Woody Allen plays “drop that name” in “Irrational Man,” a brittle tragicomedy mimicking Dostoevsky that manages to run briskly through a catalogue of philosophers before settling on Sartre and existentialism as the key to a plot more reminiscent of “Columbo” than Hitchcock. Allen’s script would be an impressive display of erudition for a college sophomore, but it certainly doesn’t cut very deep—the way “Blue Jasmine,” for example, did—and the lackadaisical construction and direction leave its attempts at tension feeling feeble indeed.

The plot revolves around Abe Lucas (Joachin Phoenix), a noted philosophy professor, specializing in situational ethics, who arrives for a summer session at Braylin, a small liberal-arts college in Rhode Island. Rumors swirl around him even before he arrives on campus. Though he’s acknowledged as a brilliant scholar by all, he’s said to be an alcoholic rogue who preys on his students, or a man devastated by the loss of his wife to a close friend, or one grief-stricken over the death of a buddy in the Middle East—or all (or none) of the above. What’s immediately clear is that Lucas does drink heavily, and is depressed and remote. It emerges that he can’t perform sexually, and is suffering from writer’s block in trying to complete a book on Heidegger’s Nazi ties. At one student party he’ll even go so far as to demonstrate the meaning of Russian roulette by aiming a loaded gun at his temple and clicking the trigger. And at least from this quarter, his classroom presentations on individual thinkers come across as pretty rudimentary.

One aspect of the rumor mill does prove true, however, at least as two people are concerned—his attractiveness to women. Faculty wife Rita Richards (Parker Posey) throws herself at him, wanting an affair that could lead to their running off together. And student Jill Pollard (Emma Stone), whose work he praises as showing genuine promise, quickly grows infatuated, enthusing about him so endlessly that her nice, tolerant boyfriend Roy (Jamie Blackley) becomes increasingly irritated. Initially Lucas resists getting involved with either, but eventually he succumbs to Rita’s advances (it’s during their first night together that his incapacity in bed is revealed) and spends more and more time with Jill, disclosing to her his profound disappointment that all his past efforts to make the world a better place through activism and service have had no effect, leading to the glum conclusion that no one can make a difference. He’s one of those academics who, after years of grappling with matters of principle, suffers a mid-life crisis when he concludes that it’s all a waste of time.

But Abe’s attitude changes when he and Jill overhear a woman talking about a legal case in which she might lose custody of her children because the judge appears to be unfairly siding with her ex-husband. It’s this incident that spurs Lucas to intervene in order to rectify an injustice, and thereby infuse his life with purpose again. He plans the perfect murder of the judge, for which he could never be suspected as he would have absolutely no motive (shades of “Strangers on a Train,” though without the quid-pro-quo). He goes through with it, finding personal rejuvenation in the very decision to make a choice and act on it.

Abe’s euphoria is clearly based on the existentialist notion that it’s the very act of choosing that defines us—and it links up with Dostoevsky’s “Notes from the Underground,” in which one finds the proposition that it isn’t rational choice, but choice itself, whether for good or ill, that’s important. The murder also automatically calls to mind “Crime and Punishment,” which indicates the course the plot might take, especially if Allen added some mordant humor to the mix. (Nabokov, after all, who was no admirer of Dostoevsky, derided the novel as “Crime and Pun”—an idea that Allen might have taken to heart.)

But Woody doesn’t go there. Instead Lucas remains one of those arrogant villains familiar from Peter Falk’s old detective series. We know he’s guilty, but he appears untouchable, and he gloats over his success—and the positive turn his life has taken. Of course, his “perfect” murder turns out not to have been perfect at all, and Jill becomes increasingly suspicious of him as a result of what can only be termed bits of dumb luck. He appears willing to confess to the crime when an innocent person is arrested for it, but that’s just a ruse to lull Jill into a false sense of security while he makes other arrangements. After all, as Agatha Christie often pointed out, murder is easy after you commit the first one. Or is it? Allen ties things up with a jokey twist-of-fate resolution that’s really little more than a cheap parlor trick so effortful in its execution that it ends the picture with a dull thud.

If Allen’s script is weak in all departments—including dialogue that’s unremittingly stilted—and his direction prosaic, however, Phoenix manages to transcend the auteur’s failings with a performance that’s more nuanced and thoughtful than the character he’s playing. Stone, by contrast, is unremarkable, and Posey’s fluttery ditziness has seldom seemed broader. The rest of the cast do what’s expected of them without adding much to the page, but visually the movie is quite attractive, with cinematographer Darius Khondji making good use of the campus of Salve Regina University and the surrounding Newport area.

“Irrational Man” isn’t one of Allen’s worst films—it’s breezy though inconsequential, and generally holds your interest. But it’s intellectually shallow despite rather show-offish attempts to appear philosophically sophisticated in dealing with ethical issues.