 Hi, welcome to our Coursera course. This is the first time we've ever taught an online course, and we're very excited about it. I'm Walter Synod Armstrong from Duke University and my co-teacher is Ron Netta from the University of North Carolina at Chapel Hill. Say hi, Ron. Hi. Thanks. This is going to be a great course. It's going to cover a lot of important practical issues, raise some fascinating theoretical questions. We'll also try to have some fun, because there are lots of wacky examples where people make silly mistakes in arguments in everyday life, and we'll try to teach you how to avoid those. The title of the course is Think Again, How to Reason and Argue, and the title pretty much tells you what the course is about. We'll try to teach you to think again about a wide range of issues that affect your life in various ways. We're not going to try to convert you to our point of view or teach you to believe what we believe. Instead, we want you to think in a new way and in a deeper way about the issues that matter to you most. The subtitle of the course, How to Reason and Argue, tells you that we're going to focus on a particular type of thinking, namely reasoning, because most people don't want to be arbitrary or have unjustified beliefs. They want to have reasons for what they think and do. But how do you get reasons? Well, we're going to approach reasons by way of arguments, because arguments are just ways to express reasons. And if you can understand arguments, you can understand reasons. And if you can formulate good arguments, you can have good reasons for the ways in which you think and behave. So that's one way in which it's important to understand arguments, namely to get better reasons for your own beliefs and actions. But another way in which it's very important to understand arguments is to avoid mistakes, because there's lots of charlatans out there who are going to try to convince you to think the way they want you to think and to behave the way they want you to behave by giving you bad arguments. So you need to spot them and avoid them. Just think about it. Use car salesmen who tries to convince you to buy a car because it looks really cool and you'll look even cooler if you're sitting in the car. Well, that might be a good reason to buy a car and it might not. And you're going to have to figure out which kinds of arguments to believe and which kinds not to believe. Consider another example. Say, a lawyer in a courtroom and you're sitting in the jury and they're going to try to convince you either to find the defendant guilty or to find the defendant not guilty. But either way, you don't want your decision to be like flipping a coin. You want to have reasons for what you're thinking and for the verdict that you reach as a member of the jury. Or an evangelist tries to convert you to their religious beliefs and gets you to give up your old religious beliefs. Well, you don't want to make that kind of decision arbitrarily either because it's so important. And then what about your personal life? You might have a friend who says, let's go for a cross country trip. It'll be great. Well, maybe it will and maybe it won't. But you don't want to commit yourself to such a big endeavor without having thought it through properly. How are we going to study arguments? Well, in this course we'll have four parts. The first part will teach you how to analyze arguments. That might seem really simple. You just read the passage and hear what they're saying. But actually it's quite hard because some passages or some sets of words, if we're talking about spoken language, contain arguments and others don't. Here's an example. Consider a letter to the editor. Some letters to the editor don't have arguments at all. They just say, thank people for having behaved in nice ways or done nice things. On the other hand, other letters to the editor include arguments. They try to convince you to vote for a certain political candidate, for example. So you need to distinguish which passages include arguments and which passages don't include arguments. Then you need to look at those passages and figure out which of the words, which parts of those passages contain the argument. Then you need to separate out those parts, put them in a certain order, which we'll call standard form. And often these arguments will have missing parts and you'll have to supply those missing parts or suppressed premises in order to get a full picture of how the argument works. And that's what we'll do in part one. Then in part two, once we've got the argument in shape, we can start to evaluate it. But evaluations are going to depend a lot on what the purpose of the argument is. Some arguments try to be valid in a logical way. And those are deductive arguments. So we'll start first by looking at deductive arguments and the formal structure of deductive arguments. We'll look at propositional logic, then categorical logic. That'll be part two of the course. Then in part three, we'll look at a different kind of argument, inductive arguments that don't even try to be deductively valid. Here there are just a lot of different kinds. So we'll look at statistical generalizations, applying generalizations down to particular cases. We'll look at inference to the best explanation and arguments from analogy. We'll look at causal reasoning and probability and decision making. So there'll be a lot of different types of inductive arguments covered in part three. Then in part four, we'll look at fallacies. These are common but very tempting ways to make mistakes in arguments. Some of them have to do with vagueness, others have to do with ambiguity. Some of them are irrelevance, like arguments add hominem and appeals to ignorance. And we'll also look at a major fallacy called begging the question that people commit all the time. And in the end, we'll teach you a general method for spotting and avoiding these common mistakes. So that'll be part four. And at the end of each part, we'll have a short quiz with some questions to make sure you understood. So we're very glad to have you in this course and we're very honored that there's so many students in this course. But that raises one problem, namely we cannot answer emails from students. So please do not email us individually. There will be discussion forums where you can go and talk to other students about the material in the course. And I bet that if you go to those forums, not only will you get your questions answered, but if you go to those forums and help answer other people's questions, everybody will learn more. And that's what this course is all about. So thanks very much for joining us on this adventure. And we hope you stick with it because we've got a lot of fun and a lot of important things to cover. One final recommendation. We've done these lectures so that you can just watch the lectures by themselves and do the exercises and take the quizzes. However, if you're listening to a lecture and you have a little trouble understanding it, or if you're really fascinated and you want to get more detail, then there is an accompanying textbook called Understanding Arguments by myself and Robert Fogeland. Many, many, many of the best ideas in this course come from him. He's been a leader in this field of understanding arguments for many decades, and I know an awful lot to him and I really appreciate that. So I wanted to do a little shout out of thanks to Robert Fogeland before we get started on this course in the next lecture. We'll hope the first lecture convinced you that arguments really matter. Of course, they're not the only thing that matters. There's more to life than reason and arguments. But they are something that matters and they matter a lot. So we need to understand arguments. Now the first step in understanding arguments is to figure out what arguments are. And the first step in understanding what arguments are is to figure out what arguments are not because we want to distinguish arguments from all of those things that don't count as arguing. And the best source of information about what arguments are not is, of course, Monty Python. Well, that was pretty silly, wasn't it? But in the midst of all that silliness, we find some truth because after all, many members of the Monty Python troupe were philosophy majors. So each room represents a kind of thing that we need to distinguish from arguments. So let's think first about getting hit on the head lessons. Arguments are not like hitting people on the head. You hit people on the head when you wrestle. The point is that arguments are not fights. You don't win an argument by hitting somebody on the head. Sometimes little children say that their parents are arguing when they're really having a verbal fight. All this fighting reminds me of my parents. Damn it, George. I told you if you didn't quit drinking, I'd leave you. Well, I guess that makes you a liar because I'm drunk as hell and you're still here. But you cannot win an argument just by yelling at someone. That doesn't make the argument any better because that's not the point of arguing. Another room in the Monty Python skit involves abuse. Don't give me that you snotty-face-heaver parrot dropping. Now abuse is one of the things you do with language, but it's not the same as arguing. You cannot win an argument simply by calling your opponent a stupid git. Stupid git. And the point of this course is not to teach you to go back and abuse your roommate by calling them nasty names. That will not help you win any argument. It also won't help you win any friends. And another room in the skit has to do with complaining. But all those complaints don't amount to an argument either. They're just expressing your emotion about the situation. Arguing is something different from all of those rooms. So what is arguing? Well, at one point, one of the characters says, Well, an argument is not the same as contradiction. Can be? No, it can't. So what do they mean by a contradiction? In British English, to say a contradiction is just to deny the person or contradict what they said. But contradicting what the person said, that is denying it, is not arguing. I can say, What do you think is the best flavor of ice cream in the world? Well, I have my favorite. I know what the best flavor is. The best flavor is Ben and Jerry's coconut almond fudge chip ice cream. There's nothing better. And then you say, No, it isn't. Well, you haven't argued that it isn't, and I haven't argued that it is. We're just disagreeing with each other. We haven't given any reason for any of the positions that we've adopted yet. So, as Monty Python says later on, a different character, argument is an intellectual process. It's a process not just of asserting your views, but of giving some kind of reason for your views. So the next definition that Monty Python gives of an argument is that an argument is a connected series of statements to establish a proposition. I take it they mean intended to establish a certain proposition. So that's a pretty cool definition if you think about it, because it tells you what an argument is made of. It's a series of statements, and statements are made in language. So arguments are made of language. It also tells you what the purpose of argument it is. The purpose of argument, they say, is to establish a certain proposition. So now we have a pretty neat definition of argument. This definition gives us a nice contrast, because there are lots of other series of statements or sentences that don't count as arguments because they're not intended to establish a proposition. Consider, for example, a novel which has statements about what's going on, but it's not necessarily trying to establish any particular proposition, or a dictionary might have a series of definitions, but it's not intended to establish a certain proposition. Instead, novels and dictionaries order sentences in a different way. They order them either chronologically or alphabetically, whereas arguments are trying to put statements into a certain structure that reflects the order of reasoning in order to establish the proposition, according to Monty Python. But Monty Python, no matter how great they are, and they are great, didn't get it quite right because the purpose of an argument is not always to establish a proposition, because some propositions that are conclusions of arguments we already knew. Consider, for example, a mathematical proof. If someone tries to prove the Pythagorean theorem in geometry, people already believe the theorem. They already knew that it was true, so they weren't trying to establish the proposition, but the proof does something else. It shows you how that proposition is connected to the axioms of the system and helps you understand why the proposition is true, and we'll see that other arguments, like explanations, do the same thing. So sometimes, arguments are intended to establish a proposition, like Monty Python said, but in other cases, they're intended to help us understand the proposition and the reasons why the proposition is true. So we want to distinguish reasons to believe that the proposition is true from reasons why the proposition is true, and arguments can do both of those things. So we need a somewhat broader definition of argument to cover these different kinds of reasons. We'll think of an argument as a connected series of sentences or statements or propositions where some of these sentences or statements or propositions are premises, and one of them is the conclusion, and the ones that are premises are intended to provide some kind of reason for the one that's the conclusion. This definition is useful in many ways. First of all, it tells us what the parts of the arguments are, the premises and the conclusion. Secondly, it tells you what the argument's made of. It's made of a language, because sentences and statements and propositions are made in language. Third, it tells you the purpose of argument to give a reason for the conclusion. Fourth, a nice feature is that it's very flexible because there are lots of different kinds of reasons. We don't want our definition to be too narrow because then it won't cover all the different kinds of arguments, and the notion of reason captures the different kinds of relations between the premises and the conclusion in different kinds of arguments. So let's do a few quick exercises to make sure that you understand how this definition works. Welcome back. In the previous lecture we saw a definition of argument as a connected series of sentences, statements or propositions where some of those sentences, statements and propositions are premises and one of them is a conclusion and the premises are intended to give some kind of reason for the conclusion. In this lecture we're going to look at the purposes for which people give arguments because the purposes are crucial in determining what an object is. Take, for example, an artifact that you might find in an archaeological site. You won't be able to figure out whether it's a really big screwdriver or a really small spatula unless you know whether the people who used it intended it to screw screws or to pick up food that they were cooking. So to understand arguments we need to understand the purposes for arguments and that means why does somebody bother to give an argument instead of just asserting the conclusion without an argument? We'll just think about it. If you went to a used car lot and the salesman said you ought to buy that Mustang, would that convince you? Not a chance. But if the salesman said you ought to buy that Mustang because it looks really cool and it goes really fast or maybe it has great gas mileage or whatever and gives you a series of reasons then you might be convinced to buy the Mustang. So that's one purpose of arguments to try to convince you to do things or to believe things that you wouldn't otherwise do or believe. So this purpose is persuading or convincing. And if you think about it, what the salesman is trying to do is he's trying to change your mental states. He's trying to make you believe something that you didn't believe or do something that you didn't do. So he's trying to bring about an effect in the world. But that's just one purpose of arguments. We don't always act like salesmen. Sometimes instead of trying to change people's beliefs we're simply trying to give them a reason for their belief or for our belief and to give them a reason is not necessarily to convince them or persuade them or change their beliefs. When we're simply trying to give them a reason to believe the conclusion we're going to call that justification. So imagine that you're a friend. You're not a salesman, you're a friend. Imagine that your friend is thinking about buying a car and doesn't know which one to buy. You might say, well, I think you ought to buy the Mustang because it looks really good and it goes really fast and it's actually got pretty good gas mileage and it's quite reliable or whatever. You're not necessarily trying to convince her to buy that car. It'd be fine with you if she bought any car she wanted, any car that would make her happy. You're trying to talk about the reasons for buying the car so that she can make her own decision in that sense you're trying to justify that decision or that belief that the Mustang is the best car for her to buy and not necessarily to convince her or persuade her. If she comes up with great reasons to the contrary, you're perfectly happy whereas the salesman wouldn't be. But notice that you might give exactly the same reasons that the salesman did. Exactly the same argument that the salesman did. The difference lies in the purpose because the salesman is trying to convince her to change her beliefs and actions but your goal with your friend is to discuss the reasons for her decision or action. So you're thinking about justification and the salesman was thinking about persuasion. Now it really matters whether your goal is justification or persuasion because there's a big difference here. If you're trying to justify your friend's belief or your friend's action, then you're trying to give her good reasons. The salesman can convince her or persuade her with bad reasons. So it doesn't matter to his purposes whether the arguments that he gives are any good or bad as long as they work to affect that change in the world. Whereas you care about whether your arguments and your reasons are good reasons or arguments because you're trying to justify that belief or that action. And of course people can try to do all of these things at once. They can mix them together in various ways and that can get complicated. So when someone gives you an argument you need to ask a series of questions. The first thing you need to ask is is this person trying to change my mind or change my behavior? If so, then their goal is persuasion or to convince you. Then you need to ask are they trying to give reasons for changing my mind or for believing if I already believed it? Well if they're doing that then their goal is justification. And if you go down that series of questions you'll be able to understand what the purpose of giving the argument is at least for this range of cases. So let's do a few exercises just to make sure that you understand justification before we go on to the next purpose of argument which will be explanation. Hi again. In a previous offering of this course one student made a great point about persuasion and justification and the relation between those two. She did it in an argument that she presented for the entire class and I think we can all learn by listening to her. So here it is. Strong arguments don't always persuade everyone by Jessica Hyde from the United Kingdom. It's not enough for an argument to be strong, valid, and sound to be persuasive. You can have an argument for which every premise is genuinely true and where every conceivable flaw in the argument is negated and still not have it be persuasive. There will almost always be someone who either misunderstands the argument or blindly believes the opposite of a premise in face of facts. Human beings aren't always logical and don't always believe scientifically proven cause and effect. Religious and cultural beliefs can be too hard to overcome. So, even the best arguments can have disbelievers. Thank you, Jessica. What a great argument. I'm convinced. Remember, to persuade someone is to convince them or change their mind into believing what you wanted them to believe and what you were trying to get them to believe. Whereas justifying is giving them a reason to believe your conclusion. And those are different because, as Jessica argues very well, sometimes people make mistakes. You give a perfectly good argument with perfectly good premises and it's formulated as clearly as could ever be expected and yet they don't understand it or they don't believe your premises and so they're not persuaded. But still, you did give a good argument. So, you succeeded in justifying your belief. But was it a good argument if you were trying to persuade them? Well, maybe not. If your purpose was to persuade them, then it might matter to you that you didn't persuade them. Whereas if your purpose was to justify the conclusion, to give a reason to believe it, then you did succeed in that purpose. So, whether you see it as a good argument or not is going to depend a lot on what your purpose is. As Jessica points out, sometimes you're going to want to persuade and it's not always going to be easy to turn an argument that justifies and gives a good reason into one that persuades. That is going to depend on making sure that they do accept your premises and that they do understand your arguments. And that's yet another trick that we haven't discussed perhaps as much as we should have. And we learn another lesson from one of the student comments on Jessica's argument. Here it is. From Judith, I think Jessica has opened a very interesting discussion with her argument. Thank you, Jessica. I appreciate that. We do too. What I'm learning is the purpose of an argument is to state with clarity and some degree of certainty an opinion or point of view a valid strong and sound argument in and of itself may never persuade or convert anyone to adopt a different way of thinking. So what? What a strong argument does is communicate clearly what one thinks and why they think it. So I guess the benchmark of success for many arguments is not complete persuasion but is how clearly one is understood. If someone's intent is to blindly refute everything, that's not an intellectually honest engagement. I've found that in constructing better, more thoughtful arguments, people may not agree with me but they're far more considerate of what I have to say. And by using much of what we're learning, I'm listening much more intently to other views. Yes, Jessica, many things do defy logic. We just keep trying to do our best. Thank you, Judith. What a great point. Because what you've done is you've shown us that there are other goals of arguments in addition to persuasion and justification. The one you mentioned was understanding. Sometimes the point of an argument is not to bring other people over to your point of view but just to make them understand why you hold the position that you do. You're trying to show them your reasons even if you know that those reasons are not reasons that they, themselves, are going to accept. Well, why would you want to do that? As you say, because it makes them more considerate of what you believe and of you. Because if we understand each other and the reasons why we hold our positions, we'll respect each other more and be more considerate. Not always. Of course there are going to be exceptions. But as a general trend, we're going to get along with each other much better if we understand why we disagree and what reasons we have. The example where this is not working is politics. Everybody knows that politicians just yell at each other and don't really listen to each other. They just scream out what's going to appeal to their base without thinking about what the real reasons are for the positions they're holding. I think they'd be a lot better off and we'd be a lot better off if they were to take Judith's lesson and say give us the reasons so that we can understand why you're adopting that position. We'll give you our reasons so you can understand why we're adopting our position and then we can seek a compromise by satisfying the values that we both are most concerned about. And arguments can play a role then in helping us cooperate with each other and live with each other and compromise on the very important issues that we all face. Another lesson that Jessica and Judith have taught us is don't set your sights too high. If your goal is to persuade everybody, you're going to be constantly frustrated because there are always going to be people out there who don't understand your argument or who understand it but are obstinate to accept your premise no matter how well you argue for it. So if you try to convince everybody you're not going to succeed. So give it up. You can't convince or persuade everyone. Still you can accomplish a lot. You can help them understand you you can come to understand them and you can give them good reasons to believe your conclusion. Well, that's a lot and that can be very important even if they're not persuaded. And you if you're justified in believing your conclusion can have reason to believe that the fault lies with them not with you when they don't accept your conclusion. Of course you probably can't convince that. You can't convince them that the fault lies with them not with you but still you might have accomplished your goals if your goals are reasonable namely to increase understanding to find the reasons for your belief and to present those reasons in ways that people ought to understand and accept. That's what justification is and that's what understanding is and those can be extremely valuable in arguments even if there's still some people out there who aren't persuaded. As I said in the first lecture arguments are used for many purposes and in the lecture just before this one we saw that it can be used for persuasion and also for justification of various sorts but persuasion and justification are not the only purposes for which arguments are given arguments are also given in order to explain things so we're going to spend this lecture talking about explanation indeed what we're going to try to do is to explain explanation we explain things all the time and I'm going to give an example that will probably really take off my co-teacher Ron because he's from Chapel Hill but my example is somebody might ask why did the Duke basketball team win the national championship in 2010 the answer might be that they had great players and a great coach because they got lucky you have to have some luck to win a national championship but in any case an explanation of that event is a reason why it happened so to explain something is to give a reason why it happened or to answer a question about why it happened notice that when you explain something you assume that it's true it wouldn't make any sense to ask why did Duke win the national championship in 2011 because they didn't you can only ask why this thing happened if it happened so we've already got one difference between explanation and justification and persuasion when you try to persuade someone to believe something that thing doesn't have to be true and they don't have to have believed it in advance when you justify something you can justify belief in something that they don't already believe but when you explain something both the arguer and the audience are assuming that that thing happened that the conclusion is true and they're looking for the reasons why it happened so if the goal of explanation is not to persuade or to justify and the arguer and the audience both already believe the conclusion then what's the point what's the goal of explanation the goal of explanation is to increase understanding not to it is true but to help us understand why it's true and we can do that in a number of different ways they're actually according to Aristotle four different types of causes he would call them but we would probably call them explanations the first he called efficient causation we'll just call it causal explanation and that tells you why something happened why did the bridge collapse because there was an earthquake and the bridge collapsed the second type of explanation he called teleological or purposeful explanation because it's looking at the purpose or the telos or the goal why did Joe go to the grocery store to buy milk his goal of buying milk is what explains why he went to the grocery store third type of explanation is formal why does this peg not fit into this hole and the answer is because the peg is square and the hole is round that's why it doesn't fit in the hole and that explains it that helps you understand why it didn't fit the fourth kind of explanation is material why is this golf club so light why is it way so little the answer might be because it's made out of graphite that helps you understand why the weight is so low on this golf club it would be a lot heavier if it were made out of steel so we can have four different types of explanation we can have causal we can have teleological we can have formal and we can have material and all of those different types of explanation are aimed at helping us to understand why something happened so did you hear that train whistle we want to ask why does the train emit such a loud noise well one answer might be that what causes it to make that noise is that the conductor pull lever on the train which creates that noise that would be a causal explanation another explanation might be the teleological explanation the train was crossing an intersection with cars and wanted the cars to know that they're coming another explanation might be a formal explanation because the whistle on the top of the train has a certain shape that makes the air come out with a certain vibration and a final explanation might be a material explanation because air has a certain density and a certain material that makes it create that kind of sound so we can give all four types of explanations for the same event here's another example we can apply all four types of explanation to a single event Joe jumped out of an airplane that's what caused him to fall but then why did he jump out of the airplane to get excitement why did he fall so fast because of his shape it was aerodynamic and because of the material that he was made out of heavy flesh which was a lot denser than the surrounding air so all four of those factors go into an explanation of why Joe fell when he jumped out of the airplane so next we need to talk about the forms of explanation you can actually give explanations in several different forms for example if somebody said why did you move to Duke I might tell a story about things that happened before I moved to Duke that led me to want to move to Duke and I could talk about moving to Duke and all the nice people here and so on you can give explanations in the form of narratives like that that's not going to imply that everybody in similar circumstances is going to behave in exactly the same way so you're not going to get general principles out of those types of narrative explanations but other explanations are given in the form of arguments and that's the kind that we're going to be interested in here the form in which explanations occur in arguments is really pretty simple one premise usually states some kind of general principle that can apply to a lot of different situations the second premise talks about the current situation and says that those types of features that the principal mentions are instantiated in this case and then the conclusion says that explains why it happened this way in this case for example if we want to know why objects fall right so there's a book and it falls we want to explain that we need to cite a general principle but notice that not all objects fall some objects actually rise helium balloons rise so we need a principle that's going to explain why some objects fall and other objects rise then we'll understand why helium balloons rise just to stick with that example and the answer is that when an object is suspended freely in a medium where the medium is more dense than the object then it rises and when an object is suspended freely in a medium where the object is more dense than the medium then it falls so you can explain why helium balloons rise by having as your first premise whenever an object is freely suspended in a medium like a gas or a liquid and the medium is more dense than the object then the object rises in circumstances in this particular case the helium balloon is less dense than the air that surrounds it therefore the helium balloon rises and that explains why the helium balloon rises and you can see how you give another argument to explain why the book fell now this form of argument gives some people the impression that any generalization can be used for explanation but that's not quite right one example is Bode's law Bode's law says that .4 plus .3 times 2 to the n can be used to predict all the distances between planets and the sun where n is the number of the planet so if n is Venus then n is 0, Earth is 1, Mars is 2 and so on this law was actually used to predict both the largest asteroid belt series and also Uranus so this law is a generalization that held for all the planets that they knew in Bode's day and also used to predict new observations of planets, pretty cool it actually turns out to fail when you get to other planets including Neptune and Pluto but still it worked pretty well for the data that they had but nobody thought that this law explained why the planets were that far from the sun they happened to fall in that pattern it could be used to predict but it didn't explain why they were the distance that they actually were from the sun so Bode's law is an example where you can get a prediction without explanation now let's look at the reverse an example where you have explanation without prediction you should just imagine that a woman is HIV positive and she gets pregnant and has a baby and the baby is also HIV positive how did the kid become HIV positive well the explanation is that the mother was HIV positive and they were sharing blood but notice that you cannot predict whether the mother is HIV positive that the child will be HIV positive because less than half of the children born to mothers who are HIV positive are themselves HIV positive you also cannot use the fact that the mother is HIV positive to justify the claim that the child is HIV positive if you want to know whether the child is HIV positive you need to check its blood so in this example we have an explanation of why the child is HIV positive when it is but we don't get any prediction that it will be HIV positive and we don't justify the belief that the child is HIV positive so you can have explanation without prediction and without justification so then more positively what is the goal of explanation well the goal of explanation is a particular phenomenon into a general pattern and that's what all these explanations do why do you want to fit them into a general pattern is simply to increase your understanding of why they came about they came about because they fit into this particular type of pattern and this kind of understanding of fitting them into a well-known pattern is useful because most of the things that we want to explain are kind of weird, unusual bewildering, surprising phenomenon that's when you need an explanation because fitting into the pattern makes it a little less bewildering a little less surprising because it shows that it's kind of like other things that have happened before and that's what Bode's law does not do because Bode's law although it holds for all the planets that have been observed in the day of Bode it doesn't explain anything else it doesn't fit into a larger pattern of the planets around other solar systems and now that we've discovered planets we found many planets around other stars that don't seem to follow Bode's law at all so it doesn't fit our solar system into a general pattern and that's why even though it's a generalization and was used to predict other planets it does not provide an explanation of why the planets are certain distances from the sun so now we've learned a little bit about what explanation is and what explanation is not explanation is an attempt to fit a particular phenomenon into a general pattern in order to increase our understanding of why it happened and to remove bewilderment or surprise explanation is not persuasion or justification or generalization or prediction those are other uses of argument a variety of different uses of argument but we've only scratched the surface there can be lots more and lots more to say about each of these so if you want to learn more about these purposes of argument a good place to start would be chapter one of the accompanying text understanding arguments but we're going to leave this topic for now and turn to a separate topic in order to understand something you want to know not just its purpose but the material which it's made so the next few lectures will be about the material out of which arguments are made namely language last time we discussed what arguments are for their purposes we saw that arguments have at least three purposes namely persuasion justification and explanation we also saw that one way to explain something is to cite its purpose so we can understand why Joe went to the store by seeing that he went to the store because he wanted some milk so his purpose was to get milk similarly we can understand arguments by looking at their purposes and that's what we did last time but this time we're looking at a different kind of explanation as we saw one way to explain things is to look at the material so you want to understand why a MacBook Air is so light the answer is it's made out of aluminum similarly if we want to understand arguments we're going to gain understanding by looking carefully at the material that they're made out of and we saw that arguments are sets of sentences statements and propositions so that means they're made out of language so in this lecture and the next few we're going to look at the nature of language in order to better understand arguments so if we know that arguments are made out of language we know that the only creatures who can give arguments are ones that can use language now some people think that other animals can use language and there's a minimum kind of language that other animals can use but other animals cannot use language that's complex enough to make arguments it might seem that there's some exceptions here's one possibility but no matter what it sounds like this goat is not really arguing maybe he's fighting maybe he's fending off what he takes to be an enemy but he's not arguing so if other animals can use language we can't define humans as the animal that talks but we can define humans as the animal that argues or as Aristotle said the rational animal the animal that reasons because other animals don't do that humans are the only one that argues and reasons in this sense so we can understand humans and arguments better if we understand language better now I can't tell you everything that needs to be said about language you'd need to take a linguistics course for that and I recommend that you try one but here I'm only going to be able to make four basic points about language first of all, language is important second, it's conventional third, it's representational and fourth, it's social that should at least get us going in understanding what arguments are made of first, language is important it would be extremely difficult to live life without language just try to imagine what it would be like it's really hard to imagine but think about someone like Helen Keller who was born able to see and hear but very shortly thereafter lost her ability to see and hear and it was only much later in life that she gained the ability to use language because she never had that in her early years and when she gained that ability she was amazed it has a name W-A-T when Helen Keller gained the ability to use language and to communicate she didn't become able to see or hear she still couldn't see or hear but she could do amazing things she went around the country giving presentations she graduated from Radcliffe College all of that was made available to her simply by adding language and communication to her life so language is extremely useful and that explains why it's all around us just imagine walking down the streets of a city and all the signs that you'd see you just see words here there and everywhere and now we have a mystery if we're not paying attention to language then how can we use it so well to achieve so many purposes the answer to that lies in the second general feature of language that I want to talk about language is conventional what's a convention remember that in the United States people drive on the right hand side of the road that's our convention but what does that mean it means that there's a general pattern of behavior that most people throughout society obey on a regular basis and they criticize people who deviate from that pattern and the same applies to language we have certain patterns of using words in certain ways and when people deviate from those patterns we criticize them we say they're misspeaking or it's ungrammatical of course conventions can vary everybody knows that there are many countries around the world where people don't drive on the right hand side of the road they drive on the left hand side of the road the United Kingdom is one of them but there are lots more and the same applies to language you can have the same word that's used to mean very different things in different languages the most notorious example is football in the United States it's used to refer to American football whereas in the rest of the world it's used to refer to what Americans call soccer and people in the rest of the world think that America is kind of silly because you don't use your feet on the ball except for punting and place kicking in football but whether it makes sense or not the point here is simply that the conventions can vary from part of the world to the other and of course you can do that with any word you could in English use the word money to refer to socks at least the English language could have done that it didn't but it could have so in this way conventions seem to be kind of arbitrary they could have been very different but language is far from completely arbitrary because the conventions of language have limits and two of these limits that I want to emphasize come from the fact that language is also representational and social so first language is representational when we use language we're often trying to refer to objects in the world and describe facts in the world and you can't change those objects or those facts merely by changing your language one good story to illustrate this is about the young Lincoln when he was a lawyer he supposedly examined a witness during a trial and he said okay how many legs does a horse have and the witness said four and then Lincoln said well if we call a tail a leg then how many legs does a horse have and the witness said well then I suppose the horse would have five legs and Lincoln said absolutely not that's wrong calling a tail a leg doesn't make it a leg and the point of the story whether it's true historically or not is that language cannot change the facts of the world it can't make horses have five legs if you merely change your language here's another example suppose that you don't have much money but you happen to have a lot of socks in your drawer well you could say I'm going to use the word money to refer to socks and now all of a sudden I've got lots of money I'm not poor anymore it ain't going to work and that's because language again can't change your financial situation because that's the fact about the world not about how you're using the word socks or the word money and the other limit on the conventions of language comes from the fact that language is social sure sometimes we talk to ourselves and use language to write things down notes to ourselves for example without other people around but basically language evolved because of its social function and what that means is that there's a point in following the conventions of the language as shared by the rest of the society that speaks that language you know I've always thought that it was kind of silly that grapefruits are called grapefruits sure they're fruits but they don't look like grapes at all they look more like lemons they're like really big lemons and that's why I think they ought to be called mega lemons but if I went to a restaurant and I wanted to order grapefruit juice so I turned to the the service person and said I'd like some mega lemon juice I probably wouldn't get what I wanted and so even if I think the language is not using the right conventions there's a point in following the conventions of the language in order to be able to communicate with other people and get what I want and again the great philosophers Monty Python saw this very well when they produced their little clip called the man who speaks only in anagrams our first guest in the studio tonight is a man who talks entirely in anagrams Tassi Kriacht do you enjoy this? I storm certainly odd, Revy Chumso and what's your name? Hamrag, Hamrag Yattlerot so the point is obvious, namely language is shared and once it's shared then it makes sense to actually follow the conventions of society even if you don't like them overall then language is important and it's conventional in ways that might seem arbitrary but actually it's limited in important ways by the fact that language is so representational and social but it's kind of cheap to say language is conventional which are the conventions which are the rules that language follows and this is actually extremely complex because language follows rules or conventions at many different levels just take a real simple example you walk into a pizza shop and you say gimme pepperoni well the person then fixes a pepperoni pizza but how did that work that you said gimme pepperoni well first of all notice that you had to use words that were meaningful to the person you were speaking to gimme wasn't a word in English a long time ago but this person understands gimme as a word and therefore they can understand but in addition to those semantic constraints you also have to have physical production constraints you have to say it loud enough if the pizza shop is really noisy then you have to speak pretty loudly to get the person behind the counter to understand what you're saying you also have to put the words in the right order if instead of saying gimme a pepperoni pizza you said pizza a gimme pepperoni they might not understand at all what you're saying so there's structural combination rules that you have to follow as well and there are also etiquette rules in some pizza places if you just said gimme pepperoni the waiter might say well forget it sir I don't serve such impolite people I certainly would say that to my son if my son said gimme pepperoni I wouldn't get him a pizza I'd say you need to ask me properly so rules of etiquette can also get in the way of communication and cooperation so language operates at all of these levels physical production syntax or the rules of grammar and etiquette now all this might seem obvious to you it probably should be obvious to you but the rules of language are not always obvious and that's what we're going to be learning throughout this course I'll start with a simple example what's this well that is a finger but what's this that is a singer this is not a finger that's not a singer why do we pronounce the word finger with a hard G and the word singer with a soft G that's a rule that we all follow but very few people know the rule behind that pronunciation so do you know the rule take a little while and think about it have you got it yet okay I'll tell you the answer when a word ends in NGER and it's derived from a verb that ends in NG then you get a soft G like singer but when the word that ends in NGER is not derived from a verb that ends in NG then you get either a hard G like finger or a kind of medium G like plunger or danger now when do you get that medium G or that hard G that's a trickier question I don't know the answer to that one we use language according to rules without knowing what the rules are we don't have to be conscious of the rules at all and a lot of what we're going to be doing in this course is looking behind our language to try to figure out the rules that govern the way we use language especially when we're making arguments in order to better understand what we're doing some of the answers we give will be obvious once you mention them but I bet you hadn't thought of them before the rules that we've looked at so far apply to every use of language but we want to focus on those rules that are important specifically to arguments at least normally misspelling or mispronouncing a word doesn't affect an argument of course if you pronounce one word so that it sounds like another word it can be very confusing and people won't understand you or if you misspell it so badly they don't know what word you wanted the argument's not going to work but normally misspelling and mispronunciation don't make the argument bad instead what affects the argument is what's going to affect the proposition that's getting expressed the meaning of the sentence because that's going to affect whether the premises justify the conclusion or whether they explain the conclusion and so we need to focus on those rules of language that in particular deal with the meanings of words and of sentences so what's meaning well, one thing I can tell you is we're not going to be talking about the meaning of life in this course the meaning of life is a totally different topic we're also not going to be talking about whether clouds mean rain in the sense of giving some indication or evidence that there's going to be rain we're concerned with the meanings of words and sentences in language we're concerned with linguistic meaning in particular so how are we going to understand linguistic meaning well one way to think about the meanings of words and sentences is to ask how you would explain them to someone who doesn't understand them like a small child or someone who doesn't speak this language well if somebody said what's the meaning of the word chair you might go well when I use the word chair I'm referring to these things something like this when I say I'm sitting on the chair what I mean is my body is above the chair and so that approach to teaching language suggests to many people that what words mean is the same as what they refer to and what sentences mean are the facts that they try to describe now that view of language is often called the referential or descriptive view of language so is this referential or inadequate no no no no absolutely not that theory does not cover a lot of language that's extremely important just think about greeting someone in the morning hello are you referring to an object when you say hello or think about the word not in a sentence and the word not is going to be crucial to arguments but does the word not refer to something well if it did then there would be more objects in the room when I'm not sitting on the chair than when I am sitting on the chair so you cannot understand the meanings of many words like hello or not or for that matter am or sitting many words don't fit this referential or descriptive theory of meaning so if meaning is not reference or description what is it so here we are going to take our cue from Ludwig Wittgenstein the great 20th century Austrian philosopher who argued that meaning is use if you want to understand the meaning of the word hello you don't look for some object that it refers to you ask how is it used and the answer is obvious it's used to greet people if you want to understand the meaning of the question where is the library the answer is well that question is used to inquire about the library to ask where the library is if you want to understand the meaning of an imperative like give me a pizza then that is a way of ordering a pizza you are using that phrase to order a pizza so the meaning of the phrase is given by the way those words are used in normal situations by competent speakers of the language this point about meaning being used is very important to the language of argument as we saw the word not does not refer to an additional object the same goes for the word and when you say I am sitting in the chair and I am in the office the word and doesn't refer to an object either so if you want to understand what the word and is used to do then we have to think about what people do with it and what they do is they conjoin different sentences they don't add an extra object or an extra fact they just conjoin sentences and form a whole sentence out of two parts each of which was a sentence to begin with of course the word and is not always used to conjoin sentences we can say things like Roberto and Olivia went to Sao Paulo together and Roberto is not a sentence Olivia is not a sentence there are people not sentences and there weren't three things that went to Sao Paulo together Roberto, Olivia and this third thing and whatever that is still the word and is used to conjoin in this case it's used to conjoin things or people in the previous examples it was used to conjoin sentences but if we want to know what the word and means we shouldn't be looking for some object that it refers to instead we should be describing how it's used and what it's used to do namely it's used to conjoin and when we look more closely at the uses of language we see that language is used in a lot of different ways use is diverse just take a simple example I'd like to give you a little piece of personal advice you want to floss your teeth every day so what did I just do I made a bunch of words I made physical motion in the air but in addition those words were meaningful you ought to floss your teeth every day each of those words is meaningful in the language and I put them together in an order that was grammatical so the whole thing makes sense when you make a meaningful utterance like that we're going to say you perform a linguistic act and there's a linguistic level of the use of language that we will study in one lecture the next lecture but in addition when I said you ought to floss your teeth every day I also