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To question is not merely to know that one lacks knowledge but to love knowledge passionately, to pursue it and never give up…

“…by indirections find directions out…” ~Hamlet, 2.1

Socrates teachingThe Meno holds a distinguished place in the St. John’s curriculum. As the first Platonic dialogue that our freshmen read, it is the gateway to all the philosophic works to come, both ancient and modern. I must acknowledge at the outset my debt to a former tutor and dean of our college—Jacob Klein, whose books on the Meno and on Greek mathematics have greatly influenced the reading of the Meno that you are about to hear.

As its subtitle indicates, the Meno is about virtue, but roughly a third of the way through the conversation, the focus shifts to the theme of learning. Meno, you recall, becomes frustrated by his inability to answer Socrates’ question about virtue and tries to sabotage the whole undertaking with a paradox: How can anyone learn, since, if he doesn’t already know what he’s looking for, he won’t know it when he finds it, and if he does know, why search? Socrates responds to the paradox with a myth, which tells us that learning is possible because our souls are immortal and have seen the truth of all things, truth that we have forgotten as a result of being born. What we call learning is really recollection or calling back, anamnêsis. To learn, in the precise sense, is not to acquire but to recover. Socrates enlists the aid of mathematics to demonstrate the truth of this teaching. Through a series of questions, he gets one of Meno’s slave boys to solve the geometrical problem of doubling the square.

The central role of recollection in the Meno raises many questions. Why does Socrates present recollection in the context of a myth? Why, in order to illustrate the truth of the myth, does he appeal to mathematics, in particular geometry? What makes the problem of doubling the square especially fitting? And finally, what does recollection have to do with virtue, the ostensible topic of the dialogue? I will address these questions after taking us through the conversation that leads up to Socrates’ myth.

The Meno is indeed about virtue, but it is more deeply about Meno: about his soul and the effect that contact with Socrates has on it. The dialogue is also about Anytus, who appears later in the drama and was one of Socrates’ principal accusers at the trial that led to Socrates’ conviction and death. In the Meno, Anytus warns Socrates that what he is doing, questioning the virtue of respected Athenian statesmen, is likely to get him into trouble (94E-95A). Then there is the slave boy—the only one in the drama who does not resist Socrates and who manifestly learns something. The dialogue is also about him.

The conversation begins with a question posed by Meno:

“Can you tell me, Socrates, whether virtue is something teachable? Or is it not teachable, but something that comes from practice? Or is it something neither from practice nor from learning, but something that comes to human beings by nature, or some other way?”[*]

Meno does not ask “How is virtue acquired?” but whether Socrates is able to tell him how virtue is acquired, whether Socrates has a speech or answer in him ready to hand. Meno’s question is artfully constructed and has a nice ring to it—no doubt the influence of Gorgias, the famous rhetorician whom Meno greatly admires. Socrates’ reply sidesteps Meno’s question and redirects the conversation. It becomes clear that Socrates means to turn the tables on Meno, put him in the hot seat of interrogation. Socrates gets personal, even referring at one point to Meno’s lover, Aristippus (70B). He observes that Meno is from Thessaly, a city that has apparently enjoyed a recent influx of wisdom, thanks to the arrival of Gorgias. In the course of the dialogue we learn that Meno is young, wellborn, wealthy, handsome and spoiled. He is used to being obeyed and appears eager to rule Socrates. He is also fairly intelligent and not uneducated: he has read the great writers of the day and can easily follow a mathematical demonstration.

In his evasion of Meno’s question, Socrates comically depicts wisdom as a commodity that can move from place to place, owner to owner, like material wealth (a recurring theme in the dialogue). Wisdom moves as the sophists or professional teachers move—from city to city. Socrates then gets to his main point: he is so far from knowing how virtue is acquired that he doesn’t even know what virtue is! All of Athens is in this condition, he says. Meno’s Thessaly is rich in Gorgian wisdom, while Socrates’ Athens is wisdom-poor. Socrates’ whole effort will be to get Meno to share Socrates’ knowledge of ignorance, to move him from presumed wealth to realized poverty.

