Crank Bayesians: Swinburne & Unwin

Deepak Chopra uses “science” to spew bullshit. That does not discredit science. The Kalam Cosmological Argument uses “logic” to spew bullshit. That does not discredit logic. Politicians use “statistics” to spew bullshit. That does not discredit statistics. By exactly the same reasoning, cranks using Bayes’ Theorem to spew bullshit, does not discredit Bayes’ Theorem. It only discredits the cranks. Who are abusing science, logic, statistics, and Bayesian reasoning, with bullshit premises. And then capitalizing on the prestige of the technique they employ to extract bullshit from bullshit—hoping that no one notices it’s all just GIGO.

Last week I wrote What Is Bayes’ Theorem & How Do You Use It. This week, I’m writing about bullshit uses of Bayes’ Theorem. This time in particular, I mean attempts by liars or fools with Ph.D.s in their names to argue that “Bayes’ Theorem” proves God exists. The two most prominent examples of this are Stephen Unwin, in The Probability of God: A Simple Calculation That Proves the Ultimate Truth (2003), and Richard Swinburne, in The Existence of God (2nd ed. 2004). So let’s look at those.

Unwin calls himself a “recovering theoretical physicist.” He used to work in quantum gravity. Now he’s a risk analyst. Neither shows in his book. He concludes the probability that God exists is 67%. Seriously. There are many places where he goes wrong in getting there. But I won’t explore every single little problem. I’ll cut right to the chase of where he fundamentally goes wrong. Swinburne, with advanced degrees in philosophy and theology, concludes the probability is at least above 50%. He vaguely insists, chapter after chapter, that it must be much higher, but he doesn’t commit to any numbers. He just concludes it’s ‘surely much more’ than 50%.

Swinburne of course also argued “from the resurrection” that the probability God exists is much higher than 50%, in yet another book, The Resurrection of God Incarnate. Which is also filled with standard bogus Christian premises. He just translates his bogus premises into numerical notation. That doesn’t make them any less bogus. I already refute all Bayesian arguments that “Jesus was probably resurrected by God” with a correct Bayesian model in The Christian Delusion (pp. 291-315). I see no need to repeat any of that here. But if you check that out you’ll notice, Swinburne just repeats the usual false claims about the evidence, and builds his probabilities on those false claims. But false claims in, only gets you a false claim out.

So I’ll just address Swinburne’s Bayesian case for “the existence of God” being more likely than not (sans appeal to ancient dream cults and unsourced hagiographies). Which Unwin pretty much just dumbs down into an even more idiotic Bayesian case for the existence of God being twice as likely as not. First I’ll address the flaws in their assignment of prior probability; then the flaws in their assignment of consequent probabilities (the likelihoods). The lessons here will help inform anyone on how to use Bayesian reasoning properly.

Starting with Ridiculous Priors

All the usual fallacies are deployed by Unwin and Swinburne. False premises. Illogical steps of reasoning. But the fundamental scam Uwin and Swinburne both pull is the scam fundamental to all Christian apologetics: leaving stuff out. I discuss this already, and in relation to Bayesian reasoning, in Bayesian Counter-Apologetics. Which has also been fundamental to my critical series on Keller’s Reasons for God (which I’m about half the way through with). When you put the stuff back in, that they hide from their readers, their arguments end up with the opposite conclusion. Even using their own method.

Swinburne never says what his prior probability of God is, except that it is higher than all other possible explanations. Unwin starts with a prior probability of 0.50 (even odds). But that would only make sense if you start by disregarding all prior evidence of science and history; which requires you to put all that evidence back in on the other end. They don’t. And even then, you can only logically get to a 50/50 prior if you start with a definition of God that does not presuppose any theological assumptions about him—like that he’s good or evil; or all powerful and all knowing, or limited; or even a person or not. Unwin & Swinburne both fail to ever meet this condition, although they fail in different ways. In Swinburne’s case, he simply never shows that his theism has a higher prior than the simplest nontheistic alternative. He never even discusses any.

That makes their starting point already bogus. It would be bogus even if they were to do this using standard Aristotelian syllogistic logic. It doesn’t become more credible the moment they call it Bayesian. That’s just a fancy cover for what the rest of us call bullshit. Like “Creation Science” or “Compassionate Conservatism.” Prior probabilities can’t just be whatever you want them to be. They have to be justified. And not only that. You also have to account for the consequences of the way you build out your Bayesian model. Swinburne and Unwin violate both conditions.

Priors Must Be Conditioned

Usually we should be justifying our priors on our background knowledge. Not background beliefs. Background knowledge. (See my previous discussion of the Arbitrary Priors Fallacy.) If someone using Bayes’ Theorem ignores the b in P(h|b), their prior probability is logically invalid. Because P(h|b) means the probability of h is conditional on b. And b means “background knowledge.” And that means everything humans now know about the nature of the world, and people, and everything else. If you ignore everything we’ve learned about the world, you will not be deriving a valid prior. Theists try to get around this by using a “logical” prior, a prior that ignores everything humanity has learned about the world. That can only be valid if you put all that knowledge back in, later on in the equation (it goes then into e, as evidence to be explained). What Swinburne and Unwin do, is start with a logical prior, and then conveniently “forget” to put all the information they left out of b, back in as e.

When faced with some phenomenon we want to explain—like what causes lightning or genetic complexity—we look at what has actually turned out to be the explanation of everything else similar through all past time; and what has turned out to be false. We then can have a rough frequency estimate of how often it’s been “magic and ghosts” (of which gods are only a subset), and how often it’s something decidedly not like either. So far, after hundreds of years of millions of scientific investigations, nothing has ever turned out to be explained by magic or ghosts. Everything has turned out to be explained by mindless physical phenomena; especially countless things we used to claim were caused by magic or ghosts. So based on our background knowledge, “magic and ghosts” are literally the least likely explanation of anything. That’s not an opinion. That’s not a mere belief. That’s a material fact of a vast array of frequency data, accumulated by thousands of experts over hundreds of years. In other words, that is a clear fact of reality. Denying it is literally insane.

