The Geometry of Virtue
Plato’s Meno

2,243 words

Socrates: Tell me, boy, do you know that a figure like this is a square?
Boy: I do.
— Plato, Meno

But geometric existence is not psychic existence.
— Jacques Derrida, Introduction to Edmund Husserl’s The Origin of Geometry

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The dialogue known as Meno is generally placed in the early period of the Platonic corpus. It is an excellent introduction to Plato, and nothing like as demanding as Republic or Laws, both of which are often flung at unsuspecting and unprepared undergraduates. The dialogue in the Meno (we should never forget that Plato’s philosophy is conversational, some of the longer monologues such as Republic or Timaeus notwithstanding) concerns the nature of virtue, but features a curious episode concerning both geometry and Plato’s theory of the transmigration of souls. I’ll give a brief overview of the dialogue, but I want specifically to concentrate on the segment in which a slave-boy – who is never named – belonging to Socrates’ companion and interlocutor in the dialogue, Meno, appears to show a knowledge of geometry he did not – could not – have gained from experience. The problem of the origin of this commutation of knowledge – which concerns geometry but also virtue – has come back after all these centuries to haunt us today, and provide just as many questions as Socrates had for those in conversation with him. Plato does not provide all that many answers (this is the legacy of Socratic skepticism) but he shows how to frame the right questions. This will be the great lesson Heidegger understood.

Meno himself was a politician from the Greek state of Thessaly, and perhaps was on Jacobean playwright John Webster’s mind when he had Cornelia – a Cassandra-like figure – say the following in his play The White Devil (first performed in 1612, and published in 1613):

O that this fair garden
Had with all poison’d herbs of Thessaly

At first been planted; made a nursery
For witchcraft, rather than a burial plot
For both your honours!

Perhaps Thessaly was known for its poisonous politicians. A politician has just arrived in Webster’s scene, after all. Certainly, Meno wishes to know something important to today’s politicians (and cultural ruling class), at least in style if not in substance. His central question opens the dialogue:

Can you tell me, Socrates, whether virtue is acquired by teaching or by practice, or if neither by teaching or by practice, then whether it comes to man by nature, or in some other way?

The Ancient Greek term Plato uses, and which translates as “virtue” (any definitions I use concerning Plato come from the Liddell-Scott dictionary), is ἀρετή, or aretē, which also translates as “excellence” or “goodness.”

Classical Greek terms are often polyvalent, having more than one meaning when translated into English (consider logos). “Excellence” and “goodness” are interesting readings of aretē, in the context of virtue. A serial killer can be “excellent” or “good” at his preferred line of work. Does this mean he is virtuous? Socrates voices many of these ambiguities through his various interlocutors in the Dialogues. One of the great Platonic lessons is the fragility of definition, something the effect of which we are currently seeing in the West, almost two-and-a-half millennia after Plato wrote his dialogues and effectively founded white Western philosophy.

The conversation about the nature of virtue is, as noted, as clear an example of Socratic dialogue as anyone new to Plato could wish for, but here it is of secondary importance in the context of Meno. We’ll get back to its present-day incarnation, but what holds the attention in Meno is not virtue, but geometry.

Socrates suggests that “there is no teaching, but only recollection”, and Meno requests an example. Socrates calls over a slave-boy owned by Meno and asks him simple questions based on a square Socrates has marked in the dust. The puzzle of the square presented to Meno’s (nameless) slave-boy is visual, and that should be stressed. Therefore, if you are a naturally geometric/visual thinker, you can sketch it out for yourself either mentally or on paper. If, like myself, you are a linguistic, abstract and non-spatial thinker, this is a very good explanation of the geometrical details of this section.

To begin with, the boy answers Socrates’ questions about the expansion of a square by believing that to double the sides of the square is to double the area. Gradually, although he does not yet know the amount of increase necessary, he sees that doubling the sides does far more than double the area, and so he knows that he is wrong. Here we have the first seeds of Socratic humility. Socrates knows that he does not know.

Meno’s slave-boy is advancing towards knowledge, or at least its possibility, by the recognition of the limits of that knowledge. As for Socrates and Meno, they are left with two options for the acquisition (or inherence) of virtue: It is either natural or taught. At Meno’s request, and despite the strange swerve into geometry, the conversation returns to the acquisition of virtue (via teaching or a natural predisposition). This pair will be joined at the end of the dialogue by a tertium quid, a strange opt-out from the argument, but of the pair, teaching is the more straightforward. Plato has much to say about it in Laws and Republic. What of virtue being natural? How did it get there? And how does it sit with us, we readers of Plato?

The innate ability of Meno’s slave to grasp basic geometric principles, Plato calls anamnesis. This means “recollection” or, more literally “unforgetting.” We recognize the root of our own English word, “amnesia”, and anamnesis is constructed using the alpha privative (the first one or two letters, which turn an Ancient Greek word into its opposite). Perhaps we can find a more modern example of this recollection than a square drawn in the dust in the Athenian square if we move from Ancient Philosophy to modern psychology, and pay a visit to Sally and Ann.

Sally and Ann – also known as “Naughty Ann”, for reasons which will become apparent – are two dolls who live together in a doll’s house. They are used to create scenarios for a range of psychological tests – the “Sally-Ann Test” – on young children, and have been since their inception in the 1980s. The overall results of the testing bear a startling resemblance to Platonic anamnesis. The test produces a certain response in children up to a particular age, then the result changes.

