 So, it's almost cliche to say that appearances can be deceiving. We don't have to go very far with many observations to see how this is true. There are optical illusions, which are seen for fun. We look at optical illusions. There are, from a certain perspective, if we look out into the world, if we look out right now, it looks like the earth is flat, but from a different perspective, let's say, higher up. It looks like the earth is round. The physical sciences tell us that appearances are deceiving all the time. Modern physics tells us that solid objects like this, it's very hard. It's mostly empty space. I'm looking around me now and I see lots of green and I smell wet wood. It just rained a little while ago. Yet, biology, chemistry, and some neurology, and even some physics, tells us that, well, that color and that scent, that doesn't exist out here. That happens right back somewhere back there in the back of the brain. There's a difference between appearance on the one hand and reality on the other. Parmentities and Xeno are going to push on this distinction between appearance and reality, and they're going to come up with some pretty surprising conclusions. We have some pretty strong intuitions about how we react or interact with the world around us. One of these intuitions is that our perceptions help to give us a coherent account of what's around us. Right now, I see green leaves and I smell wet wood, wet earth. I feel a little bit of a breeze coming off from the sides and it's actually nice outside. It's not that hot at all. It's kind of pleasant. I'm having these different perceptions and from these perceptions, I can give you a coherent account. I just did. The leaves are green. The bark is wet. The ground is wet. There's a little breeze. In fact, this is the whole idea behind the news industry, that people telling other people what they saw, they can give a coherent account. This is a pretty standard intuition that our perceptions can give us a coherent account of the world around us. The idea is that our perceptions can give us a coherent account of the world around us. You'll push the idea even further. If our perceptions are reliable indicators of the world around us, then our perceptions can give us a coherent account of the world around us. Perception is one way that we encounter the world. Another way is the use of reason. The content of reason basically is something like this. It's using concepts. Reason also uses logical inference. Reason allows us to critically think, so to evaluate our thoughts, compare to one another and see which ones are true and which ones are false. We use reason a lot. This idea of critical thinking, this idea of inference from evidence, fuels our physical sciences and mathematics. Without reason, we wouldn't be able to use these at all. We would simply have perceptions. We use both reason and perception in our interactions with the world and trying to understand the world. However, another big intuition that we have is that if there's a conflict between reason and perception, then reason wins out. Reason wins out. You've seen this happen a lot. Our perception is that these objects around us are solid, that there's no space between the edges. Modern physics tells us that matter is made up of mostly empty space. Our perception, if we're just looking right on the ground, is that the earth is flat. Through more advanced inference, through the use of further technology, especially pictures from space, we know that the earth is spherical. If there's a conflict between reason and perception, we think that reason wins out. Reason trumps perception. Parminides is a huge fan of reason. He's a real big believer in the idea that if there's a conflict between reason and perception, reason wins. Let's see how he uses this with, like I said, some rather surprising results. One of the things that permittees wants to address right away is, well, talking about nothing. To start off his discussion about nothing, first, maybe a few notes about when we're talking about something. This tree that's behind me here, I can say lots of true things about this tree. That right now the bark is a little moist because of the rain, that the tree is rigid, that the needles of the tree are green. If I were to rub the bark, the bark would be rough. I've said some true things about the tree. The reason why they're true is because there's something there, there's something that exists, and I've accurately described properties that belong to the tree. If I say something false, then I'm ascribing properties to something that are incorrect. If I said that the tree is fluffy like a kitten, then I've said something false because very clearly you can't pet that tree nearly as well as you can pet a kitten. The idea behind saying something is true is that you're ascribing properties accurately to the tree. The idea behind something false is that you've spoken the wrong properties about the tree, or about any object that exists. In addition to thinking about trees, I want you to think about unicorns. Unicorns are horses with a single spiral horn projecting from the forehead. They're magical creatures, usually they're white. They have certain magical properties and they're very shy. The only people that tend to be able to approach them are young women. In addition to unicorns, think about the garbubal. A garbubal is a creature that strongly resembles a flagpole and it's made of brownies. They tend to grant wishes and they live in a narrow strip of forest in Canada. As well as the unicorn and the garbubal, I want you to consider dragons. Dragons are fluffy puppies that walk upon clouds and bark rainbows. In addition, once a day they are able to grant a magical doggie biscuit to dog owners to give to their dogs. We've got garbubals, we've got unicorns, we've got garbubals and we've got dragons. You probably thought that making some kind of sense when I was talking about unicorns. You've heard about unicorns and you've seen movies and you might even have at some point have had a little unicorn poster