rationalskepticism.org

Looks like sophistry to me. Setting out the historical techniques he wants to talk he lists the criterion of embarrassment as "if it was embarrassing it must be true". Now I'm no defender of the criterion, but to attack it in such a caricatured strawman of a form is just silly.

Then there's lots and lots of equations. As VazScep said in a recent philosophy thread: "if you write it in symbols it's 50% more true". Obviously this is supposed to look rigourous because this guy like totally gets math and he's speaking to an audience that generally doesn't.

Notice that Carrier works through his equations on the neutral proposition that Jerusalem had a public library and then, when explaining the advantages of Bayes theorem brings in Historical Jesus examples as in

For example, as Porter and Thiessen have both observed, it’s inherently unlikely
that any Christian author would include anything embarrassing in a written account of his
beliefs, since he could choose to include or omit whatever he wanted. In contrast, it’s
inherently likely that anything a Christian author included in his account, he did so for a
deliberate reason, to accomplish something he wanted to accomplish, since that’s how all
authors behave, especially those with a specific aim of persuasion or communication of
approved views. Therefore, already the prior probability that a seemingly embarrassing
detail in a Christian text is in there because it is true is low, whereas the prior probability
that it is in there for a specific reason regardless of its truth is high.

and

For example, Paul refers to James the Pillar as the Brother of the Lord, and to the
Brothers of the Lord as a general category of authority besides the Apostles. It is assumed
this confirms the historicity of Jesus. But which is more likely, that a historical (hence
biological) brother of Jesus would be called the Brother of the Lord, or that he would be
called the Brother of Jesus? In contrast, if we theorize that ‘Brother of the Lord’ is a rank
in the Church, not a biological status, then the probability that we would hear of
authorities being called by that title is just as high, and therefore that Paul mentions this
title is not by itself sufficient evidence to decide between the two competing theories of
how that title came about.

Notice that these don't actually contain any mathematical thinking at all. It's the usual argument presented in the usual format. Presumably now it's rigourous though, because it's an example of the advantages of maths. And anyway,

You can use Bayesian reasoning without attempting any math, but the
math keeps you honest, and it forces you to ask the right questions, to test your
assumptions and intuitions, and to actually give relative weights to hypotheses and
evidence that are not all equally likely.

That's handy isn't it? I was worried we might have to do some work here, so it's a relief to know that mathematical rigour transfers to these standard arguments from the equations on the previous page by a sort of logical osmosis.

Even better

Bayes’ Theorem has been proven formally valid. Any argument that violates a valid
form of argument is itself invalid. Therefore any argument that violates Bayes’ Theorem
is invalid. All valid historical arguments are described by Bayes’ Theorem. Therefore any
historical argument that cannot be described by a correct application of Bayes’ Theorem
is invalid. Therefore Bayes’ Theorem is a good method of testing any historical argument
for validity.

... so nerny-ner-ner-ner-ner.

I say bullshit.