We often hear it said that historians deal with probabilities, not certainties. Thus Bart Ehrman explains in his latest book:
Historians, of course, can ask what probably happened in the past, for example, in the earthly ministry of Jesus with his disciples. And historians can establish with relative levels of probability that this, that, or the other tradition is likely something that happened or didn’t happen. But history is all a matter of such greater or lesser probabilities. When dealing with a figure such as Jesus, these probabilities are established only by critically examining the memories that were recorded by later authors.
Ehrman, Bart D. (2016-03-01). Jesus Before the Gospels: How the Earliest Christians Remembered, Changed, and Invented Their Stories of the Savior (p. 31). HarperCollins. Kindle Edition. [My bolded emphasis in all quotations.]
Interestingly Ehrman assumes as a certainty (not probability) that the gospel narratives were sourced from “memories” of Jesus (whether personally experienced or fabricated memories) and sidesteps an entire area of biblical scholarship that argues the evangelists themselves imaginatively created the narratives of Jesus inspired by analogous tales in the Jewish Scriptures and other writings. He also uses the language — e.g. “that were recorded by” — we associate with historical “reports” or “records” thus further entrenching his bias in the mind of the reader. But we’ll leave Ehrman’s own contradictions aside for now and focus on the more general principle.
Anyone who has read scholarly works relating to Christian origins is familiar with the language of probability, possibility, maybe, likelihood, etc. Too often, however, this same language magically transforms itself as the argument proceeds into certainty. As Jacob Neusner in Rabbinic Literature and the New Testament complained of “pseudocritical” scholarship, it is commonly characterized a number of faults including
the use of “presumably,” “must” or “may have been,” and “perhaps,” a few sentences later magically converted into “was” and “certainly.” (p. 88)
A serious possibility
But a few days later, Kent was chatting with a senior State Department official who casually asked, “By the way, what did you people mean by the expression ‘serious possibility’? What kind of odds did you have in mind?” Kent said he was pessimistic. He felt the odds were about 65 to 35 in favor of an attack. The official was startled. He and his colleagues had taken “serious possibility” to mean much lower odds. Disturbed, Kent went back to his team. They had all agreed to use “serious possibility” in the NIE so Kent asked each person, in turn, what he thought it meant. One analyst said it meant odds of about 80 to 20, or four times more likely than not that there would be an invasion. Another thought it meant odds of 20 to 80— exactly the opposite. Other answers were scattered between those extremes.
Tetlock, Philip; Gardner, Dan (2015-09-24). Superforecasting: The Art and Science of Prediction (Kindle Locations 858-864). Random House. Kindle Edition.
A fair chance
When in 1961 President Kennedy sought to know the chance a small army of Cuban expatriates landing at the Bay of Pigs would have in toppling Fidel Castro his Chiefs of Staff concluded that the plan had a “fair chance” of success.
The man who wrote the words “fair chance” later said he had in mind odds of 3 to 1 against success. But Kennedy was never told precisely what “fair chance” meant and, not unreasonably, he took it to be a much more positive assessment.
Tetlock, Philip; Gardner, Dan (2015-09-24). Superforecasting: The Art and Science of Prediction (Kindle Locations 872-873). Random House. Kindle Edition.
Sherman Kent of the CIA’s Office of National Estimates sought a remedy by setting out more precise meanings:
But the chart was never adopted.
Objections to using numbers
People liked clarity and precision in principle but when it came time to make clear and precise forecasts they weren’t so keen on numbers.
- Some said it felt unnatural or awkward, which it does when you’ve spent a lifetime using vague language, but that’s a weak argument against change.
- Others expressed an aesthetic revulsion. Language has its own poetry, they felt, and it’s tacky to talk explicitly about numerical odds. It makes you sound like a bookie. Kent wasn’t impressed. “I’d rather be a bookie than a goddamn poet,” was his legendary response.
Tetlock, Philip; Gardner, Dan (2015-09-24). Superforecasting: The Art and Science of Prediction (Kindle Locations 890-894). Random House. Kindle Edition. (My own formatting in all quotations)
Of course numbers can give a false impression of certainty and exactness where neither is possible.
[Y]ou cannot convert vague and dubious approximations (not to speak of nonsense and half-truths) into a mathematical science simply by transcribing them into the symbolism of mathematics. (Stanislav Andreski, Social Sciences As Sorcery, 131)
But there remains an honest use of numbers:
A more serious objection— then and now— is that expressing a probability estimate with a number may imply to the reader that it is an objective fact, not the subjective judgment it is. That is a danger. But the answer is not to do away with numbers. It’s to inform readers that numbers, just like words, only express estimates— opinions— and nothing more.
Similarly, it might be argued that the precision of a number implicitly says “the forecaster knows with exactitude that this number is right.” But that’s not intended and shouldn’t be inferred.
Also, bear in mind that words like “serious possibility” suggest the same thing numbers do, the only real difference being that numbers make it explicit, reducing the risk of confusion.
And they have another benefit: vague thoughts are easily expressed with vague language but when forecasters are forced to translate terms like “serious possibility” into numbers, they have to think carefully about how they are thinking, a process known as metacognition. Forecasters who practice get better at distinguishing finer degrees of uncertainty, just as artists get better at distinguishing subtler shades of gray.
Tetlock, Philip; Gardner, Dan (2015-09-24). Superforecasting: The Art and Science of Prediction (Kindle Locations 895-903). Random House. Kindle Edition.
Then there is the question of accountability and what Tetlock labels “the wrong-side-of-maybe fallacy.” It is easy to conclude that the weather forecaster was wrong if she said there was a 70% chance of rain and it didn’t rain but of course she was not wrong. Or at least we cannot tell from just one forecast like that. The only way to know if the forecaster is accurate is if we took a hundred occasions on which she predicted a 70% chance of rain and saw that it rained on around 70 of those 100 days. It is very easy to fallaciously assume that a probability figure has been proved wrong. So no wonder elastic language is so widely preferred:
So what’s the safe thing to do? Stick with elastic language. Forecasters who use “a fair chance” and “a serious possibility” can even make the wrong-side-of-maybe fallacy work for them: If the event happens, “a fair chance” can retroactively be stretched to mean something considerably bigger than 50%— so the forecaster nailed it. If it doesn’t happen, it can be shrunk to something much smaller than 50%— and again the forecaster nailed it. With perverse incentives like these, it’s no wonder people prefer rubbery words over firm numbers.
Tetlock, Philip; Gardner, Dan (2015-09-24). Superforecasting: The Art and Science of Prediction (Kindle Locations 917-921). Random House. Kindle Edition.
Tetlock and Gardner inform us that the Office of National Estimate’s move to using numbers only gathered pace “after the debacle over Saddam Hussein’s supposed weapons of mass destruction, and the wholesale reforms that followed”.
When CIA analysts told President Obama they were “70%” or “90%” sure the mystery man in a Pakistani compound was Osama bin Laden, it was a small, posthumous triumph for Sherman Kent. In some other fields, numbers have become standard. “Slight chance of showers” has given way to “30% chance of showers” in weather forecasts. But hopelessly vague language is still so common, particularly in the media, that we rarely notice how vacuous it is. It just slips by.
Tetlock, Philip; Gardner, Dan (2015-09-24). Superforecasting: The Art and Science of Prediction (Kindle Locations 925-928). Random House. Kindle Edition.
Hopelessly vague language is also common in historical studies of early Christianity. Let’s look again at those opening two quotations from Ehrman and Neusner:
Historians, of course, can ask what probably happened in the past, for example, in the earthly ministry of Jesus with his disciples. And historians can establish with relative levels of probability that this, that, or the other tradition is likely something that happened or didn’t happen. But history is all a matter of such greater or lesser probabilities. When dealing with a figure such as Jesus, these probabilities are established only by critically examining the memories that were recorded by later authors.
and
the use of “presumably,” “must” or “may have been,” and “perhaps,” a few sentences later magically converted into “was” and “certainly.”
Now compare these words with another passage from Ehrman also in Jesus Before the Gospels:
And so, for example, in what context would stories emerge about Jesus’s conflicts with the Pharisees, ending in a clever one-liner? Probably in a context where the Christians themselves were being confronted by non-Christian Jews, over their refusal, for example, to keep the Jewish laws of Sabbath. Since such stories show how Jesus bested the Pharisees on such issues, they would provide a sanction for the behavior of Christians decades later. Or in what context would stories of Jesus healing the sick or raising the dead emerge? Probably in contexts where Christians were trying to prove to outsiders that Jesus was the Son of God who had come in fulfillment of the prophecies of the healing power of the coming messiah. These stories, in other words, are not so much about Jesus as they are about the community that was telling the stories.
Ehrman, Bart D. (2016-03-01). Jesus Before the Gospels: How the Earliest Christians Remembered, Changed, and Invented Their Stories of the Savior (p. 48). HarperCollins. Kindle Edition.
“Would” indicates a mind-game, an imaginary historical scenario for which we have no evidence. “Probably” indicates a guess that is based on what we imagine would be happening in our imaginary scenario. “Are about” and “was telling” are unambiguous definite statements that we can “know”. See how the magic works.
Now Ehrman might be able to provide clear rationales for his conclusion in a work directed to a more scholarly audience but the point is that he has failed to do so here he has let his readers down.
Contrast the works of Richard Carrier. Proving history : Bayes’s theorem and the quest for the historical Jesus is like Tetlock and Gardner’s Superforecasting in which the argument for clearer thought and argumentation is presented. On the Historicity of Jesus: Why We Might Have Reason for Doubt is a demonstration of how to apply clearer argumentation that moves beyond the vague language that has long served the academy so well.
Neusner refers to “magic”. It really should be a mystery to everyone how such mind-games and guesses can pass as serious works of “history”. Carrier’s promotion of explicitly using Bayesian analysis is a genuine (and giant) step forward.
Neil Godfrey
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Ehrman’s language can be quite elastic. An event can be plausible in one paragraph, only to become something that “must have” happened in the next.
This sort of exercise has nothing to do with historical inquiry. It is bizarre make-believe scenarios built upon and elaborating the fundamental yet unsupported premise. I once compared how genuine historical inquiry into the development of social memory works: Tales of Jesus and Moses: Two Ways to Apply Social Memory in Historical Studies.
Suppose you had to give a modern account as to how Julius Caesar overcame Pompey and took control of
Italy. If you just look at the facts of the situation: Pompey had most of the Senate/Populace/Army behind
me him and Caesar was violating the laws of the Republic, in fact was declared an enemy of the Republic.
How in the world can Caesar drive Pompey out of Italy and eventually to a death by beheading in Egypt
a few years later ?
Now suppose most of those historical facts are missing from your account.
Yet you know, or at least believe that Caesar drove Pompey out of Italy, then out of Greece
and finally to Egypt…or was this a myth made up by Octavian to justify his becoming Caesar,
even though he, himself, was no great general. Octavian must have had all the histories of Rome
re-written once he became Emperor…in fact he was the illegitimate son of Antony who never suspected
his own son would hunt him and Cleopatra down in Egypt…and even kill his second cousin, Caesarea…
in double fact, Octavian arranged with his true father – Antony to have Julius Caesar assassinated.
If Jesus is a myth, then how do you explain Peter, Paul, James and John convincing contemporaries
of the mythical Jesus to convert to Christianity and why did the Jews persecute a sect based on
an imaginary man ? Jews accounts of Jesus and prayers agains the followers of the Nazarean
never deny that Jesus existed, only that He was not the Messiah.
Tim, you were not there, neither was I, but this type of pseudo- scholarship is sad in that it ignores a
simple truth – Jesus lived, His life influenced the Apostles and the Jews fought against it to the bitter
end, but they lost out.
How do you account for millions of Greeks believing in Zeus? By your argument, obviously Zeus must have been a real being.
We are not discussing whether Jesus was divine.
Just whether there is enough historical evidence to say that He lived.
The example of Zeus shows that often an obviously mythical being was taken as real. The fact that many believed in someone, does not prove that he existed.
“If Jesus is a myth, then how do you explain Peter, Paul, James and John convincing contemporaries
of the mythical Jesus to convert to Christianity and why did the Jews persecute a sect based on
an imaginary man?”
The same way Mormons converted thousands of followers based on the testimony of Joseph Smith. The same way Muslims converted billions based on the testimony of Mohammad.
But if you want to know what Paul actually converted people TO, reading his letters in their actual, pre-Gospel context tells you that apparently none of his converts needed any direct evidence; they seemed to be content with the visions of the apostles and hidden codes in the Old Testament. The life of Jesus, human being, was apparently of no concern, to Paul or anyone he was writing to. How did he do it? He must have been an extraordinarily persuasive man, but there have been others at least as persuasive, with evidence at least as poor, who have been arguably even more successful.
You miss the point.
Discussing whether Jesus lived or not.
Not His divinity.
You are the one who has introduced Jesus’s messiahship and divinity in your first comment. You fault us for not trusting documents that are primarily dedicated to persuading us to believe Jesus was the Christ and Son of God. (And you avoid my challenge to examine for yourself those other documents supposedly referring to Christians or Jesus.) It is clear that the question and methods used to answer it are only important to you because they are fundamental to your religious belief system.
Neil,
Can you please point out where I introduce Jesus’s messiahship and divinity in my first post ?
My inquiry and remarks are whether one should, as a historian, say there
is evidence, sufficient evidence in one’s view, to say that a man named
Jesus lived in first century Palestine, who was later said, by His followers
to be the Christ.
Yes. Here, in your first comment:
This is the standard apologetic argument used to “prove” Jesus was resurrected. I am sure you don’t mean to suggest that the apostles endured persecution because they believed Jesus existed as a historical figure. Of course not. You are implying that they suffered because of their beliefs about the divine identity of that person.
Then you conclude with:
You give away your entirely religious interest in the historicity of Jesus in that last line. It is clear that for you the historicity of Jesus is a matter of religious faith. It is based on believing religious texts telling you to believe that God entered history in the man Jesus.
You seem to be very reluctant indeed to bother responding to my answers to your questions there.
Again you have ignored my responses. So I’ll ask again: Do you think historians should take any literature at of any kind at face value to know what happened in the past? Do you think early Christian texts should be assessed any differently from any other ancient text before deciding what information they can reliably yield?
You replied to a much earlier post.
Any historian should look at all sources.
Then the historian has to decide which sources he
thinks are more important/more trustworthy and
write his history.
If you wish to write a history of Christianity in the
first century AD, examine every document you can find and weigh it in the balance of your judgement.
It would be fine if you explain why you take this text
more seriously than another and why you interpret the
text this way than that.
As for reliability, because we were not there,
we cannot speak reliably but only what we judge
to be the case or not.
I’m still waiting for you to engage with my response to your first comment.
What you say here about historical method is all truism. No one disagrees with any of it. So what, specifically, do you see as a fault with my arguments and methods? Do you know what my arguments and methods are? Or have you just come crashing in on assumptions and rumours of what you think I write? Please don’t repeat any of the appeals to incredulity in your previous comments — first engage with my responses to those appeals before repeating them. Or better still, try to engage with a particular fault you see with a particular claim or argument of mine. (i.e. stop trolling)
George, why do you bring up the question of mythicism here? Did you read the post? It is not about mythicism but something much more significant, a much larger question. (At least it is of more significance and broader relevance to anyone interested in the historical inquiry into Christian origins. Believers in a god-man Jesus will have other ideas but they don’t count as far as I’m concerned.)
But this once I will address your question though it does not conform to our comment policy that comments must be relevant to the post:
Your comment contravenes our comment guidelines by being irrelevant to the post. But I’ll address your points just this once more:
I addressed your previous comment and you are simply repeating some of the same arguments here. If you comment I think it is good form to read responses to your comments and engage with the arguments raised — don’t just repeat yourself and ignore the responses you get.
I have no evidence that Peter, James and John did convert anyone to “Christianity” — nor even Paul. The evidence i see before me indicates that there were people like Paul who led a certain sect within the panorama of Second Temple Judaism and that this sect over time came to distinguish itself more clearly from other Jewish sects. There is no evidence at all that prior to the fall of the Temple in 70 CE that anyone had any notion of a historical Jesus such as we read about in the gospels.
I don’t know of any evidence that Jews did persecute any such sect, at least prior to the second century. Paul himself said that he was personally attacked but that
was because he taught that the death of Jesus meant an end to the Law. Moreover, I think there were Jewish rivalries among certain sects but I don’t know what difference it would have made if some of them taught normal Second Temple Jewish ideas such as a heavenly Messiah figure who was an angelic or spirit being and only appeared in the form of a man.
You’ve evidently been reading a lot of apologetic propaganda. I invite you to take up the quest to actually see and read in translation the evidence for that Jewish prayer against the followers of “the Nazorean”. You might be surprised at what it actually says and how much certain apologists must read into it. As for your second assertion, what evidence are you relying upon exactly?
I trust you’ll attempt to seriously engage with some of the responses to your comments and are not here just to troll.
