Is an Appeal to Consensus an Argument?

Christoph also wrote:

Perhaps I should indeed stick to writing books not blog post comments since I am apparently not able to communicate effectively in that context.

“Chris, you are surely ripping Carrier’s qualification statement out of context. You have totally disregarded the sentences either side of the one sentence you have addressed and into which you impute thoughts that are contrary to the clearly stated context. In the previous sentences Carrier makes it clear that he does not believe the James in Gal.1:19 is the brother of John — I even quoted that section in my previous comment.”
I know what he says. My point was that if someone writes the conditional clause “if he meant James the Pillar, then he did not mean he was literally the brother of Jesus—as that James appears to have been the brother of John, not Jesus,” he demonstrates that he hasn’t read or is not willing to engage with the relevant literature on the subject. I am sorry for apparently implying something about Carrier’s actual position that I never intended to do.
“If you are basing this assertion on a sentence taken out of context and impute to it a meaning that contradicts Carrier’s clear argument in the sentences either side, then your justification for your assertion is invalid.”

I wholeheartedly agree.

“I have yet to see you give a fallacious example of his estimation of likelihoods. A sentence taken out of context and made to mean the opposite of what the context makes clear he is arguing is not a valid example.”

Is it possible that this is because yourself have a mistaken view of how likelihoods work?
I appreciate the more systematic manner in which you try to apply to theorem to the data here: https://vridar.org/2012/04/22/putting-james-the-brother-of-the-lord-to-a-bayesian-test/. Still, it’s definitely not correct what you are doing.

“Again, how much have you read of OHJ? Surely it is clear that Carrier does not fall into this “sin” of focusing on numbers and overlooking the real point. He explains quite clearly how the same reasoning can be done without numbers at all.”

Oh, he does again and again. For example, he concludes on Acts that there is at best a likelihood-factor of 0.72 for historicity and it worst 0.2. He then writes: “Conversely, nothing in Acts is unexpected on minimal mythicism, as on that account anything historicizing in it is a mythical invention of Luke’s …, while the omissions and vanishing acts would be inevitable result of there being no historical Jesus.” Here, he’s using “normal” language to say that nothing of that evidence is “unexpected” within the framework of his hypothesis. That’s fine (even though I’d strongly disagree on the individual points). Then he continues: “So the same consequent probabilities on -h can be treated as all 100% across the board.” He adds a footnote, saying that even if not, that doesn’t matter, since the ratio will always be the same. Now, this is surely an absurd claim. I’ve never seen any scholar who works on historical matters using Bayes, who dared to say that P (EIH) = 1! Whether or not some evidence can be “explained” by a hypothesis and whether it is thus “expectable” doesn’t tell us anything about the likelihood. Surely, there are many different ways of writing fiction about Jesus, so even if Luke’s version is the most probable one, it’s still just one among very many possibilities. Again, using θριαμβεύειν in order to refer to the Roman triumph is not “unexpected” in light of the fact that (almost) all its occurrences are used in that way. So a reference to the Roman triumph would “explain” the word choice. But – no – it still doesn’t tell us anything about the likelihoods. Carrier gets that wrong. At almost every point. I used the James example simply because it’s very clear because we are here dealing with a tiny little piece of evidence and not so many assumptions influence the decision (such as how “reliable” Acts is anyway, etc.).

“And again, you have entirely overlooked the key point in Carrier’s argument on this particular point — that Carrier accepts that Galatians 1:19 and James the brother of the Lord must be used as SUPPORT FOR HISTORICITY! So your complaint about him botching the argument by being totally lost in numbers falls by the wayside. He concedes that his argument to the contrary may not be persuasive!”

