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?

Ignorant Amos (IA) and David Cortright (DC) agree with me on using BT appropriately, but they disagree between themselves on how to determine when there's enough evidence to use BT. DC said:
I don't think that Bayes Theorem is the right tool to try and prove or disprove the existence of Jesus as an historical figure. John has an article about on the matter. I am an atheist and not necessarily a mythicist in the classical sense but I don't believe that Jesus was in fact an historical figure for other reasons not normally debated on. I have read all of John's books except for 'The Outsider Test For Faith.' On Bayes Theorem there is no objective outside sources to utilize as a referent for the existence of Jesus. A lot of what is utilized is the gospels themselves which I see as highly suspect and view them more as propaganda to bolster a belief system than an actual biography of Christ.
"There is literally no objective evidence for the existence of Jesus", DC said. "That depends on what one considers objective evidence," replied IA. "There are no reliable contemporary outside sources to corroborate his existence and what we do have is highly questionable," said DC. "You are preaching to the converted", replied IA. "The problem is not convincing ourselves, but those that think otherwise", IA continued. DC said, "a large majority of the so called life of Jesus is literally taken from O.T. stories retold out of context and applied to a fictional figure." IA replied, "I know all this, but it is the others that need convincing. Furthermore, that has nothing to do with the existence of an itinerant preacher who was later mythologised, which is the secular historicist position." DC concluded, "BT only works when we have good evidence to plug in. However, there is no actual good evidence for a historical Jesus to begin with. So, BT is not really useful in this particular case." IA concluded, "It works regardless of the level of evidence. The conclusion is dependant on what sort of evidence. The better the evidence, the better the conclusion." LINK.

Richard Carrier has argued that the probability of Jesus' existence is 1 in 3 if we grant the most favorable interpretations of the evidence. But it's down to 1 in 12,000 if we don't grant the most favorable interpretations of the evidence.

I have argued that since BT is mathematical equation only exact figures will do. Try multiplying 1,2,3,4...9 times 9,8,7,6...1. It cannot be done. I have also argued that we should NOT base our calculations on the most favorable interpretations of the evidence, if we want to get to the truth. What other mathematical equation is granted higher numbers than required by the data? None! So inputting numbers that are not exact ones misleads people, as does inputting numbers higher than the data allows. That's two good reasons why BT cannot, nor should not, be used on nonsensical miraculous claims. Therefore, Carrier's closer-to-the-truth calculation is 1 in 12k, which is surely a lot of time wasted with Bayes. It also helps legitimize a historical view of Jesus by taking it so seriously. Additionally, Carrier's efforts will not be able to convince people any better, but instead, has the backfire effect of convincing fewer people who sludge through the math.

By contrast DC thinks
There is literally no objective evidence for the existence of Jesus. Jesus personally never wrote one word that was preserved for posterity's sake. There are no reliable contemporary outside sources to corroborate his existence and what we do have is highly questionable. Not to mention the fact that a large majority of the so called life of Jesus is literally taken from O.T. stories retold out of context and applied to a fictional figure.
So whether someone uses BT in assessing the possibility that there was a historical person behind Jesus depends on the credibility of the evidence. Carrier seems to think Bayes is useful here because there is some credible evidence. DC doesn't. They each choose based on their views of the evidence. So considering these questions is like specifying which whisker when plucked, no longer leaves a man with a beard. ;-)

How can the strength of the evidence be determined apart from Bayes?

We can use the Look & See Test, which I just made up. If you don't see it when it should be there, you can conclude it probability doesn't exist.

We can assess the credibility of any alleged evidence over against our previous Background Knowledge. That's an assessment depending on how extensive our knowledge is, and whether it was gained from objective evidence and/or credible testimony, rather than from faith.

We can use the Inference to the Best Explanation.

We can use Sagan's Razor as I wrote about in the aforementioned infidels paper: "Extraordinary claims require extraordinary evidence” (ECREE).

We can use Hitchens’ Razor: “What can be asserted without evidence can also be dismissed without evidence.”

We’ve been reasoning about objective evidence and changing our minds based on the available evidence throughout human history. We’ve also been weighing alternative hypotheses and seeking the best explanation of the evidence for as long as we’ve been reasoning well. So what ends up being called Bayesian reasoning is a cluster of separate questions reasonable people seek answers for when seeking the best conclusion from the available evidence. There’s nothing about Bayesian reasoning we didn’t already do before Bayes quantified it. Every question Bayes asks was already being asked and answered before Thomas Bayes quantified that process. So there’s nothing about what is being called “Bayesian reasoning” that’s specifically due to BT. One can ask and answer these questions and call it Bayesian reasoning if they want to do so. But it’s not something that originated with BT, nor is it doing any math, nor is this reasoning helpful unless there is first some objective evidence.

No prior, no Bayes. God belief priors matter but only if one has a god belief. If one doesn't have a god belief then that prior doesn't matter in assessing the evidence.

