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The points you bring up, Carolyn, are very interesting. We (the authors) had many discussions about them during the years we have worked on this problem. Since I am avoiding grading final reports for an engineering class this morning, I thought I might add a few comments to a question you actually addressed to James Tabor.

Let me say, first, that there are many different ways to condition the question one asks about the name associations and the chemistry. These conditions have a bearing on the answers one calculates. Let me provide one example.

Let's stipulate that the family of Jesus occupies a tomb in the Jerusalem area and further stipulate there are about one-thousand tombs in the area. Finally, assume the name frequencies of Tal Ilan pertain. In the Charlesworth volume Mark Elliot and I, using a Bayesian approach, started with a priori probability of 0.001 (0.1%) that this is the tomb of that family. In effect we are saying that any one of the thousand could equally be that tomb. The name association, as you mentioned, is not so common as people imagine from how common the individual names are. Just using Jesus son of Joseph, Joses, and Mary we arrive at a likelihood of 460, which makes the posterior probability 46%. In other words, just looking at the inscription evidence and our assumptions, one should believe there is even odds of this (Talpiot) being the tomb.

Now let's use all the same conditioning, but add James to the list of names in the tomb. Not "James son of Joseph brother of Jesus", nor "James son of Joseph", but just James. Now the posterior probability rises to 92% or thereabouts. Many people would see this as a near certainty, but one should keep in mind that there is still 1 in 11 odds of this being an unrelated tomb coincidentally having similar names. So, this is not a sure thing exactly, although it is getting closer. And there is the possibility which we discussed in this latest paper that the James ossuary could originate elsewhere but again by chance resembles the Talpiot ossuaries chemically. This is not calculable at present, but some of the ways this could happen have very small likelihood.
Now you ask "where do we go...?" Had you asked this question in 2008 I would have said there is not likely more physical evidence than the inscriptions and so there is nowhere to go. One of James Tabor's blog posts speaks of notes and other physical evidence about the Talpiot tomb that is lost. I assumed anything worthwhile pursuing was lost. Yet, there was still chemical evidence to examine which I did not learn of until five years ago. So, there is always hope something unexpected may turn up. Generally it just requires a bit of insight into how something might happen. Aryeh had such an insipration.
Now an interesting question is, what became of the metallic artifacts the James ossuary apparently contained? I have no idea if we should ever locate them, but they would add additional evidence. There is also, I think, a further story to tell using the lead isotope data; but this involves more speculation than should have gone into this most recent paper, and perhaps Aryeh or Moshe will weigh in on it in a subsequent report.
Something which I hope comes from our paper is a recognition that even small quantities of material hold significant information, and that the extreme cleaning that some artifacts receive should perhaps be rethought.

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