...no, that would go in the standard curriculum.

...okay then.

Including if she points out that any time you previously went into some sort of question, expecting yourself to see something that super persuaded you about theory1 being true, and then, you ended up super persuaded of theory1, you were clearly being incoherent going in, so probably whatever you ended up persuaded about was wrong?

...yes?

Though Keltham would not say that the conclusion you reached is probably wrong?  Maybe you expected to end up persuaded that the Sun would still be lit the next day, that doesn't mean the Sun goes out?  The saying out of dath ilan is 'reversed stupidity is not intelligence': to reliably be wrong about yes-or-no questions 99% of the time, you'd need sufficiently good evidence and well-processed information that you could be right 99% of the time just by flipping the answers.

So if you look back and notice you were persuaded of something by garbage reasoning, you just undo the update from that.  You don't conclude that you now have positive knowledge pointing strongly in the opposite direction.

(Asmodia feels a sudden nervous worry that the average dath ilani, in terms of what sort of mental caution they aspire to, and how hard they are on themselves about it, may in fact be pretty well into and maybe past what she and her fellow Golarionites were visualizing when Keltham kept talking about 'Keepers'.)

...Asmodia informs Keltham that she's making a judgment call that her fellow Golarionites not trying to be Keepers, should maybe not be told about that stuff for another few days until they get a chance to take in the base principles of #6.

...because they've got a huge backlog of stuff they've convinced themselves of for bad reasons?

What if they've ever read a book written in Golarion and believed anything inside it?

...right.  Okay, sure, first give them a chance to master some of the basic principles and applications, before pointing them in the direction of any bulk-scale mental housecleaning.

And on to #7.

"You can expect to end up persuaded of the truth, right, while not knowing what it is, like you can do a test thinking 'this test will reveal'" Asmodeus's will "the truth' and that's not being incoherent?" asks Meritxell, who has been mostly quiet as she tries to absorb this. Abrogail's Chosen can't be any worse than Nethys's or Cayden Cailean's. 

"Correct.  You can calculate that, in fact, unless I'm missing something -"

Asmodia scribbles on the wall a bit.  Let's say that you're not sure whether somebody is a cleric or a wizard, clerics wear red-with-black-and-gold-trim with 90% probability and anything else with 10% probability, wizards wear red-with-black-and-gold-trim with 20% probability and anything else with 80% probability, and somebody starts out five times as likely to be 'at least a first-circle wizard' than 'at least a first-circle cleric' which sounds vaguely right to Asmodia.

Then, supposing the 1/6 case where somebody is a cleric, after you observe what they're wearing, you expect with 90% probability to conclude that they're 1/5 * 9/2 = 9/10 = 0.9 times as likely to be a cleric as a wizard, and with 10% probability to conclude that they're 1/5 * 1/8 = 1/40 = 0.025 times as likely to be a cleric as a wizard.

Supposing the 5/6 case where somebody is a wizard, you expect with 80% probability that you conclude that they're 40 times as likely to be a wizard as a cleric, and with 20% probability that you conclude they're 0.9 times as likely to be a cleric as a wizard.

So if you close your eyes and don't look at their clothes, you think that you've got a 5/6 chance of losing... about a quarter of a factor of two, and a 1/6 chance of losing... about two and a half factors of two, so on average you lose... a tad more than half a factor of two?  Three-fifths of a two?

And if you do look... uh... it's basically going to work out to, she's approximating here, 1/6 of one factor of two, plus 1/60 of five and a half factors of two so maybe a tenth of a factor of two, plus 5/6ths of 20% of one factor of two so 1/6 of a factor of two, plus 5/6ths of 80% of basically not any factors of two, which all works out to 1/6 + 1/6 + 1/10 or 1/3 + 1/10 so about 43% of a two.  Roughly.  But less than half of a two.

There's obviously going to be some sort of theorem saying that you always do better by seeing more stuff, in fact, this is so obvious that Asmodia doesn't really want to slow down and figure out how to prove it -

"Not exactly.  The theorem says that you can't coherently expect to do worse on average by making more observations.  You never expect to lose more factors of two in total expectation, or on average.  You might get unlucky and lose some in a particular case."

"And if you're wrong about what the evidence means, if you're wrong about the factors P(evidence ◁ hypothesis), you can see what's really there and update away from reality as a result, because you didn't correctly model the entanglement between evidence and reality."

