The Purloined Letter: a note on what's missing

I was enjoying the luxury of meditation, in profound silence; intently and exclusively occupied with mentally discussing certain topics which had formed matter for conversation at an earlier period of the evening; I had been sitting in the dark, and now arose for the purpose of lighting a lamp, but sat down again, without doing so, requiring reflection to better purpose in the dark. That the difficulty now, I hope, is very simple indeed, and I can manage it sufficiently well; but I thought the details of it odd. Simple and odd, and not exactly that, either. The very simplicity of the thing which puts at fault such an idea. And what, after all, is the matter on hand?

The above is extracted from the opening to "The Purloined Letter", steganographically (i.e. by process of elimination, preserving word order); I had thought to devise a full first-person narrative in this manner but found that task too difficult, so it will serve instead to introduce consideration of an aspect of this short story (my favorite) which I have not seen remarked upon.

There's a hole in the story, but not the one that the critical commentary I've seen addresses (taken in by the nullity that is the contents of the letter). Instead, I mean a hole in the logic, something said which is contradicted by something left unsaid. Dupin's reasoning seems perfect, but one extrapolation appears to be unwarranted, at odds with everything that led up to it:

" [...] But I had an object apart from these considerations. You know my political prepossessions. In this matter, I act as a partisan of the lady concerned. For eighteen months the Minister has had her in his power. She has now him in hers; since, being unaware that the letter is not in his possession, he will proceed with his exactions as if it was. Thus will he inevitably commit himself, at once, to his political destruction. His downfall, too, will not be more precipitate than awkward. [...]"

Contexting this (renowned verbifier Alexander Haig's abusage), the letter came into the Minister's possession in full view of the lady concerned, and his knowledge of her knowledge of this conferred its power. But the repossession of the letter, unbeknownst to the Minister, is not accompanied with the information that the Minister remains in the dark about its loss:

"In that case," replied Dupin, opening a drawer, and producing a check-book, "you may as well fill me up a check for the amount mentioned. When you have signed it, I will hand you the letter."

I was astounded. The Prefect appeared absolutely thunderstricken. For some minutes he remained speechless and motionless, less, looking incredulously at my friend with open mouth, and eyes that seemed starting from their sockets; then, apparently in some measure, he seized a pen, and after several pauses and vacant stares, finally filled up and signed a check for fifty thousand francs, and handed it across the table to Dupin. The latter examined it carefully and deposited it in his pocket-book; then, unlocking an escritoire, took thence a letter and gave it to the Prefect. This functionary grasped it in a perfect agony of joy, opened it with a trembling hand, cast a rapid glance at its contents, and then, scrambling and struggling to the door, rushed at length unceremoniously from the room and from the house, without having uttered a syllable since Dupin had requested him to fill up the check.

When he had gone, my friend entered into some explanations.

So the Prefect departs without any notion that the Minister still believes himself in possession of the letter; the Prefect, and by extension that exalted personage for whom he is agent, does not know that the Minister does not know. The question is, who will first discover this state of affairs? Every indication would seem to favor the Minister in this regard: his powers of discernment already having been demonstrated in the original theft, supported by the digression on games (an identification of the reasoner's intellect with that of his opponent. [...] And the identification [...] of the reasoner's intellect with that of his opponent, depends, if I understand you aright upon the accuracy with which the opponent's intellect is admeasured. [NB: I particularly like the interpolation of "if I understand you aright"]) and the following adumbration of the false duality between poet and mathematician (with another nice touch: Bryant, in his very learned 'Mythology,' mentions an analogous source of error, when he says that 'although the Pagan fables are not believed, yet we forget ourselves continually, and make inferences from them as existing realities.'). The repossession of the letter will change the behavior of both the Prefect and of the exalted lady in response to and even prior to any attempted continued usage of the Minister's supposed but now non-existent power. The Prefect's diligence in tracking the Minister will relent; any subsequent audience with the lady will evince changed circumstances by her newly-found confidence in dealings with the Minister. So Dupin's supposition that the Minister "will proceed with his exactions" is flawed, and so too the consequent "political destruction ... not ... more precipitate than awkward." While this course of events is indeed possible, it presupposes an unlikely blind spot in the Minister's dealings, and suggests a blind spot in Dupin's. But I do not think that this is a point that Poe overlooked in his composition of this tale, but rather something hidden in plain view for the astute reader (who, me?) to discover.