Bayesian Historicity

[Peter Kirby]

Thanks for this example and for its explanation.

No problem.

BTW could you provide that link to your essay mentioned above again.

http://infidels.org/library/modern/peter_kirby/tomb/

[Leucius Charinus]

I was a little disappointed that Carrier did not provide a Bayesian analysis of some of the known forgeries. (I may have missed this in which case please correct me). For example I understand Carrier thinks the TF is a forgery. Has he made a case study of this hypothesis using Bayesian stats? I am intrigued how Carrier will introduce forgeries into a Bayesian equation. I don't think its a simple exercise but I might be wrong.

For example how are we to define the historicity of the TF using a Bayesian approach? A value between 0 and 1?

Thanks for any observations.



LC

[neilgodfrey]

I was a little disappointed that Carrier did not provide a Bayesian analysis of some of the known forgeries. (I may have missed this in which case please correct me). For example I understand Carrier thinks the TF is a forgery. Has he made a case study of this hypothesis using Bayesian stats? I am intrigued how Carrier will introduce forgeries into a Bayesian equation. I don't think its a simple exercise but I might be wrong.

For example how are we to define the historicity of the TF using a Bayesian approach? A value between 0 and 1?

Thanks for any observations.



LC

Not sure if this is the sort of response you are looking for, but I would think this question could be broken down the same way Carrier breaks down the question of historicity. That is, into a series of sub-hypotheses to be tested and then brought together at the end.

So if we start with the words "He was the Christ" in the TF and ask what probability this sentence would have been written by Josephus we would include nothing higher than 0.1.

Next hypothesis: that some of the words in the TF can be slightly modified to yield a probability that Josephus would have said such a thing. This one is more complex and needs to consider arguments for and against. Given Carrier's case against I think he'd say he was generous granting such an alternative possibility 0.2. I can't see how anyone assessing the pros and cons could argue higher than 0.4.

Or maybe this is not what you were looking for?

[junego]

I was a little disappointed that Carrier did not provide a Bayesian analysis of some of the known forgeries. (I may have missed this in which case please correct me). For example I understand Carrier thinks the TF is a forgery. Has he made a case study of this hypothesis using Bayesian stats? I am intrigued how Carrier will introduce forgeries into a Bayesian equation. I don't think its a simple exercise but I might be wrong.

For example how are we to define the historicity of the TF using a Bayesian approach? A value between 0 and 1?

Thanks for any observations.



LC

In Hitler Homer Bible Christ Carrier gives his Bayesian analysis of why he thinks the Tacitus quote about Nero's persecution of Christians is most likely redacted/interpolated for his article "The Prospect of a Christian Interpolation in Tacitus' Annals". The publisher, Vigiliae Christianae, wouldn't allow it in the final article because it was too mathy. Reading that analysis gives clues about how he might apply Bayes to the TF, it would have been nice if he had done the same for the article he did get published about the interpolations in Josephus, which is also in HHBC, buying the ebook being the easiest way I could access both articles.

Brief take on his application of Bayes to Tacitus (I'm not vouching for anything, jes reportin' whut he rote )
a) He gives the prior probability of any reference to Jesus (he's not clear if he means any ref to Jesus/Christ/Christians but the context of the discussion seems to mean J/C/C) in non-Christian literature is not genuine as 1 in 200 or 200:1 that it is genuine. (He gives a range of 10:1 to 400:1 and picks 200:1 as a middle ground.)

b) Evidence 1: Tacitus' description (called the TT hereafter) had no influence on any of the stories/descriptions of Nero's persecutions that we currently have before the 4th century. The probability of this evidence if the TT is genuine he gives as 20:1 for interpolation.

c) Evidence 2: There are no Christian tales or traditions outside the TT that preserve information about this martyrdom described in the TT until the Paul-Seneca letter forgeries of the late 4th century. He gives a probability of this evidence if the TT is genuine as 5:1 for interpolation.

d) Evidence 3: In particular, Christian authors of 2nd to 4th centuries who we know referenced Tacitus and /or were interested in martyrdom tales do not mention the TT or the persecution after Rome burned. He puts the probability of this evidence if the TT is genuine as 5:1 for interpolation

e) Evidence 4: The description of events in Annals seems to fit the violent Chrestians, as described by Suetonius and expelled by Claudius, and not the nonviolent Christians. He gives his probability of this evidence if the TT is genuine as 4:5 for authenticity.