"You just can't coherently expect that to happen to you.  Any time you're like, 'oh no, I should not look there, that will probably lead me further away from the truth', you are doing something very strange and wrong, and in particular, you actually believe one thing, but believe you believe another.  Like, you actually know, on some level or in some part of you, that really clerics wear red and wizards don't.  But you think you believe, maybe because you remember reading it in a book, that wizards wear red and clerics don't, and you expect about yourself that if you check their clothing you'll do a calculation based on what you read in the book.  So one slice through you, the part that really knows how things work, expects the verbal-calculations part of you to arrive at the wrong answer."

"What you do in this case obviously is say 'wait what?' and figure out what you actually expect, reconcile that whole bizarre thing where you actually believe one thing, but believe you believe another.  And then go look.  There's a whole separate skill and art form about that, which I'll maybe get to in a few days if nothing slows me down?"

"Keeper-only."

"No.  This is eight-year-old stuff and the rest of it's not going to make sense otherwise."

"Asmodia, I am worried that I have given you the wrong impression about exactly which forms of reasoning are dangerous, that stuff is not."

"...Keeper-only for at least the next several days?"

"For somebody who believed about herself that she didn't want to try to be a Keeper, you sure are trying to Keep things."

"But fine, I can probably find material a few days out that doesn't require people to distinguish meta-levels of self-modeling or access the subjective difference between endorsement and anticipation."

"What am I doing wrong if I think, that person over there has a Splendour of thirty, if I talk to her I'm definitely going to end up believing whatever she says, even knowing that if I talk to her I'll believe whatever she says -"

"I mean, in practice, what you're doing wrong is that you shouldn't talk to her - but - um.  I'm not sure how to put this.  Being a dath ilani - I mean an ilani - maybe I should just say, the closer you come to a Keeper, or an ideal-agent - the better you are at Law, the more that somebody with high Splendour can't convince you of which province the assassin came from, any more than they can convince you of, um, 1 + 2 = 5.  Or the more math you know, the harder it is to convince you of that."

"Back in Ostenso you'd have had an easier time convincing me that 1 + 2 = 5 in some other plane of existence, because I wouldn't know anything about the Law of Validity or what it really means that 1 + 2 = 3.  I'd have read that book arguing that the assassin of the Prefect of Tandak came on a ship from Whitemarch, and maybe been suspicious but not really have been able to say what was wrong.  So somebody with high Splendour could've convinced me of that, and now they couldn't.  Or at least it'd take a higher Splendour."

"Or to downgrade the proverb's profoundness a few steps, your strength in the Way is the degree to which it takes a higher Splendour to convince you of false things and a lower Splendour to convince you of true things."

Meritxell looks like she actually thinks that's maybe more profound than the original version.

"I should also note that to whatever extent an augmented Splendour of 30 does not actually act as irresistible direct mind control and you get any chance to think about things, the obvious reconciliation is to try to decide in advance, 'How incredibly persuasive of an argument should I expect to hear from somebody with Splendour 30, if they are trying to convince me of a true thing, compared to how likely I am to hear that level of persuasiveness if they're trying to convince me of a false thing?'  And then if you really expect that your predictions there are correct, and not just way underestimating how persuasive they'll sound for false things - and you think you'll actually get the chance to implement that rule, instead of them just effectively mind-controlling you - then you could try to update off that conversation."

"I mean, in practice, to first order, the answer is just not to talk to them if you think they're liable to deploy irresistible Splendour on convincing you of false things.  To second order, if you've got to talk to them anyways, go find a Lawful entity with Splendour 30 and pay them to spend a few days arguing true and false things to you until you're correctly calibrated on what it sounds like to hear a true versus false argument at Splendour 30, and if it turns out you can't learn that, go back to the first-order nope."

"I will keep that in mind if I ever need to talk to the demon lord Nocticula or something," says Meritxell very seriously.

"Okay I'm sorry but we all work on Project Lawful here and now that you've raised this topic I am going to need the one-paragraph explanation just in case it somehow comes up even if you might otherwise think that was improbable."

" - Nocticula is an extremely powerful not-quite-a-god entity in the Abyss and both has absurdly high Splendour and is the kind of person who'd use it to talk people into false things because she'd think it was funny. I really can't think how it'd come up. Maybe she'll object when we close the Worldwound?"

One of the candidate hires that Cheliax is supposed to send him, being Nocticula in disguise, is not very much more improbable than other things that have happened to him recently.

But, okay, there's been a reassuringly low hit rate when he tries to guess that sort of thing specifically and in advance.

"Fair enough.  Probably nothing will happen there, so long as there are not in fact and in reality any 'tropes' lurking about."

Message:  Meritxell, going forwards, and subject to policy approval by Sevar, I think that in the name of prudence we start not mentioning certain things even if we would've been talking about them in an alterCheliax that doesn't believe in tropes.