In tragedies, of course, bad things happen, and, what is more, they happen to good people, even if those good people are flawed. If everybody got what they deserved, it wouldn't be a tragedy; what makes a tragedy is that little cracks in character, or situation, or the like, end up ruining or destroying people who don't deserve it. Thus tragedies naturally evoke sympathetic suffering (pity) or fear, or at least something like these things. Thus we have the puzzle: the exquisite delight of tragedy comes from suffering and fear due to vivid imagination of destructive or painful evil. Hence the paradox. To some extent, of course, an analogue of this paradox is found with all kinds of fictions: people delight in reading, or watching, bad things happen to people in all sorts of stories. But in tragedy it finds its baldest form. Great tragedies are readable and watchable because they make our hearts ache and our consciences tremble. They are just short of more than we can bear.
Perhaps because it has had so much attention over so many centuries, the available responses to the paradox are much more complicated and permeable than we find with the paradox of fiction. Rather than think of positions one might take with respect to the paradox, it's perhaps best to divide the field by two criteria: first, by whether a position denies any part of the paradox; and second, for those who accept all the parts of the paradox, what means they might use to explain it.
Relatively few people reject any element of the paradox. At first glance, it seems quite obvious that people at least often delight in tragedies, that this delight is at least often tied to sympathetic feelings of suffering and fear, and that sympathetic feelings of suffering and fear are often very un-delightful outside of the context of tragedy. But one could take a deflationary position to this, and argue that either we don't feel anything in response to tragic literature and drama or that we don't actually have any particular aversion to the feelings of pity and fear. The only way to make much sense of the first is if we don't, in fact, feel anything in response to literature and drama generally; and, indeed, almost the only arguments I have ever seen for this option assume a pretend theory of fiction, like Walton's theory of quasi-emotions. It still leaves the puzzle of why we enjoy pretending to suffer and fear sympathetically, but if we don't actually pity or fear in response to Oedipus, it does take some bite out of the paradox. As for the second, it is more interesting, and has in its favor the fact that, as spectators, at least, human beings often do seem to take an active interest in bad happenings, to which they arguably are not necessarily averse: people gawking at a car crash, for instance. This approach is arguably a little disturbing, but there may be something to it.
More often, however, people have accepted the basic elements of the paradox, and thus are committed to saying that it is paradoxical but true. And then, of course, the task is to determine why this combination of elements that seems puzzling actually makes sense in some way. A number of different tools in the toolbox have been proposed for this.
(1) We have what could be called the classical or (perhaps less misleadingly in most cases) neo-classical instruments for explaining the paradox. These are usually traced back to Aristotle, but receive their full development as answers to the paradox of tragedy in particular during early modern classicism. They basically come down to mimesis, catharsis, and wonder (with catharsis being most appealed to and wonder being least appealed to). (a) As rational animals we have a natural delight in good representations or imitations (which is what 'mimesis' means); good tragedies are good representations. (b) It's difficult to pin down what catharsis is supposed to be (Aristotle uses the word only once), but we do have some basic outlines, and different theories of catharsis have tended to build on them. Aristotle tells us that tragedy arouses pity and fear in order to cleanse them. By this we could mean that tragic drama makes us less susceptible to pity and fear by removing (purging) them. Or we could mean that tragic drama purifies pity and fear so that they are more noble and no longer tainted by baser desires. The word could be intended to suggest either, and both of these have been assumed at various times. (c) Despite its importance for neo-classical approaches to tragedy, catharsis does not play a major role in Aristotle's account of tragedy. The real work in Aristotle's account, and what he perhaps proposes catharsis as preparatory for, is thaumaston, which is wonder in something like both senses of the English word: wondering about and wondering at. When we compliment a literary work or movie or play by saying, after having experienced it, 'That is astounding; it really makes you think', that's along the general lines of what Aristotle is getting at. Wonder is on Aristotle's account the aim of poetic art in general, of which tragic art is one species; in which case it would make sense to think of tragic art as art that produces wonder by way of pity and fear. Aristotle certainly thinks that there is a connection among pity, fear, and wonder: the things that most cause wonder are often things that could also easily cause pity and fear. Wonder itself, however, is something very suitable to us as rational animals and out of which we draw many benefits. And later discussions of the sublime will tend to build on similar connections between pity and fear on the one hand and the sublime on the other, so that accounts on which catharsis is a sort of sublimation into something higher are perhaps variants of this appeal to wonder.
