Showing posts with label Bayes Theorem. Show all posts
Showing posts with label Bayes Theorem. Show all posts

Quote of the Day On Bayes Theorem by josephpalazzo

josephpalazzo replied in Debunking Christianity: Here's Bayes Theorem:
In the denominator P(B) must refer to actual data, not some possibility. This also goes for all the other variables P(AlB), P(BlA) and P(A). As example, what is the probability of turning head on tossing a fair coin, which is 1/2. That number, 1/2, can be verified by tossing a fair coin 1000 times, 10,000 times and so on. It's not a guess, nor some divine revelation of some desirable event. If there is no verifiable data, Bayes Theorem is totally useless..

Additional Thoughts On Using Bayes' Theorem

No one should expect that a good argument is one that convinces reasonable people. What we should expect is that an argument is a good one, or a strong one, or very strong one, irrespective of whether it is a convincing one. Even though I know this, I still try to come up with arguments that are convincing to most reasonable people. I expect kickback from Christian believers. What can annoy me is kickback from other atheists and agnostics, especially if they don't let it go after a while, until they say nothing new I haven't considered before. BTW: A person can annoy me on one issue but be very informative, completely delightful and insightful on most everything else. That describes Ignorant Amos. In fact, the commenters here seem to be the best I've seen anywhere!

I have defended the use of Hitchens’ Razor over the use of Bayes’ Theorem (BT) when assessing miracles like a virgin birthed deity and the resurrection of Jesus. I have argued that BT cannot and should not be applied to claims which are nonsense, and that miraculous claims in the ancient Biblical past are all nonsense! They are all nonsense because there is absolutely no credible evidence for any of them. I have also argued that the goal of atheists should be to change minds, and that fewer minds are changed the more we respond with greater and greater sophistication. Doing so also legitimizes nonsense by giving believers undue credibility. I agree with philosopher Julian Baggini who said, "Converts are won at the more general level." [] For responding to fundamentalist philosophy only encourages fundamentalist philosophers. On the general level even ridicule changes minds.

I don’t object to using BT when it’s applied appropriately to questions for which we have prior objective data to determine their initial likelihood, along with subsequent data to help us in our final probability calculations. It’s an excellent tool when these conditions obtain. So a new provocative question arises, one I didn't address: What is the best tool for assessing the possibility that a historical person existed behind the Jesus character in the Gospels?

How To Avoid Definitional Apologetics

I see Ben Watkins joined Jeffery Lowder and Johno Pearce [The Tippling Philosopher] in calling himself a "Philosopher." I have resisted calling myself a philosopher because I have held to a higher standard. No more. I am a philosopher. You can call me that. If they are then I am. If my degreed educational credentials and years of college teaching and published books on philosophical issues doesn't call for it then something's wrong. I don't say this to demean them. I say this to join them, especially when it comes to any and all disagreements on the PoR that we may have between us [See Lowder Ignorance Tag below]. In fairness, a lot of philosophers disagree with me on the value of PoR and the use of Bayes Theorem, so I'm not asking for agreement, only a discussion between philosophers in addressing what I say. I think internet atheists who are addressing PoR questions should stop what they're doing until they read my book Unapologetic: Why Philosophy of Religion Must End. Full Stop. 
My case in point today concerns how to avoid Definitional Apologetics.
Over the last decade I have found that one bastion for Christian apologists has been philosophy, especially the philosophy of religion. The scholars have honed their definitional apologetics in such a fine-tuned manner that when engaging them in this discipline, it’s like trying to catch a greased pig. Or, to switch metaphors, trying to chase them down the rabbit’s hole in an endless and ultimately fruitless quest for definitions. What’s an extraordinary claim? What constitutes evidence? What’s the definition of supernatural? What’s the scientific method? What’s a miracle? What’s a basic belief? What’s a veridical religious experience? What’s evil? They do this just like others have done over questions like, “What is the definition of pornography?” And then they gerrymander around the plain simple facts of experience. I would rather deal in concrete examples like a virgin who supposedly had a baby and a man who supposedly was raised from the dead. [From Unapologetic: Why Philosophy of Religion Must End, p. 28]

