Plato, Mathematician and Myth-Maker

Pisano, Giovanni, 1240?-1320?. c.1284. Siena Duomo: det.: Plato. Place: Museo dell’Opera del Duomo (Siena, Italy). https://library-artstor-org.proxy.library.nd.edu/asset/ARTSTOR_103_41822000532257.

The Republic, The Symposium, The Phaedrus, The Apology, and The Phaedo––these are just a few of the works of Plato that were not widely available throughout most of the Middle Ages. No extended depiction of the most just city in the Republic. No discussion of love in The Symposium and The Phaedrus. No self-defense for Socrates at his trial as found in The Apology, and no final dialogue before his suicide as found in The Phaedo. For lovers of great texts, especially Plato, such news can be shocking. What kind of Plato does a person know if they don’t have these key works? How much of Socrates’ life and Plato’s philosophy could even be known? These are the questions that many medieval scholars of the Latin Platonist tradition have dedicated their lives and careers to answering, and the answers can be quite surprising.

One aspect of this research that ought to be appreciated by the wider reading public (outside of the narrow confines of medievalists) is that Plato’s Timaeus wasthe most widely available Platonic work throughout most of the Middle Ages. In fact, examining the text of the Timaeus and why itwas such one of the few Platonic texts preserved reveals how peculiarly modern our current canon of Platonic literature is.

What we value in Plato was not necessarily what late antique or medieval readers valued, and yet, their ability to read well meant that they understood a lot more than might be supposed. An attention to the reception history of Plato’s Timaeus can give modern readers of Plato a better appreciation for the importance of both mathematics and poetry in Platonic philosophy.

The Timaeus is Plato’s work on the origins of the universe. It begins with a dialogue between Timaeus, Socrates, Hermocrates, and Critias, in which Socrates expresses a desire for a “moving image” of the city they had been talking about the day before. The summary of the previous day’s discussion appears to bear some resemblance to the conversation found in the Republic although scholars are divided over whether this summary perfectly matches the Republic that we now possess. Regardless of its accuracy, this summary would have been the closest a medieval reader would have had to a taste of the Republic. The opening dialogue covers all sorts of fascinating topics from Solon’s visit to Egypt, oral culture, the mythic origins of writing, and the myth of Atlantis, but the bulk of the work features a narration about the origins of the universe recounted by the Pythagorean, Timaeus.

The Timaeus was received in the Middle Ages through three main channels of Latin translations: the translation of Calcidius (which ends at 53b), the translation of Cicero (available but not widely used or even known, which ends at 42b), and the excerpts from the Ciceronian translation of the Timaeus that can be found in Augustine’s City of God. Although it does not contain the whole text of the Timaeus, Calcidius’ translation is much more complete than Cicero’s: rather than giving merely the speech of Timaeus like Cicero’s translation does, it includes the opening dialogue (even though the commentary itself ignores it).

Most modern Plato scholars would probably not choose The Timaeus as theone and only work they could save from destruction for all time. But, a better understanding of who Calcidius was and why he wrote the commentary on the Timaeus suggests that the preservation of the Timaeus in the Latin West was not an accident of fate. Rather, the results of Gretchen Reydams-Schills’ lifelong study of Calcidius give a plausible reason for why Calcidius’ commentary may have been the Platonic work of choice for many late antique philosophers.

Reydams-Schils argues that Calcidius wrote his commentary as an introduction to the Platonic corpus, essentially reversing the Middle Platonic curriculum, which traditionally ended with the Timaeus. One major piece of evidence for this theory is that Calcidius’ commentary often reserves discussion of harder philosophical concepts for the end of the commentary.Furthermore, unlike the Neoplatonists, Calcidius did not read the Timaeus synoptically and believed strongly in the importance of sequential reading of the Platonic corpus. In Calcidus’ Platonic curriculum, the Timaeus came first with its teachings on natural justice, then the Republic with its teaching of positive justice, and finally, the Parmenides came with its teaching of the forms and intelligible realities. Calcidius believed that a thorough understanding of mathematics was necessary for understanding of almost all of the Platonic works, which is why his commentary on the Timaeus turns out to be something like a crash course in Pythagorean mathematics.

Thus, although the Timaeus was one of the only Platonic works available throughout the early Middle Ages, Calcidius’ commentary gave readers some introduction to the entire Platonic corpus as well as a great deal of Pythagorean mathematics. Perhaps there might be good reason for a philosopher to save The Timaeus (especially a copy with Calcidius’ commentary)from a burning building!

Plato; Chalcidius (translation). Timaeus. Manuscript. Place: Bodleian Library, University of Oxford, <a href=’http://www.bodley.ox.ac.uk/’>http://www.bodley.ox.ac.uk/</a>. https://library-artstor-org.proxy.library.nd.edu/asset/BODLEIAN_10310768399.

