When I am dead, compassionate hands will throw me over the railing; my tomb will be the unfathomable air . . . 

The narrator understands that he is close to death, and he wants to create a history of the Library before he dies. He knows that, due to the make-up of his universe, there is a necessary way that his body will be disposed of. In this universe, his body will fall, decaying and dissolving into dust during the fall, since the fall will be endless. There is no concern about this future, just acknowledgement and acceptance. Presumably he has both seen this happen, as well as been told about the process. This knowledge urges him to create the document he does.

Infidels claim that the rule in the Library is not “sense,” but “non-sense,” and that “rationality” (even humble, pure coincidence) is an almost miraculous exception.

By calling those that doubt the sense of the Library “infidels,” the narrator reveals himself to be a true believer in the mysterious ways of the Library. Even as he presents the disparate ways that people use the Library and the various machinations of the Library itself, he is one of those who have spent their lives believing that the Library can provide the answers they seek, if only they can find the correct tome. In his insistence that there must be some rationale behind the existence of the Library, he illustrates the difference between those that can believe in something they cannot grasp and those who cannot. He cannot understand those who refuse to believe in the Library, even as he lays out all the ways that the Library resists understanding.