My review of Richard Carrier's "On the Historicity of Jesus"

[timhendrix]

Andrewcriddle: You are absolutely correct. Thanks for pointing it out I will keep it in mind for the next revision.

Giuseppe: I also recall Carrier saying something to that effect in PH and he certainly does in his chapter on the cosmological argument in "The end of Christianity". You can do the computation with a 50% prior and if you are interested in the numerical answer is 49% and 0.12% probability of historicity. However I don't think it really solves anything. If you for instance consider the trial-example with Bob, depending on how the defense formulates the various hypothesis a 50% prior will either give the right result or allow you to be off by a factor of about 10'000. An additional problem is that when your hypothesis is the conjunction on several elements should you then consider each to have a 50% prior or all of them to have a 50% prior taken together?

[MrMacSon]

More reviews of Carrier's use of Bayes Theorem -

https://www.quora.com/What-is-your-opin ... rd-Carrier

http://www.patheos.com/blogs/exploringo ... story.html

https://irrco.wordpress.com/2012/09/08/ ... d-carrier/ --

Elliott
December 10, 2014 at 9:20 pm

I think Carrier is fine with using Bayes’s Theorem as a tool for evaluating claims about history, although I wish that he had perhaps gotten a mathematician to write up the discussion of BT. Either this or he could have included an appendix where he goes in to detail about it. Preferably this appendix would have a brief explanation of set theory and probability theory. I agree with the author of this post that Carrier’s treatment of the relevant math is very hard to follow, and could be cleared up by just using some notation, the art majors be dammed!

That being said I do want to defend his use of the more complicated form of BT. Since Carrier trying to get people to consider how well different hypotheses explain the set of evidence that we have, I think he’s ok with breaking up P(E) into it’s different parts. Now I wish he had bothered to explain what exactly he mentioned by “e.b” right away rather than when he did, or nothe worries so much about the distinction between “e” and “b”,


Ian
December 12, 2014 at 2:45 am

I’ve written a few more posts on why Carrier isn’t fine using BT in this way.

I think he’s ok with breaking up P(E) into it’s different parts.

The problem is twofold

a) He doesn’t say he’s breaking it up into different parts, in fact he doesn’t discuss the fact that the denom is P(E) at all. I suspect this is because, if you say “The probability of the evidence” it will be much clearer that you’ve no hope of actually coming up with a sane number, whereas by obfuscating this it makes it less obvious.

b) Breaking up an expression like that, really just substituting P(E) for an expression that evaluates to P(E), is only justified if the component parts are more easily acquirable than the whole. If you’ve got a reasonable likelihood of knowing P(E|H) and P(E|~H) to a degree of accuracy that is much higher than you would if you estimated P(E). The two are not equivalent practically, since more terms independently acquired introduces more independent sources of error. There are cases where it is advisable to use this, but not this one.

So I still stand by my assessment that this form of BT is only used because it is more bamboozly than the simpler form. An assessment which I think is backed up by his lack of desire to explain the probability to his readership, and his tendency to further obfuscate the equation with background knowledge.

[timhendrix]

He doesn’t say he’s breaking it up into different parts, in fact he doesn’t discuss the fact that the denom is P(E) at all. I suspect this is because, if you say “The probability of the evidence” it will be much clearer that you’ve no hope of actually coming up with a sane number, whereas by obfuscating this it makes it less obvious.

Although I agree on Ian on most of his points on Carrier I don't think this is a reasonable criticism. I think Carrier would (and should) argue that he does not compute P(E) because he does not have to and because it would make his computation more difficult. Bayes theorem can be written as:

P(H|E) / P(~H | E) = P(E | H) / P(E |~H) x P(H)/P(~H)

So that only the ratio of the likelihoods are required, P(E | H) / P(E |~H). This is useful if the likelihoods are only known up to a multiplicative factor, or that our estimate of this ratio is believed to be easier to make than each of the two terms individually. There is nothing odious about this trick and it is easy to find references where it or very similar ideas are employed.

More pressingly, when we use Bayesian-type arguments in common sense reasoning (as many psychologists and social scientists would agree we do all the time!) we all the time ask ourselves to evaluate if some piece of evidence is more naturally explained given a hypothesis is true than if it is false. This is exactly a judgement of the ratio P(E | H) / P(E |~H), and it would not be fair to say this type of common-sense reasoning is suspicious, or obfuscating, because we cannot judge P(E) which we in most circumstances no doubt can't hope to do.

[Peter Kirby]

By the way, Tim, I have been looking forward to reading your piece but haven't been able to find the time to get past a couple pages yet. Hopefully soon. I might even have something worthwhile to say about it.

I have my own personal set of reservations about Carrier's approach, but it doesn't appear to be a subset of yours (or vice-versa).

