It depends on why they no longer doubt. If they now know via personal experience that "X" is true, then their belief has become a fact, and belief is no longer irrelevant. However, if they no longer doubt based solely upon their own blindly presumed certainty, then their belief has become their delusion. It may turn out to be correct, or it may not. But it remains a delusion until it becomes a fact one way or another. And I think self-delusion is a dangerous condition that we should avoid whenever possible.
OK, so we agree that a belief includes some doubt otherwise it is either fact or delusion.
Yes self-delusion is dangerous, but so is a knife. Both can be used as tools when used properly. Self-delusion can be useful if it is temporary and if the implications of the true belief ( aka delusion ) can be tested.
We are duplicitous beings. Yes. We can hold contradicting positions simultaneously. But that doesn't excuse us answering to the positive force of logic.
Have I proposed excusing the answering to positive logic? Maybe I have, but, I'm not even sure what that means.
Why do you keep saying this? It is precisely our skepticism that drives us to test our presumptions. AND why we should avoid raising those resumptions to the level of "belief", beforehand.
If, as was established at the beginning of your reply, a belief without doubt is either fact or delusion, then the differences between presumption and belief are negligable.
You keep calling our skeptical presumptions, "beliefs". But they are just skeptical presumptions. They are possibilities that we have assigned some degree of probability to, but that we need to test to become fact. And I don't see why you keep interjecting 'belief' in to this process. I see no need for belief in any part of it.
We're still squabbling about the definition of belief. Maybe if I approached it this way we could find some common ground:
What if, the skeptical presumption could not be tested for one reason or another? Maybe the technology is not available or does not exist yet. Are you suggesting that the investigation simply halts until the tech becomes available? I'm suggesting that it's possible in some circumstances to skip over the need for testing the presumption, look at the implications where the presumption is true, and then go back and reassess the presumption. The same is true for beliefs.
The reason I keep repeating this same idea is because I haven't seen you address it directly. So far the focus has been on what you think a belief is vs. a skeptical presumption.