(Beiträge zur Altertumskunde 341) Gabriele Cornelli - Plato’s Styles and Characters Between Literature and Philosophy-Walter de Gruyter (2016)
particular association with tyrants” (Gribble 1999 loc. 1094).
Thus, the very concept of pleonexia, which as we have seen was central to
the political rhetoric of the late fifth century, turns out also to reveal an unpre-
cedented gender connotation, referring to intemperance in sexual desires, in an-
other example of the overlapping of the two areas.
That Alcibiades’ sexual paranomia, his lack of masculinity, is primarily a po-
litical issue is also underlined by Gherchanoc: “sa feminité est présentée comme
un atout politique même si elle est du ressort de la critique” (Gherchanoc 2003/4,
A very well attested tradition portrays the young Alcibiades, in fact, as the
favorite of many aristocratic lovers: always ready to be the object of the pleasure
of others, not by constraint, but precisely because he is unable to control his own
sexual desire. The same picture, indeed, emerges in the Platonic Symposium. See
especially the statement (219b-d) regarding the ploy of “throwing himself under
the covers” of Socrates to seduce him and spend the night with him.
A sexually deviant figure is a recipe for comedy, obviously. Aristophanes
calls Alcibiades euruproktos (vagrant, Acarn. 716), while Eupolis represents the
sexual role of Alcibiades as a woman’s role (fr. 171 K–A).
For a description of this culture of sexual appearance see Éloi & Dupont (2001).
But how to articulate this description with the one – also present in tradition
– of Alcibiades as a womanizer? One must express, of course, a further herme-
neutic caution: the short circuit suggested by this question may depend more
on the modern description of gender relations, which not necessarily correspond
to the same description within the ancient world. In fact, Davidson appropriately
notes that, even more than his own passivity, his most feminine feature, accord-
ing to ancient Greek ethics of gender, would be his inability to control his desire
(Davidson 1997, 167–182). Likewise states Gribble (1999, loc. 1025), who thus sol-
ves the seeming contradiction just mentioned: “because the key issue in deter-
mining ‘ethical gender’ is the attitude of the subject to pleasure, even as active
sexual agent the kinaidos remains assimilated to the feminine”, especially when
The complex web of gender relations representation, when referring to the
ancient world and, more precisely to Alcibiades, is far from the simple natural-
izing dichotomy man/woman, if one assumes that an adulterer and a womanizer
can be considered generally feminine. An ancient comic fragment by Ferecrates
is in fact symptomatic of this gender perspective: “for not being a man (aner),
Alcibiades, it seems, is now the husband (aner) of all women around him”
(fr. 164 K–A). For not being a man, that is, for not controlling his desires –
that one being the most defining representation of the male – Alcibiades is an
Later tradition does not cease to collect several anecdotes that represent his
specific sexual paranomia from the history of the trip to Abydos, in the company
of his uncle Axioco, in which both are said to have slept with the same woman,
Medontis, and to have claimed the paternity of the child that was from her born.
There is also the incident at Melos, where once again political and sexual
excesses outrageously intertwined: after having decreed the mass enslavement
of the inhabitants of the island of Melos (Thuc. V, 84ss), Alcibiades bought to
himself a Melian woman and had a son with her. Andocides in his speech
against Alcibiades, notes with revolt that the son of Alcibiades, born from a Me-
lian slave within the context of the island’s and its inhabitants’ destruction,
would most certainly be another enemy of Athens.With the result that Alcibiades
therefore, as an Athenian general, is creating, with his sexual excesses, new en-
emies for the city (Andocides. In Alcibiadem 22–23).
Alcibiades dies fighting, referring conventionally to a manly death. However
even in the traditions that mention his death, the representation of Alcibiades’
femininity is strongly present. In fact, Plutarch, as is usual in his Parallel
Cf. Davidson (1997, 165).
He longs for him, he hates him and he wants him for himself
Lives, at the end of the life of Alcibiades briefly symbolizes his existence in the
final hours, using two representations unequivocally feminine (Plutarch 2011,
17). On the one hand, in the ultimate premonitory dream of his death, a courte-
san applied cosmetics in him “and as if he was a woman, combed his hair”
(39.2). On the other hand, after his death in battle, Alcibiades is dressed for
the obsequies with woman’s robes: “Timandra [his companion then] collected
his corpse, wrapped it and covered it with her own clothes” (39.7). Therefore,
the last image of Alcibiades refers symbolically to his gender paranomia.
However, probably the best description of Alcibiades gender paranomia can
still be found in the very Platonic Symposium, in the reversal of roles between
lover and beloved, a central topos to the economy of the dialogue as a whole:
Alcibiades is the one in love with Socrates, and not vice versa (222b).
On page 213d quoted above, Socrates expressed his fear of Alcibiades’ mania
and philerastia. Alcibiades, in fact, mask and the very incarnation of Eros, is as
powerful and surreptitious as him (205d). He is the paradigm of the tyrannical
man, well described at the end of Book VIII of the Republic. But here in the Sym-
posium, eros tyrannos is also reversed, as Alcibiades regrets twice having been
put into slavery by Socrates, feeling obligated to love him: thus, the tyrannical
man par excellence, he uses the adverb andrapododos, “like a slave”, and the
preposition hypo, “under”, to show this subjection to Socrates (215Ee). Alci-
biades says bluntly that sometimes he even has the desire to see Socrates
dead, to get rid of this tyranny (216c). Certainly a post factum reference, gently
tragic, from Plato to his already dead mentor, but also an affirmation of the nui-
sance that Socrates-Eros would have provoked at the Athenian polis elite, which
Alcibiades is here representing.