“I trust you’ll attempt to seriously engage with some of the responses to your comments and are not here just to troll.”
I doubt that very much. George Watson was banhammered from Cross Examined on Patheos after hundreds of comments of his unsupported nonsense being addressed without any rational engagement in discourse. The same off topic stuff he has posted here and more. Stuff that has been addressed ad nauseam, over and over again, c/w with links to some articles as evidence in support over here.
He has had the answers, but has decided to press reset and start fresh on a site he has not yet been excluded from commenting. I just hope that it was not my doing that led him here in the first place.
George is a troll to be sure, not really interested in any answers to his presuppositions. He is here to derail and his tactic’s include the Gish Gallop. BTW, he was a professor of Logic, Epistemology and Philosophy at THE top public uni in the U.S., among much more Walter Mitty claims, be warned.
The general question is what counts as Historical Evidence and do what degree can
we say it is probable that the events/persons claimed happened/existed.
If you wish to say that because you do not trust the Gospels, do not trust the Letters in the
New Testament, do not trust any Roman mention of Christians and do not think the Jewish
prayers and condemnations of Nazorean(s) really apply to Christians, then how do you explain
the spread of Christianity in the first century if Jesus did not live ?
Why do you ignore my reply to the first time you asked this question?
Do you really believe a historian should uncritically accept at face value all source materials and their versions of events?
Neil,
This is a reply to the longer reply you made at: 9:36 UTC.
If you wish to claim that no one was converted to being a follow of Jesus until
the temple was destroyed in 70 AD, you are very much in the minority among scholars,
which is fine but then it seems incumbent upon you to explain how Christianity arose
after the Temple was destroyed. You can suppose that once the authority of the Sadducees
ended with the destruction of the Temple and so whatever various forms of Judaism existed
were now free to find their own way without fearing behind brought to trial before the
High Priest, if you wish. Or you may choose to ignore trying to explain how the Church came
into existence after 70’s AD and just say: I can find no convincing historical evidence.
In that case, why don’t the writers of the Gospel/Paul just have Christ crucified weeks before
the rebellion against the Romans began and then tie in the destruction of Jerusalem to the
failure of the Jews to accept the Christ. Or move it to 132 AD just before the final rebellion.
Much tidier. Of course you don’t have to speculate on why they did not, just say:
I have no evidence.
But it is not that there is no evidence, but that you reject the evidence other accept, and one can rightly wonder, if a pristine Gospel and Trial Records of the High Priest and of Pilate were found
and dated to 35 AD, would you accept them as Historical or some ancient forgery or modern forgery
and if so why.
What power after the second rebellion did Jews have to persecute anyone ?
If, after the first rebellion the Jews no longer had a High Priest or King to try the brand new
Christians, why should Paul renounce the Law and say he was persecuted by the Jews – they
had know religious/civil power to do anything against Paul, let alone enforce the Law of God.
Why doesn’t Paul and others in the New Testament just say:
See the Leaders of the Jews handed Jesus over to the Romans, the Procurator did not want to crucify
Him, but he did so to please the High Priest and the mob.
Now God has destroyed Jerusalem and the Temple and the Law is no more…
You can ignore trying to answer those questions, but no serious scholar is going to take your
simple dismissal of Jesus/Paul/Peter/James, the trial and death of Jesus unless you can
answer questions along those lines.
It is rather as if all the copies of the Declaration of Independence were lost when the
British burned Washington and you are going around saying:
See, we don’t actually have the original Declaration, I see no evidence that it was written in
1776…if fact it is a product of Andrew Jackson…
The prayers against the Nazareans, and the Talmudic references have been attacked by those
who cannot bear the thought that Jesus lived. I will stand with the Jewish scholars who accept
that they refer to Jesus and Christians. However, if you wish to cite some sources for me to
read concerning them, I am willing to read them.
If you have any Ancient Jewish text that says explicitly that Jesus never lived
please let me know, as I have been asking people for one(s) for years.
I hope that I have answered the question you wanted asked.
I find the web-site somewhat confusing and have had a hard time finding your reply
and to which reply of mine your are making reference.
I wrote no such thing. Your reading comprehension is too lacking to have a reasonable conversation.
You have absolutely no idea of what I have written and argued about the evidence, do you. So why are you bothering to waste your time here? Nor do you have the slightest skill in mind-reading.
I see you do just absolutely love to concoct a lot of imaginary arguments that you think are genuine alternatives in my own thinking yet have not bothered to try to find out one single post where I explain my own views. You ignore my own comments and the links I have included in them to explain more detail and proceed to suggest I must be thinking any one of some other range of utter nonsense.
Goodbye, Mr Troll. Welcome to my spam list.
“… how do you explain Peter, Paul, James and John convincing contemporaries
of ‘the mythical Jesus’ to convert to Christianity” — How does Mormonism work? How does Islam work?
“and why did the Jews persecute a sect based on an imaginary man?” –perhaps they didn’t. Perhaps the persecutions are way overstated?
” Jews accounts of Jesus and prayers against the followers of the Nazarean never deny that Jesus existed, only that He was not the Messiah” Appeal to belief is a fallacy
“Contrast the works of Richard Carrier. Proving history : Bayes’s theorem and the quest for the historical Jesus is like Tetlock and Gardner’s Superforecasting in which the argument for clearer thought and argumentation is presented. On the Historicity of Jesus: Why We Might Have Reason for Doubt is a demonstration of how to apply clearer argumentation that moves beyond the vague language that has long served the academy so well.”
I have to disagree. In PH and OHJ Carrier is well aware of the benefits using probabilities could potentially give us (self-consistent ways of doing inference), however he ignores that those benefits assumes we have the *right* probabilities and the *right* logical structure of the propositions which we certainly do not. In addition, PH provides the reader with a very inaccurate picture of Bayesian probability theory. To give two examples from PH and OHJ:
1) The only serious application of Bayes theorem in PH is to the criteria of embarrassment. It is treated without a variable indicating if a text is actually embarrassing. I dare say this oversight is only possible when one decides to frame an otherwise simple intuition symbolically. It is also why Carrier concludes the criteria works in reverse and other treatments reverses that conclusion. So which is correct?
2) In OHJ Carriers use of reference classes in conjunction with the Rank-Raglan criteria is simply a textbook example of a fallacious statistical argument in which a method (reference classes) is applied in a manner obviously contrary to where it is applicable. The argument implies that given the four Gospels alone, Jesus almost certainly did not exist. There is a caricature of statisticians as people who ignores the real complexity of a problem in favor of a too simple model treated as objectively true, for instance the statistician who woke up after his wedding and wondered: “At this rate where will I make room for the other 7 women in a week?”. In treating the rank-raglan criteria Carrier is exactly arguing we should ignore all the historical details in the Gospel compilation and focus on their resemblance in some aspects to other documents which are very different.
This is also a good example of where Carrier believes that the use of Bayes theorem guarantee coherent results but appears not to be aware that reference classes violates Bayes theorem such that that result does not hold.
Did you read the book?
Ignoring the real complexity is exact opposite of what he does, which is probably the most complex case on historicity to date,
and Rank-Raglan criteria alone are hardly presented as sufficient to establish non-historicity.
Reference classes work fine, we don’t normally believe in existence of RR heroes, unless there’s some evidence to the contrary,
and this evidence is exactly what historicists fail to provide thus far.
Yes, I have read both books. I do not know if the books are the most complex case on historicity and my comments do not relate to the validity of the historical information found in the books (I am not the right person to ask). What I wrote in my post is that given the *Gospels alone* Jesus very likely did not exist (I believe it is about 6% chance he existed) according to OHJ.
Reference classes work well as an approximation in some cases, not so well in other. My claim is that the case Carrier considers is one where they do not work well. I agree most RR heroes do not exist, however the problem with such an argument is that it ignores the historical circumstances. For instance, most people mentioned in surviving Josepheus manuscripts do exist, so a similar prior computed based on that information alone would give Jesus almost certainly did exist. You can read arguments supporting these claims in my review you like.
Setting aside that we can’t be sure if Josephus mentioned him (and he most probably didn’t), notice that the first half of Antiquities deals almost exclusively with nonexistent people, some of them belonging to the RR class.
Anyway this objection is not valid, because even if we assigned the ‘mentioned by Josephus’ class probability close to 1, and included both that and RR, it wouldn’t affect the prior, because probabilities are multiplicative.
It has to be so, otherwise we could get insanely high prior in case of characters like Spiderman, by assigning them to the ‘people with names’ class.
That’s why we have to use the ‘comic book superheroes’ class in case of Spiderman, and the RR class in case of Jesus, possibly along with any other relevant classes.
Hi,
I am on my ipad so this will be brief. You are right probability theory in principle allowed any decomposition, but that result simply does not hold when one use reference Classes and assign probabilities from frequencies. If you believe otherwise, please just try to find any reference that proves the claim.
re spiderman, what we ought to do is use all available information. Reference Classes is throwing away information.
No, that’s not how it works.
Nothing is thrown away. Given the evidence is good enough, it can counter the prior.
Now RR is important information itself.
See, there’s no physical evidence, all we got is claims, so, the real question is, how credible are these claims?
What RR says, is that at the place and time people often claimed that fictitious characters with the specific set of attributes existed. This is indeed a relevant information, do you have any good reasons you choose to throw it away?
When you say nothing is thrown away, do you mean what we ought to do or what Carrier does?
I do not advocate ignoring the rank raglan information.
Can i ask you a question: do you believe that only given the gospels there is a 93% chance jesus did not exist?
Replying to the comment below, there’s no button there for some reason.
“Can i ask you a question: do you believe that only given the gospels there is a 93% chance jesus did not exist?”
That’s not what Carrier argues in the book.
He says that gospels have no effect on probability, and that I agree.
Most gospel information about JC is nonsense, so there’s no reason to believe in what’s left, therefore gospels provide no useful information.
On the other hand, if all we had were gospels, there would be no reason to consider historicity of a hypothetical man about whom nothing can be known for sure.
I agree Carrier says the Gospels have no effect on the probability Jesus existed, however if you follow his assumptions that’s not what actually argues. Just do the math, with the same symbols as in OHJ:
h : Jesus is historical (i.e. the scenario Carrier outlines)
~h : Jesus is not historical (i.e. the scenario Carrier outlines)
Gospels : Evidence of the gospels
Then Carrier assumes:
P(Gospels|h) = P(Gospels|~h)
in which case:
P(h|Gospels) = P(Gospels | h)P(h) / (P(Gospels | h)P(h) + P(Gospels | ~h)P(~h) ) = P(h) = 6.25%
I take it you do not agree with that conclusion?
No, I’m sure that’s not the case.
6,25% is the lower bound of the prior probability, the upper being 33%
Of course, if the gospels are irrelevant, then if you take into account only RR and the gospels, then the lower bound is 6,25%, but that’s not gospels alone, as you seem to interpret it.
However, you may have a point, even if it’s not how Carrier puts it,
because if we ignored the RR at the prior probability stage, then we’d be allowed to count the fact that the gospel character fits the RR class as evidence, and that would make gospels evidence against historicity, instead of being irrelevant.
Hi Zbykow,
6.25% is the most realistic estimate of the probability according to Carrier, 33% is the most absolutely most optimistic bound.
The probability I compute, P(~h|Gospels.b), *is* only based on the Gospels as evidence. According to Carrier, the RR class is supposed to be the *prior* probability and so this is correct use of terminology.
Asides that, how do we know that Jesus belongs to the RR reference class? To say that Jesus belongs to the Rank Raglan reference class is to say he was born of a virgin, that he was attempted murdered as a baby, that he meets a mysterious death, etc. etc. These things are known from the Gospels. So when we condition on the Gospels, we condition on the information that places Carrier in the RR reference class. Thus the 6.25% (or 33% as a most optimistic estimate) chance of Jesus existence appears directly implied in the text. Do you agree?
if we ignored the RR at the prior probability stage, then we’d be allowed to count the fact that the gospel character fits the RR class as evidence, and that would make gospels evidence against historicity, instead of being irrelevant.
Yes that’s what Carrier says but try to think about how that argument would have to run. We would have to say that all the biographical information the Gospels supposedly provides us about Jesus is irrelevant, however what is very relevant is that the Gospels says he is e.g. born of a virgin (along with the other pieces of information) and *those* facts strongly supports our claim Jesus was mythical to a certainty of 93.75%. So we have:
born of a virgin: Historically very significant.
Preaching work: Irrelevant.
Dies atop a hill: Very significant
Said to dine with friends: irrelevant
etc. etc.
“born of a virgin: Historically very significant.
Preaching work: Irrelevant.”
No, nobody says that claims of him being born of a virgin have any historical significance. In fact, we pretty much know he wasn’t, if he existed.
Historical significance of the claims is one thing, claims themselves another.
Historical Jesus is one thing, the gospel protagonist another.
Unlike the facts about the hypothetical historical Jesus, we can tell for sure what these claims say about the literary character, historical or not.
We are 100% sure, that the literary character JC as portrayed in the gospels belongs to the RR class.
Since we know that RR hero characters are usually fictional, then it follows that most likely there’s no historical figure behind the gospel stories, and nothing in them has any historical significance.
i
[i]i[/i]
No, nobody says that claims of him being born of a virgin have any historical significance. (…) We are 100% sure, that the literary character JC as portrayed in the gospels belongs to the RR class. [i.e. that he was born by a virgin among other things]
Since we know that RR hero characters are usually fictional, then it follows that most likely there’s no historical figure behind the gospel stories,
Okay I am a bit confused. According to you, the Gospels have little or no value in terms of establishing historicity. However you also appears(?) to agree with Carriers Rank-Raglan prior and so the conclusion implied in OHJ that conditional only on the Gospels the chance Jesus did not exist is most reasonably 93.25%? If not, could you tell what probability in the computation I showed you believe to be wrong? I can assure you they are all taken from OHJ.
We are 100% sure, that the literary character JC as portrayed in the gospels belongs to the RR class.
Since we know that RR hero characters are usually fictional, then it follows that most likely there’s no historical figure behind the gospel stories, and nothing in them has any historical significance.
We are also sure Jesus was a jew (and since most jews existed…) we are also sure Jesus is mentioned in our Josepheus manuscripts (and since most who are mentioned…) and so on and on.
Okay I am a bit confused. According to you, the Gospels have little or no value in terms of establishing historicity.
It was about historical significance.
Just like Spiderman comic books, they have virtually no historical significance, but they are strong evidence against historicity of Peter Parker, if you cared to undertake such an inquiry.
We are also sure Jesus was a jew (and since most jews existed…) we are also sure Jesus is mentioned in our Josepheus manuscripts (and since most who are mentioned…) and so on and on.
Not at all, we are not even close to being sure he was a Jew, since we can’t be sure he even existed.
We’re only sure that the literary character is claimed to be a Jew.
Then again, you are free to include as many relevant classes as you like, but generic classes lake that won’t improve your odds anyway.
Zbykow: I am not following you with Spiderman. So the Gospels are evidence against historicity?
I can’t help but noticing you did not address my questions in my previous post.
Then again, you are free to include as many relevant classes as you like, but generic classes lake that won’t improve your odds anyway.
Okay, but I am not interested in improving any odds. I am interested in how we ensure the use of other classes allows us to arrive at consistent results in practice. Say, suppose you begin with the “thought to be a jew”-class, then try to consider what probabilities you would have to assign to the gospels to arrive at consistent results.
“So the Gospels are evidence against historicity?”
In conjunction with our knowledge about the world and literature, yes they are.
“Say, suppose you begin with the “thought to be a jew”-class”
That would mean I failed to think of anything more specific and relevant to the problem, or that I really desired for the character to turn out to be historical.
Even take something like “A character from ancient religious literature said to be a Jew”. Not so obvious now huh?
Really, if you wanted to find out if Spiderman was historical, would the only class you could think of be “said to be an American”?
In conjunction with our knowledge about the world and literature, yes they are.
I.e. you agree that P(~h|Gospels.b) = 93.75% (according to our best estimates)?. I am just curious because it seems very counter-intuitive to me.
That would mean I failed to think of anything more specific and relevant to the problem, or that I really desired for the character to turn out to be historical.
But isn’t it a bit of an odd feature that you got so many classes to choose from (and based on what criteria?) and they all seems to require very careful arguments to arrive at the same result?
Really, if you wanted to find out if Spiderman was historical, would the only class you could think of be “said to be an American”?
I think you misunderstand my position. I do not agree that reference classes can be used in this manner because I believe you enviably end up violating the rules of probability theory, i.e. you are not being Bayesian. Please notice this is just the mainstream view in statistics, I do not think you can find any textbook which support this usage of reference classes contrary to the impression OHJ might leave one with.
“I.e. you agree that P(~h|Gospels.b) = 93.75% (according to our best estimates)?. I am just curious because it seems very counter-intuitive to me.”
What’s counter intuitive about that?
IMO the probability is about the same as in case of any other ancient literary supernatural being, so 93% seems to be within the range.