[timhendrix]

There is a longer (critical) discussion about this review over at Neil's blog vridar.com:
http://vridar.org/2016/04/15/what-does- ... ment-77669

[Secret Alias]

The more interesting question for me is - which one(s) of these avatars you debate with is/are Carrier himself? There aren't this many smart people who argue with someone with your depth of knowledge FOR THAT LONG unless they had a personal stake in the debate. "Here is where you're wrong ..." after you've just proved you know what the f- you're talking about sounds like Carrier.

[maryhelena]

The more interesting question for me is - which one(s) of these avatars you debate with is/are Carrier himself? There aren't this many smart people who argue with someone with your depth of knowledge FOR THAT LONG unless they had a personal stake in the debate. "Here is where you're wrong ..." after you've just proved you know what the f- you're talking about sounds like Carrier.

Interesting....

It does seem obvious that 'Zbykow' has a vested interest in the discussion rather than simply an academic interest.

[maryhelena]

There is a longer (critical) discussion about this review over at Neil's blog vridar.com:
http://vridar.org/2016/04/15/what-does- ... ment-77669

I notice that 'Zbykow' has not accepted your invitation to come to this forum to further the discussion....

[timhendrix]

Just to provide the Reader's digest version of the central point of the argument on the Vridar thread:

The conclusion of OHJ is the probability of what Carrier calls the "minimal mythical Jesus theory", denoted by ~h. The minimal myth theory contains (by Carriers own definition) several sub-components, for instance that Jesus underwent burial and resurrection in the supernatural realm. Accordingly Carrier defines:

~h : Jesus did not exist AND died, was burried and resurrected in the supernatural realm AND ...

What Carrier computes in OHJ is then the probability of ~h given the evidence and thereby he obtains:

p(~h|All evidence) = 99.99%.

I point out two main issues on the thread:
The first thing I point out is that if we accept Carriers computation we can also compute the probability of ~h given that we only know about the Gospels (i.e. we don't know anything about Paul). In this manner we obtain:

p(~h|Gospels) = 93.75% (According to OHJ).

Arguably this number is unreasonable. It means that only given the information in the Gospels, we can conclude there is at least 93.75% chance that Jesus was buried and resurrected in the supernatural realm. However to my mind it seems plainly impossible to see how such a conclusion can be established only from the Gospels. Where, exactly, do they say Jesus was buried in the supernatural realm?
If we accept this number is too high (Zbykow: If you are reading this, do you think this conclusion is reasonable?), that implies that something must have gone wrong in OHJ as the conclusion is only based on the numbers in OHJ and basic probability theory.

The second point under discussion on vridar relates to how the result, p(~h|Gospels) = 93.75%, is established. In OHJ, the most important element is the application of reference classes to the Rank-Raglan mythical hero type.
Simply stated, the Rank-Raglan (RR) mythical hero type is a hero who has certain properties, for instance "born of a virgin" and so on. Jesus matches this hero type very closely and so does other non-existing heroes such as Moses.
The basic idea employed in OHJ is then to compute the prior probability of ~h (i.e. the probability of ~h before considering the evidence) as:

p(~h | RR) = (Members of the RR hero class who are not historical)/(Members of the RR hero class)

By simply counting heroes and dividing we obtain the result p(~h|RR) = 93.75%*.
The basic problem here is that the use of a reference class for a probability of the form p(A|B) assumes the computation:

p(A|B) = (Members of B who are also A)/(Member of B)

Accordingly, a direct application suggest we instead write:

p(~h | RR) = (Members of the RR hero class who are ~h, i.e. died and were raised in the supernatural realm)/(Members of the RR hero class)

However since for instance Moses (as far as we know) were not thought to have been buried and resurrected in the supernatural realm he would not be counted in the above and hence we would obtain a much lower probability for p(~h|RR) than the 93.75% Carrier relies upon. Another way to phrase this is that Carriers use of reference classes embodies the following (fallacious) statistical syllogism:

"Jesus belongs to the set of RR heroes. A fraction of 93.75% of the RR heroes have property A but not B. Therefore there is a 93.75% chance Jesus has property A and B".

This type of inference is obviously fallacious, but it is exactly the same concept that underlies the use of the RR hero type to establish the prior for ~h.

This is by no means the only problem with the RR hero class, for instance we have to argue how the probability p(~h|RR) arises in our computation (Zbykow: I would be very interested in your answer to the questions I have raised regarding to this issue, in particular why you think the computation I offer is wrong). Personally, I consider the use of reference classes to this type of problem to be fundamentally flawed and I find it difficult to imagine a statistician who think this was a good idea.


*I have simplified the presentation above slightly, for instance omitted background knowledge in the conditional probabilities. Carrier uses Laplace rule of succession in addition to the reference classes to estimate the prior probability, however this does not change the above argument.

[andrewcriddle]

Hi Tim

There have been various Raglan threads here which you possibly might find of interest
viewtopic.php?f=3&t=1052
viewtopic.php?f=3&t=1160

Andrew Criddle