Carrier's numbers and math in OHJ

[cienfuegos]

Carrier's book doesn't rest only on his math (essentially multiplying the odds together and applying p(h)=O(h)/(O(h)+O(~h)) in order to find the final overall probabilities for h). It rests mostly on Carrier's input data which is most controversial.
For example, that thread discussed extensively Carrier's argument against "seed of David" (Romans 1:3) and there is absolutely no chance that argument is valid in any degree and for multiple reasons. And with a 0, and accepting Carrier's math, the odds for "made from sperm" (OHJ p. 594) become 2/0 (best for historicity) and 1/0 (worst for historicity), which would make the overall result of all consequent & prior odds indicating 100 % probability for historicity, not only for "best odds on H" (p. 599) but also for "worst odds on H" (p. 600).

Cordially Bernard

Re: seed of David. Again, it is your opinion that "there is absolutely no chance" that Carrier's argument is valid here. So you want to turn that opinion in a 100% probability that Paul here refers to a historical Jesus, son of, at least Mary and, maybe, Joseph (Poor Joseph, right?). However, we also know that some great non-mythicist luminaries in NT scholarship have considered this to be an interpolation, part of a later formulaic creed. Carrier just chooses not to include that argument, but that alone would reduce the odds from 100% probability that Paul referred to the son of Mary and Joseph here. If some non-mythicist scholars questioned the authenticity of the passage, then we cannot take Bernard's opinion over the opinion of scholars. We don't know if those scholars were correct, but considering that they were some of the most respected scholars of the modern era (such as Loisy), we have to give the possibility some consideration. The degree itself is questionable. There are other oddities that also reduce the probability that Jesus was referring to an earthly Jesus recently killed by Romans. For example, while referring to Jesus as the "seed of David," Paul never mentions his mother, Mary. To Paul, Jesus' mother is largely irrelevant, just a conduit for the "making" of Jesus. So while not decisive, of course, it again lowers the probability from Bernard's 100%. Then there is Carrier's "seed of David" argument. Again, we can agree it is not conclusive, Carrier does not claim it is, but it again lowers the probability that Paul is referring to a recent Jesus who lived on Earth and interacted with other people, some of whom Paul was personally acquainted.

[Bernard Muller]

to cienfuegos,

Yes I always understood there are other mythicist arguments against "seed of David" in Romans 1:3.
But my thread is about numbers and math in Carrier's OHJ only, and I had to consider only Carrier's arguments.
On many instances, I found Carrier's arguments being a lot worse than arguments of other mythicists (such as Doherty). That's my opinion, and "Made from sperm" would be a good example of that.

I do not see why Paul would have any need to mention "Mary" &/or "Joseph" here.

I thought also about "seed of David" being an (or part of an) interpolation, but Ro 15:12 also confirms "seed of David".

Also I understand "seed of David" might be part of a hymn predating the epistle, but even so, that does not change anything because Paul did adopt it.

And then, of course, there are some (probably most mythicists) who think Paul and all his epistles are 2nd century fabrications.

So maybe 100/1 is too high considering ALL mythicist arguments against "seed of David".

Cordially, Bernard

[cienfuegos]

That is a major question for me in how Carrier uses Bayes. For example, for the prior probability, Carrier uses the Rank-Raglan scale, and comes up with 1:15 odds as worst case for historicity. Assuming for argument's sake that Carrier is correct. But he uses it later in his Bayes to give odds of 15:1 to his ¬h, which is his "crucified celestial Jesus". And I can't see why the Rank-Raglan scale can be used to support such a Jesus.

Switch it around so that "h" becomes "crucified celestial Jesus", and then apply the Rank-Raglan scale as a reference class of beings who started out as a celestial being. If those odds are different (and it seems to me they would be), then it shows some kind of disconnect between "h" as MH (Minimal Historicity) and "¬h" as MM (Minimal Mythicism).

Carrier does write on page 30 on OHJ that "In Proving History I demonstrated that we can parcel out the entire prior probability-space to just four classes of hypothesis altogether", and he eliminates 2 of them, to leave us with MH and MM. So maybe Carrier has good reasons to do this listed in Proving History, a book I haven't read. But on the face of it, doesn't it seem strange that "h" is MH, while "¬h" is MM rather than "¬MH"?

It is a little strange.

Carrier seems to justify it basically on the assumption that the probability space of (¬h AND ¬"MM") is small, even miniscule. That assumption, combined with the convenience of simplifying things, leads him to treat ¬h as his "MM."