(2) The influence of neo-classical discussions of tragedy cannot be underestimated. But other means of making sense of the paradoxical nature of tragedy have been proposed. Far and away the most important of these is conversion, and the most influential account of conversion is found in Hume's important discussion of the paradox of tragedy in Of Tragedy. The basic idea behind conversionary theories is the recognition that identifying the psychological regularities in play in tragic spectatorship holds some promise for making sense of the paradox by giving an explanation of how the normally unpleasant could be converted into something pleasant. Hume denies that we enjoy the pity and fear induced by tragic drama; he builds on Fontenelle's suggestion "that the movement of pleasure, pushed a little too far, becomes pain; and that the movement of pain, a little moderated, becomes pleasure." Hume attempts to undergird his account by showing that this sort of process is actually quite common. Plenty of passions give force to opposing passions: novelty is pleasant, but it can add its force to the shock of unpleasant passions; curiosity, jealousy, and our response to challenges and trials provide additional examples. What is most distinctively Humean, however, is the notion that in tragedy this conversion is affected by eloquence:
The genius required to paint objects in a lively manner, the art employed in collecting all the pathetic circumstances, the judgment displayed in disposing them: the exercise, I say, of these noble talents, together with the force of expression and beauty of oratorial numbers, diffuse the highest satisfaction on the audience, and excite the most delightful movements. By this means, the uneasiness of the melancholy passions is not only overpowered and effaced by something stronger of an opposite kind, but the whole impulse of those passions is converted into pleasure, and swells the delight which the eloquence raises in us.
That is, our feelings of pity and fear in watching a good tragedy have a context. This context is one of great poetry and narrative art, which is itself pleasing. In this context, we not only barely feel the pain of sorrow, indignation, and the like, but their very force and impulse is itself transferred to the pleasure we take in the eloquent context. To this Hume adds the neo-classical point that imitation is itself agreeable. And with these three elements: conversion, eloquence, and mimesis, we have the full Humean account. Hume does insist, however, that our passions are not infinitely malleable: some things are so awful that even the best eloquence cannot do much to soften them.
And this is perhaps a weakness in Hume's own account. Hume notes that the popular fashion on the English stage of his time was very violent and bloody tragedy -- shock drama. And as we know in our day, some people have an astounding appetite for torture films. As Hume would have it, these things should not be pleasant -- but this seems difficult to square with their popularity. What is more, given the role played by eloquence, it is difficult to see how one could take pleasure in badly written tragedies. But some people apparently seem to do so.
One advantage of conversion is that it does seem to have many analogues. Consider the paradox of chili peppers: chili peppers irritate the mouth; people don't like things that irritate the mouth (irritation in the mouth is unpleasant); people really like chili peppers. (We could run a similar line with allergen addictions.) Why? Well, the conversion theorist could have a fairly plausible answer: the irritation is giving force to the pleasure that arises from the body's attempt to respond to the irritation. And thus people who really like chili peppers, like them the hotter (i.e., the more irritating) they are. Really intense tragedies are, so to speak, the habenero or bhut jolokia or naga viper chilis of art: the pain gives force to the pleasure.
(3) More recently people have proposed the use of additional tools for making sense of the paradox. There are several of these, but four are perhaps especially notable.
(a) control: Control theorists hold that the key difference between bad happenings in tragedy and bad happenings in real-life is that we have complete control over the former: you can walk out of the theater, you can put the book down. In this sense, the pleasure of tragedy is analogous to what some people see as the explanation for the pleasure some tkae in rape fantasies, or indeed in a lot of other fantasies, sexual and otherwise. It's not that they like the object of fantasy but that they like the intense stir of the emotion to the extent that they themselves are in control of the stirring. Of course, on its own it seems to leave something of the paradox untouched: yes, control can affect one's pleasure in things, but why would one find tragic events, or fantasies of being raped, or any such thing at all, with or without control?
A variant of control theory appeals to power, arguing that what we like about tragedy is that it offers an occasion to express our power over ourselves by giving us either a reminder of our own ability to endure or by giving us an opportunity to overcome fear and pity.
