Around 1905 or 1906, Sigmund Freud wrote an essay, unpublished in his lifetime, called “Psychopathic Characters on the Stage.” The essay addressed the question of what we, as spectators, get out of watching people go crazy. Freud’s theory was that we’re fascinated by crazy characters because they help us express our own repressed impulses. Drama, of course, can’t express our fantasies too literally; when that happens, we call it pornography and walk out of the theatre. Instead, a good playwright maneuvers our desires into the light using a mixture of titillation and censure, fantasy and irony, obscenity and euphemism, daring and reproach. A good play, Freud wrote, provokes “not merely an enjoyment of the liberation but a resistance to it as well.” That resistance is key. It lets us enjoy our desires without quite admitting that they’re ours.

“Hamlet,” Freud thought, best exemplified the appeal of managed self-expression. Watching “Hamlet,” we think that it’s about revenge—a familiar, safe subject. In fact, “Hamlet” is about desire. The real engine of the play is Oedipal. Caught up in Hamlet’s quest to kill Claudius—and reassured by his self-censure—we can safely, and perhaps unconsciously, explore those desires. Freud thought that prudery and denial had for centuries prevented critics from acknowledging the play’s propulsive undercurrent, which, he believed, the new psychoanalytic vocabulary made it possible to acknowledge. “The conflict in ‘Hamlet’ is so effectively concealed,” he wrote, “that it was left to me to unearth it.”

Freud’s hilarious (and no doubt self-conscious) boast is doubly resonant in “Stay, Illusion!,” the thoughtful, fascinating, and difficult new book about “Hamlet,” by Simon Critchley and Jamieson Webster. Critchley, a philosopher at the New School, and Webster, a psychoanalyst, can’t help but thrill to Freud’s “delightfully arrogant assertion”: they are, after all, writing a book about “Hamlet,” and you only do that if you believe that nearly every great thinker in Western literature has gotten it wrong. At the same time, they resist the idea that “the Oedipus complex provides the definitive interpretation of ‘Hamlet.’ ” Critchley and Webster, a married couple, have clearly been conducting a long-running two-person seminar on “Hamlet.” They call their book the “late-flowering fruit of a shared obsession.” Their book convenes a sort of literary-philosophical-psychoanalytic roundtable—featuring Hegel, Nietzsche, Benjamin, Joyce, and Lacan, among others—to question Freud’s interpretation.

Desire and its repression, they conclude, might be too small a frame for “Hamlet.” It’s better to think about the play in terms of love and its internal contradictions. They argue that we tell the story wrong when we say that Freud used the idea of the Oedipus complex to understand “Hamlet.” In fact, it was the other way around: “Hamlet” helped Freud understand, and perhaps even invent, psychoanalysis. The Oedipus complex is a misnomer. It should be called the Hamlet complex.

Critchley and Webster are proud as well as nervous about the fact that they’re “outsiders to the world of Shakespeare criticism.” “What is staged in ‘Hamlet,’ ” they write, “touches very close to the experience of being a psychoanalyst, that is, someone who has to listen to patients day after day, hour after hour.” Rather than get caught up in the “game of scholarship and interpretation,” their plan is to “cup [their] ear”—that is, to attend to and elaborate on the themes that the play obsesses about. Nothingness is one of those themes; it comes up over and over in the text of the play. (Ophelia to Hamlet: “You are naught, you are naught.” Hamlet to himself: “How weary, stale, flat, and unprofitable / Seem to me all the uses of this world!”) Is “Hamlet,” they wonder, “a nihilist drama”? Love or, more accurately, the failure to love is also a theme. Shame is another. (“For us,” they write, “at its deepest, this is a play about shame.”)

Accounting for the action of the play, to most people, means accounting for Hamlet’s famous “delay” in killing Claudius. (This delay was Shakespeare’s big innovation when he wrote his own version of the already extant Hamlet story: in earlier versions, Hamlet either flew swiftly to his revenge or spent a long time meticulously planning it.) Broadly speaking, there have been two explanations for the delay. The first is that Hamlet waits because he is a sane person in an insane world. To begin with, he is unsure about trusting the ghost and must stage “The Mouse-Trap,” the play within the play, to verify Claudius’s guilt. Then, later, Hamlet must confront his own thoughtful, nonviolent nature. After Hamlet tells Ophelia, “Get thee to a nunnery!,” she rebukes him this way:

O, what a noble mind is here o’erthrown!

The courtier’s, soldier’s, scholar’s, eye, tongue, sword,

Th’expentency and rose of the fair state,

The glass of fashion and the mould of form,

Th’observ’d of all observers, quite, quite down!

Hamlet, in other words, is a well-rounded person; to kill Claudius, he has to narrow himself into a kind of action hero. That requires time and psychic work. Taken to its logical conclusion, this reading of “Hamlet” suggests that the word “delay” actually does him a disservice. What sane person, finding himself in Hamlet’s position, wouldn’t delay? Perhaps there’s something a little unhinged about the whole problem. In the nineties, in a brilliant essay called “Hamlet’s Dull Revenge,” the writer René Girard faulted critics for writing as though “no more was needed than some ghost to ask for it, and the average professor of literature would massacre his entire household without batting an eyelash.” Our response to “Hamlet,” he thought, said more about our bloodlust (and about the roots of theatre in religious sacrifice) than it did about Shakespeare. Some critics have brought gender into the discussion: most “Hamlet” criticism has been written by men, and perhaps they’ve yearned for a manly, decisive killer-hero.

Webster and Critchley recoil from this line of argument. They incline toward the Freudian reading of “Hamlet,” which holds that Hamlet delays because he feels guilty. Hamlet’s problem, they argue, isn’t really that he’s hesitant about violence. Rather, it’s that the possibility of being violent fills him with shame. In “Hamlet,” they write, shame is pervasive; it has settled on Elsinore like a fog. For Freud, Hamlet’s shame has to do with his Oedipal desires. But for Webster and Critchley it’s more abstract. It has to do with the shame of needing to love, the shame about the emptiness that, they hold, is at the center of the experience of love.

The idea of love as something tied to emptiness or nothingness is central to psychoanalysis. Often, Webster and Critchley write, we’re inclined to think of love as the opposite of emptiness—we see it as “a system of mutual favors” that acts as a kind of bonus to life, a surplus. Instead, we love because we lack. Inside each of us there’s an emptiness, and that emptiness can never be filled. None of us can ever be loved enough—by our parents, by our children, by our husbands or wives. The bottomlessness of our need for love means that, even in our most stable, permanent, and healthy relationships, love “can only be renewed and invented anew, again and again. I love you. I love you. I love you.” Each time you declare your love, you admit that there’s a lack in yourself. And when two people are in love with one another, they’re offering up their equivalent emptinesses. When love works, it makes something out of nothing.