 In this chapter, Russell explicitly states that what he's trying to do is answer the question how we to know which of our beliefs are true. And if he's doing that, he's going about it kind of a sideways way. So what he explicitly does, or the conclusion that it reaches at the end of this chapter, is this distinction between knowledge, error, and probable opinion. So if he's answering the question how we to know which of our beliefs are true, then what he's doing is saying, look, here's the three kinds of beliefs that we have, at least the three kinds of beliefs that we firmly hold. And if your belief is knowledge, then it's true. If it's error, then it's false. If it's probable opinion, then anyway, we don't really know. So if he's doing that, again, he's going about it very sideways. At least what he actually accomplishes, what he really gets done in this chapter, is provide this distinction between knowledge, error, and probable opinion. So I think it's probably best to think that what he's trying to do in this chapter is tell us what is knowledge compared to error and probable opinion. His answer is that knowledge is a firmly held belief that's true. It's either derived, it's either derivative knowledge, or it's a tuition. And that that intuition is an intuition held to the highest degree of self-evidence. So that's kind of piecing it all together there. And we're going to take a look at this, again, piece by piece. So maybe the first question we want to ask is, why do we bother with knowledge as opposed to, you know, why do we have all these qualifications with knowledge? Why don't I just say that true belief is knowledge? Well, you know, we can have all kinds of true beliefs, but not have any reasons for them. Somebody who can just go around making lucky guesses, right, would have a true belief, but we don't think that's knowledge. When we think we have knowledge, we think that we have at least some kind of justification for that. So, you know, suppose, you know, I take my lucky, I take my magic eight ball, right? I got my magic eight ball and I ask the magic eight ball, hey, magic eight ball. You know, I take it and I shake it and say, hey, magic eight ball, will it rain today? And I shake it and it comes up and says it is certainly so. And I say, oh, wow, great, it's going to rain. So I grab my umbrella and I walk outside and it happens to be raining. Well, we don't think that's knowledge, we think that's just luck. If we want knowledge, we want to have some kind of justification for it. If it's just true belief, you know, you could, you know, just get lucky, but not have any justification. So that's the first question that Russell kind of set aside is whether true belief is knowledge. No, right? You need something more than true belief. You need to have reason. You need to have some kind of justification. So the second question to ask is why do we have, why are we dealing with, why do we include derivation and intuition? Why not just have derivation? Well, you know, derivation is one very obvious kind of reasoning. So, hey, we're going to include that. Well, what about, you know, intuition? Well, as we discussed in that chapter on intuitive knowledge, derivations are at some point going to rest on some kind of a priori justification, on some kind of intuitive knowledge. So we can't just have this, you know, just to kind of recall some of the arguments, we can't just have this infinite regress of reasons. Human minds don't work that way. Our minds are finite. So if we keep going back with our derivation, we're going to stop at some point. You know, the two big principles that Russell talks about, where we don't have any further justification for on their justified a priori, will be the principle of induction. Those are two big ones. And, you know, something he said time and time again. All knowledge, all derivations rest on those two principles at some point. So you're going to have derivative knowledge. Sure, that's going to be included in our conception of knowledge, but not just derivations. It's also going to have to have intuitions. What Russell has left us with is this kind of a taxonomy of beliefs. So what all three of these kinds of beliefs have in common is that they're firmly held. So we'll have that at the top. The next division we'll look at is truth versus error, right, or truth versus false. If the belief is true, right, so we're headed in the direction of knowledge, but if it's false, right, the belief is false, that's just error. It doesn't matter what kind of justification you have for it. If the belief is false, it's error. Okay, so that's one distinction. The next distinction is whether it's known through derivation or through intuition. If it's not known through either one of those, it's merely a true belief. And as we just said, mere true beliefs are not knowledge. So then we look at the kind of justification beyond that, right? So we've got derivation, we've got intuition. At bottom, all derivation is going to rest on intuition. So the next distinction is whether this intuition has the highest degree of self-evidence or something less than the highest degree of self-evidence. If it's the highest degree of self-evidence, it's knowledge. If it's less than that, it's probable opinion. Now, something the Russell talks about, he gives some examples here and there, and he kind of alludes to this, that knowledge is not an all or nothing affair, right? When we've got knowledge compared to probable opinion, well, there's going to be some degree of self-evidence, so there's kind of a gradient scale of knowledge. Now, he's not clear where the line is, and that's just something that's probably going to be handled on a case-by-case basis. But when we're dealing with knowledge, it says knowledge that has the highest degree of self-evidence contrasts to something less than the highest degree. If it's less than the highest degree, it's just probable knowledge. Without any kind of derivation or intuition, it's just true belief. And if it's false, then you have error. Finally, the question that Russell leaves us with is, what's supposed to be this difference in the degree of self-evidence? Well, he gives two major kinds of self-evidence. The first is self-evidence in the sense that the subject is acquainted with the fact. Now, remember in the previous chapter, we had this correspondence through your truth, where you have the subject, you have the fact, and you have the correspondence between them. And when there's the correspondence between the subject and the fact, between the belief and the fact, I should say between the belief and the fact, then you have truth. Without the correspondence, it's false. Now, that's just a mere true belief so far. Now, if we add acquaintance with the fact, then we have this first kind of guarantee of self-evidence. Acquaintance with the fact we have that first kind of guarantee of self-evidence. The example that Russell gives is Desdemona's love for Casio. Now, Desdemona is acquainted with her feeling of Casio. So, she's acquainted with that fact. We're interesting enough, she's the only person acquainted with that fact, since it's Desdemona's feelings. So, Russell has this somewhat mysterious passage where at most one person is acquainted with any particular. Okay. But we