on your wall. However, when I started talking about garbubals, you were undoubtedly confused. You've never heard of garbubals. You've never heard of flagpole resembling stacks of brownies that granted wishes somewhere in Canada. And even more so when I started talking about dragons, you thought, wait a minute, dragons are not puppies that run across clouds, barking rainbows. Dragons are some variety of lizard, usually very large, usually breathing fire and usually flying. So you thought that I would probably speak insensibly in the first case but the second two cases I was speaking very nonsensibly. Well, paramedics wonders why. You say, well, garbubals, you're talking nonsense with garbubals because no such thing is ever heard of, no such thing exists. Sure, but unicorns don't exist either. Unicorns, there are no horses with single spirally horns coming out of their forehead that are magical and are very shy. There's no such thing. It makes no sense to talk about garbubals. I mean, if you say it makes no sense to talk about garbubals because they don't exist, well, it doesn't make any sense to talk about unicorns either. In fact, that's Zeno's point. It doesn't make sense to talk about unicorns. Unicorns don't exist. You might have thought that I was just being really wacky when I was talking about dragons as puppies. Well, what exactly have I said that's false there? I've said that dragons are puppies that jump rainbows, I'm sorry, they jump across clouds and bark rainbows. But it's not as if every dragon you've seen does not look like a puppy. You haven't seen any dragons. Dragons don't exist. So really what this boils down to, what Parmanides is getting at, is that just as it's kind of nonsense to talk about garbubals and dragons, it's also nonsense to talk about unicorns. In fact, it's nonsense to talk about anything that doesn't exist. Remember what we said about truth. Truth dealt with ascribing properties to subjects. Well, things that don't exist can't have properties one way or another. So basically, talking about nothing is, well, nothing. It's senseless. It's useless. Well, Parmanides pushes on this idea that you can't say anything sensible about nothing. His point is that really that you can't say anything true or false about nothing. So for instance, here in my hand, I've got nothing. What does that mean? That I have something on my hand that is not? Just utter the contradiction. How many nothings do I have in my hand? Do I have one? Do I have 98? Do I have 1,262? Do I have zero? Well, yeah, zero nothings. But how is it that I have, I possess in my hand nothing? It doesn't make any sense. So Parmanides pushes on this idea about nothing. It doesn't make any sense. We can't say anything sensible one way or another about nothing. You might be thinking, okay, that's a cute philosophy party trick. We can't talk about nothing. Never mind the fact that you just spent a lot of time doing it. But so what? What's the upshot? I'm not worried about talking about nothing. Yeah, you're right. There's just not a whole lot to worry about with talking about nothing. So what? Well, Parmanides has something some more news for you. It's like, well, okay, so you've seen an ice cube, right? And if you've left an ice cube out on like a countertop, an ice cube melts. It turns and changes from an ice cube into a puddle of water. Well, what are we saying when we say this? So we're saying that something is changing into something else, right? A ice cube is turning into water. What's this supposed to mean? If we're saying that something changes into something else, we're saying, well, that first one thing exists and then after that something else exists. Well, Parmanides is kind of cocking his eye about this Wednesday, okay. Well, if we say that first one thing exists and then something else exists, well, we're saying that the first thing has ceased to exist and the second thing starts to exist. Well, if the first thing ceases to exist, we're talking about nothing. We're saying there is an ice cube that does not exist. We're saying there is an ice cube that is not. That's nonsense. That's utter nonsense. We can't coherently talk about ice cubes not existing, right? How many non-existent ice cubes are surrounding me right now? None. There's nothing I could say about non-existent ice cubes. Well, what does this mean? Well, this means that our perceptions can't give us, I mean, our perception is that the ice cube is melting, is changing from an ice cube into water, but we don't have a coherent account of that change. Because any time we try to give a coherent account, it involves nothing, which we can't talk about. You might try a different approach. You might say that the water comes from the ice cube. That the water comes from the ice cube. Well, you've got a real problem here, because then you're saying that first there's an ice cube, then there's not an ice cube, and then water comes from what's not an ice cube. Now you're saying that something exists that comes from something that doesn't exist. Well, that's really bad. That's not a coherent account of change either. So what do we have? We have that our perceptions can't give us a coherent account of change, and the reason why they can't give us a coherent account of change is that we can't talk about nothing. So once again, our perceptions are deceiving us. They're leading us astray here. Even if you try to appeal somewhere else, you know, the chemists in the group are thinking, well, yeah, of course, the cube doesn't cease to exist, and the water starts to exist. What is happening is that there's a change in properties and something that does exist. So you have dihydrogen monoxide that is changing properties from a solid to a liquid. So we're relying on the change in properties again, and we're appealing to this idea of truth. We're saying, well, there's something that exists and it has these properties. I don't think primanities is going to let you get away with that either, because if you're talking about a change in properties, you're talking about