“But isn’t it a bit of an odd feature that you got so many classes to choose from (and based on what criteria?) and they all seems to require very careful arguments to arrive at the same result?”
No, the best class usually affects the result the most, if you use some generic classes along with RR, you still get about the same probability as if you used RR alone.
“I do not think you can find any textbook which support this usage of reference classes contrary to the impression OHJ might leave one with.”
Because it is very basic, the principle is used extensively e.g opinion polls, it’s just so obvious there’s no need to rediscover it every time it’s used.
Hi zbykow,
What’s counter intuitive about that?
IMO the probability is about the same as in case of any other ancient literary supernatural being, so 93% seems to be within the rang
Well, for starters I don’t see how it follows given only the Gospels that Jesus underwent a death burial and resurrection in the supernatural realm as is part of ~h. What you are saying is this is 93% certain given only the Gospels but I don’t think that probability is very intuitive.
No, the best class usually affects the result the most, if you use some generic classes along with RR, you still get about the same probability as if you used RR alone.
What does it mean to use a generic class alongside the RR?
Because it is very basic, the principle is used extensively e.g opinion polls, it’s just so obvious there’s no need to rediscover it every time it’s used.
The question put forth in polls are very simple (i.e. well-specified) and so simply counting the frequencies is quite accurate (I.e. you are interested in answering: “Given you only know a person is from the population in a given country, how would he or she answer this question”. I.e. you have very limited information).
That’s why I consider it quite different than what Carrier is doing. I don’t know how we can come to a sort of agreement on this issue. You seem to be of the opinion that the use of reference classes as Carrier use them is unproblematic and so common in statistics nobody would bat an eye; I believe it is so obviously asking for problems that it is highly controversial!. I suppose we could solve it by finding references in the literature that support our view. Here is one which discuss the problems of using reference classes:
http://philrsss.anu.edu.au/people-defaults/alanh/papers/rcp_your_problem_too.pdf
“for starters I don’t see how it follows given only the Gospels that Jesus underwent a death burial and resurrection in the supernatural realm”
You said you feel it’s counter intuitive that gospels are evidence for non historicity,
so please don’t redefine your problem in the middle of an argument.
Of course supernatural realm don’t necessarily follows from gospels, and we already are discussing the realm issue elsewhere.
“What does it mean to use a generic class alongside the RR?”
A subject may belong to more than one class. You can choose to include more than one and compute the probability the usual way.
“The question put forth in polls are very simple (i.e. well-specified) and so simply counting the frequencies is quite accurate”
Just as in our case. How many known members of the RR class are believed to be historical figures? Simple enough.
Any more evidence we got go elsewhere, and because of how BT works, given the evidence is strong enough we still could get a result way above the initial prior, possibly close to 1.
You said you feel it’s counter intuitive that gospels are evidence for non historicity,
so please don’t redefine your problem in the middle of an argument.
Of course supernatural realm don’t necessarily follows from gospels, and we already are discussing the realm issue elsewhere.
Right from the beginning I have been talking about Carriers hypothesis of mythicism ~h and all my questions/assertions has been about ~h. You may consider another idea about mythicism and it may be very plausible given only the Gospels, but this is not what I or Carrier discuss and we do not have the numbers in OHJ to talk about it. All there is to my point is that according to Carrier the probability of ~h given only the Gospels is 93% (p(~h | Gospels.b) = 93%) and ~h includes the information about death and burial in the supernatural realm. It seems we are in agreement that this number is worryingly high.
A subject may belong to more than one class. You can choose to include more than one and compute the probability the usual way.
You can take the union of two classes.. combining two classes otherwise does not appear immediately obvious to me.
Just as in our case. How many known members of the RR class are believed to be historical figures? Simple enough.
Any more evidence we got go elsewhere, and because of how BT works, given the evidence is strong enough we still could get a result way above the initial prior, possibly close to 1.
You misunderstand what I mean by simple. Take the case of P(Influenza|Fever). This is a simple case because the reference class is only those about which we know they have Fever. This is little information and there are many that matches all that information.
If we take Jesus then we have p(~h|b). But b is all our background information which Carrier spend about 100 pages to itemize. This is far from simple and so Carrier rather choose another reference class (The RR information). This brings us to the entire discussion about loss of information, approximations and so on and on. I would recommend you to try to work out what happens symbolically and perhaps give the article i linked a look.
“~h includes the information about death and burial in the supernatural realm.”
Yes it does, and RR does not, yet it’s still OK, because ~h still belongs to the RR class. RR is not the same thing as ~h and RR heroes need not all be identical.
“But b is all our background information which Carrier spend about 100 pages to itemize. This is far from simple and so Carrier rather choose another reference class (The RR information). This brings us to the entire discussion about loss of information”
Yes, that’s the idea, and your worries about loss of information are unjustified, since all information that’s left is accounted for elsewhere.
Try looking at the whole equation, instead of just a tiny part of it.
zbykow:
Yes it does, and RR does not, yet it’s still OK, because ~h still belongs to the RR class. RR is not the same thing as ~h and RR heroes need not all be identical.
Okay lets back up a moment. I hate to ask you the same question again and again, but I am honestly interested in your view and I feel you are avoiding the question:
Do you agree with the proposition that there is a 93.75% chance that ~h is true given only the Gospels [i.e. p(~h|Gospels.b) = 93.75% as is implied by OHJ]. That is, given only the gospels, there is a 93.75% chance Jesus underwent a death and resurrection in the supernatural realm?
Yes, that’s the idea, and your worries about loss of information are unjustified, since all information that’s left is accounted for elsewhere.
How do you know this? I.e. how do we prove this to someone who might doubt this is the case? I would invite you to re-write the probabilities in OHJ and see where that information is supposed to go.
“Do you agree with the proposition that there is a 93.75% chance that ~h is true given only the Gospels”
Once again:
1. Nobody but you says that (given ~h is as it stands in OHJ)
2. Yes it’s within range (given ~h is as it stands in PH)
3. Yes it’s within range, if you asked about ‘not h’
“How do you know this? I.e. how do we prove this to someone who might doubt this is the case?”
I’d encourage him to read the book.
All information left goes in P(e|h.b) and P(e|~h.b)
So to paraphrase your response, yes, you agree with the proposition that
P(~h|Gospels.h) = 93.75% (using our most plausible estimates)
where ~h includes the proposition that Jesus underwent death and burial in heaven?. I.e. that there is (at least) a 93.75% that Jesus underwent death and burial in heaven given only the Gospels?
I agree in a trivial sense that “I am the only one who says that”. However I showed how it follows from Carriers assumptions symbolically above; if you believe there is an error please point it out and I will happily acknowledge to be wrong. It is like if i say that a=3 and b=4 then i have not strictly speaking said that a+b=7, however it is certainly implied.
I’d encourage him to read the book.
All information left goes in P(e|h.b) and P(e|~h.b)
Not if we replace all the information in b with a lesser set of information (the RR information). Carrier newer proves this in OHJ and with good reasons. If you are interested, i could show you the computation?
No, that’s the opposite of what I wrote.
It also doesn’t follow from Carrier’s assumptions. In your example it follows from both gospels and his argument that the only significant version of non-historicity is ~h which comes from elsewhere.
That’s not gospels alone.
“Not if we replace all the information in b with a lesser set of information (the RR information).”
But we don’t.
RR is only used to compute the prior, all evidence is still weighed using all of b minus RR.
Zbykow: Okay, so what we have so far is:
1) It cannot be concluded that p(~H | Gospels.h) = 93.75% based on OHJ and in fact this is quite plausibly not true
2) It is however formally true (by simple computation, see above) that we can derive p(~h|Gospels.h) = 93.75% by applying Bayes to the numbers given in OHJ (that’s what I did above)
3) This is explained by there being some kind of formal (or at least syntactical) inaccuracy in OHJ which allows us to derive a false result, i.e. the “only significant version of non-historicity” argument.
It seems like we agree on 1 and 2, 3 is my attempt to restate what you wrote.
RR is only used to compute the prior, all evidence is still weighed using all of b minus RR.
I’m trying to work out what alternative decomposition you have in mind and I am not quite following you. Would you mind writing out what computation you have in mind?
What really goes on is this:
~H – Jesus is a mythical person historicized
~h – the usual supernatural realm etc..
What he does for the most part, is bayesian reasoning for H/~H
then he argues that ~h is the only valid version of ~H
However, in the book it appears in reverse order, hence the confusion.
Yes, he could put it better and make distinction between the two, but once you understand the argument, it doesn’t affect the conclusions.
Zbykow:
Well, saying that the symbols mean something else than how they are defined in OHJ makes it a bit hard for me to follow the conversation because I got the impression Carrier used the same definition of ~h throughout the book.. Perhaps I can ask him this on his blog.
The central issue remains, I think, that p(~h|b) != p(~H|b) because ~h contains more elements than ~H. So what probability is it that we compute? If we change between ~h and ~H when discussing the prior and the probability of the evidence, we still need to compute the probability of ~h to account for the difference. I don’t see anything in the text to suggest how this is supposed to be done.
“I got the impression Carrier used the same definition of ~h throughout the book.”
Yes but in 3.3 he also says that technically ~h should be ~H.
If you don’t agree with his reasons why they are about the same, for you it just becomes ~H and you can stop loosing sleep about that supernatural realm.
“The central issue remains, I think, that p(~h|b) != p(~H|b)”
These are just prior probabilities, they could be different, but in this case they’re equal, because they use the same reference class.
If you were making the argument, you could choose different.
If you really want something to be different, technically it’s P(~H|e.b) greater or equal than P(~h|e.b)
but remember we work with estimates, don’t try too hard making it into exact science.
Hi again Zbykow,
Yes but in 3.3 he also says that technically ~h should be ~H.
This is not the reading I get from 3.3. The way I read Carrier is that he defines ~h as including e.g. the burial and resurrection in the supernatural realm and then consistently use ~h throughout the book. 3.3 acknowledges that ~h is a subset of ~H, however he also argues that this can be ignored (based on an argument that I consider to be plainly faulty) and then proceeds with just using ~h in the subsequent chapters.
To take up a previous thread, I am still not absolutely clear where you stand with regards to the result
p(~h | Gospels.b) = 93.75%.
Which I have mentioned many times (see above). We seem to agree it follows (symbolically) from the assumptions made in OHJ and that, as it stands, do not conform to our intuitive judgement. However do I understand you correct to be saying that this result should really saying:
p(~H | Gospels.b) = 93.75%?
Because Carrier, at some point during OHJ, was imprecise in which probabilities represents ~h and ~H?
If you don’t agree with his reasons why they are about the same, for you it just becomes ~H and you can stop loosing sleep about that supernatural realm.
But I think it matters greatly if we use ~h or ~H in terms of the overall argument. Are you saying that it makes no difference in terms of explaining the evidence if ~h is replaced by ~H? I.e. that is it equally easy to explain e.g. the Gospels if we simply assume Jesus did not exist (~H) as it is if we assume Jesus did not exist but subsequent Christians came to believe or taught Jesus DID exist? (~h)?
Suppose you have two groups of people. About one group, you are told they simply don’t believe Muhammed exist, and about the other group you are told they believe Muhammed does exist or at least wish to teach this.
Over the next couple of decades, which of these two groups do you think are more likely to write something that resembles historical tales about Muhammed? (i.e. the Gospels)? The group about whom you don’t know if they believe Muhammed exists, or the group about which you know that they believe Muhammed exists?
We can raise the same question about the other more specific criteria which are part of ~h. For instance, if we assume a group teaches or believes Jesus died and was resurrected in the supernatural realm, whereas for another group we are not told such a thing, which group do you think more plausibly will leave behind stories like those of Paul where Jesus undergoes a form of death and resurrection?
If you really want something to be different, technically it’s P(~H|e.b) greater or equal than P(~h|e.b)
Indeed! And by the same logic, it is p(P5|b) greater than or equal to p(~h|b) = 93.75%. This alone does not teach us much except that we need to establish the probability of ~h since it may differ from ~H.
Look, I think many times in this argument you are more critical of what I say but accept what Carrier says and re-phrase it as statistical arguments; that’s understandable since I am a random person on the internet and Carrier has at least published one book which discusses Bayes. However I see these issues as quite black-and-white and Carriers argument for why what he does works (like why we can use ~h rather than ~H in 3.3) as very plainly falling apart when they are translated back into statements about probabilities. This is also why I think Carrier chooses to phrase these arguments in words and not using probabilities; something which is quite odd since the central argument in PH is that arguments should be stated using probabilities.
I implore you to go over these arguments, try to phrase them symbolically and see if they can indeed be made to work. When Carrier for instance says that the information not being used in the RR reference class “goes elsewhere” (a sentiment I believe you accept), try to work out what that actually means symbolically using the product rule. Wherefrom does the RR criteria information come and whereto does the background information not part of the RR criteria go? It isn’t exactly pretty and it is certainly not simple.
Just a last thought. I think we are discussing something about which it seems we both agree there is an objective truth. If you take the issues we have discussed in this thread, what would at this point convince you of one of the points I have made?
“Are you saying that it makes no difference in terms of explaining the evidence if ~h is replaced by ~H?”
In this case yes, because every argument in favor of non-historicity he makes is compatible with both. Your best bet would be to try and find some evidence expected on ~H but not on ~h.
“I.e. that is it equally easy to explain e.g. the Gospels if we simply assume Jesus did not exist (~H) as it is if we assume Jesus did not exist but subsequent Christians came to believe or taught Jesus DID exist? (~h)?”
If you put it this way they’d be exactly same thing, because “subsequent…” is already a part of background knowledge.
Also note that on ~h both subsequent and precedent communities believed or taught he did exist. They only disagreed on the nature of this existence.
You seem to be missing this point in your Muhammad example.
“And by the same logic, it is p(P5|b) greater than or equal to p(~h|b) = 93.75%. This alone does not teach us much except that we need to establish the probability of ~h since it may differ from ~H.”
You overestimate the significance of P5. It’s a given and IMO it shouldn’t even be a part of the hypothesis, but if it is it doesn’t hurt.
P5 is not the reason why ~h and ~H are not the same, P1-P4 are.
As to the 93% question, you seem to be unsatisfied with my answers so far and I can’t help it. Why don’t you just say what bothers you about it?
“Are you saying that it makes no difference in terms of explaining the evidence if ~h is replaced by ~H?”
In this case yes, because every argument in favor of non-historicity he makes is compatible with both. Your best bet would be to try and find some evidence expected on ~H but not on ~h.
“I.e. that is it equally easy to explain e.g. the Gospels if we simply assume Jesus did not exist (~H) as it is if we assume Jesus did not exist but subsequent Christians came to believe or taught Jesus DID exist? (~h)?”
If you put it this way they’d be exactly same thing, because “subsequent…” is already a part of background knowledge.
I think we are talking past each other. I realize for the most part I keep pointing at isolated aspects of the argument (“look! ~h is not ~H”) and you keep giving reasons why these isolated problems can be fixed with additional assumptions (i.e. “subsequent…” is part of our background knowledge). Then I say: “Yes, but in that case …” and around it goes. I am sure you also find this a bit frustrating :-).
If you look at my review, I have discussed most of the things we have brought up. For instance, the proposal that there are “things” in our background knowledge that guarantees the additional elements in ~h (compared to ~H), such as Jesus being crucified and burried in the supernatural realm, is discussed in my review of OHJ from p23 bottom to p27. I 100% agree we can easily think about something in our background knowledge that would do that!
The central claim in my review is not that each and every of these additional assumptions in and by themselves and strictly speaking are wrong, but when you look at the various assumptions together things break in a major way.
How does this happen in this case? Well, it is quite easy. You suggest in your above response that there is information in b such that the additional elements in ~h (compared to ~H) becomes exceedingly plausible. For instance, suppose we could add to b the information:
C1 : “later church tradition about an earthly Jesus”
(In this case there is an issue about the timing here, namely what “later” means. I take it that “later” means sometimes around the time of the Gospel compilation, that is within 50 years of the “supernatural Jesus” tradition found in Paul (according to Carrier).
Similarly, we can add other elements to our background knowledge that guarantees the other parts of ~h over ~H. Lets call all these parts C and then we have that b is composed of C and some other background information B. I.e.
b = B . C.
Then, conditional on b (which contains C) it is true that subsequent christians came to believe (or at least teach) that Jesus had an earthly existence. It’s trivially true now!
So why do I keep complaining? Well, if we take Bayes theorem seriously we have to take serious the assumptions it build upon. That means that when we add information to b (such as C) we have to be able to account for where that information goes in subsequent computations. In my review (p.24), I provide an example of how (seemingly) trivial information added to our background knowledge can dramatically affect our conclusions . That’s why I advocate we should be careful and not just rely on our intuitive judgement but actual computations and very clear definitions.
This is also why I keep asking you what formulas your arguments rest upon because to me it is not clear at all. So what formula is it that you use? Do you have something concrete in mind or is it more an intuition?