You don’t have to yell at me. I never said anything else. My point was that even to entertain the thought that perhaps “there is at best no difference in probability and at worst a difference favouring myth” shows that Carrier has clearly not understood how Bayes’s theorem works at all., I don’t care how he incorporates it in the end into his final calculation, what he graciously “admits.” The fact alone that he is able to write such a sentence shows that he has not understood the very basics of Bayesian confirmation. I know this sounds harsh, and if I see how your reactions to my comments have evolved I can see that you are increasingly getting frustrated with me. I’m sorry for that because I see that you also are really interested in the matter – and frustrated with people who just attack Carrier ad hominem. I didn’t want to do that. I just don’t want to interact with him because I am convinced that his argument is deeply flawed beyond redemption.
Let me try to explain with reference to your blogpost, which does a really nice job in translating Bayes into terminology understandable to people not familiar with probability theory. You correctly “translate” the likelihood-factor into the following task: “The next value we need to enter is one to indicate how expected the evidence is if the explanation is true.” Now, what’s the hypothesis and what’s the evidence? You write: “So the explanation, or hypothesis, that I decide to test is: That James, whom Paul meets according to this letter, was a sibling of Jesus. That’s my initial explanation for this verse, or in particular this phrase, ‘James the brother of the Lord’, being there.”
So the situation looks like that: we might have some prior convictions concerning whether in antiquity there existed a person called James (a strange way of rendering the Greek name, by the way, we Germans are much more faithful to the original here ). That includes extra-biblical evidence (ossuary, etc.), evidence from Acts, potential writings by such a person, etc. Then we come to Paul and we encounter the phrase “James the brother of the Lord” (well, it’s a Greek phrase, but we’ll just keep the translation for a moment). So the question is, how this “new” evidence influences the value of our priors, which might differ a lot, to be sure. I don’t want to talk about how the posteriors look in the end and whether Paul’s mention of James actually settles the case. I am not interested in that at all. I just want to look at which hypothesis the evidence favours and how it is doing that – because I believe both you and Carrier are wrong on that.

Let’s look at how you determine the two relevant likelihoods:
“Well, if our hypothesis were true, yes, we would expect someone who met James to inform readers of his letter that the James he met was indeed the brother of Jesus if that’s what “Lord” refers to. (And certainly Jesus is called “Lord” very often elsewhere. So is God, but Jesus is too.) So to that extent the evidence is just what we would expect.“

Good observation. Of course, whether it’s really expected or not will depend to some degree on whether at that point in time there actually were two persons called James in Jerusalem, i.e. it’s only then something we would expect an author to necessarily do if there is reason for confusion (and even then authors sometimes fail to clarify). So I guess you might be a little too optimistic here on behalf of the physical-brother-hypothesis.

“Against this, however, is the problem that if our hypothesis were true — that James, a leader of the church, really was a sibling of Jesus — we would expect to find supporting claims to this effect in the contemporary or near contemporary literature.”

