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.

Some Prior Problems with Bayes
It's argued Bayes' Theorem would expose the weaknesses of a view. In many cases, yes, but not when it comes to magical mythical miraculous ones. Does using Bayes' Theorem expose presuppositionalism as a sham when presuppositionalists boldly assign a 100% prior probability to their god and their Christianity? I submit the answer is an emphatic no. They are not embarrassed to say so either. Neither are others.

I don't think Bayes does any better or worse than using good arguments. Not using Bayes would communicate better to others because the math hurts. Using it may actually be less likely to make a bigger difference.

Doug Kruger, author of the book What is Atheism? summed up one of my main criticisms of using Bayes in our faith related magical mythical, miraculous debates:

This hits home when considering that Richard Swinburne argued that given the existence of God it was 97% probable that Jesus was raised up from the dead. Really? Math never led to a more insane position than his.

The problem with using Bayes as a tool to evaluate magical mythical miraculous claims is that there are no hard data to go by. If one wants to calculate how many Firestone tires will go bad on Ford trucks, there are data to work with. We can calculate how many tires go bad generally speaking, and how many tires go bad on trucks, etc. Then we can state the probabilities. There's data to make a probability calculation. Magic doesn't provide any data from which to calculate. When it comes to whether pigs can fly, for instance (a magical claim if I ever heard one), the only data we have is that no pig has ever flown. There is no data that they have done so to work out any probabilities for others to fly.  Pigs don't fly. They can't.

The math can only work where there is pre-existing data, like predictions about how many huge floods the city of Houston, Texas, will have.

Assigning claims with a 0% prior probability.

In Bayesian terms we cannot assign a 0% prior probability. In order for the math to work there must be some probability calculation to start. Otherwise, no matter what the evidence is, the probability of any given claim will always be zero. For 0 times any number will always result in 0. Now most people interpret this to mean every claim has a nonzero probability to it. But that's only possible if every claim has a nonzero probability to it! The alternative is that if there's a claim having a zero initial probability to it then it cannot be evaluated by means of Bayes. That is, these types of claims cannot be evaluated by Bayes. That's my interpretation. We all agree there's at least one category of claims that has a zero prior probability to them, logically impossible ones. I think there are others. 

If someone says we should never ever assign anything but nonzero priors to logically possible events, the problem is that none of us actually do that. We are certain trees don't talk, that roadways don't have feelings, that cartoon characters cannot leap out of their media and attack us, that it's impossible to live on the surface of the sun for a few billion years starting today without the aid of any technology, and that pigs cannot fly.

If we assign a zero prior probability that means we're closed to assertions of evidence otherwise. To do so is to say we cannot change. So how can we change our minds? Are we locked into the math. Can we not escape it? The answer is simple. Math follows reality. Math does not dictate the inputs. Reality dictates the mathematical inputs.

There are many people who are certain they're right about faith, like this fellow I interviewed, even though they admit they could be wrong about everything else. If they knew about Bayes' Theorem they would assign a 0% prior to the probability they could be wrong, just like I would've done even though I changed my mind.

Categories of impossible claims

There are the logically impossible category of claims. There are the physical/empirical category of claims so impossible they go beyond being virtually impossible to impossibilities. There are the meaningless self-referentially incoherent is category of claims which are impossible.

Much of the debate centers around my being closed-minded to the later two categories of impossibilities. It's to assign them a Bayesian 0% prior probability. To be closed-minded is to claim my mind cannot be changed about them. I argue there are times when closed-minded is a virtue.

1. Logically impossible is category of claims are contradictory and hence impossible. End of story. This we should all agree about. What would be up for debate is whether or not a particular claim is contradictory, such as whether a god outside of time can act in time, or whether an omnibenelovent omnipotent god created our universe.

2. Empirical/physical impossible is category of claims concern that which violate our natural laws. This type of impossibility depends on how well we understand the laws of the universe. But we do understand a great deal about them. There are many laws that are inviolable as general rules with the math that helps us understand them, like gravity, Newtonian laws of motion, Maxwell's equations, and Einstein's equations. It is impossible they will fail for us in a given time frame, the one we live in, the one I'm commenting about. I take it every human being has died or will die. The one thing we can be sure about is death. It's certain. If we find a way to extend life indefinitely the universe itself will suffer a heat death, and with it we will die. But it's certain we will die. To construct a nonzero prior for a Bayesian calculation for any of these physical impossibilities is crazy.

