Bayes Theorem Is a Math Equation, So Math Must Be Used!

Let's talk about Bayes Theorem one last, and I mean last, last time (until later). I've seen a lot of tribalism on this issue. If you like a person who disagrees with me, you'll tend to agree with him. If instead you like me, you'll tend to agree with me. But if people truly want to think for themselves rather than align with a tribe, just honestly consider this post. Keep in mind I am not objecting to Bayes Theorem. It's the best way to figure out what is probable when there is data to work from. Here is a really good explanation of it, complete with a video.

But what about unique Christian miracle claims? Let's consider the belief that a virgin birthed god incarnate in the ancient world. If it happened *cough* it's a unique miraculous historical event (on Christian grounds). It's a good example since many other Christian miracles are unique to Christianity. To get Bayes rolling one must suggest a mathematical number representing the prior probability of such a miracle taking place. Without picking a specific number based on bonafide previous data as the prior probability, Bayes cannot get off the ground.

My Major Objection With Bayes Theorem

I've written a lot about Bayes Theorem, where I've laid out some of its problems. [See TAG below]. The major objection I have with believers who use Bayes Theorem to evaluate ancient miracle claims of faith, is that by doing so it disingenuously gives them the appearance of proving these miracles to be true, since after all, the math shows it, stupid! This is how William Lane Craig used it in his March 2006 debate on the resurrection of Jesus with Bart Ehrman, saying,

In calculating the probability of Jesus’ resurrection, the only factor he (Ehrman) considers is the intrinsic probability of the resurrection alone [Pr(R/B)]. He just ignores all of the other factors. And that’s just mathematically fallacious. The probability of the resurrection could still be very high even though the Pr(R/B) alone is terribly low. Specifically, Dr. Ehrman just ignores the crucial factors of the probability of the naturalistic alternatives to the resurrection. [Transcript PDF, page 16]

Who can argue against the math, right? Ehrman had a bit of difficulty but he still did well in that debate.

Bayes Theorem & My Pet Pig Porky

This is my concrete pet pig named Porky. It cannot fly. What are the mathematical odds it grew wings and flew since I last saw it? Come on, be honest! What bizarre world do you have to concoct to change a zero chance into a probability?

Let's say there is a society of believers who claim there was a concrete pig that flew in the ancient world.

So you get out your Bayesian calculator and consider the prior probability. No known concrete pig has even flown. What do you do? Someone suggests that for the sake of argument you should be generous. So you put down a wildly improbable figure of 10% prior probability. Why? That's granting way way too much from the get go! People who use Bayes are lying whenever they grant these generous numbers. The number should be so low it's indistinguishable from zero. Then there is no more math to be done.

Robert Conner On Jesus Studies and the Use of Bayes Theorem

I have asked crucial questions of the use of Bayes Theorem before. [See Tag Below] So it's refreshing to see others share my skepticism. Professors Louise Antony and Dan Lambert don't think it applies to miraculous historical claims either, to say the least! Now Dr. William M. Briggs weighs in.

[Y]ou may not be surprised to learn there is not one, but two books which argue that a fixed, firm number may be put on the proposition, "God exists." The first, by Stephen Unwin, is called The Probability of God: A Simple Calculation That Proves the Ultimate Truth, in which he uses Bayes’s theorem to demonstrate, with probability one minus epsilon, that the Christian God exists.

This is countered by Proving History: Bayes’s Theorem and the Quest for the Historical Jesus by Richard Carrier, who uses Bayes’s theorem to prove, with probability one minus epsilon, that the Christian God does not exist because Jesus himself never did.

Briggs: "These authors would help themselves better, and contribute to a more fruitful discussion about Jesus, by explicating the evidence and eschewing unnecessary quantification."

Robert Conner comments:

Dr. Richard C. Miller On Fantasy, Bayes and the Impossibility of Miracles

Dr. Miller recently began blogging at Hume's Bible, an important resource for the rest of us. In his most recent post he writes On the Impossibility of Miracles. This is something I've been addressing.