The Meno is the only Platonic dialogue that begins with what could be called a philosophic question. The question, however, does not arise from Meno’s perplexity about virtue but from his curiosity about Socrates’ opinion of virtue. Meno, who collects the opinions of the wise in various cities and reports back to his fellow intellectuals back home, is disappointed at Socrates’ confession of ignorance. Must he return to Thessaly empty handed? Socrates goes on to expand his claim. Not only are he and his fellow Athenians ignorant of virtue: he has never met anyone who knows, not even the great Gorgias, whose answer about virtue Socrates pretends not to remember (71C-D).

The opening of the Meno signals the importance of the question as such. What is a question? A question can be rhetorical, a statement in disguise, sometimes sarcastic. “Is that the best you can do?” or “You call that dancing?” A question can be posed in order to show how clever we are. There’s something of that in Meno’s question, which is no doubt intended to impress Socrates. There are also questions that seek information, whether from curiosity or need, questions like “Who’s your favorite composer?” or “How do you get to the hotel from here?” or “What is the mass of the earth?” Once the answer to these sorts of questions is given, questioning stops; the need has been met. This, too, applies to Meno’s question, since Meno is curious about what Socrates has to say and wants information from him. Questions are also used to interrogate, that is, to elicit from someone responses that expose difficulties, contradictions and guilt. Socrates does this regularly with his respondents: he questions them in order to convict them of ignorance. He puts them on trial.

But a question may also spring from deep perplexity about something we long to know, something that has weight and importance for us, even urgency. This kind of question is the beginning of a quest. One asks the question in order to pursue it, and one pursues it in order to know what does not merely seem to be true but is true. Socrates interrogates others, but he also claims to be searching for a knowledge he does not yet possess. As he questions others, Socrates, by his own account, is in the grip of questions and questioning. The Socratic question “What is it?” is not aimed ultimately at an answer, even if answers are necessary in order to make headway. Socrates tempts others to answer his questions, I would suggest, in the hope that they will come to realize that answers, even good ones, are not enough. The question born of perplexity does not seek an answer but rather understanding and insight. To what extent this understanding and insight can be formulated in speech is one of the great themes of the Platonic dialogues.

Speech adds another dimension to our understanding of Meno, who is speech-obsessed: that is why he admires Gorgias. Obsession with speech is clearly not restricted to Meno. Any of us can fall under the spell of speech, whether as speakers or listeners, especially artfully composed speech or rhetoric, which gives its practitioner tremendous power over the souls of others. A good rhetorician can easily persuade his auditors that he is wise, that he knows what he is talking about. That is how the ambitious rise to power. Rhetoric and politics are connected, and Meno, who surely has political aspirations, wants to be masterful in speech so that he may be masterful in other ways as well. Socrates alludes to this political streak in Meno when he accuses him of having the tyrannical disposition of good-looking people who are used to getting what they want (76B-C). By struggling to get Meno to join him in the quest for virtue, Socrates is attempting to cure Meno’s habit, his addiction to high-sounding speech and the lust for honor and power that go with it. This is the central deed of Plato’s Meno. If his rage for rhetoric can be cured, or at least tempered, Meno would return to Thessaly a better man. A gentler healthier Meno, as Socrates says hopefully in the final speech of the dialogue, may even benefit Athens by tempering the anger of Anytus (100B).

Socrates’ admission of ignorance is perplexing. Socrates does not simply think or feel that he doesn’t know what virtue is but rather claims to know that he doesn’t know. This seems like an act of humility but is in fact a boast—a claim to know something. How, we wonder, is such knowing possible? How can one know that one doesn’t know something? The wonder lies in the determinateness of realized ignorance. In some uncanny way we are capable of pointing to and locating precisely that of which we are ignorant. “I don’t know” means “I don’t know this.” The precise designation of the unknown as such would be impossible if we didn’t in some way know what we don’t know—know in the sense of recognize and identify.

By claiming to know that he doesn’t know what virtue is, Socrates is saying, in effect: “I know that virtue is perplexing, and moreover, I know why.” Socrates’ claim to know his ignorance surely springs from long experience, from his dialectical journeys through the land of virtue and his many encounters with the strange creatures that dwell therein. These creatures are the problems that the philosopher finds enticing but that others find only an obstacle, a pain and a rebuke. In Greek, the verb “to question,” eresthai, resembles the verb “to love” in the erotic sense, eran, from which we get the noun “eros.” The word play sheds light on what it means to ask genuine questions. To question is not merely to know that one lacks knowledge but to love knowledge passionately, to pursue it and never give up. This erotic poverty-at-work is philosophy.

