and sound, was over a hundred pages long. There was clearly nothing obvious about this statement of logical impossibility. And proving it required an extraordinarily arduous series of thousands of statements.

I provide this example to make a crucial point: if God is logically impossible, it could well be that the proof of this fact will require a hundred pages of propositions, and four hundred more years to discover. If anyone is even looking for it–unlike the quest to prove Fermat’s last theorem, to my knowledge no one is (they are only looking for simple proofs, of which there may be none). So it may never be discovered. Thus the fact that no such proof has been discovered is not a valid argument against the logical impossibility of God, any more than it would have been an argument against the logical impossibility of the equation in Fermat’s last theorem, or an argument against the logical impossibility of countless other logically impossible things we have yet to discover or may never do. Thus, suspecting the logical impossibility of God does not require a formal proof of its impossibility. We can have clues enough, as there were in the case of Fermat’s last theorem.

Second, it must be noted that concepts do not entail realities. Concepts, in the sense of potential entities (and not in the different sense of entertained or encoded thoughts), can exist necessarily, and exist always and everywhere, but concepts can’t think and act. Many ontological arguments for the existence of God are actually disguised arguments for the existence of the concept of God. But a concept of a God is not itself a God. That people can conceive of an entity is simply not the same thing as that entity existing. Fiction affords too many examples for me to have to belabor the point.

But here’s the rub. Even in terms of probabilities on cosmic scales, not every fiction will materialize. The movie Star Wars will never be acted out for real, not even in some vastly distant Boltzmann world, because it actually incorporates logical impossibilities (such as sound in a vacuum), systemic impossibilities (any civilization with such technology would not use humans to aim ship-to-ship weaponry, much less engage spaceships at proximities that even American naval commanders would consider absurd, which facts entail actual logical impossibilities between the human intelligence displayed in the film, and such stupid behaviors), and, of course, physical impossibilities (such as The Force, which as represented in the film no configuration of our universe, outside of computer simulated universes–take note–could ever produce, not at any probability).

This example is again crucial: we do not notice anything logically impossible about Star Wars; indeed, we are watching it, so how can it be logically impossible? But of course we are not actually watching Star Wars happen in reality. We are watching a dramatization that covertly persuades our brains to imagine that what is happening is happening, when in fact none of it actually is. Except, of course, in the “fourth wall” sense: filming the movie Star Wars is not logically impossible, but that’s all just trickery, the statements the characters make are literally false, the actors are not the characters they portray but are only pretending to be, the space battles were not filmed in outer space, and so on. When we actually try to translate all this into a real world system, only then will we notice the logical impossibilities that prevent any such drama from ever actually occurring, not at any probability, no matter how vanishingly small.

This is like Fermat’s Last Theorem: we can “imagine” that 2^45 + 3^45 = 4^45 is a true proposition. Especially if we don’t know how to run the math or lack a calculator to test it with. We can still understand every symbol, and the meaning of the statement as a whole. And there is no obvious contradiction among these parts. Indeed, we could even run the math with a calculator, make an error we didn’t catch, and thus conclude that that statement is indeed true after all! It happens to be false. In fact, not just false, but logically impossible. Yet that does not prevent our brains from imagining, even believing it is true. Thus, we can conceive of something as being true, that in fact is impossible. Therefore, our being able to conceive of something does not mean it is logically possible. And the more complex the thing we are asked to imagine, the easier it will be for us to overlook any logical impossibilities in its arrangement. We instead busy ourselves with imagining the parts and their juxtaposition. But that’s not the same thing.

