 It's just, I can't ask for a more gorgeous morning to get started. So as we discussed last time, if you reject Hume's conclusion, you have to reject at least one of the premises. And rejecting a premise, any proposition, commits you to its logical contradictory. Alright, so let's look at the first premise. If the principle of induction can be proven, then either it can be proven using demonstrative reasoning or moral reasoning. And we looked at some examples of this. I mean, this is where the relations of ideas and matters of fact come in, alright? Now moral reasoning doesn't mean reasoning using right and wrong, good and bad. Moral reasoning, he means something like habitual reasoning, how we're used to. And reasoning using matters of fact, yeah, alright, we're really used to it. Moral reasoning also includes the principle of induction. We use it a lot. Demonstrative reasoning uses the relations of ideas. We looked at that before. So if the principle of induction can be proven, then either it's proven through demonstrative reasoning or it's proven through moral reasoning. And these are the only two ways that we know anything according to Hume. Okay. Well, if we reject this premise, then we're saying this. We're saying that the principle of induction can be proven, alright? But it's false that the principle of induction can be proven either with demonstrative reasoning or with moral reasoning. Huh. Well, you know, for Hume, this is, you know, Hume's like, yeah, what else are you going to use, right? The only two that we got. Well, how about we put a thumbtack in this one, right? We'll come back to this one later because this is going to have some strange results. I mean, what this means is if it's proven, it's not proven through simply in virtues of the meanings of the terms or, you know, it's not proven through habitual reasoning, what we're used to or everyday reasoning. Oh, gosh, if it's not going to be one of these two, what's it going to be? Well, it's too gorgeous to wait around any longer. Let's go hit the trail. All right, so next premise. If the principle of induction can be proven using demonstrative reasoning, then there's a contradiction and the denial of the principle of induction. So remember, this is what's involved with demonstrative reasoning. It's true simply, it's using true and virtue relations of ideas, meanings true simply and virtue of the meanings of the terms. If you, you know, all squares have four sides is true simply in virtue of the words all four squares and sides in half, right? So if the principle of induction can be proven using demonstrative reasoning, then there's a contradiction and the denial of the principle of induction. Remember, the principle of induction says the future will resemble the past. All right. Well, if this premise is false, then we are committed to its logical contradictory. Its logical contradictory is the principle of induction can be proven using demonstrative reasoning. And it's false that there's a denial, excuse me, and it's false that there's a contradiction and the denial of the principle of induction. Well, you have to have a contradiction and the denial of the principle of induction in order for it to be proven using demonstrative reasoning. So once this is saying it can be proven using demonstrative reasoning, but it can't be proven using demonstrative reasoning, that's a logical contradiction. So this premise, if we say this premise is false, we are committed to a logical contradiction, which is not good, right? We can't use logical contradictions and reasoning. Next premise. It is false that there is a contradiction and the denial and the principle of induction. So this is what Hume claims. You take the principle of induction, which says the future will resemble the past. You say it's false and you don't have a contradiction. Okay, so if we're going to say, if we're going to deny this premise, we're saying that there is a contradiction in the denial of the principle of induction. Okay, well, hmm, what would that be, right? So what does, so there's a contradiction, right? We'll have to look at the meanings of the terms, all right? Well, what does the future mean? What will happen? What does the past mean? What has already happened? Okay, so if we say that there's a contradiction and the denial of the principle of induction, we say, well, it is false that the future will resemble the past. Now, you know, immediately that sentence sounds odd. I mean, we're really used to the principle of induction, right? So immediately we think, well, gosh, that, you know, there has to be something wrong there and saying it's false that the future will resemble the past. Okay, it might in fact be false, right? But then that's dealing with a matter of fact, not a relation of ideas. If it's a relation of ideas, right, we have to have a contradiction to say, you know, one part says the other part is false. You know, so when we say it's false that all squares have four sides, we're saying that some four-sided figure does not have four sides, right? That's a direct contradiction. But we don't have that when we say it's false that the future will resemble the past. The future just means what's already happened, the past means what has happened. So this one's not going to work. Okay, well, there's a climb. All right, well, this looks like a good place to stop in. Look at the next premise. If the principle of induction can be proven using moral reasoning, then the principle can be proven by observing that it has been effective in the past and inferring that it will be effective in the future. And this conditional reason-wise is this is just the definitional part of moral reasoning, right? We, this is how we habitually reason. It has happened in the past, so it will happen in the future. Okay, so if we deny this premise, we say the principle of induction