The game of the reversal of roles serves simultaneously as a compliment, as
high as possible, to Socrates as even superior to Eros himself and as the true in-
carnation of a philosopher, but also, once again, the reverse of the dramatic plot,
serves to endorse the suspicions that Alcibiades, in his multiple paranomiai, was
ultimately trying to achieve tyranny.
The introduction in the speech of Diotima of the theme of the mysteries’ ini-
tiation can be analyzed in the same way as in the case of the presence of a lex-
icon linked to the herms. Mentioned already was the serious charge against Al-
cibiades of having participated in a parody of the mysteries, a charge that led to
his first defection and “was a/the? source, not the least important one, of the de-
feat of Athens” (Thuc. VI, 15, 3). It is therefore impossible not to think that Plato,
always a most able “weaver of words”, has presented the discourse of Diotima,
just before the entrance of Alcibiades, referring to a double initiation into the
mysteries, having in mind the rhetorical plan of the scenic effect of this approach
onto the figure of Alcibiades.
The rhetorical game of Plato, so clever and suggestive, designed along the
lines above, ends up reinforcing the suspicions about Alcibiades, at the same
time as it seeks an opposite effect: that is, the planning of a renewed apology
for Socrates and his hetairia.
Socrates, at the end of the speech of Alcibiades, debunks the “satyric and
Silenic drama” hidden behind the compliment: that is, the lover’s intention of
separating his beloved from Agathon, so that he can be with him (222c). All
the rhetorical construction of the speech of Alcibiades would have thus been
woven by an erotic story. As in much of ancient iconography, where Eros and Pei-
tho appear side by side, the relationship between the two deities, love and per-
suasion, structures the whole Symposium dialogue, from the prologue to the
speech of Alcibiades.
But this plot to hide is not only related to the charge that Socrates directs
towards him at the end, that the praise was for other persuasion purposes.
The thesis here proposed is that the story that Plato is hiding in his logos sokra-
tikos – which is always erotikos par excellence – is that of an apology for Socra-
tes, built with great literary skill, with plenty of implied references and lexical
tricks. An apology that the eromenos Plato, in love with his mentor Socrates,
judges to be only possible by “separating”, albeit post-mortem, his memory
from that of Alcibiades, within a precise and articulated strategy of memory po-
licing. The latter will thus be the only one to blame for his own malpractices, in-
cluding perhaps the very death of Socrates, which Plato would plausibly attrib-
ute largely to the fatal connection of the two.
The diverse representation of gender in the ancient Greek world, distinct
from the dichotomy of male and female sex roles to which we are accustomed
by our modernity, can reveal more precisely the rhetorical strategy of Plato in
his use of Alcibiades’ erotic paranomia as a symptom of a character politically
dangerous because of his immoderate seduction exercised of Socrates and Ath-
This Platonic apology, which follows an investment on a policy of memory, is
based, ultimately, in a clever rhetorical strategy, which emphasizes the now tra-
ditional sexual paranomia of Alcibiades, in order to make him guilty of an at-
tempted excessive and outrageous seduction not only of Socrates, but of the
polis. Reusing comic and oratorical/rhetorical motifs of his time, therefore,
Plato deepens the j’accuse against Alcibiades, trying to withdraw him from the
orbit of Socrates and the Socratics.
It is finally impossible not to notice that in facing Alcibiades’ case this way,
Plato himself acts according to the script of his character, Alcibiades: inspired by
Eros and Peitho, he does “anything” to separate Socrates from the other erome-
nos. “With the intention that I love you and nobody else” (222d) – these are the
He longs for him, he hates him and he wants him for himself
words that Socrates directs to Alcibiades. But much of Plato’s work, and espe-
cially the Symposium, is also an attempt to win Socrates over, to keep him
only for himself, to rescue the memory of his beloved mentor, highly disputed
in the literature of the beginning of the fourth century. Thus, the Socratic dia-
logues of Plato end up looking very much like the compliment of a lover –
just like that of Alcibiades – that is, with a seductive declaration of love.
Fiction and reality, drama and authorship thus coincide, undoubtedly result-
ing in one of the most exciting and daring literary and philosophical works of all
Anthistenes. F. Decleva Caizzi. Antisthenis Fragmenta. Milan: Istituto Editoriale Cisalpino,
Aristophanes. N.G. Wilson. Aristophanis Fabulae. Oxford: Oxford University Press, 2007.
Casertano, G. (2007). Paradigmi della verità in Platone. Roma: Editori Riuniti.
Centrone, B. (1999). Introduzione a Platone Simpósio. Turin: Einaudi.
Cornelli, G. & Chevitarese, A. (2010). ‘Socrate e Platone tra golpe oligarchico e restaurazione
democratica (404–403 a.C.)’. In Rossetti, L. & Stavru, A. Socratica 2008. Studies in
Ancient Socratic Literature. Bari: Levante ed.