Religious Studies On William Vanderburgh's Book, "David Hume On Miracles, Evidence, and Probability"

Religious Studies recently reviewed the book by William Vanderburgh: David Hume on Miracles, Evidence, and Probability. In the Appendix to my own book on miracles I reviewed it very favorably as well. Here are some snippets from the short review:
In David Hume on Miracles, Evidence, and Probability William L. Vanderburgh presents a concise defence of David Hume’s ‘Of Miracles’. By providing a more in-depth look at the relevant biographical details of Hume as well as an expanded investigation of Hume’s broader epistemology, Vanderburgh argues that many commentators, both historical and contemporary, have either misunderstood or misrepresented Hume. At the heart of Vanderburgh’s defence of Hume is the rejection of the arguments put forth by Hume commentators such as Richard Price, John Earman, and others who have attempted to interpret ‘Of Miracles’ from a Bayesian perspective. Vanderburgh argues that approaching Hume’s epistemology from this perspective is fundamentally wrong and that Hume’s argument ought to be interpreted using a non-mathematical probability framework.

What’s Wrong With Using Bayes Theorem to Evaluate Miracles?

In a previous post I spoke on the topic, Miracle Claims Asserted Without Relevant Objective Evidence Can Be Dismissed. Period! At the end I had some closing thoughts about Bayes Theorem and miracles. I'm highlighting it for thought below.
What’s Wrong With Using Bayes Theorem to Evaluate Miracles?
Now I want to end by talking briefly about Bayes Theorem. In his writings and talks Richard Carrier does a good job of explaining it.

Miracle Claims Asserted Without Relevant Objective Evidence Can Be Dismissed!


I recorded a video talk for two virtual conferences this past Labor Day weekend, for the International eConference on Atheism, put on by the Global Center for Religious Research, and for the Dragon Con Skeptic Track. I'm very grateful for these two opportunities. That video will be released sometime soon. In what follows is the text of my talk. Please share if you want others to discuss it with you. Enjoy the discussion!

Today I’m arguing, along the same lines as Christopher Hitchens did, that “What can be asserted without evidence can also be dismissed without evidence.” [God Is Not Great: How Religion Poisons Everything (New York, Twelve. 2007), p.150.] Specifically I’m arguing that “Miracle Claims Asserted Without Relevant Objective Evidence Can Be Dismissed. Period!”

I think all reasonable people would agree. Without any relevant objective evidence miracle claims shouldn’t be entertained, considered, believed, or even debunked. I intend to go further to argue that as far as we can tell, all, or almost all miracle assertions, lack any relevant objective evidence, and as such, can be dismissed out of hand, per Hitchens.

Whose Abject Failure? William L. Vanderburgh Tweets On Hume and Bayesianism

I reviewed Dr. Vanderburgh's book in defense of David Hume in the Appendix to my anthology, "The Case against Miracles." [Click on his book image to find out more.] Amazingly, Vanderburgh sums up his conclusion in one short Tweet! Tim McGrew, supposedly an "international expert" on miracles (but not my expert!), is in the dark on how to understand David Hume on miracles.