To illustrate the problems we get into, you wrote previously: RR is only used to compute the prior, all evidence is still weighed using all of b minus RR.. Lets try to make this concrete. You are saying there is other information R (presumably, part of the Gospels in the case of Jesus) which contains the RR relevant prior information. That is, the prior as established by the RR reference classes is really:
p(~H|R)
where
R : “Rank-Raglan information (born of a virgin, etc.)”
In addition to this we have to account for the difference between ~h and ~H. Lets suppose
~h = ~H . M
where M are the additional 5 elements of myth we have discussed up to this point (died and rose from the dead in the supernatural realm and so on).
So what exactly is it that you have in mind? My own thoughts is that we start from the joint distribution:
p(E,~H,M,R,B,C)
Since we want to use our RR prior we should have a factor p(~H|R). So:
p(E,M,B,C|~H,R)p(~H|R)p(R)
(we can ignore p(R) since it is just a constant). But what then? If C guarantees M (the additional elements in ~h compared to ~M) then we should condition M on C. Then we obtain:
p(E,B|~H,M,R,C)p(M|~H,C,R)p(C|~H,R)p(~H|R)p(R)
Using p(M|~H,C,R) = 1 by assumption (this is what places limits on what C can be) then
p(E,B|~H,M,R,C)p(C|~H,R)p(~H|R)p(R)
Okay so we got some of the way, but notice that this expression has two interesting features which differs from what is in OHJ:
1) Background information now figures as the evidence 2) we have a new conditional expression, P(C|~H,R).
To focus on the last expression neither you, Carrier or I have specified what C is. However if we assume C is a specific piece of information which makes “died in the supernatural realm” very plausible, presumably such a piece of information is at least somewhat surprising given only ~H and RR. After all, as far as I know, most of the RR-type hero figures are not thought to have died in the supernatural realm and had a resurrection, so even a basic frequency computation such as Carriers would push down this number. How likely? How unlikely? Well, to begin to answer those questions we got to specify what C is.
Ofcourse, the above does not capture your description RR is only used to compute the prior, all evidence is still weighed using all of b minus RR., so if you got some other computation in mind please just write it.
I don’t want to win an argument by demanding you give formulas, but I have tried to base my evaluation of OHJ on how well it conforms to the basic rules of probability — which is what Carrier himself suggest. I can appreciate we can have reasoned disagreement, however I hope you accept why I am reluctant to just accept reasoning which is not specific (from a formal point of view) and which is contrary to what I think I have derived.
Re. the p(~h|Gospels.b) = 93.75%. I think we are in agreement the result seems absurd if taken literally (i.e. with ~h rather than ~H) since the Gospels are not evidence that Jesus was buried in the supernatural realm. If you replace ~h with ~H, the result becomes more reasonable but I still don’t think the Gospels provide strong enough evidence to warrant such a conclusion. That’s just my own thoughts.
“p(~h|Gospels.b) = 93.75%. I think we are in agreement the result seems absurd if taken literally (i.e. with ~h rather than ~H) since the Gospels are not evidence that Jesus was buried in the supernatural realm.”
Here’s the mistake. They don’t have to support every single statement of the hypothesis. They only must not contradict any of them.
If we assume that either h or ~h is true, and conclude that gospels contradict h then they are indeed evidence for ~h.
“as far as I know, most of the RR-type hero figures are not thought to have died in the supernatural realm and had a resurrection, so even a basic frequency computation such as Carriers would push down this number.”
Another of the same kind.
An RR hero must only meet the RR criteria, anything else is irrelevant, it doesn’t matter if they were ever thought to live in a supernatural realm or to like ice cream, that doesn’t make them RR heroes any less.
“if we assume C is a specific piece of information which makes “died in the supernatural realm” very plausible, presumably such a piece of information is at least somewhat surprising given only ~H and RR”
Not surprising at all. It supports ~H and is not in conflict with RR.
“That means that when we add information to b (such as C) we have to be able to account for where that information goes in subsequent computations.[…]I provide an example of how (seemingly) trivial information added to our background knowledge can dramatically affect our conclusions . “
We don’t add anything to background knowledge. It’s just all we have at our disposal, and it goes simply wherever it’s relevant.
We can only fail to realize the relevance of some piece, or be ignorant of, or withhold if we’re dishonest.
That a piece of knowledge can change our conclusions is a truism.
Your calculations look all kinds of wrong.
M is not difference between ~H and ~h, its what they have in common. it doesn’t belong in background knowledge (it so happens that P5 does but it’s redundant as a part of ~h), and you freely swap e for b and h and back.
Look, if you used RR to calculate the prior, you can’t use it to judge the evidence, that means you can’t say gospels argue against h cause the character is portrayed as an RR hero, even if you think it’s the case, because it’s already accounted for, simple as that.
Carrier’s formula might look like P(h|RR) * P(e|h.(b-RR)) /…
Here’s the mistake. They don’t have to support every single statement of the hypothesis. They only must not contradict any of them.
If we assume that either h or ~h is true, and conclude that gospels contradict h then they are indeed evidence for ~h.
So in your view, my mistake is that the statement p(~h|Gospels.b)=93.75% does not imply directly that each of the components in ~h (such as Jesus being buried in the supernatural real) is at least 93.75% probable? I thought we had already agreed on this and that the conclusion seemed implausible. Otherwise just look above where I show this is indeed implied.
Insofar as your comment, we already agree that ~h and ~H (bare mythicism) are not the same. So we can’t assume that either h or ~h are true (despite what the notation might lead us to think). So even if we say the Gospels “contradict” h, by which I assume you mean p(h|Gospels.b) is low, we cant conclude that p(~h|Gospels.b) is high.
Tim: “as far as I know, most of the RR-type hero figures are not thought to have died in the supernatural realm and had a resurrection, so even a basic frequency computation such as Carriers would push down this number.”
Another of the same kind.
An RR hero must only meet the RR criteria, anything else is irrelevant, it doesn’t matter if they were ever thought to live in a supernatural realm or to like ice cream, that doesn’t make them RR heroes any less.
Well, ~h (which is what Carrier computes the prior of) include “buried in the supernatural realm”. So if i simply compute the prior probability of ~h using the RR reference class it is:
p(~h|RR) = (Characters in RR which matches ~h, which by definition includes being burried in the supernatural realm)/(Characters in RR)
(which is what a reference class suggest we do — if you don’t believe so please just provide a reference or your own definition) we get that p(~h|RR) is very low. You can say: No, I prefer to substitute ~h with something else. But this is just saying that you decide to not follow the definition or that you prefer to compute the prior probability of something else. Or you can say: No, I prefer to substitute h rather than ~h in the above definition and then use the result to conclude p(~h|RR) is high. However why make this choice and not the other? At best, it shows that the process of using reference classes is arbitrary. Do you see the problem?
If you want a reference on the above, just start with wikipedia: https://en.wikipedia.org/wiki/Reference_class_problem and notice that in the article G is ~h. Please notice that *I* don’t think this is a valid way to determine a prior.
Your calculations look all kinds of wrong.
M is not difference between ~H and ~h, its what they have in common.
it doesn’t belong in background knowledge (it so happens that P5 does but it’s redundant as a part of ~h), and you freely swap e for b and h and back.
I think you go wrong here. Since ~h (Carriers myth theory) contains ~H (bare myth) what ~h and ~H have in common is exactly ~H (think about it). I defined M as being what is added to ~H to produce ~h: I.e. that Jesus was burried in the supernatural realm etc. This is just some basic notation so we have something concrete to talk about.
What do you mean I freely swap e for b and h? Please just provide whatever computation you have in mind and if it agrees with the rules of probability theory I am convinced.
Look, if you used RR to calculate the prior, you can’t use it to judge the evidence, that means you can’t say gospels argue against h cause the character is portrayed as an RR hero, even if you think it’s the case, because it’s already accounted for, simple as that.
Carrier’s formula might look like P(h|RR) * P(e|h.(b-RR)) /…
You are arguing based on what your intuition tells you we should do and not what probability theory actually tells us we have to do. Probability theory has to be the arbiter of truth and what you are saying just does not follow as far as I can see. Please just start with p(~h|b.E) and try to derive your expression, I promise you that it can’t be done symbolically.
I am not trying to browbeat you with math, however we must recognize we are arguing about what is essentially dressed up high-school math. If i wrote down a derivation of (for instance) the derivative of a function, and you told me that it “looked wrong”, I think it would be a fair request that you provided your derivation or at least showed exactly where I went wrong, exactly. I know it is impressive when Carrier (who has written a book on the subject) says that something can or can’t be done. He is very skilled rhetorically and convincing, but on this particular topic he is quite often wrong and if you notice very rarely provide math to substantiate what he says.
If you wish to continue the discussion we could perhaps do it on earlywritings.com:
http://earlywritings.com/forum/viewtopic.php?f=3&t=2224
“I think you go wrong here. Since ~h (Carriers myth theory) contains ~H (bare myth) what ~h and ~H have in common is exactly ~H (think about it). I defined M as being what is added to ~H to produce ~h”
This.
~h is a subset of ~H, period. A guy said to be living in a supernatural realm (~h) is by definition, mythical (~H), however there are other variants of myth which don’t involve this (still ~H but not ~h).
Sorry. You can’t derive anything that makes sense, mathematically or otherwise, if you’re making basic mistakes like this.
Hi again Zbykow,
This.
~h is a subset of ~H, period. A guy said to be living in a supernatural realm (~h) is by definition, mythical (~H), however there are other variants of myth which don’t involve this (still ~H but not ~h).
Ah, I see why the confusion arises. So far we have talked about ~h and ~H as logical propositions. For instance in my definition above:
~h = ~H . M
the use of periods (and) and negation (~) indicates that we are discussing logical propositions. You are correct that if ~H and ~h are considered as sets then the set (~h) is a subset of (~H) and in that case it is true that the set ~h is contained in ~H. However, considered as propositions the definition of ~h is a series of conjunctions which encompass ~H:
~h = ~H . (myth element 1) . (myth element 2) … (myth element 5).
It is in this sense I meant ~H is what ~h and ~H have in common. None of this affects my derivation of the above formulas; they are just assuming a notation where we use logical propositions as we have used up to this point. Again I must re-ask the question: Where do I go wrong in your view? What is the right computation? .
By the way, if we assume set notation, then when you write:
M is not difference between ~H and ~h, its what they have in common.
Then what ~h and ~H have in common is the intersection of these two sets (~h) and (~H). In this case that would still not be M (considered as a set) but (~h). If you wish to accuse someone of being flat out wrong on the math it is advisable to check the computations twice :-).
By the way, regarding your comment: “Carrier’s formula might look like P(h|RR) * P(e|h.(b-RR))”, can you provide the derivation that leads to that? I am still not seeing it at all.
By the way, I invite you to discuss this topic further at earlywritings.com.
“It is in this sense I meant ~H is what ~h and ~H have in common.”
~H is not what ~h and ~H have in common, in any sense, ~h is.
I got a hunch that you still think P5 is somehow incompatible with ~H, but this is already going too long.
The issues you are struggling with are known and are addressed in the book, if you understand the reasons and disagree then you should argue them directly instead of reinventing the wheel.
Thanks for the invitation, I’m not sure I feel like registering another account,
but I’ve taken a look and noticed somebody already suspects I am Carrier.
I’m not going to deny nor admit, but i guess that means my English doesn’t suck that bad after all.
Hello again,
~H is not what ~h and ~H have in common, in any sense, ~h is.
If we consider them as sets, I 100% agree. If we consider them as logical propositions, which we have up to this point, then
~h = ~H . M
(As I wrote above). I must admit I find your comment puzzling since you earlier wrote that M (and not ~h) was what ~h and ~H had in common: M is not difference between ~H and ~h, its what they have in common..
Anyway I digress. With this issue out of the way, you claim that the computation I gave was wrong or deficient. Can you point out specifically where it is wrong or, alternatively, what the right computation is which takes into account the various factors that has been introduced in this conversation? (M, C, R, etc.).
We both agree that what determines a valid argument is how it conforms to Bayes theorem and since you claim that my computation is wrong or somehow not describing the problem I am simply asking you to show what you have in mind.
You earlier wrote that Carrier’s formula might look like P(h|RR) * P(e|h.(b-RR)) /…. Since to my mind this formula does not follow at all, I wonder if you would supply the computation which lead you to this conclusion?
The issues you are struggling with are known and are addressed in the book,
Look, I am simply asking you to substantiate a simple formal claim you yourself have made. I have written a 50 page review of OHJ where I point out what I consider to be quite apparent deficiencies in the argument and gave specific reasons why. I do not think that saying I should read the book again is a reasonable or convincing response by any standard. Don’t you also want to get to the bottom of this?
I do not want to make you responsible for what Carrier says and if your argument differs from Carriers it may indeed be correct. But surely it is reasonable to ask you to substantiate your own claims on this thread. I asked you earlier what could make you change your mind and I would like to re-ask this question since I really wish we could end this conversation on a positive note.
In my case, if you simply substantiate your formal claims with the derivations you have in mind that would convince me.
Good evening,
T.
I can give you that in a trivial sense, if you count the number of items, then you could say that ~h contains ~H because it has more items, but that doesn’t help calculation wise, unless you really just want to count items. This is just misleading.
What you really need is two runs of BT, one H vs. ~H, another ~h vs. what’s left of ~H, you could even combine them in one formula if you will, I’m not gonna bother.
But this still ends up equivalent to what Carrier did, unless you find some evidence supporting some other variant of ~H (like a conspiracy to invent fleshy JC from day one).
Notice that whatever happens to ~h, it still doesn’t look any different for H(istoricity), and that seems to be what everybody is interested in.
Hello again,
I can give you that in a trivial sense, if you count the number of items, then you could say that ~h contains ~H because it has more items, but that doesn’t help calculation wise, unless you really just want to count items. This is just misleading.
I am sorry but I fail to see where I have written anything misleading. We were using one notation at first (logical propositions), and then I think you changed to set notation. If you wish to change to set notation (in which case ~h and ~H are two subsets of some event space) then you should say that the set (~h) is contained in (more specifically, a subset of) (~H). Anyway, I think this is a rather silly point to debate, I would much rather hear you elaborate on your alternative proposal to Carriers computation:
What you really need is two runs of BT, one H vs. ~H, another ~h vs. what’s left of ~H, you could even combine them in one formula if you will, I’m not gonna bother.
But this still ends up equivalent to what Carrier did, unless you find some evidence supporting some other variant of ~H (like a conspiracy to invent fleshy JC from day one).
Well, if you scroll up this is exactly what I was trying to do: Keep the distinction between ~h and ~H in mind and carry out a computation which took both terms into account. You wrote that “Your calculations look all kinds of wrong.”, I am simply wondering what your reasons are for this conclusion? What is the correct computation?
I think our discussion started with a much more interesting topic, namely the justification of the RR prior. To start at the top, you could perhaps simply state your position: Do you think it is reasonable to conclude that:
p(~h | Gospels.b) = 93.75%
(i.e. that given the gospels there is, using the reasonable estimate by Carrier, at least a 93.75% chance Jesus was buried and resurrected in outer space?).
Secondly, I assume we can agree that the way reference classes are normally thought to be used is that (otherwise just see the wikipedia reference I provided or read the other document by Alan Hajek):
P(A|B) = (Number of elements that matches A and B) / (Number of elements that matches B)
Then if we use A = ~h and B = RR this would suggest that the correct estimate of the RR prior, using the Laplace rule, is:
P(~h|RR) = (Number RR heroes who did not exist, were buried in the supernatural realm, etc. + 1) / (Number of RR heroes + 2)
however it would not seem that for instance Moses or some of the other heroes were buried in the supernatural realm. You have suggested various possibilities to overcome this difficulty, I am simply asking you to state which one you believe is correct mathematically.
Again, I am hoping we can make some progress in this conversation and perhaps end on some point of agreement. If you have any proposals for how we could make progress please just let me know. As it is, I am finding it very difficult to keeping track of your positions and particularly why you hold them despite us having discussed this for 40 posts.
Let me ask you a simple question first.
Forget ~h as it appears in OHJ, forget the supernatural burial etc.
If we were testing the most generic hypotheses:
H – he was historical
~H – he was not.
Do you think Rank-Raglan hero would be a valid reference class, or not?
Hi Zbykow,
I appreciate your question and I will try to answer it as accurately as possible.
Do you think Rank-Raglan hero would be a valid reference class, or not?
If I answer the question directly, yes, the Rank-Raglan hero class would be a valid reference class if defined narrowly and exactly as: “matching more than X criteria according to Rank and Raglan”. That’s because a reference class is just a set with a clear definition from which we can phrase statements about probability. So: “even number of vowels in the name according to this source” could also be a valid reference class. A “reference class” is basically just a well-defined set.
Now I take it that what you are really interested in is asking me if we can estimate ~H using the Rank-Raglan hero reference class. That is a much harder question.
