The Slave Boy Experiment in Plato's 'Meno'

What does the famous demonstration prove?

One of the most famous passages in all of Plato's works—indeed, in all of philosophy—occurs in the middle of the Meno. Meno asks Socrates if he can prove the truth of his strange claim that "all learning is recollection" (a claim that Socrates connects to the idea of reincarnation). Socrates responds by calling over an enslaved boy and, after establishing that he has had no mathematical training, gives him a geometry problem.

The Geometry Problem

The boy is asked how to double the area of a square. His confident first answer is that you achieve this by doubling the length of the sides. Socrates shows him that this, in fact, creates a square four times larger than the original. The boy then suggests extending the sides by half their length. Socrates points out that this would turn a 2x2 square (area = 4) into a 3x3 square (area = 9). At this point, the boy gives up and declares himself at a loss. Socrates then guides him by means of simple step-by-step questions to the correct answer, which is to use the diagonal of the original square as the base for the new square.

The Soul Immortal

According to Socrates, the boy's ability to reach the truth and recognize it as such proves that he already had this knowledge within him; the questions he was asked simply "stirred it up," making it easier for him to recollect it. He argues, further, that since the boy didn't acquire such knowledge in this life, he must have acquired it at some earlier time; in fact, Socrates says, he must have always known it, which indicates that the soul is immortal. Moreover, what has been shown for geometry also holds for every other branch of knowledge: the soul, in some sense, already possesses the truth about all things.

Some of Socrates' inferences here are clearly a bit of a stretch. Why should we believe that an innate ability to reason mathematically implies that the soul is immortal? Or that we already possess within us empirical knowledge about such things as the theory of evolution, or the history of Greece? Socrates himself, in fact, acknowledges that he can't be certain about some of his conclusions. Nevertheless, he evidently believes that the demonstration with the enslaved boy proves something. But does it? And if so, what?

One view is that the passage proves that we have innate ideas—a kind of knowledge we are quite literally born with. This doctrine is one of the most disputed in the history of philosophy. Descartes, who was clearly influenced by Plato, defended it. He argues, for instance, that God imprints an idea of Himself on each mind that he creates. Since every human being possesses this idea, faith in God is available to all. And because the idea of God is the idea of an infinitely perfect being, it makes possible other knowledge which depends on the notions of infinity and perfection, notions that we could never arrive at from experience.

The doctrine of innate ideas is closely associated with the rationalist philosophies of thinkers like Descartes and Leibniz. It was fiercely attacked by John Locke, the first of the major British empiricists. Book One of Locke's Essay on Human Understanding is a famous polemic against the whole doctrine. According to Locke, the mind at birth is a "tabula rasa," a blank slate. Everything we eventually know is learned from experience.

Since the 17th century (when Descartes and Locke produced their works), the empiricist skepticism regarding innate ideas has generally had the upper hand. Nevertheless, a version of the doctrine was revived by the linguist Noam Chomsky. Chomsky was struck by the remarkable achievement of every child in learning language. Within three years, most children have mastered their native language to such an extent that they can produce an unlimited number of original sentences. This ability goes far beyond what they can have learned simply by listening to what others say: the output exceeds the input. Chomsky argues that what makes this possible is an innate capacity for learning language, a capacity that involves intuitively recognizing what he calls the "universal grammar"—the deep structure—that all human languages share.

A Priori

Although the specific doctrine of innate knowledge presented in the Meno finds few takers today, the more general view that we know some things a priori—i.e. prior to experience—is still widely held. Mathematics, in particular, is thought to exemplify this sort of knowledge. We don't arrive at theorems in geometry or arithmetic by conducting empirical research; we establish truths of this sort simply by reasoning. Socrates may prove his theorem using a diagram drawn with a stick in the dirt but we understand immediately that the theorem is necessarily and universally true. It applies to all squares, regardless of how big they are, what they are made of, when they exist, or where they exist.

Many readers complain that the boy does not really discover how to double the area of a square himself: Socrates guides him to the answer with leading questions. This is true. The boy would probably not have arrived at the answer by himself. But this objection misses the deeper point of the demonstration: the boy is not simply learning a formula that he then repeats without real understanding (the way most of us are doing when we say something like, "e = mc squared"). When he agrees that a certain proposition is true or an inference is valid, he does so because he grasps the truth of the matter for himself. In principle, therefore, he could discover the theorem in question, and many others, just by thinking very hard. And so could we all.

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