gave you a piece of friendly advice I advised you and notice that even if you don't follow my advice I still advised you and if you don't follow my advice and your teeth rot out then I can say look you should have listened to me you ought to floss your teeth every day so the speech act level occurs even when it doesn't affect your actions at all that's the second level of use of language the speech act level and we'll talk about that in more detail two lectures from now the third level of language has to do with the production of certain effects maybe when I say you ought to floss your teeth every day I persuade you and what that means is I bring about a certain effect in your behavior or your thought or your attitudes well that's what we're going to call the conversational level and conversational acts are the acts of bringing about those effects and persuasion is one example so now we have three levels of language we have the linguistic level which is the meaningful utterance producing a meaningful utterance we have the speech act level advising is a nice paradigm that which can be accomplished even if you're not persuaded and we have persuading you which is the conversational level so there's the linguistic level the speech act level and the conversational level and each of these levels will be explored in more detail in one of the next three lectures but here's a little warning and you have a choice the material in the next three lectures is a little bit more abstract but it's fascinating and we're going to try to make it fun and it's really important to understand how your language works but it's not absolutely essential to the things that we're going to cover in the rest of this course so it's up to you you can listen to these three lectures if you want and there will be some exercises throughout those lectures that will test your understanding but none of that material is going to be on the quiz so you can listen to the next three lectures in order to be able to go through the rest of the course and do well on the quiz at the end of this part so as we saw last time there are three distinct levels of language linguistic level, the speech level and the conversational level and all of these levels of meaning affect arguments so in the next three lectures we want to work through these levels one by one and this lecture is going to deal in particular with the linguistic level of language and the production of a meaningful utterance so in order to perform a linguistic act all you have to do is utter a set of words that are meaningful that fit together according to the semantics that is the meanings of particular words and the syntax or the grammar of the language in general for example, it's easy it's easy in a linguistic act because it's as a contraction it's allowed to contract it and is according to the rules of English and easy as a word so it's easy follows the semantics and the syntax of the language of English that's all there is to it although linguistic acts are really simple they do require some special components that are worth separating out for example they require meaningful words when you simply hum a tune like mm-hmm then you're not performing a linguistic act because there are no meaningful words in it but when you sing a song I love Miranda and Nicholas too then you are performing a linguistic act because you uttered words that were meaningful when they were put together in that way and I've been taking this for granted but of course the words you utter have to be meaningful it's not going to be a linguistic act if you utter what looks like a sentence namely a set of sounds that look like words if they're not really words so if you say twas brilig in the sly thee toes did gyron gimbal in the wave and so on from Lewis Carroll's famous Jabberwocky poem then it's not going to be a linguistic act if those words are not meaningful words in any language and you can also get nonsense when you take words that have meanings and put them together in an order that doesn't make any sense my dog has fleas makes sense but dog fleas my has doesn't make any sense so meaningful words with the wrong grammatical structure won't work and Noam Chomsky from MIT taught us that you can also get nonsense if you take words that make sense and you put them together with the right grammatical structure but they still don't fit together because of the relation between the meanings his example here was colorless green ideas sleep furiously what does that mean colorless green ideas sleep furiously well colorless makes sense green that's a word ideas sleep furiously each of those words make sense and they're each in their appropriate grammatical role but altogether it doesn't make any sense so there are lots of ways you can get nonsense in language and when you do you're not performing a linguistic act now there's some really fun examples where it's not clear whether or not the utterance is meaningful some of these examples among my favorites are garden path sentences here's one the man who whistles tunes pianos wait a minute what does that mean if you think of it as the man who whistles tunes is one unit then you don't understand what the word pianos is doing because the man who whistles tunes sounds like a reference to a particular man and pianos is not a verb but if you think of it as the man who whistles is one unit and the second unit is tunes pianos so it's the man who whistles tunes pianos then it makes sense because it's the man who's whistling also tunes pianos so you have to be able to carve the set of words up into the right units and see what grammatical structure they have in order to understand the sentence because tunes can either be a verb which tells you what the man is doing to the pianos or it can be a noun which refers to the thing that the man is whistling and you have to get those grammatical categories straight and the garden path sentences lead you astray and make you think of it in the wrong way and there will be some more examples of that in the exercises but my favorite example of all is buffalo, buffalo, buffalo what does that mean well buffalo are American bison okay but buffalo the word buffalo in English that is can also be used as a verb to refer to tricking or fooling someone so you can have buffalo, American bison buffaloing that is tricking or fooling buffalo, American bison buffalo, buffalo, buffalo but you can go even further because there's a city in New York named Buffalo and of course there can be buffalo that is American bison from the city of Buffalo, New York and when they trick or fool other by American bison from Buffalo, New York then you have buffalo, buffalo buffalo, buffalo, buffalo or buffalo, buffalo, buffalo, buffalo buffalo which doesn't sound like a meaningful utterance but it is and you can go even further you can actually build it out to 11 straight utterances of the word buffalo buffalo, buffalo, buffalo, buffalo, buffalo buffalo, buffalo, buffalo and tell me what that means I'm not going to explain it to you because it takes a while to explain it but if you think about it you might be able to figure it out and even if you can't figure out 11 buffaloes in a row the point still holds because the point is just that sometimes what doesn't seem meaningful turns out to be meaningful and if you're careful and charitable and do your best to interpret what it really means there are other utterances that don't seem to make sense at first and when you can make sense out of them then they're linguistic acts for now I don't have time to go into any detail on semantics or syntax although we will discuss some details when we discuss vagueness and ambiguity in the discussion of fallacies later in this course but I hope that the linguistic level is pretty simple and understandable so we can go on and look in more detail at the speech act level the second level of language that we want to discuss is speech acts we already saw one instance in the example of advising when I advised you to floss your teeth every day but the clearest examples probably occur in games and in ceremonies one famous incident that occurred I believe in a Yankees game was when a batter had two strikes and three balls and the pitcher threw the ball near the strike zone and the batter didn't swing so the umpire didn't say anything and the batter turned to the umpire and said well ump, am I out or was that a walk and the umpire said you ain't nothing till I say so and that's the lesson of speech acts with a speech act the saying so that makes you so and the rules of baseball mean that you're out and it was a strike if the umpire says so now maybe the umpire should have called a ball when he called a strike or should have called a strike when he called a ball but it doesn't matter because if he makes a mistake and calls it a strike then you're out so the next kind of example involves ceremonies imagine that you're at a traditional marriage ceremony the bride and the groom show up with an officiant in an appropriate location and the officiant says to the man do you take this woman to be your lawfully wedded wife and he says I do then the officiant turns to the bride and says you take this man to be your lawfully wedded husband and she says I do then the officiant says I now pronounce you husband and wife that's pretty cool by uttering those words he made them husband and wife the words change their relationship in a legal way in a religious way and in a personal way and just by uttering words and notice also that you can use a special little word to explain this you can say that he thereby pronounced them husband and wife by uttering the words I now pronounce you husband and wife he thereby pronounced them husband and wife because it was right then and there in those words by means of those words that he made them husband and wife provide us with a nice general test called the thereby test here's a certain pattern of words if I say I blank then I thereby blank I blank by means of saying I blank now sometimes filling in that blank with some words will make sense but it won't make sense with other words and that'll provide a test because when you can fill in that blank with a verb it makes sense then that verb names a speech act so for example if I say I now pronounce you man and wife then I thereby pronounce you man and wife my speech act is pronouncing you and if I say I apologize I thereby apologize notice that what the formula does is it takes you from the words which are in quotation marks of the thereby test to the world because when it's not inside quotation marks on the right side of the thereby test it refers to the world so when it's in quotation marks it's about the words when it's not in quotation marks on the right side it refers to the world and the formula takes you from the words to the world and that's what's tricky about it it's amazing that you can actually use your words to change but only in the special case of speech acts of course all of this works only in the right circumstances you can't just randomly walk up to any couple on the street and say I now pronounce you husband and wife just try it excuse me I wanted to say something I now pronounce you husband and wife thank you whoa, I'm lucky they didn't hit me you obviously cannot pronounce people husband and wife if you're not an efficient they're not a bride and a groom who have said I do it has to occur in the right circumstances and sometimes which circumstances are the right circumstances will be very controversial people argue about whether a man can marry a man or a woman can marry a woman the ones who think that you can't think that marriage has as part of its appropriate circumstances that only people of different genders can get married a man can marry a woman but can't marry another man whereas other people think that a man can marry a man and a woman can marry a woman so it's going to be controversial which circumstances are appropriate for a marriage ceremony but everybody agrees that you can't just do it randomly to any old couple on the street so everybody agrees that there are going to be limits and that the speech act works only in the appropriate circumstances and we can build that into the thereby test in the appropriate words if I say I blank in the appropriate circumstances then I thereby blank but it's only in the appropriate circumstances that you can perform the speech act by uttering the words now we can use the thereby test to pick out speech acts because it works for a lot of different examples if I say I promise to meet you for lunch tomorrow in the appropriate circumstances then I thereby promise to meet you for lunch tomorrow so promising is the speech act if I say I thank you for inviting me to your party and throwing such a great party by the way then I do thereby thank you for inviting me to your party and for throwing such a good party by the way so thanking is the speech act if I say I apologize for tripping over your legs then I thereby apologize for tripping over your legs notice the circumstances matter in all these cases if I say I apologize then I did apologize but it was an insincere apology because the circumstances weren't right since I didn't have the appropriate feelings but I still did apologize now in contrast whether I promise you or threaten you depends on whether the thing that I promise or threaten to do is something that you want to do it then I'm promising but if you don't want me to do it then I might be threatening so your attitudes towards the thing that I'm going to do determines whether my speech act is a promise or a threat in all of these cases the circumstances are going to matter so in that example the circumstances affect which speech act I perform but in other cases the circumstances affect whether I really perform any speech act at all or fail to perform the speech act that I was trying to here's an example of that if I say to you, I bet you that Duke will win the next national championship and I think Ram Netta might be foolish enough to take that bet then what if he responds by saying no, I won't bet you now, have I performed a speech act of betting no, have I performed another speech act not really what have I performed sometimes when the circumstances aren't right you perform a different speech act and sometimes when the circumstances aren't right you don't perform any speech act at all it really is very sensitive to the particular circumstances in which you're speaking but why do we care about speech acts here when we're supposed to be studying arguments, well that's because arguing is a speech act you argue with language it's one of those things that you do in using language in a certain way you're intending to provide reasons and you're providing what you take to be a reason to justify or explain the conclusion and justifying and explaining are other things that you do with language those are speech acts too so when we're studying arguments we're studying a particular kind of speech acts and that's why it makes it important to understand speech acts because we need to view arguing in the context of these other speech acts that I've just discussed now there's an awful lot more to say about speech acts and I can't say it here in these lectures I just want to give the idea in a very basic and simple way if you want more detail we have a more extended discussion of speech acts in the accompanying book understanding arguments but just to make sure you understand the basics let's do a few exercises first and then in the next lecture we'll go on to talk about conversational acts so now we've discussed two levels of language the linguistic level the speech act level in this lecture we want to look at the third level of language not only the level of conversational acts the basic idea is really simple we use language to bring about a change in the world for example I might turn to a friend and say could you loan me your car well what am I doing I'm performing a speech act of requesting or asking a favor something like that but am I doing it just for its own sake ask a favor just in order to be asking a favor like it was fun to ask a favor no I was asking a favor to bring about a certain effect I wanted him to hand over the keys to his car so I could use it and I wanted him to give me permission to use his car so I could do it legally so I'm trying to bring about a change not only the physical location of the keys but also in the legal rights that I have with regard to his car so I'm trying to bring about a change in the world simply by uttering those words could you please loan me your car it happens all the time here's another example suppose my friend is wondering whether the moon is full and I say the moon is full am I uttering those words just to expel hot air no am I uttering those words just to express my own belief no I'm trying to inform my friend I'm trying to bring about a change in my friend's beliefs and that's to bring about an effect in the world so that's a conversational act to bring about the effect in the world of informing my friend informing is a conversational act and almost all speech acts have particular effects that are associated with them when you ask a question you're trying to bring about someone answering the question when you apologize you're trying to bring about forgiveness to somebody you're trying to bring about the person relying on your promise in order to believe that you're going to do it so speech acts are often associated with particular effects that the speaker intends to bring about and the bringing about of that effect is the conversational act so if we want an official definition of a conversational act we can say that the conversational act is the bringing about of the intended effect which is the standard effect for the kind of speech act that the speaker is performing that's what a conversational act is now since the conversational act is the bringing about of the standard effect the conversational act does not occur when that effect does not occur and that might seem weird that what kind of act you perform depends on whether the effect occurs maybe several seconds maybe even longer in the future but it's not that weird when you think about it because if you pull the trigger of a gun that's pointed at someone then whether your act of pulling the trigger is an act of killing depends on whether the person dies and yet the person's death is something independent of it it's an effect that occurs maybe quite a while in the future but your act wasn't an act of killing unless the person died and that's the story of conversational acts your act is not this conversational act the fact occurs it has to be the intended effect that's the standard effect for the kind of speech act that you're performing so the really tricky question is how are we going to bring about these effects because it's not so easy think about how other people bring about effects think about a baker baking a cake well the baker needs to get together the right ingredients and bring them to the right place and get the right amount of ingredients the baker fills the entire kitchen with flour he's not going to have any room left over to bake the cake and he has to bring the right ingredients that means if instead of bringing flour he brings gravel he can't bake a cake and he has to put together those ingredients in the right way in the right order for example you can't mix them in the wrong order the cake won't work out it has to bake it for the right amount of time and so on and so on the effect of a good cake well the same thing applies to conversational acts there are going to be rules that have to be followed in order to bring about the conversational act that you're trying to bring about that is in order to have that intended effect of the speech act in the circumstances and the same kind of rules apply to any rational person trying to pursue any goal whenever you want to bring about an effect you have to follow certain general rules and so it applies to people who are trying to bring about effects by language that is to people who are trying to perform conversational acts if you want to inform someone that is to have an effect on their beliefs then you need to speak in a certain way and if you want to promise someone that is to get them to rely on you that's the conversational act associated with the speech act of promising but you're not going to get them to rely on you unless you follow certain rules that you're going to understand are the rules of language that enable us to bring about these effects that are the conversational acts now in this question Paul Grice helps us out a lot he's one of the great philosophers of the 20th century and he laid out a series of rules governing conversational acts he called them the conversational maxims and we're going to look at them one by one Grice focuses in on context where people are stating things cooperating with each other and trying to inform each other he's not trying to provide a general theory so it's for statements in a cooperative context so the first maxim is the rule of quantity and it basically says don't say more than is required for the purpose that you're trying to achieve if you say too many words the point gets lost in the words so you shouldn't say more than you need for the purpose at hand the second part of the rule of quantity you shouldn't say too little because if you say too little then that's going to be misleading and it's not going to fulfill your purpose because the person that you're talking to won't have all the information that they need second rule is the rule of quality the rule of quality says don't say what you don't believe to be true don't lie, don't mislead, don't deceive but also this is the second part of the rule of quality don't say something that you lack adequate justification for because you shouldn't just be talking off the top of your head with no reason to believe what you're saying these are all pretty common sense rules but they weren't apparent to people until Grice formulated them the third rule is the rule of relevance and it's the toughest of all the rule of relevance says be relevant look, it's short I'll grant you that but it really is kind of tricky to apply the rule because you have to figure out what's relevant and we'll see some problems with that but for now just remember that it should be obvious when you're talking about a subject and you want to achieve a certain purpose and the person you're talking to is cooperating with you as Grice is assuming then you ought to be talking about things that are relevant and if you change the subject you're just leading and the fourth conversational maxim is the rule of manner it says be brief, be orderly avoid obscurity and avoid ambiguity pretty simple, it's all about style because if you're not brief enough people won't pay attention to you if it's not orderly people will get confused by that and if you're ambiguous or obscure then people won't understand what you're saying so these four rules are followed by speakers they're cooperating with each other when people aren't cooperating they're trying to trick or deceive each other they might violate these rules and mislead people by abusing these rules but when they're cooperating these are the rules they follow and that makes them able to deceive people by violating them and also notice that these rules might not be completely clear to you you might not have ever thought of them before but now that you mention them they probably seem pretty obvious but that's another rule that we saw before regarding pronunciation that's a rule that you hadn't thought of before but once it's pointed out it seems kind of obvious well that's what Grice has done but he's shown us the rules governing conversational acts that enable us to bring about certain effects by language now we can use these rules to understand what's going on in a lot of conversations imagine you're in a restaurant and the waiter walks up to your table and says well for dessert what is that ice cream? well what has that waiter suggested? he's suggested that that's all you can have cake, ice cream, well he didn't mention pie so you can't have pie because if he's a good waiter and he knows that they have pie back there and you could order it then you ought to be telling you about the pie he would be violating the rule of quantity that is not providing you all the relevant information if he said you can have cake or ice cream you also have pie but he didn't mention pie so because you assume that he's cooperating with you and trying to get you what you want to eat since he is your waiter after all there must not be pie available so you say I'll take ice cream even though you would have preferred pie what's happening here is called conversational implication when the waiter said you can have cake or ice cream he was conversationaly implying that you can't have pie and the reason that he conversationaly implied that is because if he were cooperating and following the conversational rules or maxims then he would have mentioned pie so you assume that since he said only cake or ice cream that you can't have pie he in effect conversationaly implied that you cannot have pie and the way you figure that out you took what he said a little background knowledge about him being a waiter and having certain goals and what happens in restaurants performed a little mini calculation using the maxim of quantity and inferred that he must believe that you can't have pie and of course since he's a waiter he ought to know whether you can have something else or not and therefore you can't have pie but what if he was a customer at another table and he knew there was only one slice of pie back there and he didn't want you to order it and he said you can have cake or ice cream and didn't mention the pie so you wouldn't order it and his favorite customer would get it instead of you well he still conversationaly implied that you can't have pie but he misled you he misled you because he was trying to get the pie for somebody else he was not cooperating with you so the tricky thing about these conversational maxims is they work perfectly fine when you're cooperating with the person and trying to give them all of the information that they need for your common purpose with that other person but if you're not cooperating then you can use them to mislead the other person and that's the double edged sword of conversational implication but one of the features of conversational implication is really important to arguments and that's that you can cancel conversational implications the waiter can say you can have cake or ice cream oh yeah and you can also have pie and when he said and also you can have pie he did not take back you can have cake or ice cream because you can still have cake or ice cream it's just that you can also have pie so he can cancel the conversational implication that you cannot have pie by saying oh yeah so with a conversational implication if a certain sentence p conversational implies another sentence q then you can deny q and p still might be true and that's an important fact because it distinguishes conversational implications from logical entailments or logical implications if I say Alice is my sister then that implies Alice is female and I can't go Alice is my sister oh yeah and she's not female that doesn't make any sense because she's not female she can't be my sister because that's a logical implication or entailment but with a conversational implication instead you can deny what is conversational implied and the original sentence is still true so if the waiter says you can have cake or ice cream and then I find out that he's been saving the table then I can come up to him and say wait a minute you lied to me he didn't really lie to me because what he said was still true I could have cake or ice cream it's still true I can have cake or ice cream he didn't say anything false to me he simply didn't mention the pie that I could also have so that's very different in the case of conversational implication than in the case of logical entailment and that'll be important to us especially when we get to formal logic in a later part of this course so let me give you another example that's more important as a politician says I've got a policy that's going to reduce crime by getting criminals off the streets and the policy is lock them all up when people are suspected of crimes you lock them all up that's going to get criminals off the street well that might convince people if they don't notice that he's left out another fact he's not just going to get people off the street who are criminals he's going to get lots of other people off the street too he didn't give you all the relevant information like the waiter who misled you with the pie he suggested that his policy will solve the problem of crime by putting people in prison who would commit crimes and just left out the other relevant fact there's lots of other people in prison too so he has adversely implied that there's no other relevant facts to consider by only mentioning that it's going to reduce the crime rate and you have to be good at looking through that implication and asking yes, but is there something he's leaving out and that's often what you need to do in order to avoid being misled by sleazy politicians and other people who leave out the relevant information for the issue that you're talking about now of course the politician might not care that he misled you that might be the goal he wants to persuade you and he doesn't care whether he misleads you because it's persuasion not justification that he's interested in in addition he's got his defense ready he can say I didn't say anything false what I said was true if we put all those potential criminals in jail we're going to reduce the crime rate maybe it's also true that we're going to put some innocent people in jail but we will reduce the crime rate and that's what I said this is maximum of quantity does is it tells us exactly why we have a criticism of him now we can say he's not cooperating because he's not following the conversational maximum of quantity he's not giving us all the relevant information that we need in order to achieve our purpose if we have a common purpose and this politician is pretending to have a common purpose with us the good of the country when actually he doesn't have a common purpose with us he just wants to get elected and so Gries gives us an insight into what's going on when we get misled in those contexts and also what we need to do to respond through those types of bad arguments now this distinction between conversational implication and logical entailment is crucial to arguments because it tells us something about how to refute arguments when you don't like the premise of an argument because it's misleading because it conversationaly implies something false that's not a way to show that the premise is false in order to show it's false you have to show that it actually logically entails something that's false then you can infer that the premise itself is false this will become important later when we look at the role of conversational implication and logical entailment in arguments but for now the important thing is to understand the distinction between conversational implication and logical entailment the speakers usually follow these conversational maxims that Gries enunciated when they speak and when they're cooperating but they don't always follow these maxims sometimes they violate them and of course as always there's a lot more to be said about conversational acts if you want to learn more about conversational acts you should look at the chapter in understanding arguments and the text that accompanies this course but I think we've learned enough about conversational acts to move on because so far we've looked at language in general at the linguistic level, at the speech act level and at the conversational act level now we want to take these lessons and apply them more specifically to the language of argument that is the particular kind of language that gets used in arguments and that's what will be the topic for the next few lectures welcome to week two in week one we talked about language in general this week we want to talk about how language is used in one particular context namely the context of arguments we need to understand the language of argument in order to be able to spot an argument that is to determine when a passage contains an argument and what part of the passage is that argument so how can we tell when an argument is being given well recall the definition of an argument as a series of sentences statements or propositions where some of them are premises and one of them is a conclusion and the premises are intended to give a reason for the conclusion so the real question of when an argument is being given comes down to the question of when certain sentences are intended as reasons for other sentences now the answer is that we can tell a person's intentions speaking by which words they choose so there are going to be certain words that indicate that some sentences are reasons for others just compare these two sentences I am tall and I am good at sports and compare that to I am tall so I am good at sports now notice that you can take the first sentence I am tall and I am good at sports and switch it around and I am tall switching doesn't make any difference but it's very different if you say I am tall so I am good at sports that's very different from I am good at sports so I am tall so we know from the fact that you can switch around the and sentence and you cannot switch around the so sentence the word so introduces something very different from just conjoining the two claims but then what's the difference is that when you use the word and you're simply stating the two facts I am tall I am good at sports and the and says that they're both true but when you use the word so you're indicating that one of them is a reason for the other if you say I am tall so I am good at sports then you're suggesting that the reason why you're good at sports is that you're tall but if you say I am good at sports so I am tall then you're indicating that the fact that you're good at sports is some kind of evidence that you must be tall maybe because you can only be good at sports if you're tall which isn't true that just shows it's a bad argument but it is an argument because by using the word so you're indicating that one of the sentences is a reason for the other of course the word so is not the only word that plays this role in arguments or has this function you can also say I am tall therefore I am good at sports or I am tall thus I am good at sports or I am tall hence I am good at sports or I am tall accordingly I am good at sports all of these different pairs of sentences play the same role they indicate that there's an argument there namely the fact that I'm tall is a reason for the conclusion that I am good at sports so we're going to call all of these words argument markers because they indicate the presence of an argument next we want to distinguish two different kinds of argument markers so far we've looked at so and therefore and thus and accordingly each of those indicates that the sentence right after it is a conclusion and the other sentence in the pair is a premise so we're going to call these conclusion markers because they indicate that the sentence right after them is a conclusion but there are other argument markers that also indicate arguments in the same way but what they indicate is that the sentence after them is a reason or a premise not a conclusion for example I could say I'm good at sports because I am tall now the word because indicates that the fact that I'm tall is a reason for the conclusion that I'm good at sports it doesn't mean that the sentence after the word because is a conclusion instead it means that the sentence after the word because is a reason or a premise so we're going to call it a reason marker or a premise marker and there are other reason markers as well you could say I am good at sports for I am tall I am good at sports as I am tall I am good at sports for the reason that I am tall I am good at sports and the reason why is that I am tall there are lots of different ways to indicate that the fact that I am tall is a reason for the conclusion that I'm good at sports all of these words both the conclusion markers and the reason markers indicate that there's an argument present but only in some cases you can't just look at the word and figure out whether it's an argument marker or not you have to think about the role that it's playing a perfect example of that is another reason marker since you can say I'm good at sports since I am tall and then it looks like you're presenting the fact that you're tall as a reason why you're good at sports but the word since doesn't always play that role after all you can say the sun has been up since 7 o'clock this morning and that doesn't mean that somehow the sun has an alarm clock that causes it to come up right at 7 o'clock all it's saying is that the sun has been up after the time of 7 o'clock and all times since then it doesn't indicate any kind of rational relation such as the fact that it's 7 o'clock being a reason why the sun came up oh what about this one it's been raining since my vacation began very disappointing but you're not saying that it's raining because your vacation began as if there's some kind of plot against you in the nature of weather that would be very paranoid all you're saying is that it has been raining every day since the time when your vacation began or every day after your vacation began so the since there indicates just a temporal relation not some kind of rational relation and what this shows us is that you can't just look for the word since you always mark it as an argument marker you have to think about what the word sense is doing in that context and that'll be true for a lot of other reason markers and conclusion markers as well here's another example of the same point but with a conclusion marker the word so sometimes indicates that the sentence after it's a conclusion and the sentence before it's a reason but it can also indicate something entirely different you don't need to eat so much so there doesn't indicate that much is a reason for anything the word so is getting used in an entirely different way that should be obvious but the point again is that you can't just look for the word so and label it as an argument marker you have to think about the function that is playing in the particular context but then how can we tell what role a word is playing in a particular context here's a little trick try substituting another word that's clearly an argument marker that is it's clearly a reason marker or a conclusion marker for the original word that you weren't so sure about here's an example he's so cool does that mean he's because cool no if you substitute because for so the meaning changes entirely not even clear what it means or how about he's therefore cool that doesn't make much sense either so in this case you can't substitute another argument marker because or therefore for the original word so without changing the meaning of the sentence entirely and that shows you that in the original sentence the word so was not being used as an argument marker or reason marker or conclusion marker here's another example well since he left college he's been unemployed well are you saying that because he left college he's unemployed maybe if that's what you're saying then you can substitute the word because without changing the meaning of the sentence and then the word since was being used as a reason marker in that case but probably not simply that since the time when he left college he's been unemployed and then if that's what you mean then when you substitute because for since it changes the meaning and that would show that in that context the word is not playing the role of an argument marker or a reason marker because it changes the meaning to substitute something like because that's clearly an argument marker on the other hand you might have a similar claim where you can substitute it since he failed out of college he's unemployed now somebody says that they don't just mean since the time when he failed out of college he's unemployed probably the meaning has not changed if you simply said because he failed out of college he's unemployed so since you can substitute because for since in that sentence in that sentence the word since is probably being used as an argument marker that's the role it's playing that's its function that's how it's being used and notice also that you can tell that the word since in that sentence is a reason marker instead of a conclusion marker because you can substitute because and you cannot substitute therefore therefore he failed out of college he's been unemployed that doesn't make a lot of sense so if you can substitute because without changing the meaning then the original word since in this case was being used as a reason marker you cannot substitute the word therefore that shows it's not being used as a conclusion marker so you can use this substitution test to determine whether the words being used as a reason marker or as a conclusion marker or as no indicator whatsoever of an argument but in some entirely different way one last word that we have to talk about is that little word if sometimes it's linked with the word then in an if then clause which is also called a conditional we'll talk a lot about conditionals later in this course but for now I just want to make one point the word if might seem like an argument marker because it's often used in arguments for example I might say if I'm rich enough I can buy a baseball team I am rich enough so I can buy a baseball team that would be an argument but if all I say is if I'm rich enough I can buy a baseball team when I know I'm not rich enough so I would never assert the if clause that says I'm rich enough then that little if sentence is not being used to indicate an argument at all it's just saying if I am rich enough then I can buy a baseball team it's not saying that I am rich enough and it's not saying that I can buy a baseball team so the word if by itself does not indicate an argument it sets a pattern for argument if one thing then another well the one thing therefore the other but the if one thing then another doesn't by itself indicate any argument at all because it doesn't assert that if clause which is also called the antecedent of the conditional so we are not going to count the word if as an argument marker to identify an argument pretty simple huh but just to make sure you've got it straight let's do a few exercises now that we've identified arguments and we've also identified premises and conclusions we need to put them in order the actual word order doesn't always tell us the order of argument compare these two sentences because I am a professor I teach classes I teach classes in those two examples the words I am a professor in one instance occur at the beginning and at the other instance occur at the end but they actually express exactly the same argument namely the fact that I am a professor is a reason why I teach classes but contrast both of those with this example I teach classes so I must be a professor the point there must be something like nobody but professors can teach classes and whether or not that's true the point here is that's a different argument from the first one and we need to represent the difference between these two arguments very carefully in order to show what is shared by the first two examples that's different from the third example we put the arguments in what's called standard form and it's really easy basically you put the premise down and if there's another premise you put that down then you draw a line then you put what I call a dot pyramid it's basically three little dots with two at the bottom and one at the top and then you put the conclusion after that it's also useful we'll see why later but it's useful to number the premises and to number the conclusion so that we can refer back to the premise and conclusion with the number instead of having to repeat it all the time and that's all there is to standard form you just put down the premises on different lines then you draw a line put the little dot pyramid and then write down the conclusion and then number them all that's it and this standard form accomplishes what we wanted to namely it helps to show what's common so the first two examples at the beginning of this lecture that distinguishes them from the third example so the first two examples were I teach classes because I'm a professor and because I'm a professor I teach classes there the senate says the premise that goes above the line is I'm a professor and the conclusion that goes below the line and next to the dot pyramid is I teach classes but the next example the third example at the beginning of the lecture was I teach classes so I must be a professor now that means that I am a professor is the conclusion that goes below the line next to the dot pyramid and the premise is I teach classes so when you put these two in standard form right next to each other it makes it absolutely clear what the difference is and what's in common to the first two that distinguishes them from the third one no matter how easy I think it's still worthwhile to do a few exercises just to make sure we've got it straight because this notion of standard form will become important later now we've learned how to identify an argument and put it in standard form we've also learned from the definition of argument that the premises are intended to be reasons great intended to be a reason for the conclusion well intentions are nice but success is better what we need to figure out is when the person succeeds in giving premises that really are reasons for the conclusion for simplicity let's focus on arguments whose purpose is justification then the question is do the premises justify you in believing the conclusion well, imagine that you don't know whether there's any life on Mars you have no evidence one way or the other then you ask a friend and the friend says I know there's life on Mars I can prove it to you here this argument will show you that there's life on Mars there is at least one bacterium on Mars therefore there is life on Mars now notice that if the premise is true the conclusion has got to be true and if you and your friend are justifying and believing the premise then you and your friend are also justifying and believing the conclusion so this argument looks pretty good so far but of course you have to ask your friend how do you know that there's at least one bacterium on Mars and suppose your friend says well, I'm just guessing then the argument is clearly no good if there's no reason to believe the premise because your friend is just guessing then you're not justifying and believing that premise and if you're not justifying and believing the premise then how can that premise make you justified in believing the conclusion more generally an argument cannot justify you in believing the conclusion thus you're justified in accepting the premises of that argument now suppose your friend says but I do have a reason for the premise I do then we have to ask what kind of reason is it and at that point your friend needs to express that reason and how do we express reasons in arguments so your friend has to give another argument for the premise where the premise of the first argument is the conclusion of the second argument but wait a minute now we've got a problem because that second argument is itself going to have premises and you have to be justified in believing those so the premises of the second argument have to be the conclusion of a third argument and so on and so on because the third argument needs premises that have to be justified so they have to be the conclusion of another argument that have premises and those have to be the conclusion of another argument and so on and so on it looks like we've got a real problem here in order for the premises to be justified they have to be backed up by an argument but the argument has premises of its own that have to be backed up by another argument and so on and so on this problem is called the problem of the skeptical regress because you regress back to one argument after another after another after another after another and it's hard to see how that regress is ever going to come to an end there seem to be only three ways to get around the skeptical regress the first is to start with a premise that's unjustified if it's unjustified then it doesn't need an argument to back it up and that means that you're not going to have this chain of arguments going back and back and back and back and back and back the second possibility is to have a structure where the arguments move in a circle one claim is justified by another which is justified by another which is justified by another which is justified by the first claim and they just move in a circle the third possibility is that the chain of arguments goes back infinitely it never stops every claim has an argument to back it up and there's no end so you never have a premise which doesn't have an argument to back it up because it's infinite those seem to be the three main options here to avoid the skeptical regress the first possibility then is to start with a premise that's unjustified and that seems pretty neat if you can get away with it but we already saw why that won't work we saw your friend arguing that there's life on Mars because there's at least one bacterium on Mars and he was just guessing if you just guess at your premises you have no reason to believe them then an argument that uses those premises cannot justify you in believing the conclusion but in addition just think about it this way you could prove anything if we let you start with unjustified premises if you can just make up your premises for no reason then there's no stopping you from believing whatever including things that are obviously false so it seems to be a real problem to start with premises that are unjustified next the second way to respond to the skeptical regress is to use a circular structure and it's kind of neat if you think about it because if you want to prove one claim you prove it on the basis of another claim and then you prove that second claim on the basis of a third and that third on the basis of fourth and the fourth on the basis of fifth and the fifth on the basis of the first and now you've got this circle and the argument's going a circle but that means that every premise has an argument to back it up because you can keep going around the circle forever but if you think about it a little bit it'll be obvious that that's no good and that can be shown by looking at the smallest circle there is so suppose your friend says I can prove there's life on Mars here's my argument there's life on Mars clearly that's no good and the reason why it's no good is that if you didn't know whether there's life on Mars to begin with you wouldn't know whether the premise was true because if you don't know the conclusion you can't know the premise since the premise is the conclusion so if you're not justified in believing the conclusion to begin with you're not justified in believing the premise and that means that the argument didn't really get you anywhere it just ends up where it started and in addition it has the same problem we saw in the first approach involving unjustified premises because you can use circular arguments to prove anything you can prove there's life on Mars there's life on Mars therefore there's life on Mars you can prove there's no life on Mars there's no life on Mars therefore there's no life on Mars you can do it either way and the fact that an argument can be used either way to prove either conclusion suggests there's a big problem of argument so now we're down to the third and final way to get around the skeptical regress and that's to use an infinite chain of arguments but if you think about it in a concrete case you'll see why that's a problem as well suppose your friend says there's life on Mars and I can prove it and you say fine give me your reason well there's at least one bacterium on Mars therefore there's life on Mars and you go okay fine but how do you know there's at least one bacterium on Mars I've got another argument he says there are at least two bacteria on Mars therefore there's at least one bacterium on Mars but how do you know there's at least two well there are at least three bacteria on Mars therefore there are at least two bacteria on Mars but how do you know there are at least three well there are at least four so there are at least three well there are at least five so there are at least four literally six or at least five, and so on and so on and so on. You could go on infinitely. So an infinite chain of arguments would allow you to prove that there's life on Mars, even if you have no evidence whatsoever of any bacteria, because you're going to have an argument. But if the premise that you're arguing from doesn't have an independent justification, then the infinite chain is going to be no good at all in justifying the conclusion of that argument. So many people see this skeptical regress as a deep and serious philosophical issue. If the unjustified premise approach doesn't work and the circular argument structure doesn't work and the infinite chain of arguments doesn't work, then it's hard to see how we can get around the problem, which is to say, it's hard to see how any kind of argument could ever justify us in believing anything. Philosophers really scratch their heads about that for a long time and worry about it. It keeps them up at night. But we're going to have to look at how practical people solve a similar problem in everyday life. So how do we solve the skeptical regress problem in everyday life? Well, there are various tricks that you can use. For example, one way is to just start from assumptions that everybody shares. So if I say, well, you really ought to buy a Honda, because Hondas are very reliable cars, then I'm assuming that you want your car to be reliable. You don't like to have to take it into the mechanic all the time. You don't want it to break down on the road. And if you want reliability and I want reliability, then we can start from the assumption that reliability is a good thing and that that's a reason to buy a car that is reliable. But of course, you might say, well, but our Honda is reliable. And then I might appeal to an authority. Well, it's obvious that they are. Or Consumer Reports has done a study that shows that they're reliable. And I can appeal to an authority. And if