3) There are meaningless self-referentially incoherent category of claims that defy our language which are impossible. Examples are having the Joker leap out of a Batman comic book to attack us, or riding Disney's elephant Dumbo, or having sex with Bugs Bunny.

Test Case, Can Pigs Fly?

I figure it's a 0% prior probability that pigs can fly. I'll change it the day pigs can fly. Without data one can't even make a prediction of probability other than 0% for magical mythical cartoonist type claims. It's impossible to do anything else. So we're told that a pig flying has a 1 and a billion chance of happening. But this is clearly guesswork without any data. Without data how can we possibly say what the odds are? The odds could be stated to be 1 and 10 billion, or 1 and 100 billion, or 1 and a trillion, or 10 to the 100th power, and more, and more. This is a question we debated quite a bit, which is a case of category two impossibilities, but may also be a category three impossibility since the terms "flying" and "pig" may be contradictory. If a pig grew wings strong enough to allow it to fly it would no longer be a pig, right?

You can test whether pigs can fly. Start throwing them off a cliff one by one. When you kill off the whole species it will be proved with certainty they couldn't. But we don't have to test it. We can simply postulate the result as a prior probability based on the nature of pigs and aerodynamics. For those unwilling to do this, let the slaughter begin, along with the arrests.

Ed Babinski puts this in better perspective. If someone still thinks it's possible pigs can fly then provide the conditions that low them to fly, or say you're just guessing without any factual data at all, or admit you need to rethink what you've accepted from authority figures who have a vested interested in playing nice with Christian apologists, by granting their impossibilities for the sake of argument:
To be sure, earth pigs in their present evolutionary form cannot defy the present gravity and atmospheric pressures of the planet on which they are found, and they cannot fly in the sense of rising rather than their expected falling to the ground after say leaping off the cliff, nor would one consider them flying if one were to empower them mechanically or via humans genetically engineering some functional wings, or any other appendages with which pigs are not normally born, nor does riding in a plane, helicopter or space-going vehicle count as a "pig flying," nor being shot out of a canon, or their lungs over inflated with helium, nor having them eat metal and then pushing them via magnetic repulsion heavenward.

 Part of my problem is with words, even the word "pig." At what point does a "pig" as we currently know them to be in this tiny slice of geological time evolve into something that we feel it's time to define by some other word? A word does not equal the thing, the map does not equal the territory, and no model equals reality. And what about the word "fly?" What does that mean? When does falling at an angle become "gliding" rather than "falling?" And at what angle might "gliding" become defined as "flying?" These are the old question of particles of and heap, how many particles does it take to become a heap? When does a puddle become a pond, a pond become a lake, a lake become a sea, a sea become an ocean? Words are slippery things, nature is always changing to one degree or another. But always changing in some ways. No single word captures what things ARE, since things are verbs, not nouns. We are all moving pictures. In fact we are tiny squiggles left over from the Big Bang, still in motion. Like tossing a jar of ink at a wall and noting how the splatter fans out into tiny tendrils on the walls. We are each a tiny tendril of a Big Bang. All things are related yet changing.
Regarding the second category of impossibilities:

Is it possible that someone some day will roll a 6 sided die and get a 7? What kind of magic is this? I've been told I know nothing about probability theory. What kind of magic is that? I've already rolled a die ten thousand times in my life and I'm here to say my experiments show a 7 never came up. How about you? I suppose we could add up the number of times 7.5 billion people have rolled a die and conclude something different? NO! Not possible, and yet someone who knows more about probability theory says I'm wrong, that it's possible a 7 could come up.

It is impossible for me to build a spaceship and fly it to the moon before midnight tonight (45 minutes). The chances are zero. Anyone open to me doing this is, well, crazy as a loon. *Sorry*

 Would anyone honestly be interested in investigating my claim to have created a time machine and using it to "turn back time" and preventing my grandparents from ever having met, and then arriving back before the time I made the time machine? Impossible? Yes. Interested or closed-minded to the evidence?

What are the odds I can jump off a mountain today and survive without a scratch, then fly to the moon and discover it's made of green cheese then be back home again by nightfall?

What are the odds that right now I have returned from traveling back in time to the year 500 CE, where I jumped off a mountain cliff and survived without a scratch, then turned invisible and flew to the moon to discover it's made of green cheese, and am now a pink unicorn writing this post, even though I refuse to even attempt to do all of this? Your position is absurd! Admit it, some things are impossible and have a zero probability to them, things for which you are closed minded about such that no conceivable evidence could convince you otherwise.