None of what I am saying explains how it is possible to know what one doesn’t know. Nevertheless such knowing underlies the act of engaging in philosophy. To ask questions, as Socrates does, is to bring the questionable as such to light, to determine and articulate the precise ground of the question. A Socratic refutation of someone’s opinion or answer, then, is more than an indictment of that person’s ignorance: it is also the revelation of why the question was necessary in the first place, why it has a ground in the nature of the thing that is being asked about.

Let us go back to the dialogue to see how questions are at work there. Socrates wants to turn Meno from his question about how virtue is acquired to what virtue is (71D). This, Socrates claims, is the right question to ask. But why is it the right question? What does the question “What is it?” reveal that other questions that might be asked about virtue, including Meno’s, do not? A possible answer is that the question about the what-ness of virtue leads directly to the problem Socrates wants Meno to confront: the problem of One and Many or, as we may also call it, the problem of the Whole. Meno keeps breaking virtue into pieces, and Socrates keeps exhorting him to keep virtue “whole and healthy” (77A). By repeatedly fragmenting virtue, Meno reveals the fragmented, disjointed condition of his soul, which is littered with other people’s opinions and proclamations about virtue. Meno is himself a Many in need of a One.

Meno’s first answer to Socrates’ question is a list that gives examples of virtue but not what the examples have in common. There’s the virtue of a man, a woman, a child, and a slave (71E). The list is democratic: everybody has a virtue, depending on his or her station in life. The list simply reports what is conventionally thought to be proper or to be one’s place. It sheds no light on what virtue is according to nature, although it does point to virtue as having something to do with proper human functioning within a household and a city. Socrates playfully compares the many virtues in Meno’s list to a swarm of bees—not, we must note, to the well-ordered colony. The list, in other words, lacks not only the commonality of what all virtues share but also the unity of an organized whole, even though all the functions and roles Meno lists point to and presuppose such a whole. A city or any sort of community is not a heap of isolated virtues but a network and interweaving of virtues and functions. By making virtue a heap, Meno falsifies the one-in-many that constitutes communal life.

Socrates urges Meno to say what all virtues (and all bees) have in common by referring to “some one and the same form” of virtue (72C). Form, here, is eidos, which comes from the Greek verb meaning “to see.” An eidos in ordinary Greek is a look, something to be seen, and can refer to someone’s figure, especially one that is beautiful. In the Meno Socrates does not advocate anything like a “theory of the forms.” He says, along more practical lines, that anyone who was being asked what all virtues have in common would, in answering, “do well” (in Greek, do beautifully, kalôs) to look “off and away” toward the self-same form (72C-D). The form here is hypothesized, or perhaps more accurately postulated. If indeed there is such a form, then speech that tries to define has a goal and target that is not itself a speech. The non-verbal eidos, which is not to be confused with an answer and can only be seen by the intellect, is what we intend and aim at when we try to define virtue—unless, of course, we are only looking for how we use the word “virtue.” The eidos is the purely intelligible correlate of the question: What is it?

The eidos gives inquisitive speech its focus and also its measure. On the supposition of an eidos of virtue, we can be proven wrong about what we think and say virtue is: we can miss the mark. The eidos guards the possibility of error and so keeps us honest. But it is also that which arouses questioning and the desire to go beyond convention, opinion and “what people say”—the desire to see what something is by nature or in itself. In its power to induce wonder, desire and pursuit, the eidos functions as a source of intelligible beauty—of truth itself in its radiance and power to inspire and entice. Meno is nowhere near this erotic experience. He is too much the beloved (as Socrates had implied in his sly comment about Aristippus) and not enough the lover.

