Meno's Paradox

“Meno asks Socrates: "And how will you inquire into a thing when you are wholly ignorant of what it is? Even if you happen to bump right into it, how will you know it is the thing you didn't know?" Socrates rephrases the question, which has come to be the canonical statement of the paradox: "[A] man cannot search either for what he knows or for what he does not know[.] He cannot search for what he knows--since he knows it, there is no need to search--nor for what he does not know, for he does not know what to look for."
Socrates responds to this sophistical paradox with a mythos (poetic story) according to which souls are immortal and have learned everything prior to transmigrating into the human body. Since the soul has had contact with real things prior to birth, we have only to 'recollect' them when alive. Such recollection requires Socratic questioning, which according to Socrates is not teaching. Socrates demonstrates his method of questioning and recollection by interrogating a slave who is ignorant of geometry.
Socrates begins one of the most influential dialogues of Western philosophy regarding the argument for inborn knowledge. By drawing geometric figures in the ground Socrates demonstrates that the slave is initially unaware of the length that a side must be in order to double the area of a square with two-foot sides. The slave guesses first that the original side must be doubled in length (four feet), and when this proves too much, that it must be three feet. This is still too much, and the slave is at a loss. Socrates claims that before he got hold of him the slave (who has been picked at random from Meno's entourage) might have thought he could speak "well and fluently" on the subject of a square double the size of a given square. Socrates comments that this "numbing" he caused in the slave has done him no harm and has even benefited him.
Socrates then draws a second square figure using the diagonal of the original square. Each diagonal cuts each two foot square in half, yielding an area of two square feet. The square composed of four of the eight interior triangular areas is eight square feet, double that of the original area. He gets the slave to agree that this is twice the size of the original square and says that he has "spontaneously recovered" knowledge he knew from a past life without having been taught. Socrates is satisfied that new beliefs were "newly aroused" in the slave. After witnessing the example with the slave boy, Meno tells Socrates that he thinks that Socrates is correct in his theory of recollection, to which Socrates replies, “I think I am. I shouldn’t like to take my oath on the whole story, but one thing I am ready to fight for as long as I can, in word and act—that is, that we shall be better, braver, and more active men if we believe it right to look for what we don’t know...” ~ Wikipedia
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“What exactly is inquiry? What conditions must be satisfied if one is to be able to inquire into something and to find answers to the questions one is considering? What is knowledge, and is knowledge needed for inquiry? If knowledge isn’t needed, what alternative cognitive condition will do? In addition to these general questions, considering Meno’s Paradox in the context of the Meno also requires one to ask: Why does Meno think Socrates is vulnerable to the paradox? How exactly do Meno and Socrates understand the paradox? How, and how well, does Socrates reply to it?...
The dialogue begins with Meno and Socrates inquiring what virtue is. Socrates says that neither of them knows what it is, and that they therefore don’t know anything at all about virtue. Their inquiry eventually fails, insofar as they don’t find the answer to their question: they don’t discover what virtue is. This leads Meno to ask whether inquiry into something is possible if one doesn’t at all know what it is. For, he asks, which of the things one doesn’t know will one put forward as the thing one is inquiring into? He also asks whether, if one were to find the thing one was looking for but didn’t initially know, one would know, or realize, that one had done so. Socrates reformulates Meno’s questions as a dilemma: whether one does or doesn’t know that which one is inquiring into, inquiry is impossible. I shall call the conjunction of Meno’s questions and Socrates’ dilemma Meno’s Paradox. Meno’s Paradox challenges the very possibility of inquiry; it therefore challenges something we routinely take for granted.
Though we might think to dismiss the paradox, Plato doesn’t do so. On the contrary, he offers an elaborate three-part reply. In the first and third stages, Socrates introduces his celebrated theory of recollection, according to which we all have immortal souls that knew some range of things prenatally; inquiry and learning, he says, are recollection. Since recollection is possible, so too are inquiry and learning. Hence the conclusion of Meno’s Paradox—that inquiry is impossible—is false. The second part of his reply—which Leibniz calls ‘a very solid doctrine’ (Discourse on Metaphysics 26) is sandwiched in between the two discussions of the theory of recollection. In it, Socrates cross-examines one of Meno’s slaves about a geometry problem. He shows how the slave, despite being untutored in geometry, can not only inquire about but also discover the right answer. This too shows that the conclusion of Meno’s Paradox is false: contrary to it, inquiry, indeed successful inquiry, is possible. If the conclusion of the paradox is false, the paradox is unsound. But where exactly does it go wrong? Is it valid but unsound? If so, what premise or premises should we reject? Or is it invalid? If so, what inference should we reject? To answer these questions, we need to understand the point of the geometrical discussion and of the theory of recollection, and how they fit together. As we shall see, this will, among other things, require us to understand Plato’s distinction between knowledge and true belief…
Thinking one doesn’t know something, and not knowing it, are different. A modest knower might know something without realizing that she knows it. Further, someone might think that she knows something, when she doesn’t. To be sure, Socrates claims that he has human wisdom, which consists, at least in part, in not thinking one knows something when one doesn’t know it; he lacks false pretenses to knowledge. But most of us lack this human wisdom; most of us, as Socrates often points out, think we know things that we in fact don’t know…”
At the beginning of the Meno, Meno asks Socrates whether virtue is teachable. Socrates replies that he doesn’t know the answer to that question or, indeed, anything at all about virtue. For he doesn’t know at all what virtue is; and, if one doesn’t know what something is, one doesn’t know anything about it. Meno agrees; and, after being questioned by Socrates, he discovers that he doesn’t know what virtue is either. Hence he concludes that, like Socrates, he doesn’t know anything about virtue. Frustrated by his failure to explain what virtue is, he turns to the offensive and asks Socrates three related questions: But how will you inquire into this, Socrates, when you don’t at all know what it is? For what sort of thing, from among those you don’t know, will you put forward as the thing you’re inquiring into? And even if you really encounter it, how will you know that this is the thing you didn’t know? Socrates replies: I understand the sort of thing you want to say, Meno. Do you see what an eristic argument you’re introducing, that it’s not possible for someone to inquire either into that which he knows or into that which he doesn’t know? For he wouldn’t inquire into that which he knows (for he knows it, and there’s no need for such a person to inquire)…
About foreknowledge—or about prior cognition, if knowledge isn’t needed—concerns its content: what must one know, or have some sort of grasp of, to be in a position to inquire? Suppose one is inquiring what the real essence of virtue is. Must one already know what it is? So the matching version of a foreknowledge principle might seem to imply. But there are other possibilities, all of which have been advocated either as what one should say or as what one or another philosopher at issue here thinks. For example, it’s been argued that, to inquire what virtue is, one must know, or in some way grasp, a feature true of all and only cases of virtue; or a feature true of all cases of virtue; or a feature that enables one to distinguish virtue from other things with which it might easily be confused; or a feature that enables one to represent virtue to oneself in some way. On yet another view, all one needs to do is to understand what the question being considered means.
It’s not plausible to think that we can inquire into something only if we know its real essence. Scientists were able to inquire about water before they knew, or even believed, that it is H2O. If we need to know something’s real essence to inquire into it, the scope of inquiry will be considerably more limited than we take it to be. Surely knowing, or in some way cognizing, just some sort of distinguishing mark, where that falls short of knowing something’s essence, will do?”
~ Gail Fine, The Possibility of Inquiry: Meno's Paradox from Socrates to Sextus