“A house divided against itself cannot stand,” Abraham Lincoln declared in his 1858 speech presaging the Civil War. Such a house sits at the heart of Mat Johnson’s ribald, incisive novel “Loving Day.” Bequeathed to the narrator, Warren Duffy, by his deceased father, it’s a roofless, ramshackle mansion in a black neighborhood in Philadelphia: “I look at the buckling floors. I look at the cracks in all the walls, the evidence of a foundation crumbling beneath us. I smell the char of the fire, the sweet reek of mold, the insult of mouse urine. I see a million things that have to be fixed, restored, corrected, each one impossible and each task mandatory for me to escape again.”

The house is haunted. There are ghosts, mostly of neighborhood crackheads — that is, if we take Warren’s word for it; our narrator’s psyche is as wrecked as his inheritance. An “inept” comic book artist — “My work is too realistic, too sober” — he has moved back to America from Wales after a failed business and broken marriage. He’s wrecked, too, by his liminal ­racial status: His father was an Irishman, his mother was black and he comfortably claims neither — call him a man divided against himself. “I am a racial optical illusion,” he says.

Warren lives and breathes what W. E. B. Du Bois called double consciousness, by which the American black person is “always looking at one’s self through the eyes of others. . . . One ever feels his two-ness, — an American, a Negro; two souls, two thoughts, two unreconciled strivings; two warring ideals in one dark body.” Except Warren’s body is white, making things even thornier; he’s perpetually performing a black identity that isn’t written all over his face — as when he describes “letting my black voice come out, to compensate for my ambiguous appearance. Let the bass take over my tongue. Let the South of Mom’s ancestry inform the rhythm of my words in a way few white men could pull off.”

In “Loving Day,” Johnson, author of the graphic novel “Incognegro” and the novel “Pym,” delivers an extended literary metaphor about race and mixed-race in America. It’s a semi-autobiographical one — he has called the book “my coming out as a mulatto” — that can at times feel belabored, but the novel ultimately triumphs because it is razor-sharp, sci-fi-flavored satire in the vein of George Schuyler, playfully evocative of black folklore à la Joel Chandler Harris — yet it never feels like a cold theoretical exercise. “Loving Day” is that rare mélange: cerebral comedy with pathos.