Meno’s second definition moves from a collection of virtues to the single virtue of ruling over human beings (73C). This was in fact a prominent feature of his list. We should note that here, and elsewhere in the dialogue, Socrates keeps urging Meno to do two things as if they were one: to say what he thinks virtue is, and to recollect what Gorgias said virtue was (73C). This blurring of the distinction between what Meno thinks and what Gorgias said makes clear that Meno’s opinions about virtue are not really his own but are the echo and memory of what others have said. Socrates easily gets Meno to agree that rule over others isn’t virtue unless it is virtuous, and isn’t virtuous unless many virtues are present. Meno mentions courage, moderation, wisdom, magnificence, adding “and a great many others” (74A). He has failed yet again to keep virtue whole and healthy. But now the inquiry is at a higher level—an eidetic or formal level. The many-ness is no longer that of mere instances of virtue but rather of kinds, forms or species of virtue. Socrates here makes us wonder (even if Meno doesn’t) what all these forms have in common and in what sense they, like the parts of a city, constitute an interwoven whole, a community of virtues. Is there a single virtue that “rules” the others and makes them a whole rather than a heap? In the latter part of the dialogue, this ruling principle is intellectual virtue, wisdom, which causes all the ethical virtues to be truly good, beneficial and (one assumes) coherent or unified (88B).

Socrates urges Meno to persist in the search for “virtue as a whole” (77A). It is here that he tells Meno to keep virtue “whole and healthy,” thereby connecting the quest for a definition of virtue with a virtuous, healthy condition of soul. Meno’s third attempt combines beauty and power, and is based on the authority of an unidentified poet. Virtue, says Meno, is “just what the poet says, ‘both to rejoice and to be capable in beautiful things’” (77B). Meno has reached down into his memory-bag of Opinions of the Wise and Famous and has pulled out a speech that says more (and less) than he realizes. Socrates substitutes “good” for “beautiful” (all the better to get Meno into trouble) and introduces recognition, a kind of knowledge, into the argument. He gets Meno to agree that no one desires or wishes for bad things knowing them to be bad (78A). Since everybody desires what he thinks is good, and virtue (which in Greek means excellence) is what makes some people better than others, we must keep searching. Socrates has an opportunity here to turn Meno toward knowledge of what is truly good as the defining mark of virtue, but instead he leads Meno into another problematic answer: he suggests that one man is better than another “by being more excellent in capability” (78B).

Meno takes the bait. He opts for goodness rather than beauty and now focuses on capability or power. Virtue, he says, is “a power [dynamis] of providing good things for oneself” (78C). Power is the seed of Meno’s undoing, since power is ethically neutral and can be good or bad. Moreover, “good,” as Meno uses the word, is empty and can refer to anything at all that one wants to possess—gold and silver, for example. Contradiction easily follows, since the power of providing goods for oneself must be attended by many virtues if the power itself is to be virtuous. Socrates wraps up the refutation with an apt reference to money: Meno has broken virtue up into “small change” (79A).

The collapse of Meno’s fourth attempt to say what virtue is brings us closer to the myth of recollection. Socrates presses Meno, needles him, to continue the search: “Then answer again, from the beginning: what do you affirm virtue to be, both you and your comrade?” (79E). Once more coupling Meno and Gorgias, Socrates makes clear that the wisdom of Gorgias is on trial. Meno at this point has had it. At the beginning of the dialogue Socrates responded to Meno’s question with personal remarks: now Meno does the same to Socrates. Even before meeting him, Meno says, he heard reports that Socrates inflicted perplexity on others by posing questions they were unable to answer. Meno has learned by bitter experience that the reports are true. He says that Socrates has made him numb, torpid, “in soul and in mouth” and is therefore like “the flat torpedo-fish of the sea” (80A-B). Meno’s linkage of soul and mouth is comically suited to his obsession with Gorgian rhetoric: Meno’s soul and mouth are practically the same thing.

Socrates suggests that Meno has made an image of him so that Socrates would make an image of Meno in return. In his second reference to Meno’s vanity, Socrates observes that beautiful people “delight in having images made of them” (80C). But Socrates refuses to flatter Meno with a portrait. Instead, he corrects the torpedo fish image to make it harmonize with his claim to know that he doesn’t know: “but it is while I myself, more than anyone, am unprovided or perplexed [a-poros], that I make others unprovided or perplexed” (80C-D). Meno, to be sure, is on trial, but Socrates’ tone at this point is that of a comrade and fellow traveller, as he tells Meno: “I am willing to look with you and seek together for whatever [virtue] is” (80D). Meno rejects the offer and tries to block further inquiry with his paradox, which he no doubt heard from somebody else. Socrates takes Meno’s somewhat garbled formulation and sharpens it: inquiry seems to be impossible, since one who knows doesn’t need to seek, and one who doesn’t know doesn’t know what he’s looking for and so won’t be able to find it (80E).

