Yes, it's a learnable skill. Stage hypnotists exist.
In stage hypnosis people don't change their beliefs themselves but get lead by another person to change their beliefs.
More to the point, I wasn't focused on what's theoretically possible but what we do in day to day interactions. In day to day interactions we don't simply write new beliefs directly into our minds.
Let's suppose that you had reason to believe that the sky is blue, but found yourself believing that it was green. This would not stop you from telling people, "I found out that the sky is blue," and giving the reasons that show that it is blue (since we are assuming you had reason to believe that it is blue.) Likewise, suppose someone comes up to you and says, "I would like to bet you $100 that the sky is green and propose the following test..." No matter how you feel about the color of the sky, you are perfectly free to accept the bet...
In this video, Douglas Crockford (JavaScript MASTER) says:
1
I don't think he has "absolutely no evidence". In worlds where DOUGLAS CROCKFORD has a gut feeling about something related to programming, how often does that gut feeling end up being correct? Probably a lot more than 50% of the time. So according to Bayes, his gut feeling is definitely evidence.
The problem isn't that he lacks evidence. It's that he lacks communicable evidence. He can't say "I believe A because X, Y and Z." The best he could do is say, "just trust me, I have a feeling about this".
Well, "just trust me, I have a feeling about this" does qualify as evidence if you have a good track record, but my point is that he can't communicate the rest of the evidence his brain used to produce the resulting belief.
2
How do you handle a situation where you're having a conversation with someone and they say, "I can't explain why I believe X; I just do."
Well, as far as updating beliefs, I think the best you could do is update on the track record of the person. I don't see any way around it. For example, you should update your beliefs when you hear Douglas Crockford say that he has a gut feeling about something related to programming. But I don't see how you could do any further updating of your beliefs. You can't actually see the evidence he used, so you can't use it to update your beliefs. If you do, the Bayes Police will come find you.
Perhaps it's also worth trying to dig the evidence out of the other persons subconscious.
3
Ok, now let's talk about what you shouldn't do. You shouldn't say, "Well if you can't provide any evidence, you shouldn't believe what you do." The problem with that statement is that it assumes that the person has "no evidence". This was addressed in Section 1. It's akin to saying, "Well Douglas Crockford, you're telling me that you believe X and you have a fantastic track record, but I don't know anything about why you believe it, so I'm not going to update my beliefs at all, and you shouldn't either."
Brains are weird and fantastic thingys. They process information and produce outputs in the form of beliefs (amongst other things). Sometimes they're nice and they say, "Ok Adam - here is what you believe, and here is why you believe it". Other times they're not so nice and the conversation goes like this:
Just because brains could be mean doesn't mean they should be discounted.