Probably the most natural first attempt would be to say that curiosity is love of truth as such. That is, it's a sort of direct thirst for truth, or at least apparent truth. It's clear, however, that this is not an adequate account of curiosity. If this were an adequate account of truth, any truth would contribute to satisfying our curiosity. But it's obvious that there are lots of truths we don't care about at all. We don't generally care, for instance, whether it's true a dust particle is 2 inches from another dust particle. As Stephen Grimm has pointed out in an interesting paper on epistemic values (PDF), the question, "In virtue of what does a truth spark our curiosity?" is actually less naive than it looks, even if curiosity is love of truth.
There is another possible account that I find especially interesting, and that is the one put forward by David Hume. Hume has a whole section of Book II of the Treatise devoted to curiosity. This section is the concluding section of Book II and appears to have some sort of connection with the concluding section of Book I. As Fred Wilson has noted in a number of articles and books, Hume regularly appeals to curiosity to justify intellectual pursuits. So curiosity appears to be a very important concept for Hume, and he does have an interesting account of it. The account seems to be influenced by Cicero's discussion of it in Book One, section 13 of the De Officiis:
Above all, the search after truth and its eager pursuit are peculiar to man. And so, when we have leisure from the demands of business cares, we are eager to see, to hear, to learn something new, and we esteem a desire to know the secrets or wonders of creation as indispensable to a happy life. Thus we come to understand that what is true, simple, and genuine appeals most strongly to a man's nature.
Of course, this Ciceronian comment doesn't tell us much. But Hume expands it considerably, and what seems to have struck him most is the emphasis on leisure and the role of curiosity in the happy life. He starts by dividing truths into two kinds, those that have to do with the proportions of ideas, and those that have to do with the conformity of ideas to really existing objects. (Obviously this is a straightforward version of his well-known distinction between relations of ideas and matters of fact.) He notes that our interest in the first sort of truth is clearly not an interest in the truth as such -- such truths are not desired merely as truths. Simple arithmetical discoveries -- like the product of the numbers 3432412 and 89786234 -- don't strike us as particularly pleasant, and may even be painful. "Which is an evident proof," Hume says, "that the satisfaction, which we sometimes receive from the discover of truth, proceeds not from it, merely as such, but only as endow'd with certain qualities" (T 2.3.10).
We naturally want to ask, then, what these qualities are that render truth so agreeable to us. The first one Hume considers, which he takes to be the "principal source" of our satisfaction in discovery of truth, is the employment of our wits. We aren't impressed by simple arithmetical discoveries because even when they are genuine discoveries, they are in some sense easy and obvious. As Hume notes, this extends rather broadly. Even what is difficult in itself may be treated as uninteresting if our way of learning it was easy and obvious. Many mathematical demonstrations are of this sort -- hitting on the solution originally may have been immensely difficult; but when we are guided through it, it rarely seems so hard or so interesting. What we want are things that work our minds a bit, to fix our attentions and exert our genius, as Hume puts it.
While Hume puts a lot of emphasis on this condition, it is not the only one, and he suspects that it alone is sufficient for explaining much about our enjoyment of truth. It's not enough for the discovery to take force of mind; the truth also needs to be of some importance. Problems in algebra are infinite; but mathematicians have never treated them all equally. Instead they focus on problems that seem to be useful or important, and so do we all in most of our serious intellectual pursuits. But Hume notes that this immediately raises the question of how this evaluation of utility and importance works in the case of curiosity. On the one hand, it seems that it has something to do with beneficial consequences. On the other hand, people who are actually in the grip of serious curiosity seem to be indifferent to these consequences. What's the resolution of this paradox?
Hume argues that human beings are set up in such a way that, in addiction to real passions, we have what might be called faint images or shadows of passions. These shadow-passions are residual results of imagination and sympathy. An engineer may have a certain satisfaction in the fact that his bomb design makes it effective for its use, without having much liking for people who would benefit from its use; there's a sort of shadow-pleasure arising from sympathy with bomb users (Hume calls this sort of sympathy a 'remote sympathy') that doesn't extend outside the bare imagination, and may even be entirely contrary to the real attitude the engineer has toward bomb-users. This remote sympathy and these shadow-passions may seem a slight foundation for something as powerful as curiosity can be, but Hume argues again that the sort of satisfaction curiosity requires consists chiefly in exertion of the mind. The importance of remote sympathy and shadow-passions is not that they directly give us much pleasure in our discoveries, but that they fix our attention on the pursuit, and this fixation of attention is essential for satisfaction of curiosity.
It is not the only thing essential, however. After all, we may fix our attentions and exert our minds and never satisfy our curiosity at all -- for instance, all our efforts may be frustrated. We need some sort of success. So Hume holds that, although our satisfaction of curiosity is due less to the discovery of truth than to its pursuit, if something makes the pursuit seem futile, we are "uneasy".
Hume, apparently borrowing from Pascal, explains this by comparing philosophy with hunting. In fact, he regards the analogy as very strong, saying that "there cannot be two passions more nearly resembling each other than those of hunting and philosophy" (T 2.3.10.8). The pleasure of hunting consists in the action of mind and body (as Hume summarizes it, "the motion, the attention, the difficulty, and the uncertainty"). It's this that really makes for an enjoyable hunt. However, both the importance of the prey and the possibility of success play a serious role. Hunting for deer in a place known to have no deer, or hunting for magpies rather than pheasant, don't have the appeal of more conventional forms of hunting. Hume makes another analogy to gambling. What makes gambling enjoyable is the actual gaming. But it's difficult to enjoy gambling unless you think there is at least some minute chance that you might actually win; and few people will enjoy gambling for literally nothing (although they might gamble for something other than money, of course, like distinction). It's possible, of course, that there are particular exceptional cases, but as a general rule this seems to be so. And philosophy -- pursuit of knowledge, of whatever kind -- is in Hume's view exactly like hunting and gambling. It's the pursuit that really satisfies, but that satisfaction depends on the pursued being important or useful and being attainable.
So on the Humean view curiosity is not satisfied by truth as such, or even directly by truth at all. Rather, it is satisfied by the work done in finding acceptable solutions to important problems, where the acceptableness of the solution is not that it is true, but that it is a sign of success in the pursuit of truth (e.g., it's clearly closer to true even if we think that it's properly speaking false). It's not so much that truth is interesting as that certain topics are (see again Grimm's paper for a different sort of argument for this conclusion).
