 all squares have four sides. Is this a relation of ideas or is this a matter of fact? I just went over this in the last video, but you know it's worth repeating. All squares have four sides. It's a relation of ideas. Again by the definition of the terms, a square is an equilateral equiangular quadrilateral. It has equal sides, equal angles, and it's four-sided. So yeah, all four-sided figures have four sides. And you know that that's true whether it's squares or rectangles or what have you, right? All rectangles have four squares, four sides. All rhombuses have four sides. We can keep going. So this is true. It's simply a virtue of the meanings of the terms. We could try another way. Assume it's false, right? If we say it is false that all squares have four sides, then what follows is that some square does not have four sides. That means that some four-sided figure does not have four sides. That's a direct contradiction. If it's a direct contradiction, it's impossible that it's false. And if it's impossible that it's false, it must be true. Let's move on to the next one. So here's another one. No bird has hair. Okay. Now initially, you might think this, first of all, you might think, well, this is false because there are some birds that have hair. Well, no, no. They're actually feathers. It looks like hair, but structurally, and I'm not enough of a biologist to tell you the difference, to really break down the difference, but structurally they're feathers. They're not hair. They're very fine and very thin, but it's still hair. It's still feathers. It's not hair. Okay. So no, this is true. No bird has hair. Well, now the question is whether this is true as a relation of ideas, or this is true as a matter of fact. All right. So, well, if it's true as a relation of ideas, then it has to be true simply in virtue of the meanings of the terms. Is that the case? Well, what's the definition of bird? There's something of a technical definition. They're endothermic, right? So they're warm-blooded. They have wings. All birds have wings, but it's also part of the definition that they have feathers. So yeah, all birds have feathers, and if they have feathers, then they don't have hair. So this is true in virtue of the meanings of the terms. No bird has hair. Yeah, that's true as simply in virtue of the meanings of the terms. Hence, it's a relation of ideas. Let's try it another way. Let's assume it's false. If it's false, let's say a sunbird has hair. Now again, in order to really kind of justify this, is that some bird has hair, and I'm going to say, okay, which one? You won't be able to point to an example, because again, that structure is actually feathers. It's not hair. So if we say no bird has hair, it's false. We say some bird has hair. All right. But in virtue of the means of the terms, we're saying some feathered creature has hair. But if it has feathers, it doesn't have hair. So we're saying some non-haired creature has hair. So that's the contradiction that this can't be false. And if it can't be false, it must be true. So no bird has hair. This is true as a relation of ideas, not as a matter of fact. Here's the proposition. Every even number greater than two can be expressed as the sum of two prime numbers. Now, this is kind of a tricky one. I might be messing with you a little bit with this. We're pretty sure this is true. It's called goal box conjecture. We're pretty sure it's true. We haven't found, or we, mathematicians have not found a counter example, but they also haven't found a proof. Every even number they've encountered, and it's an astronomical huge number, right? It's a large number of even numbers that they've tested for this, for goal box conjecture. It's confirmed this conjecture. But it's not as if we have a proof. It's not as if we have a proof. Now, more than likely this is true. But it can't be true as a matter of fact, because, well, frankly, we don't experience numbers. These are concepts. These are ideas that we have in our head. So anything of mathematics is going to be justified as a relation of ideas. Currently, right now, the definition of even number doesn't include this, but it probably will at some point. Once the proof is given, then they'll throw in the definition. And whatever proof that they do offer for this, well, it's going to be a relation of ideas. They will do it definitionally. So it's probably true. Go box conjecture. It's probably true. Again, I might be messing with you a little bit. But for the sake of discussion, we're going to say that this is a relation of ideas. This is true as a relation of ideas, not as a matter of fact, because you can't experience any proof of mathematics. You can only understand it. You can only conceive of it abstractly, conceptually, as an idea in your head. The earth is more or less spherical. Okay. Is this true as a relation of ideas, or is this true as a matter of fact? Well, this might actually be both. This is a fun one. We might be able to do both. It's at least true as a matter of fact. There's quite a lot of empirical evidence that shows us that the earth is more or less spherical. We've got what? The ships coming in from the sea. We've got the shadows cast by the sun at particular times of day. The fact that every other planet we've looked at has been round, including our own moon. So as a matter of fact, gosh, this has got lots of empirical evidence. And we really don't have any empirical evidence that it's not flying out. No empirical evidence that is cuboid or cylinder or anything like that. Okay. I mean, if you take something in isolation, maybe, well, when you take the evidence together, no, it's the empirical evidence is greatly in favor of the hypothesis that you have this more of a spherical. Okay. Well, so it's at least a matter of fact. Could it have been false that the earth was more or less spherical? Well, I mean, this is where it gets fun. I did a little bit of reading up on this. The International Astronomers Union doesn't have, I mean, they have some proposed definitions for planets, but it's kind of under debate, right? You know, poor Pluto, no longer a planet. It's a dwarf planet. But, you know, they are trying to come up with the