If we count up all the things in history we at some point couldn’t explain, or thought was explained by magic or ghosts, and then securely found out what the actual cause was (so that it is now approximately a universally accepted fact of science or history), how many of those things turned out to be magic or ghosts? If the answer is zero (and it is…and anyone who denies that, is literally insane), and the number of those things is in the millions (which have reached that degree of investigation, so that it is now a known fact of the world what causes them; not just a belief or speculation), then the prior probability the next thing you ask the cause of will have been caused by magic or ghosts is logically necessarily millions to one against. And if the number of such things is in the billions, it’s billions to one against; if in the billions of trillions, then billions of trillions to one against. There is no rational escape from this consequence.

And gods, as a sub-category of magical ghosts, must have even smaller priors than that. This is also a logically necessary fact. Since the set of all “magical and ghostly causes” includes that sub-category of a very specific kind of magical ghost, the prior probability that some magical or ghostly cause is to credit is necessarily greater than the prior probability that a specific magical or ghostly cause is to credit. Claiming otherwise is well known as the conjunction fallacy. So, the claim that “either a mindless but magical Tao force caused the universe or a god caused the universe” must always be more probable than the claim that “a god caused the universe.” This becomes relevant later when we get to demarcating which god you mean (something Swinburne and Unwin violate every principle of logic doing).

But no one who ever argues for God with Bayes’ Theorem ever conditions their prior probability of God on the background database of all human knowledge, of everything we’ve learned usually ends up being the explanation of things. And that’s simply invalid on Bayes’ Theorem. Full stop. The only valid way to “escape” this is to start by positing a condition of hypothetical ignorance: assuming you don’t know all of human history and all its most secure knowledge of science and history. But even that requires you to put that missing knowledge back in later (a fact I’ll get to below).

It also requires you to obey logic in demarcating your prior probability space…

Logical Priors Have to Actually Be Logical

Such a logical prior for “god did it” can never be 0.50, as Unwin claims. Because once you start talking about an increasingly more specific God, your prior has to drop. Unwin shows no sign of understanding this; Swinburne realizes it, but attempts to end-round it (see next section). By Unwin’s method, though, one could say the probability that Thomas Jefferson’s non-interventionist God exists is 50/50 and the probability that the Vatican’s Pope-endorsing God exists is 50/50 and the probability the Vatican-condemning Allah of Islam exists is 50/50 and so on. Which is logically impossible. I hope I don’t have to explain why. The mathematical impossibility should be obvious.

Unwin makes a point of saying your theory in Bayes has to be specific enough to be meaningful, which is true, but he never gives a clear definition of what he means by God, other than that he means what the “major faiths” mean. Why he privileges the most popular faiths of just a recent fraction of human history, he never says; and he never formally spells out what properties that God is supposed to have. So he never even specifies a hypothesis to test. And there is no way to get a valid output from Bayes’ Theorem if you can’t even articulate the hypothesis you are testing with it. When Unwin says anything at all about specifying what he means by God, he makes a decision that is completely illogical on Bayesian reasoning: he in effect says it has to be a loving, compassionate, personal God who influences the world and lets us live forever in an afterlife—because that’s what’s popular today.

That is way too specific a god to have a 50/50 prior. The probability that “either a compassionate god did it or an uncompassionate god did it” must be higher than the probability that “a compassionate god did it.” And if you are demarcating logically, which by definition excludes any appeal to “background knowledge,” you have no way to argue that “a compassionate god” is more likely than the reverse. Logically, “absent all knowledge,” it’s as likely to be the one as the other. So if the “uninformed” prior probability of a supernatural cause vs. a natural cause is 50/50 (the only logically credible place to start), then the probability that that supernatural cause is a god vs. some other magic or ghost has to be 50/50, which reduces your “uninformed” prior from 0.5 now to 0.25 (0.5 x 0.5 = 0.25). Half the prior Unwin starts with. And that’s just for any god whatever. (See my discussion of reaching disciplined priors in the God debate in The End of Christianity, pp. 279-84, 404-07.)

But Unwin isn’t talking about “just any god whatever.” He adds several other properties. God, he means, is compassionate. Well, when starting uninformed as Unwin wants, the odds of that are 50/50. So now we are at a prior of 0.125 (0.5 x 0.5 x 0.5 = 0.125). And God has to be a world-influencer (and not some sit-back or dead or lost or powerless god). Which is also 50/50 (again, lacking any prior evidence either way). So now we are at a prior probability of 0.0625. We’re down to 6%. And we haven’t even considered any evidence yet. Like all that vast body of background knowledge I just mentioned, in which we’ve never found magic or ghosts of any kind (much less gods) causing anything. It only gets worse if you want to add yet more attributes to your god.

Unwin at least doesn’t try to insist God is perfectly all the things he is supposed to be (the most compassionate it’s possible to be; the most powerful it’s possible to be; the most knowing it’s possible to be; and so on). Because that screws you over even more (see below, where I get to Swinburne). Specifying a God that is literally the most complex being conceivable, will give you a prior probability that is literally the lowest probability conceivable. Infinite complexity literally entails an infinitesimal prior probability. But even if you pull an Unwin, and allow feebler, more fallible gods to be included in the possibilities covered by your hypothesis, you still can’t start with anything above 0.25 for an uninformed prior.

And when you add the attributes Unwin at least does specify, it can’t be even as high as that. You’ll be lucky if you can break even 10%. And then when you put the evidence back in, of what usually ends up explaining things we don’t understand, that “uninformed” prior drops to the point of effectively vanishing. Informed priors for gods are always absurdly low. Because that’s how the facts of history turned out. Had they turned out differently—if we lived in the world of Moses, with parted seas and magical columns of fire and voices from the sky—then we might end up with a more respectable prior probability for there being a god. But we don’t live in that world.

This is why trying this trick of starting with an uninformed prior is usually a scam. They aren’t doing it in any logically valid way. And they shouldn’t even be doing it. We have plenty of background knowledge to demarcate an informed prior from, for any “magic or ghosts” hypothesis. It’s certainly well below trillions to one against. We know it is. Because we have the data. And when we have plenty of data to give us an informed prior, if someone chooses to start arguing with an uninformed prior instead, keep your eye on your wallet. Because there’s a con on.