Darbo-Pechanski, C. (2009) Ordem do corpo, ordem do mundo: aitia, tekmêrion, sêmeion,
historion nos tratados hipocráticos do fim do século V antes de nossa era. In Peixoto,
Miriam Campolina. A saúde dos antigos: reflexões gregas e romanas. São Paulo: Loyola.
Davidson, J. (1997) Courtesans & fishcakes: the consuming passions of classical Athens,
London: Harper Perennial.
De Romilly, J. (1995) Alciabiade ou les dangers de l′ambition. Ed. de Fallois (quote from the
Italian edition. Milan: Garzanti, 1997).
Dover, K.J. (1970) Excursus: The Herms and The Mysteries. In Gomme, A. W. & Andrewes, A.
& Dover, K. J. A Historical Commentary on Thucydides. Vol. IV., Oxford: Clarendon.
Dupont, F. & Éloi, D. (2001) L’érotisme masculin dans la Rome antique. Paris, Berlin.
Eupolis. T. Kock. Comicorum Atticorum fragmenta, vol. 1. Leipzig: Teubner, 1880.
Ferrari, F. (2007). Socrates tra personaggio e mito. Milan: Rizzoli.
Gherchanoc, F. (2003). Les atours féminins des hommes: quelques représentations du
masculin-féminin dans le monde grec antique. Entre initiation, ruse, séduction et
grotesque, surpuissance et déchéance. In Revue Historique 4, n° 628, p. 739–791.
Giorgini, G. (2005). ‘Il tiranno’. In Platone. Repubblica. Vol. VI, Libri VIII-IX. Traduzione e
commento a cura di Mario Vegetti. Naples: Bibliopolis, 423–470.
Gomperz, T. (1905). Greek Thinkers. Vol. V: Plato. New York: Scribners.
Gribble, D. (1999) Alcibiades and Athens: A Study in Literary Presentation. Oxford: Clarendon
Musti, D. (2001). Il simposio. Bari: Laterza, 2001.
Nails, D. (2002). The People of Plato. A Prosopography of Plato and Other Socratics.
Nucci, M. (2009). Note alla traduzione di Platone Simpósio. Turin: Einaudi.
Nussbaum, M. (1986). The Fragility of Goodness. Luck and Ethics in Greek Tragedy and
Philosophy. Cambridge: Cambridge University Press.
Pherecrates. T. Kock. Comicorum Atticorum fragmenta, vol. 1. Leipzig: Teubner, 1880.
Pinheiro, A. E. (2011). Introdução a Xenofontes, Banquete – Apologia de Sócrates. Tradução
do grego, introdução e notas Ana Elias Pinheiro. Classica Digitalia Brasil. São Paulo:
Platonis Opera. Ed. John Burnet. Oxford: Oxford University Press, 1903.
Plutarch. Vidas Paralelas: Alcibíades e Coriolano. Tradução do grego, introdução e notas
Maria do Céu Fialho e Nuno Simões Rodrigues. Classica Digitalia Brasil. São Paulo:
Reale, G. (2005). Eros demone mediatore: il gioco delle maschere nel Simposio di Platone.
Robin, L. (1908). La theorie platonicienne de l′amour. Paris: Felix Alcan.
Rowe, Ch. (1998). Il Simposio di Platone: cinque lezioni sul dialogo e un ulteriore contributo
sul Fedone. A cura di Maurizio Migliori. Sankt Augustin: Academia Verlag.
Thucydides. History of the Peloponnesian War. Trans. by R. Warner, with Introduction and
Note by M. I. Finley. Penguin Books, London, 1972.
Vegetti, M. (2003). ‘Antropologias da Pleonexía: Cálicles, Trasímaco e Gláucon em Platão’.
Boletim do CPA. Ano VIII, n.16: 9–26.
Xenophon. Banquete – Apologia de Sócrates. Tradução do grego, introdução e notas Ana
Elias Pinheiro. Classica Digitalia Brasil. São Paulo: Annablume, 2011.
He longs for him, he hates him and he wants him for himself
Five Platonic Characters
The study of Plato is a veritable battlefield for multiple academic disciplines and
popular discourses. Most notably, the continental and Anglo-American ap-
proaches to Plato have diverged over the past decade: reading different journals,
assigning different translations, and hiring like-minded colleagues. Yet, for at
least a decade, it has been a mere caricature of analytic philosophy to say
that its method is to rip arguments out of their contexts in Plato’s dialogues in
order to represent them in propositional logic and assess their soundness. The
corresponding caricature of the continental approach to Plato has become equal-
ly inappropriate: to say that Plato’s philosophical dialectic is subordinate to a
Heideggerian hermeneutic, the sensitive interpretation of dialogues read as
wholes. I would like to preserve the rigor of the analytic approach while defend-
ing the view that Plato’s literary craft was not mere window-dressing for school-
Plato’s singular contribution, his achievement beyond pre-Socratic, sophis-
tic, literary, and rhetorical precedents, was his doubly open-ended philosophical
method, leading him to criticize most effectively even the beliefs he may have
cherished most deeply. Aporia is one open end, well known to all; the other –
and, to my mind, even more admirable – is Plato’s refusal to allow even his
most well-established starting points to be insulated from criticism. His dia-
logues are occasions to philosophize further, not dogmatic treatises.² Whatever
views he held, however he expressed them, he requires us to perform our own
intellectual labors and to reach our own conclusions by the best arguments
we can muster. In that endeavor, we are well-advised to use whatever techniques
are available to us, logical or literary. Within what Ruby Blondell has called the
“insoluble paradox of our place at the crossroads of particularity and abstrac-
tion” (2002: 303), the collective effort to establish Plato’s overarching view of
human nature has diminished our regard for the particular human beings he fea-
tures in his dialogues. My project here is to reestablish the importance of taking
Plato’s characterizations seriously on grounds that they are sometimes crucial to
understanding what Plato is arguing.