If the prior probability for authenticity of the TT is 200:1
And the probability for interpolation after review of evidence is about 625:1. (20/1 x 5/1 x 5/1 x 5/4 = 2500/4).
Then that gives a bit over 3 times more likely that the TT is interpolated than not per Carrier's probabilities and calculations (625/200 = 3.125) or about 75% chance of interpolation.

[Leucius Charinus]

Thanks very much neilgodfrey on the TF, but junego I think has nailed the question ...

I was a little disappointed that Carrier did not provide a Bayesian analysis of some of the known forgeries. (I may have missed this in which case please correct me). For example I understand Carrier thinks the TF is a forgery. Has he made a case study of this hypothesis using Bayesian stats? I am intrigued how Carrier will introduce forgeries into a Bayesian equation. I don't think its a simple exercise but I might be wrong.

For example how are we to define the historicity of the TF using a Bayesian approach? A value between 0 and 1?

Thanks for any observations.



LC

In Hitler Homer Bible Christ Carrier gives his Bayesian analysis of why he thinks the Tacitus quote about Nero's persecution of Christians is most likely redacted/interpolated for his article "The Prospect of a Christian Interpolation in Tacitus' Annals". The publisher, Vigiliae Christianae, wouldn't allow it in the final article because it was too mathy. Reading that analysis gives clues about how he might apply Bayes to the TF, it would have been nice if he had done the same for the article he did get published about the interpolations in Josephus, which is also in HHBC, buying the ebook being the easiest way I could access both articles.

Brief take on his application of Bayes to Tacitus (I'm not vouching for anything, jes reportin' whut he rote ;) )

Many thanks junego. Appreciate the data dude. Spot on.

a) He gives the prior probability of any reference to Jesus (he's not clear if he means any ref to Jesus/Christ/Christians but the context of the discussion seems to mean J/C/C) in non-Christian literature is not genuine as 1 in 200 or 200:1 that it is genuine. (He gives a range of 10:1 to 400:1 and picks 200:1 as a middle ground.)

b) Evidence 1: Tacitus' description (called the TT hereafter) had no influence on any of the stories/descriptions of Nero's persecutions that we currently have before the 4th century. The probability of this evidence if the TT is genuine he gives as 20:1 for interpolation.

c) Evidence 2: There are no Christian tales or traditions outside the TT that preserve information about this martyrdom described in the TT until the Paul-Seneca letter forgeries of the late 4th century. He gives a probability of this evidence if the TT is genuine as 5:1 for interpolation.

d) Evidence 3: In particular, Christian authors of 2nd to 4th centuries who we know referenced Tacitus and /or were interested in martyrdom tales do not mention the TT or the persecution after Rome burned. He puts the probability of this evidence if the TT is genuine as 5:1 for interpolation

e) Evidence 4: The description of events in Annals seems to fit the violent Chrestians, as described by Suetonius and expelled by Claudius, and not the nonviolent Christians. He gives his probability of this evidence if the TT is genuine as 4:5 for authenticity.

If the prior probability for authenticity of the TT is 200:1
And the probability for interpolation after review of evidence is about 625:1. (20/1 x 5/1 x 5/1 x 5/4 = 2500/4).
Then that gives a bit over 3 times more likely that the TT is interpolated than not per Carrier's probabilities and calculations (625/200 = 3.125) or about 75% chance of interpolation.