The reason we are susceptible to this error is that when we imagine and conceive, we build models using pieces of things we know exist. We know light exists. We know swords exist. So why not a sword made out of light? We do not trouble ourselves with working out, first, how it could possibly be that a light saber has a practical finite length, and can be stopped (and with a loud report) by another beam of light just like the colliding of swords. Even lasers that could cut us in half cannot “ricochet” off of other laser beams like swords. They would pass right through each other. But we understand how lasers work. We understand how swords work. So we build a model of laser swords in our head, borrowing the bits we want from each. But that in no way entails we could ever actually make a light saber. In this case such a thing at least is “logically” possible (the technology would be needlessly elaborate, whereas just cutting the guy in half with an actual laser would be easier; there’s a reason police and soldiers don’t fight much with swords anymore). But the point is, its physical impossibility does not for a moment deter us from imagining it, either. In fact, we can imagine it without even working out whether it is possible or not to build one. Because we are using models from other things and superficially combining them, not troubling ourselves with “checking the math” that would be necessary to connect them. Just like imagining, or even convincing ourselves, that 2^45 + 3^45 = 4^45.

In a computer simulated universe, of course, we could have working light sabers, and sounds in space, and all manner of absurdly constructed worlds, but only because the elaborate physical machinery underlying the simulation connects all the logical and physical dots to make that happen. In other words, the logical possibility of all these things is dependent on being run as a simulation in a computer, whether a game console, a futuristic Matrix, or (as we usually settle for) the human brain. Take away that substructure, and many of these things are no longer physically or in some cases even logically possible. Thus being able to simulate something does not means its existence is possible outside the simulation. Being able to simulate it only proves that it is logically possible for it to exist in a sim; in other words, it is possible as a sim. But outside a sim, it could well be logically impossible. Just as Star Wars certainly is.

And this is where we get to the problem of disembodied minds. When we simulate things in the computer of our minds, we can indeed simulate light sabers without any of the elaborate technology that would actually be needed to make a real light saber, we can indeed simulate sounds in space, and impossible conjunctions of intelligence and stupidity (a common feature of fiction well mocked in Galaxy Quest: “What is this thing? I mean there’s no useful purpose for there to be a bunch of choppy, crushy things in the middle of a hallway!” “Relax, Gwen.” “No! I mean we shouldn’t have to do this! It makes no logical sense! Why is this here?!”). But we can only do that because we have a complex machine to do it with: our brains. So instead of the elaborate technology needed to make an actual light saber, we are using the elaborate technology of a brain to do all the same work. The logical and physical possibility of a light saber in our imagination is therefore dependent on a physical brain of staggering complexity.

For this reason, the mere fact that we can imagine something, that we can conceive of it, does not mean it is logically possible. Because it might only be logically possible inside a computer system simulating it (in this case, that being our brain). We can’t “conceive” of something apart from the machinery of our brain, so we can’t ever actually test the logical possibility of something outside our brain. We can only ever test the logical possibility of simulating something in a brain. And that’s a significant limitation we cannot overlook. We think we can imagine a god not dependent on a material brain, but in fact we can’t. We can only imagine a god dependent on a material brain: ours. The fact that “god sims” can only be run on a physical brain actually argues that god cannot exist outside of a physical framework to give rise to him. (Of course, I am assuming science has well nigh proven that minds do not exist but for complex physical brains: see Sense and Goodness without God III.6, pp. 135-60; The End of Christianity, pp. 298-302, 305-32; and my Argument from Mind-Brain Dysteleology.) So is God really conceivable outside of a complex simulation machine? Probably not.

Think about it: we know that a light saber in our brain is dependent on complex neural machinery to maintain its juxtaposition of properties, but that outside our brain that juxtaposition would require a vastly more complicated machinery (which in fact we know nothing about; and need not know anything about to simulate the device in our brains). So what reason do we have to believe God is any different? If you think about it, a light saber without any underlying machinery starts to look fairly inconceivable. And it may well be logically impossible. Because if it wasn’t, surely we would have seen countless examples by now of “property conjunctions” without the underlying machinery. Yet in fact, after trillions of dollars and billions of man hours of hard core science across four centuries, we have never discovered even one case. Instead, we have found, in billions upon billions of cases across every discipline and area of human experience, that nothing exists without that underlying machinery. Like Fermat’s impossible quadratic, this counts in the evidence column for God being just as impossible. All supernatural things, in fact. So clue number one is pretty strong.