I am grateful for the friendship and the comments of our community in Brasília 2012, and for
the support the IPS and UNESCO provided.
This is the theme for which I argued in Nails 1995.
Appreciating the characters’ individual roles within familial, social, and re-
ligious structures could deepen our understanding of some philosophical issues
– human nature, epistemology, or justice and education in the polis. We have
long used Athenian history and law to explain aspects of the dialogues that
would otherwise be obscure.³ All too often, however, we have contented our-
selves with a phrase or two handed down from the nineteenth century about per-
sons – a time when little was known and the texts were being established.
Thanks primarily to classicists’ early adoption of computer databases, we now
know much more about Plato’s characters than the old footnotes suggested, so
the possibilities for understanding have been considerably extended.⁴
No one discusses the Charmides without mentioning Critias’s future leader-
ship of the Thirty, or the Republic without noting that Glaucon and Adeimantus
are Plato’s brothers. Some of Plato’s dialogues, the Laches for example, assume a
high level of familiarity with then-recent past events and the reputations of the
persons represented – some of whom were still alive and active in Athens when
Plato was writing his dialogues. I will focus on five actual people, two men and
three women, whose lives and later reputations among Plato’s audiences may be
more important to understanding Plato’s text than has previously been realized
– but I have not selected the famous ones. What I hope to show is that the range
of plausible interpretations of the texts, and the range of understandings of Pla-
to’s milieu, and perhaps that of Socrates as well, can be reduced and focused if a
character had a career and a reputation in Athens already known to Plato’s au-
dience; discernible personalities matter to our interpretations, or so I shall at-
tempt to establish.
Meno of Thessaly, son of Alexidemus,⁵ became a mercenary general under the
command of Cyrus. We meet him in Plato’s dialogue when he is visiting Athens
in late 402 as the guest of Anytus before he leaves on the military campaign that
Xenophon will immortalize in the Anabasis. Meno was vicious. Xenophon is
E.g. especially Theaetetus, Euthyphro, Apology, Crito, and Phaedo.
The caveat is that we cannot confidently assume that what Plato’s audience believed about a
character is what happened to survive into our own time. We have before us a partial, fragment-
ed record of ancient prosopography, so we cannot afford to be complaisant about the informa-
tion that we have.
Apart from his appearance in Plato’s Meno, Meno appears in Xenophon’s Anabasis 1.2.6–3.1,
fragments 27–28 of Ctesias, and in Diodorus Siculus 14.19.8–9, 14.27.2–3.
pleased to list his vices with examples (greed, betrayal, hunger for power, deceit,
malice, selfishness); he wasted the lives of his men, and he participated in their
injustices, plundering the countryside. Xenophon counts Meno as having de-
served the Persians’ torture of him for a year before finally executing him by tor-
ture (Anabasis 2.6.21–29). Plato presents none of Xenophon’s facts because, of
course, none of this had happened yet in 402.What Plato’s audience can surmise
decades later is that – for all the talk of virtue – Meno was not made a better man
by his conversation with Socrates. Meno is one of Socrates’s tragic failures. Be-
cause Meno’s malevolent behavior was still ahead of him, however, commenta-
tors in the philosophical traditions have had little to say about Meno’s character,
which is a mistake from the perspective I am taking here.
The Meno – and in this I follow Leibniz’s Discourse on Metaphysics §26 – is
not about virtue, excellence, aretê. It is about learning, inquiring by a method
capable of leading one to valid inferences from true premises, to knowledge.
In particular, the dialogue emphasizes learning as different from the transfer
of information. Gorgias tried but failed to transfer information to Meno. Informa-
tion-transfer can produce true beliefs, but it cannot produce knowledge and it is
not a method practiced by Socrates, who adjusted his techniques to fit his inter-
locutors. Leibniz, a sensitive reader of Plato’s dialogues, made light of those who
took Plato’s remarks on anamnesis literally, those who believed that Socratic
priests and priestesses were conjuring immortal souls in possession of all knowl-
edge. For Leibniz, anamnesis is learning, learning by inference from what is al-
ready known – familiar from Sherlock Holmes. Leibniz loved Plato’s “beautiful
experiment” with Meno’s intelligent slave.⁶ While the slave proves capable of
learning, Meno does not. That contrast (and nothing about virtue) is the take-
home message of Plato’s Meno.