Given the above (thanks btw) I have some questions:

a) Does the 75% chance of interpolation translate as a 25% chance of being genuine?

b) If historicity is defined as "historical genuineness" then - according to the assessment above - is the historicity of the TT 25%?

c) Is it therefore true, in general, that a simple percentage between 0 and 100% is adequate to express the historicity of any given event, identity, text, etc?

d) In the specific case of the HJ the historicity of Jesus is being assessed. What was Carrier's estimate again? Is it true that .... Assuming 1/20 or 5%, does this translate to a 5% historicity of Jesus? Likewise people arguing for the historical Jesus must take a historicity value between 51 and 100, whereas those arguing for an MJ must take a historicity between 0 and 49, leaving the 50% fencesitters?


Thanks for any comments.




LC

[andrewcriddle]

In Hitler Homer Bible Christ Carrier gives his Bayesian analysis of why he thinks the Tacitus quote about Nero's persecution of Christians is most likely redacted/interpolated for his article "The Prospect of a Christian Interpolation in Tacitus' Annals". The publisher, Vigiliae Christianae, wouldn't allow it in the final article because it was too mathy. Reading that analysis gives clues about how he might apply Bayes to the TF, it would have been nice if he had done the same for the article he did get published about the interpolations in Josephus, which is also in HHBC, buying the ebook being the easiest way I could access both articles.

Brief take on his application of Bayes to Tacitus (I'm not vouching for anything, jes reportin' whut he rote )
a) He gives the prior probability of any reference to Jesus (he's not clear if he means any ref to Jesus/Christ/Christians but the context of the discussion seems to mean J/C/C) in non-Christian literature is not genuine as 1 in 200 or 200:1 that it is genuine. (He gives a range of 10:1 to 400:1 and picks 200:1 as a middle ground.)

b) Evidence 1: Tacitus' description (called the TT hereafter) had no influence on any of the stories/descriptions of Nero's persecutions that we currently have before the 4th century. The probability of this evidence if the TT is genuine he gives as 20:1 for interpolation.

c) Evidence 2: There are no Christian tales or traditions outside the TT that preserve information about this martyrdom described in the TT until the Paul-Seneca letter forgeries of the late 4th century. He gives a probability of this evidence if the TT is genuine as 5:1 for interpolation.

d) Evidence 3: In particular, Christian authors of 2nd to 4th centuries who we know referenced Tacitus and /or were interested in martyrdom tales do not mention the TT or the persecution after Rome burned. He puts the probability of this evidence if the TT is genuine as 5:1 for interpolation

e) Evidence 4: The description of events in Annals seems to fit the violent Chrestians, as described by Suetonius and expelled by Claudius, and not the nonviolent Christians. He gives his probability of this evidence if the TT is genuine as 4:5 for authenticity.

If the prior probability for authenticity of the TT is 200:1
And the probability for interpolation after review of evidence is about 625:1. (20/1 x 5/1 x 5/1 x 5/4 = 2500/4).
Then that gives a bit over 3 times more likely that the TT is interpolated than not per Carrier's probabilities and calculations (625/200 = 3.125) or about 75% chance of interpolation.

This appears to assume that b) Evidence 1 c) Evidence 2) and d) Evidence 3 are independent probabilities, this seems unlikely to be even approximately true.

Andrew Criddle

[Peter Kirby]

a) Does the 75% chance of interpolation translate as a 25% chance of being genuine?

Yes, if you define "genuine" as "not an interpolation." Otherwise genuine is less than 25%, by the amount of "not genuine and not an interpolation." (For example, if you think there is a 1% chance of "not genuine and not an interpolation," i.e. because the Ant. as a whole is not genuine, then you arrive at a 24% chance that the passage is genuine.)

However Carrier likes to smooth small numbers out of his work, which means that he is doing estimates and not calculations. Thus he'd still estimate it at 25% even if the calculation is off because he's more interested in an estimate. Not crazy, given that none of these numbers are firm anyway.

b) If historicity is defined as "historical genuineness" then - according to the assessment above - is the historicity of the TT 25%?

