[T]he Muslim woman has actually thought through the implications of her faith enough to actually want to persuade others, and has ranked the different reasons for disagreement for their plausibility. This is the same kind of person who would watch that they’re going above and beyond to adhere to their faith’s requirements.
On my reading, this implies that, if you think that the woman is devout, you should think it less likely that Yvain lied when he reported his conversation with her.
Here’s why:
Let ARGUES be the proposition that an arbitrary Muslim woman in Cairo is willing to argue for creationism with a stranger.
Let DEVOUT be the probability that an arbitrary Muslim woman in Cairo is devout—that is, that she “would watch that [she’s] going above and beyond to adhere to [her] faith’s requirements.”
You consider p(ARGUES | DEVOUT) to be low enough to justify calling Yvain a liar. Thus, DEVOUT must refer to a devotion strong enough to make p(ARGUES | DEVOUT) this small. But, I claim, you should consider p(ARGUES) to be even smaller.
On my reading, you assert above that, if the woman argues for creationism, she is very likely to be devout. That is,
(1) p(DEVOUT | ARGUES) > 1 - epsilon,
where epsilon is small enough to justify your omission of any phrase like “very likely to be”. On my reading, this makes epsilon small enough so that, in a cosmopolitan city like Cairo,
(2) p(DEVOUT) < 1 - epsilon,
where, again, DEVOUT refers to a devotion strong enough to make p(ARGUES | DEVOUT) small enough to justify calling Yvain a liar.
On my reading, this implies that, if you think that the woman is devout, you should think it less likely that Yvain lied when he reported his conversation with her.
Here’s why:
Let ARGUES be the proposition that an arbitrary Muslim woman in Cairo is willing to argue for creationism with a stranger.
Let DEVOUT be the probability that an arbitrary Muslim woman in Cairo is devout—that is, that she “would watch that [she’s] going above and beyond to adhere to [her] faith’s requirements.”
You consider p(ARGUES | DEVOUT) to be low enough to justify calling Yvain a liar. Thus, DEVOUT must refer to a devotion strong enough to make p(ARGUES | DEVOUT) this small. But, I claim, you should consider p(ARGUES) to be even smaller.
On my reading, you assert above that, if the woman argues for creationism, she is very likely to be devout. That is,
where epsilon is small enough to justify your omission of any phrase like “very likely to be”. On my reading, this makes epsilon small enough so that, in a cosmopolitan city like Cairo,
where, again, DEVOUT refers to a devotion strong enough to make p(ARGUES | DEVOUT) small enough to justify calling Yvain a liar.
Putting (1) and (2) together gives
Therefore,
so that p(ARGUES) < p(ARGUES | DEVOUT), as claimed.
ETA: Edited to correct typo in derivation.
ETA2: Sorry, more corrections to the argument . . .