you accept that authority, go, ah, Consumer Reports, we can trust them, then my argument's going to work. You're going to have a reason to believe the conclusion, and it might persuade you and make you come to believe the conclusion. But suppose that someone is going to raise an objection. They say, well, Consumer Reports has been wrong before. They might be wrong this time. Well, then I need to discount that objection. I need to respond to it and say, well, maybe they have been wrong sometimes. But this time they've got a good study and it was careful or whatever. And the but means I'm discounting the objection that you have raised. And I might even discount it in advance. Or I might just guard my claim. I might say, well, they might be right in this case. Or they're probably right without claiming that they definitely are right. So I can assure you by citing some kind of authority, I can discount objections. And I can guard my premises by saying, well, it's probably right. Instead of saying it's definitely right. And those are three ways of solving the skeptical regress problem in everyday life that we're going to look at in much more detail in the next three lectures. But the point of this lecture has been more general. In order to solve the skeptical regress problem, you have to find some assumptions that you and your audience share. They might be assumptions about the premises of your arguments. They might be assumptions about authorities that supposedly support your premises and that they accept as authorities or whatever. But there have to be some assumptions that you share with your audience in order to get the argument going. And that's kind of tricky because it's going to depend on the context. If you're dealing with an audience that shares a lot of your assumptions, then argument's going to be relatively easy. But if you're dealing with an audience that doesn't share any of your assumptions, it's going to be impossible. And in areas where there's lots of disagreement, it's going to be hard to get your arguments going because your premises are going to be questioned and denied or rejected by the people in the audience. So what these tricks do is they give you ways to get the argument going, but they're not going to work in every case. And we'll have to look at that as we're looking at these three different ways to solve the skeptical regress problem in the next three lectures. In the previous lecture, we looked at the skeptical regress problem and I kind of introduced three different ways of solving that problem in practical life, namely assuring, guarding, and discounting. Those are three ways to solve the skeptical regress problem in practical life. And in the next three lectures, what we're going to do is look at each of these in much more detail and more carefully so as to understand how they work. Let's begin with assuring. Here's an example. I assure you that smoking is bad for your health. If I say I assure you that I'm trying to get you to accept that claim on my authority. Now, I might have some reason for saying that smoking is bad for your health, namely, I've read the US Surgeon General's report which cites the scientific evidence to show the smoking is bad for your health. But notice that I don't actually say it. When I say, well, it's obvious that smoking is bad for your health or everybody knows that smoking is bad for your health or I assure you, certainly, clearly smoking is bad for your health. Then what I'm doing is I am trying to get you to accept that premise without actually citing the Surgeon General or anybody. I haven't cited the evidence. I simply have indicated to you, I do have evidence. I do have a reason to believe that smoking is bad for your health, but I haven't given you what the reason is. So what good is that? It's a lot of good because what it means is that if I don't give the reason, you can't question the reason. If I simply say everybody believes it, it's certainly true, then you can't ask whether those people who believe it have any reason to believe it or whether I have any reason to be so certain about it. If I don't give the reason, I've cut off your attack on the reason that I would give. So assuring is kind of tricky. I say I assure you and if you can trust me, that's fine, but if you can't trust me, then you should be asking, well, what kind of reason does he really have? Now, there are many ways to assure people. There are three kinds that we're gonna look at. Authoritative, reflexive, and abusive. Let's start with authoritative. Authority is just what it says, it cites an authority. So I might say, I assure you the smoking is bad for your health. The surgeon general has shown that smoking is bad for your health and I cite an authority, the surgeon general. Okay, fine, but have you seen the studies? Have I cited the numbers? If I told you when the studies were done, how many subjects, under what circumstances, which statistical tests were used, how do you know it's causation of correlation and so on and so on? No, I just say the surgeon general has shown this and you're supposed to take my word for it that those are good studies unless of course you share my assumption that the surgeon general is trustworthy. So that's the way an authoritative assurance works. It cites an authority that the audience shares as an authority with the other person. They share the assumption that that authority is trustworthy. Now sometimes it's the surgeon general and the surgeon general is pretty reliable but you also get this kind of thing from reporters. They say an unimpeachable source close to the president has assured me that the president's plans are such and such and they cite an unimpeachable source but they won't tell you what the source is and they won't tell you how the source knew it was true. So they're citing an authority but they're not telling you what the authority is or what reason the authority has or what the authority claims. Now if you trust that authority then that's fine and if the authority's reliable then you might be safe but if you don't know who the authority is or where they got their information there can be problems. And here's my favorite, here's my favorite. I sometimes hear students say but Professor Sinan Armstrong, my teacher in the other course said that blah, blah, blah, blah. Well, why do you trust your professors? I mean, why do you trust me? You shouldn't be trusting me or your other professors any more than you're trusting an unimpeachable source close to the president. So you have to trust somebody sometime and you have to decide who you're gonna trust and then it's gonna be okay to cite an authority in this kind of assurance but you have to watch out for tricks when people start citing authorities that aren't really authorities because even the best authorities sometimes do studies that aren't very careful and might even be wrong. A second kind of assurance is what I call reflexive. Reflexive because it's talking about yourself. I believe that, I know that, I am certain that, I feel sure that. And you're citing something about your own mental state. You feel sure, great, you feel sure but why do you feel sure? Notice however that this assurance works because people don't wanna question what other people feel sure about. If I say, well, I feel sure that this is gonna happen. In many societies it's gonna be implied to go, well, I don't feel sure, matter of fact, I think you're wrong or why do you feel sure? Because then you're questioning the person and if that's impolite then using this type of phrase, I am certain that will get people to shut up and not say anything. So here's an example from Monty Python. Now let's get one thing quite clear. I most definitely told you. But my favorite is when people say, I've held this opinion for years I've thought about it year after year. It's really bothered me and you know, after careful consideration, I've come to the conclusion that blah, blah, blah, whatever. And you're supposed to say, well, since you've thought about it so much, I'll save myself a lot of trouble thinking about it and trust you and go along with what you say. Well, if you let other people do your thinking for you then that's up to you. But you're gonna be misled in some cases because they've thought about it for years and years and gotten themselves in a tizzy and ended up with the wrong conclusion. So the fact that somebody's thought about it for years doesn't necessarily mean it's right. But somehow in conversation, when you say I've thought about it for a long time and checked all the sources I could, then people take the fact that you've reached a certain conclusion to be okay for them to reach the same conclusion. And that's how this reflexive type of assurance works. But the most fun of all is the abuse of assurance. Here's another example from Monty Python. No, no, nonsense. Maybe he's right. Maybe it is nonsense. But the point is that he gets you to accept what he believes by abusing you and calling it nonsense. And the same thing happens to him sometimes. Nobody but a fool would think that. Everybody knows this. If you say everybody knows it, then you're saying, well, if you don't know it, then you're a dummy. And so they're abusing you in order to get you to agree with them by making a conditional abuse that applies to you only if you don't agree with them. And you don't wanna be a dummy. You don't wanna speak nonsense. You don't wanna say something that's stupid. So somebody says, you'd have to be stupid to disagree with me about this. Then that's going to incline you to agree with them. Some of these abusive assurances are a little bit more subtle. So it's worth mentioning one that's used all the time. And this is what might be called appeal to common sense. So it says it's just common sense that such and such. And it doesn't matter what the such and such is. The point here is simply that if you deny that, then you're telling that person you lack common sense. And nobody wants to lack common sense. So by saying it's just common sense that it's just plain common sense. People say it all the time, but what they're doing is they're abusing their opponents by saying that their opponents lack common sense. So it's a little bit more subtle, but it shows that abusive assurances occur either subtly or openly all the time. So we've seen three different types of assurances, okay? The first is authoritative, the second is reflexive, and the third is abusive. And they're all used in common speech to stop the skeptical regress problem. So why do we need any of these assurances in the first place? And the answer is we've got limited time. You know, you can't go out and check every study. You can't go out and look into every issue. You've just got to accept authorities and listen to other people and learn from them, or you'll never be able to figure out the issues that matter to you in life. So assuring can be a perfectly good thing. If you trust the surgeon general of the United States instead of going out and starting your own laboratory and doing your own statistical studies, there's absolutely nothing wrong with that. But when you start trusting authorities that are not worthwhile or not trustworthy, then you can get yourself into trouble. And we'll talk later in the course about ways to tell which authorities are reliable or trustworthy and which ones are not. That tells you why assurances are needed in general. But what about particular cases? Well, when you're talking to a certain audience, if they share your trust of a certain authority, or if they trust you when you give a reflexive assurance, or if what you're saying really is something that everybody with common sense believes in, then again, it can be perfectly fine to use an assurance. It saves you the time of having to go check out every issue, and it helps you avoid the skeptical regress problem in a very practical way. So assuring can be a really useful tool in argument, but you have to be careful, because assurances are also subject to a lot of tricks that you have to learn to watch out for. We've already seen that you can cite authorities that aren't trustworthy, and that's kind of obvious. But something that's maybe a little less obvious is that people use assurances at points in their argument in order to distract you. If something really is questionable, they often say, well, that's obvious in order to get you to not pay attention to it. So when someone says, that's obvious, it's certain, I'm sure, it's worth looking carefully at what they're so sure about and asking yourself whether you agree with them, because people try to paper over the cracks in their arguments with these assurances, at least in some cases, and you have to learn to watch out for that. Another trick is when assurances get dropped, people will start off saying, he believes this, I believe that, and then they drop in and start talking as if it's true. My favorite example of this was a case a few years ago when there was a person caught in Germany for cannibalism, and it started off with the reporters saying, well, he, the person accused of cannibalism, says that there are lots of other cannibals in Germany. And then it becomes, it is reported that there are lots of cannibals in Germany. And then it became sources have said that as if the sources are reliable. And pretty soon they were saying, there are lots of cannibals in Germany. And it moved from he believes it to there are lots of them. And that's the trick of dropping the assurance in a way that can be illegitimate. So assurances can be useful, and they can also be misleading. And that's gonna be true of all the different ways of stopping the skeptical regress. There can be uses and abuses of all of these tricks. For assurances, we wanna have an assurance when, first of all, somebody might question it, second, that audience accepts the authority that is being referred to, and third, it would be too much trouble to actually cite the study and all the numbers and the evidence in the particular people. But assurances are not appropriate when nobody would question the claim anyway, then why are you wasting your time assuring people? When the authority that you're basing your assurance on is not really trustworthy, because then why should they believe your assurances? And third, when you've got plenty of time and it would be really easy to give the reason straightforwardly instead of simply assuring them. So you've got good and bad uses of assurances, and I hope we understand what they are and how to distinguish them. But let's do a few exercises just to make sure that we've got the general idea. The second common move in arguments that's supposed to solve the skeptical regress problem is guarding. The basic idea of guarding is very simple. It's just making the premises of your argument weaker so that there'll be fewer ways in which your opponents can raise trouble for them or show that they're false. So here's an example. So someone says, we ought not to build any new nuclear power plants, because they'll explode. Now wait a minute, how do you know that any of them really will explode? How can you tell that in the future? You don't even know what kinds of standards they're gonna be built to. So someone can object to that argument by saying you're not justified in asserting that premise that these new nuclear power plants will explode. So how do you stop that problem? Well, you simply say, well we ought not to build any new nuclear power plants because some of them might explode or even weaker because I believe that some of them might explode. Now we've got a premise. I believe that some of the new nuclear power plants might explode. That's gonna be hard to deny. What's an opponent gonna do? Show that you don't really believe it? Show that it's not true that they might explode, that there's no possibility that they'll explode or that any of them will explode. You're not claiming all of them will, just some of them. So by guarding the premise in this way, you make it more likely to be true and less subject to objection. And that's what guarding does. It enables you to start an argument with that premise if other people agree that it's true because it's so weak. And get them to agree to share your assumption by weakening your premises. Now of course, what happens now is someone says, wait a minute, they might explode. Sure, and the sun might not come up tomorrow. All kinds of things might not happen or might happen. Might's too weak to establish that we shouldn't have new nuclear power plants. So what you're suggesting is not just that it might happen but that it's likely to happen. And if the chance of it happening really is so slight as to be negligible, then you weaken the premise too much and it's not gonna follow that we shouldn't have nuclear power plants. So the issue's gonna come down to is the risk of them exploding or some of them exploding enough to justify the conclusion that we ought not to have them. And that's gonna depend on exactly how much risk there is and by looking at the guarding term, at the might term and questioning it and saying, can we replace might with probably or something like that? Then we're gonna have a better handle on how to assess the argument. So when you see someone using guarding like this, you need to ask why did they put in the guard and have they put in too much guarding? That is weakened it so much that the conclusion no longer follows. So the general trick of guarding is to weaken the premise so it's gonna be harder to deny. And that's how your argument gets going. But there are at least three different ways to do this. One is the extent, the other is probability and the other is mental. First, guarding by extent. We need a new alcohol officer on our campus because all students drink too much. Well, that's clearly false. Not all students drink too much. Most students drink too much. Well, not most, maybe not most. Many students drink too much. Okay, too many because it's too much. Some students drink too much. Notice that you can guard or weaken the claim, the premise from all students drink too much to most students drink too much to many students drink too much to some students drink too much. And as you move down that scale, the premise gets harder and harder to deny. So whether this counts as guarding depends on the expectation. If you expect the claim that most or all students drink too much, then it's guarding to say many or certainly to say some. But if you don't expect that many or most or all, then to say some is simply to say that you're talking about some. So it's guarding when you weaken it beyond what would otherwise be expected in the context. This standard is gonna be hard to apply because it might be difficult to say what the expectations are of the different people involved in a conversation. But that's what guarding is. It's not guarding every time you use the word many or most. It's only guarding when you were expecting all and the person instead merely claimed many. The second kind of guarding concerns probability. Some people would say it's absolutely certain that O.J. Simpson killed his wife. And other people say, well, he probably killed his wife or it's likely that he killed his wife. And others will say there's a chance he killed his wife. And others will say he might have killed his wife. So when you change from it's certain to its probable or it's likely or there's a chance we might have, again, you're moving down a continuum and the further you move down that continuum, the easier it is to defend your premise because you're claiming less. And the question is going to be whether you've done it too much. If you simply say he might have killed his wife, therefore he ought to be convicted. That's clearly wrong. If you say he probably killed his wife, so we ought to be convicted. That might be wrong too if there's a strong burden on the prosecution to prove guilt beyond a reasonable doubt. But you don't want to require that it's certain that he killed his wife because then you'll never be able to convict any criminals. So you need something like almost certain. You know, which is a bit of a fudge word or beyond a reasonable doubt. In any case, however you assess whether or not he should have been convicted, depending on how you assess how likely it was that he really did what he was accused of, apart from all those questions, the point here is simply that in arguments in general, you can make the argument more defensible by weakening the premise. So there are fewer ways to show that the premise is wrong. And that's the second type of guarding. Now the third kind of guarding we can call mental because it has to do with the mental state of the person asserting the premise. You might say, well I know that the president is 50 years old. But you might say, I believe that the president is 50 years old. You might say, I tend to believe or I'm inclined to believe that the president is 50 years old. And there's another continuum. As you move from knowledge to belief to inclination to believe, again, you're making the premise weaker and weaker which makes it harder and harder to question or deny or doubt that premise. So you've avoided a problem for your argument and potentially this is a way to stop the skeptical regress. Now the third common move in arguments to protect premises and avoid the skeptical regress is discounting. Discounting is basically citing a possible objection that you think other people might be thinking of in order to head it off by providing a quick and dirty response to it right then and there. For example, you might be talking to someone and say, well I'm thinking of buying that ring and it's really beautiful. And you're thinking, well they're gonna object that the ring is very expensive too. So you say, well the ring is expensive but it's beautiful. So what you're doing is citing the objection. It's kind of odd if you think about it. If you wanna buy the ring, why are you saying that it's expensive? And the reason is that you have already cited that objection which makes it less likely that a person on the other side who doesn't want you to buy the ring is gonna say it because you've already said, I know that but it's more important to me that the ring is beautiful so I wanna buy it. So when you say the ring is expensive but it's beautiful, you're saying that it's expensive, that's the first thing. You're saying that it's beautiful, that's the second thing. You're saying with the word but that there's a contrast between the two and you're indicating that the fact that it's beautiful is more important than the fact that it's expensive. You're saying all of that simply by saying that the ring is expensive but it is beautiful. So first to say that the ring is expensive but it's beautiful is to say two things. It's like saying the ring is expensive and it's beautiful but in other ways it's very different from and because if you say the ring is expensive and it's beautiful, you can switch them around. It's beautiful and it's expensive. It's expensive and it's beautiful, it's beautiful and it's expensive, you can say it either way. If you say it's expensive but it's beautiful, very different from saying it's beautiful, but it's expensive. Think about it. If you were trying to argue for buying the ring, which would you say? Well, I would say it's expensive, but it's beautiful. And if I'm trying to argue against buying the ring, I would say it's beautiful, but it's expensive. Because the word but indicates that the sentence after it is in some way more important than the other clause. You're discounting the other objection and signing after the but clause the reason for the belief or action that you favor. Thus, and and but are very different. The sentences on either side of and are reversible, and the sentences on either side of but are not reversible. And there are other words that are discounting phrases like but that work the same way, but fall in a different place. Consider the word although. You can say although the ring is expensive, it's beautiful. And that sounds like the ring is expensive, but it's beautiful. Those are the sentences that someone would use if they're arguing for buying the ring because they want to emphasize that the ring is beautiful. The difference is that the word but occurs right before the clause that's getting emphasized. Whereas the word although occurs before the clause that's de emphasized, and it's the other clause that cites what's the speaker takes to be more important. So but and although are each discounting words, but the but occurs before the emphasize clause and although occurs before the de emphasize clause. What's common to these words like button although is that they do three things. They assert two claims, they contrast those two claims, and they indicate that one of those claims is more important than the other. And there are lots of words that perform these functions. It's not just button although, you have even if, even though, whereas, nevertheless, nonetheless, still. And as with other words that we've been studying, like argument markers, for example, some of these words get used in other ways. So the word still isn't always a discounting term. You say he's sitting still. You're not discounting an objection. It's when you use the word still at the beginning of the sentence, still, the diamond is beautiful, or something like that. Then the word still is going to use a discounting word. And like with the other words we've studied, if you want to know in a particular case, whether the word still is being used as a discounting word, you ask whether you can substitute a different discounting word. And the sentence will function in basically the same way and mean basically the same thing. And if it does, then still is being used as a discounting word. And if it's not, then it's not being used as a discounting word. So we can use this substitution method to test for what the function of the word is. So why do people use discounting words like these? They use them in order to head off objections because if you state the objection first, then your opponent seems a little silly to be saying it again. You just responded to that. And so you can defend your premises or protect your premises and avoid the skeptical regress by discounting the kinds of objections that people would raise that might seem to call for further argument. And that's a perfectly legitimate use. Sometimes you want to do that. You don't want to let your opponent raise an objection because that might be misleading and gets you off on a tangent. And it's a perfectly effective and useful legitimate move in an argument. But you also have to watch out because there's some tricks associated with discounting terms. In particular, I want to talk about the trick of discounting straw people. Well, one effective move in argument, if you're just trying to persuade people, is to make them not see the problems with your position. And one way to do that is to say, I've got five objections I'm going to respond to. You might say this, but you might say that, however, you might say this, whereas, you might say that, still, you might say that, although. And you discount each of those five objections. And yet what you do is you get to pick the objections, right? So you can pick the easiest objections, not the hardest objections. And then you've got the whole discussion focusing on the easiest objections. And as people are trying to keep all five of those in their mind straight, they forget about the other objections, which might be even stronger. So you discount these straw people, straw meaning easy to knock over easy to destroy, and make people forget about the objections that are harder to destroy, they're going to cause more serious problems for your theory. So if you don't really want to know whether your theory is right or wrong, you're just trying to persuade people that can be an effective move. And if you don't want to be persuaded by people who are trying to trick you like that, then you have to watch out for other people discounting straw men and not facing the really more difficult objections to their views. And here's an even trickier trick, you can combine this trick of discounting straw people with other tricks that we saw for other words. So suppose somebody says, Well, you know, the President is all in favor of some kind of public health service, but a public health service is not going to solve all of the medical problems of our people. So I think the President is off on the wrong track. Well, notice what's happened here is you've discounted the objection that the public health service is going to solve all of the medical problems of our people. Whoever thought that a public health service would solve all of the medical problems of the people. So you're discounting a straw man by using an unguarded term all. You put the unguarded term in the mouth of the objector by not guarding it, you make their view more susceptible to refutation and make it easier for you to respond to that objection. Whereas the objector really would never have used the unguarded term, but would have used a guarding term like most or many of the health problems of our people. So by using discounting terms along with guarding terms and also assuring terms, you can make moves in argument that will point people towards issues that are framed in the way you want them to be framed, instead of the way that they want them to be framed. That's the trick that you have to learn to watch out for. So here's a simple rule of thumb. When you think someone is trying to use discounting terms to lead you to look at the easiest objections instead of the most difficult objections, then you can think about just forgetting the ones that this person mentions and ask, what did they leave off the list? It has a rule of thumb. That's usually a good idea. But it's not always going to work. You're going to have to use your judgment. Still try it. Maybe it'll work in some of the cases where you want to stop other people from tricking you. Now you should have a pretty good grasp on assuring, guarding and discounting three common moves in argument that are aimed at stopping the skeptical regress and building common assumptions with the people you're talking to. Let's do a few exercises in order to contrast these three and make sure you understand them. There's one more kind of language that we need to discuss because it's also used to stop the skeptical regress, much like assuring and guarding and discounting. And this language is evaluative. Just imagine that a politician says, you ought to support my health care plan because it would be good for the country. What is the word good doing here? Now some philosophers are going to tell you that the word good is just a way of expressing your emotions or maybe telling you what to do. So the politician is saying, yay for my health care plan or telling you in an imperative form you ought to support my health care plan. But that can't really be the whole story because when someone says yay duke like I do when I cheer for the duke team, first of all, I'm not saying that the team is good. I might cheer for the duke team even when I know they're not good. And secondly, you can't ask me why. If I go yay duke, it doesn't make any sense if you turn to me and say, but why? Why yay duke? That doesn't make any sense. So merely to express your emotions with something like yay duke is very different from saying duke has a good team and saying yay for my health care plan is very different from saying that the health care plan is good for the country. Similarly, if I say I don't like fish so we shouldn't have fish for dinner. Well, I don't really owe you a reason. I can just say I just don't like the taste of fish. End of story. Leave me alone. I don't owe you a reason for why I don't like fish. I just don't. But if I say it's immoral to eat fish, it's wrong to eat fish. You ought not to eat fish. It's a very different story. Now I owe you a reason. If I say it's immoral to eat fish, I need to say what's immoral about it. I need to point to some feature of eating fish that makes it immoral. I can't just use that valueative language without some kind of reason to back it up. That would be illegitimate. So what that shows is that merely expressing preferences is very different from making an evaluation and saying that something is good or bad or right or wrong or immoral or moral. One way to capture this feature of valueative language is to interpret a word like good as meets the standards and bad as violates the standards. Notice it's very vague because it doesn't tell you what the standards are and those standards will change from one context to another. If you're talking about a good painting, the standards of a good painting are different from when you're talking about say a good investment where the standards are going to be completely different from the aesthetic case. So if we interpret good as meets the standards and we say my healthcare program is good for the country, then that means it meets the standards for what will make the country function in a certain way. Whereas if we say eating fish is immoral, what we're saying is that eating fish violates a certain kind of standard and more specifically it's a moral standard. That's why we use the word immoral. So we can interpret this language in terms of meeting or violating standards and then to give the reason why it's good or bad or right or wrong or moral or immoral, we can cite the standard and apply it to the case in order to give a reason for why the evaluation holds. But now here's the trick. When we call it good, we don't say what the standards are. We leave that up to the context to specify what kind of standards we're talking about. So it's kind of like assuring. When you say I assure you and you might cite some authority or tell them that you do have some reason and you don't tell them what the reason is. When you call it good you say it does meet the standards but you don't say what the standards are. So by alluding to the standards without actually laying them out, you have made your claim a little more defensible because if you laid out the standards they might be questionable and your audience would know exactly what to question and what to deny and how to object. But if you simply say it's good and all you're saying is it meets the standards then you've avoided an objection and made your premise more defensible. And that's how this type of evaluative language might help to stave off the skeptical regress. And here's another way evaluation can help. We don't always have to agree about what the standards are. Suppose you're driving down the road and I say you know we ought to turn left here and you say yeah we ought to turn left here. Well I might think that we ought to turn left here because that's going to be a quicker way to get to our destination. But you might think that we ought to turn left here because that's going to be a more beautiful view and you'll be able to look out on the hills. But we can agree that we ought to turn left here because we both agree that turning left meets the standards even though my standards are efficiency and getting there quickly and your standards are aesthetic and getting beautiful views. So if you can get more people to agree to your premises simply by saying this healthcare plan will be good for the country without saying exactly how it's going to be good then you've avoided people disputing your objections because they can agree to it since they can use their own standards to determine whether it's good or not. And that can be yet another way to avoid the skeptical regress. Notice that evaluation can occur at a lot of different levels. We have some words that are very abstract like good and bad and ought and ought not should should not right wrong. And those words can be used in a lot of different contexts. You can have the wrong investment or a good investment or an investment that you ought to make but you can also drive on the right path or a bad path or a way that you ought not to go. And so you can have navigational standards and economic standards but they can all be expressed by these very general and abstract evaluative words like good and bad and right and wrong and ought and ought not should and should not and so on. But other evaluative words are much more specific. Now for example you can call a painting beautiful or ugly but you don't call fertilizer beautiful or ugly. You would never say that a stock is beautiful or ugly. They're just not the kind of thing to be evaluated in that way. So an evaluative word like beautiful or ugly is more specific. It only applies to a small range of things whereas other words apply like good and bad apply to almost anything. Here's another example. Cruel or brave. A person can be cruel or brave but you can't say that a painting is cruel or brave or a desk is cruel or brave or a chair is cruel or brave. A chair might be comfortable but a painting is not comfortable and a soldier is not comfortable. Soldiers are brave or not. Chairs are comfortable or not but chairs are not brave or not and soldiers are not comfortable or not. So these evaluative words like brave or cowardly and beautiful or ugly or comfortable or uncomfortable apply only to limited ranges of things rather than to just about anything. So we have very general or abstract evaluative words and we have more specific or concrete evaluative words and of course which ones are specific or concrete will vary. Some are more concrete than others. It's not an absolute dichotomy but some words that are evaluative really will apply to almost anything and other words apply to a more limited class and they vary in how limited that class of things that they apply to will be. So you might ask why are all these words evaluative words? Think about it when if you want to explain a more limited evaluative word like beautiful you want to explain what it means you need to define it in terms of the more general words like good. If you want to say it's beautiful you can say that kind of means looks good. I know that's not quite right but basically when you want to define the word beautiful you need to cite one of the more general words good and then cite the specific way in which it's good namely the way it looks. And when you want to say an economic word like bargain bargain means a good price. It sells for a good price and a good price is a low price. So when you define what a bargain is you need to cite the word good in order to define bargain. So the relation between these very general evaluative words and the more specific evaluative words that makes them all evaluative is that you need to define the specific evaluative words in terms of the more general ones. So it all comes down to what makes something evaluative is its connection to what's good or bad or right or wrong or what ought or ought not to be done or should or shouldn't be done and so on. Now the trickiest cases of evaluative words are words that are contextually evaluative. They don't actually get defined by good or bad or right or wrong as their general meaning but they do suggest an evaluation in a particular context. Let me give you an example of what I mean. A conservative politician might criticize her opponent by saying well his policies are way too liberal. Now by calling them liberal is that a criticism? Well she intends it as a criticism but does the word liberal mean that it's bad? Not really if you think about it because the opponent might say I'm proud to be a liberal. Being liberal is good. Yes it's liberal. So what? Yes it's liberal. Nothing wrong with that. The word liberal by itself doesn't mean that it's bad even though the conservative thinks that things that are liberal are bad. So that word liberal is not evaluative in the strict sense because it doesn't get defined by the words good or bad or right or wrong or should or should not. It's only evaluative in the context. It suggests an evaluation because of the assumptions of the speaker but it doesn't in and of itself mean that anything is bad or good for that matter. Because of this difference we will call language evaluative only when it's openly and literally evaluative so that it gets defined in terms of words like good or bad or right or wrong and not when it's merely contextually evaluative that is in the context given the assumptions of the speaker this person means to be suggesting an evaluation. If they're not openly saying this is good or bad or right or wrong then they're not really using what language that we will call evaluative but there are a couple of tricky examples that are worth bringing up okay. You might think that if you take two good things and put them together it gets even better and when you add a bad thing to a good thing it makes it worse at least that's the way it usually works but notice that when you say something's good that suggests it's good but when you say that's pretty good then you just add it pretty which is something good to the word good but pretty good it's not really any better than good it might even be worse but then you can add a negative word in the middle yeah that was pretty darn good well that means it's very good so you've actually taken a negative word darn and put it in the middle of two positive words pretty and good and made something that means very good so you really have to think carefully about exactly what the language means it's not going to be a simple formula of adding and subtracting goods and bads to figure out whether the language is evaluative. Now another word that's surprising is the word too I like spicy foods so when I say this food is spicy that's good or at least it's neutral to say it spicy to me means I am probably going to like it but notice that if we just add that little word too if I were to say this food is too spicy that means it's bad the little word too takes a positive evaluation or sometimes just something that's neutral and makes it bad so the word too is actually a negative evaluative word because it turns what was neutral or positive into something bad it moves it in that negative evaluative direction so it's a negative evaluative word so is there anything wrong with using a evaluative language no some people seem to think that you shouldn't evaluate at all you should just describe they're just kidding themselves try going through life without deciding what's good or bad or right or wrong or what you ought or ought not to do you can't really live your life with making evaluations at some point so it's a mistake to think that evaluation is always bad of course when you do evaluate it's not like saying yay duke you have to give a reason so you should think about the standards that you're applying and why they apply to this case that's going to be your reason for evaluating the thing is good or bad that's often going to be hard to come up with the exact standards that you're applying because people tend to think of things as good or bad without getting very specific about what the standards are so you're not always going to be able to tell people what your standards are and when you ask them they're not always going to be able to specify what their standards are but it's still going to be a useful exercise whenever you make an evaluation to think about why you think this thing is good or bad or right or wrong what are the standards that you're applying and when somebody disagrees with you to ask about what their standards are so that you can understand where the disagreement is coming from although evaluation can be very useful and legitimate it can also be dangerous because some people use evaluative terms without reasons let's call that slanting you slant when you use an evaluative word and don't give any justification for that use of the word so you might call somebody an idiot or a queer and you're using an evaluative word or at least you take it to be negatively evaluative and you haven't given any reason why there's anything wrong with what you're calling that nasty word now that's slanting if you don't have any reason and that can be terribly illegitimate when do people do it well they typically do it when they don't have any reason if you don't have any reason for your evaluation you just use some nasty name like you idiot and so when people start using language like that when they start slanting then that's a good indication to you as a critic that that's the point at which their argument is probably weak they're using that kind of language to paper over cracks as I put it before in their argument so as to hide what's the real weakness so we can use evaluative language in arguments and how it gets placed at certain points to signal where the weaknesses and the strengths in the argument are so now what we've got is we've got argument markers we've got assuring terms guarding terms discounting terms evaluative language and in the next few lectures we're going to look at a general technique that looks at all those different types of language and uses those different categories to analyze some real passages that we found in newspapers but before that let's do a few exercises just to make sure that you understand evaluation so far we've looked at the language of argument in some detail because we've separated the reason markers from conclusion markers we've talked about assuring and guarding and discounting and evaluative words so we've picked out a lot of different words in language that play distinct roles in arguments but what we need to do for a real argument is to bring it all together and show how these types of words can work together in a single passage and to do that we're going to learn a method called close analysis and what you do with close analysis is you simply take a passage and you mark the words in that passage that play those roles so a reason marker you can mark with an r and a conclusion marker you can mark with a c assuring term you mark with an a a guarding term you mark with g a discounting term you mark with d an evaluative term you mark with e and if it's clear you put a plus or a minus to indicate whether it's positive evaluation or negative evaluation now these marks will just be scratching the surface there's obviously a lot more that you can do and need to do in order to fully understand the passage so when it's a discounting term you ought to think about which objection is being discounted and you also ought to think about the rhetorical moves the metaphors and irony we'll look at rhetorical questions and we'll basically go through the passage very carefully word by word in order to figure out what's going on in that passage so how do you learn the technique the answer is very simple you practice and then you practice again and then you practice and practice and practice and practice practice won't make perfect because nothing's perfect but practice will surely help a lot and we'll get better and better the more we practice so in this lecture what we're going to do is go through one example in a lot of detail and mark it up very carefully in order to practice the method of close analysis the particular example we chose for this lecture is by robert redford it's an op ad that was written for the washington post we chose it because it's an interesting issue it's about the environment but it's not an issue that people will necessarily have very strong emotions about because you might not even know the particular part of the environment that he's talking about we also chose it because it's a really good argument you learn how to analyze arguments and how to formulate your own arguments by looking at good examples of course it's fun to tear down bad examples but we need a nice model of a good argument in order to see what's lacking in the arguments that are bad so we're going to go through an example partly because it's actually a pretty good argument we're also going to go through this passage because it's really thick with these argument words so you'll see that we're marking a lot of different things and we'll have to go through it paragraph by paragraph and sentence by sentence and word by word in great detail this lecture will seem like it's looking at the passage with a microscope and that's the point to learn to analyze with a microscope the passage is where people give arguments okay so the first sentence says just over a year ago president clinton created the grand staircase escalante national monument to protect once and for all some of utah's extraordinary red rock canyon country word number one just well justice is a good thing right so that must be an evaluative word no one of the first lessons in close analysis is that simply because you have the word just doesn't mean you're talking about justice when he says just over a year ago he means slightly over a year ago or somewhat over a year ago or sometime over a year ago so maybe he's guarding you might want to mark this one as a guarding term by putting a g out there but he's not using an evaluation to say just over a year ago well why would he guard because he's not very precise he's not going to say 17 days over a year ago he's saying just over a year ago so that nobody will raise a question at this point he does not want people raising questions this early in the op-ed so let's keep going just over a year ago president clinton created the grand staircase escalante national monument to protect once and for all some of the extraordinary red rock country okay what about the word two might seem like not much because it's such a short word but it's actually doing a lot of work there if you think about it we actually i think should mark it as a an argument marker of some sort is it a reason marker or is it a conclusion marker we'll come back to that but first let's get clear that it's an argument marker of some sort when he says that he created the monument to protect once and for all he means in order to protect because he wanted to protect once and for all some of that country it's an explanation of why he created it it's giving you the teleological explanation which tells you the purpose for which he created it so the bit that comes out protect once and for all some of the country is the reason why he created it that explains the conclusion that he did create it so this is a reason marker now the next word protect well you might think that protect is a neutral word because after all protectionism is criticized by some people but actually to protect something is to keep it safe to keep it safe from harm to keep it safe from bad things happening to it so to explain what counts as protection and what doesn't count as protection you have to cite what's good or bad and that makes it an evaluative word and in this case protecting is a good thing so it gets marked as e plus okay the next words are once and for all what does once and for all do nothing some of these words are going to get marked as nothing whatsoever because once and for all doesn't guard it says once and for all it's the absolute limit but the next word some and what does that do that guards it's saying that what's protected is not all of utah's red rock country it's only some of it and it's important for him to guard that because he wants to say later on as we'll see that there's lots of it outside the monument that's not getting protected so he wants to guard it and say it's not all that's going to be important to his argument now utah's pretty neutral unless you're from that state then you love it and you might say that's an evaluative word but let's skip that group of people right now extraordinary what about extraordinary is that an evaluative word might seem to be an evaluative word because clearly what redford means is extraordinarily beautiful or extraordinarily good red rock country but the word extraordinary doesn't say extraordinarily good you can have things that are extraordinarily bad to say it's extraordinary to say it's out of the ordinary and the red rock country might be extraordinarily ugly so the word extraordinary itself is not by itself an evaluative word so it should be marked as nothing and red rock country also is going to be neutral it's beautiful stuff but simply describe it as made out of red rock doesn't say that it's beautiful even though we all know that it is just look at the picture so now we finish a whole sentence isn't that great a whole sentence all right and all we did was find six things to mark in that sentence well four were marked and two were nothing but it shows you that you can go through a single sentence and do a lot of analysis in order to figure out what's going on and we're just getting started now let's move on to the second sentence starts in response to plans of the dutch company to mine coal president clinton uses authority to establish the new monument and so on let's go to in response to when does that tell you it tells you that what's coming after it explains why president clinton used his authority it was a response to the plans of the dutch company which means that it's an explanation notice that the previous explanation says why clinton wanted to do it in general this explanation tells you why president clinton did it at that particular time rather than earlier or later it's because he was responding to particular plans by a particular company so the in response to is an argument marker now is it a reason marker or a conclusion marker well the conclusion the thing that's getting explained is that clinton uses authority so this must be a reason or a premise marker you can also put p for premise marker or r for reason marker now in response to plans of the dutch company and elects to mine coal on the caparo its plateau president clinton used his authority under the antiquities act to establish the new monument now this is actually a pretty tricky one we know that the plans of the company are the premise that explains the conclusion that clinton used his authority but what's the word underdoing well under means is the antiquities act that gave him that authority that explains why he had that authority and justified him in doing what he was doing namely establishing the monument so the word under suggests that there's another argument in the background here that the antiquities act gives the president the authority to establish monuments and president clinton used that authority so the antiquities act is again a premise or as i said you can call it a reason marker for the premise that the antiquities act gives the president that authority and that justifies clinton and using his authority or explains why he was able to establish the monument and the word to also indicates that what comes after it is establishing the new monument that's what he was trying to do that also is an argument that explains