[MUSIC] What are we to think of this exhibition? It is easy to protest that Socrates has been teaching the slave, that he has in fact just given the slave a very nice geometry lesson. But that's not using teaching in the very restricted way Socrates is when he contrasts teaching with inquiry. Inquiry is where you figure out the answer by yourself or yourselves, whereas teaching is having somebody else give you the correct answer. Think of being given a list of names and dates to memorize for a history test. That's what Socrates has in mind as teaching. Of course, we might protest, the slave hasn't in fact figured it out all on his own. He has figured out the answers to the step by step questions that Socrates asks him, but he hasn't been the one to figure out which questions to ask. And asking the right questions here is crucial for solving the problem. If Socrates hadn't been there asking the questions he did, would the slave have figured out the side of the double square is built on a diagonal? It doesn't seem likely. But keep in mind the bigger point Socrates is trying to make. Meno has despaired of whether the sort of inquiry Socrates engages in, question and answer, can ever arrive at the right answer. While we must grant that getting the correct answer depends on asking the right questions. Let's think about what we need in order to ask the right questions. Certainly it is very helpful to have someone who already knows the answer and has figured out the right questions to ask. But is it necessary? Isn't it possible to come up with the right questions by trial and error? By collaboration, by hard work, maybe sheer luck? By learning from one's mistakes and keeping an open mind about what will count as an answer? Where do we think this proof came from in the first place? Most likely, it came from a community of inquirers trying one strategy, trying another, giving up for a while. Coming back with new questions to ask and new strategies to take, and going on in this manner until finally, someone does hit upon the line of questioning that solves the problem. Socrates doesn't claim that just anyone can come up with the right questions on their own or certainly not in the first half hour they set out to solve the problem in. His claim about what just anyone can do, is that we all have it in us to answer the step by step questions correctly when we consider the matter carefully. Just as the slave in able to answer when Socrates asks him to figure out the area of the three foot by three foot square, for instance. Okay, we might grant to Socrates that we all have it in us to inquire successfully into problems like, what is the side of the double square. Our native mathematical ability makes most of us able to recognize the correct answers to the step by step questions that lead to the correct solution. But why should we suppose that the same is true of inquiry into questions of the sort that Meno and Socrates are asking? Like, what is virtue? Or Euthyphro's question, what is piety? These are what philosophers call normative questions, questions about right and wrong, about good and bad. Well, Socrates' proposal is that questions about virtue and goodness and indeed all philosophical questions are like mathematics and geometry in one crucial respect. A respect that Heraclitus captured in his declaration, I searched into myself. When we set out to answer such questions as what virtue is, or whether it is pious to prosecute your own father, or what knowledge is, we don't turn over rocks, drill into the Earth, look for genetic mutations, or by and large engage in the methods of empirical inquiry. Rather, Socrates points out, we proceed by examining what we believe about piety, about virtue, about knowledge. Not just accepting uncritically when it first occurs to us, or what sounds impressive when we hear from somebody like Gorgias. But, comparing it with other things we believe, noting conflicts, and then resolving the conflicts. And we do this in conversation with other people to make sure we aren't overlooking problems and challenges in what seems fine to us when we first think about it. This is a kind of internal housekeeping of our beliefs. And in the case of mathematics and geometry, it is a perfectly respectable way of inquiring and arriving at trustworthy answers. Now, many readers today might still be inclined to resist. Well, mathematics and geometry are objective. Their questions have right and wrong answers, whereas questions about virtue, about what's good and bad, are just matters of opinion. But this is a substantive philosophical position. Think about how you might go about defending it. Plato thinks that questions about value, and indeed all philosophical questions, are as objective as mathematics and geometry. He notes a substantial similarity in the way we go about addressing these questions. That is, we look into ourselves. He notes the success we achieve on the mathematical front. And then he proposes a theory that explains our success in the mathematical case, and predicts the possibility of success in the ethical and the philosophical case. If we are going to resist Plato on this point, the onus is on us to come up with an alternative theory of what sort of thing good and bad are. A theory on which they are substantially different from mathematical and geometrical objects like squares and triangles. That is, we have to engage in the sort of inquiry, that is a philosophical inquiry, that he is exhorting Meno to engage in. As we go forward in our study of Plato, we will see more of the theory of goodness that he develops, including its relation to mathematics and geometry. That will be in the Republic and the Timaeus. But before we leave the Meno, we can see how he treats a different philosophical question. What is knowledge?