By my lights, what Plato does make explicit in the dialogue should be
enough to put anyone on guard. And against what should we be defending our-
selves? Against the view that the point of the dialogue is to identify the nature of
virtue. Consider some of what Plato does tell us: (i) Aristippus is Meno’s lover
(Meno 70b) although, by Athenian standards, Meno is already too old to be a be-
loved; and it transpires that he still has more than one lover (76b).⁷ (ii) If we can
judge a man by the company he keeps, as Socrates says we might (95d–e) then
we could also note that Meno’s Athenian host, Anytus (90b), though a democrat
when we meet him with Meno, had been an early supporter of the Thirty and had
‘Boy’ is a misnomer; Meno was not taking children on campaign with him, and elderly slaves
—as in other cultures—were nevertheless called ‘boy’.
Xenophon adds that Meno also had a bearded beloved, Tharypus (Anabasis 2.6.28)—a further
and double breach of convention.
Five Platonic Characters
even earlier invented a new way to bribe juries.⁸ Later, he will be one of Socrat-
es’s three accusers.⁹ (iii) Meno has trouble remembering and repeating what he
is supposed to have learned from Gorgias. (iv) Socrates has to remind Meno that
Meno’s account of virtue as the ability to rule over people requires the modifier
‘justly and not unjustly’ (73d). (v) Socrates tells Meno, “you are forever giving or-
ders in a discussion, as spoiled people do, who behave like tyrants as long as
they are young” (76b). (vi) Plato’s Socrates alludes to Meno’s future failure to be-
come better when he predicts, “you would agree, if you did not have to go away
before the mysteries as you told me yesterday, but could remain and be initiated”
In short, had we been a part of Plato’s ancient audience, we would not seek
to understand virtue by reading the Meno any more than we would now seek to
understand virtue by reading a dialogue between some contemporary villain –
Bashar al-Assad or George Bush – and a philosopher like Socrates.
My second example of a misunderstood Platonic character whose actual biogra-
phy can aid our understanding is the Athenian Theaetetus of Sunium, son of Eu-
phronius, one of the great mathematicians of the ancient world,¹¹ though as ugly
as Meno was beautiful. In this case, the received view of Theaetetus has had a
misleading effect on the history of mathematics as well as on Platonic scholar-
For most of the twentieth century, it has been thought that Theaetetus stud-
ied and taught mathematics in Plato’s Academy and was Plato’s associate there
for nearly twenty years until his death in the Corinthian battle of 369,¹² and that
Plato wrote the Theaetetus as a memorial to him when he died. I will explain in a
moment why that poignant story is not possible, but I want first to say why we
should care. In the twentieth century, cemented through the influence of Gregory
Vlastos, major mathematical discoveries in the West were moved forward – into
Plato’s mature lifetime rather than that of Socrates; hence it was necessary to
keep Theaetetus alive into the period that we have come to think of as Plato’s
Pseudo-Aristotle, Athenian Constitution 27.5 and 34.3.
Socrates implicitly disparages Anytus by praising his father (90a–b) and then pointing out
that such praiseworthy men are unable to bring up praiseworthy sons (93d–94c).
Translations of Meno are those of Grube as revised by Cooper.
Biographical material is adapted from Nails 2002.
Burnyeat 1990: 3. Translations of Theaetetus are from this edition of the dialogue.
maturity. According to Vlastos,¹³ Plato discovered and was significantly changed
by mathematics after writing his Socratic dialogues; the encounter with the
mathematics of his associate, Theaetetus, marked a philosophical turning
point for Plato’s so-called theory of forms.
In fact, as argued in David Fowler’s monumental The Mathematics of Plato’s
Academy, the claim makes no historical or biographical sense. When Theaetetus
actually died, in 391, there was not yet an Academy of Plato. Plato learned math-
ematics as the other Athenian youths of his era did – and the mathematics he
learned had already been established before and during the lifetime of Socrates.
So much for a brief sketch of matters, the details of which I will now fill in on
three fronts: evidence for the death of Theaetetus, the flawed account of the his-
tory of ancient mathematics, and the modern philosophical counterpart to that
flawed ancient mathematical story. Along the way, one can see how Plato’s dia-
logue has been interpreted and reinterpreted to fit such external constraints.
We know exactly when the Theaetetus takes place: in the months immedi-
ately preceding Socrates’s death, at which time Theaetetus is meirakion, but
on the young side, for he is not fully grown (155b); and Socrates says to the ge-
ometry master, Theodorus, “Look at the company then. They are all children but
you” (168d).We also know that the dramatic frame of the dialogue, with Euclides
and Terpsion, explicitly depicts Theaetetus’s impending death. Plato tells us so.
There is no doubt either that Theaetetus was a very great mathematician
whose work was codified in Euclid’s Elements but, as often happens with
known individuals from the ancient world, other mathematical discoveries
whose authors were unknown were later ascribed to the known Theaetetus.
The first scholium to book 13 of Euclid states, for example, that Theaetetus
added the octahedron and icosahedron to the Pythagoreans’ cube, pyramid
and dodecahedron for the total of five regular solids (Timaeus 54d–55c). He
was also credited with the two means of Timaeus (31b–32b), the mean of Parme-
nides (154b–d), incommensurability (Meno, Theaetetus), rational and irrational
cube roots (Theaetetus 148b) and continuous quantities. The provenance of
these attributions is uncertain. Understandably, the question began to be
asked whether Theaetetus could have accomplished it all by 391, in less than
a decade following Socrates’s death.
