Act III, scene ii of David Hume in the Library of Babel

Pictured above is a sample page from a random book in the imaginary world of Jorge Luis Borges’ short story Library of Babel. (Words that are English-sounding are highlighted for reference, though these are no more frequent than random chance predicts.) Since the text of every volume in the Universal Library is randomly generated, and since a decoder book has yet to be found, how can we find any meaning in these lines? Are they just meaningless gibberish (i.e. “non-sense”), or do they contain deep secrets waiting to be discovered? To this end, the antepenultimate paragraph of Borges’ short story begins thus:

Infidels claim that the rule in the Library is not “sense,” but “non-sense,” and that “rationality” (even humble, pure coherence) is an almost miraculous exception. They speak, I know, of “the feverish Library, whose random volumes constantly threaten to transmogrify into others, so that they affirm all things, deny all things, and confound and confuse all things, like some mad and hallucinating deity.” Those words, which not only proclaim disorder but exemplify it as well, prove, as all can see, the infidels’ deplorable taste and desperate ignorance. For while the Library contains all verbal structures, all the variations allowed by the twenty-five orthographic symbols, it includes not a single absolute piece of nonsense. [parenthetical in the original]

The reference to infidels in this passage is quite curious, for as it happens, David Hume was commonly referred to as “the Great Infidel” during his lifetime for his skeptical religious views. (See generally Rasmussen 2017.) By way of example, consider Hume’s hyper-rational argument against miracles. (Hume 1748) For Hume, “no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish ….” (Ibid., Para. 13) To put Hume’s argument in the context of Borges’ Library of Babel, which possibility is more likely: (A) that the pages pictured on pages 14 and 19 above, for example, which we know were randomly generated, is just meaningless gibberish—let’s call this the non-sense hypothesis—or (B) that these pages have some deeper secret meaning?

For his part, Borges’ narrator rejects the non-sense hypothesis out of hand. For him (or her!), the Universal Library “includes not a single absolute piece of nonsense.” But this belief poses a Humean puzzle. If our narrator were a true Humean, his degree of belief about any disputed fact (e.g. about whether any given line of any given page of any given volume in the Universal Library is “non-sense” or not) should correspond to the amount of relevant evidence available to him, or in the immortal words of David Hume: “A wise man, therefore, proportions his belief to the evidence.” (Hume 1748, Para. 4) Does this puzzle have a solution?

UNRELATED POSTSCRIPT: Today (2 May) is the one-year anniversary of the death of my idealistic father, Don Francisco Guerra. (See my post “A little piece of Cuba has died.”) To my dad, you will always be missed and and your memory, never forgotten.