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.
There are two insurmountable problems here. First, there's no bonafide previous data to work from even on Christian grounds, because they claim only one virgin gave birth to an incarnate god in the ancient world. Since that's the case atheist objectors are suggesting an approximate range of numbers instead. This leads to insurmountable problem number two. We cannot multiply or divide an approximate range of numbers. To use the math they must pick a specific odds number, not a range of numbers. What number should they pick? Is it 1 billion to 1 odds, or 100 trillion to 1 odds? What if that number is larger, 100 trillion to 1 odds, or larger? How can they know? Pick one and use it in your Bayesian equation if you claim to use Bayes, for it is a math equation! You can't pick a number because there is no data and you can't pick a range of numbers if you're doing Bayes. Period.
At some point we approach a number that is equal to zero. Borel's Law states that in some specific physical examples "phenomena with very low probabilities do not occur," odds below 1 in 10 to the 50 power.
Now imagine claiming to use Sir Isaac Newton's 2nd law of motion equation, F=ma, without putting any specific numbers into it. That's what some people are doing with Bayesian math. You cannot claim to be doing math without using specific mathematical inputs, period. Anyone who claims to do this is being disingenuous, or ignorant, or both. Sorry.
You may largely be thinking like a Bayesian or following the logic of Bayes, but you are not doing BAYES since it is a mathematical equation.
That no one can guess the priors matters. Only real data can be imputed, otherwise we're unreasonably giving away far too much ground to Bayesian apologists, who only ask that we grant such claims a minuscule chance. For if we do, then with their god all things become probable (anything an apologist wants anyway) not just possible, and there is no way to stop that train dead in its tracks on its way to the heavenly city.
I think this is as close to a refutation as is needed for using Bayes to determine the probability of the virgin birthed god and with it, the resurrection of Jesus. The numbers have just hoisted them on their own petard. For how can we determine the prior probability of the unique Christian resurrection miracle claim (on Christian grounds) unless there are other bonafide resurrections we can gather data from? Again. Pick that number and show why it can approximate all the numbers on a continuum between 1 billion and 100 trillion.
Discussion:
Richard Carrier John, YOU are the one saying the probability is vanishingly small. So YOU are the one who needs to tell US what probability YOU mean by that: How small? One way to answer this is to ask yourself: What evidence would convince me it was true? Then ask how improbable it is that that evidence will turn up. That indicates your prior assumption. And you can't say "no evidence conceivable could ever convince me" because that's literally rejecting evidence-based reasoning; you are then just affirming a dogma, and can never then know what's true, because you will reject all evidence of it. And you can't say "the evidence that could convince me has a literally zero probability" because that constitutes asserting you are omniscient and infallible, which is the same error (no one is omniscient; no one is infallible; so to claim you are, is bonkers). I know you won't listen to anything I just said. But I post it here so people can get a handle on the madness you are trying to sell here, and it's discrediting atheists. Theists are going to quote you saying you can never be wrong and will reject any and all evidence no matter what it was. And that will be the story of you.
John W. Loftus Richard, you ask what evidence could turn up to show a virgin birthed god incarnate? You assume incorrectly that I live in a vacuum with a blank slate of a mind behind a veil of ignorance in a cave. Truth is, I know more about the history of such a claim than most people on the planet. You cannot expect me to erase what I know and start over. There are many things I know that would have to be overturned, plus overcoming how someone could be 100% man and 100% god with nothing essential left out. I just don't see anything that could convince me god incarnate was born of a virgin in the 1st century ancient world. History itself would have to be re-written; evidence would have to disappear; contradictory conceptions must be shown to be not contradictory. So, given what I know, nothing could convince me. I assign the prior probability to be a big fat zero, or so close to zero the numbers are indistinguishable.
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.
There are two insurmountable problems here. First, there's no bonafide previous data to work from even on Christian grounds, because they claim only one virgin gave birth to an incarnate god in the ancient world. Since that's the case atheist objectors are suggesting an approximate range of numbers instead. This leads to insurmountable problem number two. We cannot multiply or divide an approximate range of numbers. To use the math they must pick a specific odds number, not a range of numbers. What number should they pick? Is it 1 billion to 1 odds, or 100 trillion to 1 odds? What if that number is larger, 100 trillion to 1 odds, or larger? How can they know? Pick one and use it in your Bayesian equation if you claim to use Bayes, for it is a math equation! You can't pick a number because there is no data and you can't pick a range of numbers if you're doing Bayes. Period.
At some point we approach a number that is equal to zero. Borel's Law states that in some specific physical examples "phenomena with very low probabilities do not occur," odds below 1 in 10 to the 50 power.
Now imagine claiming to use Sir Isaac Newton's 2nd law of motion equation, F=ma, without putting any specific numbers into it. That's what some people are doing with Bayesian math. You cannot claim to be doing math without using specific mathematical inputs, period. Anyone who claims to do this is being disingenuous, or ignorant, or both. Sorry.
You may largely be thinking like a Bayesian or following the logic of Bayes, but you are not doing BAYES since it is a mathematical equation.
That no one can guess the priors matters. Only real data can be imputed, otherwise we're unreasonably giving away far too much ground to Bayesian apologists, who only ask that we grant such claims a minuscule chance. For if we do, then with their god all things become probable (anything an apologist wants anyway) not just possible, and there is no way to stop that train dead in its tracks on its way to the heavenly city.
I think this is as close to a refutation as is needed for using Bayes to determine the probability of the virgin birthed god and with it, the resurrection of Jesus. The numbers have just hoisted them on their own petard. For how can we determine the prior probability of the unique Christian resurrection miracle claim (on Christian grounds) unless there are other bonafide resurrections we can gather data from? Again. Pick that number and show why it can approximate all the numbers on a continuum between 1 billion and 100 trillion.
