>> Just to remind you, or in case you're just dropping in, let me ask you that quiz question from the previous video again, rephrasing it, just a bit, for variety. When you think about an ethical problem, what should I do? Do you set about solving it the same way you try to solve some problem on your homework, for your math class? A, yes. B, no. Ya'll said b right, because you're not insane? On the other hand, if you're like Plato, and actually had the opposite reaction, apparently, so it would seem, then just bear with me as I attempt to make your more sensible colleagues more receptive stuff to this crazy stuff I'm selling on Plato's behalf, unless he's lying. Another little quiz. Alright, you're so smart. If ethics isn't like math, it must be because ethical thinking has some feature or property, or features that math thinking lacks. So what is it, bright eyes? What's ethics got that math ain't got, and vice versa? I'm not going to use the in-video quiz system this time, because I don't want to compose any MCQ style a through e set of possible answers. I want you to do that. Pause this video. Jot down a few key words that seem to you to get at the essential differences between math thinking and ethics thinking. First thing that comes to your head. That is, how is thinking about how should I live questions qualitatively different from doing that problem set for your math class? Are you done? You jotted down your answers? All right. Coursera hasn't implemented mind-reading technology yet, so I'm forced to guess. I'm guessing that a lot of you say ethics is subjective or a matter of personal feelings, the kind of inner truth or truth for me, whereas math is this objective, impersonal thing. Ethics equal subjective, math equals objective. That's what makes them different. I realize, of course, that many of you probably didn't say that. That's fair enough. But this is the one I'm picking, because I think it's typical enough, and we can warm up on it, in an interesting way. Say it again, ethics equals subjective stuff, math equals objective stuff. I could tackle it from either direction. First, do you really think ethics is subjective? Lot of people say things like that, but that would seem to imply that thoughts like, murder is wrong are just subjective preferences. You like murder, I don't. I say potato, you say potatoe. I say wrongful death, you say fun. People have their little ways. But let's tackle it from the other side. Math is objective. No, math is the most subjective thing there is. What do I mean by that? You do it all in your head. What could be more subjective than something you do all in your head? Here, let me prove it to you. A quiz. So it's going to be tough. What's 2 plus 2? A, 5. B, 4. C, I don't know. B sounds better than a when I just think about it, but I would still like to test that armchair hypothesis empirically in the lab, just to be sure. The answer is b. More specifically, a is wrong, b is right, and c is crazy. You don't need to go out and add two apples to two apples to get four apples, or two aircraft carriers to two aircraft carriers to get four aircraft carriers. The additive function does not need empirical testing. When it comes to adding, you can tell what the right answer is by thinking about it. But saying b is right, and c is therefore crazy seems tantamount to saying math is not scientific or testable. Not if we take science to be empirical. Galileo famously said, mathematics is the language of science. But is mathematics itself science? Well, it's not an empirical science. What does that mean? The number 2 is not an empirical entity, like an apple or an aircraft carrier. We call it a natural number, but it's not a thing that exists in the natural world. You'll never watch a documentary on the Nature Channel in which you hear one of those intrepid, British voiceovers. We've been tracking this elusive number through the line for days now and tonight, we're hoping to catch our first, real glimpse. Math, just doesn't work like that. But the point of my quiz question was a little different. Empirical science is the sort of thing that could turn out to be wrong tomorrow, because tomorrow brings new data. You think all swans are white. Tomorrow, you see your first black swan, so much for your theory about swans. Math doesn't work like that. It's more certain. Why? Because it's subjective. You can do it in your head. And nothing outside your head is going to count against it. 2 plus 2 is 4. Nothing you observe in the lab tomorrow could possible disprove that. We aren't going to trudge along the number line and find ourselves in a place where the additive function no longer functions. Well, so what? Here's what. If ethics is subjective, why that just goes to show how much like math it probably is, because math seems pretty subjective. It's all in here, whatever that means. Let's try another angle We aren't going to find out tomorrow that two plus two wasn't four, after all. And you know what else we're not going to find out tomorrow? That murder is right after all. And that just goes to show, ethics is like math. You do it in your head, so there are no surprises. No, wait, that's wrong. Math is full of surprises. The beautiful thing about math, about geometry let's say. It's precisely it's potential for combining utter certainty with complete surprise. There's a story about the English