Swinburne’s Absurdly Complex Simplicity

Unlike Unwin, Swinburne hyper-specifies his God hypothesis, to be the most specific and most complex being conceivable. He then pretends this doesn’t leave him with the lowest prior probability conceivable. He instead claims his hypothesis is the simplest of all possible hypotheses. He offers no logically valid arguments for that conclusion. He engages in arduous handwaving about God not having a body and therefore being simple, and a bunch of other nonsense like that. But none of it has any logical validity. He never reaches any conclusion of simplicity by any valid or sound syllogism. And note that none of this uses Bayesian reasoning. So he is fabricating a bullshit premise with a ton of bullshit arguments, before even getting to “inputting” that Frankenstein’s monster of bullshit into a Bayesian equation. And that’s why his using Bayes is just a con. It’s GIGO. All the way down.

When asking about the probability of “getting one thing rather than another,” and you are choosing to ignore actual evidence of what we usually get, then you have to use a definition of complexity from information theory, exactly as argued by creationists William Dembski and Michael Behe. One of the only things they’ve ever been right about. Because underlying probability is permutation theory. And permutation theory is just another aspect of information theory. Prior probability in the pure logical space of possibilities (again, that means, absent appeal to background knowledge) is a function of the complexity of the informational structure of a thing, formally called the Kolmogorov Complexity, but otherwise known as its Descriptive Complexity: how complex the shortest possible description of a thing is, is inversely proportional to how much of the total prior probability space it occupies. This becomes problematic with complicated propositions, but that means trying to start with uninformed priors built solely out of their information content is problematic. So anyone who wants to use that method, has to resolve those problems; Swinburne doesn’t.

But whatever method you use to logically demarcate the prior probability space, it remains the case that the more specific the thing you propose, the more improbable it is on prior considerations alone. What material it is made of is irrelevant. Swinburne’s Medieval claptrap about bodiless simplicity is 100% Grade A bullshit. It has no logical effect on an uninformed prior. And we already saw an informed prior doesn’t get a prior for God any bigger than an atom on a flea’s ass.

As I said before, the probability of a specific god, must be included in (and thus lower than) the probability of just “any” god. And if you pick a god out of a hat from among all logically possible gods, the number of gods you can pick that are flawed—not perfectly compassionate nor all powerful or omniscient and so on—is vastly greater than the number of gods that are perfect on every dimension you care to require. And in pure logical space—again, that means, absent the ability to appeal to any evidence yet—every possible god is equally probable (and when you start putting evidence in, your priors for gods only get lower). So the probability of just “getting” a perfect god at random, prior to informing yourself with background knowledge of what we usually get, is infinitesimal (and when informing yourself with background knowledge of what we usually get, we know we never get this). So the prior probability of that absurdity is smaller than literally any other god conceivable. So it’s actually contrary to the formal logic of Bayesian reasoning to argue a “perfect” God logically occupies even half the probability space of all possible gods—much less all of it!

Swinburne’s Bayesian argument is thus pseudologic from start to finish. It doesn’t even make sense.

Walk it through, and see what I mean.

Swinburne starts with God being a person. Yet already a person is more complex than, say, a single quantum particle. Think about it. We could propose that a single quantum particle once existed, with only a single property: that by having no stability it will inevitably explode into a completely random multiverse—which by virtue of that fact alone, would inevitably include our universe, among countless others wholly disordered and uninhabited. Random chance automatically does this, once you get enough ‘random stuff’ (see The God Impossible); and assigning a single dimensionless particle the single property of randomly exploding into an infinite amount of completely random stuff, is pretty darned simple. Now think about how much you would have to specify, to make that particle a person. You’d have to add countless properties, of a highly specific kind. That’s always going to be vastly more complex than a mindless particle with one or two totally simple physical properties.

Now walk through every other property the same way.

Omniscience? That is an extremely vast and specific array of structure. It doesn’t matter if the structure isn’t physical. It’s logically possible for a bodiless mind to have a small amount of knowledge. Or to have a bunch of incorrect knowledge. There is only one way for a mind to have all and only correct knowledge; yet countlessly more ways for a bodiless mind to have incorrect knowledge and only a random selection of knowledge. Thus, of all the bodiless persons that are logically possible, Swinburne is proposing literally the rarest and most complex of them all. Obviously, a mind with a little knowledge and not all of it correct, is simpler than a mind with all knowledge and all of it correct. So it is impossible to claim an omniscient mind is “the simplest kind of person that there could be.”

Likewise for omnipotence and omnibenevolence. Swinburne says totally crazy shit like that a being with all possible powers is simpler than a being of only a few powers “in just the same way” that “the hypothesis that some particle has zero mass, or infinite velocity, is simpler than the hypothesis that it has” a specific mass or velocity. But he never constructs any formally valid argument here. Adding powers, increases complexity, in just the same way adding mass increases a particle’s complexity. Infinite velocity is a single power. Omnipotence is all powers. Therefore omnipotence is never analogous to a particle of zero mass or infinite velocity. It is, literally, the exact opposite of that.

Swinburne tries to prop up this bucket of crazy by arguing that “a finite limitation cries out for an explanation of why there is just that particular limit, in a way that limitlessness does not.” But that’s not the case when you are picking gods at random out of a hat. If gods have no cause, then their limitations will have no cause either. By Swinburne’s own definition of gods. And even if we had to posit causes for why a god had some powers and not others, you need more explanations for why a god would have all powers, rather than only a few of them. It’s already pretty far from sense to propose that any powers can be possessed without a body, that any knowledge can be possessed without a physical structure to keep connections of information correctly intact. But to propose a magical ghost has all of everything, requires one of the most remarkable explanations conceivable.

