Since curiosity is an emotion, I suspect that some people will object to treating curiosity as a part of rationality. A popular belief about “rationality” is that rationality opposes all emotion—that all our sadness and all our joy are automatically anti-logical by virtue of being feelings. Yet strangely enough, I can’t find any theorem of probability theory which proves that I should appear ice-cold and expressionless.
When people think of “emotion” and “rationality” as opposed, I suspect that they are really thinking of System 1 and System 2—fast perceptual judgments versus slow deliberative judgments. System 2’s deliberative judgments aren’t always true, and System 1’s perceptual judgments aren’t always false; so it is very important to distinguish that dichotomy from “rationality.” Both systems can serve the goal of truth, or defeat it, depending on how they are used.
For my part, I label an emotion as “not rational” if it rests on mistaken beliefs, or rather, on mistake-producing epistemic conduct. “If the iron approaches your face, and you believe it is hot, and it is cool, the Way opposes your fear. If the iron approaches your face, and you believe it is cool, and it is hot, the Way opposes your calm.” Conversely, an emotion that is evoked by correct beliefs or truth-conducive thinking is a “rational emotion”; and this has the advantage of letting us regard calm as an emotional state, rather than a privileged default.
So is rationality orthogonal to feeling? No; our emotions arise from our models of reality. If I believe that my dead brother has been discovered alive, I will be happy; if I wake up and realize it was a dream, I will be sad. P. C. Hodgell said: “That which can be destroyed by the truth should be.” My dreaming self’s happiness was opposed by truth. My sadness on waking is rational; there is no truth which destroys it.
Rationality begins by asking how-the-world-is, but spreads virally to any other thought which depends on how we think the world is. Your beliefs about “how-the-world-is” can concern anything you think is out there in reality, anything that either does or does not exist, any member of the class “things that can make other things happen.” If you believe that there is a goblin in your closet that ties your shoes’ laces together, then this is a belief about how-the-world-is. Your shoes are real—you can pick them up. If there’s something out there that can reach out and tie your shoelaces together, it must be real too, part of the vast web of causes and effects we call the “universe.”
Feeling angry at the goblin who tied your shoelaces involves a state of mind that is not just about how-the-world-is. Suppose that, as a Buddhist or a lobotomy patient or just a very phlegmatic person, finding your shoelaces tied together didn’t make you angry. This wouldn’t affect what you expected to see in the world—you’d still expect to open up your closet and find your shoelaces tied together. Your anger or calm shouldn’t affect your best guess here, because what happens in your closet does not depend on your emotional state of mind; though it may take some effort to think that clearly.
But the angry feeling is tangled up with a state of mind that is about how-the-world-is; you become angry because you think the goblin tied your shoelaces. The criterion of rationality spreads virally, from the initial question of whether or not a goblin tied your shoelaces, to the resulting anger.
Becoming more rational—arriving at better estimates of how-the-world-is—can diminish feelings or intensify them. Sometimes we run away from strong feelings by denying the facts, by flinching away from the view of the world that gave rise to the powerful emotion. If so, then as you study the skills of rationality and train yourself not to deny facts, your feelings will become stronger.
In my early days I was never quite certain whether it was all right to feel things strongly—whether it was allowed, whether it was proper. I do not think this confusion arose only from my youthful misunderstanding of rationality. I have observed similar troubles in people who do not even aspire to be rationalists; when they are happy, they wonder if they are really allowed to be happy, and when they are sad, they are never quite sure whether to run away from the emotion or not. Since the days of Socrates at least, and probably long before, the way to appear cultured and sophisticated has been to never let anyone see you care strongly about anything. It’s embarrassing to feel—it’s just not done in polite society. You should see the strange looks I get when people realize how much I care about rationality. It’s not the unusual subject, I think, but that they’re not used to seeing sane adults who visibly care about anything.
But I know, now, that there’s nothing wrong with feeling strongly. Ever since I adopted the rule of “That which can be destroyed by the truth should be,” I’ve also come to realize “That which the truth nourishes should thrive.” When something good happens, I am happy, and there is no confusion in my mind about whether it is rational for me to be happy. When something terrible happens, I do not flee my sadness by searching for fake consolations and false silver linings. I visualize the past and future of humankind, the tens of billions of deaths over our history, the misery and fear, the search for answers, the trembling hands reaching upward out of so much blood, what we could become someday when we make the stars our cities, all that darkness and all that light—I know that I can never truly understand it, and I haven’t the words to say. Despite all my philosophy I am still embarrassed to confess strong emotions, and you’re probably uncomfortable hearing them. But I know, now, that it is rational to feel.
Well that really depends what the decision is and what the circumstantial factors are. As I said in my last comment, decisions are made by a combination of emotion and reason. Emotions tell you where you want to go, and reason tells you how to get there. Whether or not a decision is reasonable depends on (1) was it an effective (and efficient, though that's somewhat less important) way of achieving your goal? Did it actually produce the outcome desired by your emotions? And (2) was it consistint with reality and the facts? Was the decision based on accurate information?
Taking the example you gave, of a family member being hurt by someone else in an accident, your emotions in reaction to this event are likely to be very charged. You just lost someone that was important to you, and you're bound to feel hurt. It's also very common to feel angry and to want revenge on (or justice for) the person that was responsible. It's not clear to me why the human default is to assign guilt without evaluting the situation first to see whether or not the person actually is guilty, but that does seem to be the common response. In this case, it would be up to a jury to decide whether this constituted manslaughter. It's most probable that the jury, having no vested interests besides ensuring justice, would be able to come to the most rational conclusion.
That said, if you are being truly rational about it and if your emotions are telling you your goal is to find out who (if anyone) was responsible, then your conclusion should be no different than that of the jury's. Of course, most people do allow their emotions to bias them, and aren't rational (thus the need for the jury). But if you are being rational about it, and your goal truly is about discovering the guilt or innocence of the parties involved, then how you feel about the situation is what is motivating your search, and reason and evidence should be what determined your answer. If you really don't have enough evidence, and the evidence you do have doesn't point more in one direction than the other, then yes, the rational conclusion would be simply to admit that you don't know.
One should be careful to inspect what exactly that emotional motivation actually is, if it's to determine guilt or innocence, to learn the truth about the situation, and not to find someone to blame so that you can feel better about it. (Although, how it would make you feel better to condemn a potentially innocent person when it will do nothing to bring back your family member nor help anyone else is a mystery to me. Alas, human beings have a lot of nonsensical intuitions.)
That said, if you're honest about your intentions, and what you really want is to blame someone else, and not to find the truth, and the possibility of blaming someone innocent isn't inconsistent with other explicit or implicit pro-social goals of yours, then to point the finger without basing your conclusion on the examination of the evidence isn't strictly irrational, since it would be consistent with your goals, to which the facts aren't relevant. However, that sort of approach would be pretty anti-social, and I doubt anyone having that goal would be honest enough to admit it. If your stated goal is to find the truth, then the only honest thing to do is look at the evidence, follow it, and be prepared that it might go either way.
It does no good to write in the bottom line before you start if your goal is to find out the truth. You won't arrive at the truth that way, and if your emotions tell you the truth is what you want, then that behavior would be irrational. In the words of Eliezer Yudkowsky, "Your effectiveness as a rationalist is determined by whichever algorithm actually writes the bottom line of your thoughts." I strongly recommend you read Eliezer's posts The Bottom Line as well as Rationalization, as they address the issue you seem to be struggling with.