definition for planet. They're working actively at it. And one of the conditions is that it has a large enough mass to have, I think it's called hydrostasis is the technical term. And the idea is that the gravity affects, you know, every point on the surface, roughly the same. Well, if it affects every point on the surface, roughly the same, then you're going to have a spherical mass. Okay. And that is, that's up for consideration, but there's not unanimous agreement. I think actually, it was number two, the first one was something else. Anyway, I can't remember. It's fun, you know, look at the sub by this debate about what the definition of planet is. There's more things that you might consider. So, you know, at the very least, everybody seems to agree that it has more or less elliptical orbit around the sun. That seems to be one thing. Well, one is, you know, it's not orbiting another planet. It's not, you know, it's clearing the path. Although that definition might not work because, you know, apparently there's still some things like the path of the earth, for example. So, there's not necessarily a consensus on the definition of planet. There's even a debate about whether, you know, okay, you stay round, but we got elliptical, we got oblong, these things can be possible given the masses of certain objects and saving title forces, for example. So, you know, what's going to do it? How are we going to define round? There's a lot, there's actually some significant debate about whether round should be included as a definition. Okay. So, well, if there is enough debate, I think there is. If there is enough debate, at least for the purposes of this discussion, it's not true as a relation of ideas. And it's not true as a relation, it's true as a matter of fact. Because we don't have this definition that works so nicely and neatly for planet. So, it's a matter of fact. Murder is morally wrong. Okay. So, one thing to say is I've had a surprising number of people in classes say, well, it's just not true. Wait, what? I'm not sure you were paying attention. Some people would just argue, well, it's not true. Okay, well, if you, I guess if you really want to argue this that there's no truth to morality, then a whole bunch of things are going to follow, such as like slavery was not wrong, racism was not wrong, sexism is not wrong. Right. If you're just simply saying there is no morality, so this claim is neither true nor false. Okay, have fun with that. But you're giving up a whole lot that I don't think you really want to give up. And if there is no morality, then I can arbitrarily give you an F for no good reason. Now, you think there's a problem with that. So, I seriously doubt that you think there is no morality. Right. Some people disagree to say, well, they say, well, not all killing is wrong. I agree, not all killing is wrong. At least, you know, this is possibilities here. Not all killing is wrong. If you're a hardcore pacifist, then all killing is wrong. Sure. But the statement is that murder is morally wrong. Not killing is morally wrong. There's a difference between killing and murder. Right. Now, if you look it up, amongst other things, other definitions, right, well, murder is immoral killing. Right. So, this is true simply in virtue of the meaning of the term. Murder is morally wrong. Immoral killing is immoral or immoral killing is morally wrong. Right. This is true simply in virtues of the meanings of the terms. Now, again, you might have somebody, well, people disagree about what counts as murder. Well, of course they do. Right. We've seen people disagree by what counts as a planet. Some people disagree with counts as a plant. Some people disagree with counts as a tree. Right. There's disagreement, but that doesn't mean that the statement is false. Right. The fact that people disagree about what counts as immoral killing. Okay. I mean, that's something interesting and we could talk about that, but that doesn't mean there's no such thing as murder. All right. So, this is true as a relation of ideas. It's not a matter of fact. This is true as a relation of ideas. It's true simply in virtue of the meanings of the terms. If we, you know, again, try to assume it's false. Let's say some murder is morally permissible. So, we're saying some morally wrong killing is morally permissible. No. Right. Let's say it's both immoral and permissible. No, it doesn't work that way. Right. That's a contradiction in terms. So, this is true as a relation of ideas. All right. Here's one. Objects fall to the earth at a rate of 30 feet per second per second. This is not a typo. That's what it means to say that something falls to the earth at a rate of 30 feet per second squared. So, objects fall at a rate of 30 feet per second per second. Now, sometimes people attempted to think this is a relation of ideas. Right. This is the rate at which objects fall to the earth. But this could be false. The mass of the earth can, and by the way, has changed. I mean, there's lots of other, there are astronomers who believe that, for instance, the moon came from the earth at some point, right? And earth was still in this very hot molten state. Something crashed into it, maybe Mars, something like that, or something the size of Mars and knocked off a chunk of it. And that's how the moon was formed. Well, if that's the case, then what was the earth, had a piece knocked off, changed the mass. The water on the planet, on earth, is not produced by the earth. We have a fixed, we have a finite amount of water that the planet doesn't generate water. So, that water came from somewhere likely with some kind of comet. Well, once the comet hit the earth, and so the earth was hard and rocky and cool enough, I guess, at this point. And once this comet of ice, water ice hit the earth, well, guess what, that changed the mass of the earth. So, yeah, this rate at which objects fall to the earth is a function of the mass of the planet. Objects fall at a different rate on different planets that had different mass. So, you've seen the pictures of Neil Armstrong and the moon bouncing around because the earth, the gravitational pull of the moon is significantly less than the earth. So, this is, this could be false, right? Objects could have fallen at a rate of 19 feet per second per second to the earth, or 48 feet per second per second to the earth. It could have been a variety of things. This is true through experience. We figured this out through experience, through experiment specifically. So, this is true as a matter of fact, not as a relation of ideas. This is true as a matter of fact. If a person has a conditional and asserts the antecedent, the consequent necessarily follows. Now, semester after semester, I'm disheartened by the fact that nobody knows what I'm talking about when I give this proposition. This is one of the rules of reason that I gave you in the text. It's called modus ponens. Now, I'm just going to kind of skip to the chase. This is true as a relation of ideas. When you take the meanings of the terms, this proposition is true. So, a conditional is a proposition such that the antecedent is sufficient for the consequent. The antecedent is defined as what is sufficient for the consequent. Consequent is defined as what is necessary for the antecedent. Now, when you assert something that's sufficient for something else, the second thing necessarily follows, right? That's what it means to be sufficient. If one is true, the second must also be true. So, here's a conditional. If an animal is a dog, then that animal is warm-blooded. That's a true conditional. All dogs have warm blood. They're endothermic. So, take my puppy, Penny. Penny is a dog. It follows necessarily that Penny is warm-blooded. So, this is true as a relation of ideas. This is not true as a matter of fact. This is true as a relation of ideas. It's impossible for this to be false. There's some conditional such that a certain antecedent and the consequent does not follow. Well, if that's true, then the consequent follows and it does not follow. We've got a contradiction given the meanings of the terms. So, it can't be false if the consequent doesn't follow in any conditional. So, either the consequent follows and it doesn't follow, or it's a conditional and it's not a conditional, or you're set the instinct or you don't desert the antecedent. It's one of the contradictions that's going to come into place. So, this is true as a relation to ideas. This is true simply in virtue of the meanings of the terms and its denial is false. It must be false. So, it must be true. The physical universe has existed for a finite period of time. Okay. Now, let me just, again, this is true. Right. As I said, all the propositions we're talking about today, they are true. The question is whether they're true as a relation of ideas or true as a matter of fact. By the way, there were a lot of people that thought the universe had always existed that it was an infinite amount of time that it had existed. So, I think Aristotle was one of them. I don't know the exact history. Most astronomers subscribe to something called the steady state theory of the universe, meaning that the universe was static and essentially didn't change very much and it was neither expanding or contracting. And I don't know whether, I don't think that they, I don't know whether, you know, like a eternal existence or an infinite existence necessarily is implied with that. But, you know, the Big Bang theory was not a prominent theory, right, up until basically recent time. I want to say the 1950s. Even Einstein subscribed to the steady state theory of the universe. It wasn't until a Belgian Catholic priest by the name of George Lamarte, I think I'd say he says his name, George Lamarte. I think an American would say George is Lamarte, right? I think you pronounce it George Lamarte. He formulated the Big Bang, the theory of the Big Bang and it was empirically verified, I believe, by Hubble. I think it was Hubble. My grasp of the history isn't the best. I don't take my word for it. You should take a look for it. Look it up yourself. But the theory that the universe started with the Big Bang and therefore has existed for a finite period of time is relatively new in that sense, right? We did not always have this Big Bang theory. So you might say, well, okay, so this is true as a matter of fact. Well, I don't know about that. Now, I might get in trouble for this, but I want to say the universe has existed for an infinite amount of time. The physical universe has existed for an infinite amount of time. It's not only contrary to empirical evidence, but results in a self-contradiction. So, you know, the universe has existed for an infinite amount of time. How would that work? If the universe has existed for an infinite amount of time, then that means that an infinite amount of time has passed. Go to the past infinite amount of time. That's kind of like saying you're at the last number, right? I am at the end of the number line. Well, there isn't an end of the number line. The number line is infinite. So to say that an infinite amount of time has passed is to say that an limitless amount of time has ended. And if a limitless amount of time has ended, it has a limit. So it's both a limitless and limited amount of time. So now I want to say that this is true not only as a matter of fact, as at least a matter of fact, but it's true as a relation of ideas, right? That's how we could justify it as a relation of ideas that the proposition the physical universe has existed for an infinite amount of time is a self-contradiction. So, at least from my money, this is true as a relation of ideas. All right. So we've had, we've looked at this distinction between the relations of ideas and matters of fact. For Hume, these are both true, right? These propositions are both true. The question is how they're justified. Matters of fact are justified through experience. Hume is still basically an empiricist and the relations of ideas are true simply in virtue of the meanings of the terms. It's definitionally true. All right. Now, this distinction might seem a little difficult, but it's also how he approaches his proof, his question about how or whether the principle of induction is justified. So, this distinction is key when we take a look at his argument when he says that the principle of induction is not justified.