 So it's probably not immediately obvious that Russell has a mind with this chapter. To kind of catch up, remember what he's already done is he's already talked about a priori justification of these general principles. And, you know, you try to explain how we come to know the components, the parts of these general principles. That's the universals. And we're acquainted with the universals. Now, acquaintance with the universals doesn't get us whether a judgment in the universals is true or false. It just kind of gets the ball rolling. So in this chapter, he's trying to elaborate on this notion of self-evident. Now, remember when we were looking back at the principle of induction and the principle of inference, one of the things that made specifically the principle of inference self-evident, is that you have to use the principle of inference. If you try to prove the principle of inference, you're going to have to use the principle of inference. If you try to disprove the principle of inference, you still have to use the principle of inference. So this principle of inference must be used. It's indispensable. And this is what he says initially in this chapter, is that these principles are self-evident in the sense that they are used in demonstrations, in logical demonstrations or arguments. You have to use them. They're indispensable in these logical demonstrations, but they themselves cannot be demonstrated. We can't prove the principle of induction by using the principle of induction. We can't prove the principle of inference by using the principle of inference. And similarly, we can't use the principle of inference in order to prove the principle of induction. It doesn't work that way, or induction to prove inference. It doesn't work. So initially this is what he says, is that these principles, they're self-evident in the sense that they are not the products of demonstration, but they are used in demonstrations. Okay. Now the principle of inference and the principle of induction are two general principles. But there are plenty of principles that we use that are not the product of demonstration. And the question is, you say, well, yeah, they're self-evident, but some of them are maybe, I don't know, are they as obvious as the rest? Are they as justified as the rest? Just because we start with a principle, does that mean it's justified? So a lot of what he's doing in this section is he's exploring different examples of these general principles that are self-evident in the sense that they are not capable of demonstration, but they're used in demonstrations. They're self-evident in that way. But self-evidence, this certainty about these self-evident principles comes in degrees. So the idea of all rolling, we're going to start looking at what has the most certainty. And the most, probably the most certainty that you have right now is that you are having experiences. So these are these so-called truths of perceptions. Now to be clear, the truth is not so much that you're absolutely certain that I'm wearing a red shirt. No, that's not it. But the truth of perception would be, or this judgment of perception is that there is existing some kind of perception. There's the existence of the perception that is redness and that you could put together the shape and everything else that you put together. We've been through this exercise where we have the various kinds of universes that we apply to this thing here and you have this truth of the perception that you are experiencing red shirtness. We call it that kind of hand wave as to what kind of universal that is. So this is the judgment of perception that you are right now in fact having these experiences. That would be that would be an intuitive judgment intuitive knowledge right off the bat and it's a judgment of perception and has the most if not absolutely guaranteed certainty. Now what he's dealing with here is again you can't infer you can't demonstrate that you're having this perception. You're just simply having it and this perception would in fact be used in some kind of demonstration some kind of knowledge. In fact the knowledge that I am wearing a red shirt your perceptions would be used in that demonstration but it's not the product of the demonstration. So these judgments of perception these are held with certainty this guarantee of truth also some logical principles so what Russell has in mind here probably the principle of inference once again the principle of inference that's held with certainty there's just no way to doubt that and maybe some basics in mathematics basics and logic probably with the three laws of thought whatever the law of identity the law of contradiction the law of the excluded middle these would be known with certainty. Their self evidence is held to that degree so there's self evidence in the sense that you have to use them in a demonstration but they're not the product demonstration and they have the highest degree if not the absolute guarantee of certainty. Pop quiz do you remember what I just said on my head? Of course you do. That's an immediate memory you just finished seeing me with a hat on my head this is an immediate memory and that's held with just a little bit less certainty than exceptions and logical principles after all there could be some doubt you could be hallucinating or whatever we can think of our favorite skeptical hypothesis to creep in just a little bit of doubt into your immediate memory of what I was wearing on my what I was wearing on my head memory is the whole thing that gets Russell started on degrees of certainty with intuitive judgments you have plenty of intuitive knowledge based upon memory lots in fact but memory is one of those things that's notoriously subject to error so we've creeped down just a little bit further down the line for intuitive knowledge that's held with just a little bit less certainty from judgments of perception and these logical principles so next down the line moving down our degree of certainty we've had these judgments of perception principles right below that's going to be immediate memory and then below that is your judgments about induction your inductive principles so this is going to be your degree of knowledge that the principle of induction is going to hold and remember induction is great but there is some degree of error with induction so we're moving down the line induction is still really high it's just below immediate memory but or maybe right even with even memory it's right about there but there's still a little room for doubt for induction it's still self evident you have to use it and it can't be the product of demonstration but there is a little room for error so induction well more memories and probably some derivations from inference and induction excuse me so the further back the memory is supposed to the further back the event is the memory is supposed to recall the less degree of certainty you have the less degree of certainty you have for breakfast this morning I had eggs I had that yesterday I had kind of an oatmeal crunch with some milk the day before that it's getting less clear now I believe I probably had that oatmeal crunch again I keep going back and I'm remembering it with less less certainty now in addition to distance I think it's worth mentioning maybe the detail so if the detail is really particular you're probably not going to be able to remember very well the degree of certainty is going to be a lot less so for instance what was the word I used to begin the last scene how did I begin the last scene what words did I use that just happened but you probably don't remember that first word so memory the further back it goes into the past and I would probably include in there at least the degree of specificity of the detail the less certain you are it's still intuitive knowledge in the sense that it's not demonstrated but it's used in demonstration but the certainty it's eroding away little by little but it's eroding away so as we're going down our scale of certainty with our intuitive knowledge we also have to consider complex calculations or complex derivations from these basic principles that we have so the law of identity the law of contradiction these are all real obviously start out with them but when you start applying them and deriving more and more complicated theorems you start sliding down in certainty so everybody is going to say of course the law of contradiction is true and of course the law of excluded middle is true what happens when you combine them how well do you all do with combining them so what this means is something like this the proposition it is false that p and q is equivalent to either not p or not q or here's the proposition it is false that either p or q well that's equivalent to not p and not q so I say that really fast but it took somebody to sit down and figure that out and there was a little short proof involved but it was like hey guess what this is true but we've ebbed away a little bit of that certainty you might also see this with complex practical computations so 2 plus 4 is easy 4 plus 4 is easy 8 plus 8 is easy 16 plus 16 is 32 32 and 32 is 64 64 is 128 128 is 156 sorry 256 see so our confidence starts eroding away the further along down these complications we go even though it all starts with this obvious intuitive knowledge this knowledge we have a certainty so these calculations what we derive from these basic principles they're getting to be less and less certain kind of right around the same area we have ethical principles so always do what's good you know probably held usually that's right but sometimes I have to do the wrong thing you know you're trying to reason this way about ethical propositions and you know Russell just kind of puts them you know immediately down low on this the scale of certainty as to how certain we are with these self-evident because you kind of have to start with propositions like this self-evident principles but still held with a you know less degree of certainty than something like the principle of inference so what do we have with these self with these self-evident principles well we had two kinds of certainty this absolute guarantee of certainty pretty much just our judgments of perception and abstract logical principles and then it kind of goes downhill from there recent memory induction memories fit you know the further memories of things happening in the past you know further along in the past you know this complex equate you know complex kind of derivations of the truth ethical principles it goes down from there now Russell's told us that we have these degree of certainty and so the question is what's that supposed to mean and how do you have something that's kind of sort of certain or has certainty only to a degree well to answer that question he says well we got to take a look at the nature of truth and truth and error and that's the topic of the next chapter