No.

c) Is it therefore true, in general, that a simple percentage between 0 and 100% is adequate to express the historicity of any given event, identity, text, etc?

Therefore? Not really. This seems more like an axiom of a probability theory interpretation of epistemology than an actual conclusion. To my mind, anyway.

d) In the specific case of the HJ the historicity of Jesus is being assessed. What was Carrier's estimate again? Is it true that .... Assuming 1/20 or 5%, does this translate to a 5% historicity of Jesus? Likewise people arguing for the historical Jesus must take a historicity value between 51 and 100, whereas those arguing for an MJ must take a historicity between 0 and 49, leaving the 50% fencesitters?

Ontologically, at least in the common way of thinking, there is only one answer. History happened a certain way.

Some of those events that happened might actually seem improbable to us now. This is another way of saying that we are fallible.

How much you want to hedge (or how eager you are to declare) before making a fallible judgment tends to be a very personal thing, especially when there are no real stakes involved (i.e., your next meal or ability to procreate or any other goal, etc., doesn't depend on this answer).

So you could have two different people come to the same estimate (e.g., 60%) and yet want to hold different attitudes! One wants to declare himself quite uncertain, while the other wants to press the consideration of a balance of available, considered evidence in favor of it.

...

If there were real stakes involved, you could use the estimate as a factor in a payoff matrix to help you make a decision. Let's be crude and say that two drinks at a bar cost $10 and that the rational agent values bedding a person at the bar at $200. Simplify and say that this is the only approach.

If the estimate is anywhere above 5% for a random person, then the investment has a positive payoff. So we see that a person can act rationally on a belief, even if the firmness (shakiness) of that belief is only at a sad 5% odds.

However if there is no payoff there is no rational way to decide whether to use that belief. Since it is only theoretical, it seems a little bit absurd to act on the information in any way, even to the extent of "forming a belief." Then why do people do so?

...

In reality there are no consequences for the existence or non-existence of a historical Jesus, but there are consequences of identity. Identity comes from forming a belief in this case. Forming a belief in favor of a historical Jesus puts you in a category; that category can offer you access to benefits including peer approval. Forming the opposite belief also has its own benefits with different peers.

There are also consequences in terms of cognitive dissonance. The cost is low for most people to maintain a belief in a historical Jesus because that is their status quo. But the cost can be high for a few people who have studied the evidence and found it wanting. They get more benefits on this level from rejecting a belief in a historical Jesus.

...

Okay so where do the historical probability estimates come into play? They are not factors in a payoff matrix. They have nothing to do with identity. The only intersection is with cognitive dissonance.

Basically a person who has a very high estimate of an opinion will have a lot of cognitive dissonance from attempting not to believe it. One way to get this kind of cognitive dissonance from attempting to abandon a belief is from having a reasoned opinion in favor of the belief based on the kind of estimation that Carrier (or Goodacre, etc.) attempts to do.

However you should wonder why we go through all that trouble! And this leads back to the question of identity, especially in this case. The most respected appeal for trying to get others to change opinion (and thus change identity) is the appeal to reason. Yes, there are plenty of appeals to naked self interest in the form of verbal abuse and beating the drums. But that tiny little needle wavering between "probable" and "improbable" is what the most respected people in education try to read, because we've learned from past mistakes and ignorance that it is important to get some people at least to try to read that kind of stuff carefully.

Fundamentally, someone who is pressing the consideration of a balance of evidence on a historical question such as this one is saying that the most respected people in the field should recognize that fact if they were reading correctly and that, as a result, those with an education (designed by these historians) should be getting that answer and, if they were going to do the most noble thing, should adopt that identity.

...

