In philosophy, there is a curious problem that occurs when one encounters an argument whose conclusion one does not like, but one nonetheless cannot seem to defeat. One is presented with a dilemma: Do I accept the results of this argument, or do I reject them? The curious problem that results is that people often refuse to accept the argument, even with no apparently good reason to do so. Let me explain this scenario a little further, for those who are not familiar with the way argument works in philosophy (it actually works this way in all disciplines, but it is not often as explicitly laid out as it almost always is in an academic philosophy setting). Philosophers are very proud of their mastery of logic, the discipline that investigates valid argument and reasoning, and are likely to appeal to two facts about logic when presenting or critiquing an argument: (1) There are two ways you can defeat an argument: a) you can question the validity of the form of the argument, or b) you can question the truth of one or more of the premises; (2) If you cannot do either of the things mentioned in (1), then you must accept the conclusion of the argument (I am tempted to use "ought," instead of "must," to demonstrate the normative aspect of the rationality criterion. However, I imagine for most readers the difference will be elided, so I won't bother. But keep in mind that the sense in which one "must" accept the conclusion of an argument is more of a moral duty than an example of strict causal necessity. This will be important later.). Let's call (1) Logic 101 and (2) the Criterion of Rationality.
Logic 101 is basically accepted by everyone. If you can show that an argument doesn't have a valid argument form (i.e. Modus Ponens, Modus Tollens, among other classics), then you don't have to take the argument seriously. Additionally, if you can reasonably object to the truth of one or more of the premises, you have additional reason to reject the argument. There does not seem to be much room to argue with the principles of Logic 101.
(2), the Criterion of Rationality, is additionally almost universally accepted. However, I think it is far more questionable. I should perhaps attenuate my statement that it is universally accepted. In Anglo-American Analytic philosophy, there is almost no controversy as to the truth of the Criterion of Rationality (Those in other disciplines and/or styles of philosophy might not be so willing to embrace this idea.). Let's think, first of all, about what a logically valid argument entails. For a argument to be logically valid, it must be the case that if the premises are true, it is not possible for the conclusion to be false. The truth of the premises guarantees the truth of the conclusion. Notice that nothing in here says anything about accepting the results of such an argument. Most philosophers take the implication of this fact about logically valid arguments to say that one must accept the results of a sound argument (a sound argument is an argument that has a valid argument form, and all true premises). But does this follow?
It certainly seems crazy to deny it, or at least irrational. Indeed, this is often how philosophers explain what is going on when someone is presented with an indefeasibly sound argument, yet they refuse to accept the consequences of said argument. The person in this situation is behaving irrationally.
But are they? While I don't have a fully developed response to this claim, it seems to me that there is a sense in which one must own an argument before it can reach that level of acceptance. One cannot be compelled purely by the formal majesty of logic, and it seems incorrect to accuse those not so compelled of "irrationality." There is something deeply rational, in its positive normative sense, in delaying judgment, even in the face of such apparently inescapable evidence. The type of acceptance the philosopher thinks logical argument imposes is supposed to be relatively simple, the acceptance of a proposition. Before you heard this argument, you believed that p; now you believe that not-p. Or maybe you had a void which p now fills. Sounds straightforward enough, right? This is a ludicrous symbolization of how beliefs work, however. Our beliefs are not atomistic in this sense, unattached to other beliefs (this is controversial in philosophy, but let's just go with it for now). To borrow a phrase from Quine, they exist in an interlocking web with all our other beliefs (I have some qualms about belief talk, but it's really not worth making this any more complicated than it already is, so let's just press onward.). A change in belief is a traumatic episode, especially if one's belief is central in one's web of beliefs. Is it really "rational" to rip apart one's web of beliefs in the face of such uncompelling evidence as a sound argument? Doesn't the conclusion have to seize one in a manner more meaningful that the inexorability of logical necessity? Philosophers need to think about this problem far more seriously than they have to date, and not just accuse those who fall prey to it of irrationality. It is far more pervasive and important as a phenomenon, I think, than has been heretofore acknowledged.
I will stop at this point, having taken this as far as I can at the moment. For those who care, I was inspired by an essay by James Conant in this collection entitled "Nietzsche's Perfectionism: A Reading of Schopenhauer as Educator." While not explicitly about this problem, I think Nietzsche's idea of "becoming what one is" as a centrally moral concept, a becoming that occurs only with extreme difficulty, and after much denial of what one is, is a useful place to begin illuminating the question of why it is that "logic" is not enough for rationality. Or maybe rationality isn't enough for being human?
UPDATE: I just wanted to include a quotation from Heinrich von Kleist, who Nietzsche approvingly cites in Schopenhauer as Educator: "Not long ago I became acquainted with the Kantian philosophy...I have no reason to fear it will shatter you so profoundly and painfully as it has me...If the point of this thought does not penetrate your heart, do not smile at one who feels wounded by it in the deepest and most sacred part of his being."