Neil
I think we agree that "Marc Antony was Julius' ally" is in the first instance a plot point within the play. I am confident (and you aren't?) that a typical undergraduate can recognize that some plot points are also fact claims about the real-life Julius. That's how some of the plot points came to be incorporated into the play: Bill thought that maybe that's how things might really had been.
The casual student needn't be complete nor inerrrantly accurate about such classifications in order to learn from the play. The students' world will not come crashing down if they think the comet is entirely fanciful, for instance, nor if instead they think they could easily identify the comet in some astonomical database (but won't bother to, at least not now). And yes, it is perfectly clear that in attempting the classification problem, the students will use background information such as what people have said about the play and its author. There's nothing wrong with that, IMO.
I don't think we drifted very far from the OP: it's a hard problem with many aspects. Also, I don't think we're moving in circles YET, but as a precuation against that, I'd like to push on in the light of something that a third party recently contributed to our discussion.
I noted in your reply to
andrewcriddle the following:
If methods for finding more from hitherto unreliable sources are discovered then fine, they can be tested and we can see where they go in the long run.
That doesn't sound very Bayesian. A key feature of Bayes since the time of Laplace is the "anytime" character of its norms. In the long run, we're all dead (as John Maynard Keynes remarked, a vigorous Bayesian critic). A useful-to-mortals heuristic guide to uncertain reasoning must address the meantime, making the most we can here and now of whatever little we may have.
Applied to Julius Caesar, we have the luxury of consulting better sources than the play (including, as
andrew pointed out, Shakespeare's own sources). We can instead consult the play alone, if we judge that is satisfactory for whatever moved us individually to seek information about Julius.
If all I know about Julius Caesar is what I read in Shakespeare, then I won't be teaching ancient history at Yale anytime soon. As it happens, I won't ever be teaching anything at Yale anyway, so I'd be foolish to bother much about that when making my information consumption decisions.
In a similar vein,
If all we had was Iamblichus ...
That, too, is an important feature of Bayes, that we can do counterfactual hypothetical reasoning about what we would believe if we had more or less information than we actually do. But methodological caution number one: we never have "only" some one piece of potential evidence, there is always background information, otherwise we could neither understand the meaty questions (we'd be stuck at "What's a Pythagoras?") nor appreciate the evidence's potential.
... we would have no way to get a handle on his narrative in order to assess the historical value of certain data in its narrative.
But we could make some estimates, because there is at least the serious possibility that some historical information has survived its incorporation into the narrative in hand. Maybe we get no further than the formulation of viable hypotheses ... that's still better than "What's a Pythagoras?" and it's heursitic reasoning about the human past - what I, if not you, call "history."