why he did it he had the authority but you don't always exercise your authority right and so the point of exercising the authority the reason why he exercises authority was to establish the new monument again it might seem tricky to keep citing the word to as an argument marker but think about it you can substitute in order to he uses authority in order to establish the new monument or because he wanted to establish the new monument and we learned a few lectures ago that if you can substitute another argument marker for this particular word then that shows that in this case the word to is getting used as an argument marker in this case the premise because it's his wanting to establish the monument that explains why he used his authority okay here's a tricky one what about the word authority well that's a really tricky word and sometimes it's not completely clear how you want to mark it right you might think that this word is getting used as a discounting word namely answering a potential objection some people might say he didn't have the authority to do that but you might think it's a positive evaluation having authority is a good thing and you might think that it's an argument marker because it's a reason why he would have the ability to set up the monument namely that he had the authority but it doesn't actually say openly any of those things so i would probably mark that as a nothing but i think it's better just put a question mark because sometimes words are not going to have one clear function or another you know we're doing our best to put them into these little bins of the different types of words but sometimes they're not going to fall neatly into one or the other and you just have to recognize that of course when it comes to the quizzes we're not going to ask you about those kinds of words but it's worth knowing that they're there okay now let's move on setting aside for protection what he described as some of the most remarkable land in the world again what is that telling you setting aside for protection that it tells you why he uses authority to establish the monument so again we've got an implicit reason here but notice there's just a space there's no actual word they can be marked as an argument marker but still there is a separate argument here he set it aside for the protection that was why he established the monument that's why he uses authority to establish the monument if you want to include that part of the argument as well okay for protection protection again that's going to be evaluative right because to protect something is to keep it safe from harm harm is bad so protecting it must be good when you explain what protection is you're going to need to use the words good and bad as we saw in the first sentence what about these little quotation marks i love quotation marks you got to watch out for them what he described as some of the most remarkable land in the world why is robert redford quoting president clinton and saying how clinton described this land because if you're trying to convince clinton and trying to convince the general public to try to convince clinton there's nothing better than quoting clinton himself i mean after all clinton can't say i'm not an authority right so those quotation marks and saying that he described it that all amounts to assuring he's assuring clinton that that has to be true because after all you said it yourself and then he says i couldn't agree more well that's a different type of assuring remember when we saw that some assuring terms were authoritative and other assuring terms were reflexive well quoting president clinton is an authoritative assurance it's citing an authority i couldn't agree more says how much he agrees or how much certainty he has it certainly suggests and so he seems to be assuring you but on a different basis clinton and i both agree we might disagree about other things but we agree about this which gives you some reason to be sure that it must be true next four over two decades the word four is sometimes an argument marker is it an argument marker here no how can you tell that it's actually nothing here but how can you tell that try substituting an argument marker you can't say because over two decades many have fought battle over battle it's not because it's just saying during that period the term four and the words after it over two decades are simply being used to indicate time not to indicate any kind of reason in this case so it should be marked as nothing many have fought battle after battle is that a guarding term sometimes many is a guarding term instead of saying all you say many but here you're saying many have fought battle after battle nobody thinks all have fought battle after battle to keep the mining conglomerates from to spoiling the country after all the mining conglomerates themselves didn't so it can't be all so nobody would expect the word all so in this case the word many is not functioning to guard the term by weakening it because it never started out as the strong claim all there was nothing to weaken they fought battle after battle well you might think that battles are a bad thing so you might mark that as e minus because after all conflict is a bad thing and in battles people get hurt and try to hurt each other so to explain what a battle is you need to introduce an evaluative word and what did they fight those battles for to keep mining conglomerates from the spoiling the treasures right again two can be seen as in order to that's why they fought the battle it explains the battle or because they wanted to keep the mining conglomerates from the spoiling the countries so it looks like two there is indicating the premise in an argument that explains why they fought battle after battle okay mining conglomerates is mining bad no are conglomerates bad not necessarily you can explain what a conglomerate is without talking about good or bad from dispoiling now wait a minute now we've got an evaluative term it's an evaluative negative term dispoiling means spoiling things are making them bad and what about treasures treasures is going to be an evaluative plus term because treasures are good things now the next word of the last sentence of this paragraph just a temporal indicator so that's nothing we thought okay thought means it's not really true he's just guarding it it's not really true that some of it was safe we thought it was some of it was safe or even at least some of it was safe now that's going to be a guarding term because it's not saying all of it was safe it's just a little part of it and that'll become important later in the argument whoa look at this diagram it's got letters all over the place and they're running into each other that shows you what close analysis does when you start looking in detail a lot of the different words are doing things that you can find out by trying to put them into these different categories so we've finished the first paragraph the entire paragraph oh my god onto the second paragraph the first sentence is really simple not so of course it's referring back to the last sentence of the first paragraph we said now we thought at least some of it was safe and saying no it wasn't safe so what are we going to say about this sentence well what about the little word so so can be an argument marker it can indicate that what follows it is a conclusion but is that what it's doing here i don't think so as we just saw like and i don't think so the word so can be used in many ways where it's not an argument marker and this is saying it's not so it's not that way so there's no argument here so that would get marked with a big in for nothing now what about shocking as it sounds shocking well is shocking always bad remember we saw in the first paragraph the word stunning well stunning stuns you and shocking shocks you and it's telling you that you have some kind of reaction but it's not telling you whether that reaction is due to the thing being good or the thing being bad you can get shocked by something good or bad it can be shockingly good or shockingly bad and so the word shocking by itself doesn't indicate that it's e plus or e minus so again we get a nothing i mentioned it only because it's clear that robert redford thinks that shocking is bad that this should not have happened he's suggesting that it's bad but the word shocking itself is not an evaluative word what about as it sounds well he's saying that it sounds that way he's not saying that it is that way he's not saying that it may sound that way he's saying that it does sound that way which is to say it seems that way to him which is not to say it really is true so he's guarding the claim he's not saying that it really is shocking he's saying that it seems shocking so he's guarding the claims in order to avoid someone objecting that it's not really all that shocking after all he's saying well it sounds shocking and in order to make that part of his argument more defensible because it's not really essential to his argument that it's shocking or not so what's supposed to be shocking clinton's bureau of land management or blm has approved oil drilling within the monument notice that there's no guarding at all here he just states it they did it they approved oil drilling within the monument and that's because it's not really something he's arguing for he's actually opposed to it it's something that his opponents might support but he doesn't so he doesn't want to guard it since he wants to say it just happened as a matter of fact that they approved it so there's nothing that we need to mark in that particular sentence next sentence blm or the bureau of land management has given conico incorporated a subsidiary of the corporate giant dupont permission to drill for oil and gas in the heart of the new monument well there's a lot going on here that we could mention no blm has given conico a subsidiary that explains how they got permission by citing the blm it's a subsidiary of the corporate giant dupont he's certainly suggesting that giant suggested he's the small guy you know up against the big corporate giant it might even have some connotation of corporate giants being bad but it doesn't actually say that and so again giant should be marked as nothing what about permission to say that someone's permitted to do something is to say that it's not wrong that's what permitted means now of course if you're talking about a legal permission then to say that it's permitted is to say that it's not legally wrong it's not forbidden by law it still might be morally wrong but at least it's legally permitted means it's not legally forbidden and so if forbidden and wrong are valued of words to deny them and say it's not wrong looks like an evaluative as well but one of the interesting things about this evaluative word is it's not clear whether it's positive or negative it means it's not wrong but that doesn't mean it is good or is right it simply means it's not forbidden so it's not clear whether to put plus or minus i'll just leave it as a plain e in that case okay now what did they have permission to do to drill for oil and gas in the heart of the new monument okay that's what the permission was a permission to do the word to there is not being used as an argument marker in this case because you can't say they get permission in order to right what they get permission to do was to drill okay what about drill well clearly robert redford doesn't want them to drill so he thinks that's bad but he didn't say it's bad he just calls it drilling and they're drilling for oil and gas well a lot of people think that oil and gas are good things but they don't say here that they're good they're simply saying that they're oil and gas the coolest part of this sentence i think is that metaphor at the end i mean you've got this image that there's this this poor monument and somebody's drilling right in its heart you know like what could be crueler than to drill in the heart of a young monument the poor innocent thing so this metaphor of the heart is a nice rhetorical device that fits with the drilling and is building up people's opposition to what redford wants them to be opposed to but it does actually give an argument it's just stating it in a flowery or metaphorical way that'll get their feelings going okay you may wonder notice he doesn't say you do wonder he says you may wonder so this is tell me a guarding term so you should mark it with g you may wonder as i do as is sometimes used as an argument marker but here you're not saying that you wonder because i do or i wonder because you do the word because can't be substituted for as so to say as i do is simply to conjoin the two and say you wonder and i also wonder or you may wonder because i don't know whether you are or not and i do and what we wonder is how can this happen now we have a rhetorical question how can this happen well that's obviously suggesting it shouldn't have happened you know how could something have gone so wrong as it did in this case but he doesn't actually say that he simply asked the rhetorical questions and that's really the trick of rhetorical questions notice there are a bunch of them here wasn't the whole purpose this didn't the president say he was doing this then these three sentences in a row are all rhetorical questions so what's the trick of rhetorical questions the point of a rhetorical question is to get you to give the answer if i say how can this happen and someone thinks to themselves well the government messes up all the time then you've got that audience member who answered the question to be saying it themselves and there's nothing more forceful in an argument than to get your audience to say it themselves when you don't have to say it and that's the trick of a rhetorical question and what redford's doing here is putting three of them right in a row so that you'll have to go along with him three times in a row and then that obviously has an effect on your feeling like you're with him on you feeling like you agree with him that's the effect he's trying to create by using these rhetorical questions okay what's the whole purpose of creating notice the whole purpose is to preserve that phrase the whole purpose goes with it because we say the purpose is to preserve and there as before in the previous paragraph we're signaling an explanation because if you want to explain why clinton created the monument then the answer was to preserve the colorful cliffs and sweeping arches and so on so this is going to be an explanation and to say that's the purpose is to say that you created it because you wanted to preserve or in order to preserve then this whole purpose marks the conclusion and the to preserve marks the premise and we have a little argument he wanted to preserve his colorful cliffs therefore he created the monument and we've got the conclusion marked by the whole purpose and the premise or the reason marked by the word two okay preserve we've already seen a word a lot like that namely protect and we saw that when you protect something it has to be good preserve also means to preserve it against things that would harm it if harm's bad then preserving and protecting against harm must be good so we can mark that as e plus it's colorful cliffs colorful sounds good but of course colorful just means it's colorful sweeping arches broad and sweeping in curves well that sounds good it sounds beautiful the way he describes it and it surely is as you can see in any picture but sweeping doesn't itself say it's good or beautiful or so on and other extraordinary we already saw extraordinary so colorful sweeping and extraordinary they're certainly being used here by redford to suggest that these are good but they're not openly saying they're good so we don't want to mark those as evaluative words but resources now resources are things that can give you abilities when you have more resources you're able to do more so abilities sounds like a good thing and resources are the things that make you more able they give you more freedom and more power so at least many people would want to mark that as an e plus word some of these are going to be questionable they're not as obvious as others so i'm suggesting one way of interpreting this passage and i hope you're following along but if you have some questions about the particular cases that's going to be natural it's partly because our language is not totally precise okay large-scale mineral development well that's not bad if it's done in the right places so i don't think that's evaluative either didn't the president say that he was saving these lands well didn't the president say that he was saving these lands well that suggests that he's assuring you that in fact he was saving these lands he should know whether that's what he was doing since after all that's what he you know did himself so he should be able to say what he did and why didn't the president say he was saving saving could be marked as e plus just like protect and preserve because it saves it from something bad happening these lands from mining companies for our children and grandchildren now what about the word for this explains again why he's saving these lands he's saving them for our grandchildren and children that means the reason for saving these lands is to benefit our grandchildren and children so four is going to be a reason or premise marker it marks the reason or premise that justifies saving the lands and explains why in fact the president did want to save the lands okay so now we're through with paragraph two and i hope you're kind of getting the feel for how to do close analysis and so what i want to do now is give you a chance to practice the skill on your own we'll put up paragraph three mark certain words and your task in the exercise will be to put the right letter next to or to indicate the function of that word in the paragraph and the letter you put should be either r or b for premise marker c for conclusion marker a for assuring g for guarding d for discounting e plus e minus four positive and negative evaluation and you can go through the third paragraph yourself in the exercise welcome back now you've done paragraph three yourselves and we're going to go on to paragraph four might seem like we're doing an awful lot of this but remember the only way to learn close analysis is to practice practice practice practice practice over and over again on as many passages as you can find so we're going to spend one more lecture going through paragraphs four and five of robert redford's piece in the washington post from 1997 the title was a piece of god's handiwork paragraph four starts sounds like washington double speak to me well what is it that sounds like washington doubles speak to him it's the sentence at the end of the previous paragraph that you analyzed and that's the claim that they issued the permit without a full review using an abbreviated review and they didn't even look at the leases on other federal lands so he's saying that sounds like the kind of thing washington does when they double speak double speaks obviously a metaphor right it's a metaphor for saying one thing to one person another thing to another person or sometimes saying one thing that seems to mean one thing when what they really mean is another thing but however you interpret the metaphor of double speak it's not good so we can indicate that double speaking is a negative evaluation and it's a metaphor but clearly negative in its meaning you wouldn't say someone who's speaking properly is double speak notice however that he has this phrase sounds like and it sounds like it to him what sounds like doing well he's not saying that it is washington double speak so he's guarding it he's weakening the claim he's not saying it is he's saying it sounds like and so that can be labeled as a guarding term okay so he's guarded that claim but now he's going to go on and argue against the plan that washington was using i've spent considerable time on these extraordinary lands for years i've spent four years let's just circle that whole thing to indicate that whole phrase because it's all doing the same thing what's it doing it's assuring you he's saying because i have spent so much time on these lands i spent so many years on them you can trust me to know what's going on i've got the evidence notice like other assuring terms it's not giving you the evidence it's saying you ought to trust me because i've got the evidence i've had the experience so it's a perfect example of assuring because it's saying that he has reasons without actually giving the reasons and that's why you can't question his reasons because you haven't spent considerable time on those extraordinary lands and of course he follows that up with another assuring term he says and i know when you say i know that's an assuring term a mental assuring term because it's describing the mental state as being one of knowledge knowledge implies truth than to say i know it is to imply that it's true to assure you that it's true okay and what does he know he knows that an oil rig in their midst would have a major impact what about that a major impact okay now he's clearly saying it would be a bad impact but does he come out and say it's bad no he just says it's major okay so it's not an evaluative term that would be labeled as nothing if nothing is an option so clearly suggesting that it's bad but he's not saying it so it shouldn't be marked as an evaluative term okay next what's more well what's more is kind of a conjunction but what came before this was an argument that it would have a major impact based on his assurance and so when he says what's more he's suggesting that what's going to come next is yet another argument for why we shouldn't have these these permits issued he's going to tell you other bad things about them so that can be a premise marker because what comes after it is the premise they want to drill to find oil well we can say to find oil it's in order to find oil that is going to explain why they want to drill it's a teleological explanation as we saw in an earlier lecture and so that is going to be a reason marker because their desire to find oil is what explains their desire to want to drill okay inevitably what's that assuring it's assuring you that it's obviously true there's no way around it it is inevitable what's inevitable more rigs more roads new pipelines toxic waste and bright lights would follow to get the oil out okay he's assuring you that all of those things are going to happen the previous argument before the what's more was simply an oil rig notice it's just an oil rig one oil rig up there in that sentence but now we've got more rigs more roads new pipelines so if an oil rig has a major impact all of this other stuff is going to have a lot more of an impact that's the point of the what's more he's adding additional reasons why the permits should not be issued okay and they would follow that means it's going to follow what in time it's just temporal it's not saying anything more than it's going to follow at a later time but they're going to follow to get the oil out that explains why they would follow because right you would need them in order to get the oil out so that's going to be an argument marker itself is it a reason marker or is it a conclusion marker well the conclusion is that all that's going to follow right and the premise is that it's needed in order to get the oil out so this is going to be a premise marker and the conclusion is that you get all that stuff the pipelines the roads the waste and so on okay so those are his reasons against giving a permit and then he says the BLM couldn't see this okay just states it as a fact but what's the but doing there remember what kind of word a but is but is a discounting term he's answering an objection the objection is well you say all that would follow but the BLM would disagree with you and they looked at it very carefully and they're an authority or an expert so the answer to that objection is the US Fish and Wildlife Service and the Environmental Protection Agency did see this notice that what comes after the but is more important than what came before it what he's doing he's saying that there's a contrast between what the BLM couldn't see and what the US Fish and Wildlife Service and the Environmental Protection Agency did see but in addition to the contrast between those two he's also saying it's more important that the US Fish and Wildlife Service and the Environmental Protection Agency did see it okay so what comes after the but is taken to be more important and what did they see both of these agencies recognized recognized implies you can't recognize things that aren't true you know if you see somebody and you say I recognize my sister and it wasn't your sister you didn't really recognize them so to say you recognize is to assure people that it's really true the devastating now devastating can't be good so that's e-minus effects of extensive oil drilling extensive is that bad no extensive oil drilling's good in the right places gives us the kind of energy we need to be able to accomplish the goals that we want maybe you wish you didn't need extensive oil drilling but if you need it then it's good when it's done in the right place and that drilling would have it devastating effects on this area and then those two agencies urge the BLM to refuse to allow it okay why in order to protect the monument and again we've seen this kind of argument repeatedly at several points during this particular op ad that's saying that the goal is to protect the monument and that's what justifies urging the BLM to refuse to allow it so this is going to be a premise marker we've seen in order to protect in order to preserve uh because we want to protect and so on he keeps repeating that that's not a bad thing many times when someone's giving an argument they repeat pretty much the same words as in other areas because they're giving several arguments for a single conclusion we'll actually see how those different reasons can fit together in the next section of the course but for now all we're doing is marking the words in in order to is a premise marker we finished four paragraphs all right we're almost done now we're on to paragraph five and it starts maybe the problem comes from giving management responsibility for this monument to the BLM what about the word maybe the word maybe is about as clear a case as you can get of a guarding term it's saying it might be the case it might not be the case i'm not going to definitely claim that's where the problem comes from i'm just suggesting that maybe so somebody comes along and says that's not really true i i'm going to say well maybe it's true that's all i was claiming and so i'm now able to defend my premise okay problem what about problem gotta be e-minus right another clear example because you can't have good things if there are problems sure you can have problems on math tests that are good but that's not the kind of problem we're talking about here these kinds of problems are bad and so that word gets marked as e-minus so the problem comes from namely is explained by giving management responsibility for this monument to the BLM so comes from can get marked as a premise marker it's the giving management responsibility to the BLM that explains why there's a problem in the first place and that could be put in the form of an argument that explanation could okay so why is giving management responsibility to the BLM create a problem because the next sentence tells you this is the BLM's first national monument first time they've ever done this almost all the other monuments are managed by the national park service okay nothing wrong in itself with being the first there always has to be a first so there's nothing evaluative there what about almost all clearly guarding right because it's not all it's almost all so the claim is more defensible almost all the others are managed by the national park service the park services mission is to protect the resources under its care okay protect good resources good so those both get E plus while what about the word while let's not completely clear you could read this as simply setting up a contrast between the park services mission and the bureau's mission but you can also read it as responding to an objection well doesn't the government protect those resources and the answer is well the park service does but the bureau has a different role the bureau has always sought to accommodate economic uses okay so if you read that while as but and you replace it with but it seems to make sense the park services mission is to protect but the bureau has always it looks like you can replace it with the discounting term which means that while is functioning here as a discounting term okay the bureau has always sought no guarding there it's always sought that right to accommodate economic uses of those resources under its care even so starts the next sentence what is even so doing well even so is a discounting term because it's discounting an objection the objection is well they've always sought to accommodate those uses well then how do you explain the fact that they got off to such a good start they seem to be okay they seem to be that's a guarding term it's not saying they were it's saying they seem to be getting off to a good start good boy there's an evaluative plus you can't beat that for a clear evaluative plus to a good start by enlisting broad public involvement in developing a management plan for the area well what was good about it they enlisted broad public involvement therefore it was good looks like by enlisting could be a premise marker the premise is enlist they enlisted broad public involvement therefore they got off to a good start yet what's yet another discounting term the agency's decision to allow drilling in the monument completely undercuts this process just as it's beginning the objection is so they got off to a good start what's the problem if they enlisted broad public involvement what's the problem well that's the objection and the response is now they've decided to allow drilling in the monument and that completely undercuts the process that did enlist public involvement right so the yet is discounting the objection that says there's no problem here they're doing just fine they got broad public involvement they're saying the response to that objection is but now they have not got public involvement they're doing it without a complete review and so on as mentioned in the preceding paragraph the agency's decision to allow oil drilling in the monument completely no guarding right completely undercuts when it's that strong a word like completely you can almost say it's i'm assuring you it's not just partially undercutting it's completely undercutting that's a way of of making you confident that it really does at least partially undercut the process and undercuts sounds like something bad i suppose you might not want to mark it as evaluative because you know you could undercut a bad process and that would be a good thing so literally you probably should not mark that as evaluative but it's clear what robert redford thinks about undercutting this process and now just just stands for justice doesn't it no remember from the very first word of this op ed just is nothing here it means at the same time when it was beginning it's not an evaluative term even though just sometimes means something about being just or fair or good here it doesn't mean that at all so we're back to the very word that we began this op ed with and so that seems like a good place to stop i'll stop marking here there are other things you could mark there are other things to discuss these paragraphs these op eds are always extremely complex and interesting to try to get the details straight but i'll give you a chance to look at the next three paragraphs they're all pretty short and look at those paragraphs and see if you can do a close analysis on those because as i've emphasized several times the best indeed the only way to learn close analysis is to practice practice practice practice practice welcome to week three in weeks one and two we already learned a lot about how to identify and analyze arguments we can do close analysis we can identify the premises in conclusion we can put them in standard form what's next well the next step is to take those parts and put them in a certain order and fill in the missing gaps we need to learn how to reconstruct arguments are you ready well there are lots of ways to reconstruct i mean think about constructing a house or a building in order to construct a good building you gotta know what the goal is what the standards of a good building are the same thing goes for reconstructing arguments in order to reconstruct an argument properly we need to know what the standards are for reconstruction we're trying to reconstruct it so as to meet those standards because the goal is not to reconstruct the argument in order to make it look bad the point is going to be to reconstruct arguments so as to make them look good because by making your opponents look bad or silly that doesn't do anybody any good if you want to learn about their perspective and you want to learn from their views then you need to reconstruct their argument so as to make it look as good as possible and to do that you need to know about the standards for arguments that is the standards that make arguments good or bad so what we're going to do this week is we're going to look first at some standards for arguments validity and soundness in particular and then we're going to use those standards to develop a method called reconstruction or deep analysis i'll explain those terms later and then we're going to apply that method to a few concrete examples in order to be able to take a passage and take those premises and conclusions and fill them out and get a full fledged argument that if we've done it properly will be as good as it can be and that we can learn from that's the goal now because an argument consists of premises and a conclusion and the premises are supposed to be related in the right way to the conclusion there can be two main ways for an argument to go wrong two main vices of argument you might say the first is there might be something wrong with the premises in particular they might be false or at least one of them might be false second there might be something bad about the relation between the premises and the conclusion the premises might fail to give a good reason for the conclusion now each of these problems is something that we need to avoid and when we do avoid them we get the corresponding virtues namely validity and soundness and those are the two notions that we want to discuss in this lecture and the next let's begin with the relation between the premises and the conclusion what kind of relation between the premises and the conclusion is good for an argument or makes an argument good well that depends some arguments are deductive and others are not so let's focus for a moment on deductive arguments in deductive arguments the conclusion is supposed to follow from the premises what does that mean i mean what does it mean for a conclusion to follow from the premises that's a really hard notion to pin down so what logicians usually do and what we're going to do is focus instead on the notion of validity and the idea is that a deductive argument is trying to structure itself so that it's valid and we'll explain what validity is but for now i want to emphasize that we're only talking about deductive arguments there's going to be another class of arguments called inductive arguments that we'll get to later in this course where they don't even pretend to be valid they don't even pretend that the conclusion follows from the premises but just for simplicity let's focus on deductive arguments now and the idea is that the deductive argument should be structured in such a way that it's valid then the next question is what's validity let's start with a simple example suppose that you know mary but you don't know her children however you do know that she has one child who is pregnant and you also know that only daughters can become pregnant so you have all that you need to know in order to draw further conclusion namely mary has at least one daughter so here's the argument mary has a child who is pregnant only daughters can become pregnant therefore mary has at least one daughter now if you think about it there's just no way no possibility that both of those premises are true and the conclusion's false that is the feature that we're going to call validity more generally we can define validity in an argument so that an argument is valid if and only if it's not possible for the premises to be true and the conclusion falls that is it's not possible for there to be a situation where both of those whole that is a situation where the premises are true and the conclusion is also false now that might strike you as a pretty simple notion but actually that little word possible is a problem how do you tell what's possible or what's not possible well there's no mechanical solution to that and we'll struggle with that a little bit throughout this course but for now since we're right at the start let's think of it this way is there any way for you to tell a coherent story where the premises are true and the conclusion's false can you describe a situation with that combination of truth values that is the premises being true and the conclusion falls in the same situation if you can tell a coherent story with that combination then it's possible and the argument's not valid but if there's no way to tell a coherent story where the premises are true and the conclusion's false then the argument's valid now let's try that test on our example Mary has a child who is pregnant only daughters can be pregnant therefore Mary has a daughter so is there any way to tell a coherent story where the two premises are true that is where Mary has a child who is pregnant and only daughters can be pregnant but the conclusion's false Mary does not have a daughter well just try suppose Mary has only one child and it's a son there's the conclusion is false good what about that but then is that son pregnant well if the son is not pregnant then the first premise is false Mary doesn't have a child who is pregnant but if the son is pregnant somehow don't ask me how but if the son is pregnant then the second premise is not true it can't be true that only daughters can be pregnant because this child is a son okay what if Mary has two children try that try to tell the story that way Mary has a daughter and a son now she's got a child who is pregnant the daughter and only daughters can be pregnant but she has a son wait a minute she's got a son and a daughter so now the conclusion's true because she does have a daughter even though she also has a son oh oh wait how about this one what if Mary has a child who is biologically female but sees himself as a male and so she sees that child as a male but that child is pregnant because after all they're biologically female now are the premises true and the conclusion false does that story make sense wait a minute either her child is a daughter or her child is a son now if it's a daughter and it's pregnant no problem the conclusion's true if it's a son because that child sees himself as a male then you've got a choice well what about the first premise the first premise is going to be true she does have a child who is pregnant but what about the second premise only daughters can be pregnant wait a minute if that really is a son if we're going to call that a son then it's no longer true that only daughters can be pregnant so now the second premise is false so try it again try it with you know sex changes and try it with her maphrodites tell the story any way you want about Mary's children and there's no way that both premises come out true when the conclusion's false that shows that the argument is valid it might be just that we can't imagine the coherent story which makes it invalid but the fact that we've tried hard and looked at all the possibilities we can think of at least gives us a good reason to think that this argument is valid now some people like to think of it in the reverse direction they say let's imagine that the conclusion's false and then if it has to be the case that at least one of the premises is false the argument's valid then you can define validity as it's necessarily the case that if the conclusion is false one of the premises is false or in every possible situation if the conclusion's false one of the premises is false we can apply this new account of validity to the same old example it's gotta be the case that if Mary doesn't have a daughter then she doesn't have a child who is pregnant or else there are at least some children who are pregnant who are not daughters so notice in this case you're reasoning back from the falsehood of the conclusion to at least one of the premises has to be false whereas in the earlier definition you were saying it's not possible in the situations where the premises are true for the conclusion to be false you can look at it either way either direction just pick the one that works for you and go with that definition because in the end the two definitions are equivalent it's just a matter of what's going to help you understand which arguments are valid and which ones are not in addition to understand what validity is it's also very important to understand what validity is not a lot of people get confused by the notion of validity in this context because they're thinking that to call an argument valid must be to call it good right you call a driver's license valid when it's good in the eyes of the law but that's not what we're talking about here the notion of validity is getting used by logicians here is a technical notion and it's very very very important to remember that to call an argument valid is not to call it good for some arguments like deductive arguments being valid might be necessary for them to be good but it's not enough and we'll see a lot of examples of that later on the second point about what validity is not is that validity does not depend on whether the premises and the conclusion are actually true or false instead it depends on what's possible whether there's a certain combination true premises and a false conclusion that's even possible so whether the premise is actually true in the actual world is not what's at issue and we can see this by seeing that some arguments with false premises can still be valid and some arguments with true conclusions can be invalid so let's look at some examples of that indeed there are four possibilities because remember the conclusion could be true or false and the premises could be all true or at least one false so we've got four possibilities and all of those are possible except for one the one combination that's not possible for valid arguments is true premises and a false conclusion but if you've got true premises and a true conclusion it might be valid it might not if you've got false premises and a true conclusion it might be valid it might not if you've got false premises and a false conclusion it might be valid it might not so let's look at some examples each of those possibilities in order to better understand the relation between premises and conclusion that exists when the argument is valid. It's hard to give examples with true premises and false conclusion or any of these other combinations when the truth is controversial. So we're going to have a really simple example, and we're going to start just by stipulating what the facts are. We're going to assume that all Ford cars have four tires, but some Ford cars do not have four doors. We're also going to assume that Henry's car is a Ford that has four doors and Jane's car is a Chrysler that has only two doors, not four doors. And we're just going to take those facts for granted and assume that that's the situation we're talking about. And then we can give examples of all the combinations that we discussed before. Let's begin with true premises and a true conclusion. Here's an example. All Ford cars have four tires. Henry's car is a Ford, so Henry's car has four tires. Are the premises true? Well, yeah, our assumptions tell us that all Ford cars have four tires, and then Henry's car is a Ford. What about the conclusion? Is that true? Sure. That's another one of our assumptions. Henry's car has four tires. But the fact that the premises are true and the conclusion's also true doesn't yet tell us it's valid because to be valid, it has to be impossible for the premises to be true and the conclusion false. There has to be no coherent story where the premises are true and the conclusions false. So what about this case? Is it valid? Well, is it possible? Is there any way to tell a coherent story where? All Ford cars have four tires. Henry's car is a Ford, but Henry's car does not have four tires. Just try. One way to tell that you're not gonna be able to do it is to reason backwards. Assume that the conclusion's false, that Henry's car does not have four tires. Maybe it's got six tires. Well, then how could both premises be true? If Henry's car is still a Ford and it has six tires, then the first premise is not true because the first premise is that all Ford cars have four tires and Henry's car would then, under that assumption, be a Ford car without four tires but with six tires instead so the first premise would be false. Well, another possibility is that Henry's car has six tires and it's not a Ford and then you could have the first premise true. All Fords have four tires but you couldn't have the second premise true, namely that Henry's car is a Ford. So there's no way when the conclusion is false for both premises to be true and that shows you that the argument is valid. Nonetheless, there are other examples where the premises are true and the conclusion is true but the argument is not valid. Instead, it's invalid. Here's an example of that combination. All Ford cars have four tires. Henry's car has four tires. Therefore, Henry's car is a Ford. Now, in this new argument, are all the premises true? Yes, the first premise says all Ford cars have four tires and that's true by our assumptions. The second premise says Henry's car has four tires and that's also true by our assumptions and is the conclusion true? Yes, our assumptions also tell us that Henry's car is a Ford but is it possible? Is there any way to tell a coherent story where those premises are true and the conclusion's false? Yes, absolutely. All that has to happen is that Jane and Henry switch cars. Then the first premises can be true because all Ford cars have four tires and the second premise is going to be true because Henry's car has four tires. Of course, now it's a Chrysler because he got it from Jane but the conclusion is going to be false. Henry's car is not a Ford because Ford and Chrysler are different companies so if he switches cars with Jane and he has a Chrysler then he doesn't have a Ford. His car is not a Ford. So now you've got a situation where the premises are true and the conclusion false. It's not the actual situation but it's a possible situation. You can tell a coherent story where the premises are true and the conclusion's false and that tells you that the argument is invalid. Next, let's consider an example with false premises and a true conclusion. Premise one, all Fords have four doors. Premise two, Henry's car is a Ford. Conclusion, Henry's car has four doors. Is the first premise true? No, it's not true that all Fords have four doors. Our assumptions tell us that. Second, is Henry's car a Ford? That's true. So one of the premises is false and the other one's true. That means they're not all true and the conclusion is that true. Yes, it is true that Henry's car has four doors. But remember, the fact that that's actually the case doesn't tell us whether or not it's valid. So is it valid? That depends on whether it's possible for the premises to be true and the conclusion false. Premises aren't actually true but is there a possible story that you can tell that would be coherent where the premises are true and the conclusion's false? That's the test of validity. So let's apply it to this case. Let's just imagine that the conclusion's false. That Henry's car does not have four doors. It's only got two doors. Then, there are really only two possibilities. Either it's a Ford or it's not a Ford. If it is a Ford, then the first premise is false. It's not true that all Fords have four doors. But if Henry's car is not a Ford, then the second premise is false because it says that Henry's car is a Ford. So there's no coherent way in which it could possibly be true that both of these premises are true and the conclusion's false. So this argument's valid. And notice that that shows that an argument can be valid even though it's got a false premise. Now, you might be thinking to yourself, this is crazy. How can an argument be valid when one of its premises is false? An argument's no good when its premises are false. Notice what that does. That confuses the notion of valid, like in a valid driver's license, where to be valid is good with the technical notion of validity that we're using here. The technical notion of validity that we're using here has to do with the relation between the premises and the conclusion. And in particular, it has to do with possibilities and not with the actual falsehood of the premise. So what we have to ask ourselves is, what would happen if it really were true that all Fords have four doors? It's not true in the actual world, but we're concerned with possibility. And if all Fords did have four doors and if Henry's car was a Ford, then it would have to have four doors. So that possibility of the premise being true, even though it's not, is what's crucial for determining validity because it's not possible for the premises to be true and the conclusion false. That makes it valid in our technical sense, even if it's not valid in the common sense notion of validity as goodness. We're not saying that the argument's a good argument. We're saying that it meets this technical definitional validity that logicians use. Now the only combination of truth values and premise and conclusion that you cannot get with a valid argument is to have true premises and a false conclusion. So here's an example of that. Premise one, some Ford cars do not have four doors. Premise two, Henry's car is a Ford. Conclusion, Henry's car does not have four doors. The premises by our assumptions are both true and the conclusion's false. And it's not valid because it's easy to see how it might be possible for the premises to be true and the conclusion false. It's simple. Even if some Fords don't have four doors, Henry's car is one of the Fords that does have four doors. And then both the premises can be true and the conclusion's false. So that's how you can get an invalid argument with true premises and a false conclusion. But you don't really even need that. Look, every argument that has true premises and a false conclusion has to be invalid because if it does in fact actually have true premises and a false conclusion, then it's possible for it to have true premises and a false conclusion. So you can know right off the bat that every argument with true premises and a false conclusion is invalid. What you can't know is for the other combinations. Then you have to think through what's possible instead of simply what's actual. We haven't been through all of the possibilities, but we have seen that you can have invalid arguments with true premises and true conclusions and you can have valid arguments with false premises and true conclusions. And we've got a little table that shows us the other possibilities. Instead of going through all of those other possibilities myself, I think it'd be better if you did a few exercises and that'll make sure that you understand this notion of validity before we go on and try to show how validity is related to soundness. The next question is probably been bothering you ever since very early on in the previous lecture. Namely, if valid arguments can have false premises, then what good are they? Sure, there's this technical logician's notion of a valid argument, but why should we care whether arguments are valid if valid arguments can be really bad? Validity might be necessary for an argument to be good or at least for a deductive argument to be good, because remember, they're also inductive arguments. But even though it's necessary, it's not enough. You can have a horrible argument that's still valid. The great thing about validity is that when a valid argument has true premises, then you get something that really is valuable, namely soundness. Because if you know that the premises are true and you also know that it's not possible for the premises to be true and the conclusion false, then you know the conclusion must be true. So in a sound argument, the conclusion has to be true. And that is what makes it valuable. Because if we can get a deductive argument to be sound, then you really got something. What you've got is a true conclusion. Officially then, a sound argument is one where the premises are true and the argument is valid. And we've got the same combinations of truth and falsity as possibilities that we had in valid arguments. You can have both premises and conclusion are true. And then if it's valid, the argument's sound, and if it's not valid, it's not. Or you can have the premises are true and the conclusions false, and then it can't be valid. But if it's invalid, it's not sound. Or you can have the premises are false and the conclusions true, and then if it's valid, it's not sound, and if it's invalid, it's not sound. Or you can have both the premises and the conclusion are false, and then it's not going to be sound whether it's valid or not. So the only combination where it's sound is when the premises are true and the argument is valid. And in that case, you know that the conclusion is true. What about lack of soundness? Well, there are two ways for an argument to fail to be sound. Namely, either the argument can be invalid or one of its premises can be false. So it's a lot easier for an argument to be unsound. And we know that a deductive argument tries to be valid. And of course, it wants its premises to be true. So a deductive argument is trying to be sound. And when it fails to be sound, it's not going to be any good. Now, the next question is, how can you know? If you don't know whether the premises are true, you're not going to know whether the arguments sound. Well, not quite, because if the argument's valid and you know it's valid, then you don't know whether it's sound unless you know the