Plenty of people go their whole life never thinking of challenging the claim, of looking to verify it. The thought never crosses their mind.
Do you have any evidence that this is the case? In my experience, it's not. Most people tend to feel that coming up with an argument for why their particular beliefs are true is extremely important, it's just that they then fall into patterns of confirmation/disconfirmation bias, affect bias, and mind-projection fallacy. A person raised in a fundamentalist Christian home is taught that there are really true and verifiable explanations for the specifics of why evolution is wrong. There's a huge propensity to find ambiguity intolerable. The more dogmatically an assertion is held, the more intolerable ambiguity becomes.
The cases where error exists due to sheer lack of curiosity don't appear to be common. But in those cases, maybe a more fundamental question to ask is why there is a lack of curiosity. Perhaps it is social convention to accept an idea and it would be uncomfortable to challenge it. Perhaps adherence to a particular idea has provided a reasonable amount of comfort and consistency in a tribe's history and if they cannot imagine increases in their success and comfort, there is little motivation to stray from the accepted dogma. These types of question cast light on what this sort of mistake is, which is different from hypocrisy/akrasia. I'm just not sure this question is (a) an important distinction or (b) worth adding on to this particular thread. It might be worth creating a new discussion thread for it though, to get more thoughts than just my own.
What are we to think when someone says with their lips that they desire truth, but by their other cognitive deeds choose comfortable illusions over reality (or comfortable cynicism over reality)?
Robin Hanson has labeled such individuals hypocrites. In the traditional sense of the term, a hypocrite is a moral liar: someone who says a morality which they do not, themselves, believe. On the other hand, we don't always live up to the goals we set for ourselves. If I really believe that I ought to exercise at least 3 times per week, but I don't always do so, am I properly termed a "hypocrite"? The term akrasia, meaning "weakness of will" or "failure of self-control", seems more appropriate. Even if I tell all my friends that they ought to exercise 3 times per week, that doesn't necessarily make me a hypocrite. It's good advice. (Now, if I claimed to always exercise 3 times per week, knowing that this claim was false, that would be dishonest.)
Accusations of hypocrisy garner a lot more attention than accusations of akrasia - because hypocrisy is a deliberate transgression. It is tempting to say "hypocrisy" when you really mean "akrasia", because you'll get more attention, but that can cause damage to innocent bystanders. In akrasia, your transgression is your failure of will - it's fine that you advocate going to the gym more often, you just need to live up to the principle yourself. In hypocrisy, the transgression is claiming to care: you have no right to publicly advocate the moral principle, because (the accuser says) you don't believe in it yourself.
Will Wilkinson asked Hanson: "Would it be a kind of victory if people who now say that they care about truth, but who really don't, started admitting that they really don't?"
But much more importantly: who says that people who claim to care about truth, and then deceive themselves, "really don't care" about the truth? Why not say that they really care about the truth (as is right and proper), but they aren't living up to their own morals?
It may be standard practice in economics to deduce "preferences" from actions rather than declarations, but that's because you're trying to predict, in a scientific sense, what the subject will do next - trying to build good economic models. Moral philosophy is a different bag o' worms. At the very least, it is a controversial step in moral reasoning to decide that people's emotional impulses and subconscious pressures, rather than their declarative moral reasoning processes and the words that issue from their lips, constitute their "real selves". We should then call akrasia, not weakness of will, but strength of will.
To put the dilemma more sharply: The one comes before you and pleads, "I know that I have many times been guilty of self-deception. I have bought lottery tickets, I have overestimated my driving skills, I have planned optimistically, I have refused to confront contradictory evidence. I am weak. And yet I desire to do better. Will you help me?"
So that is words issuing from the lips, which say one thing. And it may be that the one has committed other deeds which say something else. Who is the real person? Does that question have an answer, or only a definition?
I do not frame an answer. It is only needful for me to know that something has asked for my help. There is something here that can ally to me, in our quest for truth - whether or not you call it the "real self". Whether or not, for that matter, you call me my "real self". If the word "I", when I use it, does not refer to the cognitive pattern that authors these words on your computer screen, what does it refer to? And if the words that issue from some other's lips should declare me to be a ghost, then I will seek out my fellow truthseeking ghosts, and have company in my phantom quest.