Thus, an argument for the non-historicity of Jesus is an argument that people should not be Jesus-believers but rather should shed that identity, particularly if they are the kind of people who like being considered reasonable. Some are more willing to send that message, some are less, even apart from disagreements about the nature of the evidence.

[Leucius Charinus]

a) Does the 75% chance of interpolation translate as a 25% chance of being genuine?

Yes, if you define "genuine" as "not an interpolation." Otherwise genuine is less than 25%, by the amount of "not genuine and not an interpolation." (For example, if you think there is a 1% chance of "not genuine and not an interpolation," i.e. because the Ant. as a whole is not genuine, then you arrive at a 24% chance that the passage is genuine.)

Yes. Fair point. I understand this.

b) If historicity is defined as "historical genuineness" then - according to the assessment above - is the historicity of the TT 25%?

No.

I take it that the 'no' is qualified by what you have written above. However given these qualifications and a correspondence between "genuineness" and "historicity", do you agree that the answer is 'yes'.

c) Is it therefore true, in general, that a simple percentage between 0 and 100% is adequate to express the historicity of any given event, identity, text, etc?

Therefore? Not really. This seems more like an axiom of a probability theory interpretation of epistemology than an actual conclusion. To my mind, anyway.

Thanks. Yes this is more of "an axiom of a probability theory interpretation of epistemology". However this is what I am attempting to ascertain. The end point of this is the following statement.

d) In the specific case of the HJ the historicity of Jesus is being assessed. What was Carrier's estimate again? Is it true that .... Assuming 1/20 or 5%, does this translate to a 5% historicity of Jesus? Likewise people arguing for the historical Jesus must take a historicity value between 51 and 100, whereas those arguing for an MJ must take a historicity between 0 and 49, leaving the 50% fencesitters?

Ontologically, at least in the common way of thinking, there is only one answer. History happened a certain way.

Of course. The problem is that we don't know the specific and certain sequence of events of that history. Hence the utility of probability and Bayes.

It appears to me therefore that our assessment the historicity (i.e. genuineness) of any historical event must always remain hypothetical and therefore probabilistic. It therefore follows that this assessment must always be able to be reflected in a probability. Either expressed as a percentage or a decimal between 0 and 1. This is essentially all I wish to ascertain.

So you could have two different people come to the same estimate (e.g., 60%) and yet want to hold different attitudes! One wants to declare himself quite uncertain, while the other wants to press the consideration of a balance of available, considered evidence in favor of it.

That's a good point and in fact represents the reason I asked the question above. This 60% assessment can easily represent different attitudes. Two investigators may arrive at the same summary assessment but their detail underpinnings could be entirely different. What therefore is actually represented in the 60% assessment (I assume of "historicity" of something)? I guess the answer is only a "one dimensional" summary position.

In reality there are no consequences for the existence or non-existence of a historical Jesus, but there are consequences of identity. Identity comes from forming a belief in this case. Forming a belief in favor of a historical Jesus puts you in a category; that category can offer you access to benefits including peer approval. Forming the opposite belief also has its own benefits with different peers.

This sounds like something from the field of sociology. There are IMO however massive consequences for the existence or non-existence of a historical Jesus in the field of history because of the implications. If Jesus did not exist then someone has made a terrible mistake in their assessment of history. This mistake could be unintentional, or it could represent a misunderstanding somewhere in the scribal transmission of the "Jesus Story". Many myth theories seem to fit in to this category. It seems to me that the Doherty/Carrier Mythical Jesus fits in to this category. One generation of scribes write a "heavenly (non historical) Jesus story" and then a subsequent generation of scribes treated the myth as history and historicised it.

However it is just as likely and reasonable that the "mistake" was intentional and someone (or some organisation) simply lied in presenting a fictitious story as religious history. This is not a misunderstanding but rather a purposeful fraudulent misrepresentation of the historical truth.