In fact, Swinburne’s appeal to “you have to explain why it is limited to that” is self-defeating. If there is nothing in place to limit God, there is nothing in place to maintain his knowledge or powers as always perfect and complete and correct. Because that, too, is a limitation. In other words, in the complete absence of anything holding him in exactly that one form, he would dissolve into a perpetually changing random chaos of beliefs and abilities. But what incredibly complex thing must we posit that not only can always hold God together in exactly that one perfect and complete and correct structure, but also actually knows what a perfect and complete and correct structure is, so as to hold him only in that form and no other? Is there a meta-God who knows what all correct knowledge is, and what all the available powers are, and thus that meta-God holds God’s mind-space together in that one correct and complete way? But then, what holds that meta-God’s knowledge in place? Like the proverbial turtles…is it gods all the way down?

It gets worse with omnibenevolence. If God being bodiless makes him infinitely everything, he’d have to be infinitely evil, too. Or infinitely indifferent. Or infinitely lustful. Or whatever crazy thing you can think of. To specify him as only maximized on a single dimension like “compassion” is getting so hyper-specific, that the probability space has to include many other logical possibilities to the contrary. And therefore the entire logical space occupied by “all possible gods” cannot be fully or even half occupied by “infinitely compassionate” gods. You have to get hyper-specific to posit such a thing. And we are hell and gone now from the actual simplicity of a single mindless quantum particle with the single property of having no other power but inevitably exploding into an infinite collection of completely random stuff.

So, no, Swinburne’s god is not the simplest god imaginable. Nor the simplest thing imaginable. There is no disciplined logical argument to that conclusion anywhere in his book. And again, we haven’t even gotten to his using Bayes’ Theorem at this point. So we have from the start, illogical premises pulled out of his ass, based on no evidence or valid logic, and defended instead with weird and illogical fancies. So when he gets to “inputting” them into Bayes, we are already in crazy land. Not anywhere near reality-based reasoning.

It’s only worse that Swinburne’s hyper-specific God is actually maximally the worst at explaining observations; for example, the observed horrors and inequities in the world are far more expected on a non-compassionate or non-omnipotent god (if its explicable on any god hypothesis at all). Which means his God is the least credible explanation of the world we actually find ourselves in, even if we wanted to appeal to gods at all to explain it. So why would he even want to propose a thesis that actually performs maximally poorly in explaining observations? Oh, right. He’s a delusional Godist. He needs his weirdly specific God to exist so he can live forever. Evidence be damned. Never mind that by his own reasoning, an evil god is a better explanation than his.

So an honest use of Bayes’ Theorem doesn’t help him. Just as an honest use of science and logic won’t help him. That’s why Swinburne, like all theists, must abuse science and logic, and thus Bayes’ Theorem, to rationalize their irrational delusions.

Cherry Picking for God

That’s how they invent a bogus prior. They avoid starting with an informed prior. Because they know an honest, informed prior for god-explanations is virtually zero. Because every time we’ve ever gotten to find out, nothing previously unexplained or explained by gods has ever turned out to be explained by gods. And we’re going on millions and trillions of such things by now. Theists can’t accept reality. They have to avoid reality. So they have to avoid an informed prior. So they resort to the tactic of starting with an uninformed prior. But then, when they do that, they come up with logically impossible demarcations of the prior probability space. And then never put the information back in that they left out.

Here is what an honest Bayesian procedure would look like:

Starting at a hypothetical uninformed state (no background evidence; but for a priori facts, like math & logic), the prior probability that the cause of any as-yet unexplained thing is supernatural (rather than natural) is 50/50. That the cause is a god (and not some impersonal supernatural force), is at best 50/50. Leaving us with at best a prior probability of 0.25 (1 in 4; making the odds 3 to 1 against). And even that is too high. Because persons are way more complex than simple mindless forces. But let’s assume we don’t know that. We still at this point only have “a disembodied supernatural person with some sort of intelligence, intentions, and powers,” and not an omni- god of any kind, nor are we assuming anything about how kind this person is, or anything else about their plans. Remember, we are supposed to be pretending we have no information yet—so we don’t have any reason to prefer an omni-god to any other, or a kind god to any other, or anything else.

Okay. So trying to start with an uninformed prior we get a dubious 0.25 prior at best. But now we have to put all the information back in that we left out. Millions and billions of instances of finding out what really causes things, have never turned up a god causing any of them, or any supernatural cause whatever. The odds that that is what we’d find, over and over again, after all this time, if there are supernatural causes and magical ghosts causing things, is millions or billions to one against (or worse), which works out to a decimal probability of “at most” 0.000001. Meanwhile, the probability that this is what we’d find, and continually over all this time and after all that looking, if there are no supernatural causes (gods or otherwise) is fully 100%, which in decimal is simply 1. The likelihood ratio is therefore less than a million to one against any conceivable god hypothesis.

Put that evidence back in, therefore, and we get 1/3 x 1/1,000,000 = three million to one against. Our updated prior is now millions to one against. Right where we would have started, had we not played this game of starting with an uninformed prior and just started with an informed prior like any honest person would do. There is no escaping the consequences of the evidence. Take the evidence out, to avoid a place you don’t like, and when you put it back in, you end up in the same place you didn’t like. And really, honest Bayesians don’t play this game (except rhetorically, to argue a fortiori: see Proving History, index, s.v. “a fortiori“). They start with informed priors. And informed priors don’t get you anything substantially above zero for gods as the explanation of anything.

This is how all Christian apologetics works. They cherry pick what evidence to include in their logical formulas, and what evidence to leave out. But just as with any other logical formula, if you leave evidence out of your Bayesian model, it will not generate a valid result. And the biggest bulk of evidence Unwin & Swinburne leave out, is all past knowledge of what usually turns out to explain things, all the things we once didn’t understand or blamed gods for, which we have since discovered the truth of. Everything else (all the things we still haven’t conclusively discovered the causes of, because we currently lack access to the means to find out) is nondeterminative. It could be any explanation; and the odds of which, are decided by the frequency of what’s turned out to be the case when we did have access to the means to find out.