In the 1910s, modern classical scholars began to suppose that he could not
(Caveing 1996). They found a later battle in Corinth, a famous one in 369, and
attached Theaetetus’s death to that one, giving him twenty-two more years to
Vlastos 1991 is a consolidation of his views, but they had been appearing in lectures and
articles by then since the 1970s.
Five Platonic Characters
move mathematics forward. The suggestion was immediately and eagerly accept-
ed, reinforcing a second important catalyst for re-dating the death of Theaetetus.
Namely, from the eighteenth century, philosophers had a strong desire to make
the Theaetetus the threshold for Plato’s abandonment of forms as he “devel-
oped” and turned to the issues introduced in the Statesman and Sophist, dia-
logues with dramatic dates after the Theaetetus and with an overlap of charac-
I pause to note, though this is not the place to argue, that the Theaetetus
does not abandon the forms. Forms are discussed there (185c–186d) as objects
of knowledge – not of the senses – naming “being and not being, likeness
and unlikeness, same and different; also one, and any other number applied
to them…beautiful and ugly, good and bad…hardness…softness.”¹⁴ They are
what is stable against Heraclitean flux.
Nevertheless, this direction of Platonic interpretation was comfortably sup-
ported by the claim that the mathematics of the Theaetetus is derived from Pla-
to’s time, not Socrates’ – a claim based on the false premise that Theaetetus died
in 369. The fact is that Theodorus, who was a rough contemporary of Socrates,
made his discoveries by about 440, when both the concept and theorem neces-
sary to prove similar rectangles by the method of anthyphairesis were available
to him (Artmann 1994: 22). Neglecting that detail, historians of mathematics were
swayed by a desire to locate and date ancient mathematical developments with-
in the Academy itself; Fowler (1999: 360) says Theaetetus’s death in 369 was
“generally regarded as one fixed point, perhaps the only secure fixed point, in
the shifting sands of the incommensurability issue” – yet he himself rightly
doubted its truth. The year 369 for the death of Theaetetus raises four problems,
explicit in Thesleff 1990: 149–50, that are together insuperable: (i) Athens was
not mustering 46-year-old academics for hoplite combat in 369, (ii) Theaetetus’s
skillful soldiering (142b–c) was far more likely to have been exhibited when he
was of military age, 24, than at 46. (iii) Euclides’s 30-kilometer walk, from which
he has just returned as the dialogue’s frame begins, is more likely for a man of 59
than for a man of 81. (iv) The remark of Socrates that seems so prescient to Eu-
clides and Terpsion, the query whether Theaetetus will live to grow up (142c–d),
is appropriately applied to a man who dies before reaching 30, but not for one
who reaches 46. Theaetetus died in 391, and the mathematics that fascinated
Plato had already been established.
As John McDowell points out in the notes to his 1973 translation of Theaetetus, it is no good
supposing that when Socrates reneges (183c) on his promise to discuss Parmenides (181a–b), he
is merely postponing the discussion to the Sophist. The discussion of Parmenides in that dia-
logue is on a different subject.
Both the Meno and the Theaetetus are dialogues illustrating geometrical
proof by the diagrammatic method. Our earliest texts use the term διάγραμμα
for ‘diagram’ and ‘proof’ interchangeably, and both Plato and Aristotle continue
that practice.While Socrates in the Republic distinguishes the methods of geome-
ters from those of dialecticians, if I am right that the failing was in the practice –
not the subject matter – then we are warranted in gathering the techniques of the
mathematicians under the umbrella term ‘dialectical method’ – our most prom-
ising means of achieving such “pieces of knowledge”¹⁵ as are possible for mor-
tals. I take ‘dialectical method’ to be a flexible term in the dialogues. It is a boot-
strapping method, a piecemeal method, the various techniques of which we use
when we don’t already have knowledge but desire it and seek it systematically.
Some of the mathematicians’ methods are used often enough to ensure that
we ought to take them as components of the dialectical method. Myles Burnyeat
has made much of the first: (i) the crucial relationship between definition in
mathematics and philosophy.¹⁶ Glenn Morrow has explored further similarities
between the elenchus and the procedures of the mathematicians; (ii) Socrates in-
sists on deductive implication, tracing the consequences of common opinions,
even in practical matters; (iii) avoidance of contradiction; and (iv) methodical,
sometimes tedious, demonstration (Morrow 1970: 319–20). Most philosophers
have shied away from saying that (v) the method of hypothesis was another
key way in which Socrates’s practice was like that of the mathematicians, though
it is introduced as a geometer’s method.¹⁷ The passage implies knowledge of
conic sections, and philosophers have generally considered that discovery late,
despite the evidence of Democritus.¹⁸ That brings me to …
A short history of mathematics in two parts: ancient and modern. Standard
histories of ancient mathematics told the same tale from the Renaissance to the
late twentieth century. Here is David Fowler’s succinct version:
The early Pythagoreans based their mathematics on commensurable magnitudes (or on ra-
tional numbers, or on common fractions m/n), but their discovery of the phenomenon of
incommensurability (or the irrationality of the square root of 2) showed that this was inad-
McDowell’s translation, throughout the aviary section of the Theaetetus, for ἐπιστῆμαι; cf.
the Rowe translation of Symposium 207e6, reserving ‘branches of knowledge’ or ‘sciences’ for
μαθήματα. See now Benson 2012.