Well, this is an aspect that influences the prior (i.e. updates an earlier prior to the posterior which becomes the new prior). So it’s a fine comment but has nothing to do with determining the likelihood in question here, to be sure. That applies to all the aspects you list in red. Now, don’t get me wrong: these are important aspects to be considered. They might have an immense effect on how the priors of the two competing hypotheses looks like. But if we turn to Gal 1:19 as evidence and what to decide, which one is the best “explanation for this verse, or in particular this phrase, ‘James the brother of the Lord’” we can’t of course take it into account at this stage.
So your conclusion that “we can assign a probability of 0.05 to the expectedness of the evidence that we do have given our hypothesis is true” now actually presupposes that the evidence in question is not what you said in the beginning, i.e. you take an earlier prior in order to show how low the likelihood is. In my opinion, it’s better to focus on tiny bits of evidence and do many rounds of confirmation. Of course it’s possible to take the whole bunch of evidence at once but then you have to be very clear about what the “new” evidence is that is taken into account and what is part of the prior. So in my opinion, if you set out to explain Gal 1:19, you should incorporate all the red evidence you mention as background knowledge into the prior under the heading “So the first value I need to enter is ‘How typical the explanation is’.” In fact, I even believe you have to do so because you use the Gospels’ talk about siblings of Jesus as background knowledge for the prior but then you re-address the same material for the likelihood. That’s confusing it best. Better to concentrate on Gal 1:19, and use the rest for the prior (or write a blog post series in which you incorporate all that background knowledge successively into an original agnostic prior). Again, I am not interested in the posterior here so I’ll just agree with your assessment of all that other evidence. So I think it might be fine to say:
“The prior of the person called ‘James’ in Gal 1:19 being intended to be understood as a physical relative of a person called ‘Jesus’ is 0.05.”
So what’s the likelihood P (“brother of Jesus” I Hypothesis physical relative)? You seem to imply that it is close to 1. From my experience with actual data analysis on similar questions, it’s more like 0.1 or so, i.e. there are just too many factors that might influence an author in not using this phrase even if he or she wanted to make such a reference. Also, there are of course other ways for saying the same thing, such as “brother of Jesus,” “brother of the Messiah,” “the other son of Mary,” etc.
Ok, so let’s assume the prior is so bad. This might mean that even a really good likelihood doesn’t change much, granted. But the likelihood of 0.2 is indeed decent and what we are interested in is which hypothesis is favoured – which has after all nothing to do with which hypothesis has the higher posterior.
Ok, so how does the likelihood compare to the likelihood of the alternative?
You write: ”How expected is the evidence [i.e., the verse Gal 1:19 and more specifically the phrase “brother of the Lord”] if our hypothesis were not true. That is, how expected is our evidence if James were not literally in real life the brother of Jesus?”
Well put. Then you continue you: “Given the considerations listed above, I would say that the evidence is just what we would expect if James were not a literal sibling of Jesus.”
But is it? Apparently you are again thinking of all the evidence that you adduce in red. Again, if you claim to analyse Gal 1:19 as evidence, then this is not allowed and all this has to be used as background knowledge for the prior. So I think what you should have been saying is: “No matter how low the original prior is, all the evidence I’ve adduced above has resulted in an extremely low new prior, with which we now address Gal 1:19.” Alternatively you can, again, of course incorporate all the evidence at once but then please don’t say you are evaluating explanations for Gal 1:19. The reason why I prefer doing it step by step is because it is then clear where the numbers come from. For example: who did you actually incorporate the “brother of the Lord”-reference, the allegedly new evidence that you set out to incorporate? The following statement might work for the evidence as a whole, but certainly not for the “brother of the Lord”-evidence itself: “So how expected is the evidence if our hypothesis were not true? I have to say it is ‘extremely probable’: that is, 0.99.” Of course, Carrier would say that even if you focus on this tiny piece of evidence (as you claim you’d do and as he claims he would do in that section) that’s above right. But he grants that perhaps the likelihood is not 100% but just half as “good” as the alternative likelihood. So if we take the likelihood P (“brother of the Lord” I Physical relative) to be 0.1, the likelihood of P (“brother of the Lord” I Fellow Christian) would be 0.05. It’s difficult to see how you deal with Carrier’s actual assessment because you lump together all the evidence and do not differentiate between different stages of updating (which, again, is fine in principle – but then requires you to specify evidence and explanation differently at the outset). But how does the likelihood really look like?
My most basic point is this: CARRIER DOES NOT ADDUCE THE EVIDENCE THAT IS ABSOLUTELY NECESSARY FOR DETERMINING THE LIKELIHOOD. And neither do you. There’s only one way to find out if you are really interested in statistical values for likelihoods: count how often Paul uses the expression to communicate that thought and count how often he uses other expressions for the same thought. So let’s assume he indeed uses the expression “brother(s) of the Lord” twice in order to communicate the concept of ‘fellow believer.’ Carrier seems to imply that this means the likelihood is high. It doesn’t imply anything of that sort. What we would have to do is to go through the Pauline corpus and watch out for the expressions that Carrier adduces on p. 584 (any many others) in footnote 94. So let’s say Paul refers 100 times in his letters to other Christians and he uses the expression “brother(s) of the lord” twice for that but other options at the 98 other places. That would mean that the likelihood for every individual randomly picked passage would be P (“brother(s) of the Lord” I fellow Christians) = 0.02, i.e. what we would actually expect each and every time Paul makes a reference to such a person is that he uses a different phrase and only in 2% of these cases he will use the phrase “brother(s) of the lord.”
Of course, all these numbers have nothing to do with reality but are only there for illustrative purpose. I don’t care about the actual numbers. And I care even less about the resulting posteriors. What I care about is that you can only come up with a likelihood if you take a look at these alternative ways of expressing the same thought. And Carrier doesn’t do that and you don’t do that and therefore it’s just not possible for you to speak about likelihoods.
Now perhaps you might understand why I found it so outrageous that Carrier at least entertains the possibility that Gal 1:19 might favour mysticism (or is at least not far worse than the physical-brother alternative). The fact that he can manage to entertain such a thought implies that he hasn’t understood how likelihoods work. For if he had understood the conceptof likelihood-rations he would have had to think at least for a second: “The expression ‘brother of the Lord’ is a less obvious choice for a physical relative than it is for the concept of a fellow believer.” And he can’t be serious about that, can he? Of course, saying “brother of X” is quite a default solution for referring to a brother. But on the other hand, even if it’s possible to refer like that to a fellow Christian, it’s certainly not the first choice and he himself never claims so. But without this claim you can’t have a likelihood even being close to favouring mysticism. You just can’t.