And lest you think you can pull a Cartesian Demon on us and say “but God prevents us finding out he causes anything,” note that that means God doesn’t want you to know he caused anything. Because he is trying to deceive you into thinking he didn’t. So for all we know, he didn’t. Because then, on your own silly theory, things he did cause look exactly like things he didn’t cause. So you can never know he causes anything. Saying God wanted it that way, doesn’t change the fact that you can never claim to know God causes anything. So this doesn’t get you evidence for God. Worse, positing God has this very hyper-specific and bizarre motive to make the evidence, all the evidence, look exactly like there is no God, makes God even more complicated, and therefore even more unlikely. Like all Cartesian Demons, which are the least likely explanation of anything. No evidence. And an even more microscopic prior. That kind of God is never going to be credible. Any more than “we are in The Matrix” is credible. Indeed, those two hypotheses (Cartesian Demon God and The Matrix) look identical in all present observation. You can’t tell them apart.

So “explaining away” the fact that all the evidence looks exactly like there is no God, does not get you evidence for God. It’s just admitting there is no evidence for God.

The rest of Unwin & Swinburne’s cases just repeat this same scam. It’s all just a standard Cherry Picking Fallacy. That they put that fallacy in Bayesian notation, does not change the fact that it’s a fallacy. The conclusion is still invalid. Whether reached logically or mathematically, it doesn’t matter. A fallacious argument, is a fallacious argument.

Unwin’s Cherrypicks

Unwin claims a total likelihood ratio of 2 to 3 in favor of God, for six items of evidence. Giving him final odds of 2 to 3 in favor of God. He leaves out all other evidence. Which is mistake number one. Even besides what I just showed (regarding the vastly well-documented background frequency of god-explanations turning out to be true), you can see what happens when you put all the evidence he leaves out, back in, by reading my article on Bayesian Counter-Apologetics. Unwin also generates absurd likelihoods for the six items of evidence he cherry picks. So he errs both by omitting data, and by bullshitting about the data he includes.

Unwin lists six items of evidence to consider for and against his hypothesis, which in his own words are:

  • The recognition of goodness.
  • The existence of moral evil.
  • The existence of natural evil.
  • Intra-natural miracles.
  • Extra-natural miracles.
  • Religious experiences.

He assigns likelihood ratios to these as follows:

  • Our ability to recognize goodness is 10 to 1 more likely if God exists (10/1).
  • The existence of moral (human) evil is half as likely if God exists (1/2).
  • The existence of natural (nonhuman) evil is a tenth as likely if God exists (1/10).
  • Intra-natural miracles (lucky outcomes) are twice as likely if God exists (2/1).
  • Extra-natural miracles (being reported) are equally likely if God exists or not (1/1).
  • Religious experiences are twice as likely if God exists (2/1).

He then multiplies these likelihood ratios together to get his master likelihood ratio of 10/1 x 1/2 x 1/10 x 2/1 x 1/1 x 2/1 = 40/20 = 4/2 = 2/1 = 2 to 1 in favor, which is 67%. Since he started with a bogus prior of even odds, which is 1/1, his final calculation remains at a 67% chance there is a God. Total bullshit.

We’ve already seen why it’s bullshit at the level of his priors. It is not “even odds” that something as-yet-unexplained will be explained by gods. Gods in fact have proven to be the least likely explanation of anything. And we’ve already seen what happens when you put that evidence back in, which he left out. Just on that alone, we’d have to add 1/1,000,000 to his math, which would dump the odds of God down to half a million to one against even on his own model. And that’s already way too high, because “million to one against on current background knowledge” is way too low. It’s actually somewhere far lower than that.

But it’s worse when we add in all the evidence.

Unwin left out: that the lethality of the cosmos is highly improbable on any god hypothesis; that all apparent nonhuman design in the universe looks much more like it was mindlessly rather than mindfully caused, and is thus also highly improbable on any god hypothesis; that our dependence on complex brains for thought and memory is highly improbable on any god hypothesis; that the deeply flawed engineering of our own capacity to reason is highly improbable on any god hypothesis; that the vast historical and cultural inconsistency in religious experiences is highly improbable on any god hypothesis (contrary to what Unwin says); and that all religions have progressed and evolved culturally and not presciently, accurately, or morally, showing no divine guidance for hundreds or even thousands of years, is highly improbable on any god hypothesis tested by Unwin or Swinburne. These are each tens if not thousands of times more likely if there is no such god. But even if we imagine each as only twice as likely without a god, that’s 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/64 against. So now we are 1/64 x 1/500,000 = 32 million to one against, even on Unwin’s own model!

But adding in the evidence he left out isn’t the only way an honest Bayesian has to correct his math. Because even what Unwin included, he implausibly scores. Indeed, his result is entirely dependent on his highly ridiculous over-scoring of a single piece of cherry-picked evidence: human recognition of goodness. He claims that’s ten times more likely if a God existed. But he gets this absurd result, by again ignoring and leaving out almost all the relevant evidence in the matter. That morality is an evolved human construct that has continually changed over time is highly improbable on any god hypothesis; as is the fact that our current moral understanding has been solely the product of our own experimentation over millennia, and was never the revealed moral code in any holy text, ever, in the entire history of humanity.

To the contrary of Unwin, that we wouldn’t believe (nor ever be told, by any god) that slavery (Leviticus 25:44-46) and the subordination of women (1 Timothy 2:11-15) were immoral, for thousands of years, and had to figure it out ourselves from our rudimentary animal empathy (a naturally evolved trait in all social animals), and even fight bloody wars to convince our peers, so that in fact we’ve only admitted as a species that those were immoral for barely more than a hundred years—despite living in civilizations for thousands of years, and having existed as a species for hundreds of thousands of years more—is extraordinarily improbable if our “sense of goodness” came from a god. That’s at least ten times less likely on Unwin’s god hypothesis; not the other way around. Which now gets us 3.2 billion to one against the existence of Unwin’s god (since his 10/1 in favor on this item of evidence reverses to 1/10 against, increasing the odds against by a factor of 10 x 10 = 100, and 32 million x 100 is 3200 million, which is 3.2 billion).