Carrier claims we can use the Smell Test in his book, Proving History: Bayes's Theorem and the Quest for the Historical Jesus. A quick look at Wiktionary tells us it is "An informal method for determining whether something is authentic, credible, or ethical, by using one's common sense or sense of propriety." But come on now. Common sense has been notoriously wrong. Common knowledge. Common. Riiiiiight! Carrier explains:

The ‘Smell Test’ is a common methodological principle in the study of myth, legend, and hagiography. This test can be most simply stated as “if it sounds unbelievable, it probably is.” When we hear tales of talking dogs and flying wizards, we don't take them seriously, even for a moment. We immediately rule them out as fabrications. We usually don't investigate. We don't wait until we can find evidence against the claim. We know right from the start the tale is bogus. It is certainly ubiquitously accepted by historians in every field.
Then he inserts a whole boatload of arguments and assumptions.
It is suspiciously only rejected by religious believers, and then only when it's applied to amazing claims they prefer to believe. They ground this rejection in the claim that we shouldn't be biased against the supernatural, and God can do anything. Yet if they honestly believed in those principles they would be compelled to concede the miracle claims of every religion “because you shouldn't be biased against the supernatural, and God can do anything.” This includes all the pagan miracles (incredible apparitions of goddesses, mass resurrections of cooked fish, wondrous healings, and teleportations), Muslim miracles (splitting moons, wailing trees, flights to outer space), Buddhist miracles (bilocation, levitation, creating golden ladders with a mere thought), and indeed every and any amazing claim whatever. Tales “proving” reincarnation? We can't reject them—because God can do anything. Ghosts confirming to the living that heaven is run by a Chinese magnate and his staff? We can't rule it out. That would be bias against the supernatural.

Honestly living that way would be impossible. You would have to believe everything you read or hear unless you can specifically present evidence sufficient to discount it: an impossible task. You would be left with a belief system hopelessly frightening and contradictory—and mired in a thousand false beliefs. Such behavior also goes against all established background knowledge, which contains endless examples of miracle claims refuted by fortuitous inquiry (and no good case of any miracle claim surviving such inquiry). In other words, our bias against the supernatural is warranted, just as our bias against the honesty of politicians is warranted: we've caught them being dishonest so many times it would be foolish to implicitly trust anyone in politics. Likewise, amazing tales: we've caught them being fabricated so many times it would be foolish to implicitly trust any of them.

The Smell Test thus represents an intuitive recognition of: (a) the low prior probability of the events described (i.e., P(h|b) (b) the ease with which the evidence could be fabricated (i.e., P(e|~h.b) is always high, unless we have sufficient evidence to the contrary), in fact often the ease with which such an event if real would produce or entail much better evidence (i.e., P(e|h.b) is often low); (c) how typically miracle claims are deliberately positioned in places and times where a reliable verification is impossible (and when such verification is possible, are refuted), which fact alone makes them all inherently suspicious; and (d) sometimes the similarity of a miracle story to other tales told in the same time and culture is additionally suspect, like the odd frequency with which gods in the ancient West rose from the dead, transformed water into wine, or resurrected dead fish, oddities that curiously never occur anymore, and which are so culturally specific as to suggest more obvious origins in storytelling a thousand false beliefs. Such behavior also goes against all established background knowledge, which contains endless examples of miracle claims refuted by fortuitous inquiry (and no good case of any miracle claim surviving such inquiry).
Carrier thinks the Smell Test incorporates Hitchen's Razor, Sagan's Razor, and the OTF. It also suspiciously looks just like another part of Bayes. Imagine that? Those are different tests. I defy someone to show me they are all one and the same tests. When one has a hammer...

Carrier says the Smell Test is "intuitive" to everyone but 85-90% of the people on the planet who believe in religious faiths and paranomal claims galore. That's why the Smell Test won't work with them, so he has to insert an argument within the test against doing so. He also is claiming that Hitchen's Razor, Sagan's Razor, the OTF, and Bayes are all intuitive. The claim that good reasoning is "intuitive" betrays a type of overconfidence that is badly mistaken. As a former college instructor in critical thinking I know for a fact we have to teach even the best of best, in the best occupations, how to reason well. I taught lawyers and detectives how to think, so I know. No, good reasoning is not intuitive. It takes effort and study. So where is the evidence for his claim that the Smell Test (and with it part of Bayes) is intuitive, that people use it even when they're not conscious of doing so, including people who lived before Thomas Bayes did, even people who badly misuse it, even people who basically flunked out of math in High School?

The Smell Test is dependent on a scientific framework that does not come from Bayes. Take Bayes back in time to the witch hunts and you'll see that the Smell Test would conclude Floyd's cow died because of a neighbor's spell. So if witch-hunting superstitious people knew of Bayes they could conclude spells are real.

Bayes would be ineffective within a superstitious framework. Just consider how many theists use it beginning with Bishop Bayes himself, stretching for a couple centuries to Richard Swinburne and the McGrews!

What's missing?

Skepticisim and scientific understanding. Skepticism based in science kills superstition. His Smell Test could ONLY be advocated by someone with a modern scientific framework. Bayes doesn't do that all by itself. But Hitchen's Razor, Sagan's Razor, and the OTF do. [The OTF forces believers to consider the objective evidence aganist their own faith.] If there is no credible evidence for a claim then using Bayes is a waste of time. Ridicule it.


John W. Loftus is a philosopher and counter-apologist credited with 12 critically acclaimed books, including The Case against Miracles, God and Horrendous Suffering, and Varieties of Jesus Mythicism. Please support DC by sharing our posts, or by subscribing, donating, or buying our books at Amazon. Thank you so much!