“I might be mistaken here, but I think you are implying that because ‘brother of the Lord’ in Galatians 1:19 refers to a physical sibling of Jesus (I agree, and accept your odds of 1000:1 in favour of that being so) that that somehow puts to rest the question of the existence of Jesus. You appear to be overlooking other evidence and problems raised as a result of this passage in Galatians as addressed in the other posts I linked. But those are going beyond Carrier’s argument.
Am I right in thinking that this is the only section of Carrier’s book you have read, and that only partially?”

No to all of that. I just picked this example because I think it’s very clear here to show that Carrier doesn’t understand Bayes at all. In fact, as I said, you might be right about the other evidence and about the priors in light of this evidence but if one claims to do another round of updating one has to do it right. Again: perhaps the posterior will still be worse than for mysticism. I don’t care for this purpose. What I care about is that the updating is done in a way that respects the structures of Bayes’s theorem. And this example demonstrates that Carrier doesn’t do that here. It’s the same at many other places, but here it’s quite obvious. Also, it demonstrates that at a very fundamental level Carrier hasn’t understood Bayes. If you still can’t see that I am sorry because, again, it’s a rather fundamental mistake, something that can happen in a blog post perhaps or happens to students when they are first confronted with the task but which is unacceptable in scholarly literature. If you do understand my concern and you go through the book again, you’ll see that Carrier does exactly this mistake over and over again. But apparently you’ve at least so far made the same mistake. At least your blog post did not show awareness of how the language of “explanation” and “expecting” evidence needs to be translated into an empirical assessment.

And then further:

P.s.: I’d personally evaluate the hypothesis of a gloss in a separate analysis. Again, much will depend on the prior – i.e. how frequent one thinks such glosses are in general and in such situations which this kind of manuscript evidence – but also how probable it is that there was a scribe who felt the necessity to clarify which James was meant and that he was physically related to Jesus. The likelihood for this hypothesis will naturally increase the more specific assumptions we make about the scribe (i.e. we can imagine a scribe who with high probability would render every mention of James into “James, the brother of the Lord”) – which will in turn cause the prior to decrease. Or we can keep the hypothesis more general, which will be good for its prior but would then of course also decrease the likelihood-value (just as Paul had different ways of referring to a potential physical relative, a scrive would also – unless of course we can identify a certain setting where Jesus was always addresses as “Lord,” etc.).

You can read the entire thing, as well as the mythicist side of things that Christoph was trying to engage with, on the blog Vridar.