[MUSIC] Let's think about the distinction between knowledge and true belief. This is a topic in epistemology. Remember what that word means? It's relatively easy to distinguish between knowledge and belief, since you can believe things that aren't true, but you can't know things that aren't true. But that won't help to distinguish between knowledge and true belief. Here's one way in which epistemologists today think about the difference. Suppose I believe that 317 is a prime number. As a matter of fact, it is. So my belief is true. But suppose I believe this because I think that every odd number is prime. Or because I've memorized a list of what I've been told are prime numbers, but they are really numbers of winning lottery tickets. We'd be disinclined to say in that case, that my true belief that 317 is prime counts as knowledge, because it seems entirely accidental that I got it right. Knowledge is a way of getting things right for the right reasons or by the right methods. But true belief can come about by any method, reliable or unreliable. So that's one way of distinguishing between knowledge or true belief. How does Socrates distinguish them? Well in the latter part of the Meno, starting around 99b, when Socrates proposes that Athenian politicians have true belief, rather than knowledge about how to run the city well. He suggests that their true beliefs are divinely inspired. That they simply popped into the heads of Pericles and Themistocles, as if in a dream, not connected to any understanding at all about how to run the city well. Now, this is hardly a flattering picture of true belief or of these politicians. It really annoys Anides who considers himself to be a successful politician. But more to the present point, which is the difference between knowledge and true belief, Socrates seems to be suggesting that knowledge differs from true belief by the method by which it is acquired. For example did it just pop into your head as well as by whether you understand what you believe. This is connected to another point he makes when he asks Mino to consider why it's better to have knowledge than mere true belief? He proposes that knowledge is more stable than true belief. He explains that true beliefs are like untethered animals which can wander off, whereas knowledge is tied down, always there when you need it. Think about the example I gave of believing truly that 317 is prime, but based on the bad reasoning that all odd numbers are prime. Let me show you how that true belief could wander off. I might announce to you with full confidence that 317 is a prime number. You might ask me why I think so and I would say because it's an odd number and all odd numbers are prime. Are you sure, you might ask. What is 3 times 3? I would answer, 9. And then you might follow up, so 9 is divisible by 3? I would say yes. So is 9 prime? And I would say no, clearly not. But is 9 odd or even? You might ask. And I would say odd. And so you would say, so nine is odd, but it's not prime. Yes. And so do you still believe that all odd numbers are prime? I guess not. Then if you asked me, do you still think that 317 is a prime number? I am likely to say I am not sure. Since I've just lost my reason for thinking that it is prime. So now I've just lost hold of a perfectly good true belief. That 317 is prime. It wandered off because I had a false understanding of what made it true. By contrast, if I had a good reason for believing that 317 was prime, my grip on that true belief would be more secure. Now, back to the Meno, Socrates claims that what ties down a true belief to make it knowledge is what he calls reasoning out the explanation. Such reasoning out, he says to Meno, is recollection, as we agreed before. When they, that is true beliefs, are tied down, they become bits of knowledge then they stay put. He is referring back to the end of the geometry episode in the passage we considered a little earlier. Which concludes by claiming that the slave does not yet know that the double square is built on the diagonal only has true belief. But, Socrates says, if someone asks him these same questions many times and in many ways, you know that in the end he will have knowledge of them that is no less exact than anyone else's. Now asking the slave these same questions again is to take him through the steps of the geometrical proof again. And doing so in many ways I gather will involve taking a slightly different tack on different occasions or altering an inessential feature of the diagram. For example, you could do without constructing the nine foot square and you could flip the diagram horizontally or vertically and so on. You get the idea. Once the slave has mastered this proof in all its variations, he will really understand why the double square is built on the diagonal. And will be unlikely to change his mind on the question or forget the answer. He'll be in a much better position than someone who has memorized the answer along with a bunch of other formulas for a geometry test but forgets the answer after the course is over or maybe even before that after the exam is over. So let's conclude by connecting this picture of knowledge to the priority of definition, which is also about knowledge. If I don't know what x is, then I don't know anything about x. Now that we know to be on the lookout for the distinction between knowledge and true belief, we can see that this principle allows us to have true beliefs about whether virtue is teachable, even if we don't know the answer to the hard question, what is virtue? But the principle does indicate that if we have true beliefs about virtue what will make them knowledge rather than mere true belief will depend on having an answer to that definitional question. Indeed, it will depend on knowing that answer. When we turn next to the Republic, we will get a fuller picture of what Plato thinks the answers to these definitional questions are like as well as what it takes to gain knowledge of them.