Discussion:
Richard Carrier John, YOU are the one saying the probability is vanishingly small. So YOU are the one who needs to tell US what probability YOU mean by that: How small? One way to answer this is to ask yourself: What evidence would convince me it was true? Then ask how improbable it is that that evidence will turn up. That indicates your prior assumption. And you can't say "no evidence conceivable could ever convince me" because that's literally rejecting evidence-based reasoning; you are then just affirming a dogma, and can never then know what's true, because you will reject all evidence of it. And you can't say "the evidence that could convince me has a literally zero probability" because that constitutes asserting you are omniscient and infallible, which is the same error (no one is omniscient; no one is infallible; so to claim you are, is bonkers). I know you won't listen to anything I just said. But I post it here so people can get a handle on the madness you are trying to sell here, and it's discrediting atheists. Theists are going to quote you saying you can never be wrong and will reject any and all evidence no matter what it was. And that will be the story of you.
John W. Loftus Richard, you ask what evidence could turn up to show a virgin birthed god incarnate? You assume incorrectly that I live in a vacuum with a blank slate of a mind behind a veil of ignorance in a cave. Truth is, I know more about the history of such a claim than most people on the planet. You cannot expect me to erase what I know and start over. There are many things I know that would have to be overturned, plus overcoming how someone could be 100% man and 100% god with nothing essential left out. I just don't see anything that could convince me god incarnate was born of a virgin in the 1st century ancient world. History itself would have to be re-written; evidence would have to disappear; contradictory conceptions must be shown to be not contradictory. So, given what I know, nothing could convince me. I assign the prior probability to be a big fat zero, or so close to zero the numbers are indistinguishable.
John W. Loftus What number would YOU assign the prior probability?
John W. Loftus Richard, next you might ask me if my mind would be convinced if this supposed god-man personally appeared to me.
Since this has not happened let's do the math. Per above, I would consider such an experience to have a zero chance of happening. History would have to be re-written, evidence overturned and the logic of an incarnate god shown to be illogical.
John W. Loftus Now you might say I arrived at this conclusion due to a Bayesian analysis. Not a mathematical one, which is a main point of mine, but by Bayesian logic in some sense, but not in your sense, since at no point did I use math to come up with it. And at no point in my off repeated use of Bayesian logic did I get the prior probability correct until I came to the conclusion I now know to be correct, after years of study.Since this has not happened let's do the math. Per above, I would consider such an experience to have a zero chance of happening. History would have to be re-written, evidence overturned and the logic of an incarnate god shown to be illogical.
Richard Carrier John, "Since this has not happened let's do the math. Per above, I would consider such an experience to have a zero chance of happening. History would have to be re-written, evidence overturned and the logic of an incarnate god shown to be illogical."
You clearly don't understand here how probability works. That's frustrating. Obviously if a God could possibly show you that indeed, Satan has kept you inside an illusion that caused you to misperceive all the evidence (thereby indeed realizing all you thought about history and so on was wrong), you'd change your mind just as you said you would. There are other things that could happen (e.g. God could be evil, and thus indeed consistently with all history have sown confusion in the evidence on purpose, and also at the same time have effected a virgin birth in the first century). Each of those things is not logically impossible. Since "zero probability" is a strict synonym of "logically impossible," it is logically necessarily the case that anything that is NOT logically impossible (and therefore is logically possible) has a NON-zero probability. But of course, the Satan and Evil God scenarios, though possible, we agree are extremely improbable (see my blog for why it is logically valid to conclude Cartesian Demons are extremely improbable). That's not zero. It's just really, really close to zero. But there's a difference. And that difference is what makes it logically possible for you to change your mind, if ever you get evidence enough to realize the Satan or Evil God scenarios (or anything else) is true. And yes, this is all Bayesian. Your conclusion that the Satan and Evil God scenarios are extremely improbable, is Bayesian. Your conclusion that virgin births are false without first being convinced of something like the Satan or Evil God scenario, is Bayesian. It's Bayesian all the way down. And you really need to learn this. Because not knowing it, is going to make it easy for Christian apologists to use you as a poster boy for atheists being dogmatists and not knowing how logic works.
John W. Loftus Richard, as before, if any of these suggestions of yours is to be, then the past must be changed, existing evidence must disappear and that which is illogical must become logical. This is the case with one of these Christian beliefs, so it's much more true of the Christian religion itself.
I'm an equal opportunity atheist, exempting no faith-based claim without any objective evidence to it. I consider Scientology to have a zero possibility to it, as I do to Islam, Hinduism, the John Frum cargo cults, and the others. I do so because there is no objective evidence to them. The best explanation for this abysmal lack of evidence is that they are not true. So what else should I say? It's disingenuous and ignorant to hold out a possibility for them all, so it's better to be honest and say none of them are possibly true. Listen, is it true you don't think anything can convince you of any of them or not? Bayes makes you dishonest.
Furthermore, it looks like you have a hammer and everything looks like a nail. To you, every reasonable person uses Bayes. You claim I used it even though I didn't know of it when rejecting my former religion, much less did I ever use the math in the equation. I looked for the objective evidence for these extraordinary claims and found none, so I rejected them. I concluded that atheism is the best explanation of what I discovered, the woeful lack of evidence.
John W. Loftus While thinking in terms of all of Bayes is better, there are parts of Bayes that do well on their own. In many cases, especially in miraculous ones, all we need to do is to look for the objective evidence of an extraordinary claim and then ask what is the best explanation for the abysmal lack of evidence. The prior possibilities of Bayes need not come into play.
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