 In the previous lecture, we talked about whether an argument is valid or not valid. Valid would mean that if the premises are true, then the conclusion is true as well. If your argument is invalid, then you actually have a logical fallacy. There's no guarantee that the conclusion will be true. Now, if your argument is valid, that means that if the premises are true, then the conclusion is true also. Now, the big word here is if. Valid argument is important, and we can prove conditional statements are true, but what if the premises isn't true? Then we can't necessarily guarantee the conclusion because the valid argument only says if the premises are true. We say that an argument is sound if the argument is valid and the premises are actually true. So if you have a valid argument and the premises are true, then you get the conclusion. This is basically just the law of detachment here, the modus ponens. And so this is what we consider a sound argument. An argument is unsound if it's not sound. Now, of course, if an argument is invalid, then it's unsound. But of course, if your argument is valid, but the premises are false, then you still have an unsound argument. And so soundness is a very important attribute you look for in an argument here. An argument can be unsound even if it's valid. You have to make sure the premises are true as well. Now, even if you're not necessarily throwing these type of fallacies into a mathematical proof, one should still be aware and very cautious about these type of fallacies as they show up in everywhere in modern day life. We can imagine that people who fight with each other on social media or on other websites and forums and things like that, or lawyers trying to persuade juries to believe someone's innocence or guilty, politicians trying to convince you to vote for him or her based upon various statements they make. Oftentimes, these courtroom dramas, these political debates, the culture wars are throwing these logical fallacies at each other all the time, and they're not rooted in mathematics and not rooted in logic. We have to be very careful that we see through the fallacies that are thrown at us, and more important, we also don't throw them at others as well. Truth should be discovered only by valid and sound techniques. These fallacies have to be cautious about it because no truth will be found there. One of perhaps the most common logical fallacies that you can see, especially if you read social media, is the so-called ad hominem argument. You'll see a lot of these arguments, these fallacies, I should say, have Latin names attached to it, and this is just from the tradition that logicians attach to these names as they studied them for a long, long time. The word ad hominem here from Latin would actually mean to the person. An ad hominem argument actually attacks the person making a statement or argument and ignores the argument they're making themselves. So for example, Jane says that whales aren't fish, but she's only in the second grade, so she can't be right. This argument is not attacking whether whales are fish or not, which I hope most of us understand that whales aren't fish. It's actually a true statement. It's attacking Jane because Jane's only in the second grade. What does she know about zoology? She can't be right. You're discrediting her credentials, therefore we can discount what she says because maybe her credentials aren't good enough. We're not attacking the argument here. The person's attacking Jane because she's not good enough to know such a thing, even though she's right in this situation. Now, these insults can attack so much credibility. They can attack their angle, their perspective. They can just be flat mean sometimes. You could be something like, Jane is so stupid. What does she know about whales? It's not an ad hominem argument. It doesn't necessarily have to be rude, although they often are. It just means that you're attacking the arguer and not the argument itself to make sure that you're attacking the person's words as opposed to attacking the person itself. Very related to the idea of an ad hominem attack is what's referred to as a straw man argument. The straw man argument, I think, is one of the most prevalent argument fallacies as well. Clearly, people insult each other all the time when they have debates and fights, but the straw man, I think, is actually more villainous than the ad hominem because you could be rude and insulting, but it's self-apparent that you're being rude and insulting to who you're debating with. But the straw man argument, it's kind of like logical gaslighting, in which case you misrepresent an argument in a less favorable way to make it easier to attack. So for example, here's a fictitious example of such a thing. I have to be cautious of introducing politics or other culture war type things in these videos because I don't want these videos to be a forum for people to argue about these things. Focus just on the logical fallacy in play here. Senator Jones has proposed reducing military funding by 10%. Apparently he wants us to be defenseless against all terrorists. So the idea here is, let's pretend that this is a senator for the United States here. Most people, I think, would agree that we don't want to be defenseless against terrorists. Many of us watching this video might still be alive and understand the events of what happened on September 11, 2001. That was a horrific day where thousands of people died and their lives were changed forever, those who survived it. Clearly no one in the United States, other than perhaps some extremists, want that to happen again. So the United States needs to defend itself from enemies, some of which could be classified as terrorists here, right? So there's a clear stance. We should defend ourselves. Now, on the other hand, is Senator Jones making the argument that we should not defend ourselves, that we should be defenseless? Senator Jones is making the argument that military funding should be reduced by a fixed amount, 10%. There could be a lot of reasons why Senator Jones, suppose, wants that. Maybe he wants us to be defenseless. Maybe he thinks armies are immoral. That argument could be made, but it could also be that maybe he's just like trying to be physically responsible. Maybe he's like, we can't afford all of this military funding. We have to cut it so we can sit within a budget. There are many reasons why Senator Jones could propose a decrease in funding. But if one of those reasons was he wants us to be defenseless, then that might be worth pointing out. But we don't claim, Senator Jones might not be claiming that. So we instead might misrepresent what does this mean with something that's deplorable, okay? So we've intentionally misrepresented it. Maybe even unintentionally misrepresented it because this is deplorable. This might not be. But if you equate these things as the same, then this becomes deplorable because this is deplorable, even though that's not the argument that Senator Jones makes. One has to be very, very cautious that when we discuss issues, whether mathematical, political or whatever, we make sure