 Welcome to the contents of your mind. Your mind, think of it as kind of a wall where you can place images and ideas. This is the interior. This is not what you get from your senses. This is the interior of your mind, the interior of your consciousness. And you can put whatever you want on your wall. Now what Russell has been dealing with up to this point is a priori knowledge. We're asking the question, he's asking the question about a priori knowledge. And as we talked about last time, we wondered, or he was wondering, he said that a priori knowledge is knowledge justified without experience. And this is a curious thing. Questions come up as to how this actually happens. So one way he's, in this section, he's asking the question of how a priori knowledge is possible. And to do that, he first compares, or he first looks at Kant's view about a priori. Now to kind of dive into Kant, we have to remember, we have to look at a view that he at first rejects. And Kant says that the a priori is not merely analytic. Now analytic means that the judgment, every belief, every sentence, every judgment is a subject and a predicate. And for an analytic judgment, the predicate is contained in the subject. And that's kind of an odd sense, but the idea is that whatever, you also remember we were doing the definitions, whatever you included in the definition of the subject was going to be the predicate of the judgment or is going to be one of the predicates for the judgment. So for example, the bald man is bald. This is an analytic statement. The predicate is bald is contained in the subject. Now Kant says, you know, Kant would probably allow for these analytic statements to be a priori, but it's not limited to that. You know, another kind of judgment, another kind of analytic statement in this sense is a bachelor is an unmarried male. Well, you know, that's kind of obvious because unmarried male just is the definition of bachelor. So Kant's going to say that the a priori is not merely what's analytic, but the question is for Kant, well, what is the analytic? To get into that, we have to look a little bit as to, we have to look a little bit as to what Kant thinks is going on when we're talking about knowledge. Now for Kant, there's the, there are two things involved in knowledge. There's the physical object and that's the thing of itself. Now Kant's familiar with all the skeptical problems that we've encountered up to this point. You know, Kant's several centuries before Russell, but Kant's still familiar with all these skeptical and count and skeptical problems that we encounter with Descartes and talk about down in the senses. And he, like Russell, are going to say that the thing itself, the physical object itself, is not known. This is what Russell, pretty much for the same reasons that Russell discusses when he's talking about the nature of matter. We can know how matter affects us, but the thing in itself, this is not known. That's one part of knowledge. The other part is our nature. And this is how we are affected by these objects through sensation. Now Kant's going to say that the sensations are caused by the object. He doesn't have a problem saying that. The sensations are caused by the object. This is what he calls phenomena. So the phenomena are caused by the object, and they are, in a sense, in our nature. What else is in our nature is the a priori. Is the a priori. So Kant's clear that the a priori is not merely analytic. What Kant says is the a priori is synthetic. Now the analytic is the claim, or an analytic judgment is one where the predicate is contained in the subject. Synthetic judgments are ones where the predicate is not contained in the subject. We're adding on to it. There is a synthesis, a combination of ideas. And the example that Russell gives in the book deals with mathematics. So we have the number five. These are five things. The number five, you might say, contains one, two, three, and four. Okay, that's fine. Let's also look at seven. Seven contains one, two, three, four, five. Okay, but the judgment is not that seven contains five. The judgment in mathematics here is that seven plus five is twelve. So it's when you put the idea of five and seven together that now you have twelve. This is a synthetic judgment. Now Kant tells us that all a priori judgments, not all, but there are at least some a priori judgments that are synthetic. So what kinds of judgments are these? Well, we just saw earlier it's not sensation. Okay, it's not sensation. Sensation is caused by the object. For Kant, the a priori is just limited to how we deal with these phenomena, how we organize these phenomena. They don't have anything to do with the physical object in itself. One of these kinds of judgments is time. Through the phenomena, we have different experiences. And through the a priori, we sequence these phenomena into what we call time. In addition to time, we have space. This runner is not only moving, but he's moving from left to right. Time and space and causation. The events before cause the events that happen later. And then we have comparison, comparing one set of phenomena to another, or what we might call relation. This is how, for Kant, we have synthetic judgments of space, time, causation, comparison, which gives us mathematics. These are all synthetic because we are putting the ideas together in our minds. In our nature. Russell likes a few things of what Kant has to say, but ultimately he's got a rather significant problem with Kant's view. After all, for Russell, the a priori is going to be certain knowledge or indubitable knowledge. This is going to give us things like the principle of inference that we discussed in the last video. This is going to give us claims about mathematics, which are going to be true regardless of the situation. They're supposed to be true indubitably. But a priori knowledge, for Kant, extends to phenomena only. And if so, then it's dependent upon human nature. But human nature is flawed. We've seen this. Human nature dealing with probability gives us different answers. Even nature involving the metaphysics of, you know, some of the things that Russell was talking about. We're dealing with the metaphysics, sorry, we're dealing with like value judgments or ethical theory, will give us different kinds of judgments. But if human, and we want those kinds of judgments to be indubitable, but it's dependent upon human nature, then what's known a priori can change. And if it can change, then what was once true can be false. Or worse yet, what we once believed was true, and we change our beliefs to believe what's false. Well, then if an a priori knowledge can be false, then it's false that it's indubitable or certain. So we put this together for this conclusion of a priori knowledge extends to phenomena only, and it's false that a priori knowledge is certain or indubitable knowledge. There's another problem we're talking about a priori being dependent upon human nature, is that, you know, the judgments of a priori do not apply to the physical objects themselves. When they're, you know, when we're talking about these a priori judgments, you know, it's very clear about this. The sensations are caused by the physical objects, but they are not the physical objects. And the a priori judgments we have, these synthetic judgments we have are for the phenomena only. Well, if they don't apply to the physical objects, then the a priori, again, is not always true. Because we want our a priori judgments to deal not just with our thought. You know, this is where Russell was talking about this section where he says we want the laws of thought to deal not just with our thought, but with the things themselves. Well, if the a priori judgments are not always true, then it's false that a priori knowledge is certain or indubitable once again. Well, we want our a priori judgments to be certain or indubitable. So for Russell, we must reject the idea, we must reject Kant's idea that a priori knowledge extends to phenomena only. Well, where does this leave us? Remember for Russell, we're dealing with a priori knowledge, and a priori knowledge is not of the physical objects themselves. We want our judgments to be true about the physical objects, but we don't experience them with the physical objects. Well, given what we're dealing with here with Kant, the a priori judgments are not just merely mental things. So a priori knowledge, well, Russell is getting at it, whatever it is, is not just merely mental or not just merely physical. He has this odd statement that the a priori knowledge, you know, it's knowledge and it's real, but it doesn't exist. What's that supposed to mean? Well, this is where he leads us to the idea that whatever this a priori knowledge is, it's in the world of the universals. So however Russell's going to count for how a priori knowledge is possible, it's going to be found in this world of the universals.