Clue number two is the fact that mental things are actually structurally complex by definition. I made this point about minds earlier. What maintains the “structure” of God’s mind? Rainbows? Bare supernatural brute facts? What are those exactly? Because I actually can’t conceive of anything that would work. Again, that’s not a proof, but in the right context it can be evidence against. It seems obvious that structure requires actually existing things to hold that structure. If nothing exists holding it together, then by definition nothing is holding it together. It’s circular to argue that what’s holding it together is the disembodied mental concepts themselves. Concepts can’t think or act; so disembodied mental concepts can’t “do” things either. They can’t have physical relationships to each other. They can’t have structure. They can have the concept of structure, but again concepts can’t do things; and they can have structure when we simulate them in our brains, but that gets us right back to the point: that appears to be the only way they can ever actually exist.

This is popularly known as the Argument from Physical Minds. I’ve defended an empirical version of it before, but here I am making a logical argument from physical minds: my point is that a nonphysical mind appears to be logically impossible, and not merely non-existent. I cannot prove this. But as for Fermat’s Last Theorem, that proof may be too complex, and may never be discovered. That doesn’t mean I’m wrong. The consequence of this is that if the supernatural is logically impossible, then naturalism is necessarily true. Belief in the possibility of the supernatural is then merely a cognitive error (which psychological science has more or less confirmed, as Victor Stenger explains in The End of Christianity, p. 312, with refs. in n. 27, p. 416), akin to believing that Star Wars could really happen, or that 2^45 + 3^45 = 4^45.

Is that the case? I suspect it is.

Ex Nihilo Onus Merdae Fit

A common argument against atheism is that the Big Bang proves everything had a beginning (it does not in fact prove that, but bear with me here), therefore there was once nothing, and ex nihilo nihil fit, “from nothing, comes nothing.” However, that latter premise is demonstrably false. And that spells death for theism and marvelous glory for atheism. And I don’t even mean in the Lawrence Krauss A Universe from Nothing sense, since he doesn’t actually mean “nothing” when he talks about nothing (a point I’ll get back to in a moment). No, I mean, even granting the theist’s premise that if there was no God, then there was once absolutely nothing, and therefore there cannot have been a universe, therefore the fact that we are here entails God exists, because our existence would be literally impossible otherwise. I am saying that even granting that premise, all those “therefores” don’t actually follow. They are complete non sequiturs. In fact, I am not just saying that; I’m even saying that the exact opposite is true, that when we grant that premise (the theist’s own premise!), then a whole shitload of stuff will necessarily exist. Huwah? Yeah. And not a pejorative load of shit. An actual shitload.

I’ve been asked to explain this so many times lately (going all the way back to Mike Licona in our second debate) that I’ve decided to blog it so I can just point people here (that’s kind of the reason for everything I write, really).

I am an empiricist, which means I don’t truck with a priori reasoning. But there is one good use for the latter: to deduce from a hypothesis what would be the case if that hypothesis were true (and what the case if it were false); because then you can go look and see what you observe and thus determine how likely it is that that hypothesis is true (or false). This is the basic foundation of scientific method, the “hypothetico-deductive method” (which in Proving History I demonstrate is fundamentally Bayesian, but I won’t go on about that here). This is not actually a priori, because you still have to go looking around, and your conclusion is never absolutely certain but always some matter of probability. So here I am not saying there ever was nothing. There might well have always been something. Or quite a lot of things really. The argument that that is impossible, owing to confusions about infinite sets, is also bogus, and based on fundamental ignorance of logic and mathematics (as I’ve explained before).

So I am not actually conceding the premise that there was once absolutely nothing. I’m just analyzing that as a hypothesis, to see what it entails if it were true. So here goes…

Which ‘Nothing’ Is That Again?