Miller starts by saying, "We measure human rational sanity by one’s consistent success in distinguishing clearly between fantasy and reality" and then gives an example with regard to alleged miracle claims. "Miracles, by very definition, are natural, rational impossibilities." "For, if a claim had empirical support, would we not classify such a proposal as indeed natural, not supernatural?" So he goes on to say, following Hume,

Here we may choose to end the argument, claiming a quite reasonable conclusive victory. Miracles, by very definition, are natural, rational impossibilities. When someone claims a miracle has occurred, we respond by saying that “there must be some rational explanation.” By doing this, we are implicitly recognizing as a society that miraculous claims are essentially irrational, i.e., a miraculous proposition contains one or more a priori contradictions with regard to its constituent terms (Italics mine).

This last phrase of his is very interesting. If we wish to assign a non-zero mathematical prior probability to a miracle claim, we cannot do it. For doing so means assigning a mathematical probability to something that is contradictory. Reading his explanation is worth the price of a click and a share.

Richard Carrier and Bayes' Theorem, One More Time

Richard Carrier and I may have found a partial agreement when it comes to the use of Bayes' Theorem (but maybe not).

Take this scenario:

It is impossible that as of this very moment all green highway signs will verbally discuss current events with us, if we stop to talk with them.

There are three ways to deal with this in Bayesian terms.

Does the Matrix Possibility Mean Anything Can Happen?

Kingasaurus asked the million dollar question about assigning 0% Bayesian prior probabilities to claims:

John, isn't there a non-zero chance that we're all living in the Matrix and the programming could always be changed so that pigs do fly and amputated arms are "magically" re-attached?

Wouldn't this make the possibility of absolutely anything and everything non-zero?

Great question!

Kingasaurus, those type of scenarios are literally a dime a dozen. Did you see the "Men in Black" movie where a a cat wears a charm which is another whole universe? I could be nothing but brains in a vat. A demon might be deceiving me. The whole universe might be growing larger every second, or smaller, along with us in it. I've written about a few of them before. Technically they are all mathematical possibilities, but they not only cancel each other out, they're to be regarded by those of us living in this reality as impossibilities.

The Parameters of Bayes' Theorem, Part 2

I've been debating the uses and abuses of Bayesian quantitative analysis on Facebook with my atheist friends. What started it all was a recent comment I made about Bart Ehrman's debate against William Lane Craig, where Craig used Bayes to argue against Ehrman. This is what I wrote:

I've mostly been persuaded by Louise Antony and Dan Lambert that Bayesian analysis doesn't help when it comes to historical one-of-a-kind events, especially of the miraculous kind! If correct, Christians are using this math illegitimately. We must not follow suit. If correct, this kind of analysis of "miraculous" historical events is faddish and will pass.

Second, while it's technically true that every claim, no matter how bizarre, has a nonzero probability to it, some claims can be said to be so far out of bounds the most accurate thing we can say is that such an event is impossible. This is something mathematician James Lindsay has persuaded me about. To continue to act and speak as if a certain miracle has a degree of probability to it, out of the numerous multitudes believed to have taken place, is a misuse of normal language. So when Ehrman says the miracle of the resurrection is impossible, he's correct. What other word are we to use? When does a 99.9999% improbability (or some other higher than high percent) become a possibility?

Possibilities count if an omniscient omnipotent god exists, you see. We encourage the mind of the believer to continue believing if we grant it's possible, when everything we know says it's impossible. We should avoid Bayesian analysis in historical events and stick to normal language and say it truthfully as Ehrman does, that it's impossible. Yep, impossible. The reason Christians use Bayesian math is because they can force us into admitting miraculous events are possible, and that's all they need to keep on believing. Get it?

Third, to go on to compare other bizarre alternative explanations of the resurrection hypothesis (aliens, seriously?) is an exercise in futility, since bizarre stories are by definition bizarre. Even owning an interstellar spacecraft is far more reasonable in this day than an impossible event, by far!. Are we really going to stoop so low that we have to argue the resurrection hypothesis has less explanatory power than alien interference, before we've made our point? Nonbelieving scholars have adopted this Christian language game in response to the dominance of Christianity in academia. This must stop. The best explanation of the data, BTW, is Richard C. Miller's.