But think about it again: the consequent probabilities are virtually identical with the a fortiori numbers. The prior probabilities become the posterior probabilities, with very little adjustment (33.3% prior becomes 32.3% posterior chance of h). So perhaps small numbers must be given some attention?

I will confess that I also skipped a read of Proving History.

I'm not sure what ~h would be if it isn't at least MM. Either Jesus existed as a real person sometime in history, or he didn't.

Carrier says:

The two hypotheses we are comparing are (a) that Jesus was minimally historical (Chapter 2) and (b) that Jesus was originally a cosmic being known by revelation who was later set in history through the production of allegorical myths that were later taken or intended literally (Chapter 3). the former shall be our h, while the latter is effectively ~h.

So you are correct that he seems to be holding that MM = ~h. So if we are unable to rule out ~h, we have to reject h, at least as it is formulated.

[Peter Kirby]

¬h, which is his "crucified celestial Jesus"

"¬h" as MM (Minimal Mythicism).

Carrier seems to justify it basically on the assumption that the probability space of (¬h AND ¬"MM") is small, even miniscule. That assumption, combined with the convenience of simplifying things, leads him to treat ¬h as his "MM."

I'm not sure what ~h would be if it isn't at least MM. Either Jesus existed as a real person sometime in history, or he didn't.

The two hypotheses we are comparing are (a) that Jesus was minimally historical (Chapter 2) and (b) that Jesus was originally a cosmic being known by revelation who was later set in history through the production of allegorical myths that were later taken or intended literally (Chapter 3). the former shall be our h, while the latter is effectively ~h.

So you are correct that he seems to be holding that MM = ~h.

Some trivial-to-obtain examples of (¬h AND ¬"MM") is the hypothesis of Alvar Ellegard's Jesus: One Hundred Years Before Christ or G. A. Wells' The Jesus of the Early Christians (thus, early Wells, not late Wells) or Atwill's Caesar's Messiah or drastic chronological revisionism (e.g., rejecting all known history of the Roman empire). They are not the only examples.

His "MM" may be in some sense "minimal" but it has, in fact, several components, only one of which needs to be contradicted to arrive at ¬"MM":

Jesus was originally a cosmic being known by revelation who was later set in history through the production of allegorical myths that were later taken or intended literally

So we effectively have a little disbelieving creed here:

1. Jesus was "originally a cosmic being,"
2. Said being was "known by revelation,"
3. And he was only "later set in history,"
4. Using "allegorical myths" that were only "later taken or intended literally."

Any element of that creed is removed, and you've denied "MM." For example:

1. Jesus was originally a non-cosmic being who did his activity in an ahistorical setting, or in a non-specific historical setting, or in a specific historical setting invented for him.
2. Jesus was a deliberate fiction perpetrated on others, not a sincerely held conviction for the first originators of the story.
3. Jesus was originally set in history, but as a legend without true historicity (like King Arthur or Robin Hood or William Tell).
4. Okay, even granting all of the above, what if the original gospels are not allegory at all? There goes this plank of "MM" above.

Any one of which would go some way to denying "MM" but be compatible with ¬h, the non-historicity of Jesus.

Therefore,

MM = ~h

is simply wrong.

But what Carrier actually says is:

the latter is effectively ~h.

And in discussion elsewhere, Carrier recognizes that "MM" and ~h are not actually the same but are only "effectively" treated the same in his books.

[GakuseiDon]

It is a little strange.

Carrier seems to justify it basically on the assumption that the probability space of (¬h AND ¬"MM") is small, even miniscule. That assumption, combined with the convenience of simplifying things, leads him to treat ¬h as his "MM."

But think about it again: the consequent probabilities are virtually identical with the a fortiori numbers. The prior probabilities become the posterior probabilities, with very little adjustment (33.3% prior becomes 32.3% posterior chance of h). So perhaps small numbers must be given some attention?

I will confess that I also skipped a read of Proving History.

I'm not sure what ~h would be if it isn't at least MM. Either Jesus existed as a real person sometime in history, or he didn't.

Carrier says:

The two hypotheses we are comparing are (a) that Jesus was minimally historical (Chapter 2) and (b) that Jesus was originally a cosmic being known by revelation who was later set in history through the production of allegorical myths that were later taken or intended literally (Chapter 3). the former shall be our h, while the latter is effectively ~h.

So you are correct that he seems to be holding that MM = ~h. So if we are unable to rule out ~h, we have to reject h, at least as it is formulated.

In some cases MM might well be ¬h. But it doesn't seem applicable in all cases. Take the Rank-Raglan scale. Carrier gives (as worst case for MH) the odds of 1:15. Carrier uses this in his calculation for h and ¬h.