Basically, my first concern is that I end up with a well-defined meaning of ~H and a well-defined set for the reference class. For instance, did Moses exist or not? Did this or that character satisfy a specific characteristic? What if there are different myths about the same RR hero, where in some myths he satisfy some characteristics and in others not? What if we are only very certain a character did not exist?
Then there is the problem of what it means someone existed (Jesus existed). I think we feel we know what that means intuitively, but if I was going to make that argument myself I would have to convince myself I would come up with a definition of “existed” that was specific enough to be applied to all the characters. What, for instance, if a character (Jesus or Moses) is the composite of two real persons?
I don’t bring this up here because it is a lot of vagueness but if I was going to apply reference classes I would have to convince myself about it. I think the soundest type of resolution would be of the form: According to this standard reference, the character did not exist and according to this other standard reference, it had these RR characteristics. That would at least make things explicit so lets assume we go down that road.
Then the philosophical problems. Using reference classes to my mind primarily a frequentistic concept and I would prefer to reformulate it in more Bayesian terms. For instance, why use Laplace Rules of succession? Carrier does not explain why this is invoked but obviously this requires an argument. In my world it would arise from a Beta(1,1) prior on the probability of existence, but I don’t know what Carrier have in mind and that issue would need to be resolved.
When this is done then yes, I would end up with a computation very similar to Carriers, however the computation would be:
P(H|R) = Given I only know about a Hero character he has these particular RR traits, what is the probability he is historical in the sense I have defined it.
I am not sure that statement makes perfect sense but lets run with it.
The problem is then that to connect this computation to Jesus, about whom thanks to OHJ I know about 100 pages of background information, then in order to apply Bayes theorem I would have to isolate the term P(H|R) somehow. The problem is now that b does not figure on the right-hand side of this expression and b contains information relevant to Jesus so I can’t just ignore it. I would therefore have to do a computation similar to what I have sketched above to isolate P(H|R) and I just think the result is going to be very nasty. Strictly speaking, I think I would have a better chance of obtaining P(H|E.b) by just making an educated guess, and I don’t know how I could use it to convince anyone.
While I was doing all this I would have in mind what’s know as the “reference class” problem (i.e. multiple reference classes, see the article by Hajek for an overview). Carrier treats it as a bit of a non-issue, however I think that makes him quite unique and I am not sure he is aware of the literature on this issue.. the problem is the context where other statisticians bring up the reference class problem as something worth taking very serious are quite simple compared to the setting we have just considered and the arguments Carrier provides are in my opinion very far from addressing those concerns.
To put it briefly, yes, RR can be made into a well-defined reference class, but I don’t think p(H|RR) is the “prior probability of historicity of Jesus” (in the simple sense) and I certainly would not trust an argument based around such a computation. What I would propose as better is what I discussed with Neil, but I would be careful to advance such an argument myself because I wouldn’t know how I could provide convincing evidence it was trustworthy.
Cheers,
T.
Thanks. ‘No’ would do just as well.
Given the prior probability is just a rough estimate expressing initial degree of belief before evidence is examined, it’s funny you resort to philosophical issues to try and argue against the whole idea altogether.
If Rank-Raglan hero class is useless for estimation of initial degree of belief in existence of an RR hero, then I wonder why it is we don’t believe, even though nobody cares to examine the evidence? Maybe we should revise our disbelief in historical Osiris or Dionysus.
Your objections do have some absurd implications.
Thanks. ‘No’ would do just as well.
Given the prior probability is just a rough estimate expressing initial degree of belief before evidence is examined, it’s funny you resort to philosophical issues to try and argue against the whole idea altogether.
Well, or rather, I recognize well-known issues (the reference class problem) and notice this is a situation where it seems to apply. To me it seems that if a person propose a computation, it has to be justified, especially when it heavily favors one conclusion. You can call that a philosophical issue or you could call it a scientific attitude :-).
If Rank-Raglan hero class is useless for estimation of initial degree of belief in existence of an RR hero, then I wonder why it is we don’t believe, even though nobody cares to examine the evidence?
Did I say the information used to establish the rank-raglan criteria is useless?
I think you are engaging in the following fallacy: Suppose argument A supports conclusion B. Then if I reject argument A (or at least question it) then I am not saying B is false.
There is a difference in terms of the sources we have for Jesus compared to the sources we have for Moses, and there is a difference in terms of how Jesus is portrayed compared to Zeus, and I think that Carrier along with all other historians agree this is the case.
“To me it seems that if a person propose a computation, it has to be justified, especially when it heavily favors one conclusion.”
RR based prior is justified enough for what it is, and it favors one conclusion only if evidence sucks, otherwise it has negligible effect.
“I think you are engaging in the following fallacy: Suppose argument A supports conclusion B. Then if I reject argument A (or at least question it) then I am not saying B is false.
There is a difference in terms of the sources we have for Jesus compared to the sources we have for Moses”
I think you’re engaging in the following fallacy: not understanding the “before evidence is examined” part. I also sense a straw man but that I ‘m not sure.
Of course there are differences in terms of sources for Jesus, Moses and all the rest of them. Not relevant at the prior probability stage.
“there is a difference in terms of how Jesus is portrayed compared to Zeus”
Sure there is, as well as any of them compared to any other. Not relevant at this stage.
Well, it seems that despite my best efforts to have a concrete discussion on the math and argument in OHJ we have nevertheless arrived at a discussion of opinions.
Tim: “To me it seems that if a person propose a computation, it has to be justified, especially when it heavily favors one conclusion.”
RR based prior is justified enough for what it is, and it favors one conclusion only if evidence sucks, otherwise it has negligible effect.
“justified enough for what it is” is an opinion and not an argument. It does not go far in terms of answering the reference class problem or the many issues I have raised on this thread.
I think you’re engaging in the following fallacy: not understanding the “before evidence is examined” part.
Well, again, you can think that, or you can address the question about how the evidence should be taken into account exactly. I discussed one such suggestion and you have so far dismissed it without providing a concrete alternative.
What would it take to change your mind?
For starters you could try to understand what the prior probability is, what it isn’t and what purpose it serves.
An RR prior is just fine for the following reasons:
– it’s relevant to the most fundamental aspect of both hypotheses – existence.
– it refers to common knowledge about the subject
– we have data available
Sure it’s not the only possibility, maybe not the best. Others I could think of are maybe, a protagonist in a work of fiction involving supernatural, supposed supernatural being in religious mythology, or the like, although I’m pretty sure these would turn out to be even less favorable for historicity than Carrier’s 6-30%
– it’s relevant to the most fundamental aspect of both hypotheses – existence.
Which is to say it does not establish the other properties which are part of e.g. ~h. This may not be a problem:
“James is a man. 30% of all men are are bald. Therefore there is a 30% chance James is bald and likes RnB music”.
who knows?
– it refers to common knowledge about the subject
Which is to say it only refer to a subset of the information found partly in the background knowledge and partly in the Gospels and so, if we take the Bayesian stuff seriously, we have to re-write our expression to contain a term like p(~h | RR).
This lead to the question: How should we re-write the expression to take these comments into account? You seem to believe this is not a noteworthy complication, and like Moses I remain hopeful to see it in my lifetime :-).
“Which is to say it does not establish the other properties which are part of e.g. ~h. “
We’ve put e.g. ~h aside, remember? It was about ~H.
While you still got problems with ~H there’s no point discussing additional issues introduced by ~h.
“Which is to say it only refer to a subset of the information found partly in the background knowledge and partly in the Gospels”
Yep, that’s the idea of the prior probability.
You also seem to have problems with the concept of background knowledge for some strange reason. If you understood what it is and where it kicks in, you’d know it’s not subject to calculations like yours. Typical BT formulas don’t even include this symbol, however it is obviously implied. You can’t use fingerprints as evidence unless you know they are pretty much unique, do you?
Please, try to understand the basics first, then see if you still feel the need to rewrite any expressions.
We’ve put e.g. ~h aside, remember? It was about ~H.
Okay that’s fine, but in that case we are talking about a different argument than in OHJ. Which brings me to the point I have been asking for some 20 posts: What is the new computation you are suggesting?
tim: “Which is to say it only refer to a subset of the information found partly in the background knowledge and partly in the Gospels”
Yep, that’s the idea of the prior probability.
..and the idea about Bayesian probabilities is that you got to account for all relevant information (you can read about this in for instance “Jaynes, ‘probability theory'” or any other textbook on Bayes theorem which discuss foundations). And so we are back at the above point, so for the 21’st time: Where is the other information accounted for?
You also seem to have problems with the concept of background knowledge for some strange reason. If you understood what it is and where it kicks in, you’d know it’s not subject to calculations like yours.
I will predict what is going to happen next: I will ask you to provide some sort of reference for this, then you will ignore the question or produce what amounts to your own opinion. Then I will ask you what computation you have in mind for the 22nd time and you will duck the question again.
You can’t use fingerprints as evidence unless you know they are pretty much unique, do you?
Well, not to establish guilt, but i can consider the proposition “A and B have the same fingerprint” in isolation of other fingerprint related information. I hope to learn where you are going with this line of thought :-).
Please, try to understand the basics first, then see if you still feel the need to rewrite any expressions.
What “basics” is it that I don’t understand? Any sort of textbook reference would be great at this point…
“What is the new computation you are suggesting?”
I’m not.
The old one works just fine.
“so for the 21’st time: Where is the other information accounted for?”
They call it likelihood function – P(E|H), or consequent probability as Carrier puts it,
the same factor you’re ignoring thus far for some reason.
“I will predict what is going to happen next: I will ask you to provide some sort of reference for this, then you will ignore the question or produce what amounts to your own opinion. Then I will ask you what computation you have in mind for the 22nd time and you will duck the question again.”
It is you who’s got some new computations in mind, not me.
My position is you don’t need them, and in fact, since you tried to do math on elements of background knowledge, I’m convinced you just shoot in the dark.
For starters you might want to read on bayesian inference in general, and Proving History chapter 3 section ‘mechanics of bayes’ theorem’.
I’m not. [suggesting a new computation]
Okay, then we have gone full circle and arrived at the initial questions I posed. Lets just take 2:
1) when Carrier says that
P(~h|b) = (1 + Number of RR heros that did not exist)/(2 + Number of RR heros)
this fails to take into account that ~h is not simply “not existed” but includes more properties (such as died and raised in the supernatural realm).
2) What, according to you, is the right way to approximate a conditional probability P(A|B) using a reference class?
Tim: “I will predict what is going to happen next: I will ask you to provide some sort of reference for this, then you will ignore the question or produce what amounts to your own opinion.
My position is you don’t need them
Prophecy fulfilled! :-).
since you tried to do math on elements of background knowledge, I’m convinced you just shoot in the dark.
..another assertion without proof or references to back them up.
This would be so much easier for you if you understood what the prior probability was. Given it’s a subjective measure of one’s beliefs before evidence is examined, and in fact it needn’t even be frequency based, then if you were doing the reasoning, you could just accept the consensus (you can do that if you don’t know better and are not easily surprised with miracles and oddities), assign historicity a 99% prior and live happily ever after.
Let’s just say you failed to convince me you understand any of this.
It seems you don’t know what the prior probability is (since you insist all the information has to go there), and you don’t know how BT works (since you didn’t know where all the evidence is supposed to go). I can’t help you with more reference, if you don’t understand the reference so far.
If you disagree – so be it.
This would be so much easier for you if you understood what the prior probability was
Here is a recipe I would invite you to follow when you wish to say someone is grossly incompetent on a scientific topic:
1) Find a place where the person gives a definition or says something specific on the topic
2) Find a textbook or other standard reference which provides the correct definition and quote it. Ensure only one definition is used in the literature
3) Show how the two are unambiguously in disagreement
It seems you don’t know what the prior probability is (since you insist all the information has to go there)
That’s a very odd statement since I just wrote down equations where evidence was treated separately. Also, more unfounded accusations.
and you don’t know how BT works (since you didn’t know where all the evidence is supposed to go).
More unfounded accusations
I can’t help you with more reference, if you don’t understand the reference so far.
More unfounded accusations. Asides that, what references? Proving History?
We’ve yet to see you adhere to these principles.
“Ensure only one definition is used in the literature” seems a particularly harsh requirement. Can you provide any reference to back that up?
By the way, I visited Carriers blog, and it turns out you considered suspicions I am Carrier seriously enough to ask him. Astonishing.
Can you provide any reference to back that up?
Well, zbykow, no. Intellectual honesty and rigor is a choice not something you should accept because a book says it.
By the way, I visited Carriers blog, and it turns out you considered suspicions I am Carrier seriously enough to ask him. Astonishing.
You were sort of implying you might be carrier, I thought i should ask him since you wrote you would not say so, and to make him aware someone was kind of sort of implying he was a sock while making a fool of himself…
“most people mentioned in surviving Josephus manuscripts do exist, so a similar prior computed based on that information alone would give Jesus almost certainly did exist” is a non sequitur.
Each person mentioned in Josephus should be assessed independently of each other, except (i) where information is common to certain people, or (ii) where non-Josephus information impacts collectively on people mentioned in the Josephus writings.
I think you misunderstand the argument. The criteria for belonging to that class i describe is simply that the person figures in surviving manuscripts by josepheus. By definition, that information is common.
You’re not providing a convincing argument (it’s circular; it begs-the-question).
Do you realize there are argument that some characters in Josephus may be fictional?
Are you aware that Josephus fails to record some events he is known to have been present at? (such as events during Vespasian’s visit to Alexandria).
Hi again, sorry that my posts were so muddled yesterday.
No, I was not aware that Josepheus frequently described fictive people as historical, thanks for pointing this out. Do you have a guess about how often he did that? (feel free to write me at my email, timhendrix@gmx.com).
However my point is not to demonstrate that Jesus existed because our current Josepheus sources mention him. We are in complete agreement that would be silly. My point was that the use of reference classes embodies that type of assumption.
I have written a brief outline of my argument below in response to Neil and so I won’t reiterate it here. However to take my points with respect to Josepheus:
Firstly, regarding circularity, what I wanted to say in the above is that I define a set of people (the Josepheus reference class) as those who satisfy the criteria that they are mentioned by Josepheus in our surviving documents. That’s not circular, it’s just a definition of a set.
That set should be compared to the Rank-Raglan class, those people who satisfy a certain number of the Rank-Raglan criteria.
Obviously these sets give different prior probabilities and both Carrier, you and I are aware of that problem. The underlying cause is that reference classes, when applied to something like history, invites us to abstract away information. We have to do that because no two historical situations are alike. My claim is that I think Carrier abstracts away quite important information and ends up comparing things that are not alike, see the Jesus/Moses example i discussed below.
I agree with your statement
“Each person mentioned in Josephus should be assessed independently of each other, except (i) where information is common to certain people”.
However why not also say that each person who happens to satisfy a certain number of Rank-Raglan criteria should be assessed independently?
I think there are good reasons to think the way Jesus is mentioned in our Josepheus manuscripts is different than how other historical figures from that time is mentioned, i.e. a strong case can be made for whole or partly interpolation and *that* information has to be taken into account.
However I also think there are important differences between Jesus and Moses. For instance, our sources about Jesus were written quite closely to the time where Jesus is supposed to have lived and just reading the the documents, the writings about Moses has far more of a “once upon a time” (the Fararo does not even have a a name!) kind of feeling to it. This is not mentioning the issue I raised below, that Moses is not (as far as I know!) thought to have died and raised from the dead in the supernatural realm.
Let me ask you a question: Do you believe that given the Gospels alone we can establish a probability of 93% that Jesus did not exist?
Tim wrote –
“I was not aware that Josepheus frequently described fictive people as historical, thanks for pointing this out.”
Well, I didn’t say ‘frequently’.
“Do you have a guess about how often he did that?”
I don’t know: there is discussion around a few characters, such as Judas the Galilean (aka Judas of Gamala). I think a lot of what is in Josephus is unverified.
But it’s interesting that Tacitus and Seutonius record events associated with Vespasian in Alexandria whereas Josephus does not despite Josephus almost certainly being with Vespasian when those event happened: eg. the visit to the serapeum)
MrHorse: Okay, I’m just trying to not have any obvious problems. I guess that the use of reference classes means we should only include people who are known to be historical or not, that is I am not sure how Carrier would count a figure where we don’t know if that figure is historical or not. I just assumed Josepheus nearly only talked about known people (governors, Cesars, military figures and so on) and nearly all of these would be historical.
Not by the gospels alone but if you compare them with the literature of the day, the words and deeds appear to be derivative fiction via mimesis or midrash.
What is the problem with beginning with a “guess” and then refining one’s “guess” in the light of new evidence as it emerges step by step? What is the problem with factoring in all our background knowledge?
Tim Hendrix, you don’t post a coherent argument.
What does “he ignores that those benefits assumes we have the *right* probabilities and the *right* logical structure of the propositions which we certainly do not” mean?
What are “all the ‘historical details’ in the Gospel compilation”???
Hi mrhorse,
Well, the benefits I refer to are the same that Carrier refers to: that you can rewrite a probability using for instance the product rule and still obtain the same result. That only holds if one has access to the right probabilities, not if one chooses probabilities based on a choice of reference Classes.
