Imagine that 4% of the population hears voices. Imagine further that 25% of those people are psychotic (note: this may not be the proper, technical usage of the term, but it doesn't matter to my point). No amount of explaining the situation seems to help them. The psychotic rate in the general population is thus 1%. The voices drive them crazy and make them completely dysfunctional.
Now, we know that hearing voices doesn't cause psychosis all by itself. 75% of the people who hear voices function perfectly fine. They ignore their voices, or make friends with them, or write books about them. As real as their voices seem, they are able to go on with life normally.
So, we can conclude that the psychotic people have a second thing wrong, which the non-psychotic people do not have. We'll call this disorder_2. disorder_2 may be a combination of many things, but it doesn't matter to my point. It's the set of whatever things are needed to make people with disorder_1 (hearing voices) psychotic. Note there could also be multiple separate options for what disorder_2: different ways to turn hearing voices into a problem. But this also isn't important right now.
So, what do we know about disorder_2? We know that it prevents people from understanding our advice about voices. They don't seem to listen when we tell them the voices aren't real. Or they can't figure out which voices we mean. But there's something a lot cooler than we know.
Assuming disorder_1 and disorder_2 are statistically independent, then the rate of disorder_2 in the population is an amazing 25%. So we have this thing, which is very common, and it makes people not listen to reason.
First we will consider that it might be a brain lesion. But if it is, why can't we tell people that? Why can't they step back, and know their brain is damaged, and not trust their own judgment and listen to us? Well, maybe they have a second brain lesion on the part of the brain which allows for that. But then, why can't they know *that*, and get some perspective, and figure out something to do that is rationally compatible with their brain malfunctioning? Why doesn't the person say he's really confused and just sit down, and not do anything, and ask for help, and get people to help him work out what is real? Well, maybe there is a brain lesion on the part of the brain needed for *that* too. But no matter how many brain lesions we postulate, there will always be a creative solution for how to continue rationally. Unless: there's one way there won't be a creative solution: due to all the brain lesions, the person isn't creative anymore. The person isn't a thinking human being anymore.
But most psychotic people aren't that far gone. Sure they're crazy, but they are also people. They still speak English, and do all sorts of things that a cow can't do. So let's imagine that disorder_2 is *not* a brain lesion.
What else might disorder_2 be? One possibility is that it's being irrational. Bear in mind that not all irrationality is the same. So imagine there is a specific type which is disorder_2. When someone with this form of irrationality hears voices, he can't be talked into reacting rationally, because he's not a rational person. This would explain all the data.
Now, let's consider how to treat these people. First consider treating disorder_2, assuming it is an irrationality. Suppose we have a set of arguments and explanations which cures this irrationality. This would be the best course, because we know the voices will then be harmless, and we know that being irrational will have other bad effects besides causing psychosis in people who hear voices.
Now imagine we have a drug which cures hearing voices. This would instantly cure psychosis in these people. But they would remain irrational. The cure would still be a very good thing. However, there is a danger. The person might be confirmed in his irrationality. If he believed that his only problem was disorder_1, the voices, he would wrong believe his worldview wasn't causing any problems, even though it was. If one of his friends told him that part of the problem was his irrationality, he could take his cure as proof that his irrationality was not the reason for his psychosis.
To avoid this danger, what would we need to do? It's pretty simple: we'd tell people that we are not curing their real problem. We are removing something from them which is completely harmless, but which reacts badly with their real disorder (this would be true whether the real disorder is irrationality or not). We might try an analogy to explain, like this one: they are like a man who gets angry a number of things including pillows, and we've removed all pillows from his house. Instantly, he is not angry when at home. But we haven't really cured him.
So the two primary conclusions we should take from this are:
1) irrationality may be a necessary component of many mental illnesses
2) many cures for mental illness, no matter how effective they seem to be, may be just like removing pillows. they may not be cures at all.