Before we begin, we'd just like to ask: does the name of this group scare the pants of anyone else? Because seriously… nightmares.
The Organization of Apocryphal Power (ah!) was originally founded by Ermes Marana, but it later ousted him and broke off into two rival sects. Both of these sects run around the world stealing manuscripts in hopes of finding a final, ultimate book that will prove that it is on the right side of truth. Here's where each side stands:
(1) The "Archangel of Light" group believes that it can sift through all the counterfeit and crummy books of the world and finally find "a few that bear a truth perhaps extrahuman or extraterrestrial" (11.40). Basically, they're saying that the truth is out there. And it's out there in a book.
(2) The "Archon of Shadow" group is made up of nihilists who "believe that only counterfeiting, mystification, intentional falsehood can represent absolute value in a book" (11.40). Basically, they're saying that you can't find truth in a book, because truth only emerges out of confusion and endless uncertainty.
From Calvino's standpoint, both sides are too extreme. And like Lotaria, they fail as readers because they're too caught up in the set agendas they bring to reading.