The writer of irony here is Poe, of course, and not the narrator since the narrator appears to be entirely oblivious to the ironic component of his monologue. Or is he While convention critical analysis of "The Tell-Tale Heart" engages the story from the point of view that the narrator's attempt to prove his sanity is an exercise in irony, his clearly deluded state of mind can just as easily be interpreted as a brilliantly conceived plot to escape extreme punishment for his crime by convincing the people that he is insane when he is not.
In a sense, "The Tell-Tale Heart" contains the nugget of an idea that would be fleshed out to novel-length status in Joseph Heller's Catch-22. The catch-22 in the narrator's case is that he would clearly be sane if he attempted to prove his innocence, but if he doesn't try to prove his innocence he will most likely receive capital punishment. One of the fascinating aspects of this story is that it remains unclear to whom the narrator is addressing his appeal to be found sane. It might be the police; it is more likely a judge; the most likely consideration of all is that is the warden of the prison or even a group of people gathered to watch him hang. The question of the direction of the narration is left open to interpretation, but one thing is clear. Instead of attempting to prove his innocence, the narrator's long monologue becomes a case of trying to prove his sanity.
The lack of a concrete explanation of the person or office to which the narration is addressed leaves much room for interpretation. The only aspect with even a close approximation of certainty is that the story is not being addressed to the police officers since he mentions that they were satisfied. The climax of the story is the revelation of the dead body and the story is told as a remembrance, so the most likely estimation is that the narrator is addressing some kind of court official or personage who may influence over the judgment of the narrator. The story that the narrator is telling, therefore, is most accurately realized as an appeal for mercy rather than merely an appeal to be thought sane. After all, if the exhortations to be found sane are accepted, then the judgment cannot help but be merciless. It is only if this obsessive quest to be considered sane results in the ironic reversal of being declared insane that the narration makes any sense whatever.
"The Tell-Tale Heart" can thus be said to work on two levels of dramatic irony at once. The most obvious level of irony, the one that most readers recognize and that forms the crux of so much literary analysis, is that the narrator's obsessive devotion to proving his sanity undermines that devotion to the point that it is impossible to designate him as anything other than psychotic and at least semi-delusion. The irony in this reading of "The Tell-Tale Heart" is based upon the traditional reading that irony is produced by the contradiction of what is actually being said and what is actually meant. When a reader peers closer and brings into context the potential for whom the narrator is addressing and why he would choose to prove his sanit