Fundamental to the predicament of the narrator of The Third Policeman is his lack of name, of living parentage, of acknowledged public identity, and of means adequate to order his mystifying experiences. The fantastic qualities of his environment, and his marginal status as suspected murderer now unrecognized in his hometown, contribute to his profound alienation and growing anxiety. In a reversal of ordinary continuities, the conventional dimension of this character is his soul, Joe, who in this afterlife has a name and evident comfort in his surroundings. While Joe exhibits an unshaken confidence in common sense, the narrator desperately adopts implausible identities such as the definitive annotator of the de Selby codex, an Italian soprano, and a gallant suitor of an ardent bicycle. All of his identities are adopted as a matter of literary style, a function integral to his role as literary narrator, and all fail miserably as defenses against personal chaos.
The policemen suffer no such anxiety. They are unsurprised by incomprehensible developments, and they remain happy in their devotion to even more absurd preoccupations. Sergeant Pluck stands guard against local crime, ordinarily limited to the offense of riding a bicycle without a headlamp. Policeman MacCruiskeen is the contented inventor of nesting Chinese boxes (all the way down to molecular scale) and spears so keen that their points are invisible. Fox, the third to appear and the one essential to the narrator’s cyclic conclusion, wields a mysterious substance called omnium. In complete harmony with this nightmarish milieu, these policemen control their precinct by authoritatively charting meaningless statistics and spinning knobs on inexplicable but impressive contraptions.