Belief as discussed above is therefore a secondary consideration to the actual historical reconstruction. Of course most people are not in the business of research and the formulation of historical reconstructions of Christian origins, and they simply subscribe to belief systems, some of which are conditioned, some of which are reactionary to the prevailing conditioning.



LC

[Peter Kirby]

b) If historicity is defined as "historical genuineness" then - according to the assessment above - is the historicity of the TT 25%?

No.

I take it that the 'no' is qualified by what you have written above. However given these qualifications and a correspondence between "genuineness" and "historicity", do you agree that the answer is 'yes'.

Nope. In this context, and in my understanding, the "genuineness" of the T.F. passage refers to the matter of whether Josephus wrote it, and the "historicity" of that same passage refers to the matter of whether its contents correspond to a historical reality. These are in no way the same thing.

This sounds like something from the field of sociology. There are IMO however massive consequences for the existence or non-existence of a historical Jesus in the field of history because of the implications. If Jesus did not exist then someone has made a terrible mistake in their assessment of history. This mistake could be unintentional, or it could represent a misunderstanding somewhere in the scribal transmission of the "Jesus Story". Many myth theories seem to fit in to this category. It seems to me that the Doherty/Carrier Mythical Jesus fits in to this category. One generation of scribes write a "heavenly (non historical) Jesus story" and then a subsequent generation of scribes treated the myth as history and historicised it.

However it is just as likely and reasonable that the "mistake" was intentional and someone (or some organisation) simply lied in presenting a fictitious story as religious history. This is not a misunderstanding but rather a purposeful fraudulent misrepresentation of the historical truth.

Belief as discussed above is therefore a secondary consideration to the actual historical reconstruction. Of course most people are not in the business of research and the formulation of historical reconstructions of Christian origins, and they simply subscribe to belief systems, some of which are conditioned, some of which are reactionary to the prevailing conditioning.

All of this is still no more relevant to human decision-making than finding bunnies in the clouds or archers in the stars.

And before anyone ropes in the question of contemporary religion and its practice and its potential truth value, sure, I will concede that it is relevant to human decision-making to know whether a pit of fire awaits you after death for believing the wrong things.

However, once you remove all the afterlife and ontologically-real-God stuff from consideration, the question of the existence of a historical Jesus in the past, in a secular context, just doesn't make a bit of difference to how we are to go about our lives today. Which is good! Did you really want your life to hang in the balance on this endlessly contested question? No? Then be glad that the answer doesn't really matter.

And it is the very low-stakes nature of the game (there are no consequences to face if your opinion turns out not to align with reality) that makes it hard to agree on what the relevant threshold of confidence is. Apart from questions of identity and cognitive dissonance (which vary from individual to individual and society to society), nothing is lost or gained by believing or disbelieving. And absolutely nothing is lost or gained by being wrong or right.

[Leucius Charinus]

I take it that the 'no' is qualified by what you have written above. However given these qualifications and a correspondence between "genuineness" and "historicity", do you agree that the answer is 'yes'.

Nope. In this context, and in my understanding, the "genuineness" of the T.F. passage refers to the matter of whether Josephus wrote it, and the "historicity" of that same passage refers to the matter of whether its contents correspond to a historical reality. These are in no way the same thing.

I see these as different hypotheses to be tested. There are infinite numbers of hypotheses. One is whether Josephus wrote it. One is whether Josephus wrote at least some of it. One is whether Eusebius wrote all of it. Another that he wrote part of it. Another possibility is that Josephus wrote it an he also knew all about Jesus and that he was really describing Jesus. Infinite set of possibilities. All are different.

However each of these hypothesis may or may not be "genuine" or true. Some may be antithetical pairs, where only one can be true and the other false. I guess I am using the term "the historicity of the TF" very loosely. I guess what I meant was an estimation of the truth value of the hypothesis that the TF is genuine (i.e Josephus authored it) or - alternatively, the estimation of the truth value of the hypothesis that the TF is an interpolation into Josephus by someone else.



LC