What are the odds I can self-propel myself to the sun in one hour and live on the surface for a few billion years until it ceases to burn? Zero.

Regarding the third category of impossibilities:

Regarding the third category of impossibilities, Richard C. Miller argued: "Most propositions have a zero prior probability of being true (e.g., "the moon is a triangle" or "I just had sex with Bugs Bunny" etc). The implicit definitions of their words create a logical contradiction and, as such, render most propositions false non-starters. I think this is rationally obvious and does not require an expert logician."

How many claims are actually in this third category needs to be explored. Possible examples include these claims. 
Dr. Miller:
I can tell you with 100% confidence that I cannot run a mile in 1 second. We all know what I mean by that and literally 100% of rational adults would rightfully agree with that statement. I continue to be shocked that there are individuals who find such basic rational thought so challenging.

Daniel Whittier Huber: There is no planet made entirely of Crocs shoes. / There is no sun made of bubble gum / I will not instantaneously turn multicolored or grow 5 genitalia through my nostrils.

Philippe Jean Giordana: I am Groot.

My Six Impossibilities:

My first  closed minded thought of the day: I cannot drink all of the water in Lake Tahoe by sundown today. I am close minded to any evidence that could convince me of this precisely because doing this feat would be impossible.

My second closed minded thought of the day: It's impossible for my naked unaided eyes to have X-Ray vision strong enough to accidentally look up the skirt of a woman on the other side of the earth. I am closed minded to any evidence that could convince me of this precisely because doing this feat would be impossible.

I want my detractors to notice I have never suggested a scenario where I can accomplish something, anything, with certainty. For if I say I will certainly drive a car tomorrow, that could easily turn out to be false. For I could die before then, or a nuclear warhead could be dropped near enough to kill me. Certainty on this side of the debate, the side where I claim I can certainly accomplish some feat in the split-second present, or the future, is not anything I can claim. It's always about what will certainly not happen. It's about that which I can reasonably claim under normal rules of language and logic that some events are impossible to take place. On that side of the debate I think I'm right. If you disagree you must charitably interpret the words of my closed minded thought of the day, and then show how it's possible TODAY, not tomorrow or some as yet undefined future, how I could accomplish this feat before sundown. This possibility must be a real possibility and not something completely and utterly bizarre. Go!

My third closed minded thought of the day: It's impossible that today before sundown I could fart and destroy the city I live in and survive intact, even though I ate nothing unusual nor was anything forcibly thrust into my body. I give this feat a 0% prior Bayesian probability. I am closed minded to any assertions of evidence that could convince me otherwise, precisely because doing this feat is impossible.

If you disagree you must charitably interpret the words of my closed minded thought of the day, and then show how it's possible TODAY, not tomorrow or some as yet undefined future, how I could do this feat before sundown. Your suggested possibility must be a real possibility and not something utterly bizarre without any merit at all. Go!

My fourth closed minded thought of the day: It's impossible that I could be eaten by a pride of lions, then reassembled by a witch-doctor's magic, then shot out of a cannon into space without a spacesuit for a thousand years, then to re-enter our atmosphere at a fire paced speed, hit a concrete sidewalk and walk away as if nothing had happened to me. I calculate this as a 0% prior probability for a multiple number of reasons.

My fifth closed minded thought of the day: It is impossible that the dead god Baal of the Caananites recently resurrected, and will materialize in the middle of Times Square in NY city today, then make an amputeed veteran's leg grow back before a group of medical experts. I'd give the odds of this to be a 0% prior probability hands a down, no iffs ands or buts about it.

