Each statement that he makes is valid evidence - how could you not update your probabilities? ... But then the clever arguer can make you believe anything he chooses, if there is a sufficient variety of signs to selectively report. That doesn't sound right.

What's being overlooked is that your priors before hearing the clever arguer are not the same as your priors if there were no clever arguer.

Consider the case if the clever arguer presents his case and it is obviously inadequate. Perhaps he refers to none of the usual signs of containing a diamond and the signs he does present seem unusual and inconclusive. (Assume all the usual idealizations, ie no question that he knows the facts and presents them in the best light, his motives are known and absolute, he's not attempting reverse psychology, etc) Wouldn't it seem to you that here is evidence that box B does not contain the diamond as he says? But if no clever arguer were involved, it would be a 50/50 chance.

So the prior that you're updating for each point the clever arguer makes starts out low. It crosses 0.5 at the point where his argument is about as strong as you would expect given a 50/50 chance of A or B.

What lowers it when CA begins speaking? You are predictively compensating for the biased updating you expect to do when you hear a biased but correct argument. (Idealizations are assumed here too. If we let CA begin speaking and then immediately stop him, this shouldn't persuade anybody that the diamond is in box A on the grounds that they're left with the low prior they start with.)

The answer is less clear when CA is not assumed to be clever. When he presents a feeble argument, is it because he can have no good argument, or because he couldn't find it? Ref "What evidence bad arguments".

There are really two questions in there:

• Whether the Peano arithmetic axioms correctly describe the physical world.
• Whether, given those axioms and appropriate definitions of 2 and 4 (perhaps as Church numerals), 2 + 2 = 4.

One is a question about the world, the other about a neccessary truth.

The first is about what aspect of the world we are looking at, under what definitions. 2 rabbits plus 2 rabbits may not result in 4 rabbits. So I have to assume Eliezer refers to the second question.

Can we even meaningfully ask the second question? Kind of. As David Deutsch warns, we shouldn't mistake the study of absolute truths for the possession of absolute truths. We can ask ourselves how we computed whether 2+2=4, conscious that our means of computing it may be flawed. We could in principle try many means of computing whether 2+2=4 that seem to obey the Peano axioms: fingers, abacus, other physical counters, etc. Then we could call into question our means of aggregating the computations into a single very confident answer and then our means of retaining the answer in memory.

Seems a pointless exercise to me, though. Evolution either has endowed us with mental tools that correspond to some basic neccessary truths or it hasn't. If it hadn't, we would have no good means of exploring the question.

If you happened to be a literate English speaker, you might become confused, and think that this shaped ink somehow meant that box B contained the diamond.

A sign S "means" something T when S is a reliable indicator of T. In this case, the clever arguer has sabotaged that reliability.

ISTM the parable presupposes (and needs to) that what the clever arguer produces is ordinarily a reliable indicator that box B contained the diamond, ie ordinarily means that. It would be pointless otherwise.

Therein lies a question: Is he neccessarily able to sabotage it? Posed in the contrary way, are there formats which he can't effectively sabotage but which suffice to express the interesting arguments?

There are formats that he can't sabotage, such as rigorous machine-verifiable proof, but it is a great deal of work to use them even for their natural subject matter. So yes with difficulty for math-like topics.

For science-like topics in general, I think the answer is probably that it's theoretically possible. It needs more than verifiable logic, though. Onlookers need to be able to verify experiments, and interpretive frameworks need to be managed, which is very hard.

For squishier topics, I make no answer.

What if self-deception helps us be happy? What if just running out and overcoming bias will make us - gasp! - unhappy?

You are aware, I'm sure, of studies that connect depression and freedom from bias, notably overconfidence in one's ability to control outcome.

You've already given one answer: to deliberately choose to believe what our best judgement tells us isn't so would be lunacy. Many people are psychologically able to fool themselves subtly, but fewer are able to deliberately, knowingly fool themselves.

Another answer is that even though depression leads to freedom from some biases and illusions, the converse doesn't seem to apply. Overcoming bias doesn't seem to lead to depression. I don't get the impression that a disproportionate number of people on this list are depressed. In my own experience, losing illusions doesn't make me feel depressed. Even if the illusion promised something desirable, I think what I have usually felt was more like intellectual relief, "So that's why (whatever was promised) never seemed to work."

This was surprisingly hard to explain to people; many people would read the careful explanation and hear, "Crocker's Rules mean you can say offensive things to other people."

Perhaps because it resembles the "2" part of a common verbal bully's 1-2 punch, the one that first insults you and then when you react, slurs you for allegedly not being able to handle the truth. I'm specifically thinking of the part of Crocker's Rule that goes "If you're offended, it's your fault".

Yes, I see that one is "me" and the other is "you". But the translation to "you" is so natural that even that writeup of Crocker's Rule slips into it.

I also think Crocker's Rules is an ivory-tower sort of position that starts with assumptions that just doesn't reflect the real world. Perhaps in Lee Crocker's experience, all debating opponents are at the worst mere curmudgeons who wrap truths in unpleasant rhetoric, but I doubt that's true even for him. It's certainly not my experience.

In my experience, the majority of people who this rule seems applicable to use petty and truthless rhetoric to defend minor points of lifestyle or ideology. Usually the arguing parties have already understood each other as much as they care to and are shouting their talking-points and postures past each other. It's true that usually one or both sides could stand to listen and learn, but for the people that applies to, invariably that's just what they don't want.

I won't belabor the point, but Crocker's apparent assumption about the nature of contentious rhetoric is grossly wrong in the real world.

It seems to be a common childhood experience on this list to have tried to disprove famous mathematical theorems.

Me, I tried to disprove the four-color map conjecture when I was 10 or 11. At that point it was a conjecture, not a theorem. I came up with a nice moderate size map that, after a apparently free initial labelling and a sequence of apparently forced moves, required a fifth color.

Fortunately the first thing that occured to me was to double-check my result, and of course I found a 4-color coloring.