Posted: Feb 01, 2012 11:15 pm
It sounds to me like Carrier is saying that when historians argue

"You should agree with me on this," even if you don't do it based on Bayes Theorem, you're still saying "you should agree that these things are likely."

based on an informal sense of "likelihood" what they really ought to be arguing is a faux formal sense of likelihood with percentages of likelihood arbitrarily assigned to each underlying premise.

What I point out in the book and demonstrate in detail, is that: this is how we reason all the time anyway, so if this is a valid objection to Bayes’ theorem, it’s a valid objection to all of human reasoning.

If we're reasoning this way "all the time" (and I'll concede that we often do) what does imposing Bayes Theorem upon these arguments actually add to the argument. Particularly if, as he seems to concede here

Obviously, I mean obviously, in history especially – but even in science this is often the case – we don’t have hard, scientifically verified statistical data. We don’t, we can’t poll – we can’t take a scientific phone poll of ancient Roman populations, right? Things like that, you don’t have that kind of data.

there is no way to assign these probabilities without being arbitrary.

The point I'm making is thus: if we have no way of being any more precise than "likely" or "unlikely" then what good does arbitrarily affixing a number to these assessments do?

Absolutely none as far as I can see. It's a pointless endeavor.

None of this, by the way, objects to the validity of Bayes Theorem. It objects to it's usefulness in the case of historical arguments. If we can't define the probability of any of our underlying assumptions with a reliable and applicable data set then there's simply no way we can usefully apply Bayes Theorem to the question being examined.

If we actually did have access to all the relevant data for all of our underlying assumptions then, sure, we could apply Bayes Theorem. As it is it would be an exercise in futility to attempt to do so.