Fourth, there are no posteriors that can make an impossible event (see above) a probable one. Ehrman was correct even if he fails to understand Bayesian math. In other words, Ehrman doesn't have to know Bayes Theorem to know it's impossible that Jesus raised up from the dead. He's a historian. A good one. And he's absolutely correct. So why are some nonbelieveing scholars nitpicking him to death on this issue when he's right? Or, are we saying only philosophers of religion who have been trained in this Christian language game can properly reject the resurrection hypothesis? Surely we don't want to say that. Otherwise, let these philosophers reign too. ;-)

Since that initial comment I've been in a debate about Bayes for most of this month on Facebook. To set the record straight, I was initially wrong to say "it's technically true that every claim, no matter how bizarre, has a nonzero probability to it." More on that in a moment.

The Parameters of Bayes' Theorem, Part 1

First off, Thomas Bayes (1701–1761) had a stroke of brilliance in creating his theorem! This is how we wish everyone should think when evaluating claims, events and promises. In a way, one cannot help but be in awe of it. Nothing I say is to indicate otherwise. My only beef is how it's been misused in cases where it shouldn't be used. The formula is below. Notice that the prior probability of event "B" cannot be zero. That sets the major limitation for how Bayes is used. Anything that is given a zero prior probability is not the subject for Bayes' Theorem. Got it? To use it in cases where there is a zero probability is to use it incorrectly. That's the point, not that every claim has a nonzero prior probability to it.

In the following simplified video explaining Bayes' Theorem, take a close look at the 45 second mark.



The narrator says something like this:

"Let's say you know one student in a class of twenty has the flu. Then the prior probability that a student in that class named Sally has the flu, is 1/20. That is your prior probability." Notice you have some factual information, that is, one student in a class of twenty has the flu. This is significant. First comes data, then comes prior probabilities. Bayes is dealing with factual data from the beginning. Without it there is nothing to compute. Compute?

Quote of the Day On Using Bayes' Theorem, By Richard Miller

On Facebook Dr. Miller wrote this:

Unlike what has been foisted by Carrier, Ferguson et al in these threads, prior probability in evidentialist statistics is far more subjective and typically may require/include field expert determination and any number of other inputs beyond assessment of rationality and logical validity, quite the opposite of the "anything goes" mentally we've seen exhibited here in such tiresome fashion. This is particularly true where there exists a relative paucity of informative statistics to aide in establishing prior probability, e.g., with the resurrection tale.

Interesting here, John Loftus and I are the only ones here to have studied in seminary with William L. Craig and his camp. We recognize the apologistic tactic a mile away. They rhetorically have already won. They selected Bayes then gave their mythological proposition an non-zero prior probability. Everything after that is meaningless smoke and mirrors meant to distract the masses. They've already quietly succeeded. All they needed to do, according to their camp, is show that their fairytale world is possible. Done! They've tricked you into allowing this step to frame the debate entirely to their own essential success. A more careful look at Bayes, however, shows this step to be utterly false.

There Are Many Impossible Claims Having a Probability of Zero

What are the odds that someone can self-propel themselves to the moon and back without any technological help, including oxygen tanks?

Timothy R Campbell:

I am not sure that one can utilize math or reason or probabilities when dealing with claims of miracle or magic. After all, any event that can be seen as statistically possible would then not be magic. Resurrection -and John flying to the moon through self propulsion- are impossible without magic, but would certainly be possible if magic was possible. Once someone shows definitively that magic is possible, THEN the statisticians can review their estimates!

On Facebook Richard Carrier has been arguing that every claim, except a logically impossible one, has a non-zero probability to them. He said:

The only thing that has a zero probability is that which no amount of evidence (none whatsoever) would ever warrant believing; not a thing for which we don't have that evidence, but a thing for which no such evidence can even be conceived. The only thing that qualifies, is raw uninterpreted present experience. Everything else we can be wrong about, such that some amount of evidence, *if it were presented* would warrant believing it. But when it isn't presented, we aren't warranted in believing it.

