Let's say you attempt to think nothing for 5 minutes. Will you succeed with that because you are free enough to do so? >99% of people won't. On the other hand if I want to rise my right arm I can do that successfully nearly every time.
When it comes to changing beliefs, newspaper corrections are a good example. Alice reads a newspaper saying 'Bob is evil'. The next week the newspaper writes: "We were wrong, Bob isn't an evil at all". Does that mean that Alice is now less likely to believe that 'Bob is evil'? That's no automatic effect. Being remembered of the old belief that 'Bob is evil' can strenghens the belief. That's a fact that you have to take into account when you want to think about how belief change works, but that isn't in the mental model that assumes that people simply do free will decisions to change their beliefs.
"Think nothing for 5 minutes" is not like "raise my right arm." It is like "hold my arm so still for 5 minutes than a careful observer will not even notice a jitter." It is unlikely that anyone can do either of those things on demand. But I can refrain from most complete thoughts for 5 minutes, and from large motions of my arm. My control over my thoughts is actually very similar to my control over my arm. You find dissimilarity because you are comparing the wrong things.
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.