Act III, scene i of David Hume in the Library of Babel
The last part of Jorge Luis Borges’ short story “The Library of Babel” presents a tantalizing possibility: the existence of a literary holy grail, a master index “that is the cipher and perfect compendium of all other books”:
We also have knowledge of another superstition from that period: belief in what was termed the Book-Man. On some shelf in some hexagon, it was argued, there must exist a book that is the cipher and perfect compendium of all other books, and some librarian must have examined that book; this librarian is analogous to a god. In the language of this zone there are still vestiges of the sect that worshiped that distant librarian. Many have gone in search of Him. For a hundred years, men beat every possible path—and every path in vain. How was one to locate the idolized secret hexagon that sheltered Him? Someone proposed searching by regression: To locate book A, first consult book B, which tells where book A can be found; to locate book B, first consult book C, and so on, to infinity. . . . It is in ventures such as these that I have squandered and spent my years. I cannot think it unlikely that there is such a total book on some shelf in the universe. I pray to the unknown gods that some man—even a single man, tens of centuries ago—has perused and read that book. If the honor and wisdom and joy of such a reading are not to be my own, then let them be for others. Let heaven exist, though my own place be in hell. Let me be tortured and battered and annihilated, but let there be one instant, one creature, wherein thy enormous Library may find its justification. [ellipsis in the original; footnote omitted]
Imagine if such a book really existed. This master tome would allow us to decode all the other books in the Universal Library and thus unlock the secrets and solve the mysteries contained therein. But does this miracle book really exist, and if so, will it ever be found? Or to put this question in Humean terms, is the probability p1 of locating the Universal Library’s master index higher or lower than the probability p2 that any of the miracles reported in the New Testament Gospels of the Bible really happened? [1] Alas, given the astronomical size of the Universal Library (see, e.g., William Goldbloom Bloch, The Unimaginable Mathematics of Borges’ Library of Babel, 2008) and the historical distance between our day and Biblical times, how would we even begin to quantify these Humean probability values? To be continued …
[1] Recall Hume’s original argument against miracles (Hume 1748, Para. 13) boils down to the following probabilistic test:
When any one tells me, that he saw a dead man restored to life, I immediately consider with myself, whether it be more probable, that this person should either deceive or be deceived, or that the fact, which he relates, should really have happened. I weigh the one miracle against the other; and according to the superiority, which I discover, I pronounce my decision, and always reject the greater miracle.
In other words, first we must assign two separate probability values: one to the probability p1 that the miracle really happened; the other to the probability p2 that the evidence is either mistaken or fraudulent or otherwise defective. Next, we compare p1 and p2. We should believe in the miracle only if p1 > p2.
UNRELATED POSTSCRIPT: Paging Donald Trump: let’s make May 1st “Victims of Communism Day.”
prior probability 