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? 

I've already stated My Major Objection With Bayes Theorem. Undeterred, Carrier comes up with (not ten) but nine statements that doofuses have said about Bayes. I'm represented in statements five and seven. So let's talk about them both.
Doofus Statement Number Five: Loftus: “To use the mathematical formula of Bayes’ Theorem then ipso facto it requires using specific numerical inputs, not ranges of numbers.”

Once you’ve stopped laughing at him, let me make sure we are all clear on this:

Using Bayes’ Theorem never requires you to use “specific numerical inputs.” At all.
Let's first translate Bayes into simple English:
It is a theorem about conditional probabilities: the probability that an event A occurs given that another event B has already occurred is equal to the probability that the event B occurs given that A has already occurred multiplied by the probability of occurrence of event A and divided by the probability of occurrence of event B.
Notice the words "equal" "multiplied" "divided" in this simple English description? Yep, those are mathematical words.

Next, let's quote what I said in context:

To use the mathematical formula of Bayes Theorem then ipso facto it requires using specific numerical inputs, not ranges of numbers. Yet you cannot do that because of the nature of unique Christian miracle claims in the ancient world. Math is therefore not the tool to use here.
Language based on sufficient objective evidential reasoning is the proper tool here, and words like "impossible" and "virtually impossible" are legitimate descriptions of the prior probability of these miracles without having to multiply or divide anything, and without giving deluded people a bone.
In this case Richard Carrier fails to really really understand there's a distinction between Bayes Theorem and Bayesian Reasoning. The reason Bayes Theorem works in math is because it adequately describes Bayesian Reasoning. We can reason according to Bayes without using math. We just don't plug in any numbers. No math is involved in so far as no specific numbers are required. The equation shows the probabilities of events based on other events regardless of any math.

Bayes Theorem is a theorem,  an equation, in the same way Sir Isaac Newton's 2nd law of motion, F=MA, is an equation. Mathematical equations require specific numerical inputs. Again, whenever Bayes Theorem is treated as the mathematical formula it specific numbers are used. Period. Otherwise it's not a theorem or an equation.
Carrier says,
Thomas Bayes’ paper proving Bayes’ Theorem never once used a single cardinal number (only in an appendix that gave some toy examples of its application). No proof of Bayes’ Theorem ever once uses any number. And many applications of Bayes’ Theorem involve no numbers.
Now Carrier fails to understand there's a distinction between explaining the need for a mathematical formula, and using one. Whenever the reasoning of Bayes is being explained to people, numbers are not used for the logic of the numbers needs justified. Whenever someone offers a range of probabilities for an event--as opposed to a specific number--Bayesian reasoning is being used not the math. Does he not know that the proof of Bayes is found in the logic of it, that we can't use math to prove Bayesian math? So why does he assert math is being done without the math? He cannot just assert that!...well, unless you're Richard Carrier.
Speaking of which he goes on to say:
Doofus Statement Number Seven: Loftus: “We can’t use Bayes’ Theorem to rule out miracles, because there is no data, and Bayes’ Theorem only works with data.”

Yep. A doofus said this. I’m paraphrasing. But it’s what he argued. Multiple times.

Every time anyone pointed out to him that in fact there is a ton of data on this, and that in fact he was reaching his own conclusion that miracles were too improbable to credit on all that data, this doofus just ignored them and kept repeating the argument. “Bayes only works with data. There is no data. So you can’t use Bayes.” Holy balls.

We kept trying to explain to this doofus that we were agreeing with him: miracles are too improbable to credit. What we were adding, was showing how that conclusion is logically valid. He never listened. He still doesn’t get it. Classic doofus.
His paraphrase shows he just was not listening. I said, "We can’t use Bayes’ Theorem when there is no data. Bayes’ Theorem only works with data. Since miracles like the unique Christian belief in a virgin who gave birth to a redeeming deity has no relevant prior data to work from, there's no way to do the math. That is, since there's been no other bonafide virgin birth miracles to work from, we cannot do a mathematical calculation for the Virgin Mary.

This is key, for Carrier misunderstands what my point was, which means he's the one not paying attention. I said we cannot do a Bayesian calculation for the virgin birth claim due to the lack of bonafide data. His response misunderstands what this data is:
In actual fact the reason we know, for example, that virgin born humans are impossible (colloquially speaking), is precisely because of the vast quantities of data we have that show humans don’t spontaneously conceive, and that no one exists with the power to effect one, even once. The absence of evidence is data.
To do a calculation showing the probability of the virgin birthed god we need data showing the probability of that miracle in relation to other virgin births. But here he admits all the data we have is that no virgin ever gave birth to a deity. This is my point. Yes we have that kind of data. That's all the data we have, and it all says there has never been a bonafide virgin birth. Along with plenty of data that virgin birth status was attributed to people in the ancient superstitious past who were deemed very important, nothing else. How can you calculate anything else but that virgins don't give birth to deities? How can you do the math when confronted with the claim that a virgin in the ancient world gave birth to an incarnate son of god who was 100% divine and 100% human with everything essential included? Do it! I dare you. Be foolish is you will.
Carrier continues with his misunderstanding:
But more importantly, it’s not just absent evidence. The presence of non-virgin births is positive evidence of how humans conceive. And the vast quantity of fake stories of miraculous births and beings is evidence, too—that such claims tend to be fake. That we have never reliably documented a deviation from these facts, establishes an extremely low probability it can happen (by Laplace’s Rule of Succession). That’s a low prior, entailed by vast evidence.

