I find this outline helpful. I do however have a quibble.
If you believe X because you want to, any arguments you make for X no matter how strong they sound are devoid of informational context about X and should properly be ignored by a truth-seeker.
This seems slightly inaccurate. It would imply that a truth-seeking judge would decide cases just as well (or better) without hearing from the lawyers as with, because lawyers are paid to advocate for their clients. More accurate would be:
If you believe X because you want to, your belief in X is devoid of informational context about X and should properly be ignored by a truth-seeker.
If you believe X for reasons unrelated to X being true, your testimony becomes worthless because your belief in X is not correlated with X. But arguments for X are another matter.
Example: Alice says, "There is no largest prime number," and backs it up with an argument. You are now in possession of two pieces of evidence for Alice's claim C:
(1) Alice's argument. Call this "Argument." It is evidence in the sense that p(C|argument) > p(C).
(2) Alice's own apparent belief that C. Call this "Alice." It is evidence in the sense that p(C|Alice) > p(C).
Now suppose you discover that Alice has been paid handsomely to make this statement, and that she would gladly have made the opposite claim had her boss wanted her to. If the claim in the post is correct, then both items of evidence are zeroed out, such that :
(3) p(C) = p(C|Argument) = p(C|Alice)
Whereas the correct thing to do is to zero out "Alice" but not "Argument" thus:
(4) p(C|Alice) = p(C)
(5) p(C|Argument) > p(C)
*Edited for formatting
I think this is an interesting question. If the arguer is cherry-picking evidence, we should ignore that to a large degree. We are often even justified in updating in the opposite direction of a motivated argument. In the pure mathematical case, it doesn't matter anymore, so long as we are prepared to check the proof thoroughly. It seems to break down very quickly for any other situation, though.
In principle, the Bayesian answer is that we need to account for the filtering process when updating on filtered evidence. This collides with logical uncertainty w...
Abram Demski and Grognor
Much of rationality is pattern-matching. An article on lesswrong might point out a thing to look for. Noticing this thing changes your reasoning in some way. This essay is a list of things to look for. These things are all associated, but the reader should take care not to lump them together. Each dichotomy is distinct, and although the brain will tend to abstract them into some sort of yin/yang correlated mush, in reality they have a more complicated structure; some things may be similar, but if possible, try to focus on the complex interrelationships.