First we must define “absolutely nothing.” There are actually many different kinds of nothing (John Barrow even wrote a book about it: The Book of Nothing). Krauss, for example, means by “nothing” a collapsed region of space-time governed by certain laws of quantum physics. But that’s not actually nothing. For one thing, you have space-time. That’s something. And you have “certain laws of quantum physics” (a minimal set of which he describes, and which, if it always existed, he shows would entail that a universe would arise spontaneously very much like ours, no God needed; which conclusion was also reached and demonstrated by Stephen Hawking in The Grand Design, and likewise by Victor Stenger in God: The Failed Hypothesis, pp. 132-33, with extensive support in The Fallacy of Fine Tuning and The Comprehensible Cosmos). That’s also something. Quite a few things, really. Now, Stenger has made a case (in The Comprehensible Cosmos) that those “few things” are in fact logically necessary if we presume no God exists (and thus no agency exists to decide the world should be one way rather than another); for example, if no agency exists to entail an objective reference frame or to alter the outcomes of random events, then the whole of Relativity Theory is logically entailed by default, and likewise all the laws of thermodynamics. It’s an interesting argument, but not one I will assume as proven here.

Really, my only task at present is to define what we must mean by absolutely nothing. This can only mean that nothing whatever exists except anything whose non-existence is logically impossible. That latter caveat is unavoidable for the obvious reason that if it is logically impossible for something not to exist, then there can’t have ever been a state of being where it did not exist. So if by “absolutely nothing” you mean even the non-existence of logically necessary things, then “absolutely nothing” is logically impossible, and thus there can’t ever have been “nothing” in that sense. So if that’s what theists mean by “if there was no God, then there was once absolutely nothing,” that not even logically necessary things existed, then their claim is self-refuting. We can then dismiss it out of hand. But if they allow that logically necessary things still exist even when there is otherwise nothing, then we have a “nothing exists” that is logically possible. There could have been such a state of being, of there once being nothing, in that sense.

Of course, theists will then want to introduce their ontological arguments at this point, which purport to prove that God is one of those things whose existence is logically necessary, but no such argument ever succeeds. They are all invalid or unsound (the clearest demonstration of this is to be found in Malcolm Murray’s most excellent desk reference for atheists, The Atheist’s Primer, pp. 55-73). And one could in principle pull a Victor Stenger here instead, and aim to prove that certain basic laws of physics are logically necessary. And such a task might even succeed.

But I’m not depending on any such proposal here. All I will assume is what is undeniably true: that all the fundamental propositions of logic and mathematics are necessarily true (for example, all valid and sound theorems and syllogisms are necessarily true, in the sense that, when given their premises, their conclusions cannot be false; but not in the sense that their premises are necessarily true, even if they might be), and therefore there can never have been a state of being in which they were false. For example, it can never have been the case that “if you form a polygon from only straight lines, on a flat plane, with only three sides, then the sum of the angles produced within that polygon will not equal 180 degrees.” More importantly, it can never have been the case that the basic laws of probability were false (such as complementarity, unity, and exclusivity), nor can the basic laws of logic have ever been false (as that would be logically impossible by definition; that is, to say that the laws of logic are false, is by definition to say that logically impossible things can exist, and therefore logically necessary things can in that case not exist after all…so much for God!).

One might object at this point by asking how the laws of logic can “exist” when nothing exists. There are two ways to answer that, one is to refer to the naturalist ontology of logic, whereby things like numbers and laws describe what always potentially exists, even when nothing actually exists (see my book Sense and Goodness without God III.5, pp. 119-34, esp. III.5.4-5, pp. 124-34), and when nothing actually exists, all potentials exist (because then nothing actually exists to prevent anything from potentially existing, which point I’ll revisit in a moment). But another is to simply refer back to the simple point that if the laws of logic don’t exist, then by definition that means logically impossible things can exist. Which is fine if you really want to entertain that as a hypothesis. Good luck with that (I don’t think you’ll get very far: Sense and Goodness without God II.2.2.7, pp. 42-43, and III.9.3, pp. 188-91). Meanwhile, I will simply take it as granted by all sane parties that logically impossible things can’t exist. Certainly, that is a premise most theists must accept. At least, if you can really get them to deny it, then you’ve pretty much gotten them to publicly confess to being crazy. And one hardly need continue arguing with a confessed lunatic.