Socrates makes no attempt to refute this potentially numbing paradox, nor does he mount an argument for learning as recollection. Instead he tells a myth—an inspired and poetic rather than argumentative mode of speech. The myth, as we learn, is a kind of rhetoric designed to persuade Meno that since learning is recollection, there is always hope that with persistent effort inquiry into the truth will be fruitful. Socrates here emphasizes the ethical virtues of courage and endurance. This is the first indication that recollection and the search for virtue are closely connected with being virtuous. Later in the dialogue, right after the slave boy episode, Socrates repeats the same idea in even stronger terms. He says that thinking or believing that one should seek what one does not know makes us better, that is, “more able to be brave and less lazy” than if we thought or believed that learning was something we either could not or ought not do (86B-C). For the sake of this, Socrates says: “I would surely do battle, so far as I am able, both in word and in deed” (86C). In other words, trusting in recollection is good for the whole soul and not just for the mind. Another ethical virtue Socrates had earlier connected with dialectical inquiry is gentleness (75D). Shared inquiry steers us away from contention, debate and the love of victory and honor. Realized ignorance and the pursuit of truth that it inspires civilize us and make us friends rather than combatants. Inquiry, then, combines courage and gentleness—the properly tough and the intelligently pliant. The myth of recollection is the guardian of this union of contrary ethical virtues.

Socrates introduces the myth by piquing Meno’s habitual curiosity about what other people say. Ever eager to acquire the sayings of the wise, Meno is so excited that he interrupts Socrates in mid-sentence and asks: “What was the account they gave?” Socrates responds: “A true one, it seems to me, and a beautiful one.” Socrates has accomplished at least this much: he has momentarily distracted Meno from his inquiry-killing paradox by arousing his somewhat prurient interest in “secret teachings.”

Socrates’ reference to wise men and women emphasizes that both sexes may be equal sharers in things divine, in wisdom. Socrates thus differs strongly from Meno, who limits the virtue of a woman to household management and obedience to her husband. The priests and priestesses to whom Socrates refers are in any case unconventional. Their special task is not to rave or speak in riddles, or preside over sacrifices to the gods, but to give accounts (81B). The purpose of this account, this myth, is not to preach moderation or humility before the gods, as poets like Pindar regularly do, but to spur human beings to persist in their quest for divine wisdom and the life of a god.

The key teaching of the myth is that the human soul is immortal, that it has been born and has died many times but is never destroyed. Since this is true, “one is required to live through one’s life as piously as possible” (81B). All of us, by virtue of our common humanity, have a sacred trust and a sacred obligation to our souls. The Meno never inquires into what the soul is, but like other dialogues it presents the soul as that about which we ought most to care, since the soul, like the body, can be in a healthy or an unhealthy condition. As visionary speech, the myth takes us beyond the merely ethical and raises the stakes of our earthly lives. We live not only in the mortal everyday world but also in the deathless scheme of things—in the light of eternity. The unidentified poet whom Socrates quotes speaks of Persephone, who “accepts redemption for the ancient affliction” and sends purified souls back again into the sunlit world from Hades (81B-C). These souls grow into great kings remarkable for their strength and wisdom. It is difficult to see how these mythic-religious elements fit into the teaching about recollection. The ancient affliction may be the ignorance of our ignorance, which causes us to pursue evil thinking it to be good and from which human beings need to be delivered by inquiry if they are to rule themselves like “great kings.”

Socrates proceeds to draw a conclusion from the soul’s immortality: “since the soul has been born many times and has seen all things both here and in the house of Hades, there is nothing which it has not learned” (81C). That is why the soul can in its mortal life learn: because it is recalling or summoning up what it has already “seen” and already knows. Of course, this doesn’t explain how the initial learning or coming to know took place. The myth raises all over again the very question it is designed to settle and seems to suggest an infinite regress. But the more important point that Socrates goes on to reveal is that recollection is grounded in the interconnectedness and continuity of nature, physis. All of nature, we are told, is “akin” (syngenous), and, as a result, if the soul can recall one thing it has seen, then it can (in principle at least) recall “all other things” (81D). In other words, there is a Whole. If this wholeness of nature were absent, then recollection would be like Meno’s first definition of virtue—a mere list of isolated recollection-bites. Nature, here, is not the world of plants and animals but the eternal order of eternal things, the ever-abiding realm of rationally connected natures or forms. Thanks to this interconnectedness, which resembles the organic unity of an animal or plant, the soul in its intellectual capacity can make progress in its inquiries, the various “journeys” through which the soul is rejuvenated, born again, by the prospect of recovered insights. The soul can come to realize that one virtue leads to another, is connected to another, and that all virtues are akin. The ultimate object of recollection is therefore not this nature and that nature but nature as the Whole.