Medievalists who study the textual reception of the various translations of The Timaeus have been able to identify a shift in kinds of interest in Plato over time. The primary Latin translation of the Timaeus used until the eleventh century was Cicero’s. Medieval scholars used to assume that the revival of Calcidius began with the twelfth century Platonists, but Anna Somfai has demonstrated that the proliferation of copies of Calcidius’ text and commentary began in the eleventh century when championed by Lanfranc of Bec (c.1050). The late twelfth-century actually experienced a decline of copying the Timaeus as interests shifted towards other texts.

What motivated the eleventh-century interest in Calcidius appears to have been the mathematical content of the Calcidian commentary because, by the Carolingian period, much of the actual content of the quadrivial arts had been lost, and scholars in the Middle Ages attempted to piece together what scraps of it remained from a variety of sources. Calcidius’ commentary on the Timaeus appears to have been particularly valued as a source text for the quadrivial (or mathematical) arts. As my two previous MI blogs have explored here and here, medieval thinkers in the traditional liberal arts tradition recognized that the quadrivial arts were the foundation for philosophical thought, even if they had few textual sources for actually studying them.

And although some of the interest in the kinds of mathematics found in the Timaeus and Calcidius’ commentary may have declined after the twelfth century, it was by no means lost completely. As David Albertson has demonstrated, the mathematical interest in Plato found in the work of the twelfth-century scholar, Thierry of Chartres, would eventually be picked up by the fifteenth-century scholar, Nicholas of Cusa, and many scholars have noted resonances of Cusa’s quadrivial agenda in the thinking of Leibniz, the founder of calculus:

It seems that God, when he bestowed these two sciences [arithmetic and algebra] on humankind, wanted to warn us that a much greater secret lay hidden in our intellect, of which these were but shadows. (Leibniz as quoted by Albertson, p.2)

Bernardus Silvester. Liber fortunae, also known as Experimentarius.. Manuscript. Place: Bodleian Library, University of Oxford, <a href=’http://www.bodley.ox.ac.uk/’>http://www.bodley.ox.ac.uk/</a>. https://library-artstor-org.proxy.library.nd.edu/asset/BODLEIAN_10310765350.

Even though the interest in scribal copying of the Timaeus seems to have declined somewhat by the twelfth-century, another kind of imitatio or translatio studii was being enacted by a different kind of scholar, Bernard Silvestris. He wrote a prosi-metric telling of the creation of the world that emulates Plato’s Timaeus. The title of his work, Cosmographia, roughly translates as “universe writing,” and Bernard delivered an oral performance of itbefore Pope Eugenius III in 1147. Bernard’s creative retelling of the Timaeus poetically depicts the role of imitation in the divine creation of the world in the form of “divine writing.” Performatively, the Cosmographia demonstrates that this divine writing is then imitated by poets in the form of human writing. In other words, Bernard values Plato’s Timaeus here not merely for its insights into mathematics or even the structure of the universe, but also what this mathematics in the universe implies about the mimetic nature of poetry itself.

As many literary scholars have demonstrated, much of the European literary tradition follows suit in seeing the value of Timaean Platonism for the production of literature. This interest can be seen in such diverse authors as Alan of Lille, Chrétien de Troyes, and Dante.

While I would personally be loath to give up the access to the Platonic corpus that I possess, the medieval reception of the Timaeus constantly pushes me to reconsider how I am reading that corpus. Having a large corpus of texts actually places an onus on the modern reader to ask the question of where to place the textual emphasis: Which texts of Plato should be considered central (and which ones periphery) and why? For example, should Plato’s Republic be considered his last word on poets and poetry? What would happen if Plato’s Timaeus were given more weight?

C.S. Lewis once wrote in his introduction to On the Incarnation by Athanasius:

Every age has its own outlook. It is specially good at seeing certain truths and specially liable to make certain mistakes. We all, therefore, need the books that will correct the characteristic mistakes of our own period. And that means the old books.

These words about reading the great books can also apply to reading the old books as they were read by past readers. Understanding medieval readings of Plato might very well be a good counterweight to modern presuppositions about who Plato was and what he was about. How might the idea of Plato as both a mathematician and myth-maker transform our modern understanding of Platonism and its history?

Lesley-Anne Dyer Williams is a Professor for Memoria College’s Masters of Arts in Great Books program and graduated with her doctorate from the University of Notre Dame’s Medieval Institute in 2012. She was also the founding director Liberal Arts Guild at LeTourneau University. Her research focuses upon twelfth-century Platonism and poetry, especially Thierry of Chartres and Bernard Silvestris.