Now, when nothing exists (except that which is logically necessary), then anything can happen (whose happening is logically possible). Because the only way to prevent something from happening, is to have some law or force or power or object or agency, in other words some actual thing, that prevents it. If you remove all obstacles, you allow all possibilities. This is a logically necessary truth. The only thing that is prevented, is the logically impossible. Because, as we have concluded so far, even when “nothing” exists, all logically necessary truths still exist. And here “exist” means only in the sense of being true; obviously the laws of logic aren’t made of aluminum-titanium alloy with a mass of twelve earths and located precisely one light year below galactic south; it is a fallacious prejudice to assume “existence” requires mass, substance, or discrete location, although perhaps it does require something.

For instance, I have argued that that which exists at no location or at no point in time, by definition exists never and nowhere, which is by definition not existing. So one might think that if nothing exists, no place or time exists, therefore logical truths cannot exist. However, since it is logically impossible for logical truths not to exist, if logical truths must exist at some point in spacetime, then it would follow that spacetime is logically necessary and therefore there can be no “absolute nothing” that lacks at least a singular point of spacetime (which is of course practically nothing). Thus logical necessity can prevent things from happening. But if that’s all there is, then everything else can happen, because nothing exists to prevent it.

And So the Baby Goes Out with the Bathwater…

This is why ex nihilo nihil fit is necessarily false. For that is a law. And a law is not nothing. A law is something. To say that “from nothing comes only nothing” is to say that some law of physics (like, say, the law of conservation of energy) exists to prevent nothing from generating anything else except more nothing. But if nothing exists, then that law of physics doesn’t exist. Since it is not logically necessary that nothing can only produce nothing, then when nothing exists except what is logically necessary, the law ex nihilo nihil fit doesn’t exist either. Therefore, that “absolute nothing” that once existed will not have been governed by such a law. It cannot have been. Because if it were, it would then not be nothing, but the inexplicable and arbitrary existence of something: a weird law of physics with no origin or agency. Thus it is a logical contradiction to say “there once was absolutely nothing, and that absolute nothing can only have produced nothing.”

From here on out it only gets worse for the theist. Not only will there have been nothing to prevent anything from happening, there won’t have been anything to make any one thing more likely than any other. For example, quantum mechanics entails that some things are more likely than other things; if whatever the fundamental structure is that causes quantum mechanics to work didn’t exist, then some things would not be more likely than other things. Everything would be as likely as anything else. Because the only way to make one thing more likely than something else, is for something to exist that makes the one thing more likely than the other. In some cases, logical necessity can do that. But not in every case. The number of universes that exist, for example. There is no logical necessity for there to be only one universe. Or any other specific number of them. And if nothing exists to decide how many there will be, all possible outcomes are equally likely. There being just one universe will be just as likely as there being seven of them, or a million of them, or any other number of them. And if we count all configurations, then smaller numbers actually become less probable than larger ones (as I’ll demonstrate shortly).

Getting Everything from Nothing

I draw out the consequences of this fact in The End of Christianity (ch. 12, “Neither Life Nor the Universe Appear Intelligently Designed,” note 20, pp. 408-09). I quote the relevant material here:

In our background knowledge b we have no knowledge of any law of physics that would prevent there being other universes (and no means of seeing if there are none), so the probability that there are is exactly what that probability would be if the number of universes that exist were selected at random. Of all the possible conditions that could obtain (no universe; just one universe; two universes; three; four; etc., all the way to infinitely many universes), that there would be only one universe is only one out of infinitely many alternatives. This entails it is effectively 100 percent certain an infinite multiverse exists because the probability of there being only one universe is then 1/INFINITY, which is [approximately] 0 percent. In fact, for any finite number n of universes, the probability of having only that many or less is n/INFINITY, which is still [approximately] 0 percent. If the probability of having any finite number of universes is always [approximately] 0 percent, then the probability that there is an infinite multiverse is [approximately] 100 percent. This further entails we have no need to explain why there is something rather than nothing: as then nothing (a state of exactly zero universes) also has a probability of 1/INFINITY, which is again [approximately] 0 percent. The probability that there will be something rather than nothing is therefore [approximately] 100 percent. This conclusion can only be averted if something were proved to exist that would change any of these probabilities, thereby making nothing (or only one thing) more likely than any other logical possibility. But we know of no such thing. Therefore, so far as we must conclude given what we actually know, there is an infinite multiverse, and there must necessarily be an infinite multiverse (both to a certainty of [approximately] 100 percent).