premises are true. But if you know the arguments invalid, you already know it sounds sound, even if you don't know whether the premises are true. So if you think about it, that shows why you want to be able to test for validity. Because if you can show the arguments invalid, then you'll be able to say, well, I know it's unsound, regardless of what you think about whether the premises are true or not. So there's going to be some value to validity. Namely, if you can show it's invalid, you're going to show it's unsound. And that means that the deductive argument didn't get what it wanted. So validity is going to be necessary for soundness. And soundness is going to be important because it guarantees the truth of the conclusion. And then validity derives its value from the fact that if it's not valid, it's not sound. OK, now there's a lot more to say about validity. And we'll say a lot more about validity when we get to formal logic in the second part of this course. But for now, we're just going to stick with this pretty intuitive notion of validity and see how we can use this notion of validity to reconstruct arguments. Now that we understand validity, we can use the notion of validity in reconstructing arguments. Now the point of reconstructing an argument is to put it in a shape that makes it easier for us to assess the argument more accurately and fairly for whether it's a good argument or a bad argument. And when we do the reconstruction, remember, we want to make it as good an argument as possible because you don't learn anything from putting down your enemies by making it look silly. If you want to learn from somebody else's argument, you need to put it in the best shape you can to make it look as good as possible. So that's going to be the goal of reconstruction. And we're going to accomplish that goal in a series of stages. The first stage is simply to do a close analysis. And we talked about that last week. The second stage is to get down to basics. That is to remove all the excess words and focus on the premises and conclusion that really make up the argument and then put those into standard form. The third stage is to clarify those premises. They're not always going to be as clear as you like and that's going to take some work. And it's going to include breaking them into parts. And then the next stage is to take those parts and organize them, to put them in order so you can see how the argument flows from one part to another. But not all arguments are complete. So the next stage, we have to fill in the gaps. That is, supply suppressed premises. And once we've done that, then the final stage is going to be to assess the argument. If we are able to come up with a sound reconstruction, we know that the conclusion has to be true. Because as we learned in the previous lecture, the conclusion of sound arguments is always true. But if we don't come up with a sound reconstruction, then we've got to decide, is it the fault of the argument? Or is it our own fault? Because we didn't come up with a sound reconstruction when there really is one that we didn't find. So that's going to be something we have to discuss. We're going to discuss all of these stages over the next few lectures. Now, the first stage of reconstruction is to do a close analysis. But we already learned how to do that. That was easy. Poor. Hope the rest of them are that easy. This lecture is mainly going to be about the second stage, namely getting down to basics. And what we want to do is to pull out the explicit premise and conclusion from all the other words around it. And the first step is to remove all the excess verbiage. It might seem really surprising, but people often repeat themselves. I'm sure you've all run into it. You listen to somebody give a talk, and it takes them 50 minutes to say what they could have said easily in five minutes. And one of the reasons is that they say everything 10 times. For instance, people often say the same thing twice. They repeat themselves. They say the same thing over again, and they restate the point in different words. The other sentences that mean the same thing, and they say something, and then they say it again. And they make a claim twice or more. They assert exactly what they just said. And they reformulate their claim in different words that are equivalent. They say it once, and then they say it again. You get the idea. Now, here's a real example from a US politician during a debate. I want to be honest with people. We can't eliminate this deficit. People have heard that over and over again in four years. We cannot do it. We're in too deep a hole. Now, if you think about it, it's going to be obvious that we cannot do it. Repeats, we can't eliminate this deficit, because that's what doing it is, eliminating the deficit. But also, we're in too deep a hole. Well, that's just a metaphorical way of saying the same thing. Why is the hole too deep? Because we can't get out of it. What hole is it? It's the deficit hole. So to say we can't get out of this hole, we're in too deep a hole, it's just another way of saying we can't eliminate the deficit. So in these three lines, he's already repeated himself three times. Now, why does this politician repeat himself? It might be that he thinks people will remember it better, or one version will make more sense than another. But he might have a special reason, because this was a live debate. And he had to give a 90-second answer. So he had to fill up the time. Sometimes people repeat themselves just to fill up the time. Or maybe to give himself time to think, because he didn't have a real answer ready yet. And repeat himself as easy while he thinks about what he's really going to say in the next few sentences. Fine. But repeating it still doesn't make the argument any better. And we want to get down to the basics of the argument. That is the parts of the argument that really affect how good it is. So we can cross out those repetitions that don't make the argument any better. So first, we can cross out, we cannot do it. Then we can cross out, we're in too deep a hole. We already saw that those are just repeating the claim that we can't eliminate the deficit. In addition, we can cross out, I want to be honest with people. Because that's not a reason to believe that we're in too deep a deficit. And next, we can cross out that people have heard that over and over again in four years. Well, that might be seen as a reason to believe that we're in a deficit, because everybody seems to say it. But let's assume that that's not part of this argument here, and we'll cross it out. Now, let's move on. A second form of excess verb is that is words that don't contribute to the force of the argument is what I like to call road markers. A lot of times, people, good speakers, they tell you what topic they're talking about and why they're talking about it, why it's important and worth talking about. But to say why it's an important issue and to say what issue it is doesn't provide any reason to believe that what they say about the issue is true or false. So it doesn't contribute to the argument. Here's an example from the same politician in the same debate as we just saw. This politician said, now I want to go back to the whole issue of health care, because we touched it. And I think the American people deserve to know what we would do different. Now notice that he says he's going to talk about health care, but he doesn't say anything about health care. He doesn't tell you what he's going to say about health care. All he says, he wants to go back to that issue, and he tells you why he wants to go back to that issue. But he doesn't add any reason to believe that what he's about to say about the issue is true. Now this can, of course, still be useful, because you might get confused about what the issue is, and he might be changing the topic, and he wants to signal that he is changing the topic. And that'll help his listeners, but it still doesn't add to the argument. It doesn't give you any reason for the conclusion that he's going to want to draw. We can cross out these excess words. We can cross out, now I want to go back to the whole issue of health care, because that doesn't show that his views on health care are correct. And we can cross out, because we touched it, that's a reason why we're going to that issue, but again, that doesn't give any reason why his views are correct. And we can even cross out that I think the American people deserve to know, but we would do different, because the fact that they deserve to know what you're going to do doesn't show that what you're going to do is the right thing to do. So none of these claims are really reasons that are going to be reasons for the main part of his argument, which is to support the particular views on health care that he's going to tell you about a few seconds after this. The next type of excess verbiage is tangents. People go up on tangents all the time. Here's an example. You know, you really ought to think about taking a history course. I still remember my history courses in college. There was this one time when there was a dog that one of the students brought to class and the dog barked and then he ran up on stage and he cut under the professor and knocked the professor on his rear end. It was really funny. So I think that history is a good thing to study. Now notice that all this stuff about the dog has nothing to do with history. It's no reason to take a history course instead of a philosophy course or a classics course or a science course. The same thing can happen in those courses just as well. So the tangent plays a certain role. It makes it interesting, it keeps your attention. Maybe it makes it memorable for you what he said, but it doesn't actually provide a reason why you ought to take a history course. So since those parts of the words were just a tangent that don't provide any reason, we can cross them out too because they are excess verbiage. But sometimes people go off on irrelevant tangents not just by axa because they lose their train of thought, but because they're trying to fool you. They're trying to produce what's called a red herring. The name red herring supposedly comes from somebody who crossed the red herring over the trail and then the howling couldn't track his scent anymore. And that's basically what's going on here. Sometimes people produce tangents that distract you from the main line of argument because they know that there are weaknesses in that line of argument and they don't want you to notice them. That's what a red herring is. And it's a type of tangent that you have to learn to watch out for because if you wanna see the problems in your opponent's arguments or even in your friend's arguments, then you need to not get distracted by tangents that are in effect red herrings. Yet another example of excess verbiage is, well, examples. Here's an example of that. A different politician in the same debate said this. Here's what happened. In the time that they have been in office in the last four years, 1.6 million private sector jobs have been lost. 2.7 million manufacturing jobs have been lost. And it's had real consequences in places like Cleveland, Cleveland is a wonderful, distinguished city. It's done a lot of great things, but it has the highest poverty rate in the country. One out of almost two children in Cleveland are now living in poverty. Now notice that this politician is talking about the unemployment rate in the rest of the country and the country as a whole. So why bring in Cleveland? Well, you might be saying that Cleveland shows that there's problems throughout the rest of the country, but that can't be right because Cleveland's just one example and it might be an outlier that doesn't represent the general trends. So what he's really doing with this example is he's trying to bring it down to home and make you feel for the real effects, but he doesn't come out and say that you can generalize from Cleveland to the rest of the country or that everyone else is suffering in exactly the same way. He's just giving one example. And so it doesn't really support his general claim that the unemployment is a problem throughout the whole country. That means that it's not an extra premise in the argument and we can cross it out like other forms of excess verbiage. Now we've seen that excess verbiage can take the form of repetition or road markers or tangents or examples. And people use these a lot. Matter of fact, I like to think of a general trick that people use called the trick of excess verbiage. A lot of people talk too much and they keep saying things over and over again, go off on tangents and give more examples than they really need. And all of that is a way of hiding the problem with their position. It's a trick to use too many words because the real point gets lost in the middle of those words. So you can fool people by throwing in those extra words. That's the trick of excess verbiage. But be careful. What seems like excess verbiage that's just there to trick you might really be an essential part of the argument. So what you need to do when you have a passage and you're trying to get the argument out of it is to cross out all the excess words but also look at what's left over. If what's left over is enough premises and conclusion to make a good argument, then the stuff that you crossed out probably really is excess. But if it turns out that what's left over is not a very good argument, then you ought to check all those words you crossed out and make sure that you really weren't necessary because you're not being fair to the person that you're interpreting if you crossed out something that was an essential part of the argument. In some cases are gonna be tricky. It's not gonna be clear whether or not to cross them out. Some small words that are tricky are guarding terms. Here's an example. I think Miranda's at home so we can meet her there. What's the guarding word? You already found that out when you did the close analysis, right? I think. Now one way to read this argument is that the premises I think Miranda is at home and the conclusion is we can meet her there. But that's kind of weird because the fact that you think she's at home is not what makes it true that you can meet her there. It's the fact that she is at home that it can make it the case that you can meet her there. So if the premise is about what you think and the conclusion is about where she is and where you can meet her, then the argument doesn't make any sense. So in this case, what we wanna do is to cross out the words I think because that's gonna make the argument look silly and the argument really amounts to Miranda's at home so we can meet her there. And the I think covers that whole thing. It's saying I think she's at home so I think we can meet her there but the argument doesn't involve some premise about what your thoughts are. And contrast this with a different argument. Miranda's at home so we can probably meet her there. Now there's another guarding term, right? Probably. Can you get rid of that? Well then the argument becomes Miranda's at home so we can meet her there. But that's clearly not what the speaker was trying to say if they included the word probably. They realize that the fact that she's at home right now doesn't mean that we can meet her there because it might take us a while to get there and she might leave while we're on the way. So it's not fair to the person giving the argument and it makes the argument look worse to cross out the word probably. So in that case, you wanna keep the guarding term in order to properly represent the force of the argument. So it looks like sometimes you need to keep the guarding terms and sometimes you need to cross them out. And there's not gonna be any strict rule that you can follow. You have to use your sense of what's gonna make the argument as good as possible. What's gonna fit what the speaker was really trying to say. Another tricky case is assuring terms. Suppose I'm writing a letter of recommendation and I say he is clearly a great worker. I know that. So you ought to hire him. The assuring terms are clearly and I know that. But now the question is, is the argument really first premise? He's clearly a great worker. Second premise, I know that. Conclusion, you ought to hire him. It's kinda weird again if you think about it because you're not hiring him because it's clear. If he's a great worker, but it's not clear that he's a great worker, then you still ought to hire him because he is a great worker. Or if he's a great worker and I don't know he's a great worker, you still ought to hire him because he's a great worker. The fact that I know it is irrelevant to whether you ought to hire him because that's about my mental state, it's not his abilities. So that representation of the argument doesn't really capture the force of somebody who writes this letter of recommendation. So we can cross out the words, I know that, and we can cross out clearly. And then the argument is, he's a great worker, so you ought to hire him. But contrast this example. I am certain that Jacob is cheating on his wife. So I ought to tell her. Now you might think, I am certain that is just another assuring term. So we can cross it out. And then the real argument is Jacob is cheating on his wife, so I ought to tell her. But now think about that argument. The mere fact that he's cheating on his wife doesn't mean I ought to tell her if I'm not certain. Because if I have some suspicions or I'm just guessing, but I really don't know, then I probably ought not to tell Jacob's wife that Jacob is cheating on her. So here, the force of the argument does seem to depend on my certainty. If I'm not certain, I shouldn't tell her. If I am certain, maybe I should. So we can't cross out the assuring term in this case, because that would distort the argument. Now of course, some people might disagree with that. They might say, well look, if you have some reason but you're not certain, then you ought to tell her. And that can be controversial. But we're talking here not about what those people think, but what the speaker thinks. The person giving this argument, when this person said I'm certain that Jacob is cheating on his wife, they seemed to indicate that to them, the fact that they're certain provides even even better reason why he should tell Jacob's wife. So if we want to capture what the person given the argument intended, in this case, we have to leave in the assuring term. So we've seen one example where you ought to get rid of the assuring terms and another example where you ought to keep the assuring terms. And just like with guarding terms, the same point applies. There's no mechanical rule that'll apply to every case. You have to think through the argument and decide whether crossing out those words and removing them distorts the argument or instead crossing them out makes the argument look even better. Because the point of removing excess verbiage is to get rid of the things that aren't necessary but keep everything that is necessary to make the argument look as good as it possibly can look. Finally, once we've removed all the excess verbiage, what's left over? The answer is the explicit premises and conclusion in the argument. The point of removing the excess verbiage was to separate those essential parts of the argument, those basics of the argument from all the stuff that's unnecessary. Of course, we still have to decide which ones are premises and which ones the conclusion. And that's why the close analysis helps because we indicated which one were reason markers and which ones were conclusion markers. And that lets you identify that these are the premises and that's the conclusion. And so now we can do step three. We can put the argument in standard form. We put the premises above the line and we put dot pyramid and then the conclusion below the line. And we've got the argument in standard form, which completes stage two of the reconstruction project. At this point, it's useful to look back at the passage and see whether you've gotten rid of all the excess and included all of the basics of the argument. So you can look at the passage and say, is everything that's not crossed out in a premise or a conclusion of the standard form? And if there's something that's still there in the passage that isn't used, you've got to decide at that point, is it really excess or not? And of course, if the argument looks really bad, you've got to look back and see whether it's missing something that you had crossed out as being excess verbiage when it really was an essential part of the argument. So we can use this process of putting it into standard form as a test of whether we've performed properly the other step of getting rid of excess verbiage. So steps two and three really work together in this stage two of getting down to basics. That's what helps us to use the different parts to see whether we've done each of them properly. We're right in the middle of reconstruction. We did stage one last week, because that's just close analysis. In the previous lecture, we did stage two, which is to remove excess verbiage and to put the explicit premises in conclusion into standard form. And this lecture is going to focus on stage three, which is to clarify the premises and to break them up where possible without distorting them. Let's start with step four, which is to clarify the premises and the conclusion when it's needed. So we might need to clarify them just in order to make them easier to understand or to make them less likely to mislead and all that sounds pretty good. So let's try it on this example. It was hot today, so it'll probably be hot tomorrow again. Now, we need to clarify that. What exactly counts as today? Is that the time when there's daylight? Or does it also include night, even though night is not day? And what exactly do we mean by hot? How hot was it today? And how hot will it be tomorrow? And what, after all, is heat? And what about it'll probably be hot tomorrow? Probability, that's a tough notion. We're gonna spend a whole week on that later on in my course. There are different kinds of probability. I wanna know what kinds you're talking about here. And when you ask, for example, about it will be hot tomorrow, what does will mean? It means it's gonna happen in the future. And what exactly is the future? And is the future real? Is time real? You can go a long way towards asking how to clarify that argument. But that's ridiculous. You know, we don't have to clarify a simple argument like it was hot today, so it'll probably be hot tomorrow. And it's lucky we don't have to clarify every word in the argument because you couldn't. It's after all, when you explain one of the words or give a definition for it, it's gonna be in terms of other words that then they have to get clarified and you're never gonna get to the end of it. The search for perfect clarity and absolute precision is impossible. You'll never complete that search. You'll never find perfect clarity or absolute precision. So give it up. What we should seek is not absolute precision but adequate precision. Not absolute clarity but adequate clarity. And that means that we ought to try to clear up those parts of the premises and conclusion that are likely to produce confusion later. And you have to be able to kind of predict whether this part of the argument needs to be clarified because people are gonna get confused by it. Now that's not gonna be easy. And there's no simple or mechanical rule to tell you what needs to be clarified and what doesn't need to be clarified. The only way to learn this skill is to go through some examples that'll give you models of what needs to be clarified and what doesn't. Sometimes the unclearty lies in a single word. In the 1980s, Nancy Reagan used to say, just say no to drugs. What does that mean? Well, she is telling you not to use drugs to say no when somebody offers you drugs or tries to tell you to use drugs. So in effect, she's saying, you ought not to use drugs. That's pretty clear. But now, what does she mean by drugs? Does she mean aspirin? I don't think she's telling you not to use aspirin. Does she mean prescription drugs? I don't think she's telling you not to follow the advice of your doctor and use the prescriptions that the doctor told you to take. So that can't be what she means. Well, maybe she means illegal drugs. Okay, maybe she means illegal drugs. What about heroin or cocaine? Yes, that's what she's telling you not to do. She's definitely telling you not to take illegal drugs. But then there's some things in the middle. She might be telling you not to take dangerous drugs, whether they're illegal or not. What about nicotine? What about alcohol? Those are both dangerous drugs. At least when used to excess alcohol is very dangerous and smoking can lead to lung cancer and that's how most people get nicotine. So maybe she's telling you not to take nicotine or alcohol in addition to illegal drugs like heroin and cocaine. Now it's not clear. So how do we clear it up? Well, you want Nancy Reagan's claim to look as good as possible. Remember, you're always trying to make the argument look as good as possible. And one way to make it look good is to make her claim no more than she has to claim. So she could be claiming in addition to heroin and cocaine you shouldn't take alcohol and nicotine but probably or at least more plausibly she's telling you not to take illegal drugs. So you have to choose between interpreting or saying don't take any illegal drugs and don't take any dangerous drugs. And it seems like the more charitable interpretation that makes her claim look more plausible is don't take any illegal drugs. So we could clarify her claim just say no to drugs by interpreting it to mean you ought not to take any illegal drugs. So in general then the lesson is that when there are options about how to clarify a certain sentence we ought to pick the most charitable option that makes the claim look as good as possible. Here's another example where the un-clarity can be traced to a single word but in this case it's the word that and it's not clear what it refers to. So imagine that someone argues like this. They say she claims that our strategy won't work because the enemy knows our plan but that is a big mistake. What does that refer to? That could refer to that is the word that could refer to that the enemy knows our plan. Someone says that's a mistake. They might be saying it's a mistake to think that the enemy knows our plan but it could refer to the claim that our strategy won't work. They could be saying it's a mistake to think our strategy won't work or they could be saying that the mistake is to think that the enemy knowing our plan is enough to make it not work. They might be saying it's not that it won't work because the enemy knows the plan or here's a fourth possibility. They could be saying that is a mistake to think that she claims that. That's not what she claims. So there's four different ways to interpret this argument and in order to figure out how to interpret it we have to figure out which of those is most likely as an interpretation of what the arguer is trying to say. And that's gonna depend on which one makes the argument look the best. Now in this example it's not clear which interpretation is the best because someone might give that argument in a context where they're saying the mistake is to think she claims that. But in other cases they might be saying that the mistake is to think that the enemy knows our plan. They don't really know our plan. And in other cases they might be claiming that other things are mistaken. So we need to figure out what the person is saying but that can depend on the particular context and it might vary from context to context. These unclarities seem unintentional but sometimes people use unclarity to hide problems with their argument, to try to fool you. So imagine a politician says we need to stop our enemies and stand by our friends so we must remain strong and resolute. Well if somebody starts arguing like that you ought to be asking yourself who do they think our friends are? Who do they think our enemies are? What do they mean stop our enemies? Are they calling for military action? How do they think we ought to stop our enemies? And standing by our friends does that mean we ought to support them no matter what they do? There are lots of questions that you would want to ask to clarify exactly which claim is being made before you accept something like this. Here's another claim that might be made by an opponent of the first politician. We have to help the needy. Well wait a minute, which people are needy? I mean everybody needs something. How needy do you have to be to be needy? And we ought to help the needy, well how are we gonna help them? Does that mean we just give them whatever they want? Or what are we supposed to give them? And when are we supposed to give them and how much are we willing to spend on giving it to them? Politicians on both sides of the political spectrum make vague claims that need to be clarified before you should be willing to endorse one or the other of those claims. If you try to decide what to believe before you know exactly what the claim means, before you've clarified it, you can end up committing yourself to all kinds of nonsense and all kinds of very problematic positions. You can get yourself into a lot of trouble. That's why we need to clarify the terms in arguments. Now, one special way in which premises need to be clarified is that they need to be broken up into smaller parts. Where you can do that? And the point of this is that the smaller parts are gonna be easier to understand and easier to assess for whether they're true or not. So step four, clarify the premises, belongs together with step five, break up the premises into parts. What needs to be broken up? Well, the explicit premises sometimes the conclusion as well. Here's a simple example. That shirt looks great on you and it's on sale. So you ought to buy it. We might put that in standard form like this. That shirt looks great on you and it's on sale is the premise and the conclusion is you ought to buy it. But notice that the premise has two parts joined by an and. So we could break them up and have the first premise, that shirt looks great on you and the second premise, it's on sale and then the conclusion is you ought to buy it. Breaking it up like that is supposed to make it easier to assess the premise for truth or falsehood. Now in this case, it doesn't make it much easier because it was so simple to begin with but we'll see that breaking up premises will really help when we get to more complex examples. So it makes sense to break up premises. Well, at least sometimes we should not break up premises when breaking them up distorts the argument. Here's an example of that. We still need to add either one more cup of white sugar or one more cup of brown sugar to complete the recipe. So we've got to add another cup of ingredients. Now one way to represent that argument would be to say the premise is we still need to add either one more cup of white sugar or one more cup of brown sugar and the conclusion is we have another cup of ingredients to add but we could break it up because it's got parts. We could change the argument into we still need to add one more cup of white sugar. That's the first premise and the second premise is we still need to add one more cup of brown sugar and then the conclusion is we have one more cup of ingredients to add but that argument doesn't make any sense. We got to add one of white and one of brown but you don't just have one more couple of ingredients to add. And as always, we're supposed to be making the argument look good and that change made it look bad. And the problem is that here we broke up the word or because it's one cup of white or one cup of brown and presumably you didn't know which it was or maybe you had a choice between the two but you weren't supposed to add both, that would be too much and the word or signals that. So in general, you should not break up when the word that joins the two is or but it's okay to break up when the word that joins the two is and. You still got to be careful about context it's not always going to work that way but as a general rule, that usually works. Other cases are even trickier. One particularly problematic case is dependent clauses. Here's an example. Nancy finished all her homework because all she had to do was write 25 lines of poetry and she wrote two sonnets which have 14 lines each. The dependent clauses which have 14 lines each and the question is how do we fit that into standard form? Well, here's one step. The first premise can say all she had to do was write 25 lines of poetry and the second premise can be she wrote two sonnets which have 14 lines each and then the conclusion is Nancy finished all her homework. Now the question is can we break up that second premise into two different parts? And it seems like we can. We should be able to represent the argument. So the first premise is all she had to do was write 25 lines of poetry and the second premise says she wrote two sonnets and the third premise says sonnets have 14 lines each and the conclusion is she finished all her homework. In this case, breaking down the premise actually helps us understand and assess it because we can decide whether it's really true for example that sonnets have 14 lines each. That's gonna be a question. If the answer is no, then the argument might fail. The answer is yes, at least for standard sonnets so the argument looks pretty good. Contrast that example with this one. Our legal system isn't fair because authorities go easy on white collar criminals who have been allowed to get away with their crimes in recent years. Well the premise could be authorities go easy on criminals who have been allowed to get away with their crimes in recent years and the conclusion is our legal system isn't fair. Now the question is can we break up that first premise because it has the dependent clause who have been allowed to get away with their crimes in recent years? Well that depends because the person giving the argument might be saying that authorities go easy on all white collar criminals and they might be saying that authorities only go easy on a certain subset of white collar criminals namely the subset that have been allowed to get away with their crimes in recent years. If the premise is about all white collar criminals then we can break it up. So that one premise says authorities go easy on white collar criminals and the next premise says white collar criminals have been allowed to get away with their crimes in recent years. But if the arguer is only talking about some white collar criminals and admits that other white collar criminals have not been allowed to get away with their crime then he's only saying that authorities go easy on those white collar criminals who have been allowed to get away with their crimes. subset of white collar criminals and then it would distort the argument to break it up because if you do break it up then that second premise says white collar criminals have been allowed to get away with their crimes in recent years and if some of them haven't then that premise turns out to be false so if you break it up you can criticize it by pointing out that it doesn't really apply to all white collar criminals but if you leave it as a single premise then it's not subject to that criticism so if you want to be charitable you probably ought to keep this premise together unless you know on independent grounds that the person was making that claim about all white collar criminals and not just a subset so to make that argument look better we don't break up the premise and the general lesson is that with dependent clauses like that and which and who you have to look very carefully to figure out what the speaker wanted to say and what's going to make their argument look best and use that information to determine whether or not to break up the premise there no airtight rules as always so we need to do a few exercises to practice the skill welcome back we've covered stages one through three of argument reconstruction namely close analysis get down to basics and sharpen edges in this lecture we'll cover stage four which is organized parts because it's not enough to isolate the parts and figure out what they are you need to show how they fit together in a structure so that they work together to support the conclusion of the argument to see how this works let's start with an example consider this example that fertilizer won't help the roses bloom because there's already a lot of nitrogen in the soil so the fertilizer will make the nitrogen levels too high of course so is a conclusion marker so one conclusion is that the fertilizer will make the nitrogen levels too high and then you might think that one way to put the argument into standard form goes like this premise one is that fertilizer won't make the roses bloom premise two is the nitrogen levels in the soil are already high and then the conclusion is that the fertilizer will make the nitrogen levels too high but that doesn't really make any sense if you think about it how could the fact that the roses won't bloom be a reason to believe that the nitrogen levels are too high this couldn't be a reason for that so we must have the wrong structure however there's another argument marker this time it's a premise marker because and that indicates that the claim that there's already a lot of nitrogen in the soil is a premise but what's the conclusion for that premise that's supposed to show that the fertilizer won't make the roses bloom so we've missed that part of the structure if we put it in standard form the way we first thought the trick here is that there are really two conclusions one conclusion is that the fertilizer won't help the roses bloom and another conclusion is that the fertilizer will make the nitrogen levels too high but each arguments just supposed to have one conclusion so how are we going to put this into a structure the solution is that there are two arguments one is that the nitrogen levels in the soil are already high therefore adding the fertilizer will make them too high and the second argument is that adding the fertilizer will make the nitrogen levels too high therefore the fertilizer will not make the roses bloom and notice that one argument really bills on the other because the conclusion of the first argument is really a premise in the second argument so we can represent them as two separate arguments but we can also put them together in a chain so that the argument says the nitrogen levels in the soil are already high therefore adding fertilizer will make them too high and therefore adding fertilizer will not help the roses bloom now if we take that whole structure and we try to represent it in a diagram and we represent each premise with a number which is the number that was given it in the standard form then we can simply have premise one with an arrow to premise two indicating that premise one is a reason for premise two and then another arrow going from premise two to premise three to indicate that two is a reason for three in a way we've got two premises and two conclusions because that one claim in the middle number two operates as a conclusion in the first argument and a premise in the second argument but overall I hope the diagram makes it clear why I want to call this a linear structure when you have one premise giving a reason for a conclusion which is then a premise for another conclusion then they form a line when you diagram them in the way that I'm proposing arguments can have other structures too in particular sometimes there's more than one premise associated with a single conclusion and this can happen in two ways the first we're going to call the branching structure and the second we're going to call the joint structure here's an example of the branching structure I'm not going to go to the movie with you because I don't like horror flicks besides I'm too busy the word because is a premise marker so that indicates that the conclusion is that I'm not going to go to the movie with you and there are two premises one is I don't like horror flicks and the other is I'm too busy now you might think that that could just be put in the old linear structure that we already saw but then the argument is going to look like this I don't like horror flicks therefore I'm too busy therefore I'm not going to go to the movie but wait a minute the fact that I don't like horror flicks doesn't mean I'm too busy that's not making sense maybe it's the other way around I'm too busy therefore I don't like horror flicks therefore I'm not going to go to that movie with you that doesn't make any sense either the fact that I'm too busy isn't why I don't like horror flicks the problem is there are two premises here but neither one is a reason for the other as we saw in the linear structure instead in this branching structure each premise is operating independently there's one argument I don't like horror flicks therefore I'm not going to go to that movie with you there's another argument I'm too busy therefore I'm not going to go to that movie with you and each premise by itself is a sufficient reason not to go to the movie with you I just think about it if I wasn't too busy but I didn't like horror flicks I wouldn't go to the movie but if I liked horror flicks but I was too busy I still wouldn't go to the movie so each premise by itself is enough and they operate independently that's what makes this a branching structure instead of a linear structure let's diagram it and you'll see why we call it a branching structure one way to diagram it will be to simply draw an arrow between premise one and the conclusion two and then there's a separate argument so you draw another arrow from one star another premise to conclusion two and that's okay but notice that it doesn't show you that both premises are reasons for the same conclusion so to capture that aspect of the structure that both premise one and premise one star support the same conclusion namely two it's better to diagram it so that there's an arrow that runs independently from both premises to a single instance of conclusion two as you see in the diagram on the screen and that should show you why we're calling it a branching structure because it kind of branches it looks like the branches of a tree okay it doesn't really look like the branches of a tree but you get the idea we're going to call it a branching structure next we have to separate this branching structure from what we're going to call the joint structure the difference is that in the branching structure the premises provide independent support for the conclusion whereas in this joint structure they work together and they're not going to have force independent of each other it's like the joint in your leg which joins together the calf with the thigh and if you didn't have both it wouldn't work very well so we're going to call it a joint structure here's an example for my birthday my wife always gives me either a sweater or a board game this box does not contain a sweater so this time she must have given me a board game now notice that the argument marker so indicates that the conclusion is this time she must have given me a board game and it's got two premises and you might think that they got a linear structure and the argument goes something like this my wife always gives me either a sweater or a board game therefore this box does not contain a sweater therefore this time she gave me a board game that doesn't make any sense right I mean the fact that she always gives me either a sweater or board game is no reason to believe that this box doesn't contain a sweater well okay let's try it again maybe it's a branching structure that would mean that the argument looks like this my wife always gives me either a sweater or a board game therefore this time she gave me a board game and as a separate argument this box does not contain a sweater therefore this time she must have given me a board game neither of those arguments makes any sense so it can't be a branching structure instead what we have here is the two premises working together she always gives me either a sweater or board game and the second premise this box does not contain a sweater those two premises have to work together it's only jointly working together that they can support the conclusion that this time she must have given me a board game how can we diagram this joint structure we can put a plus sign between premise one and premise two then draw a line under them to show that they work together jointly and take a line from that line and draw an arrow down to the conclusion just like in the diagram and this is what we're going to call the joint structure so we've seen the linear structure the branching structure and the joint structure and we can combine more than one of these structures into a single argument to see how to do this let's just do a slight variation on the previous example my wife always gives me either a sweater or a board game this box does not contain the sweater because it rattles when I shake it so this time she must have given me a board game this argument combines a linear structure with a joint structure there are two argument markers once a conclusion marker so and that indicates that the eventual conclusion is that she must have given me a board game this time there's also that new word because which indicates that the fact that it rattles when I shake it means that it's not a sweater so the first stage of the argument in standard form looks like this premise one this box rattles when I shake it therefore conclusion this box does not contain a sweater stage two says this box does not contain a sweater my life always gives me either a sweater or a board game so the conclusion this time she must have given me a board game and of course the conclusion of that first little argument is identical with the premise of the second argument so we can put them together into a chain we can say this box rattles when I shake it so it must not contain a sweater my wife always gives me a sweater or a board game so this time she must have given me a board game that's how we get a linear structure combined with a joint structure and we can use our diagram methods to diagram this argument the same way we did before we simply start with premise one the box rattles when I shake it draw an arrow down to its conclusion namely the box does not contain a sweater that's two and then we show that those are joint by adding a plus premise three namely my wife always gives me either a sweater or a board game draw a line under them and an arrow from those two together down to the eventual conclusion namely four that this time she must have given me a board game the fact that the top arrow goes from premise one to two but does not go from premise one to three indicates that that premise is a reason for two but is not a reason for three so when you use this method to diagram arguments you have to be careful where you draw the arrows and draw them only where there really is a rational connection that is where one claim is being presented as a reason for that particular claim that the arrows pointing towards almost all arguments can be diagram using these three simple structures that is the linear structure the branching structure the joint structure and some combination of those three you can add more premises because you can always add one plus two plus three plus four if there are four premises operating together in a joint structure and you can add extra arrows if you have a branch with more than two branches so you can cover a lot of arguments using these kinds of diagrams the method can be described in general like this you start by identifying the premises and the conclusions and you number them so that you can just have numbers instead of having to write out the whole sentence on the diagram then when they work together you put a plus sign between them and draw a line under it to indicate that they're working together they're functioning as a group then you draw an arrow from the claims that are reasons to the claims that they are reasons for and then you move them around on the diagram so that they'll form a line when it's a linear structure and branches when it's a branching structure it'll be easy to rearrange them so as to show how all of the different premises and conclusions work together in a single argumentative structure that's going to be enough to accomplish this stage of reconstruction namely to organize the parts and show how they work together in the overall argument it's been a long winding road as the Beatles used to say but we're finally at the last stages of reconstructing arguments we've looked at stage one which is close analysis stage two which is get down to basics stage three which is sharpened edges stage four is organized parts and now we're doing stage five which is fill in gaps and we'll also get to stage six which is conclude stage five really consists of four separate steps first we need to assess the argument for validity then we need to add suppressed premises enough of them to make it valid then we need to assess those suppressed premises for truth or falsehood and then we need to qualify the suppressed premises in order to make them true and the whole goal is to make the suppressed premises both plausible for their truth and enough to make the argument valid so these steps within the stage really do work in tandem together to try to make the argument good we already learned how to assess validity you simply ask is it possible for the premises to be true and the conclusion false and if so the argument is not valid and if not the argument is valid and the way you figure out whether it's possible is you try to tell a story or describe a situation and if you can describe a coherent situation where the premises are true and the conclusion is false then that shows that the argument is not really valid the main topic for today is what do you do when you assess the argument for validity and you find out it's not valid and the answer is you add suppressed premises enough of them to make the argument valid now that might seem like cheating I mean you start with an argument that's no good it's not valid and then you just throw in some extra premises in order to make it valid why isn't that just distorting the argument and making up something that wasn't there the answer is that it's not really bad and if it were bad we'd all be in bad shape because in everyday life people always take things for granted they make assumptions we do it too and if we didn't boy our arguments would be really long and boring so there's something to be said in favor of suppressing premises at least the obvious ones that people really do take for granted but we can also get tricked people can suppress premises that really are questionable and they just don't want us to see that they're making that assumption it's useful to fill out the argument with suppressed premises to make sure it really is valid because that brings those assumptions out of the open where we can assess whether or not they're true or false another reason to fill in suppressed premises is to understand the argument better because if people suppress premises then they're showing us some of their footprints along the path but if we really want to know the full path that their reasoning followed we've got to see every single footprint so the goal of bringing up the suppressed premises is to let us trace exactly where their reasoning went from one step to another so there are two goals one is to trace the full path every step and the other goal is to see if there any missteps or they're trying to hide something from us by getting rid of one of their footsteps so that's the point of bringing out suppressed premises to accomplish these goals is tricky you have to find suppressed premises that are just strong enough to make the argument valid but not so strong that they're going to be implausible because you don't want to ascribe all kinds of suppressed premises to the person that they didn't really believe and they didn't really need for their argument so it's kind of like Goldilocks and the three bears you want suppressed premises to be not too hot and not too cold but just right here's an example from a previous lecture my wife always gives me either a sweater or a board game this box does not contain a sweater because it rattles when it's shaken so this time she must have given me a board game and we put this in standard form this way first premise this box rattles when I shake it and that shows you it doesn't contain a sweater third she always gives me either a sweater or a board game conclusion this time she must have given me a board game now the first step of this argument is this box rattles when I shake it and the conclusion there is it doesn't contain a sweater that's the part of the argument that we want to focus on here and ask whether that argument is valid no the argument's not valid because it's possible for the premise to be true and the conclusion false how can that happen well my wife might be fooling me she might know that I expect either a sweater or a board game so she puts a sweater in the box and then she put little rocks around the outside so when I shake it I'll hear something so that's possible and that shows that the argument's not valid well how can we make the argument valid question here is can we add a suppressed premise that'll turn this invalid argument into a valid argument here's one that'll do the trick a box that contains a sweater doesn't rattle when shaken now the argument looks like this this box rattles when I shake it box that contains a sweater doesn't rattle when shaken so this box doesn't contain a sweater the explicit premise is that this box rattles when I shake it the suppressed premise is that a box that contains a sweater doesn't rattle when shaken and together they're supposed to support the conclusion that this box doesn't contain a sweater but do they really support that conclusion is the argument valid well it's valid only if there's no possibility that the premises are true and the conclusion is false without the suppressed premise we saw that was possible because my wife might be fooling me and putting rocks around the sweater so let's see if that's going to ruin the validity of this argument no because if the sweaters got rocks around it so it makes noise when I shake it then the premise that says a box that contains a sweater doesn't rattle when shaken turns out to be false so that's not a case where the premises are true and the conclusions