we aren't making up the strawman, right? We don't want strawman all over the place. We need to make sure we understand our points of views and our opponent's point of views so that when we attack the opponent's argument, we actually attack their arguments as opposed to a misrepresentation of them. This one kind of came up with our example of Jane in the whales, but another type of logical fallacy is an appeal to authority. This is a type of argument that attempts to use the authority of a person to prove the claim, alright? That is using the authority, the expertise, the position of a person to argue why they are right or why they are wrong. Like earlier, we mentioned that Jane was incompetent because she was only a second grader, so she lacked authority and therefore her argument then became unsound, which she was actually right despite that. So it wasn't ad hominem because we were attacking the person, not the argument, but related to that, we could try to praise the arguer or use someone's authority to present some truth. For example, a diet high in bacon can be healthy. Dr. Atkins said so. For those who don't know the historical context here, the so-called Atkins diet proposed by Dr. Atkins here basically said, you don't eat anything but meat. I'm oversimplifying that, mind you, but you basically only eat meat and that you make you lose a lot of weight. And sure enough, a lot of people lost a lot of weight by following the Atkins diet, but also a lot of people got sick and died from the Atkins diet, including Dr. Atkins himself. So one should be very cautious of these trendy diets just because some famous doctor said it's good. In fact, if any doctor says it's good, that alone does not make it right. Just the fact that you have a doctor who said something doesn't make it medical fact. Just because a scientist says a certain theory is true does not make it scientific fact. Just because a politician says something does not make it political fact. Clearly, people's authority, people's expertise informs how credible of a witness they are, but their authority alone is insufficient evidence to guarantee a sound logical argument. Let me slightly change this. What if I were to say something like, Jennifer Hudson lost weight with Weight Watchers? So their program must work. Now I apologize that people don't know who Jennifer Hudson is. She at least once upon a time was a celebrity, even if she's not now. And if you don't know what Weight Watchers is, the name kind of gives the name away. It's a weight loss program you can participate in, even if in the future you watch this video and it's no longer in business. The idea is if you have some celebrity that uses a product and it works great for them, does that mean it'll work great for me? Not necessarily. It might not. Similar to appeal to authority, this would be like appeal to celebrity. I'm not claiming that Jennifer Hudson is an expert on weight loss or anything like that. It's just she was a famous person and she lost weight using it. And I want to be like her. Is that what we're saying here? Her celebrity doesn't make it more reliable for me. Just because it worked for her doesn't mean it'll work for me, even if she's a celebrity. We sometimes give celebrities this deified status, godlike status, but it's no different from them than it is for me. Although she might have a lot more money and fame than I do. That's okay. Be cautious of appeals to authority or the authority of celebrity here will appeal to celebrity. You have to be very, very cautious about these type of things. You could also talk about an appeal to popularity. When we go to websites, we want to buy a product like maybe we go to Amazon or something. We want to buy something. Oftentimes what we do is we look at the reviews and we're like, oh, all of these people gave five star reviews. That means the product must be good. Now don't get me wrong. If a lot of people are reviewing the product is positive. It probably is a positive review, but of course there are concerns that are these authentic reviews. Are they fake? Are they bots who made it? It goes the other way around too. Are the negative reviews legitimate or just trolls who came out from under the bridge? It's hard to tell sometimes. And even still, even if all of these positive reviews are real and authentic, it's also possible that I can get the product and it could be bad for me. So the reviews, the positive reviews don't necessarily make it automatically good, but there might be some possible truth there. Probably it's useful. So you could also look to appeal to popularity just because everyone else liked it. It doesn't mean it's going to be good for me either. And so then one last one I want to mention here is what we could call an appeal to consequence. This logical fallacy concludes that a premise is true or false based upon whether it would be good if it's true or false or not. Is the consequence desirable? An example of such. Humans will travel faster than light. Faster than light travel would be beneficial for space travel, so therefore it's going to happen someday. That's an appeal to consequence. It could actually be that the laws of physics forbid humans to travel faster than light. Things like Star Wars, Star Trek, any other Star movie you can think of, they might actually be fiction. As in they will never be true because maybe that technology is impossible to do. Maybe it won't be, maybe it will. I don't know, but just saying that space travel will be good doesn't actually make it possible. So we want to avoid this type of fallacy as well. Now, similar to this appeal to consequence, you could appeal to emotion. You're not looking at the consequences of the truth statement. You're looking at the emotions of it. Does it make you feel good? Does it make us feel sad? Our feelings do not determine whether a statement is true or not. And there are lots of other logical fallacies that we could include in this video that I won't for the sake of time. We could talk about distractions. Sometimes people place diversions in their arguments to distract us from what actually matters and then make us forget what actually was being considered. You have things like hasty generalizations or guilt by association. Sometimes you say something is true or false based upon some association to something else. Like, oh, Tommy over there is guilty of a crime because Jimbo and Billy Bob were convicted guilty of the crime and Tommy is their good friend. So he's probably guilty by association. You should be very careful of such things, those type of generalizations. We do that in human language all the time, but it can sometimes creep into mathematical discourse as well. Make sure we avoid these logical fallacies that are based upon emotion and not actually upon sound reasoning. That brings us to the end of this lecture. Thanks for watching. If you learned anything in lecture 13, please like these videos. Subscribe to the channel to see more videos like this in the future. And as always, if you have any questions, feel free to post them in the comments below and I will gladly answer them as soon as I can.