[BLANK_AUDIO] As I was saying at the end of the previous video, instead of reading Socrates as a bad cognitive scientist, that is, a guy who doesn't know how to structure a clean experiment, maybe we should read him as a model educator. Let me quote a passage from Bertrand Russell, famous twentieth English philosopher, who had a special interest in math, but really, he was interested in everything. The following quote is from an essay entitled The Study of Mathematics. It's from 1910 and can be found in a volume entitled Mysticism and Logic. The essay starts by saying pretty much that this is all out of Plato. So I'm not adding anything new there. But Russell laments that mathematicians don't read Plato these days, and the classicists, they don't do math. well. Russell changed all that, by the way. Largely under his influence, English language philosophy became a lot more math- and logic-centric in the 20th century. But that's another story. Let's stick with this one essay. Quote from Russell, one of the chief ends served by mathematics when rightly taught is to awaken the learner's belief in reason, his confidence in the truth of what has been demonstrated, and in the value of demonstration. This purpose is not served by existing instruction; but it is easy to see ways in which it might be served. At present in what concerns arithmetic, the boy or girl is given a set of rules, which present themselves as neither true nor false, but as merely the will of the teacher, the way in which, for some unfathomable reason, the teacher prefers to have the game played. To get a child's eye view on the subject, I decided to commission some art, from my nine year old daughter, Violet. To her credit, she immediately grasped Russell's philosophy. I trust her little moral drama is clear enough. Maybe clear enough that I should consider transferring my daughter to a different school. No, I've met her math teacher, and she's a lovely person. I don't know where any of this is coming from. [BLANK_AUDIO] What I like about my daughter's cartoon math class is that it perfectly expresses how a wrong, sort of, mathematical education can leave you, apparently competent at mathematics, yet lacking in the sense of what math truly is. What the nature of number truly is. Those students are smiling at the end, but not because they have come to regard these opinions as their own, as we might say. But because they want to please teacher. They're merely looking to their social environment for cues as to how to get along. Indeed, as Russell goes on to argue, there's a real danger that the students are going to get the wrong idea, not just about one, two, three, four, five. But about right and good. They are in danger of developing a sense, not just that it's completely arbitrary how numbers work, but that it's completely arbitrary what right and good are. What these concepts mean. Let's read on in Russell, just a bit. Russell admits that, to some limited degree, drilling at the beginning is inevitable. Maybe it's not right to hit students over the head when they get something wrong. But, probably you have to teach numbers, at first, as if it's a song, like the alphabet song. [MUSIC] 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, then comes 11. [MUSIC] Nothing wrong with that. Kids like songs, just like Meno likes colorful myths. But you want to get past that as soon as possible, because learning a song is not how you really learn math, given what math really is. You want to get as quickly as possible, not to the point where teacher wants you to be or even to Euclid's axioms, but to where the learner actually is, to what the student truly thinks about this. Russell again, I'm quoting. The learner should be allowed at first to assume the truth of everything obvious, and should be instructed in the demonstrations of theorems which are at once startling and verifiable by actual drawing. In this way belief is generated; it is seen that reasoning may lead to startling conclusions, which nevertheless the facts will verify; and thus the instinctive distrust of whatever is abstract or rational is gradually overcome. The point, in other words, is exactly what Socrates is trying to get us to see in this example. To make the student realize that these surprising results are, must be the student's own opinions, astonishing as that is. Now, hearkening back to a question I asked you several videos ago, it doesn't follow that math is subjective. Remember how I tried to trick you into thinking math was like ethics? Seems like ages ago, I know. Anyway, Russell would hate me using that word in this connection, subjective. Math is not subjective, he would say. And Plato, he doesn't really have a word that quite corresponds to that, and if he did, he wouldn't like it either. But Russell wouldn't deny that there is a sense in which the point is to teach the student to associate math with a sense of inner truth, of your own true opinions. Which I think we more typically associate with ethics. And going with this, is a strong sense that the inner must correspond with the outer. Maybe Socrates goes a bit overboard with that reincarnation stuff. Maybe just because he's messing with Meno. What do you think? Is he just messing with Meno? But the thing about math is, you can do it in your head and the world has to be that way, too. It's like a miracle. And isn't that how you think ethics works, too? Be honest now. You can do it just by thinking about it, and it's right. It's binding on the world. If murder has to be wrong, because, just think about it, then murder is wrong! And if you don't think so, you're wrong! To put it very briefly, if only you'd been taught math right, you'd expect people to make sense when they talk about what's good and what's right. And for there to be sense to be made out of that. Russell, one last time, quote. What is best in mathematics deserves not merely to be learned as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement. Real life is, to most men, a long second-best, a perpetual compromise between the ideal and the possible. But the world of pure reason knows no compromise, no practical limitations, no barrier to the creative activity embodying in splendid edifices, the passionate aspiration after the perfect, from which all great work springs. Remote from human passions, remote, even, from the pitiful facts of nature, the generations have gradually created an ordered cosmos, where pure thought can dwell as in its natural home, and where one, at least, of our nobler impulses can escape