a property that first one property exists and then another property exists. But it's not as if the water remains solid. That's a contradiction. So we're saying that one property ceases to exist and another property starts to exist, and if we're talking about a property ceasing to exist, well, we're talking about nothing. So even talking about one thing that's going through a change in properties isn't going to do it either. We can't get a coherent account. But what are we supposed to do with this? Well, primanities is pushing on our reason series. It says, look, these are your reasons. You're the one that said if our perceptions give us a reliable count of the world, then they can give us a coherent account. You're the one that said that. You're the one that, you know, agreed that truth is talking about things that exist with properties. So what falls from that is you can't say anything true or false about what doesn't exist. So, you know, trying to talk about what doesn't exist is impossible. That's not a coherent account. You're the one that said that reason trumps perception when there's a conflict between the two. So perception does indeed deceive us. In fact, any time you try to talk about change with perception, you're going to have these problems. So our perceptions try to tell us that there's change. But reason tells us that there's never any change. Now, so far, perception is not doing well for us. You know, perception tells us that things change, that we look around the world around us and things are changing. Perception also tells us that there are many things. There are multiple things. So I'm here, there's me, there's your computer, there's you, there's your desk, these trees, and these are different objects. Well, if there are many, many objects, then there are at least two objects. So we'll consider these pebbles. And if there's two pebbles, what that means is that they're not fused together. If they were fused together, they'd be one pebble. There are fused things, like my hand is fused to my wrist, which is fused to my forearm and fused to my upper arm. And this fusion, this one object right here, well, that's my arm. And we can do several things with the rest of my appendages and have one body. Now, if there's this division in me, I don't have one body anymore. I have pieces. Well, the same thing is true with these pebbles, right? There are two pebbles that are not fused together. Well, since they're not fused together, since they're not one thing, that means that there's space between the pebbles. There's space. Even when they're close together like this, there is space between the pebbles. And we know this also from modern physics. If there weren't space between the pebbles, then there would be one thing. I put them together and I wouldn't be able to pull them apart. But no, there's space between these pebbles. Well, what's space? Well, space, if we take that traditional definition we talked about, about matter. Matter is what occupies space. Well, then if there's space, then we're talking about something that there's not. All over again. We're talking about space. All over again. We're talking about that area. So here, I've got some space. What's in this space? Nothing. Oh, no. We're back to nothing again, Parminati says. Yeah, we're back to nothing again. Well, that means that we can't give a coherent account about multiple things. Any account that we have about multiple things involves some talk about nothing. At least not reasonably. Or coherently. So Parminati is pushing on perception again. He says, look, if, you know, again our perception can't give us a coherent account about divisibility. So we don't have any reason to think that there's more than one thing, right? We have some reason to think there's one, you know, one thing. We can't coherently talk about multiple things. So what does reason tell us? Well, look at what's happened so far. Reason has told us that there is no change, right? Because all change involves nothing. Can't involve, nothing can involve, there isn't anything that exists that can involve nothing, right? Nothing is not causally reactive to anything else. You can't hold nothing. You can't make nothing a part of you. So there is no change in objects. And what else has nothing told us? Well, I'm sorry, what else has reason told us? Reason has told us that there isn't actually any division between objects. There's only one object. This is what part, this is Parmentity's conclusion. There is only one thing, right? This one is indivisible. It is one. It is unchanging. It's eternal. And Parmentity says, look, you ought to believe this. Yeah, perception tells you otherwise, but perception can deceive you. And perception can't give a coherent account for this. So perception is deceiving you. What do you have left? You have reason. You have reason. A reason says there's the one. Well, Zeno was Parmentity's student. Now, you obviously don't agree with Parmentity's. I know you don't agree with Parmentity's because you think that you exist. And if you exist, you think that you are distinct from the things around you. And you think that you go through changes. Well, a lot of other people also disagree with the Parmentity's, understandably so. But Zeno was his student. Zeno defended Parmentity's arguments against, well, the objections to them. Now, where Parmentity's gave these arguments in favor of the one, Zeno did something a little bit different. Zeno provided these paradoxes. Now, a paradox is like a reductive out of serdom. We talked about that argument before. What a paradox does is takes some common sense notions, or takes any notions, takes some of these notions, and gets a result that's either a contradiction or just nonsensical. So it's kind of like the same idea with the reductive out of serdom. With the reductive out of serdom, you assume some proposition is true. And from that proposition, you generate either a contradiction or you generate some kind of nonsense. You conclude then that the initial proposition that you assumed to be true was