I think you are both misunderstanding what Carrier is doing and what I am pointing out.JohanRonnblom wrote:As Carrier explains in great detail, a 'theory' such as 'Jesus existed' is completely useless. (...) Unless you somehow specify who this historical Jesus would be, in such a way that he is identifiable, you will achieve nothing.Tim Hendrix wrote:When I am talking about a specific hypothesis for historicity I am talking about Carriers specific, five-point scenario which falls into the general class of ahistoricity (the general class of ahistoric theories is the negation of "Jesus existed").
Now, you may not agree with Carrier's specification. (...). That is not a problem for Carrier. His calculations are obviously only relevant if the reader agrees that his hypotheses are sound and that any other Jesuses are sufficiently unlikely as to be irrelevant.
If you want to argue for another Jesus, go ahead and do that. But do not complain about Carrier's use of BT, because it is completely unrelated to that.
Carrier himself defines (and uses) the "minimal historicity" thesis which is denoted by h in OHJ. Logically, the negation of h would be the general thesis of mythicism (the negation of the proposition that Jesus existed) and if we assume we can use probabilities in this context (which both I and obviously Carrier am) it must have a probability. Please don't confuse the negation of h with what Carrier writes as the negation of h since this is a formal error in OHJ as Carrier agrees.
What I am pointing out is that Carriers particular thesis for mythicism, namely that Jesus did not exist AND his five points are correct, is contained within the general proposition that Jesus did not exist. Because it is contained within the general proposition it follows it must have a lower probability. THAT is the point I am getting at, and it has absolutely nothing to do whether I think Carriers particular theory is sound or not.
Let me illustrate this with an example:
Suppose we consider the general proposition that a person is guilty (Jesus existed). The negation of that proposition is that he is innocent (Jesus did not exist). A subset of this proposition is that the person is innocent AND someone planted his DNA at the crimescene (Jesus did not exist AND the five point myth-theory is true).
We must not confuse the probability a person is innocent with the probability he is innocent AND someone planted the evidence at the crimescene, because we can go arbitrarily wrong if we proceed in that manner. What we are dealing with is a more basic matter of logic.
Now, I am sure you will bring up that Carrier says in many places that this is irrelevant and that we can equate the probability Jesus did not exist and that his 5-point myth-theory is true. I want to pre-emt that by saying I often think there is a great deal of difference between what Carrier *says* is true about probabilities, and what he actually demonstrates as being true (or provide a rigorous argument for) in OHJ and this is certainly one of those cases. If you want to advance one of his arguments, please try to formulate it as a statement about probabilities using the rules of probability and the problems should become evidence.
Furthermore, where that discussion will bring us is exactly to the Rank-Raglan prior which we must trust computes the probability of Carriers five-point myth theory. I simply think that is a misunderstanding of what reference classes do and observe that many of Carriers examples do not fit his five-point myth theory; i.e. he is comparing apples and oranges. The problem of using reference classes in this manner is well known and collectively discussed as "the reference class problem".
Well, the gameshow only illustrates a very fundamental point about error analysis and I can't really see why you object so storngly to it. Nevermind, let us leave that aside and focus on the calculations that has to do with Carriers argument. You agree that my two general conclusions are true, i.e. that BT magnifies errors by about a factor of five in the scenario I illustrate and bias is increased by a factor of about 20, again in the scenario I use? In other words, are any of the graphs wrong?JohanRonnblom wrote: You may think so but note that you are now making up an absurd Bayesian argument, then proceeding to show why this argument is absurd. It is not Carrier's argument that you criticize, but a complete straw man of your own making.
Well, don't think it is my fault that it seems to you that I am making any kind of general argument against BT and I hope you understand why this statement is very puzzling to me.JohanRonnblom wrote: Again, it seems as though you are arguing not just about Carriers use of BT, but against BT in general. Let me ask you, do you believe that it is possible - in general - to use BT to combine several pieces of evidence for or against a proposition, in such a way that the combined accuracy increases, rather than decreases, with the number of available pieces of evidence?