Similarly, any claim that though humans don’t spontaneously conceive, nevertheless sorcerers can do it (or demons or angels or gods or faeries or extraterrestrials or timelords, or super-intelligent shades of the color blue), meets with the same vast data: everywhere we’d expect to see evidence of any such beings, we see none; but find endless fakes. The prior probability that they nevertheless still exist (so as to effect a singular virgin birth), is therefore, by Laplacean succession, absurdly small.
The data lacking I referred to was data showing some prior probability from other bonafide virgin birthed gods. Again, what he does is admit the only data we have, which makes my point. The data doesn't just show such a thing is absurdly small. That data shows no such virgin birthed god took place.
In other words, the reason the doofus is logically justified in concluding miracles have an extremely low probability, is Bayes’ Theorem.
What? He's responding by merely re-asserting his point without taking into consideration what I've said. At all. I'm saying he cannot use Bayes here, that there is no prior data to work from, that the only reasonable position to take is the one skeptics, agnostics, scientists and atheists have always taken. We say believers have the burden of proof. So show us the evidence. Without any evidence we're reasonable to conclude miracles did not take place. Why should we ever say what the numerical odds are of a virgin birthed deity before the objective evidence exists (and we KNOW there is none!)? 
Carrier duplicitously makes the difference between Baysian reasoning despite what he said earlier:
Every opportunity for miraculous powers to have been reliably evinced, turned up negative. Every time that happened throughout history, the prior probability of the miraculous was downgraded. Iterate this thousands of times, and that prior ends up absurdly low. We don’t need to know how low it is; because we already know it’s too low to give any attention to. But we do know what could change our minds, which means we do know something about how low the prior probability is: it’s exactly as low as the probability would be of the evidence that would otherwise have convinced us unless miracles were real. That’s a logically necessary truth.
Because that’s how evidence works. The only way evidence can change your mind about the probability of a thing, is by updating the probability of the thing. And the only way to update the probability of a thing in a logically valid way, is Bayes.
And when we say you are justified in declaring miracles “impossible” in that colloquial sense, because of Bayes’ Theorem, we are not saying “because you pulled out a calculator and punched some numbers in.” No. We mean the argument you reached that conclusion with, is logically validated by Bayes’ Theorem....And at no point in this process do we ever need to state a number or use a calculator. The conclusions all follow as a matter of logical necessity, from plain statements in English. Because the theorem is true. And what we just said, conforms to the theorem.
I don't assign 0 or 1 to the probabilities of miracles since I don't think math is the proper tool without data that shows a prior possibility. So I prefer words over math, words like possible, impossible, probable, extremely probable virtually certain and certain. So to say no evidence would convince me of something is not what I say, nor should I, for I'm not using Bayesian math when considering miracles. Bayesian math requires me to put a number to something I refuse to put a number to, something I don't think numbers can represent. I am always open to objective evidence as any rational person should be. My mantra is always show me the evidence. The person making an extraordinary claim has the burden of proof. Until I see that evidence there is no reason why I should think the claim is true. I can say something is impossible based on all that I know, then revise it upon observing the evidence. 

Knowledge is always contextual. That's why I say, given all that I know, it's impossible a virgin gave birth to a deity in the ancient world. I know too much about this claim. History would have to be re-written, evidence would have to disappear and that which is illogical would have to be shown logical. There is no blank slate here, no veil of ignorance either. Since human knowledge isn't absolute but contextual I can and do say such a thing is impossible based on all I know, and my claim is as good as what I know. It's the math that tries to pigeon hole us into saying what we cannot say or need not say.
Look, we already know people made up math. It works unusually well, but not at the fringes of reality. See the book by Harold Bloom on this. Numbers are strange beast sometimes. For instance, we know infinity is not a number. So not everything is quantifiable. If we were to calculate the odds of miracles they would be so abysmally small as to equal zero, per Borel's Law. But I even object to that. It forces me to play the game called Christian. For as soon as we put in a number Christians can say nothing is impossible for their god and the poof a miracle and put an absurdly high number to it too! 
Adopting math to define zero and 100% certainty in historical matters, especially unique Christian miracle claims, is doing an injustice to both math and to Christian miracle claims. Since Math's definition of zero is 0, and Math's definition of certainty is 100% one can never say something is impossible or certain. So there's no need for Bayes at 0 and 1. It's okay to say something is impossible without being forced into the math definition of 0, or certain without being forced into the math definition of 1. Math is too high of an unattainable absolute standard for human experience. It disallows us saying what is really impossible as well as that which is really certain. It makes that which is impossible possible, and that which is certain uncertain.
It's false to say the fundamentalist view of Christianity is possible, given all that I know, because that would mean history would have to be re-written, evidence would have to disappear, and that which is logical would have to become illogical.
Everything we know is that virgin birth claims of deities are false. Yes, that's data. So you should either put 0 as the prior probability or not do the math. To grant a nonzero prior probability is granting too much! That's my argument. Why don't we simply say to Christians "show me the objective evidence" then call it a day? Don't play games here. Do they, or do they not, have the burden of proof?  
The Outsider Test for Faith calls for it, that they shoulder the burden of proof. So Carrier has a choice to make. Continue endorsing the Outsider Test for Faith, or show it wrong and stick to Bayes on miracle claims like the one above.
Richard Carrier has said of the OTF:
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.