 So, Russell's tried to account for the a priori, or he's leading us to this way to account for the a priori, not by saying that they're just purely mental things, and he's saying they're not physical things, but by saying that they're universals. You know, exactly what a universal is, is a really great question. He says that, you know, that's one question that we need to answer. So, what's the nature of a universal? And the second question we need to answer is, you know, what sorts of things count as universals? What sorts of objects or what sorts of existing things count as universals? To get to, you know, but for this section, he's really going to only try to answer the second question, and that's what sorts of things count as universals, what are they? So, to understand this, well, let's take a look at a few things. This is a square. It's a big, heavy square. It falls and goes thump. Here's another square. It's a little bit more transparent than the other one. An even smaller one, very dense and opaque. Now we got a bigger one once again, and another little one off to the side. Now what you might notice is, you know, we have, was it one, two, three, four different objects here. They have different colors. They have different transparency. They have different size. They have different location. But there's something that they all have in common, and what they have in common is that they are all squares. So they are different things. They're not identical to each other. The little yellow one is very different from the rest, and the red one off to the right is very different from the rest. They're distinct from each other. It's overlapping, but they're not the same shape. They're not identical. So these individual squares, they're not the same thing, and they all look different from each other. But they all also have something in common. They have something in common, and what they have in common is squareness. What they have in common is an essence that makes them all the same kind of thing. They're not the same thing. They're distinct from each other, but they're all the same kind of thing. They are all squares. Now, this essence, this squareness, is not the same thing as these individual squares. I mean, after all, the squares are gone. They disappear. But squareness remains. You understand what squareness is. Squareness remains, even though the squares are gone, and when the squares have come back, well, they're still squareness. So these individual squares is what Russell calls a particular. They're particulars. They're individuals. What they have in common, what the particulars have in common, is the universal. And what they have in common is what makes them the same kind of thing, is their essence, what makes them the same kind of thing. This extends not just to shapes. Here we have particular hues of red. Each of these segments are all red, but they are different from each other. They're different location. They're different in appearance. They're different, you know, saturation, but we would, if we looked at them individually, we'd each see them as red. You'll notice something interesting here. These segments all look different from each other, right? Yet they are all red. Well, if they look different from each other, and they are all red, well, that means that red doesn't look like any particular segment. Whatever red is, this universal red, what they all have in common, it doesn't appear to be red. So what Russell's getting at here, the same thing with the squares that we saw earlier, whatever square it is, it doesn't look like any individual square. It's something else. Universal is not mental, but it nevertheless must be apprehended by the mind. And not just red. Any color, we have lots of colors here, and they're all very different from each other. They have different saturation, some are darker, some are lighter, some are more vivid. All these colors are very different from each other, but what makes all these different instances, all these different particulars, color, is that they all participate in the universal of color. But again, whatever color is, it doesn't look like any individual one. We can even think the same thing with shade. As we go from white to something more gray and more gray, darker and darker, all the way down till we get to black. Whatever shade is, or graying is, or whatever that shading is, it doesn't look like any particular shade of gray. The universal is what all these particulars have in common, but the universal is not identical to any particular. This idea of the universal extends to more things than shapes and colors. And we have an animal. Four legs, four hooves, tail, long neck. And here's another animal. Looks different than the first. Different color, different structure, and even a more different animal. Or there's even still some more differences with these animals, yet they all share in something in common. They all participate in the universal of horse. Now again, whatever this universal is, horse. It's not identical to any particular horse there. If it were, say, or identical to the one on the left, well, since the one on the left is different from the other two on the right, and they're distinct from the other two on the right, those other two on the right would not be horses. They'd be something else. So whatever a horse is, it's not identical to any one of particular horse. Whatever color is, it's not identical to any particular color. Whatever square is, it's not identical to any particular square. The universals, well, they're not mental or physical. It's not mental. It's not a mind or sense data. You have sense data, which you translate as red. But since this universal is not any particular shade of red, well, the universal is not in the mind. It's also not physical. These particulars can come and go, but the universal remains. It's not identical to any particular. And since it's not identical to any particular, it's not physical. It's not mental. Well, these universals, they're not temporary. They're not fleeting or mutable. We could, you know, there are in fact several animals, species of animals that have gone out of existence, but the universal remains. That essence of what makes them what they are remains, even though there's no particular things. So the universal is what the particulars have in common. This essence of particulars is what makes them what they are. Well, I think of it as the kind of the particulars. The particulars, what participates in the universal? The particulars are the individual things. But they, because of what they are, they participate in the universal. Now, particulars have existence. That means they have being in time. They come, they go. At one point, they don't exist, and they exist, and after a point, they cease to exist. But universals are different. Universals don't have existence. They have subsistence. And this is timeless being. That means that the universal is unaffected by whether the particulars exist or not. So we had some descriptions about when universals are not. Well, this is what they are. Universals are essences. They are what particulars have in common. And they're eternal.