The myth, as a mix of poetry and rhetoric, is intended to turn Meno from the mortal memorization of what people say to the immortal recalling of real knowledge, from the acquisition of fleeting external goods to the recovery of a lasting inner good, and from a mindless Many to a rationally organized One—an intelligible cosmos. It is also designed to urge Meno (to put it crudely) to get off his butt and stop being lazy, cowardly and a slave to debate tactics (81D-E). It is meant to open him up to learning. Meno is initially moved by the myth and its “secret teaching” about recollection but then lapses immediately into his view of learning as getting-something-from-a-teacher, as he asks Socrates: “Can you teach me how this can be” (81E)? Socrates responds by calling Meno a cunning rogue (in Greek a panourgos or do-anything) for trying to get Socrates to contradict himself by engaging in teaching. Meno, in his own defence, says that he spoke not with evil intent but merely “by habit.” Socrates will not teach Meno that learning is recollection, but he is willing to show him that the claim is true. He will do this for Meno’s sake by exhibiting recollection “in,” as he says, one of Meno’s “many followers” (82A-B). The only condition is that the follower speaks Greek.

The slave boy episode is remarkable for many reasons. For one thing it dramatizes a real act of learning: the boy moves from not knowing how to double the square to knowing. Moreover, the boy’s progress involves us in his act of learning: we are invited to follow each step closely and to suspend our belief that we already know the “answer.” Those of us who do not know the solution have a chance to learn it along with the slave boy, and those who do can rediscover why it is the solution.

The process of doubling the square shows what Socrates meant when he said that all nature is akin. The word “mathematics” comes from the Greek verb that means “to learn or understand” (manthanein). In mathematics, the realm of the eminently learnable, everything is rationally interconnected, and the path to the discovery of the double square is firmly rooted in the beautiful interlacing of the natures of beautifully clear objects: number, straight line and square. These objects, unlike those of our sense experience, are precisely and perfectly what they are. They are not “iffy” or “squishy” but solid and dependable. Mathematical proof reveals an eternal rather than temporal order among these objects. Consider Euclid’s proof of the Pythagorean Theorem, which says that the squares on the sides of a right triangle equal the square on the hypotenuse. In following the proof, we go through the steps in time. The steps themselves, however, are not in time but constitute a logical, non-temporal order of reasons. To use religious language suited to Socrates’ myth, the proof initiates us into an eternal cosmos—into the timeless reasons why the Pythagorean Theorem is true. Moreover, Socrates’ use of a geometric example involves the use of sensed images, diagrams, of our intended purely intelligible objects. In following the proof, we “see” in two ways: we look at the diagram with our eyes and read its meaning with our minds.

In the latter part of the dialogue, Socrates cites recollection as that which distinguishes fugitive right opinion from abiding knowledge. He defines it, this time non-mythically, as “reasoning out the cause” [my translation] (98A). Right opinion can be shaken: it can escape us, Socrates says, like a runaway slave. Seeing why something is true ties down the right opinion, turns it into knowledge and makes the truth genuinely our own. Recollection is the great stabilizer of the soul. The slave boy episode shows that mathematical thinking is the paradigm of recollection as “reasoning out the cause.” To solve the problem of the double square is to see why that square is produced by a certain line as its side. To see the cause or reason is to see what is prior; it is, in a sense, to go back—not to a previous time but to a timeless ground.