Now, if you look at the quote you gave from Carrier, ¬h represents "a cosmic being known by revelation later set in history". So Rank-Raglan provides odds in favor of "a cosmic being known by revelation later set in history" of 15:1. If that is indeed the claim being made by Carrier, then all is good from a calculation perspective. But I question whether the R-R reference class represents this.

OTOH, if the R-R reference class is not h="minimally historical" vs ¬h="a cosmic being known by revelation later set in history", then the odds can't be plugged into a Bayes Theorem where those terms are defined that way.

[Bernard Muller]

I don't see a problem with Carrier providing best/worst case odds myself. IMHO Carrier's approach is reasonable, and says more about the subjective nature of the evidence than what Carrier is doing.

The way Carrier is figuring out the worst odds is rather suspicious:
"So on this account the evidence of the Epistles, as strange as it is, is still more likely on h than on 'h, by just over 3 to 1 (and thus about three times more likely if Jesus existed, than if he didn't).
But I think that's being far too generous to historicity. Given my own estimates (which are closer to what I think the odds actually are), the evidence of the epistles is exactly 100% expected on minimal mythicism and has a probability of 6% on minimal historicity ..." (OHJ pages 594-595)

Cordially, Bernard

[GakuseiDon]

I don't see a problem with Carrier providing best/worst case odds myself. IMHO Carrier's approach is reasonable, and says more about the subjective nature of the evidence than what Carrier is doing.

The way Carrier is figuring out the worst odds is rather suspicious:
"So on this account the evidence of the Epistles, as strange as it is, is still more likely on h than on 'h, by just over 3 to 1 (and thus about three times more likely if Jesus existed, than if he didn't).
But I think that's being far too generous to historicity. Given my own estimates (which are closer to what I think the odds actually are), the evidence of the epistles is exactly 100% expected on minimal mythicism and has a probability of 6% on minimal historicity ..." (OHJ pages 594-595)

I wouldn't call the odds 'suspicious' but rather 'subjective'. IIRC Carrier does admit that upfront, and invites users to insert their own values. Given the subjective nature of the evidence available, I suspect that each person will end up with their own odds, which is a problem in itself. But the value in OHJ is that Carrier has identified the areas where historicity is weak/strong, and the areas where his celestial Jesus theory is weak/strong. There is a lot to argue over before we even start determining the odds.

Still, I see your point. For the Epistles, the odds for best case for historicity are about 3:1 (2.88:1) while for worst case for historicity is 1:16, a difference of 4500%. A huge margin of difference indeed! But Carrier does explain how he arrives at those figures.

(ETA) Someone on another board posted a link to a website where the author examines the affects of small errors in Bayes’s Theorem. The author wrote it two years ago, and is responding to Carrier's use of BT in "Proving History". I'm reading through it now: https://irrco.wordpress.com/2012/10/11/ ... s-theorem/

The author's conclusion:

• So, what can we learn?
  
  Well, for one, the inputs to Bayes’s Theorem matter. Particularly small inputs. When we’re dealing with rare evidence for rare events, then small errors in the inputs can end up giving a huge range of outputs, enough of a range that there is no usable information to be had.
  
  And those errors come from many sources, and are difficult to quantify. It is tempting to think of errors only in terms of the data acquisition error, and to ignore errors of choice and errors of reference class.
  
  These issues combine to make it very difficult to make any sensible conclusions from Bayes’s Theorem in areas where probabilities are small, data is low quality, possible reference classes abound, and statements are vague. In areas like history, for example.

Seems to support your suspicions there, Bernard. The fact that Carrier has such a huge range for "best case/worst case" for the Epistles suggests that Bayes Theorem is not applicable here, for the reasons the author defines above.

Darn it all! I don't want to become an expert on Bayes Theorem! I just want to discuss ancient thinking, one way or the other!

[Peter Kirby]

Darn it all! I don't want to become an expert on Bayes Theorem! I just want to discuss ancient thinking, one way or the other!

And that's his real crime.

It'll never catch on, IMO.

[GakuseiDon]

I found two more web pages by the same author as above. For what it's worth, the author is a scientist and an atheist. His PhD research was in the mathematics of evolution, which suggests he has a better understanding of mathematics than most.

(1) A basic introduction to Bayes Theorem: https://irrco.wordpress.com/2012/09/12/ ... troductio/

Snippet:

• I’m not sure I can imagine a way of calculating either P(H∩E) or P(E|H) for a historical event. How would we credibly calculate the probability of the New Testament, given the Historical Jesus? Or the probably of having both New Testament and Historical Jesus in some universe of possibilities? If you want to use this math, you need to justify how on earth you can put numbers on these quantities. And, as we’ll see when we talk about how these formulae magnify errors, you’ll need to do more than just guess.