can be proven using moral reasoning, but it's false that the principle can be proven by observing that it has been effective in the past and inferring it will be effective in the future. Well, this is the problem. This is just a contradiction within itself. To even reason using moral reasoning, it just means you have to observe it's happened in the past and it will happen in the future. So if we deny this premise, what we're saying is the principle can be proven using moral reasoning, but it's false that it can be proven using moral reasoning. Well, that's a direct contradiction. So this one isn't going to work. We can't use logical contradictions and reason. Okay, well, speaking of contradictions, all right, next premise. If the principle can be proven by inferring that the principle has been effective in the past, since the principle is effective in the past, it will be effective in the future, then the proof for the principle of induction uses the principle of induction. And yeah, I mean, that's what's happening. You're saying, well, I've inferred that it has been effective in the past, since it's been effective in the past, it will be effective in the future. That just, the principle of induction says is the future will resemble the past. Yeah, I'm using the principle in order to prove the principle. Okay, so if we're going to deny this premise, what we're saying then is the principle can be proven by observing that it has been effective in the past and inferring it will be effective in the future and it is false that the proof for the principle of induction uses the principle of induction, but it does. This is also a direct contradiction. Saying it has worked in the past, therefore it will work, that just is using the principle. Okay, and by the way, you're going to see a lot of people doing this and say, well, of course the proof works, the principle of induction works. It's been effective in the past and so it will be effective in the future. Okay, I mean, maybe you can do that, but your proof for the principle uses the principle, right? Okay, well, so we can't deny this premise because it results in a logical contradiction. All right, and logical contradictions can't be used in reason. It's not good news. Well, before I go down that rocky trail, maybe this is a good place to stop and look at our next premise. So if the principle of induction can be proven by using the principle, then the principle can be proven by assuming it's true. So the idea behind this premise is that if you use the principle, well, it better be true beforehand. And if it's true beforehand for the proof, well, then you're assuming it's true for the proof. Well, okay, so if the principle can be proven by using the principle, then the principle can be proven by assuming it's true. So if we deny this premise, we're saying the principle of induction can be proven by using the principle of induction, but it's false that the principle can be proven by assuming it's true. Okay, well, this looks like another direct contradiction, right? Because in order for the principle to be used in the proof for the principle, we have to assume that it's true. But then if we say it's false that it could be proven by assuming it's true, well, now we have a contradiction. And contradictions can't be used in reason. So we can't deny this premise. It is gorgeous out here. Well, it's a good thing we reached the end of our hike. The sun's starting to come up. It's going to get pretty warm pretty fast. Now it's the end of our hike, so it's time to look at the last premise. This premise says it is false that you could prove the principle of induction by assuming it's true. And if we deny this premise, we're saying, well, we can. We can prove the principle by assuming it's true. So here's my proof for the principle of induction. It's true. Now we don't have a logical contradiction here, but it's just false, right? We don't prove anything. There is nothing that we prove by assuming it's true. So if there's nothing that we can prove by assuming it's true, well, then we can't prove the principle of induction by assuming it's true. So we haven't had a lot of good options so far looking at Hume's argument and trying to reject a premise. But now remember what I said at the beginning, right? Let's put a thumb tag and reject in that first premise. Do you remember? So the first premise was if the principle of induction can be proven, then either it is proven using demonstrative reasoning or it is proven using more reasoning. And if we deny this premise, we say the principle of induction can be true or it can be proven, but it's false that it's proven using demonstrative reasoning and it's false that it's proven using more reasoning. Okay, well, what's left then? Well, remember, Hume is basically an empiricist, right? More or less, right? Let's let him slide on this whole relations of ideas stuff, but he's basically an empiricist. And what he's saying is you can't prove the principle of induction using empiricism. Is there anybody all semester long that we might have talked about mentioned early on who could say, well, you can't do it, but that doesn't mean that I can't. I can prove the principle of induction. Well, this one person, right? It's gonna, or at least several people anyway. I can prove the principle of induction and I don't have to use empiricism. Well, if you're not using empiricism, guess what you've fallen back to? You have gone back to rationalism. You're gonna prove it in some rationalist way, right? Putonic form of, you know, just the way the mind works. It's something like that, right? I've got some knowledge and I've got it non-empirically and amongst that knowledge is the principle of induction. All right. Now you could take that approach, but now you've gone back to rationalism and you've abandoned empiricism and ordered it together.