In just the same way, Unwin over-scores religious experiences as more likely if his God exists, when in fact the inconsistency of them across all time, cults, and cultures is not twice as likely if Unwin’s God exists; it’s at best twice as likely if he doesn’t. And that’s being absurdly generous to his hypothesis. Any kind of compassionate, capable God would not allow that. Nor would he produce it. So we can rule out religious experiences as coming from any such God. In fact, that they come at all, in such inconsistent ways obviously entirely driven by the cultural context in which they arise, is well nigh impossible if Unwin’s God existed. But it’s exactly what we expect if there is no god. So we have to take away his 2/1 in favor here, and put in its place at least a 1/2 against (and the latter I already did above), which now gets us 6.4 billion to one against (since also taking away the 2/1 cuts the odds in half, from 3.2mil to 1 against to 6.4mil to 1 against). And again, that’s even being extremely generous to Unwin’s hypothesis.

Unwin also over-scores natural luck. In fact the randomness of who gets lucky and when is highly improbable on any god hypothesis. It’s not at all what we’d expect; especially on the Unwin-hypothesis, which entails a compassionate god. It is, however, exactly what we expect if there is no God. So we should reverse that score, too. He claims it’s 2 to 1; in fact, it can’t even possibly be 1 to 2 at most. So the odds must drop by another factor of four (because replacing a factor of 2 in favor with a factor of 2 against, cuts the odds by a factor of 4). We are now, on Unwin’s own model, at 12.8 billion to 1 against his God existing. Just by putting back in, the evidence he left out. Again.

Note how Unwin ignores statistical reality here (that many good people get screwed by bad luck, and many bad people get lucky) and appeals to his own anecdotal experience that he usually gets what he wants, therefore God is helping him. Standard superstitious thinking. So Unwin is actually enumerating his irrational superstitious thinking into his equation. So his inputs into the Bayesian equation explain why he has a false belief in God. But since we know his inputs are irrational, when we correct them, the output starts to align with reality. And the reality isn’t what Unwin thinks. Because of his delusional superstitious mind.

Even the “meaning of life” question is evidence against the existence of any god. The bizarre fact that we are mortal is so inexplicable and unexpected on any compassionate god hypothesis, that the Jews had to invent a wildly absurd story about magic fruit and talking snakes and curses of God just to explain it. So the fact that we are mortal, combined with the fact that throughout history we have always invented our own meaning for life, and always different people have valued different things about it, is exactly what we expect if there is no god. Whereas, excuses aside, it’s not all all what we expect if there is anything like Unwin’s god. And excuses only make God more improbable. Because you have no evidence for those excuses being true, so their improbability commutes to God’s (e.g. if an excuse is only 50% likely to be true, then God’s prior probability must be halved; and so on again, for every excuse). That these things would be the case, are surely well more than twice as likely if God doesn’t exist than if he did. Which now leaves us with 25.6 billion to 1.

So here we are. Well above twenty billion to one against the existence of Unwin’s God. Even using his model. And even using absurdly generous inputs.

See what happens when you use Bayes’ Theorem honestly?

It’s never what Christian apologists want.

Swinburne’s Cherrypicks

Swinburne lists as evidence, which he claims is “more expected” on his God hypothesis (than on any godless hypothesis), the following five items (in his own words):

  • The existence of the universe & its conformity to order.
  • The existence of animals & humans with moral awareness.
  • Humans having great opportunities for cooperation in acquiring knowledge & moulding the universe.
  • The pattern of history & the existence of some evidence of miracles.
  • The occurrence of religious experiences.

Swinburne admits “the existence of morality” is not more likely if a god exists than if one doesn’t and therefore “is not” evidence for God. But conversely, he doesn’t count “divine hiddenness” as evidence against his god—for no logically valid reason. And he dismisses all the evidence of evil against the existence of a perfectly good God with the supposition that “a perfectly good God would allow it to occur only if he also provided compensatory life and death” (i.e. an afterlife prospect), although he honestly admits “the fact that evil” thus “required additional hypotheses to be added to the hypothesis of theism” in order “to save it from disconfirmation meant that the evil” still “lowered the probability of theism as such.” He suggests the odds are maybe 3 to 1 against this being the case. The only concession he makes against theism. Then, without stating any numbers, he claims that all the evidence he lists that favors theism, favors it enough to overcome that factor of 3 to 1 against. He never presents any disciplined calculation demonstrating that.

Swinburne’s math itself is largely bogus. With no numbers being stated for hardly anything ever, he never generates any actual result with Bayes’ Theorem. The only number he gives, is 3 to 1 odds against his hypothesis, and that’s ridiculous. The scale of horrors and injustices that are allowed and possible in this world is so vast, that the probability any kind person who could stop or dissuade it would fail to do so, is billions to one against. We know this, because we have had billions of kind people who would have done so if they could—and we know this, because when they could, they did. That’s how we know they were kind people. So Swinburne’s numbers are absurd. They are completely uninformed by real data in the real world about how kind beings actually behave. And yet, his 3 to 1 against, he never answers with any ratio in favor, he just handwaves an insistence that it surely must be overcome by the five items of evidence he lists as favoring god.

But those five items are bogus. His scoring of them is bogus. And he leaves out all the evidence against theism that I just enumerated Unwin also forgot to include. So his results are fake. Swinburne has rigged the equation to get his desired result, by rigging the inputs to be contrary to reality. But when your premises are contrary to reality, so will your conclusion be.

We can show this with a simple test of comparative probability. Swinburne is fabricating a hypothesis out of thin air (his weirdo perfecto God thing). So we get to do that, too. I’ll again fabricate out of the same thin air, a single postulate: that in the beginning there was a single dimensionless quantum particle with a single property, that of exploding into an infinite collection of completely random stuff. Just 100% entirely random. No intelligence. No design. No order. No complex properties of personhood. No other powers or attributes. Just that one thing.

From that postulate, it follows with deductive certainty that our universe would exist, in every single detail Swinburne lists. In other words, on that theory, all the evidence he lists is 100% expected. Which means that evidence cannot be more likely on his God hypothesis. And my postulate is vastly simpler than his. And it correlates with what we have found to cause everything else (simple, mindless physics), whereas his “magic & ghosts” explanation doesn’t (as I explained already). So on both counts my postulate logically necessarily has a vastly higher prior probability. It therefore logically necessarily has a vastly higher posterior probability. Swinburne is cooked. All by something I just made up.