The slave boy episode highlights something about which the myth is silent: the role of a guide in recollection. The boy accomplishes an act of learning, but he does so with the help of Socrates, who asks him questions and draws him out. Socrates brings out of the boy’s soul various opinions and ultimately a piece of the real knowledge that is sleeping there. This reminds us that human beings, most of us at least, need someone to shock us out of our dreamy contentment with our beloved but ill-formed opinions.

screen-shot-2016-12-15-at-2-22-23-pmLet us look more closely at how Socrates awakens recollection in the slave boy. We should notice, above all, that Socrates does with the boy what he has been doing all along with Meno: he sets a trap and pushes his respondent into error. Having established that the boy already knows what a square is, Socrates draws the square to be doubled, presumably in the sand, and calls attention to its four sides. He then divides up the area of this square into four equal, smaller squares, thus allowing the side of the original square to be, by hypothesis, two feet in length. The area of this square is clearly two feet by two feet, or four. [Fig. 1] Then Socrates asks whether there could be produced a square with double that area: eight. The boy agrees, whereupon Socrates makes the crucial move and urges the boy to do what will turn out to be impossible. “Try to tell me,” he says, “how large each line [or side] of that area will be” (82D). The boy gives the answer that will be proven false: the side, he says, will be “two times as large.” Socrates has provoked this answer by continually emphasizing doubling. If the boy had not been tempted in this way, he would have been deprived of the experience of realizing his ignorance and susceptibility to error, and of coming to see that not everything that seems reasonable is so. The boy is tricked for his own good. Socrates turns to Meno at this point and asks him to verify that he, Socrates, is not teaching anything but only asking questions. Yes, leading questions that know where they’re going.

meno fig 2Socrates then gets the boy to see that the double side produces not the double square, as the slave was led to believe, but the quadruple square with area “sixteen” (83B-C). [Fig. 2] He then gets him to see that the side of three feet won’t produce the double square either but rather a square of area “nine.” [Fig. 3] This is closer to “eight” but still not correct. But if the required side of the double square isn’t two feet, and it isn’t three, and sides larger than four feet are obviously wrong, then what can this line be if not some multiple of the unit length—some number? Socrates is in fact paving the way for a line that will involve no number-answer at all: he tells the boy that if he doesn’t want to say the right number for the length, he can just show in the diagram what line would produce the double square (83E-84A). At this point the slave does something revealing: he Meno fig 3swears, thereby showing that he is invested in the inquiry and genuinely perplexed. “But by Zeus, Socrates,” he says, “I, for one, do not know.” Socrates wants Meno to be impressed by the slave’s knowledge of his ignorance. It is good and beneficial for a human being to be undeceived regarding what he thinks he knows but in fact does not. Meno responds: “You speak the truth.”

The side of the double square, as the boy eventually learns, is the diagonal of the original square. [Fig. 4] To appreciate the significance of this, we must know two things from Greek mathematics. The first is that “number,” arithmos, refers only to assemblages of units—determinate multitudes. “One” is therefore not a number but the common measure of all numbers. The second thing we must know is that the side of a square and its diagonal are incommensurable; that is, they have no common measure of length. The diagonal, which can be easily drawn, clearly has a ratio to the side—the ratio of a line to a line—but it does not have the ratio of a whole number to a whole number. The word for ratio in Greek is the same as the word for speech: logos. The diagonal is alogos, irrational because it lacks a numerical ratio. It is “speechless” because the ratio of diagonal to side cannot be put into words by answering the question: How many units? The diagonal, in short, can be drawn and pointed out but not said.

Meno fig 4Doubling the square has a direct bearing on Meno’s obsession with speech, since the geometric solution defies speech and points out its limit. When the boy finally grasps the solution, he does what Socrates had urged him to do earlier: he points to the line that produces the double square (85B). His physical gesture is the outward sign that he has seen the truth. Socrates adds in passing that the term “diagonal” is used by the sophists, many of whom were mathematicians and professional teachers of mathematics. The reference to a geometric term points out that it is possible to recognize the line without knowing its name. To be sure, if our knowledge of anything is to be complete, we must know the technical terms; but using such terms, jargon, often results in glibness. In this case, the term “diagonal,” though useful, covers up the uniquely problematic nature of the line, which in its relation to the side cannot be spoken at all.

