So, hi, 8ish years late. I want to make sure I understand. Would this (reductionism) be somewhat like drawing a multi-leveled building of a map? I'm one of those 'don't yet fully understand the math articles' types.

It seems like the 'rational' two boxers are falling prey to the concept of belief in belief. They think that because they believe that they are people who would choose both boxes, than it doesn't matter what they choose, box B is already empty so they may as well take both. If you have all the information (except for what is in box B), than choosing both is the irrational option and the 'rational' people are rationalizing. You've just seen someone (or something) materialize two boxes from thin air, tell you they know which option you'll choose (and have evidence that they've been wrong yet), and leave. That person (or thing) has two pieces of information you don't: what's in box b and which option will be chosen. If you ignore the evidence provided in favor of the belief that you know yourself better than reality, and then call it being rational, I don't know what to tell you.

Now let's say you don't know everything. A regular person comes up and tells you one box has 1k and one has 1000k, and you can either take A and B, or just B and there is a high chance that taking A and B will result in B being empty while taking just B will result in B having the 1000k, the person offering you the boxes has l, essentially, zero credibility, you may not even believe either box has money. It doesn't matter to you whether that person knows already what you'll pick. You don't know they know, and it doesn't matter if they do. The question becomes do you run away from this crazy and possibly dangerous person, do you beleven them and take both, or do you believe them and take B? Rationally speaking, you don't lose anything by taking any of those options except for the opportunity to learn what following the other options would entail. It becomes a question of will you regret taking both and getting only 1k, oR taking only b and losing the possibility of 1k (or running away, and regretting not calling the cops re:dangerous lunatic later).

I had better phraseology and order in my head half an hour ago, but I'm typing this up on my phone and I'm losing track of my points, so I'll leave things as they are.

I doubt I'd be able to fully grasp this if I had not first read hpmor, so thanks for that. Also, eggs vs ovals.

"'I chose to believe in the existence of God—deliberately and consciously. This decision, however, has absolutely zero effect on the actual existence of God.'

If you know your belief isn't correlated to reality, how can you still believe it?"

It's the difference between someone who's afraid of heights standing twenty feet from a cliff and standing two inches from the cliff. The former knows what will happen if he moves over and looks down, the latter is looking down and feeling the fear.

If you tell yourself you believe in a wall, then you're less likely to worry about what's on the other side.

There has been sufficient evidence (in the form of my own experiences) to say that 'a thing is true.' Based upon my own education, wherein 'sufficient evidence' is described as the summary of a study, or a line in a textbook, or the words of a teacher, my own experiences that show 'a thing is true' are far more real, and so, far more evidence than is required.