When it came to the resurrection Carrier said,

I literally actually believe the probability is nonzero, and not only because I can imagine evidence that could convince me, although that's the big point to note here. I don't think resurrection happened because no such evidence has appeared. Not because no such evidence can even be conceived.

John W. Loftus: Nonzero as in
.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001?

Richard Carrier: Maybe. That's the kind of probability I'm talking about at least.

John W. Loftus: There is no difference between that number and zero.

What Are the Odds I Can Fly to the Moon and Back? Zero. A Bayesian Analysis.

Christians (and a few atheists) get butt hurt when we tell the truth that brain dead cold cadavers stay dead, that there's a zero chance one or more of them have ever come back to life. Here are the facts: 108 billion human beings have been born into the world (per one estimate), all of whom died except those still alive, 7.5 billion of us. Those of us alive will die and our deaths will be permanent just like all other species on the planet, who share with us a common ancestor, along with everyone yet to be born (no known estimates for this figure). I think we can safely say everyone born has died or will die, and never come back to life. While taxes may not always be a permanent state of affairs, death is.

Let me give an analogy. What are the odds I can fly to the Moon and back on my own via self-propulsion without the use of modern technology, not even oxygen tanks? Zero. Again, Zero.

Quote of the Day by JP415 on Ridicule and Bayes' Theroem

JP415: "What is the Bayesian probability that Muhammad split the Moon in half, or that Hercules killed the Hydra? Sometimes satire is the most effective form of refutation."

Quote of the Day On Bayes' Theorem, by Herald Newman

Herald Newman:

As somebody with a degree in mathematics, I look in disgust at every apologist who tries to use Bayes theorem to "establish the likelihood of the resurrection." Bayes theorem requires that we have an established background probability, and as far as I know, the dead stay dead. The background probability of coming back from the dead (after more than a few minutes) is 0.

Ask any school child and they'll tell you that zero times anything is always zero. Just more apologists trying to pull the wool over the eyes of their math ignorant flock.

Establish that people come back from the dead, and we can start talking about Jesus coming back from the dead.

On the Christian Use of Bayes' Theorem, by JP415 and GearHedEd

JP415:

I have an axe to grind with the way Craig, Torley, et al. used Bayes’ Theorem. It just seems like a diversionary tactic. During a debate, they break out an equation and say, “Our methods are objective! See, we’ve even got a math formula to prove it.” But when you look at the formula, you see that it’s stuffed with a bunch of unproven assumptions. They should know better. Maybe they do.

GearHedEd:

They do. Craig's entire career has been an effort to become a "respected Christian Apologist". He was already committed before he went to college. And none of the "priors" that they stuff into their Bayes' Theorem Machine are reasonable. It all comes from poorly evidenced claims in the Bible, and gets a "pass" because of where it was found.

JP415:

Yeah, it's like, "Given our prior background knowledge that Superman came from the planet Krypton, it's entirely likely that he could fly and shoot laser beams from his eyes." You could just put any old thing in there and get the results you want.

I think this analysis is basically correct, and I wish to comment further.

Quotes of the Day by Robert Conner

I wish I could get Robert as a Team Member here at DC. Here's a quote for people who insist on following the latest Christian apologetic fad of trying to quantify unique miraculous claims in ancient history using Bayes' Theorem:

I don't know much about Bayes' Theorem, but I know it's August 1, 2017 and Jesus hasn't come back yet.

Here's another one highlighting the fact that faith is pretending to know what you don't know (think of the Sophists in Socrates's day):

Celsus repeatedly noted Christians boldly opine about all sorts of things they don't and can't know, and nothing has changed in the two millennia since. Jesusplaining Christians appear to think their convictions are some kind of "smart pill"--just witness the resident apologists who infest this site with their twaddle and who never cease to pontificate about everything from the ancient documents they read only in translation to particle physics to evolutionary biology.

On Keeping it Simple Stupid!