false because the premises false in that case so by adding this premise we actually succeeded in making the argument valid the problem of course is that validity is not enough for a good argument as we saw several lectures ago you can have a valid argument that's very bad when the arguments not sound what we want really is soundness so that's why we need the next step namely check these suppressed premises for truth assess whether they're true or false and if they're not true then you need to qualify them in order to make them true because you don't want to claim that the person giving the argument was assuming this falsehood when they didn't have to so let's see if there's some way to qualify this suppressed premise in order to make it true how can we qualify this premise to make it true oh what about that little word only we could add that we could say a box that contains only a sweater doesn't rattle when shaking but the word only what exactly does that mean we need to clarify that what exactly is the word only exclude it excludes something that's the function of the word only but what does it exclude well it probably excludes other things that might make the rattling sound like if my wife put rocks in the box so we can clarify this premise by saying a box that contains only a sweater and not anything else that might make a rattling sound when shaken won't rattle when shaking well is that premise true you might quibble about details but it's close enough for now what we need to do though is to go back and determine whether when we put that suppressed premise in the arguments valid and the argument now looks like this this box does rattle when shaken and a box doesn't rattle when shaken if it contains only a sweater and not anything else that makes a rattling sound so this box doesn't contain a sweater is that valid well no for the same reason we saw before because my wife might be a trickster who puts rocks around my sweater in the birthday present box in order to fool me then the premises can be true and the conclusion false it's possible that the first premise is true this box rattles when I shake it the second premise is true a box doesn't rattle when shaken if it contains only a sweater and nothing else that makes a rattling sound but it's false that this box doesn't contain a sweater because it still does contain a sweater and it contains a sweater in addition to those pesky little rocks that make all that rattling noise well if the arguments not valid we got to go back to that other step and add another suppressed premise remember how I told you that these different steps within this stage work in tandem and what's happening is you got to check it for validity add a suppressed premise recheck it for validity maybe add another suppressed premise and that's what we're doing now so what kind of suppressed premise can we add well we could add my wife's not a trickster but basically that amounts to she wouldn't put rocks in a birthday present with a sweater in order to fool me so we can make that a little more explicit by making the suppressed premise something like this if this box contains a sweater then it contains only a sweater and it doesn't include anything else that would make a rattling sound when shaking and now we can stick that as an extra suppressed premise into the argument now the argument looks like this this box rattles when I shake it a box doesn't rattle when shaken if it contains only a sweater and not anything else that makes a rattling noise when shaken if this box contains a sweater then it contains only a sweater and doesn't contain anything else that rattles when shaken so this box does not contain a sweater now we have an argument that's valid and the suppressed premises are true at least given my wife's not a trickster which she's not I assure you and it looks like we have a sound reconstruction just what we were looking for admittedly this argument is a lot longer and more convoluted than the original and that shows why people suppress premises instead of talking the way this argument goes and of course many people would be perfectly well convinced by the original argument because they share the assumptions that are in the suppressed premises so why do we go to all the trouble to go through this process and add the suppressed premises remember the reason is that we want to understand the pathway between the premises and conclusion we want to understand how the reasoning works step by step by step and we want to do that because sometimes people are going to include suppressed premises that aren't true and we want to bring them out and make those assumptions explicit so that we can assess them for truth and falsehood and when you're talking to somebody you trust you might not have to do that and it's okay to suppress premises but when you really want to know whether the argument is any good that's when you want to fill it out with the suppressed premises the point of going into detail on this example is to illustrate this stage of reconstruction you want to assess the argument for validity and suppressed premises that make it valid check them for truth if they're not true you qualify them then you go back and see whether that qualification made the argument not valid anymore and you go back and forth and back and forth until you've got a sound reconstruction the same steps are going to apply to all kinds of suppressed premises and sure enough there are all kinds of suppressed premises so let's go through a few examples a lot more quickly in order to show the variety of suppressed premises that are assumed in arguments here's one example Abraham Lincoln turned 40 on February 12 1849 therefore Charles Darwin also turned 40 on February 12 1849 is that argument valid no chance of course it's possible for the premise to be true and the conclusion false so we have to add a suppressed premise the suppressed premise is that Abraham Lincoln and Charles Darwin were born on the same day and they were it happened to be February 12 1809 so now we filled out the argument Abraham Lincoln turned 40 on February 12 1849 Abraham Lincoln and Charles Darwin were born on the same day therefore Charles Darwin also turned 40 on February 12 1849 now is the argument valid no still not valid because Darwin might have died before 1849 so we have to add another suppressed premise namely that both Abraham Lincoln and Charles Darwin live beyond 40 so now we have a fuller argument Abraham Lincoln turned 40 on February 12 1849 Abraham Lincoln and Charles Darwin were born on the same day both of them live beyond the age of 40 therefore Charles Darwin also turned 40 on February 12 1849 now the argument looks pretty good we had to add two suppressed premises but we finally have a valid argument and what this shows is that sometimes the suppressed premises are purely factual matters in this case that they were born on the same day and that they both live beyond 40 so sometimes we have factual suppressed premises here's another quick example you ought to obey her because she's your mother here the premise is that she's your mother and the conclusions you ought to obey her well is that argument valid no way because it's possible that she's your mother but it's false that you ought to obey her when could that happen maybe she was like abusive or stupid or whatever then maybe you ought not to obey her even though she is your mother so we have to add a premise namely you ought to obey your mother now we can say she's your mother you ought to obey your mother therefore you ought to obey her but of course that suppressed premise you ought to obey your mother it's questionable because maybe she was abusive or stupid so let's add another suppressed premise that your mother was not abusive or stupid of course we also have to qualify that moral premise that you ought to obey your mother if she's not abusive or stupid and now the argument looks like this she's your mother you ought to obey your mother if she's not abusive or stupid your Your mother was not abusive or stupid, therefore you ought to obey her. Notice that here we added a moral premise about the fact that you ought to obey your mother under certain conditions, namely she's not abusive or stupid. And the second premise is she was not abusive or stupid. So we have a moral premise and a factual premise both being suppressed in the argument that you ought to obey her because she's your mother. Here's another. It's the Sabbath, so you ought to go to synagogue. Well, that's clearly not valid. One suppressed premise is you're Jewish. The other suppressed premise is you haven't been a synagogue already today on this Sabbath. And the third suppressed premise is a religious norm, namely Jews ought to go to the synagogue on the Sabbath. And you need that whole bunch of suppressed premises in order to get from the premise that it's the Sabbath to the conclusion that you ought to go to synagogue. Now, of course, all of those premises might be questionable. Some people would question them. Some people would deny them. But the point here is to figure out what's being assumed by somebody who gave the original argument. And anybody who says it's the Sabbath so you ought to go to synagogue seems to be assuming that you're Jewish, you haven't been already, and Jews ought to go to the synagogue on the Sabbath. So what these suppressed premises do is they bring out the assumptions that somebody who gave that argument must have had in mind. The last case is a little bit trickier. It has to do with linguistic suppressed premises. Janet and Bob are first cousins. Therefore, they share a grandparent. Now, in order to understand that argument, you have to know that first cousins always share a grandparent. That just follows from the definition of what a first cousin is. But it's not quite so obvious as that all biological sisters are female. And so there's even more need to bring out that linguistic suppressed premise in this case. But it's still not necessary to make the argument valid. It's just not possible that Janet and Bob are first cousins and they don't share a grandparent because the suppressed premise is purely linguistic. So it's necessarily true. So you can't possibly be first cousins without sharing a grandparent. Still, the point of bringing out linguistic suppressed premises is to show every little step along the way. The argument might be valid without those suppressed linguistic premises, but we won't understand why it's valid and why the reasoning goes through unless we add the linguistic suppressed premise. So it's worth doing that. Here's a trick. Don't kill anybody, OK? It's just between me and you. You can always make any argument valid just by adding a suppressed premise that says, if the premises are true, then the conclusion is true. But don't tell anybody because if people start doing that and they make the argument valid that way with that suppressed premise, we're never going to understand the pathway of reasoning. It makes the argument valid, but it doesn't serve the real purpose of adding suppressed premises, which is to understand the pathway of reasoning. So you can do that. It's a trick. It makes the argument valid, but it doesn't achieve our goal. Because our goal is not just to make the argument valid. It's to make the argument valid so that we can understand the pathway of reasoning. So it's important to know that trick, but don't use it unless you have to. The examples so far have been pretty trivial. I admit it. But the same points apply in very important context, such as political debates. Politicians can suppress premises in perfectly legitimate ways. They're just trying to save time and make their arguments more efficient, maybe even sometimes clearer, because you don't have to add all of those little details. But sometimes politicians abuse suppressed premises. They take things for granted that they shouldn't be taking for granted. And here's an example. A politician might argue, my opponent is soft on crime because he's opposed to the death penalty. Well, that assumes, as a suppressed premise, that anyone who's opposed to the death penalty must be soft on crime. And if the politician were to come out and say that, it would seem pretty questionable. And that's probably why he suppresses it. And then another politician might say, but my opponent is in favor of the death penalty, so he must not have read all the recent studies that show that the death penalty doesn't deter. Well, that argument assumes a suppressed premise that if you read those studies, you'd be convinced by them. And that the only point of the death penalty is deterrence. But the point is that politicians talking about extremely important issues can take things for granted that if they were brought into the light of day would be very questionable. And that's why they hide them. So when you're listening to people give arguments on important issues in your life, then you ought to be looking for these suppressed premises and asking yourself whether or not you really ought to be agreeing with them about that assumption. Finally, we've finished Reconstruction. Yippee, right? Oh, no, not quite, because there's one more stage. And that stage is drawing a conclusion. Of course, if we've come up with a sound Reconstruction, then we know that the argument's sound and we know that the conclusion is true, because every sound argument has a true conclusion. But if we don't come up with a sound Reconstruction, then what do we say? Well, we kind of ask, whose fault is it? It might be the fault of the argument. Maybe we couldn't come up with a sound Reconstruction, because there just is no sound Reconstruction. But maybe we didn't come up with a sound Reconstruction, because we just weren't imaginative enough or didn't try hard enough. Still, if we try really long and hard and charitably interpret the argument as best we can to make it look as good as we can, and we still can't make it sound, then we've at least got reason to believe that the argument's not sound. Of course, that doesn't mean that the conclusion's not true, because unsound arguments can still have true conclusions. But at least we know that this argument doesn't prove that the conclusion's true. And so this method of Reconstruction can lead us either to the belief that the argument is sound because we found a sound Reconstruction or to the conclusion that the argument's not sound because we tried long and hard to find a sound Reconstruction that didn't, but that's still not gonna show us that the conclusion of the argument is false. The point of Reconstruction then is to reach a conclusion on this issue of whether the argument's sound or not, and if we try our best and do it as well as we can and charitably, then we can be justified believing that the argument's sound or not. Now we've really done it. We're finished with Reconstruction, hooray! But we wanna go through it one more time in a detailed example to show how all the different stages fit together. And which example are we gonna pick? Well, if you've been in the course this far, I bet you can guess Robert Redford again. We're gonna look at paragraph three of his article and go through Reconstruction to show that Reconstruction gives you an even deeper understanding than when we first went through it using close analysis alone. Reconstruction begins with close analysis, so the first thing I'll do is read through the passage and mark the important words in order to do a close analysis of Redford's paragraph. The BLM says it's hands are tied. Remember, the BLM is the Bureau of Land Management. Why? Because, because is a premise marker. It's indicating that the sentence after it is a premise for the conclusion that the BLM's hands are tied. Because these lands were set aside subject to valid existing rights, you could say that valid and rights are evaluative terms, but that's not gonna matter to our analysis here. And Conoco has a lease that gives it the right to drill. And notice we've got a tricky argument marker here. Gives it. Because the point of that sentence is that it's the lease that explains why it has the right to drill or justifies the claim that it does have the right to drill. So gives it is an argument marker and in particular it has the right to drill as the conclusion, so it's a conclusion marker. Sure, Conoco has a lease. Sure is going to be an assuring term. More than one, in fact. In fact is another assuring term. But, but is going to be a discounting term indicating that there's an objection being responded to. Those leases were originally issued without sufficient environmental study or public input. Now you could think that originally is a guarding term because it's not saying that there never was sufficient environmental input. That is environmental study or public input. It might have come later just not originally, but again that's not going to play any part in the argument itself. So it could be a guarding term but you can mark it if you want. But as a result, the first three words of the next sentence, that's clearly an argument marker and it's indicating that the sentence after it is a conclusion, so it's a conclusion marker. None of them convey the valid right to drill. What's more, now we're indicating there's a separate argument, there's a new premise coming, another reason for the same conclusion in deciding to issue a permit to drill right now, the BLM did not conduct a full analysis of the environmental impacts of drilling in these incomparable lands, but discounting, right? Instead determined that there would be no significant environmental harm on the basis of, this is telling you how they reached that determination, was an abbreviated review, they had an abbreviated review that justified or explained their determination, so that's a premise marker. It didn't even look, even as a tricky one, it's discounting an objection. It's saying, well they looked a little bit, but they didn't look at this. Discounting the objection that they did look at least some. They didn't even look at drilling on the other federal leases, okay? Sounds like, clearly a guarding term, it's not saying it is, but it sounds like Washington double speak. Double speak is bad, you don't wanna double speak. To me, and maybe to me is another guarding term in the sense that it sounds that way to me, but not to others, so we could mark that as a guard as well. So, we have finished stage one of reconstructing this argument, we've done a close analysis. The next stage is to get rid of all the excess verbiage. So we'll start a new screen and do that. The BLM says its hands are tied, well, the claim is that its hands are tied, so we can get rid of the fact that the BLM says that. Why? Because we can get rid of those words because they're gonna get replaced by a dot pyramid in standard form. These lands were set aside subject to valid existing rights, good. And Conoco has a lease that gives it the right to drill, good, and we can get rid of because we're gonna have two separate premises there. That gives it, right? Well, that's gonna be an argument marker as we saw that's gonna get replaced by another dot pyramid. Sure, Conoco has a lease, more than one in fact. Now, notice there, Redford is admitting what his opponent claims, but that's not gonna be part of his argument. He's just saying, I recognize that. His argument's gonna be based on different claims so we can get rid of, sure, Conoco has a lease, more than one in fact, and the but tells you that he's just answering an objection. These leases were originally issued without sufficient environmental study or input, that's gonna be an important premise. As a result, we saw that was an argument marker gonna be replaced by a dot pyramid like the others. None of them conveyed a valid right to drill. What's more, another argument marker, so it's gonna get replaced by a dot pyramid. In deciding to issue a permit to drill now, the BLM did not conduct a full analysis, blah, blah, but instead, that's gonna be discounting terms and that's gonna be important for understanding what the sentences are doing, but it's not gonna get repeated in the premise when we put it in standard form. They determined there'd be no significant impact on the basis of an abbreviated review that didn't even look at drilling on the other federal leases. The next step is to take all the parts that weren't crossed out. They're gonna be the explicit premises and conclusion in the argument and put them into standard form. And if you think about this paragraph, there are really two arguments because at the start, what Redford tries to do is to state what the BLM's argument was to begin with and then he gives his own argument against what the BLM says. So, BLM's argument can be put in standard form like this. First premise, Conoco has a lease that gives it the right to drill. Second premise, these lands were set aside subject to valid existing rights. And those two premises lead to the conclusion that the BLM's hands are tied. Now that's the BLM's argument that Redford is arguing against. Redford's own argument on the other side starts with the premise, those leases were originally issued without sufficient environmental study or public input, second premise. In deciding to issue a permit to drill now, the BLM did not conduct a full analysis of the environmental impacts of drilling on these incomparable lands, but instead determined there would be no significant environmental harm on the basis of an abbreviated review that didn't even look at drilling on other federal leases. Those two premises lead to the conclusion that none of these conveyed a valid right to drill. And then there's another premise. These lands were set aside subject to valid existing rights. And that's supposed to leave the conclusion, this is Washington Doublespeak. Well, we'll have to see what all that means when we clarify, but that's basically the standard form. It might be a good idea to double check because you wanna make sure that every sentence you didn't cross out is somewhere there in the standard form. So let's look back at the passage where we crossed out the excess and make sure everything's there in the standard form. Okay, it's all there. The next stage is to sharpen edges and that means clarify the premises and break them up where doing so would help understand what they're really claiming. So let's look first at the BLM's argument, which simply says Conoco has a lease, these lands were set aside subject to valid rights, therefore it's hands are tied. We gotta clarify, first of all, the conclusion, it's hands are tied. What does that mean? Well, basically the BLM is claiming I can't do anything about Conoco. You know, my hands are tied. Don't hold me responsible, there's nothing I can do. Okay, they're offering an excuse. Next, premise two, these lands were set aside subject to valid existing rights. Well, what does set aside mean? It means that you're not allowed to drill there, but subject to valid existing rights means that you are allowed to drill there if you've got a valid existing right. So this premise can be restated as saying that if Conoco does have a valid existing right to drill, then the BLM must allow Conoco to drill. Okay, what about breaking up premises? What about premise one? Well, that's one that I think we're gonna have to break up because it says that Conoco has a lease that gives it the right to drill and gives it, we already marked as an argument marker, which suggests that the fact that Conoco has a lease is supposed to be a reason why it has a right to drill. So there's an argument implicit in that one sentence. And that means that we can take this whole argument and restate it something like this. Conoco has a lease. Therefore Conoco has a valid right to drill. If Conoco has a valid right to drill, then the BLM must allow Conoco to drill. Therefore the BLM must allow Conoco to drill. That is supposed to be the central force of the explicit premises and conclusions in the first part where the BLM gives its argument. The next part is Redford's response to this argument. Let's start with Redford's conclusion. What's he trying to show? He's trying to show the opposite of the BLM's argument. They're trying to show that they're hands are tied. That is that they can't stop Conoco from drilling. So Redford wants to show that they can stop Conoco from drilling or even that they must stop Conoco from drilling. So that's the conclusion he's trying to reach. What he says is, sounds like Washington double speak to me. Well, that's cause he's saying that people in Washington always say their hands are tied and can't get anything done. And he's gonna argue that their hands aren't tied because they can and must stop Conoco from drilling. So we can replace the conclusion simply with the claim that the BLM must stop Conoco from drilling. Now we know how the argument ends. So let's take those premises and conclusion and number them pretty high so that we can leave some room for the other premises that come before them. The next thing we need to do is to get an argument for that central premise, Conoco does not have any valid right to drill. Well, here's what Redford said that the leases were originally issued without sufficient environmental study or public input. And in deciding to issue a permit now, the BLM didn't conduct a full analysis. Notice that there are two parts to these claims. One is about the leases and the other is about the permit because in order to have a valid right to drill, Conoco needs to have a lease and a permit. Redford argues that there are problems with both the lease and the permit but the considerations are a little different so we need to separate those two parts into different arguments. The first part of this argument concerns the leases. He says that the leases were originally issued without sufficient environmental study or public input. Therefore, none of the leases conveyed a valid right to drill. Then the second part has to do with the permit. In deciding to issue a permit to drill now, the BLM did not conduct a full analysis. Therefore, none of the permits conveyed a valid right to drill. And the idea of the argument is gonna be that the leases don't give them a right and the permits don't give them a right so they ain't got no right. Wow, but that premise and the argument to show that the permit's not valid is a long premise with lots of different parts so we need to break it up. And we can figure out how to break it up by looking at the argument markers in the part of the passage that in effect constitute that premise. We know that there's a premise marker at the beginning, once more, a discounting term, but on the basis of is an argument marker, even is a discounting term. And that breaks that long premise into part so we can break them into A, the BLM did not conduct a full analysis of the environmental impacts of drilling on these incomparable lands. No full analysis. B, the BLM determined that there would be no significant environmental harm. C, the BLM conducted only an abbreviated review of the environmental harm. And D, the BLM didn't even look at drilling on other federal leases. What about B, the BLM determined there would be no significant environmental impact? Well that's what Renford opposes so that's not gonna be part of his argument. How do the other three claims fit together? Which is a reason for which? Well now we're into a different step, namely, organize the parts. And it's not completely clear, but it seems like Renford has two separate complaints. One is that the BLM did not look sufficiently hard at the environmental impact at this particular site, the Kupairowitz Plateau. The other complaint is that they didn't do a comparative analysis and look at other leases on other federal lands to see what happens when drilling was allowed there and when permits were issued in those other circumstances. So one claim is about this particular site and the other claim is a lack of comparison to other sites. These two points become even clearer in the next paragraph if you remember that. There he said, first, I've spent considerable time in these extraordinary lands for years and I know that an oil rig in their midst would have a major impact. So there he's talking about the impact on this particular site on these particular lands. The right after that he says, what's more? Indicating it's a separate argument, what's more? Conoco wants to drill a well to find oil. Inevitably more rigs, more roads, new pipelines, toxic waste and bright lights would follow to get the oil out. There he seems to be suggesting if you had just looked over at the other leases you'd find that when you allow oil drilling a lot more happens than you ever expected to begin with. I'm of course not agreeing with this. It might be true or it might not. My point is that this is the structure of Redford's own claims that make up his own argument. So there are two separate ways in which the review failed to be full. The first is that the BLM conducted only an abbreviated review in the sense that they didn't look carefully at this particular site itself. And the second is that the BLM didn't look at drilling at other places. Therefore the conclusion is the BLM did not conduct a full analysis. That seems to be what Redford's saying in this particular sentence. Now let's bring it all together and clean it up a little bit in the process. One, all of Conoco's leases were originally issued without sufficient environmental study or public input. That's supposed to support two, none of Conoco's leases give it a valid right to drill. Then three, the BLM conducted an abbreviated review. They didn't look as carefully as they should have at the lands. Four, the BLM didn't look at drilling on lands under the other federal leases, the comparative claim. And those two are supposed to support five. The BLM did not conduct a full analysis. And what that's supposed to show is that six, its permit does not give Conoco a valid right to drill. There are four, seven, which is supposed to follow from two and six. Conoco does not have a valid right to drill. Eight, if Conoco does not have a valid right to drill, then the BLM must not allow Conoco to drill. Therefore, the BLM must not allow Conoco to drill. Make sense? Seem fair? I hope so. I think it's a pretty good reconstruction of what Redford had in mind. As you probably noticed already, these arguments are not valid yet. So we need to go to the next stage and fill in the gaps with suppressed premises. Let's do that now. Let's start with the BLM's argument. Is the argument from one to two valid? Is it possible that Conoco has a lease but it doesn't have a valid right to drill? Well, sure. And so that argument's not valid. What do we need to add to make it valid? Well, we can add a very simple suppressed premise. If Conoco does have a lease, then it has a valid right to drill. If we add that to that premise that they do have a lease, then it'll be a valid argument to the conclusion that they have a valid right to drill. Next, is the argument from two and three to four valid? Yes, because it's not possible that Conoco has a valid right to drill. And also, if they have a valid right to drill, then the BLM must allow them to drill. And it not be true that the BLM must allow them to drill. So we can take this part of the argument, which is really the BLM's argument, but it's in Redford's passage, and reconstruct it like this. Conoco has a lease. If they have a lease, then they have a valid right to drill. So they have a valid right to drill. And if they have a valid right to drill, then the BLM has to allow them to drill. So the BLM has to allow them to drill. Now we're ready for Redford's own argument. His goal is to refute the premise that we had to add to the BLM argument in order to make that argument valid. In the previous lecture we saw that a lot of people suppress premises that are questionable. And Redford wants to show how questionable this one is. He's not gonna let them get away with that old trick. Starting with one and two, is the argument from one to two valid? No, because it's possible that the premise is true and the conclusion false. So what do we need to add to make it valid? Well, we need to add a suppressed premise. And that suppressed premise basically says, no lease that is made without sufficient environmental study and public input is valid, or conveys a valid right to drill. Then we have a valid argument from that premise plus one to the conclusion two that none of Conoco's leases give it a valid right to drill. Next comes the step from three and four to five. Is that valid? No, three and four say that they conducted an abbreviated review and they didn't look at drilling on lands and other federal leases, but those might be true. And it's still not be true that they didn't conduct a full analysis. To explain how you get five out of three and four, we have to add another suppressed premise. And that premise can simply say an analysis is not full if it's abbreviated and if it doesn't look at drilling on lands and other federal leases. Notice that I use the word and instead of or in the suppressed premise. And the reason is that I wanna make Redford's argument look as good as possible. And his premise is gonna be more defensible if he uses and instead of or. Because with and, the premise means that the review is not full if it has both of those problems. Whereas if you have or, it says that the review is not full if it has either one or the other of those problems. And some people might say, have it's only got one of those problems. It's still a full review. You know, it's a little problem. It's a little flaw. But if it's got both of those problems, then Redford's on stronger ground in saying, together they show that that's not a full review. So if I wanna make his premise look good and that's part of the point, then I wanna use and in the suppressed premise here instead of or. What about the step from five to six? Is that valid? No, here we need a suppressed premise too. Which one? Well, we could just add that if the BLM did not conduct a full analysis of the environmental impact, then the permit does not give the permit holder a valid right to drill. Because the process by which they obtain the permit is not a proper process. Next, what about the move from two and six to seven? Two says that Conoco doesn't have a lease that gives it a valid right to drill. And six says that Conoco doesn't have a permit that gives it a valid right to drill. Is it possible that both of those are true and yet the conclusion's false and Conoco does have a valid right to drill? Well, yeah, if there were some other way for it to get a valid right to drill. So to make that argument valid, we have to add another suppressed premise which says basically, you know, if the lease and the permit don't give it a valid right to drill, it ain't got none. More formally and more stilted. We can add a suppressed premise that says if none of Conoco's leases gives it a valid right to drill and Conoco's permit does not give Conoco a valid right to drill, then Conoco does not have a valid right to drill. And that should make that step of the argument valid. There's only one left. The step from seven and eight to nine. Is that valid? Yeah, it's not possible that Conoco doesn't have a valid right to drill. And if they don't have a valid right to drill, then the BLM must not allow them to drill. And not be true that the BLM must not allow Conoco to drill. So that's valid. And we don't have to add any suppressed premise to that one. And now we can take all these different explicit premises and conclusions and put them together with the suppressed premises that we just talked about. And we end up with this final reconstruction. One, all of Conoco's leases were originally issued without sufficient environmental study or public input. Two, no leases that were originally issued without sufficient environmental study or public input give the leaseholder a valid right to drill. Therefore, none of Conoco's leases give it a valid right to drill. Four, the BLM conducted an abbreviated review. Five, the BLM didn't look at drilling on lands under other federal leases. Six, an analysis is not full if it's abbreviated and it does not look at drilling on lands under other federal leases. Therefore, seven, the BLM did not conduct a full analysis of the environmental impacts of drilling on these incomparable lands. Eight, if the BLM does not conduct a full analysis of the environmental impacts of drilling in these incomparable lands before issuing a permit, then that permit does not give the permit holder a valid right to drill. Therefore, nine, Conoco's permit does not give Conoco a valid right to drill. Ten, if none of Conoco's leases gives it a valid right to drill and Conoco's permit does not give Conoco a valid right to drill, then Conoco does not have a valid right to drill. Therefore, 11, Conoco does not have a valid right to drill. 12. If conico does not have a valid right to drill, then the BLM must not allow conico to drill. Therefore, 13. The BLM must not allow conico to drill. Of course, other reconstructions could be perfectly fine, even if they differ in a few details, because not every step in this process is purely mechanical. So it doesn't always yield exactly the same results every time. But I hope that this reconstruction seems plausible as a guess at what was going on in Redford's mind and the reasons that he had for thinking that the BLM should stop the drilling. If we want, we can check to make sure this structure makes sense by trying to diagram it. So here's a diagram that I made of the structure of the argument that I just reconstructed. To the left you see one plus two and an underline under it saying that those premises work together in a joint structure and an arrow to the conclusion from those two premises, namely three. Then to the right of that you see that four, five, and six are joined, four plus five plus six in an underline, with an arrow to seven, because that's the conclusion that those three premises support. Seven plus eight is then underline to show they work jointly to lead to the conclusion nine, so there's an arrow to nine. And then there's a long underline between three, nine, and ten, that other suppressed premise that was added. That shows that three, nine, and ten work together jointly and lead to the conclusion eleven. And then eleven works together with twelve, so you have eleven plus twelve and that's underline with an arrow to thirteen. Now the fact that we can draw this diagram confirms that the argument structure makes sense. Now let's see whether you can do it yourself in the exercises. Welcome to the second unit of our course. In the first unit of the course, you learned how to listen to what someone was saying or read what they wrote and separate out the arguments that they were giving from the rest of their words. You learned what arguments are, what their parts are, and how those parts work together to achieve the various purposes of argument. Now in this second unit of the course, in the third unit that follows it, you'll learn some rules for evaluating the success of arguments. In particular in the second unit of the course, we'll focus on rules for evaluating the validity of deductive arguments and then in the third unit of the course, we'll focus on rules for evaluating the strength of inductive arguments. Recall that deductive arguments are arguments that are presented as being valid and they're successful only if they're valid. Inductive arguments in contrast are arguments that are not presented as being valid. They're presented as being strong and they're successful only to the extent that they are strong. Okay, now since in the second unit of the course, we're focusing on rules for evaluating the validity of deductive arguments, let me say a bit more now about validity and about the rules for assessing validity. See, I just got a new pet clownfish, NIMO. Now, maybe you don't know much about clownfish anatomy, but I'm going to try to persuade you right now that clownfish have gills. Here's an argument that I could give you for the conclusion that clownfish have gills. Well, catfish have gills, goldfish have gills, and sharks have gills. Therefore, clownfish have gills. Now, is that argument valid? No, it's not. It's not valid because it's possible for the premises to be true even when the conclusion is false. It could be that catfish and sharks and goldfish all have gills, even though clownfish don't. But now suppose I give you a different argument for the conclusion that clownfish have gills. Here's how this different argument goes. All fish have gills. Clownfish are a kind of fish. Therefore, clownfish have gills. Now, that argument is valid. There's no possible way for the premises of that argument to be true if the conclusion is false. Recall that in the first unit of the course, Walter defined validity as follows. He said, an argument is valid if there's no possible way for all the premises of that argument to be true while the conclusion is false. And he gave an example of an argument that was valid. The example, recall, went like this. Premise one, Mary has a child who is pregnant. Premise two, only daughters can become pregnant. Therefore, conclusion, Mary has at least one daughter. Now remember, as Walter pointed out, you can imagine situations where the first premise is false. Maybe Mary doesn't have a child who is pregnant. You can imagine situations in which the second premise is false. Maybe not only daughters can become pregnant. Maybe there's some way for sons to become pregnant. Or maybe there's some way for children of some third gender or some unspecified gender to become pregnant. And you can imagine a situation in which the conclusion is false, in which Mary doesn't have at least one daughter. But what you can't imagine, what's completely incoherent, what's completely impossible is for there to be a situation in which both of the premises are true and the conclusion is false. In any possible situation, either the premises are in any possible situation in which the premises are true, the conclusion has to be true. There's no possible situation for the premises to be true and the conclusion false. So, that's what makes that argument valid. Now, what I'd like to do right now is show that there are other arguments that have the same form as this first argument about Mary and are valid for what seems to be the same reason as the argument about Mary is valid, even though they have a completely different subject matter. So, here's another example. Consider the following argument. Premise 1. Terry has a job in which she arrests people. Premise 2. Only police officers can arrest people and therefore, conclusion, at least one of Terry's jobs is as a police officer. Now, again, maybe premise 1 of this argument is false. You can certainly imagine that it's false, right? Maybe Terry doesn't have a job in which she arrests people. Maybe premise 2 of the argument is false. You can imagine a situation in which not only police officers can arrest people. Maybe there's a world in which police officers and judges and plumbers and actors can all arrest people. And, of course, you could imagine a situation in which the conclusion is false, in which it's not true that at least one of Terry's jobs is as a police officer. But what you can't imagine, what's completely impossible, is that both of the premises of that argument are true and the conclusion is false. If both of the premises of that argument about Terry are true, the conclusion has to be true. And so the argument is valid. The argument about Terry is valid, just as the argument about Mary is valid. Now, notice the two arguments have completely different subject matters. The first is about Mary's children. The second is about Terry's jobs. But even though they have completely different subject matters, they have something in common. There seems to be something in common to their form, something signaled by their use of the terms only and at least something in common to the two arguments that explains why they're valid. To get at what this common feature is a bit more clearly, let me give a third and final example of this form. Let's see if you get the idea. So consider the following argument. Premise one, Robert has a pet who is canine. Premise two, only mammals can be canine. So conclusion, Robert has at least one pet who is mammal. Now, of course, you can imagine a situation in which Premise one is false. Maybe Robert doesn't have any canine pets. You can imagine a situation in which Premise two is false in which not only mammals are canines, maybe some canines are reptiles, or some canines are robots, or who knows. And of course, you can imagine a situation in which the conclusion is false, meaning in which Robert doesn't have any mammal pets. Maybe all of his pets are birds or reptiles, or maybe he doesn't have any pets. But in any case, you can imagine these possibilities, but what you cannot imagine, what's completely ruled out, is the possibility that the premises of that argument are true and the conclusion is false. If the premises of the argument are true, the conclusion has got to be true. And so this argument about Robert is also valid, just like the arguments about Mary and Terry were valid. But of course, this argument about Robert has a completely different subject matter than the arguments about Mary or Terry, right? One was an argument about Mary's children, the other was an argument about Terry's jobs, and this is an argument about Robert's pets. Completely different subject matters, but they're all valid. And it seems they're all valid for the same reason. They have the same form. And it's a form that's signaled by their use of the phrases only and at least. So, what we'll be doing in the second unit of the course is studying the forms of valid argument, the forms that explain why valid arguments are valid. Now, in the arguments that we just looked at, the arguments about Mary, Terry and Robert, their common form, I said, involved the use of the word only and it also involved the use of the phrase at least. Now, only and at least are both phrases that we're going to call quantifiers. And next week, in week five of the course, when we study the subject that we're going to call categorical logic, we're going to be studying in particular quantifiers like only, at least, some, all, none, and phrases like that. And we're going to be studying how the use of phrases like that, the use of quantifiers can make arguments valid, no matter what those arguments are about. If the arguments use quantifiers like only, at least, some, all, and none in certain ways, then those arguments are going to be valid regardless of their subject matter. But this week in week four, we're not going to be studying quantifiers like only or at least. Instead, we're going to be studying a kind of phrase that we're going to call a propositional connective. In particular, a kind of propositional connective that we'll call a truth functional connective. So, what are propositional connectives? What are truth functional connectives? How do they work to make arguments valid? Those questions and more we'll address in the next lecture. This week, we're going to be studying propositional logic, which is the rules that determine the validity of an argument based on the propositional connectives that are used in that argument. Now, I've said a little bit about propositional connectives, but in order to say more about what propositional connectives are, in particular, in order to give a definition of propositional connectives, I have to start out by giving a definition of propositions. So, what are propositions? A proposition is the kind of thing that can be true or false, and that can be the premise or the conclusion of an argument. Let me give you some examples to illustrate that definition. See these binoculars? These binoculars are not a proposition. They can't be true or false, and they can't be the premise or the conclusion of an argument. See this hand? This hand is not a proposition. This hand cannot be true or false, and it can't be the premise or the conclusion of an argument. But now, suppose I say, the binoculars are in my hand. Now, what I just said, that the binoculars are in my hand, that is the kind of thing that can be true or false. For instance, right now it's true, and right now it's false. It's also the kind of thing that could be the premise or the conclusion of an argument. For instance, I could say, the binoculars are in my hand. Therefore, my hand is not free to shake yours, or I could say, you just gave me the binoculars and I haven't let go of them. Therefore, the binoculars are in my hand. See? So that the binoculars are in my hand, that's a proposition. That's the kind of thing that can be true or false, and that can be the premise or the conclusion of an argument. Now, now that we know what propositions are, what's a propositional connective? A propositional connective is something that takes propositions and connects them to create new propositions. For instance, sometimes in English, the word and can work as a propositional connective. So, let me give you an example of how in English the word and can sometimes function as a propositional connective. So, consider the proposition, I'm holding the binoculars. That's a proposition. It's the kind of thing that can be true or false, and it's the kind of thing that can be the premise or the conclusion of an argument. There's also the proposition, I'm looking through the binoculars. That's the kind of thing that can be true or false, and it's the kind of thing that can be the premise or the conclusion of an argument. Well, you could use the word and to connect up those two propositions to make a new proposition. The new proposition would be I am holding the binoculars and looking through them. See, now that's a proposition. It's the kind of thing that can be true or false and it's also the kind of thing that could be the premise or the conclusion of an argument. For instance, right now it's true that I'm holding the binoculars and looking through them. Whereas right now it's false, that I'm holding the binoculars and looking through them. I could say what you're seeing right now is really happening, therefore I'm holding the binoculars and looking through them. Or I could say I'm holding the binoculars and looking through them. Therefore I should not be driving a car right now. You see? So that I'm holding the binoculars and looking through them is It's also a proposition. It's the kind of thing that can be true or false, and it's the kind of thing that can be the premise or the conclusion of an argument. But it's a proposition that we created by combining two other propositions, namely the proposition I'm holding the binoculars and the proposition I'm looking through the binoculars, by combining those two propositions with the word and. So that's an example of how the word and in English can work as a propositional connective, connecting two propositions into a third proposition. Now I just said that in English the word and functions as a propositional connective, but it doesn't always function that way, even in English. For instance, think about a sentence that uses the word and like the sentence, Jack and Jill finally talked. I can think of at least three different interpretations of that sentence, three different things that that sentence could mean. And corresponding to those three different things that the sentence could mean, three different ways that the word and is getting used in that sentence. So here's one thing the sentence could mean. Jack and Jill could be a name of a particular entity, like let's say a fast food company. There could be a fast food company called Jack and Jill, and maybe Jack and Jill, the fast food company, make some kind of special stew. And lawyers have been asking Jack and Jill to disclose the ingredients of this special stew because they find that a lot of the customers who eat this stew have been getting sick recently. So lawyers are asking Jack and Jill to disclose the ingredients and Jack and Jill refuses to do so until finally the spokesperson for Jack and Jill holds a press conference in which she discloses the ingredients of the special stew. Okay, now I might describe that situation by saying Jack and Jill finally talked, but what I mean there is that there's a particular entity, namely the company, Jack and Jill. And that company finally talked through its spokesperson, finally disclosed the ingredients of its special stew through its spokesperson. Now, on that interpretation of the sentence Jack and Jill finally talked, the word and is not being used as a propositional connective. It's not connecting to propositions and forming a larger proposition out of those two smaller propositions. Here's another way of understanding the sentence Jack and Jill finally talked. Let's suppose Jack, Jill and Roger are having a silence contest to see who among the three of them can be silent the longest. And all three of them are silent for a long period of time and you're calling in while I'm watching the silence contest, you're calling in to me periodically to find out if any one of these three contestants finally talked. And finally at one point you call in and you say, okay, has anyone talked yet? And I say, well, Jack and Jill finally talked. So Roger won the competition. Now there in that sentence when I say Jack and Jill finally talked, the word and is being used as a propositional connective. What I'm saying in effect is that Jack finally talked and Jill finally talked. So there are two propositions that I'm trying to communicate. The proposition Jack finally talked and the proposition Jill finally talked. And I'm using the word and to connect those two propositions into a larger proposition Jack and Jill finally talked. And so Roger won the competition. There the word and is being used as a propositional connective. It's just connecting the proposition Jack finally talked and the proposition Jill finally talked to form a larger proposition, Jack and Jill finally talked. And there's a third way that the word and could get used, just in that sentence Jack and Jill finally talked. Suppose Jack and Jill are a couple and recently they've been having a tough time. They've been angry and resentful and they haven't been talking to each other about the sources of their anger and resentment. Well, suppose they decide that they're going to finally get their grievances out into the open, they're going to talk to each other. Then I might say, Jack and Jill finally talked. Now there when I use the word and I'm not just connecting the proposition Jack finally talked and Jill finally talked. What I'm trying to communicate is not