Hypothesis: Since Bayes Theorem Cannot Help Us It Should be Abandoned

Here is the full title to this post:
Hypothesis: Since Bayes Theorem (i.e., the math, the equation, the formula) cannot help bring us to a consensus concerning something accepted on faith, or assess specific miracles and theistic based religions, and because it is ripe for abuse in the hands of Christian apologists who dress up their delusion with undeserved respectability, it should be abandoned for better alternative methods, by people who really want to know the truth.
This is not a case of throwing the baby out with the bathwater. There is no miracle baby to be found in the dirty bathwater. Bayes is used by people in this debate who wish to look superior than others. It's a rite of passage into a specific club of intellectuals who like the status of being considered above the rest of us. But it solves nothing, clarifies nothing, and will be thrust into the dustbin of elite faddishness as one after another intellectual wannabe comes up with their own calculations without reaching a consensus between believers and non-believers on the inputs or the resulting probabilities. As philosopher Godfrey-Smith put it, “The probabilities” in Bayes’ Theorem “that are more controversial are the prior probabilities of hypotheses, like P(h).” He asks, “What could this number possibly be measuring?” He says, we cannot “make sense of prior probabilities” [Theory and Reality: An Introduction to the Philosophy of Science (University of Chicago Press, 2003), p. 205]. He is dead on in the area I'm arguing, faith-based claims of virgin birthed deities and resurrections from the dead. And while I'm at it, gods themselves, who are supposed to exponentially increase the prior probabilities.

Bayes is a mathematical wasteland when applies to these issues. The only merit it offers is the discussion of the evidence and the ensuing arguments in defense of the inputs, which could be done without the math. So atheist apologists who argue for the use of Bayes Theorem in an area with no promise or hope of a consensus, are merely arguing for their own special status in these debates, and dividing people unnecessarily between Bayes users and non-Bayes users. The most extreme case of this is atheist apologist Richard Carrier, who thinks the rest of us are ignorant, stupid, and irrational to disagree. This only makes him feel relevant by arguing for his own irrelevancy. This is not to throw a bone at Christian apologists. I think Carrier is brilliant and has already dealt some significant death blows to the Christian faith. But on this issue his brilliancy, and undeserved superior ego, has led him to defend an irrelevant wasteland, a dead end, one that has no promise of accomplishing or solving anything.

The better tools? Science; requiring sufficient collaborative objective evidence commensurate with the type of claim; requiring claimants to shoulder the burden of proof; arguing from inference to the best explanation; using the standard of the Outsider Test for Faith; ridicule (after all, we know faith-based arguments are special pleading all the way down), and more. Carrier will respond just as believers do when it comes to their faith-based doctrines, by forcing these tools into the grid of Bayes Theorem and calling me a doofus another dozen times or more. So let's see this in practice, a friend comes up to you and says his wife gave birth to a deity. You say show me some objective evidence. We don't need Bayes at all there, do you see? I can understand why Bayesian reasoning without the math is much better when it comes to more complicated issues, but at rock bottom it's all about the evidence, just as apologist Vincent Torley was convinced by it, even though he had previously done his own Bayesian calculations. I see no reason why hammering home the lack of objective evidence won't work as well, or better than using Bayesian math. Bayes is probably worse off in terms of convincing others, for the only people who would slough through it are far less likely to be convinced by it. I've written a book on why responding to fundamentalist arguments in kind gives their beliefs a certain undeserved respectability. So my arguments against the use of Bayes are rooted there, but not found exclusively there. For as you can see I have other arguments that Bayes just doesn't help us (i.e., the math, the equation, the formula). [See Tag for more]

How Not to Be a Doofus about Bayes’ Theorem From Someone Who "Doesn't Really Understand Bayesianism"

The title is a response to two posts Richard Carrier wrote here, and recently here. If anyone disagrees with Carrier we're irrational, ignorant, foolish, and now with a newly released super-bad description, doofus/doofuses. 

I would like to catalog the variety of responses apologists and atheists have toward Bayes, but I won't. What I do know is apart from the people he mentions who "don't understand Bayes" he should also include David Hume, Apologist Michael Licona and Dan Lambert. One wonders if anyone could have argued for anything before Bayes given Carrier's praise. Pffft. What I know is that those who use Bayes come up with wildly different results with regard to the resurrection of Jesus.

--Apologist Richard Swinburne calculates the probability of the bodily resurrection of Jesus, given the existence of a god, is 97%. Swinburne should run that past a peer-review panel including Muslims Jews and Hindu's to see how that goes over. ;-) We know from a historian's perspective that's utterly idiotic! 