See the introduction to his translation (Hackett, 1990), and Burnyeat 2000.
Meno 86e4–87b2, where the hypothetico-deductive method is introduced, explicitly credit-
ing the geometers.
Morrow (1970: 313) argues that Democritus knew that a cone holds one-third the volume of a
cylinder with the same base and height.
Five Platonic Characters
equate. This provoked problems in the foundation of mathematics that were not resolved
before the discovery of the proportion theory that we find in Book V of Euclid’s Elements.¹⁹
The story persisted – persists – despite the fact that many of its presuppositions
did not pan out, as Fowler argues and Fernando Gouvêa seconds in his review. ²⁰
First, the standard view was that Greek geometry was a de-arithmetized version
of Babylonian arithmetized geometry. The latter seemed “more normal” to mod-
erns in the West, but the study of books II and X of Euclid’s Elements showed
that cannot be so. The geometrical approach was independent and, as a result,
incommensurability was not a foundational crisis in Greek mathematics but an
interesting discovery that led to significant mathematics. Second, Greek arith-
metic had no notion of common fractions as previously thought, but proceeded
by parts so, for example, “one ninth of 2 is 1/6
.” Third, the Greek notion
of ‘proportion’ (a is to b as c is to d) differed from the notion of ‘ratio’, and there
were at least three competing definitions of ‘ratio’: from music theory, astrono-
my, and mathematics. Fourth, anthyphairesis, the method of reciprocal subtrac-
tion (similar to what is now called ‘continued fractions’) was of far greater im-
portance than previously realized. Before the middle of the sixth century –
that is, a hundred years before Socrates was born – architectural drawings
were exact; materials were already available: not just wax tablets, but precisely
planed marble slabs used in the building trades (Artmann 1994: 18).²¹ Concepts
too were available, though one of the matters still in some dispute is when proof
was given for what was already intuited by working mathematicians – e.g., that
the intersection of two straight lines yields equal angles. Where mathematicians
dominate the history of their subject, proof is moved further back toward the
sixth century; and Theodorus’s fifth-century geometry lesson has been the
locus for a library’s worth of research in journals of geometry and history of sci-
ence (see figures 1–3), as well as Wilbur Knorr’s monograph on Theodorus’s ge-
Fowler 1999: 356. The point is crucial to new claims that distinguish the second edition from
the 1987 one.
My account of what is significant in Fowler 1999 is adapted from that of Gouvêa 1999.
Artmann discusses the sources, including Philebus 56b.
Fig. : Theodorus’s proof by continued
fractions in Theaetetus (Bindel )
Fig. : Theodorus’s spiral stops at step to
prevent the intrusion of √ on √ (Anderhub
Fig. : Theodorus’s proof by removing squares to prove similar rectangles by anthyphairesis
There is a modern counterpart to the flawed ancient story. In the nineteenth cen-
tury, as mathematicians explored the limits of infinite processes that defied the
visual imagination, suspicion of geometrical intuition took hold. That “visual
understanding actually conflicts with the truths of analysis” became dogma in
the early twentieth century (Giaquinto 2007: 3–8). A host of arithmetized proofs
for Theodorus’s theorem appeared then – despite the clear text of the dialogue.²²
Caveing (1996: 282): “…according to Vogt, ‘Theodoros’ lesson’ was divided into two parts of
which the geometrical one answers to the verb ἔγραφε [147d3], and the arithmetical one to the
Five Platonic Characters
Burnet in 1911 deprecated Socrates’s use of a diagram in the slave’s lesson, call-
ing it “opposed to … the process of good inquiry.”²³ Heath’s History of Greek
Mathematics reflects what turns out to have been a benighted blip. The search
for secure foundations for axiomatic systems spawned conflicting schools later
in the twentieth century,²⁴ so the dogma did finally subside.²⁵
Ancient philosophers, however, were not in the vanguard of all this activity.
Scholars were under the sway of a just-so story about ancient Greek mathemat-
ics, and in the long shadow of Heath, so mathematical developments were push-
ed further toward the fourth century, a trend at its apex with Vlastos’s view that
Plato’s discovery of advanced mathematics, as an adult with dialogues already
written, marked a turning point. It now seems certain that it would be difficult
to overemphasize the degree to which Socrates’s generation was immersed in the
visual and spatial thinking involved in geometrical proof. I do not mean Socrates
was a mathematician, but that the evidence is great that whatever mathematical
knowledge philosophers of the twentieth century attributed to Plato would as
plausibly have been attributed to Socrates, an educated fifth century Athenian.
The biography of Theaetetus is central to sorting out both the history of mathe-
matics and the interpretation of Plato.
* * *
The literature on Plato’s view of women flourishes, but works that evaluate the
degree of Plato’s feminism predominate, most of those based on explicit argu-
ments about women in Republic 5, ²⁶ with work on what women symbolize
when encountered in Plato’s dialogues taking a distant second place. In both
verb ἀποφαίνων: on the one hand mere constructions of lines, on the other logical proofs. But,
according to classical Greek syntax, if a verb in the indicative mode is accompanied with another
in the participle, the two ideas are linked, and the main one is borne by the participle, while the
other points out only a modality of the action. So Plato means ‘Theodoros proved by means of
geometrical constructions…’, that is the drawing of lines is part of the proof itself.”
