Another [book] (much consulted in this zone) is a mere labyrinth of letters whose penultimate page contains the phrase O Time thy pyramids.

Many of those who live in the Library spend their lives looking for books that make sense. When they find one that has even a modicum of legibility, it is held up as proof of a rationality at work. That this book contains an understandable phrase does not necessarily mean anything. It is one of an endless recombination of spaces and letters that happens to be able to be read. The phrase itself means nothing, but it provides someone looking for it a moment of recognition.

But those who went in quest of [the Vindications] failed to recall that the chance of a man’s finding his own Vindication, or some perfidious version of his own, can be calculated to be zero.

Someone in the past hypothesized that the Library contained every book. Many of those who heard that idea converted it into a search for the books that would contain stories about themselves. They believed that they could find justifications for their decisions and their choices, as well as books that would tell them about their futures. That search would be, for all intents and purposes, fruitless. The likelihood of finding a book about yourself, in the endless tomes of the Library, is basically nonexistent.

That reading, that justification of the words’ order and existence, is itself verbal and, ex hypothesi, already contained somewhere in the Library.

The narrator believes in the Library as a positive force. Therefore, in his mind, even seemingly nonsensical strings of letters, like “dhcmrlchtdj” are not irrational. The explanation for them exists somewhere in the library, since the Library holds every combination of words that can be written. One must only be lucky enough to come across the book containing it. This insistence is a core tenet of the narrator’s belief in the structure and rationality of the Library, despite evidence to the contrary.

I repeat: In order for a book to exist, it is sufficient that it be possible. Only the impossible is excluded.

This quote is part of a footnote attempting to explain some logical foundation of the Library. For a book to be included in the Library, it must be possible to exist. The example given is that “no book is also a staircase,” since that is an impossibility. However, any number of books about staircases, or arguing for or against the existence of staircases, can presumably be found within the shelves of the Library. This footnote illustrates the logical guardrails needed to conceptualize the seemingly unfathomable Library.