Important details are for instance that the gospels were compiled closer to the supposed events than e.g. the stories about moses.
Tim said -“Important details are for instance that the gospels were compiled closer to the supposed events than e.g. the stories about Moses.”
The gospels are *alleged* to have been complied in the late 1st century. But the documents & compilations of commentaries by the Church Fathers from the 2nd & 3rd centuries suggests that the texts gospels were still being discussed & edited then, and we hardly have firm evidence of an undisputed compilation until the Codices Sinaiticus & Vaticanus; and even they contain texts later dropped (‘the Shepherd of Hermas’ & the ‘Epistle of Barnabas’).
In saying “When dealing with a figure such as Jesus, these probabilities are established only by critically examining the memories that were recorded by later authors” (Ehrman, Bart D. (2016). Jesus Before the Gospels … (p. 31). HarperCollins. Kindle Edition), Ehrman is poisoning the well in favour of historicity- he is virtually asserting the “memories that were recorded by later authors” are recording “what probably happened in the past”. He’s being very mealy-mouthed.
Well said. That is precisely the main problem with Ehrman on the subject of Historical Jesus, and memory. He will technically acknowledge lots of problems, uncertainty. But then? Suddenly, incongruously, he reverts to his childhood, Moody Bible College belief; that Jesus is real. At least real in some minimal way.
Hi Neil, ipad version:
No problem at all! Thats exactly what I think we should do and what i think historians do! The problem is carrier ignores plainly relevant information.
I am following your discussion with Zbykow with interest. Discussion at my level is quite mundane by comparison. I really don’t see how Carrier’s application of Bayes is any different from the way other historians use it. If you have alternative factors to add then by all means do so and let’s see where your argument leads. A key benefit is that all factors that the pool of investigators consider relevant are all put on the table and fully addressed.
Hi,
The non-Haiku version: By the way other historians use Bayes, I take it you have something like this in mind: Come up with a hypothesis (Jesus existed). Figure out the intrinsic probability of that hypothesis (the prior) and the probability of the data given that the hypothesis is true and false (the likelihood). I am obviously not going to argue against that being a good idea. We can perhaps discuss if using numbers helps that much, but obviously i agree that if we do not use numbers we got to be aware of the issues you point out in this topic (I might actually steal your example for a book).
The problem as I see it is that OHJ departs from that formula in ways that are significant, but I think they only become apparent when the whole argument is considered in full which makes it unsuitable in a post like this. To give a brief overview of one issue which I think is very clearly implied in OHJ:
Carrier does not consider the hypothesis that “Jesus existed” (contra “not existed”), but rather two scenarios for historicity and mythicism. This alone is not an error, but it is important in two ways. Firstly, because when we later discuss the prior probability of historicity (or mythicism), we should consider the probability of these two scenarios because that’s what we actually use. Since the scenarios are not mutually exhaustive, there are two probabilities and not one which need to be established. Carrier only establishes one probability and and assumes the other is simply the negation. This is trivially false.
Secondly, whatever means we use for computing a prior probability must be the prior probability of these two scenarios, not simply the prior probability for “historicity”. The prior probability is estimated using reference classes. Reference classes ask us to estimate these probabilities by comparison to other members of the class, e.g. Moses. However it is obviously the phrase “Moses did not exist” differ in almost all respects to the scenario Carrier lays out for mythicism However reference classes invites us to say these two things —“Moses did not exist” and the scenario Carrier lays out for Jesus— are alike. Let me spend some more time on this point:
Suppose I consider the probability:
P(H|B)
(H could be that Jesus existed and B some background evidence, or it could be two general statements such as: It will rain tomorrow given it rained today).
When we use a reference class we count the number of things that are both H and B, N_HB, and the number of things that are only B, N_B, and estimate:
P(H|B) ~ N_HB/N_B
In Carriers case, and lets take mythicism, H is the scenario for mythicism Carrier lays out. That scenario includes that Jesus underwent a death, burial and resurrection in the supernatural realm (this is by Carriers own definition not something I believe is implied). So when Carrier places Moses in the same set, N_HB, (which he does!) there are only two options:
1) Either we read the above for what it says. In that case Carrier is saying Moses belongs to the set of people who underwent death, burial and resurrection in the supernatural realm in addition to certain other properties. That’s saying Moses was known to die, be buried and later resurrected in the supernatural realm. I don’t think that’s true.
2) Alternatively, we say we only consider H as being the property that the figure is historical. However in that case we are by definition *not* estimating the prior for the scenario Carrier lays out and which he uses in the rest of the computations.
This is also an example of why I think probabilities can obfuscate a rather simple error. To spell out the argument implied in 1 in words:
“In support of the claim that Jesus was thought initially to not exist and to have undergone a burial and resurrection in the supernatural realm is that he is alike Moses in some respects who nevertheless was not thought to have undergone a burial and resurrection in the supernatural realm”
This must be considered a very poor argument. In many ways, we could argue a more logical conclusion is that the similarities with Moses supports the view Jesus was *not* thought to have undergone a burial and resurrection in the supernatural realm. Nevertheless that argument is implied in point 1.
To connect this with my claim information is being ignored, what is being ignored here is that Jesus and Moses (and in particular the timing of the compilation of the source we have) are quite different.
There are further points. For instance, I believe it is quite clear the assumptions made by Carrier implies that given the Gospels alone we can be 93% confident Jesus did not exist. Is that reasonable?
I am sorry this is a bit OT, just let me know if you would like me to stay a bit more on the topic.
“Carrier is saying Moses belongs to the set of people who underwent death, burial and resurrection in the supernatural realm in addition to certain other properties.”
That’s not what he says.
First JC was believed to be a celestial being dwelling in a supernatural realm, then after they started believing he visited earth he gained the RR hero attributes.
Having affairs in a supernatural realm is not an RR archetype, nor would it prevent one from being an RR hero.
“I believe it is quite clear the assumptions made by Carrier implies that given the Gospels alone we can be 93% confident Jesus did not exist. Is that reasonable?”
That’s not what he says.
It’s: “the Gospels have no effect on the probability that Jesus existed, neither to raise or lower it.”
““Carrier is saying Moses belongs to the set of people who underwent death, burial and resurrection in the supernatural realm in addition to certain other properties.”
That’s not what he says.”
Okay I agree that Carrier does not say that but I am pointing out issues which are implied in what Carrier does. For instance he uses as a defining property of the hypothesis of myth that:
Like some other celestial deities, this Jesus was originally be-
lieved to have endured an ordeal of incarnation, death, burial
and resurrection in a supernatural realm. (OHJ)
So belief in a burial and resurrection in the supernatural realm is part of minimal mythisim ~h (I take it we agree so far?). To connect this to my discussion above, if you look at how a reference class works (which I describe above) it is the class of things which satisfy ~h. Now, that’s obviously a problem for Moses, so one has to treat the reference class as things which do not satisfy ~h but something less (“is historical”). However in that case the reference class is not approximating the probability ~h (which is what Carrier needs) but something else. Do you agree so far? Otherwise try to be specific in pointing out where I go wrong because I am simply not seeing it.
“I believe it is quite clear the assumptions made by Carrier implies that given the Gospels alone we can be 93% confident Jesus did not exist. Is that reasonable?”
That’s not what he says.
It’s: “the Gospels have no effect on the probability that Jesus existed, neither to raise or lower it.”
I don’t know if we are cross-posting but I already addressed this point. The statement: “given the Gospels alone we can be 93% confident Jesus did not exist” is equivalent (symbolically) to the probability:
P(~h | Gospels) = 1-P(h|Gospels)
and I compute P(h|Gospels) from Carriers numbers above to be 6.25. This is not me speculating, it is just plugging in the numbers you can find in the last chapter of OHJ. If you believe there is a mistake, feel free to point it out either here or by email. If you would like the exact quotes I provide them in my review of OHJ which you can find on my scribd account (my name links to it).
Now, I agree that Carrier properly do not wish to say that we can be 93% sure Jesus did not exist (i.e. that his scenario for mythicism is true) only given the Gospels, and I too think it is in contradiction with what he elsewhere writes. However his conclusion is based on the computation and it is the computation –and therefore the conclusion– which I am examining.
“if you look at how a reference class works (which I describe above) it is the class of things which satisfy ~h”
Here’s where you are wrong.
~h and RR are two different things. ~h is our hypothesis, reference class is one piece of evidence, a thing we know.
RR does not necessarily support the idea that the guy was initially believed to inhabit a fairyland, but it does indeed indicate that he was probably made up, which proposition is a part of ~h.
As to the 93% issue, I addressed it above.
Here’s where you are wrong.
~h and RR are two different things. ~h is our hypothesis, reference class is one piece of evidence, a thing we know.
I could be a bit strict and say a reference class is not evidence but lets leave that asides.
I gave a very brief overview of how I understood reference class to be used in OHJ above. How do you define a reference class?
Look, suppose I wanted to compute the chance a person has influenza given he has fever. I choose the reference class as: “The people who have fever” and the class I am interested in, the attribute class, as “the people who have influenza”. Then I count the number of people who have fever, N_F, and the number of people who have fever and influenza, N_IF, and then I approximate:
P(Influenza | Fever) = N_IF / N_F
In Carriers case he is interested in ~h, i.e. his scenario for mythicism. We then need to compute P(~h | b). Therefore, in a direct application, we need to count the number of people who satisfy ~h and to say that Moses is counted among these is to say he satisfy ~h. That won’t work, and what Carrier has to do is to relax the definitions one way or another.
I see. I admit that the reference class chosen to calculate the prior may seem more compatible with h than with ~h.
This boils down to the fact that the sum of h and ~h does not cover the whole spectrum. Carrier is aware of this, he explains that all other forms of historicity and non-historicity are so improbable, that they can be left out without causing much inaccuracy.
If you have problems with that, try arguing with reasons he provides in chapters 2 and 3.
The biggest problem I had with the book was that minimal myth theory wasn’t minimal enough. The PH version, simple “‘Jesus was a mythical person historicized” is more straightforward and wouldn’t cause such confusion as to why the RR class is used.
However this issue doesn’t affect the big question.
Zbykow: I am still having some troubles understanding exactly where we agree and disagree. We seem to agree that there is something fishy with the prior (I think we disagree about how fishy it is), but you accept Carriers arguments on p.55 and p 249 for why this can be ignored, so that the prior is actually correct?
Carriers argument is a bit hard to summarize, but the one on p.249 says that amongst other things that:
Finally, that subsequent Christians believed Jesus was his-
torical is an established fact in our background knowl-
edge, and therefore the probability that it is false is virtu-
ally zero; and therefore it consumes effectively all the probability-
space reserved for myth
So there is *something* in our background knowledge (Carrier does not tell what) that assures us that the additional elements of mythicism is true. So now you got to return to the example with P(Influenza | Fever). Our reference class (i.e. Fever) contains our background knowledge (where else does it go?) and by the above contain whatever information that establishes as a certainty that subsequent communities came to believe Jesus was historical. So to say Moses belongs to that class is by definition to say that same information applies to Moses. So what is that information? How can that same information be known to be available for Moses?
There are just so many problems with using reference classes the way Carrier does because it fundamentally asks us to treat things that are not alike the same way, however it is a complex subject because you got to consider it in conjunction with the other parts of the argument. Thats why I think the problems are easier illuminated by considering seeming contradictions, that’s why I focus on the 6.25%.
You chose the least interesting paragraph. It’s about the 5th proposition of the minimal myth theory, which is where h and ~h overlap, and we already know it’s true, so it has little to do with probabilities.
Look, I’m still not sure why he went with such a specific myth theory, but this is really a minor issue. Note that if you take more generic versions from Proving History and apply the same formula, everything works fine.
Zbykow:
You chose the least interesting paragraph. It’s about the 5th proposition of the minimal myth theory, which is where h and ~h overlap, and we already know it’s true, so it has little to do with probabilities.
I know that’s Carriers argument, the problem is that to my mind it seems to have obvious problems. We are trying to compute the prior of a proposition (proposition 5, lets call it P5). That this proposition happens to be true today does not mean we know the prior probability is high. That’s like saying the probability of someone winning the lottery is high because we know he won. The way we can fix that is to say that P5 is part of our background information one way or another (in what way? this is a critical point!), however in that case we should condition the other propositions which are part of ~h on P5. In particular, P5 has to enter whatever prior computation we perform and so has to be part of our reference class; however how are we to make sense of P5 in case of other figures like Moses?
I am not sure this is a minor issue.. I would be surprised if Carrier has not put thought into the scenario. It also seems to me to be much easier to explain e.g. the Gospels if we assume Jesus was thought to be historical “later” than if we do not make that assumption.
“We are trying to compute the prior of a proposition (proposition 5, lets call it P5).”
No we don’t. Why should we?
“That this proposition happens to be true today does not mean we know the prior probability is high. That’s like saying the probability of someone winning the lottery is high because we know he won.”
Yeah but see above, nobody does that so what is it you are trying to argue?
“It also seems to me to be much easier to explain e.g. the Gospels if we assume Jesus was thought to be historical “later” than if we do not make that assumption.”
Yeah, but we do make such an assumption, don’t we?
Zbykow:
Tim: “We are trying to compute the prior of a proposition (proposition 5, lets call it P5).”
Zbykow: No we don’t. Why should we?
Okay then tell me where the following argument goes wrong:
1) ~h is the proposition carrier computes the probability of (mythicism)
2) P(~h|b) is the prior probability of ~h
3) ~h contains P5
4) When we compute the prior probability of ~h this number must also reflect a prior of P5. In particular, we know the probability of P5 is larger than ~h (p(P5 | b) >= P(~h|b) ).
Yeah, but we do make such an assumption [Jesus was thought to be historical “later”], don’t we?
Yes, Carrier does! That subsequent communities came to believe (or taught) the Jesus figure was real is part of ~h by definition! (see p.53 of OHJ). This aspect of ~h must surely make it easier to explain why this is taught in the Gospels correct?
#4 is where it goes wrong.
They’re not related directly in this case, P5 might even be lower, that’s irrelevant, because we know it’s what happened.
In case you’re into nitpicking, let’s make P5 independent by removing ‘invented’. It won’t affect ~h in any way.
#4 is where it goes wrong.
They’re not related directly in this case, P5 might even be lower, that’s irrelevant, because we know it’s what happened.
I am afraid you are missing something. You agree that ~h contains P5 and P(~h|b) is the prior of ~h. However when ~h contains P5 (true by definition, see OHJ p.53) that means that
~h = P1 and P2 and … and P5 (where P1,…,P5 are the propositions that make up ~h).
in this case
p(~h|b) = p(P1 and P2 and … and P4 | P5.b)p(P5|b) = p(~h|Gospels.b) = 93.75%.
So the question I keep asking is if you agree with this conclusion, i.e. that
p(P5 | Gospels.b) >= 93.75%? (most plausibly)
If not, please point out as specifically as you please where I go wrong.
I am not trying to make you responsible for what Carrier writes, I am just trying to nail down where we might disagree and agree.
Sorry the above post was broken because the board software interpreted some of what i wrote as html tags. I include spaces around . Please disregard my above post. The argument is supposed to read:
that means that
~h = P1 and P2 and … and P5 (where P1,…,P5 are the propositions that make up ~h).
in this case
p(~h|b) = p(P1 and P2 and … and P4 | P5.b)p(P5|b) < = p(P5|b)
This holds for any proposition b. In particular
93.75% = p(~h|Gospels.b) = 93.75%? (most plausibly)
If not, please point out as specifically as you please where I go wrong.
I am not trying to make you responsible for what Carrier writes, I am just trying to nail down where we might disagree and agree.
Zbykow: The board software keeps playing tricks with me with the angled brackets. The last part of the argument is:
93.75% = p(~h|Gospels.b) less-than-or-equal p(P5 | Gospels.b)
or to state it in words:
p(P5 | Gospels.b) greater-than-or-equal 93.75%.
I.e. P5 is at least 93.75% true given the Gospels.
No, you can’t do that.
Even if you pretend P5 is uncertain, that means our evidence looks different, and there are no gospels as we know them, so I’m afraid your result would be somewhere in the realm of imaginary numbers.
Zbykow:
No, you can’t do that.
Even if you pretend P5 is uncertain, that means our evidence looks different, and there are no gospels as we know them,
I am not following this argument at all. If we assume Bayes theorem holds, everything I did is just applying basic operations from probability theory. So why can’t I do it? What step is not true? I don’t think it is reasonable when faced with a proof to say that it can’t be done without specifying why it can’t be done.
Carrier himself assumes P5 is ‘uncertain’ — it is part of his hypothesis ~h so if we can’t assign a probability to it, then there is no argument!.