Brown (1971: 204n) cites Burnet’s 1911 note to Phaedo 73a7, with approval.
Giaquinto (2007: 6) notes the phases: (i) Carnap’s conventionalism measured “convenience
and truthfulness; there is neither need nor possibility of establishing the axioms true and the
rules valid.” (ii) Quine’s holistic empiricism trumped conventionalism but did not distinguish
math and science: “Even professional mathematicians must await the verdicts of empirical sci-
ence before they can justifiably assert the truth of their mathematical beliefs.” And Gödel (1964)
Diagrammatic proofs (not mere illustrations) have begun to reemerge: cf. Brown 1999 and
There is extensive (more than the usual) overlap among these articles, chapters, and books;
see Bluestone 1987 and Tuana 1994.
strands, however, the actual women of Plato’s dialogues are themselves effective-
ly suppressed. I support a third approach, rare but not entirely unknown: that
the women represented in Plato’s dialogues should be considered in their partic-
ularity – like the men. One need not insist that Plato’s fourth-century represen-
tations of fifth-century women were perfectly accurate to value their philosoph-
ically informative function; but it is worth noting that, despite an overhaul of the
Athenian legal code undertaken in 410 and completed for implementation in
403/2, the situation for women under the law remained virtually unchanged in
Plato’s lifetime; thus women of his fourth-century family ²⁷ were subject to the
same legal restrictions as those that had affected the women of Socrates’s house-
Diotima of Mantinea, however, is not an Athenian. She is an exception to the rule
of existing contemporaneous evidence confirming Plato’s choosing his characters
from among known persons,²⁹ making her a magnet for attention, though pri-
marily insofar as she is conceived as a constructed stand-in for Socrates or
Plato. There is a current and widespread assumption that Diotima is the one
named character Plato invented out of whole cloth. David Halperin’s famous
title, “Why is Diotima a Woman?” suppresses the premise that Diotima was fab-
ricated by Plato. As Hayden Ausland (2000: 186n11) has shown in striking de-
tail, ³⁰ however, “Diotima’s fictionality is a modern development.”
Plato’s mother was Perictione, daughter of Glaucon III; Potone, daughter of Ariston, was Pla-
to’s full sister. There is no record of Athenian women attending the Academy; the two women
whose names are preserved, Axiothea of Phlius and Lasthenia of Mantinea, were from the Pelo-
ponnesus. Here and below, factual details derive from Nails 2002.
Xanthippe of course, but others possibly as well (cf. Phaedo 116b). For present purposes, I
leave aside the ubiquitous problem that affects the building of an account of the women in Pla-
to’s dialogues: sisters, in the absence of exact dates of birth, are often silently assumed to be
younger than brothers. Further, despite the typical Athenian arrangement for girls-in-their-
teens to marry men-in-their-thirties (Garland 1990: 210 –213), the practice of scholars is to
date children in relation to fathers, thirty years apart, without much regard for a woman’s actual
Philebus is the only other.
Ausland cites in evidence the testimonia in Platonis Symposium, ed. Otto Jahn, 2nd edn.,
Bonn: Marcum, 1875, 16–18; F. A. Wolf, Platons Gastmahl, Leipzig: Schwickert, 1782, xlvi (2nd
edn. , lxiv); and Plato’s nineteenth century prosopographer, G. Groen van Prinsterer, Pro-
sopographia Platonica, Leiden: Hazenberg, 1823, 125.
Five Platonic Characters
We are rightly suspicious of arguments from silence – not only because evi-
dence has a way of turning up unexpectedly, but because we can be quite certain
that we have such a small portion of the evidence – and a smaller portion for
non-Athenian individuals than for most others of the late fifth and early fourth
centuries. Yet the argument from silence has been the argument of choice that
Diotima is not historical. There is a slightly more nuanced argument that is al-
most as common. Here’s the version in the introduction to the Nehamas-Wood-
ruff translation of the Symposium: “Diotima in her speech makes an allusion to
the view Aristophanes has just presented at the banquet… This… suggests that
even if Diotima actually existed, what she is represented as saying to Socrates
cannot have been composed, as Socrates claims, long before the party during
which he relates it.” ³¹ But we do not know much about what he related.
There is no certainty that Plato contrived the whole speech of Aristophanes ex
nihilo. As with the book of Zeno in the Parmenides, or the speech of Lysias in
the Phaedrus, it has often been noted that Plato’s change of style and manner
may well reflect his brilliance as an author, or his reconstruction of an existing
original, or even his embedding of an original in his own text. ³² Moreover, the
possibility that the story was not original with Aristophanes or Plato should
not be dismissed lightly. The claim that Diotima could not in the late 440s
have alluded to a speech that Aristophanes didn’t make until 416 misses a
point Dover made in 1966: Aristophanes, or Plato, was dressing up a folk tale,
not inventing new material. There is a very similar ancient Indian myth of the
original androgyne, suggesting Indo-European beginnings. If the story was not
wholly original with Aristophanes, Plato’s pointing to that fact in the Symposium
may have been received as a mild comeuppance to Socrates’s longtime accuser. ³³
A further point about Diotima: the secure dramatic date of Agathon’s victory