(b) compensation: One could hold that we enjoy tragic unpleasantness as a means to an end: that is, we get some good out of it that, while not making the unpleasantness any less unpleasant, makes the overall experience good. There are lots of things in a tragedy we can take pleasure in: its craft and eloquence, its intricacy, its plausibility, its moral tone. The compensation theorist holds that we are attracted to tragedy despite the unpleasantness because so many other features are pleasant.
(c) meta-response: Meta-response theorists like Susan Feagin try to go up one level, as you migth expect from the 'meta' part. We do not find tragic events, tragic sorrow, or tragic fear pleasant; rather, what we find pleasant is our response to our tragic sorrow and tragic fear. We like tragedy not because pity and fear are pleasant but because by feeling pity and fear we are the sort of people we like -- in particular, that we are the sort of people who have the kind of sympathy that lets us experience negative feelings when bad things happen to others. In addition, we can take pleasure in being united in sympathy with other good people in disliking bad things. Feagin suggests that one advantage of this approach is that it shows why tragedy depends to be regarded as far more important and valuable than comedy: tragedy deals directly with matters of high moral concern. And, indeed, this was an original point of ancient Greek and Roman accounts of tragedy that sometimes has been lost in later discussions.
(d) rich experience: Rich experience theorists (Aaron Smuts has a number of good discussions of the theory) are interesting in that they tend to buck the major feature of most modern approaches to the paradox of tragedy. Most modern approaches, going back to the early modern period, see the paradox as one in which we need to explain how the unpleasant seems so pleasant. Rich experience theorists tend to see this as a red herring. We are not attracted to tragedy because it is pleasant. To be sure, the rich experience theorist is not going to deny that many things about a good tragedy will give you pleasure, nor that you might experience pleasure as a result of watching or reading something tragic. What they will say is that this is not the attractive thing about tragedy, which at root always deals with the unpleasant -- tragedy, horror, and the like are 'painful arts'. Rather, what is attractive about tragedy is that it is enriching: sitting through a tragedy, your experience of life is enriched. Faced with Oedipus Rex, or Antigone, or The Bacchae, or, indeed, even just a half-way decent horror flick, you in some sense grow as a person, have had a life of richer experience, and at relatively little cost to you. Cowper once referred to reading as armchair travelling: he, suffering from crippling depressions, could not go out into the world, but he could fight off sharks and discover new lands by reading. And, while there very different ways a rich experience theorist can go, the rich experience is building on something analogous in the discussion of 'painful art'. In effect, rich experience theorists deny that we are motivated only by pleasure: we also value a richness of life, and are willing to risk some pleasures (within limits) and experience some pains (within limits) to have it. It's a tricky point to grasp, because we tend to slide easily back into the modern assumptions that if we pursue something we find it pleasant and that it is puzzling for us to pursue something painful. But it's a very interesting suggestion.
One of the difficulties raised by the paradox of tragedy is the very diversity of possible responses. Every single one of the above suggestions is a plausible contributing factor to our pleasure in tragedy. This is why, in fact, the neo-classical and Humean approaches appeal to more than one: they are not merely interested in explaining the bare fact of enjoyment of tragedy, but in explaining the full character of our enjoyment. But, of course, accepting one, or even accepting them all, doesn't deal with the paradox. For it is entirely possible for something to increase our enjoyment of a tragedy without thereby explaining why we enjoy tragedy at all. It's this latter that needs to be addressed to make sense of the paradox; and giving a solid argument that a given contributing factor is foundational in this way is the hard part.
For my own part, I think it's fairly clear that all of the non-deflationary suggestions above have some effect on our enjoyment of tragedy. Of the deflationary approaches, I think the suggestion that we actually like (some kinds of) unpleasant things turns out to be surprisingly plausible in comparison with the suggestion that we don't have emotional responses to tragic fiction, and, indeed, it is very likely that some enjoyment of tragedy is affected to some degree by this sort of perversity. For the paradox itself, I tend to think that the neo-classical approach was on the right track, that the rich experience and meta-response approaches are recovering something important that was lost, and that the others are all merely supplementary. But what do you think?