from the dreary exile of the actual world. End quote. I haven't had a quiz in a while. Let me just say it. All answers accepted on this one. No pressure in that sense. But if there's any value in reading the Meno, I'm pretty sure that it has to involve poking with you, you with a stick until you look inside yourself and say what you really think about this quiz question. So here I go. Do you think this is right? Poke, poke. Here's the quiz. Do you think Russell is right? That is, is this opinion your own? We should study math, not just because it's useful, but in order to develop a sense of what is highest and most perfect, and to grow our sense of idealism in the face of the imperfections of the world around us. A, that is literally the craziest thing I've ever heard. It's just math. B, maybe I feel that way a little. But I never felt that way in math class. C, yes, there's something to it. But he's laying it on thick. D, you are like a god, Bertrand Russell. Never have I heard anything so inspiring and true. Also, I finally get it about Plato's Meno. Me, I'm a B with a little bit of C. Maybe one C, or I feel a little D flicker in my soul. Which is interesting, because, when I was younger, I definitely would have said A. Let me conclude this video with a final thought about Plato's attitude to math. And then, next few videos, it's virtue again, and we're done. Two videos ago, I raised the possibility that maybe, what really excites Plato is this bright idea. If we could only find something in ethics that corresponds to Euclidean axioms or postulates, well then, we'd really be ready to roll. By the way, quick fact check. Euclid actually wrote a century later. Plato didn't have actual Euclid, but he definitely had, proto-Euclid type stuff, just wanted you to be clear about the dates on that. As I was saying, if we could turn ethics into geometry, then the Socratic method, asking people pesky questions about what they think virtue is for example, might flip from the negative to the positive column. Instead of just demolishing beliefs in a very rough way, we'd be poised to build up from solid, certain foundation in a very precise way. To put it another way, Plato, he probably would be one of those guys who hates Wikipedia, right? He founded his famous academy, community of technical experts. Supposedly it said right over the door, you can't come in if you don't know math. So, no random guys wandering in and just editing the papyrus any old way. The whole point is to get past all that. And yet, and yet, what is every one, or nearly every one of these Plato, Platonic dialogues but some random guy, interlocutor, not an expert, wandering on stage and being provoked to say whatever the hell he really thinks? The whole point of writing these things as dialogues, with these sorts of characters, is that you have to start with that. Not with axioms, not even with experts, but with the half-baked opinions of some random guy. Plato was so brilliant. Just as he invented movies before there were movies so he could complain about how bad the movies are. That's the myth of the cave. So he also invented Wikipedia talk pages before there was Wikipedia, just so he could complain about how unreliable the entries are. The guy's a genius. Well that's just great. You say, good for Plato. He's a world champion complainer about how bad stuff is, before it even is. Meanwhile, what does he think we should, you know, do about how bad everything is? Here's the thing you might easily miss from the first part of the dialogue. I didn't mention it last time when I was making my quick rundown of interesting points you shouldn't miss. But it's interesting, you shouldn't miss it. At a certain point, Socrates is trying to please Meno by defining shape. He proposes that shape is the one thing that invariably accompanies color. And Minot says, but what if someone then says they don't know what color is? And Socrates says, for the purposes of good conversation, we don't need to be as strict as geometers. We don't need to drag everything back to utterly simple ideas and concepts. It is enough that Socrates and Meno, quote, should give answers which are not only true, but also make use of terms the questioner acknowledges that he knows, unquote. This is kind of ironic. Meno, of all people, is suddenly pretending to be oh, so rigorous about everything. Obviously, this is just him being a debater. It's a classic debater move. Just insist that your opponent define everything, so he bogs down and can't get anywhere. But doesn't Meno have a point? If Socrates thinks it's okay for us to start where we are, that is, just with what we agree that we think is true, what problem could he possibly have with Meno giving speeches about whether virtue can be taught, even to large audiences? Meno thinks he knows what virtue is. The audience thinks it knows what virtue is. Everyone always thinks they know about this stuff. Maybe Meno is just being a pain, suddenly asking for definitions. But two wrongs don't make a right. How can Socrates be so lax as to allow us to start with any old thing we think, as opposed to what has been absolutely established in some axiomatic fashion? That's a tough one, I think. This much is clear. Socrates is making the point that Meno should be honest, sincere. None of this speech and debate stuff. And cooperative. Again, don't just try to beat your opponent. We want to learn. This is exactly what Russell says, to inculcate the right attitude, start where the student is. Seeing what follows from what you truly think is what's important. Whether this is right or not, at least Plato and Russell agree, which is something. In mathematical terms, you might say that the contrast is between so-called synthetic geometry - that's Euclid-style stuff - and analytic geometry. Euclid stow, shows you how to start with simples and build up. But how can you start with complexes, complex figures, as it were, and break down, but in a rigorous truth-oriented sense? We still haven't solved that problem for ethics. The problems I pointed out regarding the Socratic method, they still seem to apply. We want truth. But testing for consistency is not a method for finding truth. Regarding ethical problems, starting where the student is, presumably means, in effect, just asking people what seems to them obviously true about virtue, or about the teaching of virtue. And then somehow working from there. But how do you do that rigorously? I guess that's why in the third and final section of the dialogue, we turn back to virtue.