just that each of them talked. I'm trying to communicate that each of them talked to the other. I'm trying to say that they talk to each other. So there in that third interpretation, the word and is not working just as a propositional connective. It's not just connecting the proposition that Jack finally talked and the proposition Jill finally talked. Cuz I'm trying to get across something more than just that Jack finally talked and Jill finally talked. I'm also trying to get across the point that they talk to each other. All right, that's what I'm trying to communicate there with the sentence Jack and Jill finally talked. So there, the word and is not being used as a propositional connective. So I hope I've made it clear that the word and can get used in a bunch of different ways in English. One of the ways it can get used is as a propositional connective. To connect up two propositions into a larger proposition. But that's not the only way it can get used. It can get used in other ways as well, and I've tried to give examples of those just now. What we're gonna be concerned about here is just the use of and as a propositional connective. And then we'll look at other expressions in English like or, not, but, only if and so forth that also get used as propositional connectives. We'll look at those and see how those work. Okay, so now let's consider the propositional connective and. Notice though that even when the word and is being used as a propositional connective, it can still get used in different ways. For instance, suppose I say, I took a shower and got dressed. Well there, and is being used as a propositional connective. It's connecting two propositions. The proposition, I took a shower, and the proposition, I got dressed. It's connecting those into a larger proposition, I took a shower and got dressed. But there, the word and is being used to convey a sense of temporal ordering, a sense of time. The idea is, when I say, I took a shower and got dressed. The idea is, I first took a shower and then got dressed, right? It wouldn't mean the same thing if I said, I got dressed and took a shower. But sometimes when the word and is being used as a propositional connective, there's no suggestion of temporal ordering. So for instance, if I say, if I say, I'm holding the binoculars and looking through them, there's no suggestion that I'm doing one first and then the other, right? I'm just doing both, I'm holding them and looking through them. There's no suggestion that one is happening before the other. Now in that second usage, when the word and doesn't convey any kind of temporal ordering, where it just combines two propositions into a larger proposition without conveying any sense of temporal ordering. Then I'll say the word and is not just functioning as a propositional connective, but it's functioning as what I'll call a truth functional connective. So what's a truth functional connective? A truth functional connective is a propositional connective that creates new propositions whose truth or falsity depends on nothing other than the truth or falsity of the propositions that went into creating them. Let me give you some examples to illustrate that definition. So consider again, our example, Jack and Jill finally talked, where that's used to mean just that Jack finally talked and that Jill finally talked. Okay, so when is that proposition going to be true? When is it going to be true that Jack and Jill finally talked? Well, that's going to be true whenever it's true that Jack finally talked and Jill finally talked, as long as those two conditions are true, as long as Jack finally talked and Jill finally talked, it's also going to be true that Jack and Jill finally talked. So if it's not true that Jack finally talked, then it won't be true that Jack and Jill finally talked. If it's not true that Jill finally talked, then it won't be true that Jack and Jill finally talked. But as long as it is true that Jack finally talked and that Jill finally talked, it will be true that Jack and Jill finally talked. So that use of AND is a use of AND as a truth functional connective, because it creates a new proposition Jack and Jill finally talked, the truth or falsity of which depends on nothing other than the truth or falsity of the two propositions that it connects. There are lots of other examples. So for instance, consider the use of AND as a truth functional connective in the proposition I'm holding the binoculars and looking through them. Again, when is that proposition going to be true? It's going to be true only in these cases where it's true that I'm holding my binoculars and it's also true that I'm looking through my binoculars. If both of those are true, then the whole proposition I'm holding my binoculars and looking through them will also be true. If either one of those initial propositions is false, if it's false that I'm holding the binoculars or if it's false that I'm looking through the binoculars, then the whole proposition I'm holding the binoculars and looking through them will also be false. So there again, the truth or falsity of the whole proposition depends on nothing other than the truth or falsity of the propositions that go into creating it using the truth functional connective AND. That's what shows that AND in that usage is a truth functional connective. It's that the proposition that it creates by joining other propositions is a proposition whose truth or falsity depends on nothing other than the truth or falsity of the ingredient propositions that went into creating it. That's a truth functional connective. Now in week four, this week on propositional logic, we're going to be studying truth functional connectives and how the use of truth functional connectives in argument can make those arguments valid no matter what those arguments are about. Now let's move to some examples. Now I just said that in English, the word AND functions as a propositional connective, but it doesn't always function that way, even in English. For instance, think about a sentence that uses the word AND like the sentence, Jack and Jill finally talked. I can think of at least three different interpretations of that sentence, three different things that that sentence could mean. And corresponding to those three different things that the sentence could mean, three different ways that the word AND is getting used in that sentence. So here's one thing the sentence could mean. Jack and Jill could be a name of a particular entity, like let's say a fast food company. There could be a fast food company called Jack and Jill, and maybe Jack and Jill, the fast food company, make some kind of special stew. And lawyers have been asking Jack and Jill to disclose the ingredients of this special stew because they find that a lot of the customers who eat this stew have been getting sick recently. So lawyers are asking Jack and Jill to disclose the ingredients and Jack and Jill refuses to do so until finally the spokesperson for Jack and Jill holds a press conference in which she discloses the ingredients of the special stew. Okay, I might describe that situation by saying Jack and Jill finally talked. What I mean there is that there's a particular entity, namely the company, Jack and Jill. And that company finally talked through its spokesperson, finally disclosed the ingredients of its special stew through its spokesperson. Now on that interpretation of the sentence Jack and Jill finally talked, the word AND is not being used as a propositional connective. It's not connecting to propositions and forming a larger proposition out of those two smaller propositions. Here's another way of understanding the sentence Jack and Jill finally talked. Let's suppose Jack, Jill and Roger are having a silence contest to see who among the three of them can be silent the longest. And all three of them are silent for a long period of time and you're calling in while I'm watching the silence contest, you're calling into me periodically to find out if any one of these three contestants finally talked. And finally at one point you call in and you say, okay, has anyone talked yet? And I say, well, Jack and Jill finally talked. So Roger won the competition. Now there in that sentence, when I say Jack and Jill finally talked, the word AND is being used as a propositional connective. What I'm saying in effect is that Jack finally talked and Jill finally talked. So there are two propositions that I'm trying to communicate. The proposition Jack finally talked and the proposition Jill finally talked. And I'm using the word AND to connect those two propositions into a larger proposition Jack and Jill finally talked. And so Roger won the competition. There the word AND is being used as a propositional connective. It's just connecting the proposition Jack finally talked and the proposition Jill finally talked to form a larger proposition Jack and Jill finally talked. Now there's a third way that the word AND could get used, just in that sentence, Jack and Jill finally talked. Suppose Jack and Jill are a couple and recently they've been having a tough time. They've been angry and resentful and they haven't been talking to each other about the sources of their anger and resentment. Well, suppose they decide that they're going to finally get their grievances out into the open, they're going to talk to each other. Then I might say, Jack and Jill finally talked. Now there, when I use the word AND, I'm not just connecting the proposition Jack finally talked and Jill finally talked. What I'm trying to communicate is not just that each of them talked. I'm trying to communicate that each of them talked to the other. I'm trying to say that they talk to each other. So there in that third interpretation, the word AND is not working just as a propositional connective. It's not just connecting the proposition that Jack finally talked and the proposition Jill finally talked. Because I'm trying to get across something more than just that Jack finally talked and Jill finally talked. I'm also trying to get across the point that they talk to each other. That's what I'm trying to communicate there with the sentence Jack and Jill finally talked. So there, the word AND is not being used as a propositional connective. So I hope I've made it clear that the word AND can get used in a bunch of different ways in English. One of the ways it can get used is as a propositional connective, to connect up two propositions into a larger proposition. But that's not the only way it can get used. It can get used in other ways as well, and I've tried to give examples of those just now. What we're gonna be concerned about here is just the use of AND as a propositional connective. And then we'll look at other expressions in English like or, not, but, only, if, and so forth that also get used as propositional connectives. We'll look at those and see how those work. Okay, so now let's consider the propositional connective AND. Notice though that even when the word AND is being used as a propositional connective, it can still get used in different ways. For instance, suppose I say, I took a shower and got dressed. Well, there, AND is being used as a propositional connective. It's connecting two propositions. The proposition, I took a shower, and the proposition, I got dressed. It's connecting those into a larger proposition, I took a shower and got dressed. But there, the word AND is being used to convey a sense of temporal ordering, a sense of time. The idea is, when I say, I took a shower and got dressed, the idea is, I first took a shower and then got dressed, right? It wouldn't mean the same thing if I said, I got dressed and took a shower. But sometimes when the word AND is being used as a propositional connective, there's no suggestion of temporal ordering. So for instance, if I say, if I say, I'm holding the binoculars and looking through them, there's no suggestion that I'm doing one first and then the other, right? I'm just doing both. I'm holding them and looking through them. There's no suggestion that one is happening before the other. Now in that second usage, when the word AND doesn't convey any kind of temporal ordering, where it just combines two propositions into a larger proposition without conveying any sense of temporal ordering, then I'll say the word AND is not just functioning as a propositional connective, but it's functioning as what I'll call a truth functional connective. So what's a truth functional connective? A truth functional connective is a propositional connective that creates new propositions whose truth or falsity depends on nothing other than the truth or falsity of the propositions that went into creating them. Let me give you some examples to illustrate that definition. So consider, again, our example, Jack and Jill finally talked. Where that's used to mean just that Jack finally talked and that Jill finally talked. Okay, so when is that proposition gonna be true? When is it gonna be true that Jack and Jill finally talked? Well, that's gonna be true whenever it's true that Jack finally talked and Jill finally talked, as long as those two conditions are true. As long as Jack finally talked and Jill finally talked, it's also gonna be true that Jack and Jill finally talked. So if it's not true that Jack finally talked, then it won't be true that Jack and Jill finally talked. If it's not true that Jill finally talked, then it won't be true that Jack and Jill finally talked. But as long as it is true that Jack finally talked and that Jill finally talked, it will be true that Jack and Jill finally talked. So that use of AND is a use of AND as a truth-functional connective because it creates a new proposition Jack and Jill finally talked, the truth or falsity of which depends on nothing other than the truth or falsity of the two propositions that it connects. There are lots of other examples. So for instance, consider the use of AND as a truth-functional connective in the proposition I'm holding the binoculars and looking through them. Again, when is that proposition going to be true? It's going to be true only in these cases where it's true that I'm holding my binoculars and it's also true that I'm looking through my binoculars. If both of those are true, then the whole proposition I'm holding my binoculars and looking through them will also be true. If either one of those initial propositions is false, if it's false that I'm holding the binoculars or if it's false that I'm looking through the binoculars, then the whole proposition I'm holding the binoculars and looking through them will also be false. So there again, the truth or falsity of the whole proposition depends on nothing other than the truth or falsity of the propositions that go into creating it using the truth-functional connective AND. That's what shows that AND in that usage is a truth-functional connective. It's that the proposition that it creates by joining other propositions is a proposition whose truth or falsity depends on nothing other than the truth or falsity of the ingredient propositions that went into creating it. That's a truth-functional connective. Now in week four, this week on propositional logic, we're going to be studying truth-functional connectives and how the use of truth-functional connectives in argument can make those arguments valid no matter what those arguments are about. Now let's move to some examples. In the last lecture we learned about the truth-functional connective that we called conjunction, the truth-functional connective that in English at least is sometimes expressed by certain uses of the word AND. And we learned about the truth table for conjunction. Now one thing I'd like to do in today's lecture is show how we can use the truth table for conjunction to show that certain kinds of inferences that use conjunction are going to be valid. Let me give you an example. Consider an inference that starts off with two premises. Doesn't matter what the premises are, just any two premises. Call them P and Q because it doesn't matter what they are. And then the conclusion of the inference is simply going to be the conjunction of those two premises, whatever they were. So the inference can be sketched as follows, P, Q, conclusion, P and Q. Now we can call that a conjunction-introduction inference because the conclusion of the inference uses a conjunction, it introduces a conjunction that wasn't present in either of the two premises of the inference. Now notice if you look at the first line of the truth table for conjunction you can see that any conjunction-introduction inference is going to have to be valid. Here's how you can see that. You look at the first line of the truth table for conjunction, that considers the situation in which P is true and Q is true. And in any such situation according to that truth table the conjunction P and Q is going to have to be true. So now let's take that point and apply it to the inference from the premise P and the premise Q to the conclusion P and Q. What does that first line of the truth table for conjunction tell you about that inference? Well, it tells you that in any situation in which the premises of that inference, P and Q, are both true. In any situation in which those premises are both true, the conclusion P and Q is going to have to be true. But that's just what it is for the inference to be valid. Recall that for an inference to be valid is just for it to be such that there's no possible situation where the premises are true and the conclusion is false. So from the first line of the truth table for conjunction you can see that conjunction-introduction inferences are all going to be valid. You can also see by looking at the truth table for conjunction that another kind of inference is always going to be valid. So consider an inference that starts with only one premise, a premise that conjoins two propositions. Again, never mind what the two propositions are, they could be anything. Call them P and Q because it doesn't matter what they are. So consider an argument that starts with that one premise, P and Q, and that moves to a conclusion that consists simply of one of those two premises, one of those two propositions that is conjoined in the premise. So the conclusion of the argument will be either the proposition P or the proposition Q. Now, an argument like that we can call a conjunction elimination argument because the conclusion of the argument eliminates a conjunction that occurs in the premise of the argument, right? The premise is a conjunction of two propositions, P and Q, and the conclusion is simply one of those two propositions, not conjoined to anything else. So the conclusion is either the proposition P or it's the proposition Q. Now, is that argument going to be valid? Well, if you look at the truth table for conjunction, you'll see that it is going to be valid. In any possible situation in which the premise of that argument, P and Q is true, both of the two propositions that are conjoined in that premise, both the proposition P and the proposition Q are also going to be true. So any situation in which the premise of a conjunction elimination argument is true is going to be a situation in which the conclusion of that conjunction elimination argument is true. Therefore, all conjunction elimination arguments are valid no matter what they're about. And we can see that just by looking at the truth table for conjunction. Now, conjunction introduction and conjunction elimination arguments are not the most interesting kinds of arguments there are, to be sure. But I just wanted to give a simple example for now of how we can use the truth table for a truth functional connective, in this case, the truth functional connective conjunction. How we can use the truth table for that connective to discover that certain kinds of arguments are going to be valid. In the next lecture, we'll show how we can use other kinds of truth tables for other connectives, for other truth functional connectives, to show that certain other kinds of arguments are valid. See you next time. Today, we're going to talk about the truth functional connective that we'll call disjunction. Now, disjunction is a truth functional connective that, in English, is usually expressed by means of the word OR, OR. But there are a couple different ways of using that word OR. Let me give you some examples. Suppose you ask me, who won the game last night? And I say, well, either Manchester won it or Barcelona won it. But there, I'm clearly trying to indicate that, while Manchester may have won it and Barcelona may have won it, they didn't both win the game. If Manchester was playing Barcelona last night, then they couldn't both have won. Soccer doesn't work like that. Either one team wins or the other team wins, but they can't both win. So, if I say, either Manchester won it or Barcelona won it, what I mean is that either one of two possibilities occurred, either Manchester won it or Barcelona won it. But they couldn't both have occurred. But sometimes, when I use the word OR, I don't mean to convey anything like that. For instance, suppose I say to you, this is breakfast or lunch. Now, I'm not suggesting, when I say this is breakfast or lunch, I'm not suggesting that it can't be both. It could be breakfast, it could be lunch, or it could be both. And when I say this is breakfast or lunch, I mean it could be one, it could be the other, it could be both. So there, in that second usage, I'll say OR is inclusive. It includes both of the options and the possibility of their both being true. In the first usage, where I said either Manchester won or Barcelona won, I'll say OR is exclusive. In other words, either one is true or the other is true, but they can't both be true. So OR can be used exclusively to mean that either one of two options is true, but they can't both be true. OR could be used inclusively to mean one of two options could be true, or they could both be true. Now, the truth-functional-connective disjunction is expressed in English by the use of the inclusive OR, the OR that leaves open the possibility that both of the two options could be true. So what's the truth table for the truth-functional-connective disjunction going to look like? Well, you can start with two possibilities, two propositions that are connected by the truth-functional-connective disjunction, doesn't matter what the propositions are. Just call them P and Q because it doesn't matter what they are. So there's P, there's Q, and then there's the disjunction of P and Q, which will symbolize as follows, P disjunction, which looks like a V, Q. Now, when is P disjunction Q going to be true? Remember, disjunction is expressed by the inclusive OR. So it's going to be true whenever P is true, and it's also going to be true whenever Q is true, and of course, since it's expressed by the inclusive OR, it's going to be true whenever P and Q are both true. So the truth table for disjunction is going to look like this, right? The first three lines, the lines that consider the possibility of P and Q is both being true or P is being true and Q is being false or P is being false and Q is being true, and all three of those lines, the disjunction P or Q will be true. The only scenario in which P or Q is false is the scenario in which P and Q are both false, in which neither P nor Q is true. Now that we've learned the truth table for the truth functional connective disjunction, we can use that truth table to figure out when certain arguments that use disjunction are going to be valid. For example, consider this simple argument, premise one, I'm going to tickle you with my right hand. Premise two, I'm going to tickle you with my left hand. Conclusion, I'm going to tickle you with either my right or my left hand. Is that argument valid? Well, it obviously is valid, but you can use the truth table for disjunction to explain why it's valid. Look at the truth table for disjunction again. In this argument, we have premise one, being the proposition, I'm going to tickle you with my right hand. Premise two, being the proposition, I'm going to tickle you with my left hand. And the conclusion, that's the disjunction of those two propositions. Well, what can you tell from the truth table for disjunction? What you can tell is that in a situation in which P is true and Q is true, in which both of two propositions are going to be true, the disjunction of those two propositions is also going to be true. You see, that's what you can read off from the first line of the truth table. In a situation in which each of two propositions is true, their disjunction has to be true. So, in the argument that I just gave you, which has as premise one, I'm going to tickle you with my right hand and as premise two, I'm going to tickle you with my left hand, that argument has to be valid because the conclusion of that argument is simply the disjunction of the two premises. So, there's no possible way for the premises of that argument to be true while the conclusion is false. If the premises of that argument are true, the conclusion has to be true. We could think of that argument as a kind of disjunction-introduction argument because just as in the case of a conjunction-introduction argument where the conclusion introduces a conjunction that wasn't there in the premises, in this argument, the conclusion introduces a disjunction that wasn't there in the premises. There were two premises, I'm going to tickle you with my right hand and I'm going to tickle you with my left hand. The conclusion introduces the disjunction of those two premises. The conclusion just is the disjunction of those two premises. But notice, even though that disjunction-introduction argument is valid, argument is valid, there are even simpler disjunction introduction arguments that are valid. Consider for instance the argument that starts with just one premise, could be anything, call it p, and that draws as a conclusion the disjunction of p with anything else. So let's say p is the premise I'm going to tickle you with my right hand, and then the conclusion is that it's just the disjunction of that premise I'm going to tickle you with my right hand with any other proposition, like say I'm going to tickle you with my left hand. That argument is going to have to be valid, and you can read that off the truth table for disjunction, because you can see that in any situation in which one of the disjuncts of a disjunction is true, the disjunction is going to have to be true. So any disjunction introduction argument that starts with just one premise, and that concludes the disjunction of that premise with anything else, any such argument is going to have to be valid. There's no possible way for the premise of that argument to be true, while the conclusion is false. So, all disjunction introduction arguments are valid. But what about disjunction elimination arguments? Well, remember conjunction elimination arguments are valid, because if you start off with a premise that states the conjunction of two propositions, then the conclusion that is either one of those two conjoined propositions, either one of those propositions, the conclusion is going to have to be true whenever that conjunction is true. You saw that from the truth table for conjunction. But what about with disjunction? Does it work that way with disjunction? Well, consider an argument that starts from the premise, I'm going to tickle you with either my right or my left hand. And then it draws the conclusion that is simply one of those two disjoint propositions. Let's say it draws the conclusion I'm going to tickle you with my right hand. Is that argument valid? No, it's not. Because there's a possible situation in which the premise I'm going to tickle you with either my right hand or my left hand is true, while the conclusion I'm going to tickle you with my right hand is false. Namely, the situation in which I'm going to tickle you with my left hand. In that situation, the premise would be true, but the conclusion would be false. So that disjunction elimination argument is not valid. And you can also see that by looking at the truth table for disjunction. If you look at the truth table for disjunction, you'll see that there are three possible scenarios in which the premise, I'm going to tickle you with either my right hand or my left hand is true. The three possible scenarios are the three scenarios in which both of the disjuncts are true. The first disjunct is true and the second one false, or the first disjunct is false and the second one is true. Well, there are three possible scenarios in which that disjunction is true. When I say I'm not going to tickle you with my right hand, I'm ruling out two of those scenarios, namely the two scenarios in which it's true that I tickle you with my right hand. But that still leaves open a scenario in which it's true that I'm going to tickle you with either my right hand or my left hand. But for the disjunction elimination argument to be valid, it would have to be the case that in every scenario in which the disjunction I'm going to tickle you with either my right or my left hand is true, each of those disjuncts is true. But that's not the case. And you can see that just by looking at the truth table for disjunction. So the truth table for disjunction shows you why it is that disjunction and production arguments are all valid. But simple disjunction elimination arguments that start with a premise that's just the disjunction of two propositions and end with a conclusion that is simply one of those disjoint propositions by itself. Those arguments are not valid. You can see that by the truth table from disjunction. In the last couple of lectures we've learned about the truth functional connective conjunction and we've learned about the truth functional connective disjunction. Now both of these connectives can be used to take propositions and put them together to create new propositions whose truth depends solely on the truth of the propositions that you used as their ingredients. Now in today's short lecture I just want to make the point that just as you can combine propositions using conjunction and you can combine propositions using disjunction you can also use conjunction and disjunction together to string together a bunch of propositions into a larger proposition. Let me give you an example to illustrate this point. Suppose I say I'm going to tickle you with this hand and then I say and I'm either going to tickle you with this hand or with this hand. Okay now here what I've done is string together three propositions. The proposition I'm going to tickle you with this hand and the proposition and I'm either going to tickle you with this hand or with this hand. So there we've created a new proposition by stringing together three other propositions using conjunction and disjunction. Now notice we can construct a truth table to show how the truth of the larger proposition I'm going to tickle you with this hand and with either this hand or this hand how the truth of that larger proposition depends on the truth of the propositions that go into creating it. Okay so there are three propositions that go into creating it and they're connected in different ways so one of the propositions was I'm going to tickle you with this hand. Let's find terms to distinguish the hand so I don't have to keep waving around all my hands. Let's call this hand number one. Now the proposition we can say is I'm going to tickle you with hand number one and with either hand number two or hand number three. Okay so there are three propositions that go into creating that larger proposition. So the three propositions are these. First I'm going to tickle you with hand number one. Second I'm going to tickle you with hand number two and third I'm going to tickle you with hand number three. Now we can use the truth table to show when precisely it would be true that I'm going to tickle you with hand number one and with either hand number two or hand number three. How does the truth of that whole statement depend on the truth of the three propositions that go into creating it? Well that whole statement I'm going to tickle you with hand number one and with either hand number two or hand number three is a conjunction. It's a conjunction with two conjuncts. The first conjunct is I'm going to tickle you with hand number one and the second conjunct is I'm going to tickle you with either hand number two or hand number three. So since it's a conjunction we know that for it to be true both of its conjuncts have to be true. So it has to be true that I'm going to tickle you with hand number one. So that proposition I'm I'm going to tickle you with hand number one. That proposition has to be true. Does it have to be true that I'm going to tickle you with hand number two? No. All that has to be true is that I'm either going to tickle you with hand number two or with hand number three. So that disjunction, I'm going to tickle you with hand number two or with hand number three, has to be true. But for the disjunction to be true, it doesn't have to be true that I'm going to tickle you with hand number two. After all, there's a scenario where I'm not going to tickle you with hand number two, and yet it's still true that I'm going to tickle you with either hand number two or hand number three. And for the disjunction, I'm going to tickle you with hand number two or hand number three to be true. It doesn't have to be true that I'm going to tickle you with hand number three. Again, remember, there's a scenario where I'm not going to tickle you with hand number three, but it's still going to be the case that I'm going to tickle you with either hand number two or hand number three. But what does have to be true for the disjunction to be true is that at one of those other two propositions are true. It's at least true that either I'm going to tickle you with hand number two or I'm going to tickle you with hand number three or both. But at least one of those has to be true. So for the whole proposition, I'm going to tickle you with hand number one and with hand number two or hand number three. For that whole proposition to be true, it's got to be true that I'm going to tickle you with hand number one. and it's either gotta be true that I'm gonna tickle you with hand number two or it's gotta be true that I'm gonna tickle you with hand number three. So if we look at the truth table, we can see precisely which lines are going to make the whole proposition true. So here's how we can construct a truth table for a complex proposition that combines conjunction and disjunction. And notice, by the way, when we're combining conjunction and disjunction, the order in which we combine them matters. We can say that conjunction and disjunction are not associative. What matters to determining the truth table of the proposition that they're used to create is not just the occurrence of conjunction and disjunction, but what order they're taken in. In the proposition that I considered just a moment ago, I'm gonna tickle you with hand number one and with either hand number two or hand number three. That proposition has a different truth table than the proposition, I'm gonna tickle you with hand number one and hand number two or I'm gonna tickle you with hand number three. That second proposition has a very different truth table from the first. As we can see, if we construct the two truth tables and compare them. So conjunction and disjunction are not associative. The truth table for the proposition that they create depends on the order in which we apply conjunction and disjunction. In the last few lectures, we've talked about the truth functional connectives, conjunction and disjunction. We've gone over the truth tables for those connectives and shown how we can use the truth tables to figure out when arguments that use conjunction or disjunction are valid. Now today, what I wanna do is talk about a propositional device that's not a connective but that's what I'll call an operator. It doesn't connect two propositions to make a larger proposition. Rather, what it does is it just operates on a single proposition to make another proposition. You can think of it as converting one proposition to another proposition. Now there are lots of propositional operators for instance, consider the phrase, I believe that. That's a propositional operator. You take any proposition, let's say the proposition it's raining today. And now you put I believe that in front of it and you get a new proposition. I believe that it's raining. So I believe that as an example of a propositional operator. But I wanna talk about a kind of propositional operator that is a truth functional operator. That's to say the truth or falsity of the proposition that results from applying that operator depends solely upon the truth or falsity of the proposition to which the operator is applied. Now the propositional operator I believe that is clearly not truth functional. For instance, suppose it is raining today. Suppose it's true that it's raining today. What does that tell you about whether or not I believe that it's raining today? Well nothing, it could be raining today even though I don't believe that it's raining today and could be raining today even though I do believe that it's raining today. The truth or falsity of the proposition I believe that it's raining today doesn't depend solely upon the truth or falsity of the proposition it is raining today. It depends on other things as well. It depends in particular on my psychology. So the propositional operator I believe that is not a truth functional operator. But there is a propositional operator that's truth functional. In English the propositional operator that's truth functional is expressed by the phrase it is not the case that or sometimes simply by the use of the phrase not. The propositional operator that I have in mind is called negation. Negation is a truth functional operator that takes any proposition and creates a new proposition whose truth value is the opposite of the truth value of the original proposition. So you take any proposition if it's true then the negation of that proposition is false. Take any proposition if it's false then the negation of that proposition is true. So negation is a propositional operator that's an example of a truth functional operator. The truth of the proposition results from applying negation depends solely on the truth of the proposition to which negation is applied. And that respect negation is very different from the propositional operator. I believe that. Now, I said just a moment ago that sometimes the English word not is used to express the truth functional operator negation. But it's not always used to do that. Let me give you an example. Consider the proposition. Walter has stopped beating his dogs. Okay, now that's a proposition. It's something that could be true or false and it's something that could be the premise or the conclusion of an argument. But suppose we put the word not into that proposition. I say, Walter has not stopped beating his dogs. Is that the negation of Walter has stopped beating his dogs? Well, let's think about that for a moment. Suppose it's true that Walter has stopped beating his dogs. Well, then pretty clearly it seems like it's false that Walter has not stopped beating his dogs. If he has stopped beating his dogs, then anyone who says that he's not stopped beating his dogs is saying something false. But now suppose it's false that Walter has stopped beating his dogs. Does that mean it's true that Walter has not stopped beating his dogs? Well, not necessarily. Think about the different reasons why it could be false that Walter has stopped beating his dogs. It could be false that Walter has stopped beating his dogs because he's still beating his dogs. Or it could be false that Walter has stopped beating his dogs because in fact he never did beat his dogs. Or it could be false that Walter has stopped beating his dogs That's because Walter doesn't have any dogs. For that matter, it could be false that Walter has stopped beating his dogs because there is no such person as Walter. Walter doesn't exist. Walter is a mere figment of your imagination. So there are all sorts of reasons why it could be false that Walter has stopped beating his dogs. And in some of those situations, it would not be true that Walter has not stopped beating his dogs. For instance, if Walter doesn't have any dogs, then, even though it's false that Walter has stopped beating his dogs, it's also false that Walter has not stopped beating his dogs. So in that example, the word not is not being used as negation. So suppose I say Walter has stopped beating his dogs. Not. Okay, now there, where I say not, all I'm doing is operating on the original proposition Walter has stopped beating his dogs and creating a new proposition whose truth value is the opposite of that original proposition. So if I say Walter has stopped beating his dogs, but Walter doesn't exist, or Walter never had any dogs, or Walter never did beat his dogs, in any of those situations, if I say Walter has stopped beating his dogs, not. What I just said is true. So sometimes the word not is used to express the truth functional operator negation. But often it's not used that way. Often when we want to express the truth functional operator negation, we have to use the more cumbersome English phrase, it is not the case that. Now I've told you how negation works, it operates on a particular proposition to create a new proposition whose truth value is the opposite of the truth value of the original proposition. But because negation works in such a simple way, its truth table is going to be very simple. So consider any proposition, no matter what. Any proposition, call it P. When P is true, the negation of P is going to be false, and when P is false, the negation of P is going to be true. That's how negation works. In the last several lectures we learned about the truth functional connectives, conjunction and disjunction, and we learned about the truth functional operator negation. Now today I'd like to make a point about how these truth functional devices, these connectives and operators, can be combined so as to create larger propositions out of smaller propositions. So consider this conjunction, for lunch I'm going to eat this and this. That's a conjunction, it's the conjunction of the proposition that for lunch I'm going to eat this, and the proposition that for lunch I'm going to eat this. Now if we apply negation to that conjunction, what are we saying? We're saying it's not the case that for lunch I'm going to eat this and this. Now that leaves it open that maybe for lunch I'm just going to have one of these two things, maybe just this thing, whatever that is. So if I negate a conjunction, all I'm doing is saying it's not the case that both of the two conjuncts are true. But suppose I create a disjunction out of the two propositions, that for lunch I'm going to eat this and for lunch I'm going to eat this. If I create a disjunction as follows, I say for lunch I'm either going to eat this or this. Now if I negate that, if I say it's not the case that for lunch I'm either going to eat this or this, then I'm saying something that rules out that I'm going to eat either of them for lunch. It's not just that I'm not going to eat both of them, I'm not going to eat either of them. My lunch is not going to involve this and it's also not going to involve this. So negating a conjunction gives us a different result than negating a disjunction. And that's exactly what we should expect if we look at the truth table that results from applying negation to a conjunction and applying negation to a disjunction. Remember, when we apply negation to a conjunction, we're applying negation to a proposition that's true only when both of its two conjuncts are true. In every other scenario it's false. So if we apply negation to that proposition, what do we get? We get a proposition that's going to be true in three out of four possible scenarios. It's going to be true whenever both of the conjuncts are false and it's going to be true whenever either one of the conjuncts is false. The only situation in which that proposition is going to be false is when both of the conjuncts are true. But now contrast that with applying negation to a disjunction. When we apply negation to a disjunction, we're applying negation to a proposition that's true whenever either one of its disjuncts is true. So we end up getting a proposition that's false in three out of four possible scenarios. Because it's false, so long as either one of the disjuncts is true. So applying negation to a disjunction is going to give us a different result than applying negation to a conjunction and we can see that by looking at the truth tables for negation, disjunction, and conjunction. Today's lecture is about conditionals. Conditionals are a kind of truth functional connective that we haven't discussed yet. But today we're going to introduce this new kind of truth functional connective, discuss the truth table for it, and say why it's important. It's especially important in understanding the rules by which to assess the validity of deductive arguments. Now in order to introduce this new truth functional connective, the conditional, I want to start by telling you a story. Imagine that Walter's been breaking into my office and stealing my stuff. So each day I come into my office and I find that more and more of my stuff is gone. One day he steals my electronics and the other day he steals my coffee cup and then another day he steals my clothing and then yet another day he steals my glasses. And before long there's very little stuff in my office. Now as this happens I start to get suspicious and I decide to have Walter followed by a private investigator. Just to figure out exactly whether or not Walter is stealing my stuff. So I have the private investigator follow Walter everywhere he goes, right? He follows him to his house at night. Then he follows him to the bar early in the morning. He follows him to the golf course later in the morning. Then he follows him to the water polo tournament in the afternoon. Follows him everywhere he goes. Now suppose you ask me, is the private investigator having lunch at that Cuban restaurant New Havana? Now I might say to you, well, if Walter is having lunch there, then the private investigator is having lunch there. Okay, now notice what I just said. I said if Walter is having lunch there, then the private investigator is having lunch there. That phrase if then can be used to connect two propositions. The proposition Walter is having lunch at New Havana with a proposition. The private investigator is having lunch in New Havana. So that phrase if then works as a propositional connective. It connects two propositions to make a larger proposition. But does it work as a truth functional connective? Now I'd like to argue that it does. Okay, so how are we going to argue that if then is not just a propositional connective, but is also a truth functional connective? Well, I'd like to begin by considering the following truth functional construction. Consider the negation of the conjunction of p and the negation of q. I've written that out here. The negation of the conjunction of p and the negation of q. Now suppose I say that whole proposition is true. Well, if I say that whole proposition is true, then what I'm saying is just that the negation of that proposition, in other words, just the conjunction of p and the negation of q, that that proposition is false. But what does it mean when I say that the conjunction of p and the negation of q is false? Well, what I'm saying there is that if p is true, then the negation of q has to be false, right? Because if the conjunction of p and the negation of q is false, then you can't have both of those conjuncts being true. At least one of them has to be false. So if p is true, then the other conjunct, the negation of q, has to be false. So you're saying there that if p is true, then the negation of q is false. But remember, for the negation of q to be false, it's just the same thing as for q to be true, because the negation of q has just the opposite true value of whatever q has. So to say if p is true, then the negation of q is false, is just the same as to say if p is true, then q is true. But that's exactly what you're doing whenever you use if, then, as a propositional connective. You're saying if one proposition is true, like, let's say, Walter is eating lunch at New Havana, then another proposition is true, like, let's say, the private investigator is eating lunch at New Havana. If p, then q, that proposition follows from the negation of the conjunction p and the negation of q. But while if p, then q follows from the negation of that conjunction, is it equivalent to it? Now I just argued that if p, then q follows from the negation of the conjunction p and the negation of q. But now what I'd like to do is argue that later proposition, the negation of the conjunction of p and the negation of q, that that proposition follows from if p, then q. Consider for a moment what you're saying when you say if p, then q. You're saying if p is true, then q has got to be true. So you're ruling out a certain option. You're ruling out the possibility that p is true while q is false. When you say if p, then q, you're ruling out the possibility that p is true and q is false. In other words, you're ruling out the possibility that p is true and the negation of q is true. In other words, you're saying p and the negation of q, that conjunction right there has got to be false. In other words, you're saying that the negation of the conjunction p and the negation of q is true. So you see the negation of the conjunction p and the negation of q follows from if p, then q, and if p, then q follows from the negation of the conjunction of p and the negation of q. So what that tells us is that the proposition if p, then q is going to be true in precisely the same situations as the proposition which is the negation of the conjunction p and the negation of q. So if they're true in all the same situations, that just means that they're going to have the same truth table. In other words, if p, then q is going to have a truth table and it's going to have precisely the same truth table as the negation of the conjunction of p and the negation of q. That's what we learn by noticing that if p, then q follows from the negation of the conjunction of p and the negation of q and that the negation of the conjunction of p and the negation of q follows from if p, then q is that they have the same truth table. And since if p, then q has a truth table, that proves that it's a truth functional connective. It's a propositional connective that creates propositions whose truth value depends solely on the truth values of the propositions that go into it. So it's a truth functional connective. Now that we've talked about the conditional and we've explained how the truth table for the conditional works, let's talk about some rules governing our use of the conditional and then let me say something about why the conditional is an especially important truth functional connective. So first I want to talk about a rule called modus ponens. Modus ponens says from the premises p, whatever p is, and if p, then q, whatever exactly p and q are, infer the conclusion q. That's what modus ponens says. Now notice we can use the truth table for the conditional to show that modus ponens is a good rule of inference. Look here. So suppose you know that p is true and if p, then q is true. So what does that tell you? Well, since p is true, we've got to be in one of these first two scenarios, one of the two top rows of the truth table. And since the conditional if p, then q is true, we've got to be in either the first third or fourth row of that truth table. But then what does that tell us? Well, if we've got to be in one of the two top rows and we've got to be in either the first third or fourth row, then the only possible choice is that we've got to be in the top row. In other words, we've got to be in a situation in which p is true, if p, then q is true and q is true. Another way of putting that is in any situation in which p is true and if p, then q is true, q has got to be true. And so modus ponens is a good rule of inference. If we follow modus ponens, we'll never give an invalid argument, right? No modus ponens argument can be invalid because whenever p is true and if p, then q is true, q is got to be true. Okay. So modus ponens is a good rule of inference. There's another rule called modus tollens, which says the following. From the premises not q, the negation of q and the premise if p, then q, and for the conclusion not p or the negation of p. Now, is that a good rule? Well, once again, we can use the truth table to see that it is. So here's what the two premises tell us. They tell us if p, then q is true. So we've got to be in the first, third, or fourth rows of that truth table. And they also tell us that the negation of q is true. In other words, that q itself is false, right? Because when the negation of q is true, then q is false. So that tells us we've got to be in either the second or the fourth row of that truth table. Okay. So here's what the premises tell us. We're either in the second or fourth row of the truth table and we're in either the first, third, or fourth row of the truth table. Well, the only option left is that we're in the fourth row of the truth table. In other words, if we're in a situation in which if p, then q is true and not q is true, in other words, q is false, then the only possible situation we could be in is a situation in which p is false. But of course, that's a situation in which not q is true. So if we follow modus tolens and make arguments that follow that rule, all of our arguments will be valid. Any argument that has as its premises two premises of the form if p then q and the negation of q and has as its conclusion the negation of p, any argument of that form will have to be valid. And that's what we can see using the truth table for the conditional. So modus ponens and modus tolens are two rules governing our use of the conditional and we can see using the truth table that they're both valid rules of argument, just like conjunction elimination or disjunction introduction. Okay, now I've said something about what the conditional means, what its truth table is, and what some good rules for its usage are. Why is the conditional an important truth functional connective? It's pretty clear why disjunction and conjunction are important truth functional connectives. They're very intuitive. They seem to correspond to notions that we operate with in everyday life. But what about the conditional? Here's what makes the conditional especially