I don’t think I understand your criticism of Carrier’s use of reference class. Sorry, but maybe it’s because it’s very early in the morning here and I’m only on my second coffee and I’m also only just now pulling out of a two-week long illness :-/ so I plead for patience:
I don’t see that the reference class itself is related to Carrier’s specific definition of minimal mythicism with Jesus being crucified etc in the celestial realm. It addresses only the question of whether there was a historical person behind the Jesus figure we know of today. The type of mythical or historical figure is not a factor at this stage. All it’s saying to this layman is that most figures who are said to perform magic deeds and win victories over demonic forces are not historical, though we do know that a few such figures do indeed have historical antecedents.
That’s all very general and vague and removed from any of the nitty gritty of the detailed evidence for or against the historicity of Jesus for a very good reason. If we start with a figure or point within that nitty gritty (e.g. Jesus in Josephus who writes mostly of historical figures) we are very likely to have our process skewed (question begged) from the outset. What (if any) reference class would you assign Jesus at the outset of an inquiry into his historicity?
Hi Neil,
Well it’s late evening over here and I am on my first glass of wine so that makes us even :-).
Let me start at the top. What Carrier wish to estimate is the prior probability of mythisism, P(~h|b). So whatever argument we attempt must approximate that probability. The problem is that the members of the RR reference class (such as Moses) do not actually match ~h. If we ignore that problem, it is very easy to cook up situations where we will go very wrong. I try to illustrate that with an example (Bob and his lawyer) in my review and argue why I believe this is such a situation.
As to your point, I agree that if we choose to look at Jesus, Moses, etc. only through the lens of what goes into the reference class, then indeed we can use that to estimate a prior probability of the existence of a figure about whom we only know these few things. However this would not be P(~h|b) as we would not also conclude he was buried and raised in a supernatural realm (implied in ~h). I am only sketching an argument, but do you see the potential for a difficulty?
That’s all very general and vague and removed from any of the nitty gritty of the detailed evidence for or against the historicity of Jesus for a very good reason. If we start with a figure or point within that nitty gritty (e.g. Jesus in Josephus who writes mostly of historical figures) we are very likely to have our process skewed (question begged) from the outset.
In a similar manner, can’t a person say that the RR reference class is question-begging too? As part of using the RR reference class we have to move information from the Gospels (Born of a virgin etc.) into the background information in order to place Jesus in the reference class. That is, we are not really estimating a prior, but a posterior where we condition on some specific pieces of information (Born of a virgin etc.).
What (if any) reference class would you assign Jesus at the outset of an inquiry into his historicity?
I would’t use a reference class because I don’t think they apply. I think we got to think much harder about what it means to say: “Jesus existed”. If I did not learn anything, I would go with 50% (and recognize the number was quite variable subsequently). This prior would (presumably) make the prior P(~h) much less than 50%.
I don’t understand what is required in “thinking much harder about what it means to say ‘Jesus existed’. To me it means simply that there was a historical person, Jesus, whose life was the basis of the often inflated stories in the gospels. That seems to me to be simple enough. What am I missing?
I chose the example of Jesus in Josephus to illustrate the problem of question begging because in fact there is no hard and fast straightforward datum of a Jesus in Josephus. The Jesus in Josephus is wrought with questions of ambiguities and controversy. To settle on a reference class that presumes a Jesus in Josephus is to close the door on a very large set of questions about some important evidence.
I don’t see how question begging enters when we seek to match our general understanding of the Jesus figure with a particular class of persons. If we don’t assign Jesus to be like any other category of persons then aren’t we treating him as unique? If he’s truly unique than no comparison applies and it is very hard if not impossible to conceptualize him at all.
Do you dispute the validity of the Bayesian approach?
Sorry I missed this question. I am a card-carying Baysian so I think every time we talk about a degree-of-belief about a true/false proposition we have no choice but to be Baysian. I’d say a problem with Carrier is that he is not taking the Baysian approach serious enough when he for instance applies reference classes (a frequentistic tool) and dismiss a Baysian degree-of-belief interpretation of probabilities in favor of his own frequentistic attempt.
When it comes to history I think it is natural to think about how Baysian thinking can be applied, however in ordinary Baysian analysis there are things that are known to be problematic, so I think those same issues should be raised in this context too.
Hi again,
To me it means simply that there was a historical person, Jesus, whose life was the basis of the often inflated stories in the gospels. That seems to me to be simple enough. What am I missing?
I am not sure you are missing anything. I am wondering if we get into difficulties when we translate that into more primitive logical propositions (what is the Gospels in this sense). Yesterday when I wrote it I had a sense it would be easy to imagine a problem but this morning I could not come up with anything so perhaps there aren’t.
Re. Josepheus, what I want to illustrate is one problem of using reference classes so I deliberately choose a provocative example. Since I write: “Jesus is in our surviving manuscripts by Josepheus” (and it can be made even more specific by just choosing one manuscript) it is completely well-defined and not affected by us suspecting (or knowing) Jesus was not in our original manuscripts.
According to Carriers view, this does not matter because even if we choose a reference class like this other factors in the Baysian computation will solve the problem. What I question is how well this would work in practice.
I don’t see how question begging enters when we seek to match our general understanding of the Jesus figure with a particular class of persons. If we don’t assign Jesus to be like any other category of persons then aren’t we treating him as unique? If he’s truly unique than no comparison applies and it is very hard if not impossible to conceptualize him at all.
But this is not taking Carriers argument serious. Carrier wish establish the prior probability his theory of myth and historicity, ~h and h. When we match for instance ~h to a class of people who include Moses, we comparing things that are obviously not alike (I tried to write out this syllogism above). You are right that one way or another we got to compare the existence or non-existence of Jesus to past experience, but I would be much more confident if we started out with a minimal mythicism and historicity.
To my ears what’s critical in Carrier theory in terms of establishing a prior is that the timing of the events. On his account in the early 1st century people believed Jesus was a celestial being who underwent a death and burial in space and then around the middle/late 1st century (I assume, OHJ is not specific) people had come to think Jesus was a historical person to the exclusion (or near exclusion) of the original idea. I don’t think something similar happened to the other people in his reference class such as Moses. John Frum somewhat matches the timing, but even he was not (as far as we know) thought to be celestial at first.
I think we can argue Jesus and Moses are very much alike as a class. The gospels, especially Matthew, model Jesus on Moses throughout their narratives; in non canonical Jewish writings Moses is a (virtual?) heavenly divinity and even a divinity in human form on earth.
(Aeneas is a transvaluation of Odysseus and hence their characters and accomplishments are very different but those variations can still be classified together.)
Hi Neil,
I don’t disagree Jesus and Moses are equal in some ways (like, they both match many of the RR criteria), however I also believe they are different in other ways which are relevant with respect to Carriers hypothesis for myth ~h. For instance, ~h contains the death, burial and resurrection in a supernatural realm, I think that’s plausibly a significant difference. The underlying statistical syllogism behind the RR reference class can be summarized as:
A (Jesus) is equal to B, C, D in respect to X [RR criteria]. B,C,D have property P [does not exist] with probability 93%. Therefore A have property P, Q, R, S. [not exist, death burial in supernatural realm, etc. etc.] with probability 93%.
This argument would to my mind be *greatly* improved if we left out Q, R, S.
I think we will just have to agree to disagree. I don’t see the same problems as you do with the reference class or with Carrier’s use of it. Topographical location of comparable narratives is not so significant for our purposes, imo. If it’s a major difficulty then simply use another version of mythicism (as I mentally did throughout my reading of OHJ anyway). A RR hero is an approximation, after all. That’s the nature of classification and types.
To not use a reference class of some sort does not seem to me to be failing to treat the question seriously (as I think you suggested.) Nothing can be unique or we cannot do any comparative analysis on it at all.
Okay, agree to disagree on the reference class issue. To be clear, I don’t suggest reference classes can’t be used in any circumstances, (i.e. the p(Influenza|Fever) example), but i was trying to examine what I see as difficulties in this particular use.
The point of a reference class was to help us reach an outside view of the question and understand what the likelihood of X is on the basis of comparable events. If we make an exception for one case I imagine we run into the problem of losing our bearings and being swept along by tip-of-our-nose variables.
Hi again, I am happy you couldn’t quite leave this alone (and sorry for being off-topic) :-).
I have been thinking about why we have gone amiss of each other and I think it has to do with the scope of what we are doing.. You wrote that when you read OHJ, you were mentally substituting your own ideas for mysticism, that is, you were focused on the evidence in OHJ on not the particular form of the argument. I am focusing on the specific argument as presented in OHJ in terms of how well it conforms to Bayesian thinking. If you don’t see that as an important concern (historians have done history for centuries without thinking about Bayes after all) then I am not sure there is really anything we can even agree to disagree about.
How about this plan: I first explain what I consider an obvious erroneous statistical argument, then why this relates to reference classes and finally why I think it is present in OHJ and then how I think it could be improved?
1) To give the Bad argument:
“James is a man. 30% of all men are bald. Therefore there is a 30% chance James is bald and likes RnB music”
Obviously, the problem with this argument is that the premises only supports the conclusion “there is a 30% chance James is bald”. When we add “likes RnB music” to our hypothesis about James the argument can no longer support that the hypothesis: “James is bald and likes RnB music” is true with probability 30%.
2) The bad argument using reference classes:
The above fallacy is phrases as a statistical syllogism, however the use of a reference class is really just a statistical syllogism expressed in a different way. In our example, the reference class is
M : “Is a man”
the hypothesis is:
h : “James is bald and likes RnB music”
and the conclusion can be stated as p(h | M) = 30%. (“If we assume James is a man then we can conclude there is a 30% chance James is bald and likes RnB music”). The problem is that the use of reference classes, for a general proposition h, assumes a computation of the form:
p(h | M) = (Number of people who are M and h) / (Number of people who are M)
This would in our example be:
p(h | M) = (Number of people who are men, bald and likes RnB music) / (Number of people who are men)
However this is not the same as
p(is bald | M) = (Number of people who are men and bald) / (Number of people who are men) = 30%.
This is a very simple point. It is only relying on there being a difference between “is bald and likes RnB music” and “is bald”.
3) The bad argument and OHJ:
You can properly tell where this is going :-). In terms of OHJ, Carrier uses RR (Is a Rank-Raglan hero type) instead of M, and instead of ‘is bald AND likes RnB music” carrier uses
~h : Jesus did not exist AND Jesus died, was buried and resurrected in the supernatural realm AND …. (+4 more elements)
and then crucially computes:
p(~h|RR) = (Number of heroes who satisfy the RR criteria AND did not exist) / (Number of heroes who satisfy the RR criteria).
The problem here is that “AND Jesus died, was buried and resurrected in the supernatural realm” has vanished in the above. The correct equation should be:
p(~h|RR) = (Number of heroes who satisfy the RR criteria AND did not exist AND died, was buried and resurrected in the supernatural realm AND …) / (Number of heroes who satisfy the RR criteria).
This is exactly similar to saying p(“is bald” | M) is the same as: p(“is bald and likes RnB music”|M), which is the above bad argument.
I take it that we agree that (1) is obviously wrong and that (2) is a correct representation of the definitions.. I wonder if we disagree if (3) is a correct representation of the argument given in OHJ, but i suppose we can agree that if it is then that part of the argument is at least wrong in a technical sense (if it matters is a separate question).
Practically speaking, what should we do? First off, I think it should be taken seriously that when we choose to use the RR criteria (opposed to, say, “the class of people where people believed (or at least taught) they were real within 80 years of their death”) this might bias the computation. Why not just simply consider the bare hypothesis “Jesus did not exist” and say this is true with a probability of 50% and let the information in the RR criteria, which is part of the Gospels after all, be treated like the other Gospel evidence? This seems to me to be a more natural approach.
However suppose we do want to use the RR criteria and the particular myth hypothesis ~h. In this case a more correct computation is:
p(~h | RR) = p(“Jesus did not exist AND jesus died, were buried and resurrected in the supernatural realm AND …” | RR)
= p(“Jesus died, were buried and resurrected in the supernatural realm AND …” | RR AND Jesus did not exist) p(“Jesus did not exist”| RR)
…which is guaranteed to be more favorable to historicity than the prior Carrier uses.
The discussion I have had with Zbykow (Carrier?) above revolves around the idea that there are ways to “tweak” the argument such that the above problem becomes irrelevant. To be honest, I can’t tell what Zbykow is proposing concretely, however I think there are good reasons to think this will be very difficult without ending up considering a completely new argument.
“p(~h | RR) = p(“Jesus did not exist AND jesus died, were buried and resurrected in the supernatural realm AND …” | RR)
…which is guaranteed to be more favorable to historicity than the prior Carrier uses.”
That’s incorrect, ‘supernatural realm’ is irrelevant on h, therefore it can’t be used as prior which has to be relevant for both hypotheses, otherwise probabilities wouldn’t sum up to 1 and the result would be nonsensical. You can still blame it on Carrier, because in his scenario, formally h + ~h != 1, but he did it on purpose and explained his reasons, so there’s no need for you to act like you made some shocking discovery.
However, apart from that I still find this problem interesting. Some points to consider.
– we don’t know how every single RR hero came to be one, so we can’t tell how many were ever thought to visit SR, it’s useless since we don’t have the data.
– correlation between RR features and reality (existence) is a different thing than correlation between RR features and non RR features, which are so many that prior probability of every one of them is expected to be close to zero.
– however probability that an RR hero has unique literary features is 100%
– let’s check other divine members – Zeus (aka Jupiter – self explanatory), Osiris, Hercules, Dionysus etc. they all were said to have dealings in a supernatural realm (in roman period specifically celestial). So the prior probability that a roman period RR hero was ever said to have dealings in celestial realm given we know he was also said to be divine seems to be pretty damn high.
Hi Zbykow,
Well my comments were really to Neil, I have responded to your previous remarks above. But let me address what you wrote because it might clarify some issues:
That’s incorrect, ‘supernatural realm’ is irrelevant on h, therefore it can’t be used as prior which has to be relevant for both hypotheses, otherwise probabilities wouldn’t sum up to 1 and the result would be nonsensical. You can still blame it on Carrier, because in his scenario, formally h + ~h != 1, but he did it on purpose and explained his reasons, so there’s no need for you to act like you made some shocking discovery.
I’m sorry but I don’t think what you are writing is making any sense. Firstly, “it” in the above sentence (“it cant be used as a prior”) would seem to refer to “supernatural realm” grammatically. However “supernatural realm” is not a prior but what Carrier defines as part of his proposition ~h on which the prior, that is ‘p(~h)’, is defined. I am not adding supernatural realm to anything, I am simply observing that according to Carriers definition is it part of ~h and so can’t be ignored.
Secondly, there is a logical problem. You seem to be saying that that my result would be “nonsensical” because “probabilities wouldn’t sum to up to 1”. In the very next sentence you go on to say (correctly) that the way Carrier defines his propositions the probabilities cannot be known to sum to one (because h and ~h are not each others negation despite what the notation suggests, therefore we can’t conclude that p(h) + p(~h) = 1 and most likely this will not be the case).
I am not sure why you think what I wrote is nonsensical and I would be happy to hear your argument, but it really seems like you are having your argument with Carrier and not I.
Thirdly, at no point do I claim to have made a “shocking discovery” or some cognate thereof in observing that ~h is not the negation of h. I just notice it in passing in my review because the notation could suggest otherwise. Rather, I discuss issues relating to Carriers “reasons”, as you have presented them, both in my review and on this thread. I suggest perhaps you address those?
Fourthly, the important stuff, none of this addresses the issue I actually raised to Neil, namely that a direct application of reference classes suggest we compute:
p(~h|RR) = (Number of heroes who satisfy the RR criteria AND did not exist AND died, was buried and resurrected in the supernatural realm AND …) / (Number of heroes who satisfy the RR criteria).
Whereas what Carrier computes is:
p(~h|RR) = (Number of heroes who satisfy the RR criteria AND did not exist) / (Number of heroes who satisfy the RR criteria).
And these two are obviously not alike.
This brings me to my main point: Even IF your argument was well-formed and even IF it was correct, you would still not have presented an argument for why we can use the second of the above computations in place of the first. Do you see? Carrier (not I) claims that this is the way to compute the prior, thus it is up to him (or you, if you wish to promote the argument) to provide a justification for why it is correct. This is a fundamental principle in scientific reasoning: The person who makes the claim has to provide evidence to back it up. In the case of Bayesian statistics, that would be an argument that conforms to the rules of probability theory.
Now on to your points:
– we don’t know how every single RR hero came to be one, so we can’t tell how many were ever thought to visit SR, it’s useless since we don’t have the data.
Well, if we don’t have the data, the correct way to proceed is not to ignore that we don’t have the data.
The argument is no better than it is to say: “We don’t know how many men likes RnB music, so we can’t tell how many bald men likes RnB music, thus it’s useless since we don’t have the data” and then proceed with the false computation:
p(“Bald and likes RnB music”|”Is Man”) = (Number of men who are bald)/(Number of men).
– correlation between RR features and reality (existence) is a different thing than correlation between RR features and non RR features, which are so many that prior probability of every one of them is expected to be close to zero.