--Apologist Vincent Torley calculated that "there’s about a 60-65% chance that Jesus rose from the dead." Of course, that was before he read Michael Alter's book on the resurrection, which I recommended, that had no math in it at all! How could this happen without Bayes? Oh my! But it did. Apparently the shear evidence Alter presented was enough. Wow! Who would have thunk it. 

--Apologists Timothy McGrew and Lydia McGrew calculated the odds of the resurrection of Jesus to be 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000 to 1. *Silence* *Awe* *Respect* Christians must revere them for coming up with the highest calculation any intellectual *cough* has done so far. Can anyone do better here? They need to go see a doctor and get some meds, quickly. Richard Carrier thinks Bayes helps. Okay then. Please tell us how such a useful tool can produce these wide diverse results. Tools are supposed to help. But even among apologists themselves it does no such thing. Carrier says Bayes helps us clarify where we disagree and by how much. Really? We already know this! Dressing up a delusion in math is still a delusion. Responding in kind only gives a delusion an undeserved respectability. This is a major point of mine in Unapologetic: Why Philosophy of Religion Must End. Who's the doofus again? 

In Defense of David Hume Part 6, William L. Vanderburgh On "Hume’s 'Abject Failure' Vindicated"

William L. Vanderburgh defended Hume against John Earman in a very thorough article published in 2005 in Hume Studies, titled, Of Miracles and Evidential Probability: Hume’s “Abject Failure” Vindicated [You can read the PDF right here.]. In it Vanderburgh shows David Hume probably knew of Bayes Theorem and never mentioned it for good reasons. I'm including a few of the important highlights below. I consider it an important contribution on Hume and Earman and even Bayes.

In Defense of Hume Part 5, John Earman Didn't Refute Hume, He Completed Him

It's widely touted that in his book "Hume's Abject Failure" John Earman "refuted" Hume. Did he? Consider what Richard Carrier tells us:
Earman didn't "refute" Hume, so much as he fixed Hume. Hume wrote just a few years before Thomas Bayes solved the problem Hume was beating around the edges at in his Argument against Miracles. Earman shows that reframing Hume's argument in a Bayesian framework fixes everything wrong with the original argument as worded. Hume's mistake is subtle, and arises from the imprecision of his wording and formulation. He hadn't quite known yet of the correct logical form of what he was trying to say, but it is remarkable he came very close to the same insight his contemporary Thomas Bayes did. Earman's fix rehabilitates Hume's argument...
There are definitely some of Hume's arguments that are spot on, that on their own show miracles cannot be believed based on testimonial evidence alone, especially if one is using testimonial evidence to prove a god exists and his religion is true, when compared to the laws of nature represented by Newton's laws of motion, as I argued here. At best one should suspend judgment. But more than this, Hume is not to be considered wrong, just incomplete, and that's a huge difference.

We just need to consider scientific revolutions. Paradigm changes build on each other as science progresses. The previous paradigms aren't to be considered wrong, but rather incomplete. As science progresses we recognize that the science of yesterday was not yet complete. That's it. If you've never read much of Isaac Asimov's, read his essay called The Relativity of Wrong. It will forever change how you view science. He explains why the discredited science of the past is not to be considered wrong, but rather incomplete, by discussing the changing views of the shape of the earth, from flat to spherical to pear-shaped. The same things can be said about Newton's laws of motion as completed (not falsified) by Einstein's relativity equations. Newton's equations were not wrong, even though he didn't factor time into them, as Einstein did. They just don't work at or near the speed of light. So there's no overturned or falsified theory here! In a like manner, Hume gave us the initial paradigm to evaluate testimonies to miracles which still holds true, but now Earman and others are offering other ways to examine miracles from a more complete paradigm. So no, Hume has not been refuted. He is being completed.

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?