got lots of kind, unless we think that the only knowledge we have is about our own feelings or about our own, what we get through acquaintance and the particular facts, right? He reminds us that everybody has acquaintance with the universals. So, when we're dealing with the universals and the relations between them, we are acquainted with those facts. So, 2 plus 2 equals 4, we're acquainted with that fact, because it's a universal. All right. So, that's the highest degree of self-evidence. What about the other kind, when you get something less than highest? Well, the example that Russell gives, they're a little bit interesting. There's not the most obvious criterion involved. And what he says is that just because we're acquainted with the fact does not mean we're absolutely the certain of its truth. So, this leads to an interesting distinction between the first kind of self-evidence and the second kind of self-evidence. The first kind has to deal with acquaintance. The second kind has to deal with something like confidence, maybe, is probably a good word there. So, whether we're confident in our acquaintance with the fact or confident in that belief. So, this second kind of self-evidence, I think it's fair to say, deals with certainty in the sense of confidence in a belief. So, I am really confident that the sun is shining right now. I mean, I can't shape the confidence in that belief. I'm not acquainted with that fact. This is an example that Russell gives. The fact would be the sun and the earth and the weather and the relationship of the sun to the weather and everything else like that, that would be that fact. But I'm not acquainted with any of that. I'm acquainted with my sense data. And I'm acquainted with the principle of induction. So, I'm going to infer from induction that since I see the sun shining, that the sun is shining. That's okay. So, I'm acquainted with perhaps that universal of induction. But the universal is not the sun. The principle of induction is not the sun. So, I am not acquainted with the sun. So, there's a difference between acquaintance and certainty. You can very definitely be certain, but not be acquainted. And there's probably going to be a difference between and Russell hints at this. I mean, from the opening sentence, you can be acquainted with the fact with the universal relationship between them. It doesn't mean you're certain. So, what we have here is this interesting relationship. We have the first kind of this guaranteed self-evidence. That's acquainted with the fact. We have the second kind of guaranteed self-evidence and that's the certainty or confidence. So, we've got those two kinds. Well, let's also add in true. So, let's talk about these beliefs as true. Now, if we have...it's impossible, at least given what Russell said here, it's impossible to have any beliefs that are not true and guaranteed. So, that area, that's empty. That's an empty area. We don't have any beliefs that are guaranteed where we're acquainted with the fact and it's not true. Where we have knowledge is where we have this intersection between the absolute guarantee and the first kind and the second kind. We have the certainty and the... you know, superfluous at this point, the truth. When we have anything outside the truth, outside of the certainty, outside of the truth, outside of the guarantee, well, that's just an error. Now, if we can be... since there's this distance, there's this difference between certainty and this guarantee, I'm really sure, and I think it's fair to say, given examples that Russell's given through the rest of the book, that you can be certain about beliefs that are false. Well, that's just error too. Well, what do we have left? If we are outside, completely outside any kind of guarantee and any kind of certainty, well, that means that we don't have any kind of justification whatsoever. We have no reason for the true belief. So that's just merely a true belief. Well, what about the situation where we have the guarantee but we're lacking the certainty? Well, that's something explicitly covered by Russell, and in that case, that's a probable opinion. Now, what's left when we have the certainty but not the guarantee? Given the examples that Russell has provided, especially on the book, I want to say that if we have the certainty but not the guarantee of truth, I would say that that's also probable opinion. That looks like what that is, it's probable opinion. Now, certainty is held to a matter of degree. Okay, so we've got the sliding scale from certainty down to true belief, and let's go here's what Russell says so far. Knowledge, we're sort of, it comes as a matter of degree. But what about this guarantee? Are they acquainted with the fact or not? Well, I mean, yes and no. It sure seems like acquaintance with a fact can be had to a degree as well. So when we're dealing with the universals and the relations between the universals, something like 2 plus 2 equals 4, I'm acquainted with 2 addition for inequality. So I'm acquainted with every constituent of that fact. But in the case with Desdemona and Los Casio, Desdemona is not acquainted with every constituent of that fact. Desdemona is acquainted with herself, she's acquainted with love, but she's not acquainted with Casio, given what Russell has to say. So if that's the case, then you what? Desdemona's acquainted with 2 thirds of the fact, the constituents of the fact. But Russell still wants to allow that as something, as a fact that she's directly acquainted with. Okay. Now, I don't know, we talked earlier, we talked earlier, and I said the last section had this example of the chair on top of the table, or the trash can on top of the table. Now, I'm not acquainted with the trash can, I'm not acquainted with the table, but I'm acquainted with on top of, that's a relation. So in that case, I'm acquainted with only one third of the constituents of the fact. So acquaintance with the fact can come in degrees when you're considering the constituents of the fact. Now, whether or not Russell really wants to admit this, it's hard to say, given this text. I think there's room for it, and I think it would, in the end, probably help what he has to say about knowledge. So, you know, just for kicks and grins, we're going to say there's a sliding scale between going from this first kind of certainty down to true belief, when you have, excuse me, the first kind of self-advent is down to true belief, when you have the degree of acquaintance with the constituents of the fact. So as a final kind of exercise in understanding what Russell has to say here, go back and look at the examples that he provides in the text, and try your best to determine where the first kind of guarantee of truth fits in, or the first kind of self-evidence fits in, and the second kind of self-evidence fits in. And through this way, I think you'll be able to better understand what Russell has to say. Now, a lot of what Russell has to say here regarding knowledge and improbable opinion is directly into the topic of the next chapter, and that's the limits of philosophical knowledge. Now, you know, without ruining the surprise too much, given what he has to say about knowledge or improbable opinion, philosophy, philosophical knowledge, probably not going to count as knowledge.