Says who? It is Carrier himself who adds element to mythicism, thus it is up to him to justify that he can compute a prior for his hypothesis. I am not sure I understand your argument: Are you saying the prior of mythisism ~h becomes zero if we take all features into account, therefore we just ignore some features? To me, to the extent that makes any sense, it’s just saying we should fudge the numbers because we don’t like the result.
– however probability that an RR hero has unique literary features is 100%
Agree! at last :-). That’s why I think we ought to be careful when we bundle things together in reference classes.
– let’s check other divine members – Zeus (aka Jupiter – self explanatory), Osiris, Hercules, Dionysus etc. they all were said to have dealings in a supernatural realm (in roman period specifically celestial). So the prior probability that a roman period RR hero was ever said to have dealings in celestial realm given we know he was also said to be divine seems to be pretty damn high.
Once more with the RnB example. We could say: Some men likes classical music, some likes Jazz, some have other hobbies. So the probability they like music is high. So let’s compute:
p(“Is bald and likes RnB music” | “Is man”) = (Number of men who are bald)/(Number of men)
I mean, it just didn’t make it any more correct…
If you can establish that all RR heroes “had dealings in the supernatural realm”, you could add that to the hypothesis. But it’s a lot different from “died, was buried and resurrected” which is a very specific kind of dealing.
Cheers,
T.
It seems to me that we have a different understanding of the function of (in this case) a “reference class” with respect to Bayesian analysis. If the point is to establish a generic outside comparison of the problem with the question being addressed then I don’t see how your illustration applies or is comparable to the historicity-mythicist question of Jesus.
I don’t think I follow your reply.. My understanding of a reference class when used for the estimation of a probability P(A|B) is the computation:
P(A|B) = (Number of elements that match A and B) / (Number of elements that matches B).
Could you perhaps give yours if it is different?. With regards to your second point, are we discussing a (generic) proposition “Jesus did not exist” or the theory proposed by Carrier (~h : “Jesus did not exist AND died, was buried and resurrected in the supernatural realm AND …”)? My comments apply to the later.
Yes, i am sorry i mucked up the reply, i am fighting an ipad spelling control which is not in english and changes every other word.
I have removed some trolling and abusive comments. In a few cases that has meant related responses, including one of my own, have had to go, too.
Excellent.
[Comment deleted by Neil Godfrey because of its obnoxious accusatory tone. I try to distance the blog from the abusive and hostile standard set by many of the mainstream scholars when addressing this topic.]
Once more fwiw:
The Rank-Raglan hero class is what Jesus is now, today, to us, and the question Carrier is taking on is whether this RR hero type is best explained by either originating as a historical teacher with followers who subsequently worshiped him as a god or demigod, or as a mythical concept originating in a celestial realm and who was later allegorized and placed on earth.
The RR hero class of person stands independent of both minimal historicism and minimal mythicism. The question is whether minimal historicism or minimal mythicism best explains this particular RR class of person.
The RR hero class itself neither entails being on earth with folllowers who come to worship the hero or being allegorized from some other domain into such a narrative.
It is a misunderstanding, I think, to confuse either minimalist explanation for the figure with the classification of the figure requiring explanation.
Hi Neil,
FWIW as well: I think you would be surprised how much we agree and perhaps that’s worth stressing.
First off, I agree that the RR hero class points to myth. If you told me that you had come to worship a character (“Bob”) and you went on to describe how Bob matched the RR characteristics I would think Bob was mythical. In symbols: p(“Myth” | “Matches RR characteristics”) ~ 1.
Secondly:
The Rank-Raglan hero class is what Jesus is now, today, to us, and the question (…) is whether this RR hero type is best explained by either originating as a historical teacher with followers who subsequently worshiped him as a god or demigod, or as a mythical concept originating in a celestial realm and who was later allegorized and placed on earth.
I removed Carrier from that quote. But I agree! Why did Jesus come to match the RR hero class? That is surely the important question. My only potential reservation is that we know more than just the RR characteristics, for instance we know about the time period in which Jesus originated, we know that not all Gospels contains the RR characteristics etc. and this information must (if reasonably important) be taken into account as well. But I am pretty sure we also agree on that.
The RR hero class of person stands independent of both minimal historicism and minimal mythicism. The question is whether minimal historicism or minimal mythicism best explains this particular RR class of person.
Agree as well!. But here is one caveat: When we say “whether minimal historism or minimal mythicism best explains this particular RR class of person”, I read this as a statement about probabilities of the form: p(RR-class-of-person | Myth) and p(RR-class-of-person | Historical). For instance when we say
“Bob was born in Afrika which easily explains why he speak swahili”
that is in my view opinion equivalent to saying that
p(Speak Swahili | Born in afrika)
is high.
So what has happened here is that we consider “minimal” myth/history and we have switched the ordering of the propositions. I think this is the natural way to consider the RR characteristics, namely as evidence (in the Gospels) that must be explained on either hypothesis, but this is not what Carrier is doing.
The RR hero class itself neither entails being on earth with folllowers who come to worship the hero or being allegorized from some other domain into such a narrative.
Agree!. Such a conclusion would be highly dubious just as it would be dubious to make that inference in the case of Zeus or Moses.
It is a misunderstanding, I think, to confuse either minimalist explanation for the figure with the classification of the figure requiring explanation.
I am not 100% sure what this means so no comments.
Okay so where do we disagree? I think we disagree in that I think Carrier is exactly doing the opposite of what you suggests. If we take Carriers computation serious his premise is that
P(~h|b) = (1+#mythical RR heros)/(2+#RR Heros)
So three things are being assumed here:
1) We are not considering if historicity/myth better explains the RR person, but the probability of ~h given the RR characteristics. (i.e. the opposite conditional probability you indicated above)
2) We are not considering minimal mythicism (for instance) but the full list of characteristics (buried in supernatural realm etc.) (i.e. we are concluding that the RR hero class background information DOES imply being allegorized into a historical narrative).
3) All 170+ pages of background information is being compressed into the RR list of characteristics. Essentially this is implying the background information of Zeus, Jesus and Moses can be considered the same.
Now, Carrier has arguments on all these points in particular (2). I don’t think these arguments makes a lot of sense and can survive being translated into statements about probabilities, but my main point here is simply what I think Carriers argument very plainly implies.
No, this is where we disagree. I don’t see the validity of this in the light of Raglan’s discussion of the the classification. Robin Hood fits the classification because of scattered sources, with none of the earliest ones containing everything. The Jesus figure is likewise the collation of various sources over time. Ditto historical persons who fit the class. Not everything about them that is RR-ish, I would think, fits what we find in the earliest sources.
Neil:
Tim: My only potential reservation is that we know more than just the RR characteristics
No, this is where we disagree. I don’t see the validity of this in the light of Raglan’s discussion of the the classification. Robin Hood fits the classification because of scattered sources, with none of the earliest ones containing everything. The Jesus figure is likewise the collation of various sources over time
Okay that’s actually a good point re. the issue of how well the RR characteristics are found in Mark/Matthew, I didn’t think about it.
But how about the underlying point? In your view, do you think all the background information b for Jesus is reducible to just the laundry-list of RR characteristics?
What about the other points? I mean, ~h is defined to contain the full-fledged “celestial being allegorized into an earthly man” hypothesis and Carriers computation –which simply notice Jesus matches RR characteristics– concludes that this hypothesis with all it’s properties is p(~h|b) = 93.75% probable. Do you think that sounds reasonable?
The way I take it the Jesus we know of today is a cultural composite that by and large fits the R-R classification of a hero. I think few persons in the R-R list would have all their background information conforming to the different classification facets. They figures that are included by Raglan in his book are very diverse. The question as I see it is: “How likely is it that a figure who by and large fits the RR class is explained by (a) h or (b) ~h?” I don’t know if this is adding anything to our discussion — perhaps I’m repeating myself.
As for your last question, I am not sure what you mean by “this hypothesis with all its properties”. There are properties that belong to the RR class of person but they are not the same properties as found in Carrier’s mythicist hypothesis. The properties of the latter serve to explain the properties of the former.
Added later:
Classification does not rely upon all things being similar among respective objects but only selected similarities. A kangaroo and a koala have very few obvious features in common but both are classified as marsupials — a useful classification for addressing scientific questions. Ditto for classifying the platypus with the echinda as monotremes, despite their apparent differences. Classification is about identifying certain points of commonality for specific purposes, to help us address and think about certain questions. Members of the R-R class can be as diverse as koalas are from kangaroos yet be classified together to enable useful questions to be explored.
wow 135 posts, this is getting unhealthy. I really think we are close to coming to a kind of agreement. I think the most important point is that I agree with nearly everything you write, I just think it is different on a few but important counts from what Carrier is doing in OHJ:
he way I take it the Jesus we know of today is a cultural composite that by and large fits the R-R classification of a hero. I think few persons in the R-R list would have all their background information conforming to the different classification facets. They figures that are included by Raglan in his book are very diverse.
I absolutely agree.
The question as I see it is: “How likely is it that a figure who by and large fits the RR class is explained by (a) h or (b) ~h?” I don’t know if this is adding anything to our discussion — perhaps I’m repeating myself.
I think we are repeating ourselves a bit here but it is the central issue so perhaps it is okay. :-). So first off I 100% agree with that statement, I do think it is the central issue.
But if that’s the case there is a problem: When I say ‘How well is A explained by B’ (and I am talking in terms of probabilities), then I am talking about the probability P(A|B).
Suppose for instance that I say: “That Susi bought a new roof is very well explained by the fact a Tornado removed their roof last month”. This statement is implying that P(“bought a new roof” | “Tornado removed the roof of the house”) is high.
What the statement is not implying is that P(“Tornado removed the roof of the house” | “bought a new roof”) is high. In this example it is not for instance. Are you with me so far at least as this example is concerned?
Here is the point: when you are writing: The question as I see it is:“How likely is it that a figure who by and large fits the RR class is explained by (a) h or (b) ~h?”
this is (by direct analogy) a statement about the probability:
P(“Figure that by and large fits the RR class” | h)
(or ~h). But we are not at the core of the problem: Just as in the case of the tornado-example, this probability is not
P(h | “by and large fits the RR class”)
which is what Carrier uses as his prior probability (see for instance the last chapter of OHJ). Is this making sense so far?
Don’t get me wrong, I think that what you are doing is asking exactly the right question: That what’s important here is how easily h (or ~h) explains the fact Jesus fits the Rank-Raglan hero class in terms of the Gospels. I also think the RR information is important: for starters it must mean the Gospels can’t be considered very reliable history. An additional advantage of phrasing the question in this way is that, after we have dealt with the RR hero class information, we can move on to the other pieces of evidence and so you avoid all that talk about the difference between the various RR hero characters.
But my point is that in a very basic way what you are doing is dramatically different than what Carrier is doing exactly because we shouldn’t confuse P(A|B) with P(B|A). I think that’s why a lot of the stuff I am saying (“bla bla, Jesus is different than moses, etc. etc.”) doesn’t make a lot of sense to you because in *your* way of phrasing the problem it really does not matter and you are simply noticing that. Is any of this making sense?
So does this difference between P(A|B) and P(B|A) matter? I think there are very good reasons to think that it does and most of my review focuses on that point. But this is another 135 post topic. I have tried to illustrate it with some examples, just to take the last:
As for your last question, I am not sure what you mean by “this hypothesis with all its properties”. There are properties that belong to the RR class of person but they are not the same properties as found in Carrier’s mythicist hypothesis. The properties of the latter serve to explain the properties of the former
What I mean by “all it’s [Carriers myth hypothesis] properties” I mean the 5 properties in Carriers minimal myth hypothesis ~h. They are for instance that Jesus died in the supernatural realm and that stories told about Jesus was later believed to be historical. So to re-state my question again: If you again look at Carriers prior in OHJ it is the computation:
P(~h|”Rank-Raglan information”) = (1+#Number of RR heros who did not exist)/(2+#Number of RR heros)
This computation is not using the properties of Carriers hypothesis ~h to explain the RR characteristics: that would be p(RR | ~h) and I again 100% agree that makes a lot of sense.
What Carrier is doing here is to say that the mere non-existence of a RR hero counts TOWARDS his specific hypothesis even if the heros does not match the 5 properties of his hypothesis. It goes right back to the example with the man who is bald. Suppose I computed:
P(“Is bald and likes RnB” | “Is a man”) = (1 + #Number of men who are bald)/(2 + #Number of men)
Clearly this is asking for troubles because I am ignoring the extra element of “likes RnB” (compare to the 5 elements of Carriers hypothesis). Again I am aware Carrier presents reasons for why what he does is sensible, but I think they fall apart when they are put under scrutiny.
Sorry, but it still seems to me that you are confusing RR classification points with background information.
it still seems to me that you are confusing RR classification points with background information.
According to Carrier the RR classification points are by his definition part of the background information.
In fact my point for the past many, many posts has been exactly that the prior computation in OHJ confuses the RR classification criteria with the background information which subsequently vanishes, see my second-last equation which you can verify agrees with the prior computation in OHJ.
If you are not interested in this conversation at this point that’s fine, but I had hoped you had responded to the various questions in my last post.
If you like, you are welcome to respond at the thread on the earlywritings forum or email (timhendrix@gmx.com). Don’t take this the wrong way, but I think I am presenting a quite explicit argument which draws directly from what is written in OHJ and I feel some evidence of blanket dismissal of these points rather than an argument for why I am wrong.
I do try to follow your comments but each time I come up against a line where I see confusion of RR class attributes with background evidence that I fail to see in Carrier’s argument but that you yourself appear to be making/introducing.
I don’t see where or how Carrier confuses the RR classification itself with the background information. Rather than use analogies about tornadoes etc that I do not quite see as truly analogous to the Carrier’ argument why not use the specifics from Carrier’s argument itself.
Put me down as just not getting it, if you like, but that’s how I see it. As for the earlywritings discussion I stick to quick to read topics and am not particularly interested in picking apart or finding supports for Carrier’s work (I disagree with a number of his points and agree with others, maybe one day I’ll write a review but that’s not going to be tomorrow) — there are other questions I am more interested in exploring right now.
Hi, I don’t want to put you down for not getting something (maybe it is me?), I am just think we should be able to get to the bottom of this.
I do try to follow your comments but each time I come up against a line where I see confusion of RR class attributes with background evidence that I fail to see in Carrier’s argument but that you yourself appear to be making/introducing.
I don’t see where or how Carrier confuses the RR classification itself with the background information. (…)why not use the specifics from Carrier’s argument itself.
Okay, how about I try to break this down as a list with references to OHJ and you can tell me where I might go wrong?.
1) p598 figure 2. Carrier uses P(~h|b) in the calculation for his final result (this is the prior)
2) p53, ~h is defined as “the minimal myth theory” consisting of the 5 elements on the list (including for instance that Jesus died in the supernatural realm etc.)
3) b stands for background knowledge. Background knowledge is defined in chapters 4 and 5, see p15 (top)
4) Background knowledge b includes knowledge about the Rank-Raglan hero type. See element 48 of background knowledge b on p229 and forward.
5) Jesus is mention within the background knowledge to conform to the RR hero type (see p232). background knowledge b is therefore defined to include the Rank-Raglan related information.
6) To put this together, Carrier computes the prior probability of myth, ~h, given the background knowledge b which includes the rank-raglan information by his own definition. Are you with me so far? I think this is the point which has been controversial in my last few posts and the rest of my argument basically takes offset in this observation. To summarize:
7) The computation Carrier performs for P(~h|b) is given on p234 (top). It is, for ~h, given as:
P(~h|b) = (1 + #non-historical RR heros)/(2+#RR heros)
8) Carrier therefore does not consider, as you put it, “How likely is it that a figure who by and large fits the RR class is explained by (a) h or (b) ~h?”. That computation would be (and I agree that computation would be very sensible!):
P(“Figure fits RR hero class” | ~h)
Rather Carrier considers P(~h|RR) (which is the only place where the RR information enters in the argument). This probability is accurately described as:
“An estimate of the probability of the 5-point myth theory given the background information b”
Which (by carriers computation) is reduced to simply counting any non-existing rank-raglan hero as support for the full 5-point myth theory even though they have very little in common. Why does Moses support the idea Jesus is buried in the supernatural realm when Moses dies on earth?.
All my previous examples (the bald man etc.) attempts to illustrate why I do not think this is sound, but that is perhaps a later argument.
It is this step I do not follow.
Sorry, the bolding went a bit wrong in my previous post.
Hi,
Sorry I did not notice the reply.
Tim: Which (by carriers computation) is reduced to simply counting any non-existing rank-raglan hero as support for the full 5-point myth theory even though they have very little in common.
It is this step I do not follow.
This is simply step 7:
P(~h|b) = (1 + #non-historical RR heros)/(2+#RR heros)
The counts I am referring to are simply the numbers on the right-hand side (i.e. number of non-historical RR heroes and total number of RR heroes). I agree that I don’t follow it either as such — it is completely unsound statistically — but it is what actually takes place in OHJ.