One of the highest compliments I've received from my work was written by biblical scholar Robert M. Price. Of my contributions in the co-edited book God or Godless?he said I write "with unpretentious clarity, common sense, and broad but inconspicuous erudition." If anyone wants to see how high a compliment that is then look up each word he used. Let me highlight just two of his words, unpretentious and inconspicuous.

Unpretentious: I don't seek to impress my readers with Bayesian math, or the technical philosophical, theological, or scientific terminology, nor do I use the original languages of the Biblical texts much at all. I remember teaching my first philosophy class in 1985 at the College of Lake County, in Grayslake, Illinois. I lost about half my class because the students could not understand me. Yep, that's right. Having just come from a Ph.D. program at Marquette University I didn't know how to bring the information down to college students. Over the years I learned how to communicate to the average person. My goal is to keep it as simple as possible, and no simpler. The problem with this goal is that there are some readers who think I'm ignorant, for if I was smarter and better educated it would reflect in my vocabulary. Smart, educated people, it's assumed, use the nomenclature requisite with their educational achievements.

Inconspicuous: Even though Price says I have a broad erudition, it's inconspicuous or unnoticeable. It wasn't inconspicuous to him. But it's inconspicuous to others. The people for whom it might be inconspicuous would be the uniformed and ignorant, Price intimates. [Another equally high compliment of my work, which mirrors what Price said, was written by biblical scholar Hector Avalos.] It's extremely gratifying to know some important people say such things.

Dan Lambert Doesn't Think Bayesian Analysis Helps When It Comes to History

Timothy and Lydia McGrew use a Bayesian analysis (or inference) to establish the resurrection of Jesus by a percentage of over 99%. Richard Swinburne uses it to establish that if God exists then Jesus was bodily resurrected from the grave by a percentage of 97%. However, by definition, even any given mundane (or ordinary, as opposed to an extraordinary) historical event is a unique one-of-a-kind event. And the events leading up to it, and follow it, are also unique one-of-a-kind events. So when looking to see if any given event took place in the past the historian must calculate the probability of the whole series of events, the ones that came before and after the event in question, even though all of them are unique one-of-a-kind events. How does one assign probabilities to them all when they are all dependent on each other? In one sense they are all improbable for that reason. To see this from a different perspective, consider an observer before any event takes place. All events in the future have an extremely low probability to them. No one could have predicted yesterday that I would be typing these very words today, you see. In any case, here is Lambert on Facebook taking about this subject:

Richard Carrier, James Lindsay, on the OTF

Richard Carrier writes:

James Lindsay has been doing some great blogging on how to apply Bayesian reasoning to model John Loftus’ Outsider Test for Faith (or OTF).

Formulating and extensively defending the OTF is Loftus’ greatest contribution to the philosophy of religion and atheism. His best and most thorough treatment appears as chapter four in The Christian Delusion (a book I always recommend anyway as it contains lots of great chapters by great authors; and two by me). He is writing a whole book on it now. It should be out this year (I’ve seen advanced drafts and it’s good; I’ll blog it when you can buy it). The OTF is featured at Iron Chariots (which provides examples of looser expressions of the concept throughout history) and Loftus discusses it often at Debunking Christianity.

The basic idea is that you can only have a rational faith if you test it by the same standards you apply to all other competing faiths; yet when you do that, your religion tests as false as the others, and the same reasons you use to reject those become equally valid reasons to reject yours. Though this idea has been voiced before, Loftus is the first to name it, rigorize it, and give it an extensive philosophical defense; moreover, by doing so, he is the first to cause a concerted apologetic to arise attempting to dodge it, to which he could then respond. The end result is one of the most effective and powerful arguments for atheism there is. It is, in effect, a covering argument that subsumes all other arguments for atheism into a common framework. Link

Dr. James A. Lindsay's Definition of Faith

Faith, he argues, is "a form of cognitive bias that tends to overestimate the probabilities that the hypotheses in which faith is placed predict the evidence (of the world) while underestimating the probabilities that alternative hypotheses predict the evidence we have." Or, in other words he says: