 So, we've seen Descartes where he takes a look at how we come to know things and he gives possibilities, alternate possibilities for the sources of our information. From that, he says, we really don't know what's going on around us. Hume's a little bit different than Descartes. Hume takes seriously the ideas that our sensory information just is caused by the outside world. He doesn't really question that a whole lot. However, he takes a hard look at how we come to know about the outside world or about the external world and how we come to know the world, period, and he wonders whether we actually know as much as we think we know. But he does it not through these bizarre scenarios in which we're brains and vats or evil geniuses or something like this. Instead, he just takes a look at what we actually can do and wonders whether we can do much with that. So the first thing that Hume takes a look at is the kinds of things that we can know or what he calls the objects of knowledge. And there's two main objects of knowledge that we'll deal with the first. The first is called relations of ideas. Now, the relations of ideas would be that knowledge that we have, that we derive simply from the meanings of terms, simply from the meanings of concepts. So arithmetic, geometry, even logic falls into this category. So numbers are purely conceptual matters. We don't ever observe the number one out here. I can take this camera and film around all day out here, and I never get the number one. I'd get plenty of trees, I'd get blue sky, I'd get path, that sort of thing. And I might even be able to count the trees. But how I count the trees is the self, not the concept. It's me using the concept, and that's a difference. So I'd never be able to film the number one out here. This is simply what we know without observation. What also what Hume calls a priori, a priori. So this is knowledge that we have independent of any kind of observation. Numbers, so 2 plus 2 equals 4, 4 plus 4 equals 8. The sum of any two odd numbers is an even number. If you divide an even number into two equal parts, there will always be even numbers. These are the products of knowledge through relations of ideas. That a square has four equal sides. That the interior angles of a square equal 360 degrees. I think I got 360 degrees trying to recall my eighth grade geometry here. This is all knowledge that we have simply through relations of ideas. The truth relations that are taught you in class, sufficient, necessary, contrary, sub-contrary. Those are the four possibilities and those combine to give you the complex truth relations. So that equivalent just is a proposition that is sufficient and necessary for another proposition. We can keep going on with the examples here. Now what's important about the relations of ideas is that we use demonstrative reasoning to reach conclusions using relations of ideas. Demonstrative reasoning is pretty much like I talked about in class how to describe deductive reasoning. Demonstrative reason is such that if the premises are true, the conclusion must be true. Now we can give a demonstration using the meanings of the terms for these conclusions. So we have relations of ideas and relations of ideas used demonstrative reasoning. Now an interesting thing about demonstrative reasoning is any conclusion using demonstrative reasoning is in a sense necessarily true, meaning, or absolutely true, using the truth relations that we talked about in class. Meaning that if you take the conclusion and deny it, it results in a self-contradiction. So if I have my definition of square for an equilateral, equilateral, excuse me, equilateral equi-angular quadrilateral, that's my definition of square, using demonstrative reasoning I conclude that the sum of the interior angles of a square equal 360 degrees. If I deny that, if I say it is false that the sum of the interior angles of a square equals 360 degrees, it results in a contradiction. Simply because of the meaning of what it means to be square. If I say it is false that 2 plus 2 equals 4, that results in a contradiction. If I have 2 addition, equality, and 4, I put all of this together and using demonstrative reasoning I conclude that 2 plus 2 equals 4, if I try to say that's false, that results in a self-contradiction. So this is what's interesting about the relations of ideas using demonstrative reasoning, is that the conclusion, if denied, results in a self-contradiction. Or another way of saying that is, it's the conclusions of demonstrative reasoning cannot be false, cannot be false. So this is the first kind of object of knowledge, is knowledge using relations of ideas and it uses demonstrative reasoning and its conclusions cannot be false. The second kind of object of knowledge that Hume gives us is what he calls matters of fact. Now matters of fact are different from relations of ideas because matter of facts are for example things that conclusions using matters of fact can be false. So right now I say there are cedar trees in Friedrich Wilderness Park and I know this by looking out and spotting one. Yeah there's a cedar tree right there, but its denial can be false, I'm sorry its denial can be true, excuse me its denial can be true, it could have been the case that Friedrich Wilderness Park didn't have any cedar trees. The matters of fact are what we're going to know by observation, what we're going to know by observation. So this is different than relations of ideas, the conclusions using matters of fact can be false and we do this all the time right, we have all kinds of conclusions using matters of fact, not all of them are false right, but they could be. So you're a student at San Antonio College, that could be false. It just happens to be true, as a matter of fact it is true, but it could have been false. You could have been a student at UTSA or Harvard or Yale or whatever. So our reasoning using matters of fact is what Hume calls moral reasoning, it's not moral reasoning in the sense that these are conclusions about how we are to live our life, rather I think he's meaning something like moral is an habitual kind of reasoning. So these are the two kinds of objects of knowledge. We have matters of fact and we have relations of ideas. Relations of ideas use demonstrative reasoning and the conclusions using demonstrative reasoning must be true, their denials cannot be true. And we have matters of fact, matter of fact uses moral reasoning, this is basically knowledge that we get through observation, right, through observation. So conclusions using moral reasoning can be false, they're in fact not false, one hopes, but they can be false. So we have our two kinds of reasoning, demonstrative reasoning and moral reasoning. Now we can have plenty of knowledge claims, I mean Hume's willing to take seriously the idea that we have plenty of knowledge claims simply by observation, right. So I observe there are trees, I observe there is a path, I observe there are stones lining the path, I observe it is daytime. Now these observations, well you know they're fine, right, there's nothing wrong with them, are kind of limited. These are actually not the product of reasoning at all. So a product of moral reasoning using this observation is something like this, I observe there's a path here, I conclude using moral reasoning that somebody made the path. It's a really reasonable inference, we're familiar with this all the time and we look at the path, it doesn't look like a natural formation, we're used to the idea of people coming in and building things in nature, especially parks like what I'm in now, okay. So I infer using moral reasoning that somebody built that path and I make that inference based upon experiences. And I also make that inference based upon cause and effect, cause and effect. So I look at the path and I infer it has a cause and I infer that cause is people. Somebody built that path. I look around at the trees here, I know some things about trees, I have some more reasoning about trees. I look at these trees and I know using moral reasoning that these trees produce oxygen. They process carbon monoxide, I think it's monoxide, they process carbon monoxide into oxygen. So one of the reasons why I can still breathe on this planet is because of these trees. So that's also the product of moral reasoning. And that product of moral reasoning again relies upon what I know from cause and effect. That's what I know from cause and effect. Well how do we go about this knowledge of cause and effect? Well here's something, we can't intuit cause and effect. I can't just simply look at this rock, look at this rock and then I know where it comes from. Is that even a focus? I can't simply look at this rock and know where it comes from. I don't know much about rocks. It's got some coloration there and if you can see this coloration it's got some edges. It's got some coloration here, it's even got to my eyes looks like maybe some kind of vein in there. I don't know, I don't know anything about rocks. Here's another rock and it's got different colors and here's another rock. So I look at these rocks, I don't know anything about rocks. I can't just simply look at this rock and tell you what kind it is and where it's from and how it was formed, what it's chemical composition is. I can't even tell you, I mean this one might be man-made because it's got that kind of crusty feature to it, maybe it's breaking up from a piece of concrete and I'm guessing this one is not man-made because it's got the smooth edges and some of the sharp edges there as well but I don't know. I'm just making guesses really from my limited knowledge of observations and my limited knowledge of cause and effect about this rock. So if we know anything about cause and effect of this rock, it's not intuitive, it's not going to be the product of a relation of idea. I don't have a concept of rock embedded such that its denial is false. So I can say this rock is from granite. This rock came from a large granite volcano, I don't know, I'll just make it stuff up, but that conclusion can be false. So it's not the product of an idea, a relation idea, it's not a product of the monster of reasoning about this rock. So it has to be moral reasoning and that moral reasoning relies upon cause and effect and the only way I can know cause and effect is through observation, right, because you've got your two sources either through relations of ideas or through matters of fact. Relations of ideas can't handle it. It's got to be a relation of matters of fact and that's through observation. OK, well, fine, you know, I learn about cause and effect through matters of fact, through observation. So here's, you know, I'm observing, right? I'm knowing something about this rock by observation. I know that when I throw it in the air, it comes back down. And I know this through repeated observations. I keep watching it, I bring it down. No problem. Well, here's where Hume comes in. He says, OK, you toss that in the air about a dozen or so times, right? Yeah, sure, I toss it in the air about a dozen or so times. So you know by observation that you've thrown it in the air about a dozen times and you caught it. You throw in the air, it comes up and it comes back down and you caught it. That's what you observed. And I say, yeah, that's what I observed. As I threw in the air, I saw it go up. I saw it come back down and I caught it. So Hume says, OK, so you throw it in the air a 13th time. You're going to throw in the air the 13th time. Is it going to come back down? And I say, yeah, it's going to come back down. That's what I observed. It goes up and it comes back down. Hume says, you observed it going up 12 times, it coming down 12 times. You didn't observe a 13th time. So yeah, I didn't observe the 13th time, but I observed the 12, that's enough. Hume says, well, where's the observation for the 13th time? I say, well, I'll do it right now. 13. And Hume says, yeah, now you observed the 13th time. But you didn't observe it yet. So what he's saying, Hume, he's saying I didn't know that it was going to come back down. I mean, I saw it go up and down. I saw it go up and every time I saw it go up, I saw it come back down. That's correlation. Now you throw it up and it comes back down. That's correlation. Every time I throw it up, that's correlated with it coming back down. I saw that 12 times. Why wouldn't it come back down the 13th time? Hume says, I don't know why it wouldn't come back down the 13th time. I didn't observe it. If you're drawing that knowledge only from observation, you didn't observe that 13th time. And so you don't know until you observe it. So what he's saying, Hume, I don't have any knowledge from observation. Hume says, no, of course you have knowledge of observation, but it's limited to the observations. You don't observe that 13th time. And I say, well, Hume, come on. I saw it go up 12 times. I saw it come back down 12 times. They did the 13th time. My prediction was right. So I know that the 12th time, so I know that this throwing it up causes it to come back down. I know that that's causation. Hume says, I didn't see a sign that says causation. I didn't see a magical glowing force called causation. All I saw was correlation. Go ahead, throw it again. See if a little sign called causation pops up. Okay, Hume, I'll do it. There's no sign that time, but maybe it'll pop up this time. No, there's no sign that time. Hey, there was a sign. Hume says, you're cheating. So this is Hume's point. If you're relying just upon observation, you don't see causation. All you see is the rock going up and the rock coming down. You don't see it going up and down in the future, right? So you don't know anything by observation about those future events. So you don't really have anything yet by causation. You don't know anything by causation. All you have is observation. Now, Hume is right that at most what you have is correlation with these events. And there's all kinds of reason to suggest that correlation is not causation. If you go to a website called Spurious Correlation, they'll show you what's in a 99% correlation between increase in U.S. spending in science, technology and space and the number of suicides by strangulation and suffocation. It's just simply false that U.S. spending causes people to kill themselves by strangulation. They have another correlation between per capita consumption of cheese and the number of people who have died in their beds by getting tangled up in the sheets. There's a 95% correlation between per capita increase in consumption of cheese and the number of people who die in their beds by getting tangled in the sheets. Correlation is not causation, not necessarily. I mean, it's a nice sign. We use that in the physical sciences all the time, but it's not enough to show causation. So this is Hume's point. We never observe causation. At most, what we observe is correlation. Now, the question is, does that correlation allow us to make, you know, are we justified in our predictions about the future? All right, so I've tossed the rock. That's what, 15 times now, right? 16 times, 17 times, and it comes back down. Does that mean I'm justified in saying, well, forget about causation, this point. Just, am I justified in saying that the 25th time I tossed the rock in the air is gonna come back down? All right, or every time I tossed the rock in the air it's gonna come back down. Am I justified in saying that? Well, it's starting to think Hume is nuts because I keep throwing this rock and in case we're coming back down, I don't even catch it, but it keeps coming back down, right? So, I don't know, Hume, come on. Man, what's wrong with this observation and correlation in saying that it's gonna come back down? I mean, maybe, okay, maybe, maybe, maybe. I'm not always gonna get, maybe I won't be able to infer causation because they can't observe causation, but I bet it can make a lot of observations and I can still do something with lots of knowledge about a matter of fact, using more reasoning about how the world's gonna work, right? We do a lot of time, right? It's called the physical sciences and we just do it. So, we have that, it goes up, it comes back down. I've done this, I've done this. It goes up, comes back down. Well, what's going on here? Well, remember, Hume is trying to show us. He's trying to show us that there are limits to our knowledge, all right? Now, in order for me to always know that this is gonna come back down, right? I have to be able to use my observations and infer something about what has happened to what will happen. What has happened to what will happen. This is called the principle of induction. It's the basis behind all inductive reasoning. Roughly, the idea is that the events in the future will resemble the events in the past. So, I throw it up in the air, it comes back down. I throw it up in the air, it comes back down. That's what it has happened in the past and so I infer that in the future, I'm gonna throw it one more time and in the future it's gonna come back down. There it is. That's called the principle of induction. And Hume wonders whether this principle of induction is in fact justified. Is this justified? Well, how would it be justified? Remember, we got two kinds of objects and knowledge. We got, we got relations of ideas using demonstrative reasoning and we've got matters of fact using observation. Well, let's consider the first one. If this principle of induction is justified, then either it's gonna be justified using demonstrative reasoning or it's gonna be justified using moral reasoning. Well, what about demonstrative reasoning? Can we prove the principle of induction using demonstrative reasoning? Well, what's the principle? The principle is the events in the past, excuse me, the events in the future will resemble the events in the past. All right. Now, for something to be the product of demonstrative reasoning, the conclusion can't be false, right? The conclusion can't be false. So I, you know, okay, well it can't be false. It goes up, it comes down. It goes up, it comes down. It goes up, it didn't come down that time. If the statement, the events in the future will not necessarily resemble the events in the past, it's not a contradiction, right? Future just means things that will happen. Past just means things that did happen. There's nothing about things that will happen that implies that they must happen as they've always happened, not a self-contradiction. So the principle of induction, the denial of the principle of induction is not a self-contradiction. So given what we've said so far, it can't be proven using deductive reasoning. I'm sorry, demonstrative reasoning. It's not the product of a relation of ideas. If we're a product of the relation of ideas, then saying that the future does not resemble the past would be a self-contradiction. It doesn't do that. So if there's gonna be a proof for deductive reasoning, then either it's gonna be through, excuse me, if there's gonna be a proof for the principle of induction, then it's either gonna be using demonstrative reasoning or moral reasoning. Well, we just looked at demonstrative reasoning. It can't do it. Well, what about moral reasoning? Can moral reasoning prove the principle of induction? Well, what would that be like? Well, remember, using moral reasoning, we have to use matters of fact. And using matter of fact, we make observations. Using matter of fact, matters of fact, we make observations. Okay, do we observe the principle of induction? Well, let's worry about that conundrum. Let's suppose we can observe the principle of induction. We see the principle of induction somehow. In order for us to use moral reasoning to prove the principle of induction, we have to say that the principle of induction has always worked and therefore it will work in the future. So, hey, let's look at the physical sciences. We use the principle of induction there all the time. And every time, well, most of the time anyway, enough times where we know enough of what we're doing, when we use the principle of induction, we make these great predictions and the predictions come true. That's great, right? That's really great. We're able to take the sciences and make true predictions very consistently. That's fantastic. So we conclude that the principle of induction will work in the future. Well, you see what's going on there? If we prove the principle of induction using moral reasoning, we have to argue that since it's worked in the past it will work in the future. But claiming that since it worked in the past it will work in the future just is the principle of induction. So if we use the principle of induction for moral reasoning to prove the principle of induction, we have to assume that the principle of induction is already true. But assuming it's already true, that's not a proof for the principle of induction. That's just assuming it's true. So we can't prove the principle of induction using moral reasoning. Well, if we can't, see, since we can't prove it using demonstrative reasoning and we can't prove it using moral reasoning and those are only two ways to reason we can't prove the principle of induction. Well, then that means that all of our matters of fact are simply related to observations and we don't observe a whole lot. We make a whole lot of claims besides what we observe. That limits our knowledge, a great deal. So we have this little problem with humor. It says, you know, if the principle of induction is justified then we only got two choices either using demonstrative reasoning or using moral reasoning. Demonstrative reasoning can't do it because the denial of the principle of induction is not a self-contradiction. The moral reasoning is not gonna do it because any proof using the moral reasoning relies on depends upon assumes the truth of the principle of induction. You can't prove the principle of induction by assuming it's true. So we ask him, why is it that we have this induction all the time? Why is it that we reason using the principle of induction all the time? You know, by the way, why is it that it works all the time? Well, humor's not gonna deny it works. Yeah, sure, you know, go ahead, use it. I mean, it's working, you know, why not? However, that doesn't mean we're justified. That doesn't mean we have knowledge. Well, we ask, well, why is it that we have this principle of induction? Humus says it's a matter of custom, right? It's a matter of custom. Our brains are wired to use the principle of induction all the time. And, you know, we can even point to evolutionary advantage to using the principle of induction. If we, you know, observe 10 times in a row that a tiger is going to eat you while then using the principle of induction, justified or not, you will accurately predict that in the future, that tiger will try to eat you so you stay away from tigers, right? But it doesn't mean it's justified. So, we have this principle of induction, it's using custom, it says, so what? Why isn't it justified using custom? Well, you know, there's lots of ways that our brains are wired that don't produce, brains are wired for a reason that don't produce true results. You know, the gambler's fallacy was one case. An instance of the gambler's fallacy is something like this. So I take a quarter and it's a fair quarter, meaning it's equated on both sides and I flip it in the air once, right? And I ask, what's the probability of it coming up heads? And you say, well, 50-50, right? 50% chance, and that's right, because it's a fair quarter, you flip it, come back, it comes up heads, that's a 50-50. Well, suppose I take that same quarter and I flip it 10 times in a row. Now, the probability of coming up heads is 50%, and the probability of coming up tails is 50%, and I flip it 10 times in a row, and all 10 times it comes up heads. So I ask you, what's the probability of it coming up tails when I toss it in the air the 11th time? Now, most people are really tempted to say higher than 50%, because they say, look, it came up heads all those other times, it came up heads all those other times, so the next time, it's gotta be tails, no. That's the gambler's fallacy. The gambler's fallacy presumes that events are gonna affect other events, even though they're causally unrelated. So our brains do this all the time, and there's an entire city that takes advantage of the fact that we're not really good reasoning using probabilities. What happens there stays there, right? But that's the way that our brain reasons. I mean, our brain also is wired to form stereotypes, but that's not a good way to reason. Our brain is wired to, I don't know, our brain is wired to tell us that all this stuff around us is solid, right? There's all these trees have edges, and between the edges there's no empty space, but contemporary physics tells us that these trees are full of empty space as well as you are too. So, you know, simply because our brain is wired to think in a particular way doesn't mean it's justified because there's plenty of ways that our brains are not wired, that are wired that don't reason well. So at the end of the day, when we're talking to Hume about what justifies the principle of induction, you know, Hume's gonna say you either got demonstrative or moral. Demonstrative can't do it, moral presumes it, you've got nothing. So, Hume says, all of your moral reasoning, all the conclusions using moral reasoning, you know, a lot of it might be true. Doesn't mean it's justified, and if it's not justified, you don't know it.