philosopher, Thomas Hobbes. This story might be a myth, but I think it may be an ethically improving myth all the same. As Socrates says, this is the sort of myth that makes us brave, not cowardly, when it comes to inquiry. Anyway, so, the story goes. Hobbs had never studied geometry, but one day, at the ripe old age of 40 or so, he happened to open up some gentleman's copy of Euclid's elements, that is Euclid's geometry. He read Proposition 47 from Book One and reacted. Impossible! Or, how could you know a thing like that? What Proposition 47 says, is this. In right angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle. I'm sure you do not share Hobbe's reaction, because what is the one thing that you still remember from geometry after nearly everything else has faded, the Pythagorean theorem, right? But do you really remember the proof? Because if you actually look under the Euclidean hood, it's fairly complicated. Which is to say, most of us believe the Pythagorean theorem on the basis of, what is by now, kind of an argument from authority. They say it's true. Shame on you, defiling the sacred truth of geometry with your impure modes of coming to believe, merely on the basis of hearsay. But we'll get to that. Anyway, for experimental purposes, to better recreate the state of Hobbes' mind, let me just Google up someone else's Euclid web page and pick at random a different, less memorable, point than Euclid. Na. Here we go. If as many numbers as we please, beginning from a unit, are in continued proportion, then the third from the unit is square, as are also which successively leave out one, the fourth is cubic, as are also those which leave out two, and the seventh is at once cubic and square as are also those which leave out five. That's Book 9, Proposition 8. On the one hand, you know it's true, because it's in Euclid. They say it's true that Euclid stuff. On the other hand, if you're like me, you have to think about it. Hard. It's not immediately clear what that statement is saying, let alone why it has to be true. That sentence is not the sort of sentence the human brain likes. If you're a math whiz, and you get it right away, that's great for you. For the rest of us, we have to struggle, thank you very much. But here's something we should all come together and agree about, whether we're math whizzes or just a chump like me. Try to imagine you've never encountered this kind of thing before. You are an educated, intelligent adult but you've got no math beyond the basics. You can count your change at the shop. And that's about it. And now someone says these magic Euclidean words to you. What's it going to sound like? Well, like magic. But there's no such thing as magic. You're an educated adult. You know that. So it must be a trick. As many numbers as we please. That sounds like, pick a card, any card. And now the magician tells you what the next card in the deck will be? It's like you picked a two and the guy then shows you all the rest in perfect order. That's gotta be a trick. So, now you know how Hobbes felt about the Pythagorean theorem when he first encountered it at the age of 40. Impossible! But then he studied the proof. He traced it back. He studied the whole book, read back to the axioms, that is what Euclid calls the postulates. And, when he got to them. Hobbes, his mind could not resist immediately saying yes. So, he had to admit this non-obvious thing, truly followed. Wow. Imagine how impressed you might be by geometry if school hadn't long ago drained all the magic out of it for you. It's alright, I didn't like math in school either. In fact, I didn't really like it until I studied Plato. About the age of, 30. No kidding. Speaking of kid's stuff, remember Persephone and those heroes with lightning like strength? Pretty far fetched. Especially when we consider that it's leading into the geometry stuff, right? Oh hey, that reminds me. Remember that scene from The Incredibles? The little kid, who saw Mr. Incredible lift that car that one time, and now he's kind of hanging around with this funny, sad, little look on his face? I don't have the visual rights or anything, but I don't think I'll get sued, for saying, goes a little something like this. What are you waiting for, kid? I don't know, something amazing, I guess. The kid gets his wish, doesn't he? And that's why I say, if you want to understand Thomas Hobbe's philosophy, the philosophy he did after he discovered geometry, you have to understand he didn't look like this. His true portrait, the picture of his soul, was more like this. Okay, we'll give him a bit of a mustache. He had to wait around until he was 40, but he finally saw something that was truly, authentically amazing. Geometry. We see an example of this in the dialogue by the way. Just peeking around the edges. The boy doesn't realize it, but he's on the verge of one of those really wonderful bits we, who have been forced to study math until all the wonder drains out of it, know are lurking in those depths. I don't know whether I should even say this. Well, okay, plot spoilers. It turns out the square root of eight is an irrational number. Dun, dun, dun. Wait, you knew that. Well, sure you did, you've been to school. But just think how crazy that is, irrational numbers. Wow! Mm. But this is all a dead end, isn't it? Remember where we started? I asked you to say why ethics isn't