I can kind of understand what he is saying when he describes BT, but I'm sure I'd flunk badly if given a test on even its basics.

(2) His review of Richard Carrier's use of mathematics and BT in "Proving History": https://irrco.wordpress.com/2012/09/08/ ... d-carrier/

Snippet:

• Conclusion
  
  Outside the chapters on the mathematics, I enjoyed the book, and found it entertaining to consider some of the historical content in mathematical terms. I strongly support mathematical literacy in the arts. History and biblical criticism would be better if historians had a better understanding of probability (among other topics: I do not think the lack of such knowledge is an important weakness in the field).
  
  I am also rather sympathetic to many of Carrier’s opinions, and therefore predisposed towards his conclusions. So while I consistently despaired of his claims to have shown his results mathematically, I agree with some of the conclusions, and I think that gestalts in favour of those conclusions can be supported by probability theory.
  
  But ultimately I think the book is disingenuous. It doesn’t read as a mathematical treatment of the subject, and I can’t help but think that Carrier is using Bayes’s Theorem in much the same way that apologists such as William Lane Craig use it: to give their arguments a veneer of scientific rigour that they hope cannot be challenged by their generally more math-phobic peers. To enter an argument against the overwhelming scholarly consensus with “but I have math on my side, math that has been proven, proven!” seems transparent to me, more so when the quality of the math provided in no way matches the bombast.
  
  I suspect this book was always designed to preach to the choir, and will not make much impact in scholarly circles. I hope it doesn’t become a blueprint for other similar scholarship, despite agreeing with many of its conclusions.

If the author is correct, it sounds like BT is simply not suitable when the probabilities are based on guesses. But there is still the evidence that Carrier brings up in OHJ. Whether BT is suitable or not, that evidence is still there and should be evaluated. Even the applicability of the odds Carrier presents can be discussed coherently, though until it is tied down to something more than subjective guesses, it can't be used meaningfully in Bayes Theorem.

[maryhelena]

Jesus was originally a cosmic being known by revelation who was later set in history through the production of allegorical myths that were later taken or intended literally

So we effectively have a little disbelieving creed here:

1. Jesus was "originally a cosmic being,"
2. Said being was "known by revelation,"
3. And he was only "later set in history,"
4. Using "allegorical myths" that were only "later taken or intended literally."

Any element of that creed is removed, and you've denied "MM." For example:

1. Jesus was originally a non-cosmic being who did his activity in an ahistorical setting, or in a non-specific historical setting, or in a specific historical setting invented for him.
2. Jesus was a deliberate fiction perpetrated on others, not a sincerely held conviction for the first originators of the story.
3. Jesus was originally set in history, but as a legend without true historicity (like King Arthur or Robin Hood or William Tell).
4. Okay, even granting all of the above, what if the original gospels are not allegory at all? There goes this plank of "MM" above.

Any one of which would go some way to denying "MM" but be compatible with ¬h, the non-historicity of Jesus.

Indeed - and if this is so then Earl Doherty has denied ''MM''. Yesterday, on the Vridar blog, Doherty was emphatic that ''the original 'human' figure of Jesus''........''..was not developed out of a heavenly Christ concept...''

• The simple answer is that the original ‘human’ figure of Jesus first took shape as the perceived founder of the Q-style Kingdom-of-God preaching movement centered in Galilee during the course of that movement’s evolution over time...
  
  Since this perceived founder (we don’t know if he was originally called “Jesus”) reflected and symbolized the nature and activities of the Q preachers himself, he took on their characteristics, including a Galilean origin. He was not developed out of a heavenly Christ concept–that concept belonged to a separate religious movement on the first century scene, and only with the Gospel of Mark do we see the first amalgamation of the two strands....
  
  Quite simple, really.
  
  Earl
  
  http://vridar.org/2015/01/28/was-christ ... ment-70018

my formatting

---------------------
footnote added later:

Wow - a big put-down for Carrier's work.....

• In point of fact, while not attempting to denigrate or belittle his work in any way, I—and the specialists who are quoted in the article—simply find other works that deny the existence of Jesus to be more important.
  
  Lawrence Mykytiuk
  
  comment #26
  
  http://www.biblicalarchaeology.org/dail ... sus-exist/

Maybe Carrier's use of BT is a step too far for some scholars - a step that might well put Carrier's book beyond the pale as a 'go to' book for advancing the ahistoricist position....