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What was lost that you are concerned about?

Probably next to nothing, and certainly nothing of importance was lost. Alexandria was hardly the only library in the world, and the libraries at Pergamum and later Rome herself rivaled Alexandria in scale. Antony replaced the losses of the fire during the Alexandrine War with copies made from the library at Pergamum, and libraries in gymnasia or simply founded for citizens abound during that period in the Greek world, they’re in like literally every city of any size. If anything at all was lost it was almost certainly mainly critical commentaries on various authors, as well as catalogs of their works–both the Alexandrian library and the Pergamene one were famous for producing such commentaries. Pretty much everything else of value would have existed elsewhere. It’s possible that a few (at that time probably little-known) philosophical texts might have been lost, but even such texts are likely to have had other copies elsewhere. For example, Aristotle’s didactic texts are practically unknown in the Hellenistic Period, before a first century, B.C. edition was compiled, but they existed at the very least probably both in Alexandria and the library of the Peripatetics themselves (probably also in Pergamum).

We do not lose texts because of catastrophic events that wipe out all copies of them. We lose texts because they stop being copied. Papyrus is really freaking old and even in Egypt doesn’t preserve as well as we’d like. Fragmentary papyrus finds are extremely important to Classicists, but the overwhelming majority of our texts (and pretty much all our complete ones) are known from medieval copies. The destruction of the library, whenever exactly it happened, would have had next to no impact on the transmission of texts. Imagine if we went down to the Library of Congress right now–or better yet forty years ago before the Internet–and burned all the stacks and catalogs. That would be a big deal, but would it wipe out knowledge of what was there? Besides the catalogs themselves and any supplementary material that the library had put together for its own purposes…no, not really. Those books all exist elsewhere, except for a handful of extremely rare texts and the stuff the library puts together for its own purposes. Most texts that are lost now were already lost in late antiquity or the early Middle Ages, simply because they were not copied enough. Even a brief period of unpopularity might result in a sharp decline in the survivability of an author–Catullus, despite being unanimously praised by ancient and modern critics, briefly lost popularity under the Antonines and already by late antiquity authors were lamenting the difficulty in obtaining a copy of his poems. The most likely texts to survive were the ones used in the school curricula, which is why we have so many copies of Caesar, Virgil, and Homer, or foundational philosophical texts, especially Plato and Aristotle’s didactic works (his exoteric texts had already been lost by the early Middle Ages). The loss of textual material has very little to do with catastrophic events.

After all, what would have happened if the Library had survived? The collection would be long-decayed by now–the large papyrus finds at places like Oxyrhynchus are due to a large part not to Egypt as a whole but the fact that the climate combined with the garbage heaps in which these papyri are found causes the papyri to get stuck in airless pockets and stuff. So we would know the texts by copies anyway. Alexandria was cut off from the Byzantine scholars who copied Greek (and Muslim scholars generally worked from translation), so the survival of the collection would not have influenced their work significantly. And in any case, as I keep stressing, what was in there was already known elsewhere. Even within the city of Alexandria itself several copies of those texts existed in various locations, many of them on warehouses at the harbor ready to be exported (Badian, for example, conjectured that it was one of these warehouses that Caesar’s troops set fire to, since he was nowhere near the palace complex). It might be nice to have some of the commentaries on various authors that we knew certain Alexandrian scholars put together for their private use, but commentaries are like reading footnotes, we’d rather have the texts themselves–and the texts on which the commentators were commenting existed elsewhere as well.

https://www.reddit.com/r/AskHistorians/comments/5t6op5/comment/ddkr2h6/