The fact of the matter is, the “existence of the universe & its conformity to order” is 100% expected without a god. As there is zero evidence and zero logical foundation for assuming “not existing” is the natural state of things; plenty of causes of there being something are available that are far simpler than his arbitrary magical concoction; and the arbitrary uncaused existence of Swinburne’s God is no more likely than the arbitrary uncaused existence of any other first cause, like the one I just postulated. In fact, it starts out far more likely, being vastly simpler, and far more in line with all prior discovery of what kinds of causes even exist. And that’s even assuming there was a first cause. Which there is zero evidence and zero logical foundation for assuming in the first place. So his “cosmological” evidence is bullshit. In fact, when we put all the cosmological evidence back in that he leaves out, we get exactly the opposite result: his God is the worst explanation of what we actually observe to be the case.

Likewise, “the existence” of animals and humans who through natural selection evolved neural wiring for empathy and social cooperation is not more likely on his God hypothesis. Thus “the existence of animals & humans with moral awareness” is not evidence for his God at all. It’s 100% expected on my postulate; as it is 100% expected as one of many inevitable outcomes of natural selection over billions of years. Meanwhile, the actual evidence of how we experimented with and thus invented morality over thousands of years makes no sense on the postulate of his God, but is exactly what we expect if no gods exist. Just as I explained for Unwin above.

And there is nothing “providential” in evolution eventually kicking up a neurology capable of acquiring abstract knowledge. Given billions of years, across trillions of galaxies, such an outcome is inevitable, without any gods. In fact, the defects in our ability “in acquiring knowledge and moulding the universe” are completely inexplicable on Swinburne’s hypothesis, but exactly what we expect if that ability came from mindless natural selection, and not compassionately intended and omnisciently capable design. Nor is there anything providential in “the pattern of history” or “the existence of some evidence of miracles,” as both are 100% expected without any gods involved. To the contrary, the pattern of miracles is contrary to what we should expect on Swinburne’s hypothesis. As is the pattern of history. Especially the evidence of religious experience, which is entirely inexplicable on his theory; but 100% expected on ours.

Likewise the way the universe is organized, which is actually extremely hostile to life, not convenient for it; and wholly inevitable for any godless universe that would ever be observed, but completely useless to any compassionate and capable engineer. Likewise our otherwise inexplicable dependence on physical brains. Likewise the absence of any coherent pattern of “miraculous luck” and the horribly poor state of evidence for any miracle at all. Likewise our very mortality and random cultural and historical variation in what meaning we find in life. Likewise the complete absence of any evidence of anything ever being caused by any “magic or ghosts” explanation at all, despite centuries of ardent, skilled searching.

In the end, put all that back in, all the evidence Swinburne left out, and the conclusion reverses. Nothing is more explicable on his theory than on ours. And tons of things are far more likely on our theory than on his. His likelihood ratios are simply contrary to reality. And demonstrably so. That’s all one need ever say on the matter. Bullshit in, bullshit out.


Both Unwin and Swinburne start with demonstrably illogical and completely uninformed priors. No use of Bayes’ Theorem is valid that starts that way. Informed priors, get completely different results. And both Unwin and Swinburne input absurdly incorrect likelihoods for the items of evidence they do include; and then exclude tons of evidence that tells against their conclusion. Consequently, their use of Bayes’ Theorem to prove God exists is total bullshit. When you put the evidence back in that they leave out, and drop all their illogical inferences, what you get, using Bayes’ Theorem honestly, is exactly the opposite: on the evidence we actually now have, the probability that any god exists (much less the weirdly specific gods of either Unwin or Swinburne) is billions to one against. Even at best. And really, honestly, it’s going to turn out to be trillions of times less likely than even that—once you replace their likelihoods and priors, with likelihoods and priors that are actually credible.


  1. Update:

    Thanks to a commentator:

    Recommended works criticizing Swinburne on many similar points (and some attempts at reply):

    Julia Braunsteiner-Berger, “Swinburne’s Argument for the Existence of God: A Critical Comment on Conceptual Issues,” Religious Studies 50 (2014): 359-78.

    John Ostrowick, “Is Theism a Simple, and Hence Probable, Explanation for the Universe?” South African Journal of Philosophy 31.2 (2012): 354-68.

    Jeremy Gwiazda, “Richard Swinburne, The Existence of God, and Exact Numerical Values,” Philosophia 38 (2010): 357-63.

    Jeremy Gwiazda, “Richard Swinburne’s Argument to the Simplicity of God via the Infinite,” Religious Studies 45 (2009): 487-93.

    Jeremy Gwiazda, “Richard Swinburne, The Existence of God, and Principle P,” Sophia 48 (2009): 393–98.

    Emma Beckman, “Richard Swinburne’s Inductive Argument for the Existence of God: A Critical Analysis,” Masters Thesis, Linköpings Universitet (2008).

    Don Fawkes and Tom Smythe, “Simplicity and Theology,” Religious Studies 32.2 (June 1996): 259-70.

    Richard Swinburne, “How the Divine Properties Fit Together: Reply to Gwiazda,” Religious Studies 45 (2009): 495–98.

    Richard Swinburne, “Gwiazda on the Bayesian Argument for God,” Philosophia 39 (2011): 393–96.

    Calum Miller, “Is Theism a Simple Hypothesis? The Simplicity of Omni-Properties,” Religious Studies 52 (2016): 45-61.

  2. Note: In my first release of this article I misstated Swinburne’s position on God’s prior probability. He actually argues the prior for God exceeds the prior for any other alternative, which theoretically can allow a prior below 0.5.