Lesley-Anne Dyer Williams
Public Humanities Postdoctoral Fellow
Medieval Institute
University of Notre Dame

For Further Reading:

Albertson, David. Mathematical Theologies: Nicholas of Cusa and the Legacy of Thierry of Chartres. Oxford University Press, 2014.

Baxter, Jason M. The Infinite Beauty of the World: Dante’s Encyclopedia and the Names of God. Peter Lang, 2020.

Bernardus Silvestris. Poetic Works. Edited by Winthrop Wetherbee, vol. 38, Harvard University Press, 2015.

Caiazzo, Irene. “Teaching the Quadrivium in the Twelfth-Century Schools.” A Companion to Twelfth-Century Schools, edited by Cédric Giraud, translated by Ignacio Duran, vol. 88, Brill, 2019, pp. 180–202.

Calcidius. On Plato’s Timaeus. Edited by John Magee, vol. 41, Harvard University Press, 2016.

Chenu, M. D. “The Platonisms of the Twelfth Century.” Nature, Man and Society in the Twelfth Century: Essays on New Theological Perspectives in the Latin West, translated by Jerome Taylor and Lester K. Little, vol. 37, University of Toronto Press, 1997.

Dronke, Peter. The Spell of Calcidius: Platonic Concepts and Images in the Medieval West. SISMEL edizioni del Galluzzo, 2008.

Gersh, Stephen. Middle Platonism and Neoplatonism: The Latin Tradition. Vol 1 and Vol 2. University of Notre Dame Press, 1986.

Hoenig, Christina. Plato’s Timaeus and the Latin Tradition. Cambridge University Press, 2018.

Murray, K. Sarah-Jane. From Plato to Lancelot. Syracuse University Press, 2008.

Plato. Plato’s Cosmology: The Timaeus of Plato Translated with Running Commentary. Edited by F. M Cornford, Routledge, 1937.

Reydam-Schils, Gretchen. “Myth and Poetry in the Timaeus.” Plato and the Poets, edited by Pierre Destrée and Fritz-Gregor Herrmann, Brill, 2011.

Reydams-Schils, Gretchen J. Calcidius on Plato’s Timaeus: Greek Philosophy, Latin Reception, and Christian Contexts. Cambridge University Press, 2020.

Somfai, Anna. “The Eleventh-Century Shift in the Reception of Plato’s Timaeus and Calcidius’ Commentary.” Journal of the Warburg and Courtauld Institutes, vol. 65, 2002, pp. 1–21.

Stock, Brian. Myth and Science in the Twelfth Century. Princeton University Press, 1972.

Wetherbee, Winthrop. Platonism and Poetry in the Twelfth Century. Princeton University Press, 1972.

The Raven’s False Greeting: Animal Language and Medieval Fable

Talking animals are a ubiquitous element in fables. They do not evoke wonder from human characters within the narrative, nor seem to require any explanation; this contrasts with other sorts of stories (everything from Marie de France’s Guigemar to contemporary fantasy novels) where the appearance of a talking animal signals the beginning of some rare adventure for humans. Notably, there is, however, one fable I can think of that seems to portray an animal whose ability to talk is liminal. That is, he can utter words, yet he is not really treated as a speaker. His status seems closer to that of a “real” animal who can mimic human speech, and that is in fact key to the story.

The fable in question is ascribed to Phaedrus, the author of the first extant literary fable collection. While Phaedrus wrote in the first century, his five books of fables were the basis for much of the “Romulus” tradition in prose and verse, which flourished in the Middle Ages. The aforementioned fable is called “The Traveler and the Raven” (Viator et corvus). The tale is found in “Perotti’s Appendix,” named for the Italian humanist, Niccolò Perotti (1429–80), who transmitted it; I offer a translation of it below, with the text based on Ben Edwin Perry’s edition.[1]

Manuscript illustration, from the 14th century Luttrell Psalter, of two humans and a horse harrowing a field, with two ravens hovering above them, British Library, Additional MS 42130, fol. 171r .

Quidam per agros devium carpens iter
AVE exaudivit, et moratus paululum,
adesse ut vidit nullum, corripuit gradum.
iterum salutat idem ex occulto sonus.
voce hospitali confirmatus restitit,
ut, quisquis esset, par officium reciperet.
cum circumspectans errore haesisset diu
et perdidisset tempus aliquot milium,
ostendit sese corvus et supervolans
AVE usque ingessit. tum se lusum intelligens
“At male tibi sit” inquit, “ales pessime,
qui festinantis sic detinuisti pedes.”

A certain man, taking a byway through the fields on a journey, heard “Hello!” and lingered for a moment, but when he saw that no one was there, he hastened the pace. Again, the same sound greeted him from some hidden place. He stopped, encouraged by the hospitable voice, so that whoever it was might receive an equal courtesy. When he had remained for a long time, looking around uncertainly, and lost enough time for several miles, a raven showed himself, and flying above him, incessantly repeated “Hello!” Then, realizing he had been tricked, the man said, “Damn you, wretched bird, for delaying my feet like that when I was in a hurry.”