This is an epistemological argument (it does not claim to prove there is an infinite multiverse, but only that so far as we know there is; some future knowledge might change that conclusion). But if we grant the metaphysical premise “there was once absolutely nothing,” then this epistemological argument becomes a metaphysical argument: it is then logically necessarily the case that there is an infinite multiverse.

Therefore, if we grant the theist’s premise, that there was once absolutely nothing (no spacetime, no God, and no laws of physics, beyond those that may be logically necessary), it necessarily follows that there is an infinite multiverse (or to be more precise, the probability that there wouldn’t be is infinitely near to zero). From a simple demonstration of probability, it then follows that the universe we find ourselves in will also necessarily exist (or again to be precise, the probability that a universe essentially like ours wouldn’t exist is infinitely near to zero). Therefore, the theist’s own premise entails a godless universe will exist that looks exactly (in all relevant particulars) like the one we find ourselves in. Ooops.

Proving It

The formalization of the argument proceeds as follows:

  • P1: In the beginning, there was absolutely nothing.
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  • P2: If there was absolutely nothing, then (apart from logical necessity) nothing existed to prevent anything from happening or to make any one thing happening more likely than any other thing.
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  • C1: Therefore, in the beginning, nothing existed to prevent anything from happening or to make any one thing happening more likely than any other thing.
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  • P3: Of all the logically possible things that can happen when nothing exists to prevent them from happening, continuing to be nothing is one thing, one universe popping into existence is another thing, two universes popping into existence is yet another thing, and so on all the way to infinitely many universes popping into existence, and likewise for every cardinality of infinity, and every configuration of universes.
    -
  • C2: Therefore [given logical necessity], continuing to be nothing was no more likely than one universe popping into existence, which was no more likely than two universes popping into existence, which was no more likely than infinitely many universes popping into existence, which was no more likely than any other particular number or cardinality of universes popping into existence.
    -
  • P4: If each outcome (0 universes, 1 universe, 2 universes, etc. all the way to aleph-0 universes, aleph-1 universes, etc. [note that there is more than one infinity in this sequence]) is no more likely than the next, then the probability of any finite number of universes (including zero universes) or less having popped into existence is infinitely close to zero, and the probability of some infinite number of universes having popped into existence is infinitely close to one hundred percent.
    -
  • C3: Therefore, the probability of some infinite number of universes having popped into existence is infinitely close to one hundred percent.
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  • P5: If there are infinitely many universes, and our universe has a nonzero probability of existing (as by existing it proves it does, via cogito ergo sum), then the probability that our universe would exist is infinitely close to one hundred percent (because any nonzero probability approaches one hundred percent as the number of selections approaches infinity, via the infinite monkey theorem, similar to the law of large numbers).
    -
  • C4: Therefore, if in the beginning there was absolutely nothing, then the probability that our universe would exist is infinitely close to one hundred percent.

I’ve already shown that P1, once granted, entails P2. And P4 and P5 are logically necessary truths (they can only be false if the basic laws of logic and probability are false, which, as I said, is by definition logically impossible). And C1-4 are all logically necessary if P1-5 are true (given the following connotation of P3). So that leaves P3. There are two objections sometimes raised against it. The first is that it is incomplete; the second is that its demarcation of possibilities is arbitrary or contrary to set theory. [Another objection, that infinite probability distributions are impossible, is simply false.]

As to the first objection, (1) there are presumably things that can pop into existence besides universes; and (2) there are many different kinds of universes possible, so each number of universes would represent an infinitely divided fraction of possible combinations of that many universes.

As for (2), that makes no difference to the argument. As long as nothing existed to make any particular universe more likely than any other (and given P1 and P2, nothing did), then C2 as stated remains true on P3. For example, “zero universes” would be infinitely less probable than one universe if we counted each of infinitely many singular universes as being equally likely as any other outcome, but if that’s the case, then zero universes remains no more probable than one universe, as C2 states; and in consequence, P4 also remains true as stated. And likewise for every number of universes above that. Such considerations are therefore irrelevant.

