As titles go, “Conscience” is a burdensome one. It sounds blandly moralistic, but Alice Mattison’s new novel wrestles with the irreducibly complex demands of having a conscience in an age of political depravity. Given the moral idiocy that’s infected Washington, her theme couldn’t feel more pertinent. But this novel also looks back to the crisis of a previous era and reflects on how time recalibrates our decisions.

The story comes to us in chapters narrated in confessional tones by three people. The central one is Olive, a white writer and editor in New Haven, Conn. “Paying close attention to my own history,” she tells us, “leads to trouble, confusion, and anxiety,” and then she proceeds to pay close attention to her own history with all the trouble, confusion and anxiety she predicted. Her reminiscence is sparked by an assignment to write an appreciation of a novel from the Vietnam War era. Olive knew both the author and the woman at the center of that novel; they were all friends together in school. They were once, briefly, famous.

The second narrator is Olive’s African-American husband, Griff. The son of a preacher, Griff is a high school administrator and a man of exacting principles, which once complicated his own involvement in the anti-war movement. He knew Olive’s friends, and he still feels haunted by actions he took long ago. But now his work makes him less susceptible to the pains of reminiscence. In addition to his school job, he’s the chairman of a homeless shelter, an endeavor that constantly confronts him with the cruel moral calculus of social work in our age of suspicion and scarcity.

The director of that homeless shelter is Jean, the third of these rotating narrators. She’s a divorced woman determined to meet the needs of her clients, desperate people who always require more food, more space, more attention. But her staff is limited, and her board, chaired by Griff, is frustratingly cautious about taking on additional responsibilities and risks.

If all this sounds complex, it is, but only in the same way that our own lives are complex: routines periodically interrupted by emergencies, laced with unresolved issues dragged along from the past. Mattison makes few concessions to the streamlining demands of fiction. Her story spills out across these lives, re-creating on the page the challenge of finding focus and divining some wire of meaning in the jumbled collection of our interactions and experiences. Olive, in particular, shifts constantly among the details of her work and her failing marriage and the painful feelings dredged up by remembering her old friends fighting against the war.

“It’s hard, decades later, to remember how things felt at that time,” she says, “how weary we were and yet how excited about the possibility of big change — of revolution.” Indeed, the best sections of “Conscience” involve Olive’s struggle to recall those febrile years: all the excitement of sexual liberation tangled up with the life-and-death effort of protest. “Being preoccupied by the war,” she remembers, “was something like having such a bad cold that you didn’t care what happened to your life.”

But Olive did care what happened to her life. As a dutiful student, she was self-conscious about her muted fervency: Faced with such horrors as My Lai, how much resistance is enough? Olive kept up with her classes while affecting the right attitudes and attending the right meetings, but she felt a growing distance between herself and her best friend, a passionate young woman drawn toward greater despair and more violent acts of resistance.

Now, as a professional writer — a biographer, no less — Olive is sophisticated enough to know how memories calcify into fantastical shapes that have only a tenuous relationship to what we actually did, said and felt. As she reconsiders her friend’s celebrated book about the Vietnam era, “Conscience” offers a thoughtful reflection on who gets to curate history and what responsibility we have — if any — to our loved ones’ myths.

The result is a big, messy novel of ideas encompassing more subplots involving racial tensions, sexual betrayal, shifting standards of privacy and the rights of the homeless. Some readers may find this story as inviting as a ball of tangled yarn, but “Conscience” will please those who complain that so much literary fiction is a little too neat, ironical or even adolescent. Indeed, Mattison never hesitates to let her characters worry away at what’s troubling them, cycling back over their own shame and others’ slights in a way that seems wholly, sometimes maddenly, realistic.

But the real triumph of this ruminative novel is that it transports us back to a period when exercising one’s conscience was a national emergency. And then Mattison slyly insists that we acknowledge the moral complexity of our own era with its own equally urgent demands.