Why did the man perceive the raven’s “hello” as a trick? (The word lusum, in line 10, comes from ludo, to play, and can suggest mockery or deception; I translated it as “tricked.”) Why did he not take this as a genuine greeting?

It seems that the man was expecting a human speaker, and was disappointed and annoyed to find out that the salutation came from a bird instead. But species difference doesn’t, in and of itself, seem like an adequate explanation, at least in the usual fable context where all sorts of creatures talk. Nor does the explanation for the man’s reaction lie in some perceived status imbalance between the two; reciprocity is expected in greetings, after all, even between parties of unequal standing, and it isn’t mockery for an inferior to greet a superior, or vice versa.

Complicating this is the fact that real birds can imitate human speech—parrots, most famously, but also corvids, including ravens. This raven repeats the same simple word, over and over, as a trained animal might. But the man simultaneously seems to impute malice or mischief to this animal and deny him as a legitimate interlocutor. The raven is capable of toying with him (and ravens have a longstanding, cross-cultural reputation for cleverness and tricks), but he is not capable of (or worthy of?) a conversation.

Manuscript illustration of a raven, from an early 14th century manuscript of Jacob van Maerlant’s Der Naturen Bloeme, British Library, Additional MS 11390, fol. 33r.

A traditional narrative about animal language is that it doesn’t exist—that the sounds that animals make (and this leaves aside non-aural communication, through movement, scent, etc.) are fundamentally different than human speech. Nonetheless, medieval grammarians and philosophers acknowledged that, say, a dog’s bark is not meaningless, that it might convey something of his emotional state, and that humans could pick up on this.[2] Some thinkers, too, suggested that animals can communicate with their own species in their own “language.” For example, says, Roger Bacon, hens can cluck to let their young know that food is near, or to warn them of a predator.[3]

So much for “real-life” animal language. In medieval literature, though, there may also be special talking animals (or humans gifted with a special ability to understand animals, e.g., the man who can translate between species in Culhwch and Olwen, or Canacee, with her magic ring, in Chaucer’s “Squire’s Tale”). In fables, animals’ capacity to speak is typically unremarkable, and conversations readily occur across species lines.

This fable, however, reflects none of the above scenarios. The raven doesn’t caw or croak—he says an intelligible word, in a human language, Latin. And what he says is “Ave,” a greeting. Ave is not far off from Latin avis, “bird,” although the words are etymologically unrelated; in modern Spanish and Portuguese ave means “bird”. Etymology aside, there is still the possibility of wordplay. Is the bird proclaiming what he is all along, without the man realizing it? Is that the “trick”? Was that what the bird really meant to do, or was it apt, but not necessarily done knowingly—is the raven a kind of natural sign who reiterates himself, both by appearing and by unwittingly speaking his own appearance?

In any case, the man doesn’t treat the raven’s “Ave” as a sincere speech-act from an animal who can, unsurprisingly, talk to him—he doesn’t treat it as a greeting, he treats it as a deception. (The opening moral, possibly added by Perotti, emphasizes this, declaring, “People are very often deceived by words,” Verbis saepenumero homines decipi solere).

What accounts for the man’s reaction to the raven? Fables often have talking animals, yes, but fundamentally, fables are didactic, using memorable narratives to get messages across. The raven’s real-life reputation for mischief, but above all his real-life ability to imitate speech, is what is being drawn on here. The raven in “The Traveler and the Raven” is not the genre-typical talking animal, because for him to be an actual, expected interlocutor goes against the point of the fable, which is about how words can deceive.[4] In conveying this point, “The Traveler and the Raven” both acknowledges certain animals as clever and strips a non-human character of his genre-typical linguistic capability.

Emily Mahan
PhD in Medieval Studies
University of Notre Dame

[1] Ben Edwin Perry, ed. and trans., Babrius and Phaedrus, Loeb Classical Library 436 (Cambridge: Harvard University Press, 1965), pp. 404–6.

[2] For an analysis of the shifting conceptions of the semiotics of dogs’ barking, from Aristotle to Roger Bacon, see Umberto Eco et al., “On Animal Language in the Medieval Classification of Signs,” in On the Medieval Theory of Signs, ed. Umberto Eco and Constantino Marmo (Amsterdam: Benjamins, 1989), pp. 3–41.

[3] Quoted in Eco et al., “On Animal Language,” p. 36, n. 39.

[4] Fables tend to teach the “mistrust of words,” argues Jill Mann, in From Aesop to Reynard: Beast Literature in Medieval Britain (Oxford: Oxford University Press, 2009), p. 96.