like math, and then I tried to take apart a likely answer. Ethics is subjective. Math is subjective too, plus it's full of often awesome surprises. But we're done, aren't we? I can't complete the analogy by saying now, and ethics is full of awesome surprises like math. Can I? because it's not true. Murder is wrong, murder is wrong, murder is wrong, right? Ethics, we all kind of know it already as rock certainly as we know 2 plus 2 equals 4. That's why the agony aunt column, Dear Prudence, should I break up with my boyfriend, can be written by a non technician. But then nothing gets built on this non-technical rock certainty. That's why the agony aunt column, Dear Prudence, never gets replaced by the technical equivalent of an academy math journal. I made up a joke about this once and I found, somewhat to my annoyance, that Gary Larson, the cartoonist who drew The Far Side, maybe you know it? Had beaten me to it. Anyway, here's Larson's gag, because he gets the credit. Two scientists are working together at the blackboard. I don't have the rights to get a Larson's actual cartoon, so I'll just substitute my own stock pair of Greek wise men. Yes, yes I know that, everybody knows that! But look! Four wrongs squared, minus two wrongs to the fourth power, divided by this formula, do make a right. Two wrongs don't make a right. Everyone knows that. But why shouldn't it turn out that there's some technical, mathematical logic according to which several wrongs are really right, just like negative numbers flipping over into the positive column, like we know they can do We laugh at Larson's joke, because we see the analogy, and then we see it fall to pieces, like a guy slipping on a banana peel in the realm of ideas. Thinking about wrong and right is kind of like doing moral mathematics, but then. No, it's, that's absurd. It's nothing like that. What could this formula posibly be that would make wrong, right? Nothing, right? How is ethics acquired? Do you teach or practice it? Are you born with it? Or what? If you could teach it, there is presumably a formula. But it's absurd to suppose there's a formula, because, then the formula might have weird implications. Like math. But that's silly. But can't we teach ethics? So there must be a formula, right? Let's take a step back. Could ethical truth be weird? Weird question, huh? Remember? I asked you this one back when we were sitting [UNKNOWN] because he's kind of weird. Could it turn out that the stuff you think is obviously ethically okay, is actually just flat our wrong? Morally abhorrent. Morally abhorrent squared. Cubed. Only you never knew. Seems pretty unlikely huh, your a good person. Right? You'd know if you were a bad person because then you would have what? That characteristic bad person feeling that bad people always have. If you wanted something bad you'd know it, right? A quiz to close out this rather long video. Do you think slavery is perfectly fine and morally normal? A, yes. B, no. I'm going with b, how about you? But you know what? We have in this dialogue, a slave boy. That's right. Do you find his presence a little bit morally distracting, maybe? Here's this nice kid learning math just like a kid should, but Meno owns him. And no one's saying boo about it. Well, that's normal. Ancient Athens was a slave society. We're not really sure, but probably like 70-80% of the population were slaves, maybe more. Shocking, I know. I'm not aware of any argument by any ancient Greek philosopher against slavery. That only comes later. And Athens wasn't special. Rome, ancient Greece generally, the ancient Mediterranean. It's an ugly truth, but all this nobility. Civilization was built on the backs of slaves. I'd like to think that the Meno, the dialogue, is in a subtle, unspoken way, a reproach to the institution of slavery. Here's this boy, and Socrates goes to great lengths to prove that his soul is just as fine as Meno's own. Probably even finer. Because Meno's sort of a block head. So why is Meno allowed to own a perfectly nice kid like that? So is this a crazy way to read Plato? One the one hand, there aren't any slaves in his utopia, The Republic. That says something about what he thinks, but there are slaves in his other utopia, The Laws. Honestly, if I had to guess, and I do have to guess, I don't think Plato really had a fundamental problem with slavery, not like we do today. Like everyone else in this society, he just sort of thought it was normal. And ain't that a thing? We're reading Plato for all this ancient wisdom. We're getting a bit worried about how maybe he's overexcited about geometry? That's nothing. Guy thinks slavery is okay. And we're looking to him for ethical wisdom? Here's a question for you then. If you think you know something morally, ethically, that the ancient Greeks didn't know, just for example, slavery is just wrong, wrong squared, wrong cubed, how do you think you know that thing? That's just one of those things, they say, they say slavery wrong these days. Do we know some kind of advanced moral math that they didn't have yet back then? What kind of special knowledge have we got, that they didn't have, and how did we acquire it? In your honest opinion, pause this video and jot down the first thing that occurs to you as a plausible answer to that question. Next video, some thoughts about method. Then finally, I'll get back to the dialogue.