The narrator notes that the library must contain all useful information, including predictions of the future, biographies of any person, and translations of every book in all languages.
The story repeats the theme of Borges' 1939 essay "The Total Library" ("La Biblioteca Total"), which in turn acknowledges the earlier development of this theme by Kurd Lasswitz in his 1901 story "The Universal Library" ("Die Universalbibliothek"): Certain examples that Aristotle attributes to Democritus and Leucippus clearly prefigure it, but its belated inventor is Gustav Theodor Fechner, and its first exponent, Kurd Lasswitz.
[...] In his book The Race with the Tortoise (Berlin, 1919), Dr Theodor Wolff suggests that it is a derivation from, or a parody of, Ramón Llull's thinking machine [...] The elements of his game are the universal orthographic symbols, not the words of a language [...] Lasswitz arrives at twenty-five symbols (twenty-two letters, the space, the period, the comma), whose recombinations and repetitions encompass everything possible to express in all languages.
In this story, the closest equivalent is the line, "A blasphemous sect suggested [...] that all men should juggle letters and symbols until they constructed, by an improbable gift of chance, these canonical books."
In The Library of Babel, Borges interpolates Italian mathematician Bonaventura Cavalieri's suggestion that any solid body could be conceptualized as the superimposition of an infinite number of planes.
The quote at the beginning of the story, "By this art you may contemplate the variation of the twenty-three letters," is from Robert Burton's 1621 The Anatomy of Melancholy.
In mainstream theories of natural language syntax, every syntactically valid utterance can be extended to produce a new, longer one, because of recursion.
Borges' narrator notes this fact, but believes that the Library is nevertheless infinite; he speculates that it repeats itself periodically, giving an eventual "order" to the "disorder" of the seemingly random arrangement of books.
Writes Quine, "The ultimate absurdity is now staring us in the face: a universal library of two volumes, one containing a single dot and the other a dash.