false. So what Zeno does is he takes some common sense notions and shows how they actually reduce to absurdity, how they actually result in a paradox. What he concludes then is is that you shouldn't believe common sense in this matter. Instead, you ought to believe reason. So you're just observing me walking from back there up here to the camera. This is what common sense tells you. You saw me come up to the camera. There's just no weirdness about that at all. It was a perfectly understandable and explainable event. Well, what else does common sense tell you? Well, here's something else. If I cross that distance, I had to cross at least half of that distance. Well, what does this mean? Well, you start putting the ideas together. Well, not only did I cross one distance, I crossed two distances, namely the first half and the second half. Well, that second half is a distance and there's a halfway point with that distance, namely the first quarter and the second quarter. So I didn't just cross a distance. I didn't just cross two distances. I crossed three distances. I crossed the first half, the first quarter, and the second quarter. Well, that second quarter is also a distance. It's the first eighth and the second eighth. So I didn't just cross three distances. I crossed four distances. The first half, the first quarter, the first eighth, and the second eighth. Well, the second eighth is also a distance. That's sixteenths. So I crossed five distances. The first half, the first quarter, the first eighth, the first sixteenth, and the second sixteenth. And then there's a thirty-second, right? The sixteenth can be divided into two halves, into thirty seconds. So that's six distances. First half, first quarter, first eighth, first sixteenth, first thirty-second, and second thirty-second. Well, in fact, you can keep dividing from thirty-second to sixty-fourth, from sixty-fourth to one hundred twenty-eight, from one hundred twenty-eight to three hundred fifty-six. I imagine you'll correct my math when I get back to class. You can keep dividing these distances into halves. And what do you have is that in crossing and going from here to here, I've crossed an infinite. But wait, here's something else that commonsense tells us. You can't cross an infinite. If you crossed an infinite, if you got to the end of an infinite, then the infinite has an end. But what it means to be infinite is to be without end. Wait, what's going on here? What happened? Well, Zeno says commonsense is what happened. Commonsense gave you this paradox that you at once crossed an infinite and did not cross an infinite. So we conclude commonsense is trying to tell you all this. So basically, you never crossed the end, you never crossed the distance to begin with. Commonsense says you crossed this distance, this contradiction follows. If this contradiction follows a commonsense, you didn't cross the distance at all. All movement, all change, is an illusion. I'm not going to go through the rest of the paradoxes, but this kind of gets you started. In fact, we can start constructing more paradoxes using commonsense. Commonsense leaves you astray quite a lot. This is Zeno's point. It's like, look, you want to reject permittity's conclusion because of what commonsense tells you. But commonsense results in nonsense. So we ought to listen to reason. We ought to listen to permittities. Doesn't look too good, huh? Well, here's what we have. We have permittities in Zeno pushing on a distinction between appearance and reality. And for good reason, right? Appearances don't always tell us about what's real. We know this mostly because appearances contradict each other. So what do we have? Well, we have a choice to make, permittities in Zeno say. Either we follow perception, or we follow reason. Either we follow perception, or we follow reason. Well, perception doesn't do us many favors, right? Perception so far hasn't been able to give us a coherent account. We've said already that if perception reliably tells us about the world, then we can get a coherent account based upon perception. Well, that hasn't happened, right? We keep running into contradictions. So what happens is if we follow perception, then we wind up believing a bunch of nonsense. A bunch of nonsense. Well, the other option is reason. A reason tells us that things don't change. In fact, reason tells us that there aren't things. There's just one thing. And reason tells us that there is the one. Now, you may think that conclusion is silly. You may think that the conclusion can't be accepted. But guess what? The conclusion that there's only one thing and it's unchanging, the impervious eternal one, is at least self-consistent. It doesn't generate contradictions like perception does. So our choice is to accept nonsense, to accept contradictions, or to accept the one, or to accept that there is the one as given by reason. Well, it's a pretty standard common rule of reason that you do not accept contradictions. You have to reject contradictions. You don't believe that you exist and you do not exist. You believe that you exist. Parminities and Zeno are going to say, look, very obviously, you can't believe contradictions. It just doesn't work. You wind up speaking nonsense. So what happens is you have to believe, because reason is the only other choice here, you have to believe that there is only the one. Now, you might complain to Zeno. You might complain to Parmini to say, look, I can't believe such a weird conclusion. They say, hey, these are your reasons. You're the one that said, if perception reliably tells us about the world, then it can give a coherent account. You're the one that said, when reason and perceptions conflict, we ought to follow reason. You're the one that said, using common sense notions, using your common sense notions, we started generating contradictions. We haven't been able to give a coherent account, because, like you said, we can't talk about nothing. So if you complain about the conclusion, don't complain to Parminities and Zeno. You've got to complain to yourself.