To answer your question, as I mentioned in my previous post, an analysis of a simply coin is such an example of how BT can (and do!) work and converge, as is nearly any other Bayesian model under the sun including (hopefully) the one I have been building the past weeks on my computer. You can consult the Bernstein-von-Misen theorem for a general statement about convergence.
What I point out is that what Carrier is doing is simply quite different from other applications of BT and (as a rule) his approach is very strongly affected by even weak bias. Please don't take my word for it, verify it yourself with a pocket calculator if you have doubts.
No, I don't doubt we can estimate these probabilities but now I think you are being flippant by choosing these examples. What I point out is that BT, as Carrier uses it, increases uncertainty and is very strongly affected by bias. To take the election night example, even uncertainty of 10s of percent for a very well-defined problem for which we had very good data proved to be woefully insufficient and so again I ask: Is it not reasonable to assume there is quite a great deal of uncertainty in the probabilities Carrier estimate?JohanRonnblom wrote:Do you likewise doubt that it is possible to estimate the probability that Caesar existed? That Abraham Lincoln existed? That Tim Hendrix exists? It does seem that you are getting very close to the philosophical position of radical skepticism, where nothing can be known.Tim Hendrix wrote: it is Carrier not I who makes the assumption it is possible for us to guess complicated probabilities with high fidelity. If we assume this is not possible, well, there goes Carrier's entire project.
The relevant question remains if we can estimate (non-trivial) probabilities without bias, and with as high accuracy as Carrier implies.
Well, I don't disagree that the ranking-effect might be usefull, and I have never dismissed the use of BT wholesale. At this point it seems we actually agree that a computation such as Carriers can be inverted by a small bias, you just don't see that as a potential disadvantage?JohanRonnblom wrote:This is completely unrelated to Bayes Theorem. Yes, if someone is wrong in all her arguments, then the conclusion will be wrong. This is true for every historian and every Jesus scholar out there. The use of BT, however, allows us to see what someone ranks as her strongest argument. We can then focus our energy on that argument, until we reach an agreement, or at least arrive at reasonably close estimates. And so on for the other arguments.Tim Hendrix wrote: More importantly, I think you miss the point of the section, namely the numerical stability of BT. If you don't like the gameshow just look at the graphs that are structured as Carriers actual calculation. I think you will agree that the overall conclusion holds, that a computation such as Carriers can be inverted by assuming a bias of just a few percent in the (subjectively guessed) probabilities.
Well, that is basically my entire point, that BT will increase our uncertainty by about a factor of five and bias by about a factor of 20 (in the context of Carriers use of BT). I am confused how I can be so wrong in your view when you seem to agree with what I actually conclude?JohanRonnblom wrote: In addition, we can see that if someone is making a very complex argument that she admits has uncertainty, then it may follow that a series of conclusions reached from those arguments will have increasingly diminished certainties, until they become so uncertain that they are clearly meaningless.
Yes, that is very easy. His upper and lower estimates agree many times, for instance in case of the Gospels, Josepheus, Thallus, etc. etc. Just consult the final table with his probabilities to verify this for yourself.JohanRonnblom wrote:I can't find any single instance of him making such an assumption. Can you give me an example where he does this?Tim Hendrix wrote:Well, in most cases Carrier just says he can be absolutely certain that the probabilities have ratio 1, i.e. no uncertainty at all...
To say the upper and lower estimates agree is to say there is no reasonable way a piece of evidence can be more probable on historicy than on mythicism, i.e. no uncertainty at all. In the case of the Gospels, that's obviously not what most experts on the NT think. In other words, I would claim this is a case of a probability which does have some uncertainty.
I have noticed that critique of Carrier and OHJ tends to very quickly be answered by pointing out how bad and biased other historians are. Ehrman could be forming his opinion by reading tea leaves and that should not prevent us from discussing OHJ. At any rate, if we assume Ehrman and all other historians on the NT are biased, then it is reasonable to assume Carrier too is affected by some bias. If we put that bias at just a few percent then, well, there you go.JohanRonnblom wrote: That is just how history works. How would this be any better for Ehrman or any other? I think Ehrman is massively biased. The only thing to do about that is to examine the arguments and hopefully our assessments can gradually converge, at least on some issues.