Thanks to the interlaced nature of mathematical objects, Socrates is able to show the boy how his wrong answer (the double side) can be used to find the solution of the problem. Socrates takes the quadruple square with area “sixteen” and constructs within it another square on the bias, like a diamond. [Fig. 4] It is easy to see that the area of this square is exactly half that of the quadruple square: “eight.” This is what we wanted. Socrates’ cunning use of the wrong square allows the boy to solve the problem. Error has led to truth. This use of falsehood as a means of finding something true suggests that Meno’s definitions of virtue, for all their problems, might be similarly fruitful if they were followed up with greater precision rather than abandoned.

Through his willingness to be drawn out by Socrates’ questions and to expose himself to error, Meno’s slave has done something his master, Meno, refuses to do: he has learned. The episode inverts the conventional view of who is master and who slave. The boy has demonstrated what the dialogue wants us to regard as the virtue that most makes us human and puts us in touch with our eternal selves—the virtue of recollection as openness to learning. Socrates has dramatized this for Meno in yet another attempt to induce him to inquire. Meno agrees that leading the boy to know his ignorance about the double square has not harmed him but on the contrary has made him better (84B). He also agrees that if the boy were questioned repeatedly, he would understand geometrical matters “no less precisely than anyone else” (85C). The reason is that all nature is akin, and one act of learning promises another. None of this requires teaching, says Socrates, but only questioning—the eliciting of what is already within. In the myth, since the soul is immortal and has seen everything, learning is eternally possible. Now Socrates reverses the logic: since the boy has learned something no one has taught him, truth must have been in his soul all along and his soul must be immortal (86B). This may be Socrates’ way of enticing Meno to realize that he has an intellect as well as a memory and therefore a relation to undying truth.

But Meno refuses to be inspired and reverts, as if completely unaffected by what he has just witnessed, to his original question about how virtue is acquired. Socrates relents and brings the conversation back to the theme of ruling:

Yet, Meno, if I were ruling not only myself, but you too, we would not first look at whether virtue is something teachable or not teachable before we first sought what it is itself: but since you don’t even try to rule yourself, in order indeed that you might be free, you both try to rule me and do rule me, I will yield to you—for what can I do? (86D-E)

Socrates then suggests that they proceed by hypothesis, as geometers do: if it turns out that virtue is a kind of knowledge, then virtue would come to human beings by teaching. The conclusion that Socrates and Meno reach, on the basis of a highly questionable argument, is that there are no teachers of virtue and that virtue is not practical wisdom or prudence (98E). How virtue is acquired, and what virtue itself is, remain unsolved problems—exercises left for the reader.

Here my talk ends, not just because I am out of time but also because the dialogue at this point turns away from learning as recollection in order to focus on teaching, teachers and conventional statesmen. A Platonic dialogue usually has an ascent followed by a corresponding descent. In the Meno, Socrates, under compulsion, “goes down” into the cave of conventional politics and right opinion or orthodoxy. Here he meets his nemesis—the politically correct and angry Anytus. The going down is a descent into Hades, the region from which recollection—the purifier of the soul—is meant to deliver us. Since virtue seems to be neither “by nature nor something teachable,” Socrates says, it is acquired through some unaccountable theia moira or divine dispensation (99E). He adds, however, that among the souls in Hades (that is, the city) there may be a true statesman who can make a statesman of another—a Tiresias who “has his wits about him,” while the rest are flitting shades (100A). Tiresias is the prophet whom Odysseus meets on his journey to the Underworld in the Odyssey.

Socrates, by seeking to purge Athens of its lazy attitude toward thought, thereby making his fellow citizens more civilized and moderate, is that very Tiresias, who practices the true art of statesmanship by infecting others with his knowledge of ignorance and need to inquire. The “secret teaching” about recollection is meant to turn Meno—and us—away from acquisition and toward recovery in two senses: recovery of forgotten vision and recovery of a condition of soul that is “whole and healthy.” The teaching tames the lust for what we do not possess—whether glory or wealth or rule over others or the golden opinions of the wise—by arousing the desire to turn within in order to be reunited with the wisdom to which are souls are naturally wedded. The philosopher, in his heroic life of inquiry, is like Odysseus, whose desire is not to seize foreign lands but to go back home.

This speech was originally given at the St. Michael’s College in Colchester, Vermont (October 2015). Books on the topic of this lecture may be found in The Imaginative Conservative Bookstore.

[*] All translations are from Plato’s Meno, tr. with annotations by George Anastaplo and Laurence Berns, Newburyport MA: Focus Publishing 2004.

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