    In Existence, Swinburne is cagey about what he assumes his initial and conclusory prior probability of God to be. He never states a prior. But what he weirdly does do, is actually fill almost all of the prior-probability space with “nothing,” i.e. that nothing would exist (the prior for God, he says, “might be very small” because “so improbable is it a priori that there should exist anything at all”), but that’s illogical. The probability that h = “nothing happened” would explain present observations has a prior probability of zero (literally, actually, zero). Unless “nothing” has a nonzero probability of causing everything; which Swinburne denies. So once we exclude the “nothing” hypothesis and only carve up the prior probability space with h(n) = “some brute fact event happened that caused presently observed evidence,” Swinburne’s claim that (h = God) has a higher prior than (~h) entails a prior above 0.5. He never demarcates different alternatives; he always simply compares God with “nontheism,” meaning the conjunction of all competing godless theories (such that all he need consider, he says, is whether “the hypothesis of theism makes it more likely that e will occur than it would be if theism were false”); which requires his prior to be at least 0.5. It is unclear if he ever realizes this, because he has illogically carved away almost all the prior probability space with the illogical “nothing” condition, and never reconsiders that error.

    And even if Swinburne allows “something can come from nothing” (i.e. that it has a nonzero probability), we’d then have to calculate what that probability is (Swinburne doesn’t; and he might not like the result if he did), and even apart from that, of all the a priori options you can pick out of a hat, there is no reason “nothing started it all” would be more likely than that a spontaneously existing God started it all or any other nontheistic supernatural or natural “brute fact” scenario (of which there are many godless varieties available), except by arguing that nothing is simpler than all the others; but then so are all the godless theories that (unlike Swinburne’s God) are only slightly more than nothing. Which reverses Swinburne’s conclusion. So Swinburne’s treatment of the prior either entails an illogical and unspecified prior he never properly argues is greater than any actual alternative; or entails a 0.5 prior probability (once all logically impossible scenarios are excluded from the prior probability space).

    It should also be noted that Swinburne also tries to dismiss all background evidence relating to what kinds of explanations tend to be true, with the self-contradictory argument that there are no comparands to what I call “magic and ghosts” explanations and therefore “magic and ghosts” explanations can enjoy a high prior. In the real world, the lack of comparands entails a low prior. By every definition of frequency there is. Lower, in fact, than any other type of explanation that has ever turned out to be true. Just as I argue in this article.

    1. Note the 2011 paper by Swinburne listed in a top comment above confirms my interpretation. There, in response to Gwiazda, Swinburne admits he has carved up the prior probability space into P(h|k)=0.01, P(h1|k)=0.0005, P(h2|k)=0.00001, P(h3|k)=(a very small number), P(d|k)=0.005; and the rest to P(n|k), the condition of nothing exists. Which entails Swinburne means P(n|k) = 1 – (0.01 + 0.0005 + 0.00001 + ~0 + 0.005) = 1 – 0.01551 = ~0.98449. But that’s impossible.

      Of course, the probability that nothing exists is 0 (as here we are, something), so it cannot be 0.98449. So what Swinburne must mean is either of two things: that the prior probability that n caused everything now observed is ~0.98449; or that the prior probability that there would be nothing to observe is ~0.98449. But we already showed the latter has to be zero. Because something is observed. It therefore cannot be ~0.98449. And by the same reasoning neither can the prior probability that n caused everything now observed be ~0.98449, unless n has a nonzero chance of causing everything we observe. Which then obligates Swinburne to honestly determine what that probability is. And even if we allow n to have a nonzero chance of causing everything we observe, Swinburne has no basis for believing the prior probability of n is ~0.98449. There is no evidence supporting that frequency. And there is no formal logical demonstration from him that it would even be anything significant at all, much less ~0.98449.

      These facts are easily shown by iteration:

      (1) If h is “nothing caused everything” and ~h is “something caused everything”, but nothing ever comes from nothing, then even if we assume the prior for h is 0.99, then P(h|e.k) = P(h|k)P(e|h.k) / [P(h|k)P(e|h.k) + P(~h|k)P(e|~h.k)] = (.99)(0) / (0 + 0.01) = 0 / 0.01 = 0. So the updated prior for h, once we observe something, is 0. It disappears. Because it has exactly 0 probability of causing e. Meanwhile, swap h with ~h and carry out the math and you get the prior probability that in fact something caused what we observe is 1. So Swinburne cannot mean by n that “nothing caused what we observe observe.” That can never have an iterated prior higher than 0. Unless nothing has a nonzero probability of causing everything we observe. And then Swinburne needs to figure out what that probability is.

      (2) If h is “there is nothing to observe” and ~h is “there is something to observe,” and k is background knowledge and e observations, then even if we assume the prior for h is 0.99, then P(h|e.k) = P(h|k)P(e|h.k) / [P(h|k)P(e|h.k) + P(~h|k)P(e|~h.k)] = (.99)(0) / (0 + 0.01) = 0 / 0.01 = 0. So the updated prior for h, once we observe something, is 0. It disappears. Meanwhile, swap h with ~h and carry out the math and you get the prior probability that there is something to observe is 1. So Swinburne cannot mean by n that “there is nothing to observe.” That can never have an iterated prior higher than 0.

      By the same reasoning (once you iterate accordingly), that there is something to observe is in k. We observe countless things caused by something. And we never observe a nothing causing anything. So the prior probability that something caused everything is actually high on k, not low. Certainly not 0.98449. Unless we want to get hypothetical about what an unfettered nothing can cause, e.g. a nothing so null that no laws or principles or expectations even govern what it will do. Which actually ends up getting us a very high probability of the entire universe we observe. If there truly was nothing to limit what would happen. Which of course a nothing must be. Otherwise, if something is limiting what can happen, we have a something on our hands, not a nothing.

    2. Also, since Swinburne carves the prior probability space as P(h|k)=0.01, P(h1|k)=0.0005, P(h2|k)=0.00001, P(h3|k)=(a very small number), P(d|k)=0.005, and P(n|k) = ~0.98449, once we remove n as irrelevant (because something exists, so the hypothesis that nothing would exist is 100% certain to be false), Swinburne’s priors become: P(h|k)= ~0.64, P(h1|k)= ~0.03, P(h2|k)=0.00064, P(h3|k)=(a very small number), and P(d|k)=0.32. In other words, he actually covertly assumes the prior probability for God, relative to all other substantial explanations of present observations, is 0.64. Well above 0.5. And pretty close to Unwin’s posterior probability.


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