My sixth (and very last) closed minded thought of the day: It is impossible that the dead god Yahweh, son of the dead god El (who gave him the land of Palestine and its people to rule over--Deut. 32:8-9, see link about Hector Avalos's exegesis), who had sons himself (and therefore also a wife), for some egotistic irrational reason first created a flat world 10k years ago (contra-geology) then later (on the 4th day of creation) the universe of stars and galaxies (contra-astronomy) then instantaneously created two humans (contra-evolution) to trap them with a test he foreknew they couldn't pass by allowing an evil talking snake to tempt them (who stupidly rebelled even though he knew he could never win), who subsequently sent his only begotten incarnate son into the world (yep, mathematically impossible given a 100% divine and 100% human being) through a virgin (standard fare with the ancients to people believed to be demigods) to die so that he could forgive people (even though dying to forgive makes no rational sense) who believed (even though belief is involuntary and an irrational requirement when there's no objective evidence), then arose from the dead (like Apollonius of Tyana), even though there isn't any objective evidence of this, nor of anyone else in the history of the human species, even though personal identity after death is probably an incoherent concept, and even though the resurrection story was probably written as fiction (ee Richard C. Miller's book ), who will come again (after being dead for nearly 2000 years), even though there's a probability the man Jesus may not have existed in the first place (see David Fitzgerald's books); I could go on and on....

I give the odds of this to be a 0% prior probability hands down, no iffs ands or buts about it. The only reason we talk about this and debate it is because people believe against all reasoning and objective evidence due to a host of cognitive biases and a multitude of logical fallacies.

Q.E.D. This is my point, friends. For more, read my latest books, "Unapologetic" and "How to Defend the Christian Faith: Advice from an Atheist".


How Should Atheists Deal With Magic Myth and Miracles?

My atheist detractors know of Borel's Law but even numbers that high are still considered by them to be possible. They understand logical impossibilities are 0%, but they don't understand some of these scenarios are logical impossibilities. They understand the colloquial use of the word "impossible" is different from the mathematical use of the word, but don't understand the mathematical use of it doesn't seem to correspond to reality and leads to saying anything is possible.

Shouldn't atheists use Bayes to answer believers like Richard Swinburne, William Lane Craig,  Timothy & Lydia McGrew, or Michael Licona or Vincent Torley? In my view they are the least likely to be persuaded, so if we wish to persuade them it won't work. Then there are a host of other believers who won't bother due to the math itself. They will proclaim the math proves the resurrection without actually understanding it, so it's probablya good thing some atheists respond in kind.

But so far the atheist responses grant far and away way too much for three reasons. For one, the best way to evaluate the resurrection claim is to place it within the conservative theology of which it's a part, and beyond that to put it within faith-based claims in general (see my sixth impossibility above for how to do it correctly ). For two, they should discuss what an eyewitness really is (i.e., a person who saw it with her own eyes and can honestly testify under cross-examination) and what we can legitimately consider sufficient objective evidence. For three, and this is the important point, because there is no objective data of other resurrections supported by objective evidence, we must say the prior probability of the resurrection is 0%. To start off saying there is a fifty-fifty chance Jesus was resurrected, or that we don't know if he was, when the person making the claim has the burden of proof,  is to abandon intellectual honesty. 



Geoff Williamson: "Seems to me all the talk about virtually but not exactly zero probability priors is pointless when the the virtually zero instances are logically impossible under the known laws of physics. Introducing quantum mechanics etc. is just a game akin to Douglas Adams' Improbability Drive."

Ben Davis:
After having followed this thread for a while now I find myself conflicted as I read through the arguments. I have seen sound arguments on both sides, so I can't help but think that people are just talking past one another somehow.

I only have a passing understanding of Bayes (close to but not quite zero, haha), but I can't see how anyone can come up with meaningful nonzero prior probabilities for things that make no sense or that are impossible. And if you can't start with something meaningful then you're not going to get anything meaningful when you run the numbers. If any old number will do as long as it isn't zero, then it's a pointless exercise unless you just enjoy doing the math for math's sake. It won't add any new knowledge.

This is why I think Bayes' is ripe for abuse by people who want to "prove" something that is impossible. Seems like you can just generate some random, non-zero prior values and inflate them until you get the results that seem plausible.
Calyb Alan Tittman: It's impossible for me to make the sun vanish and have the planets behave as though nothing happened by channeling some amazing psychic abilities.

Grant F. Shipley:
Traditional probability analysis acknowledges the null hypothesis as a default position: in the absence of evidence showing that the event was caused by a force beyond random events, then the null hypothesis governs, and the proposed intervening force does not exist. Bayesian probability does not rely on the null hypothesis as the starting point of analysis, but seems to believe that all events have a cause that can be ascertained. But Bayesian analysis applies (if at all) only where these is no null hypothesis, i.e., where we have already eliminated the hypothesis that the alleged force does not exist. This makes Bayesian probability analysis inapplicable to questions of the existence vel non of a supreme being.
For more see the tag "Bayes Theorem"