As to (1), if we define “universe” as “any collection of actually existing things (whether it consists of just one thing or several) that is completely separated from other collections or in some way connected to other collections but entails a fundamentally different physics from them,” then P3 remains true, and so on down the line. Because then by definition nothing else can pop into existence but some universe or other. What then distinguishes one universe from another (thereby making two universes, instead of just one universe consisting of two combined collections) is a fundamental separation or a fundamental difference in its governing physics. In the latter case those universes won’t be physically separated, but in the unity of them both, one physics will govern one region and another physics will govern the other, making for two universes, even if, for instance, they are both just different parts of one combined region of spacetime. [You could still count this binary universe as one universe, but then you would have to count its twin as one universe, i.e. a universe otherwise identical but in which the relative positions of each distinguished region are swapped in the same space-time manifold, so you still get two universes, each as likely as the other.]

This leads to the second objection: that this demarcation is improper. Isn’t one “metaverse” with two different regions of governing physics more complex than one single universe with only one governing physics, and therefore isn’t the former much less probable than the latter? Actually, no. Because we are selecting at random from the set of all possible states of being. For example, one binary metaverse will be one state of being, while a singular universe will be another state of being. Therefore the probability of selecting one or the other is equal, because in each case there is only one possibility that can manifest, and the sum of those possibilities is two. And in fact, once we start counting configurations, the odds go in the other direction. Think of a bag of infinite marbles, inside each of which is a possible outcome (a number and configuration of universes). Will it be more likely that you will draw a “one universe” marble than a “two universe” marble? To the contrary, there are far more possible configurations of two universes, so in fact there are far more “two universe” marbles in that bag than “one universe” marbles. Therefore, choosing a “one universe” outcome is not more probable than choosing a “two universe” outcome (in fact it is on this reasoning a great deal less probable). Thus, P3 as stated remains true and (in conjunction with C1) entails C2 as stated.

Therefore C2 remains true, therefore C3 remains true, and there must then be an infinite multiverse, if in the beginning there existed absolutely nothing. And that means C4 remains true, and our universe, in effect, necessarily exists. This leaves the theist in a bind. If we start with their assumption that (if there was no God) there was once absolutely nothing, then we get our universe, no God needed. There can be no doubt that “absolutely nothing” is a vastly simpler entity than any God (much less their preferred God, who just happens to have all these convenient powers and properties, and not only that, but just happens to have them in infinite degree, which has to be the luckiest existential dice roll conceivable). So if a vastly simpler hypothesis explains all the evidence, we must prefer it (because it is necessarily vastly more probable: see Proving History, pp. 81, 104-06). In other words, Occam’s Razor slits God’s throat right good.

Winning the Whac-a-Mole Twostep

But maybe P1 is false. Certainly, the theist must retreat to insisting it is, now that we’ve just proven P1 explains the universe better than his God does. Well, then something has always existed (or just existed in the beginning for no reason, either way). They say it is God. We would say it is something decidedly ungodlike; namely, a very basic physics. In other words, the basic physical assumptions of Krauss, Hawking, or Stenger. Or anyone else. It doesn’t matter. As I’ve explained before, we don’t need to know which originating physics began it all, to know it’s far more probable that some such thing did than that a god did (upon request I even postulated ten different possibilities, all of which having a greater prior probability than a God). For Krauss, Hawking, and Stenger, it’s a simple quantum vacuum (whose properties are much more basic than God’s, and every single one of which has been scientifically proven to exist, unlike any of the unique properties of God, much less his existence), from which they can deduce the universe we observe. In fact, as I prove in The End of Christianity (ch. 12, “Neither Life Nor the Universe Appear Intelligently Designed”), the scientific evidence conclusively fits the deductive predictions of that hypothesis, in precisely the way it doesn’t fit the deductive predictions of any plausible God. So if something always existed for no reason, and our options are that this something was either God or a simple quantum vacuum, the evidence confirms it was the latter. And if that’s the case, then quantum vacuum it is.