Sally and Ann both have little chests-of-drawers in which they keep their favorite and important things. Sally has a particular favorite, a glass marble. When she has to go to the shop, she checks that her marble is safely in her drawer. (The child is watching all of this, and the evolving situation is clarified verbally by the psychologist). While Sally is shopping, Naughty Ann earns her soubriquet by taking Sally’s marble (which she obviously covets) out of Sally’s drawer and putting it into her own. When Sally returns, and wishes to be reunited with her marble, the child is asked where she will look for it. Will Sally look for the marble in her drawer or in Ann’s? Up until a certain age (which differs when factored with IQ, autism, etc.), the child will answer that Sally will look in Ann’s drawer because that is where the marble is. The child knows this because s/he saw it happen, and small children are obviously strict empiricists. When the children are at a mental age to understand the situation fully, they begin to say that Sally will look in her own drawer because they have understood two important things. Firstly, what is relevant about the scenario and its attendant question is not events in the external world, but internal, psychological states. Secondly, people are able to maintain incorrect beliefs when the external world is taken back into account. There is a lot happening here. How “Platonic” is this childish epiphany?

Children are not taught this psychological and epistemological lesson, nor is there any way they can learn it from observation. Indeed, for the pre-aware child, not only does observation not help, it hinders the child’s decision-making abilities. This twin revelation, and the almost Husserlian “bracketing off” of the external world, seems simply to arrive wholesale, with some mental persuasion in the form of contextual questions. It’s certainly consistent with Platonic anamnesis.

But are we then bound to say that the children watching Sally and Naughty Ann have eternal souls which have always existed and will always exist – as Plato famously did – albeit in other bodies to which they will successively transmigrate? I’m not sure a child psychologist would get much research funding for such a project. But the Platonic use of myth does not disqualify Platonic thought. Somehow – like the gradual revealing of the properties of the square in the mind of Meno’s slave-boy – there is apparently a predisposition to recognize truths without being taught them. How about the truth of virtue? We’ll leave Sally and Ann’s tempestuous household, and return briefly to the Athenian square, before we finally return home to the present, to see what virtue has become.

Socrates But if the good are not by nature good, are they then made so by instruction?

Meno: There appears to be no other alternative, Socrates. On the supposition that virtue is knowledge, there can be no doubt that virtue is taught.

Socrates: Indeed, but what if the supposition is erroneous?

What indeed. This rather low blow by Socrates leads to the tertium quid noted: “The result seems to be… that virtue is neither natural nor acquired, but an instinct given by God to the virtuous.”

Socrates seems to shy away, at the last, from either education or anamnesis, and leaves virtue in the hands of the demiurge:

Socrates: Then, Meno, the conclusion is that virtue comes to the virtuous by the gift of God. But we shall never know the certain truth until, before asking how virtue is given, we enquire into the actual nature of virtue.

Socrates leaves abruptly, ending the dialogue, much like Pontius Pilate would do four or so centuries later when confronted with the problem of what truth is.

Back in our own precarious times, we hear a phrase (exclusively from the political right) which incorporates the subject of the Meno: Virtue signaling. We all know how this works, and how much it has been extended and amplified by the internet. For Plato, the virtuous could display their “excellence” or “goodness” only to one another or, if more powerful, to a small number of people. Now you can tell it to the world. And the self-elected virtuous of today’s market-square tend to be members (even if low-ranking) of the new Freemasonry running what’s left of our culture. In Platonic terms (and with cognitive dissonance no longer a psychical malfunction but a lifestyle choice), they believe all three of the options the Meno leaves us with:

1. Can virtue be taught? Yes, and we are the ones to teach it.
2. Is virtue inherent and needing only to be reawakened? Yes, and its laws have all the incontrovertibility of geometry.
3. Is virtue a gift from God to the virtuous? Yes, although not from God, for reasons which should be obvious. But the virtuous are the elect.

Plato’s Meno is still with us, the stakes are just higher, the truth made even more obscure by today’s version of the Sophists of whom wily Socrates was so suspicious.

As noted, the Meno is an excellent introduction to Plato, and I recommend the public domain version available as an ebook at Amazon here for two reasons. Firstly, it is free. This is the great paradox of our age. The phrase “dumbing down” has entered the English language, and refers to the banalization of culture. Quite how this happens when much classical, white, Western philosophy is available at no cost online is beyond me. Secondly, the edition is translated by Benjamin Jowett, who also provides a detailed introduction to the Meno, as he does to all the Platonic dialogues. Jowett was a brilliant Victorian classical scholar, and when buying any edition of Plato, I would recommend ensuring they are accompanied by his introduction.

White Western philosophy will not answer all your questions. Indeed, it may not answer any. But it will teach you how to frame the right questions to ask. The question posed by Plato in Meno is not, what is virtue? If it has strict laws which recognize only right and wrong answers, virtue should be as straightforward as commensuration. Rather, the question is; to what extent does virtue resemble geometry?

Although in moral terms (where virtue is, morality can never be far behind), the shortest line between two points (actually a Pythagorean discovery) is not always a straight line, and there is not a geometry of virtue, teachable and of divine provenance (or its modern, Godless equivalent). Virtue – and by extension morality – does not possess the qualities of geometric truth, and to believe it does goes against the Socratic code:

I too speak rather in ignorance; I only conjecture. And yet that knowledge (episteme) differs from true opinion (doxa) is no matter of conjecture with me. There are not many things which I profess to know, but this is most certainly one of them.

Virtue signaling, whatever it is and however grotesquely it shows itself, is not a lesson in geometry. As Nietzsche understood, there is no Euclidean morality.