important for propositional logic. Consider any argument whatsoever that has some premises and a conclusion. Let's call the premises of that argument p and the conclusion c. Now whatever that argument is, if that argument from premises p to conclusion c is valid, then the conditional, if p then c, has got to be true. And here's why. If the argument from p to c is valid, what that tells us is that there's no possible way for p to be true while c is false. But what does it mean for the conditional if p then c to be true? All it means is that if p is true, then c has got to be true. It's not the case that p is true and c is false. So whenever the argument from p to c is valid, the conditional if p then c is going to be true. And so we can use the conditional to express in the form of a single proposition the validity of an argument from premises p to conclusion c. Whatever that argument is about, the conditional can be used to express the validity of that argument. And that's what makes the conditional especially useful in propositional logic. We've been talking about the truth functional connective that I've called the conditional. And I said that in English, the conditional is normally expressed by using the phrase if then. But that statement needs some qualification. First of all, there are some occasions on which we use the phrase if then, but we're not expressing the truth functional connective, which is the conditional. In fact, we're not expressing any truth functional connective at all. For instance, if we use if then around phrases that are in the subjunctive mood, then often what we end up with is not a truth functional connective. If I say, if I had been four feet tall, then I would have been in the Guinness Book of World Records. I'm not saying something the truth or falsity of which is a product of the truth or falsity of the ingredient propositions, right? The truth or falsity of if I had been four feet tall, then I would be in the Guinness Book of World Records or I would have been in the Guinness Book of World Records depends on things other than just the truth or falsity of my being four feet tall and my being in the Guinness Book of World Records. It depends on all sorts of other things as well. So that's a situation where the phrase if then isn't being used as a truth functional connective. It's being used as a propositional connective. It builds a larger proposition out of two ingredient propositions, but there the propositional connective is not truth functional. In order for the propositional connective expressed by if and then to be truth functional, the propositions inside if and then can't be in the subjunctive mood. I should also mention that there are sometimes other phrases in English that are used to express the truth functional conditional. For instance, we sometimes just use the word if. So for instance, I might say to you the private investigator is eating lunch at New Havana, if Walter is eating lunch there. There. I just connected two propositions using the word if, but what I'm expressing is a truth functional conditional. It's the same thing as I would have been expressing if I had said if Walter is eating lunch at New Havana, then the private investigator is eating lunch at New Havana. Right? Those are just two different ways of saying the same thing. But in one case, I use the words if and then and in the other case, I just use the word if. So sometimes we express the truth functional conditional just by use of the word if. We could also use the phrase only if and that could also express the truth functional conditional. For instance, I might say Walter is eating lunch at New Havana, only if the private investigator is eating lunch at New Havana. That expresses just the same thing as saying if the private investigator is eating lunch at New Havana, then Walter is too. Right? They express just the same thing. They're true or false in just the same circumstances. It's just a different phrasing. Different phrasing, same meaning. So the truth functional conditional, while it's often expressed in English using the words if and then, is sometimes expressed using other words, and it's not always expressed by means of if then, sometimes if then, expresses propositional connectives that are not truth functional. In the next lecture, we're going to talk about by conditionals. Today, we're going to talk about a new propositional connective, a truth functional connective that I'll call the by conditional. Now what's a by conditional? In order to explain what a by conditional, let me start off by telling you the following story. And this is a true story I should add. When I was in eighth grade, I remember my first class in the morning was a math class. And there was a boy who sat next to me in math class. The teacher called him Bob. My third class later in the morning was a science class. And there was a boy who sat next to me in the science class. And the teacher called him George. And I was struck by the fact that Bob and George, who sat next to me in math and science class respectively, had the same last name. And they also bore an uncanny resemblance to each other. Well, one day, I asked Bob if he had a brother named George. And it turned out that he didn't have a brother named George. In fact, Bob was George. It was one and the same boy. And they just went by two different names to the two different teachers. But suppose that all you knew from my description of the situation was that there was a boy who sat next to me in math class named Bob and a boy who sat next to me in science class named George. And you asked me one day, was Bob born in the United States? Now, I might say to you, well, Bob was born in the United States if and only if George was. Now, there I'm using the phrase if and only if. Now, remember how the phrase if works? If I say if to connect two propositions p if q, that's equivalent to saying if q then p. But now remember how only if works. If I say p only if q, that's equivalent to saying if p then q. So when I use the phrase if and only if, I'm conjoining the conditional if p then q and the conditional if q then p. And so I get what I'll call a biconditional. A biconditional is a propositional connective that connects two propositions into a larger proposition. And the larger proposition is true just in case the two propositions that are part of it have the same truth value. In other words, the larger proposition p if and only if q is going to be true just in case p and q are both true or p and q are both false. So I could say George was born in the United States if and only if Bob was. Under what circumstances is that proposition going to be true? Well, it'll be true if George and Bob were both born in the United States, or well I guess it's misleading to say both because really there's only one boy that we're talking about. If George was born in the United States and Bob was born in the United States, it'll be true when both of those propositions are true. But it'll also be true when George was not born in the United States and Bob was not born in the United States. In other words, it'll be true when both of those two propositions are false. What makes true the proposition George was born in the United States if and only if Bob was is simply that the two propositions that are part of it, George was born in the United States and Bob was born in the United States, have the same truth value. Whatever that truth value is, whether it's the truth value true or the truth value false. As long as those two propositions have the same truth value, it's going to be true that George was born in the United States if and only if Bob was. And so the biconditional connecting those two propositions, George was born in the U.S. and Bob was born in the U.S., that biconditional is going to be true. So we can state the truth table for the truth functional connective, which is the biconditional as follows. The biconditional connects any two propositions, let's call them P and Q, doesn't matter what they are. When P is true and Q is true, then the biconditional P if and only if Q is going to be true. When P is true and Q is false, then the biconditional P if and only if Q is going to be false. When P is false and Q is true, then the biconditional P if and only if Q is going to be false. And finally, if P is false and Q is false, then the biconditional P if and only if q is going to be true. So that's the truth table for the biconditional. Now in the last couple of lectures, I described both the conditional and the biconditional as truth-functional connectives. And I've given some reason to think that they are truth-functional connectives. But you might worry that there are some examples that suggest that both the conditional and the biconditional are not truth-functional connectives. For instance, consider the sentence, if 2 plus 2 equals 4, then Pierre is the capital of South Dakota. Now there I'm using if then to express the conditional, right? I'm saying if it's true that 2 plus 2 equals 4, then it's true that Pierre is the capital of South Dakota. Now according to the truth table for the conditional, that conditional has got to be true because the first proposition, what we'll call the antecedent, the proposition that occurs right after the if, that antecedent is true. It's true that 2 plus 2 equals 4. And also the consequent, the proposition that occurs right after the then, the consequent is also true. It's true that Pierre is the capital of South Dakota. So according to the truth table for the conditional, it's going to be true that if 2 plus 2 equals 4, then Pierre is the capital of South Dakota. And now you might worry, what am I saying? This is a very strange consequence of the truth table for the conditional. Is it really true that if 2 plus 2 equals 4, then Pierre is the capital of South Dakota? And that's a very baffling thing to say. Now I want to say, I completely agree with this objection. It is a baffling thing to say that if 2 plus 2 equals 4, then Pierre is the capital of South Dakota. But just because it's a baffling thing to say, doesn't mean it's not true. Look, it's baffling that Pierre is the capital of South Dakota. But baffling as that may be, it's still true that Pierre is the capital of South Dakota. Some things are baffling even though they're true. And this is another example of that general kind of thing. It's baffling, nonetheless true. So to review, here's what we've done this week. We've learned about some truth functional connectives, like conjunction, disjunction, and the conditional, and the biconditional. And we've also learned about the truth functional operator negation. We've looked at the truth tables for these connectives and operators. The truth tables that show how the truth or falsity of the proposition that they can be used to create depends strictly on the truth or falsity of the propositions that they're applied to. And then we've looked at how those truth tables can be used to determine whether and why arguments that employ those truth functional connectives or operators are valid. Now, in order to master the skills that we've learned this week, there's no substitute for practice. And so what I'd like to recommend is that all of you practice the skills that you've learned this week using the resources that are listed. Okay, have fun. And I'll see you next week when we talk about categorical logic and quantifiers. Welcome to week five of our course, the week on categorical logic. Remember last week was on a part of deductive logic that we called propositional logic. Last week we tried to understand why certain inferences, certain arguments that use propositional connectives were valid because of the truth tables for the propositional connectives that they use. This week, we're going to be looking at arguments that are valid not because of the propositional connectives that they use. In fact, a lot of the arguments that we'll be looking at this week have no propositional connectives at all. We'll be looking at arguments that are valid for a different reason. We'll try to understand what that different reason is. But first, to review in more detail what we did last week, let's consider an example of a deductive argument that propositional logic can help us to understand. So let's look at this. Consider the following argument. Premise one. Jill is riding her bicycle if and only if John is walking to the park. You can imagine, let's say that Jill has a bicycle, but the only time she ever rides her bicycle is to meet John at the park. And the only way John ever gets to the park is by walking there. Let's say he lives just a block down from the park, so it doesn't make sense for him to get there any other way. So he only goes to the park by walking there and Jill only rides her bicycle when she's meeting him at the park. So according to premise one, Jill is riding her bicycle if and only if John is walking to the park. Premise two. John is walking to the park if and only if premise one is true. And the conclusion of the argument is therefore Jill is riding her bicycle. Now, let me ask you, is that argument valid? Is there any possible way for the premises to be true while the conclusion is false? Well, that's not obvious, is it? It takes a while to see that in fact, that argument is valid. And the way to see it is by using the truth table for the bi-conditional expressed in English by if and only if. We can use the truth table for the bi-conditional to see that that argument really is valid. Here, let me show you what I have in mind. So look here. There's the proposition Jill is riding her bicycle. Now, that proposition could be either true or false. Then there's the proposition John is walking to the park. And of course that proposition could be either true or false. So there are four possible combinations. Either Jill is riding her bicycle is true and John is walking to the park is true. Jill is riding her bicycle is true and John is walking to the park is false. Jill is riding her bicycle is false and John is walking to the park is true. Or both of those propositions are false. Those are the four possible scenarios. Now, according to premise one, Jill is riding her bicycle if and only if John is walking to the park. So, if premise one is true, that shows us that we're either in the first of those four scenarios or the last of those four scenarios. We're either in a scenario where it's true that Jill is riding her bicycle and it's true that John is walking to the park or else we're in a scenario where it's false that Jill is riding her bicycle and it's false that John is walking to the park. Okay, now consider the proposition. John is walking to the park if and only if that last statement, the statement to the left that Jill is riding her bicycle if and only if John is walking to the park, John is walking to the park if and only if that statement is true. Now, what's the truth table for that going to be? Well, the truth table for that is going to be as follows. It's going to be true whenever it's true that John is walking to the park and it's also true that Jill is riding her bicycle if and only if John is walking to the park. It's also going to be true whenever it's false that John is walking to the park and it's false that Jill is riding her bicycle if and only if John is walking to the park. So, that means that that last biconditional that John is walking to the park if and only if premise one is true. That's going to be true in the first two of our scenarios. It's going to be true when it's true that Jill is riding her bicycle and true that John is walking to the park. It's also going to be true when it's true that Jill is riding her bicycle and false that John is walking to the park. Okay, so now under what conditions will premise one and premise two of our argument be both true? Remember, premise one says Jill is riding her bicycle if and only if John is walking to the park. Premise two says John is walking to the park if and only if premise one is true. So under what conditions will those two premises be true? Well, those two premises will be true only in the first of our four scenarios because in the first of our four scenarios it'll be true that Jill is riding her bicycle if and only if John is walking to the park and in the first of our four scenarios it'll also be true that John is walking to the park if and only if that last statement premise one is also true. So that's the only scenario under which both of those premises are true. But now notice in that scenario when both of those premises are true Jill is riding her bicycle and so the argument that we just looked at is going to be valid because in any situation in which the two premises are true the conclusion is going to have to be true and we learn that by looking at the truth table for the bi-conditional. Now see that's an example of how we can use the truth table for a propositional connective like the bi-conditional to discover that a particularly tricky argument is valid. Right? We have a tricky deductive argument right here. It's not obvious whether or not it's valid but we can use the truth table for the bi-conditional to discover that the argument is valid. But remember I said we don't just use truth tables to discover when arguments are valid or that they're valid. We can also use truth tables to explain why they're valid even in cases where they're obviously valid. Right? So last week we looked at lots of examples of arguments that were obviously valid and in some cases obviously invalid and we used the truth table not to figure out that they were valid or invalid. It was already obvious that they were valid or invalid as the case may be. We used the truth table to understand why they were valid or invalid. That's what the truth table was for in those cases. Now, this week in our study of categorical logic, we want to find a method that can function like the method of truth tables to help us discover whether particular inferences are valid and why particular inferences are valid. But it's not going to be the same as the method of truth tables because truth tables only work for inferences or arguments that use truth functional connectives. But not every valid argument uses a truth functional connective. Consider a couple of the examples we looked at last week. Consider this argument from a week ago. No fish have wings. All birds have wings. All animals with gills are fish. Therefore no birds have gills. Is that argument valid? It's not immediately obvious whether or not it's valid. But it turns out that it is valid and we have a method for proving that it's valid and this method is what we'll be talking about this week. It's the central method of categorical logic. Notice also that there are other inferences which are obviously valid but the validity of which truth tables don't help us to understand. Consider for instance this example. Mary has a child who is pregnant. Only daughters can become pregnant. Therefore, Mary has at least one daughter. Now that argument is pretty obviously valid. But why? What is it about the argument that makes it valid? I said at the beginning of week four that there's something about the form of the argument. Something about the use of the terms only and at least that makes that argument valid. And any argument no matter what it's about that uses the terms only and at least in the way that this argument does is also going to be valid. But what is it about the use of those terms that makes the argument valid? Well this week in our study of categorical logic we're going to discover a way of understanding what's going on with that use of those terms only and at least those terms that we call quantifiers. We're going to discover a method of understanding quantifiers that can help us to understand why this particular argument and others that are of the same form are valid. Okay, so that's what we'll be doing this week in categorical logic. We'll be understanding how quantifiers work. But what are quantifiers? And after all, if the central words that we're going to be concerned about this week, the central concept this week is the concept of a quantifier, why is this called categorical logic anyway? Why not quantifier logic? Categorical logic is the logic of categories. Quantifiers are words like all, some, none, only, at least, and so forth. What do these things have to do with each other? We'll talk about that in the next lecture. In the last lecture, I raised the question why it is that we call the subject that we're going to study this week categorical logic, the logic of categories, when really what we're going to be doing is learning about quantifiers, quantifiers like all, some, none, only, at least, and so forth. What do categories and quantifiers have to do with each other? That's the topic of today's lecture. So first, let me talk a bit about categories and what role they can play in arguments. Now frequently, we give arguments that make use of categories of kinds of thing, consider the following argument. Brazilians speak Portuguese, Portuguese speakers understand Spanish, and therefore Brazilians understand Spanish. Now there's an argument with two premises in a conclusion, and it's an argument that talks about various categories of thing. One category of thing it talks about is Brazilians. Another category is Portuguese speakers, people who speak Portuguese, and a third category is people who understand Spanish. The argument brings those three categories into relation with each other, but how does it do that exactly? What precisely is it that the argument is telling us? Well, here's one interpretation of the argument. You could understand the argument of saying that some Brazilians speak Portuguese, certainly that's true. Maybe not all Brazilians speak Portuguese, or maybe there are some Brazilian citizens who've only recently acquired citizenship and have never learned to speak Portuguese. So some Brazilians speak Portuguese, that much, at least, is true. And some Portuguese speakers understand Spanish, of course that's true. But suppose the argument concludes from those two premises that some Brazilians understand Spanish. Would that be a valid argument? Well, although I'm confident that the conclusion of that argument is true, the argument itself wouldn't be valid, because there is a way for both premises of the argument to be true while the conclusion is false. Just imagine this. While it's true that some Brazilians speak Portuguese and some Portuguese speakers understand Spanish, you could imagine that all of the Portuguese speakers who do understand Spanish are in Portugal, not in Brazil, or in any case are in some other part of the world than Brazil, and that none of the Brazilians who speak Portuguese are among the Portuguese speakers who understand Spanish. In that circumstance, the premises could both be true while the conclusion that some Brazilians understand Spanish would be false. So the argument, even if its conclusion is true, the argument is not valid. But maybe that's not how to understand the argument that we just considered a moment ago, the argument from Brazilians speak Portuguese and Portuguese speakers understand Spanish to Brazilians understand Spanish. Maybe there's a different way to understand the argument. Maybe the right way to understand the argument is saying this. Most Brazilians speak Portuguese. Certainly that's true. And maybe the argument says is supposed to say also that most Portuguese speakers understand Spanish. I don't know if that's true, but I gather from people that it's probably true. And maybe the argument intends to draw the conclusion from those two premises that most Brazilians understand Spanish. Now would that argument be valid? Well, no, it wouldn't. Because even if the conclusion of the argument is true, there's still a possible scenario in which the premises are true while the conclusion is false. I could describe such a scenario to you. Suppose that while most Brazilians do speak Portuguese and most Portuguese speakers do understand Spanish, most Portuguese speakers, let's suppose, live outside Brazil. And the Portuguese speakers who understand Spanish are just those Portuguese speakers who live outside Brazil. So while then it would be true that most Brazilians speak Portuguese and most Portuguese speakers understand Spanish, it might not be true that most Brazilians understand Spanish because maybe that minority of Portuguese speakers who live in Brazil don't understand Spanish. The only Portuguese speakers who understand Spanish we could suppose are that majority of Portuguese speakers who live outside Brazil. Now, of course, that isn't the actual scenario, but it's a possible scenario. And since it's a possible scenario, there's a possible scenario in which the premises of the argument are true and the conclusion false. And so the argument is not valid. But maybe that's not even the correct way to understand our original argument about Brazilians. Maybe the correct way to understand our original argument is like this. Maybe the argument was intended to say all Brazilians speak Portuguese and all Portuguese speakers understand Spanish, therefore, all Brazilians understand Spanish. Now, one thing that this argument has to its credit is that it is valid. If the premises of this argument are true, if it's true that all Brazilians speak Portuguese, and it's true that all Portuguese speakers understand Spanish, then it's got to be true that all Brazilians understand Spanish. So this argument, in contrast to the last two arguments that we looked at, this argument is valid. Unfortunately, it's not sound because it's almost certainly not the case that the two premises are both true. Be that as it may, though, the argument is valid. Now, notice what we did. We started off with an initial argument that used three categories in the argument, the category of Brazilian, the category of Portuguese speaker, and the category of person who understands Spanish. Then we saw that by the use of certain modifiers, the modifiers sum, most, or all, we could make that original argument about Brazilians understanding Spanish. We could make that original argument more precise. And once we made it more precise, we could test whether or not it was valid. Okay. Now what I want to introduce is a way of testing whether or not an argument is valid when the argument is one that uses categories and quantifiers to modify those categories. The method involves the use of what we'll call Venn diagrams. A Venn diagram is a diagram that represents a number of different categories. In this simple Venn diagram, we have a representation of the category of Brazilians and we have a representation of the category of Portuguese speakers. Premise one of our original arguments stated a relation between Brazilians and Portuguese speakers. But what relation did it state? Well, that was left vague by the original statement of the argument. But then, when we looked at three different ways of making the argument more precise, we saw three different relations that could be stated. It could have said that some Brazilians are Portuguese speakers. The way of representing that would be by drawing an X right here to show that there is something, there is someone who is both a Brazilian and a Portuguese speaker. The second modification we made of the statement said most Brazilians are Portuguese speakers. Now, this week we're not going to discuss a way of representing the quantifier most in Venn diagrams. I just call it to your attention as a quantifier that can be used and frequently is used to modify categories and argument. But the third way that we interpreted our original argument about Brazilians understanding Spanish. The third way was as an argument that began by stating that all Brazilians speak Portuguese. Now, how would we represent the fact that all Brazilians speak Portuguese? Well, what are you saying when you say all Brazilians speak Portuguese? Well, you're saying that there is no Brazilian who falls outside the category of Portuguese speakers. Right? This circle right here represents the category of Portuguese speakers. And when you say all Brazilians speak Portuguese, what you're saying is that whatever Brazilians there are, they have to be inside this circle. They can't be outside the circle. They've got to be inside the circle of Portuguese speakers. So, the way to represent that is to shade out the portion of the Brazilian circle that's outside the Portuguese speaker circle. There, you're indicating that there isn't anything in the Brazilian circle. There isn't anything in the category of Brazilians that falls outside the category of Portuguese speakers. In other words, all Brazilians speak Portuguese. That's how you could represent that. And that's what we're going to do. To represent the statement, all Brazilians speak Portuguese, we simply shade out the part of the Brazilian circle that's outside the Portuguese speaker circle. And to represent some Brazilians speak Portuguese, we put an X in the Brazilian circle that's also inside the Portuguese speaker circle. And we used a Venn diagram to represent the information contained in the first premise of the argument about Brazilians. But how could we use a Venn diagram to represent the information contained in both premises and the conclusion? Well, here's how. So, here are three circles corresponding to the categories of Brazilians, Portuguese speakers, and those who understand Spanish. Now, suppose we interpret the first premise of our argument, Brazilians speak Portuguese, as saying that some Brazilians speak Portuguese. Well, as we saw already, the way to represent that is with an X right here, that's both in the circle of Brazilians and in the circle of Portuguese speakers. Okay, that represents that there is something, that X, that is both a Brazilian and a Portuguese speaker. Now, how would we represent the information that some Portuguese speakers understand Spanish? Again, we could do that with an X that is both in the circle of Portuguese speakers and in the circle of those who understand Spanish. Alright, so that represents that there is something that is both a Portuguese speaker and an understander of Spanish. But now notice, we've represented the information that some Brazilians speak Portuguese and some Portuguese speakers understand Spanish. Now, does that information imply that some Brazilians understand Spanish? If the information that some Brazilians are Portuguese speakers and some Portuguese speakers understand Spanish, if that information is true, does it follow from that, that some Brazilians understand Spanish? Well, one look at this diagram should tell us that no, it doesn't follow, because look here, right? You have a thing that is a Brazilian and a Portuguese speaker, representing the fact that some Brazilians speak Portuguese, then you have a thing that is a Portuguese speaker and understand Spanish, representing the fact that some Portuguese speakers understand Spanish. But do you have anything that is both a Brazilian and something that understands Spanish? No, not necessarily. So this diagram right here shows you that if the premises of our argument are some Brazilians are Portuguese speakers and some Portuguese speakers understand Spanish, from those premises it doesn't follow that some Brazilians understand Spanish. If you want to conclude that some Brazilians understand Spanish, your argument is not going to be valid. There's going to be a possible scenario in which the premises of your argument are true and the conclusion is false. And so we can say about this argument right here that this argument is not valid and we can understand why it's not valid by looking at this Venn diagram right here. That shows why our argument about some Brazilians being Portuguese speakers, why that argument is not valid. Okay, but now let's consider not the argument to the effect that some Brazilians speak Portuguese, let's consider the argument to the effect that all Brazilians speak Portuguese. How would we represent the information in those premises in that conclusion? Well if all Brazilians speak Portuguese what that means is that all of the Brazilians must be inside the category of Portuguese speakers so there can't be any Brazilians outside that category. Okay, so we can shade out the portion of the Brazilians circle that's outside the category of Portuguese speakers. We know there's nothing in there because all the Brazilians there are are inside the category of Portuguese speaker according to premise one of this new argument. Right, according to premise one all Brazilians are Portuguese speakers according to that premise all the Brazilians there are have to be in here. Okay premise two says all Portuguese speakers understand Spanish. Okay, well if all Portuguese speakers understand Spanish then there cannot be any Portuguese speakers who are outside the category of those who understand Spanish. Right, here's the category of those who understand Spanish and all the Portuguese speakers according to premise two have to be inside that circle. So that means that we can shade out the portion of the Portuguese speaker circle that's outside the understand Spanish circle. Right, there's there are no Portuguese speakers that fall outside the category of understanders of Spanish according to premise two of this argument. Right, that all Portuguese speakers understand Spanish. So now we can represent that information that way. Okay, now that we've represented the information contained in those two premises all Brazilians speak Portuguese and all Portuguese speakers understand Spanish. Let's ask does it follow from those two premises that all Brazilians understand Spanish? Well, let's see. Yes, it does. What Brazilians can there be there can't be any out here and there can't be any in here and of course there can't be any in here either. The only Brazilians there can be are these in here. That's the only part of the Brazilian circle that is left unshaded. Once we shaded in the circles that we had to shade in to represent the first two premises of the argument. Right, once we shaded in the part of the Brazilian circle that we had to shade in in order to represent the premise that all Brazilians were Portuguese speakers and then we also shaded in the Portuguese speaker circle outside the understanding of Spanish circle. The only part of the Brazilian circle that's left unshaded is this, which means that whatever Brazilians there are have to be in here. So if there are any Brazilians at all, they've got to understand Spanish because they're in the circle of things that understand Spanish. Therefore, all Brazilians understand Spanish and we've just used this Venn diagram to prove visually that our argument is valid. This argument back here is valid and our three circle Venn diagram shows that it's valid. In the last lecture I said that quantifiers modify categories. That's how quantifiers and categories are related to each other. Categories are kinds of things and quantifiers modify categories. They can modify them in different ways. There are different kinds of quantifiers. In today's lecture we'll talk about some of the different kinds of quantifiers and how they modify categories. We'll also talk about how the representation of these different quantifiers differs both verbally and visually using the Venn diagram. Okay, so what are the different kinds of quantifiers? Well, here are some of the different kinds of quantifiers. There's the quantifier all and we can apply this to categories. Notice by the way in this slide I'm using an uppercase F and an uppercase G to represent any category at all. So in a statement of the form all F's are G's that that's the claim that all things that fall into one category, never mind exactly what that category is. Let's just call it F. Also fall into a second category. Again, never mind what that category is. We can just call it G. There are lots of examples of this kind of claim. When you say all things of one category also fall into a second category. For instance, all dogs are mammals. All squares are rectangles. All Coursera students are human and so on. In all of these cases you're making a claim of the form that all things that fall into one category, the F category also fall into the G category. So all is one kind of quantifier and any statement of the form all F's are G's. We're going to call a statement of type A, a proposition of type A. Then there's the quantifier no, which we can use in a statement of the form no F's are G's. No things of one category also fall into a second category. So for instance, you might say no humans are reptile, no Coursera students are trees, no democracies are at war. So there are examples of statements of the form that we're going to call E and the E statement is a statement to the effect that no things that fall into one category also fall into a second category. Then there's the quantifier sum. Now the quantifier sum can be used to make statements of two very different kinds. You could say that some things that fall into one category also fall into a second category. So if you'd said some humans are female, some Coursera students are American, some Americans speak Spanish. Those are statements to the effect that some things falling into one category, the F's, also fall into a second category, the G's. Some F's are G's. Propositions of that form will call I propositions. Finally, we could also use the quantifier sum to make a different kind of statement. A statement to the effect that some things that fall into one category don't fall into a second category. Some humans are not female, some Coursera students are not American, some Americans are not Spanish speakers. Statements of that form will call O statements or propositions. They say that some things that fall into one category don't fall into a second category. Some F's are not G's. So those are the four kinds of statements we're going to focus on this week on categorical logic. We'll consider other kinds of statements as well and we'll mention some other kinds of quantifiers, but those are the ones that are going to be of primary interest to us. Now, I've talked about these different quantifiers and how they can be used to make statements of very different kinds, but now we can visually represent the differences in the information provided in these four different kinds of statements. So consider, how would we visually represent a statement of the form that all F's are G's? All things that fall into one category also fall into a second category. Well, if you wanted to say all F's are G's, let's see, how would you do that? You'd be saying that all of the F's that there are fall into the G circle, but if all the F's that there are fall into the G circle, then there can't be any F's outside the G circle, right? So the Venn diagram for all F's or G's would look like that. You'd be saying whatever F's there are, they've got to be in here, right? There can't be any outside there. So that would be the Venn diagram for all F's or G's or a proposition of the A form. Next, there are propositions of the E form. Now, how would we represent those? Well, let's see. Here's the Venn diagram for no F's or G's. When you say no F's or G's, you're saying if there are any F's at all, they can't be inside the G circle. So you've got to shade out that portion of the F circle that's inside the G circle, right? The shading implies that there's nothing there, right? So there are no F's inside the G circle, and that's how you represent no F's or G's. Next, there are statements of the I form. Some F's or G's. How would you represent those? Some F's or G's, you use an X mark to represent that there is a thing. So you use an X to represent that there is a thing that's in the F circle, and that's also in the G circle, right? So there's a thing right there. It's in the F circle. So it is an F, but it's also a G. So some F's are G's. That's how you'd represent, how you'd visually represent a statement of the I form. Finally, how about a statement of the O form? Some F's are not G's. How would you visually represent that? Well, you'd have to make an X to indicate that there is an F, right? There is a thing that is F, but it's not G. If it's not G, then it's got to be outside the G circle. So it's inside the F circle, but outside the G circle. And that's how you'd indicate visually some F's are not G's. Now, I'd like you to notice something. We've just gone over the Venn diagrams for propositions of the A, E, I, and O forms. But what I'd like you to notice, let's go back to those forms. Propositions of the A form, all F's are G's are negations of propositions of the O form. Some F's are not G's, right? If all F's are G's, then it's not going to be true that some F's are not G's. And if some F's are not G's, then it's not going to be true that all F's are G's. All F's are G's, in other words, is going to be true when and only when some F's are not G's is not true. And similarly, propositions of the E form are going to be negations of propositions of the I form, right? When is it going to be true that no F's are G's? It's going to be true that no F's are G's when and only when it's not true that some F's are G's, right? If some F's are G's, then it's not going to be true that no F's are G's. And if no F's are G's, then it's not going to be true that some F's are G's. So propositions of the A and O form are negations of each other, and propositions of the E and I form are negations of each other. And those relationships are represented visually on the Venn diagrams that we just drew, right? Consider again, the Venn diagram for propositions of the A form, propositions of the A form, the Venn diagram is going to have shading in here, but in propositions of the O form, the Venn diagram is going to have an X in here, in precisely the place where propositions of the A form had shading. Propositions of the E form are going to have shading in here, whereas propositions of the I form are going to have an X in here. So the way that we represent negation using Venn diagrams is one proposition is going to be the negation of another just in case the first has shading wherever the second has an X, or vice versa, right? If one proposition has an X wherever the other has shading, or it has shading wherever the other has an X, then the two propositions are going to be the negations of each other. That's how the relation of negation is visually represented in Venn diagrams. In the last lecture, we learned about propositions of the forms that we labeled A, E, I, and O. We learned how to represent these propositions verbally, and also how to represent them visually using Venn diagrams. Today, I want to apply those lessons to study a kind of argument that we're going to call an immediate categorical inference. So what's an immediate categorical inference? An immediate categorical inference is an inference with just one premise, and of course, one conclusion, where each of those two statements, both the premise and the conclusion, are of the form A, E, I, or O. They needn't be of the same form. One of them could be, let's say, of the E form and the other one of the O form or whatever. They needn't be of the same form, but they're each of one of those four forms. Now, these are very simple inferences, but we're going to study them today because we're going to see how we can use Venn diagrams to show that some of these inferences are valid and others aren't. Now, before we do that, let me say something about the kinds of propositions that are involved in these inferences, the A, E, I, and O propositions. Remember what those letters stand for. The A proposition is a proposition of the form all F's or G's, all things that fall into one category also fall into a second category, and E proposition is a proposition of the form no F's or G's, nothing that falls into the first category also falls into the second category. An I proposition is a proposition of the form some F's or G's, that's to say something that falls into the first category falls into the second category, and an O proposition is a proposition of the form some F's or not G's, something that falls into the first category does not fall into the second category. Now, notice in each of those propositions, there's one category that I'm indicating by use of the schematic letter F. There's one category that gets directly modified by the quantifier, right, the F category, right. I'm talking about in the a proposition I'm talking about all things that fall into that category. In the e proposition I'm talking about no things that fall into that category. In the i or the o proposition I'm talking about some things that fall into that category. So there's a category that gets directly modified by the quantifier and then there's another category that doesn't. Okay, let's introduce terminology to distinguish these two categories. We'll talk about the two categories as the subject term and the predicate term. So the category that gets directly modified by the quantifier, the F category is what we're going to call the subject term and the category that doesn't get directly modified by the quantifier is what we're going to call the predicate term. You'll see in our later lecture about syllogisms why this terminology is going to be useful. It's not going to be obvious today why it's useful, but it'll eventually become useful. Okay, so Fs are subject terms, Gs are predicate terms, and immediate categorical inferences are inferences that have one premise with the subject term and predicate term and one conclusion with the subject term and the predicate term. All right. What kinds of immediate categorical inferences are there? Well, there are lots, but the most common kind of immediate categorical inference is one that we'll call conversion. A conversion inference is an inference in which the conclusion just switches the subject term and predicate term as they occur in the premise. So if the premise is of the form of no Fs or Gs, let's say no Duke students are NFL football players, then the conclusion would be of the form no Gs or Fs. No NFL football players are Duke students. That's an example of an immediate categorical inference that's a conversion inference. It converts one e proposition to another e proposition. You could do it for other forms of proposition. So for instance, consider the conversion inference from an a proposition to another a proposition. Consider the inference from all Duke students are NFL football players. To the conclusion, all NFL football players are Duke students. Now, notice the first of those two conversion inferences is plausibly valid, whereas the second one isn't. Why is that? Well, we can see why that is. If we use Venn diagrams to visually represent the information contained in the premises of those inferences, more generally, I can say right now that conversion inferences are valid for propositions of the E and I form, but they're not valid for propositions of the A or O form. We can understand why that is using Venn diagrams. So why is it that conversion inferences from the A form to the A form are not valid? Why are they not valid? Well, let's consider. What are you saying when you say all Fs or Gs? Well, you're saying that whatever Fs there are, they're not outside the G circle. They're all in the G circle. So you represent that information by shading in the portion of the F circle that's outside the G circle in order to indicate that there's nothing there. Okay, but now once you've shaded in that portion of the F circle, does that tell you that all Gs are Fs? No. Of course, it leaves open that all Gs are Fs. I mean, it could be that all the Gs there are are in here, but shading in the portion of the F circle that's outside the G circle also leaves it open that there are plenty of Gs out here. So once we look at the Venn diagram from the inference for all Fs or Gs to all Gs or Fs, we understand why that inference is not valid. Shading in the portion of the F circle outside the G circle leaves open that there are plenty of Gs that are outside the F circle. Okay, what about the second kind of conversion inference for propositions of the E form from no Fs or Gs to no Gs or Fs? Well, let's see, how would we represent no Fs or Gs? Well, we do that by shading in the portion of the F circle that's inside the G circle, right? So that shows that no Fs are in the G circle, no Fs or Gs. But now look, if no Fs or Gs, then we can just read off from that that no Gs are Fs, right? If there are any Gs, they can't be in the area that's shaded in, right? Because what it means to shade in the area is that there's nothing there. So whatever Gs there are, they can't be inside the F circle. They've got to be outside the F circle. So if it's true that no Fs or Gs, then it's got to be true that no Gs are Fs. The Venn diagram for no Fs or Gs shows us that. So conversion inferences are invalid for A propositions, but they're valid for E propositions. What about I propositions? Well, let's see, I propositions have the form some Fs or Gs. Well, how would we represent some Fs or Gs? We would indicate that there is something that's inside the F circle. It's an F, but it's also a G. It's in the G circle. We'd indicate it with an X. Okay, but notice, once we indicate by means of that X that there's something inside the F circle that's also inside the G circle, you can just read off from that, that there's something inside the G circle that's also inside the F circle. In other words, some Gs are Fs. So once again, from the Venn diagram, you can see that if some Fs or Gs is true, then some Gs or Fs has got to be true. In other words, the conversion inference for an I proposition has got to be valid. Okay, finally, what about O propositions? Some Fs are not Gs. Well, let's see, some Fs are not Gs. How would you diagram that? Well, some Fs, so you want to use an X to indicate that there is an F, but it's not a G. So it's got to be outside the G circle. So there, you draw an X that's inside the F circle to show that it is an F, but it's outside the G circle. So it's not a G. That's how you represent that some Fs are not Gs. Okay, now does that imply that some Gs are not F? No. Maybe there are no Gs at all. For all that you've just been told, right, you're told that some Fs are not G. That doesn't tell you that there are any Gs. Or if there are any Gs, maybe all the Gs are in here. You don't know whether there are any Gs in here. So from the premise that some Fs are not Gs, you can't infer that some Gs are not F. It doesn't follow that some Gs are not F. And the Venn diagram shows us why. So this last conversion inference on propositions of the O form is not valid. And once again, you can see that from the Venn diagram for propositions of the O form. So this shows how Venn diagram, simple two circle Venn diagrams can be used to establish the validity or invalidity of immediate categorical inferences. Okay, next time we'll consider inferences of a more complicated kind. See you next time. In the last class, we talked about immediate categorical inferences, which are inferences that have a single premise and a conclusion where each of those two propositions is of the A, E, I, or O form. Today, we're going to talk about a new kind of inference called a syllogism. So what's a syllogism? Here's a definition. A syllogism is an argument that has two premises and a conclusion where all three of those propositions are of the form A, E, I, or O. Now, the conclusion is going to have two categories in it. One category that's modified by a quantifier, and we're going to call that the subject category. The other category is not modified by a quantifier. We're going to call that the predicate category. Now, the subject category is what we call the subject term of the syllogism. The predicate category, the category that's not modified by a quantifier in the conclusion, that's what we're going to call the predicate term of the syllogism. Now, every syllogism is going to have a premise that includes the subject term and another premise that includes the predicate term. Now, the premise that includes the subject term is what we're going to call the minor premise of the syllogism. And the premise that includes the predicate term is what we're going to call the major premise of the syllogism. So every syllogism is going to have two premises where one premise is the minor premise and it's going to include the subject term of the syllogism, which is the category that's modified by the quantifier in the conclusion of the syllogism. And the other premise is the major premise of the syllogism. It includes the predicate term of the syllogism, which is the category that's not modified by a quantifier in the conclusion of the syllogism. Okay, now let's look at how we can use Venn diagrams to represent the information that's carried by syllogisms and so to assess whether or not a particular syllogism is valid. In order to visually represent the information that's given in the syllogism, we need to use a Venn diagram with three circles, not just two circles, because in the syllogism we have three categories. We have the subject term, the subject category, the middle term, the G's, and the predicate term, the H's. So we need to get a Venn diagram with all three of those circles to represent the information contained in the syllogism. Now, I've described all this very abstractly. Let me give some examples so you can see how this works and how we can use Venn diagrams like this to figure out whether or not syllogisms are valid and to explain why they're valid. Okay, so consider this syllogism. All Duke students are humans. All humans are animals. Therefore, all Duke students are animals. Okay, valid or not? Well, pretty obviously it is valid. But a Venn diagram could help us to understand why it's valid. So let's diagram the information contained in the premises. So the first premise recall was that all Duke students are humans. Well, if we want to show that all Duke students are humans, that's to say that whatever Duke students there are have got to be inside the circle of the humans. So this region of the Duke student circle, this region of the circle that's outside the circle of the humans, we can shade that in to indicate that there's nothing there. Right? Nothing here because whatever Duke students there are have got to be in this region. Okay, the second premise said that all humans are animals. Well, if all humans are animals, then what that tells us is that whatever humans there are have got to be inside the circle of the animals. So we can shade in the portion of the human circle that's outside the animal circle, right? Because there aren't any humans out there. So shade that in. Okay, but now we look at the diagram with those regions shaded in. And what can we conclude? Well, we can conclude that whatever Duke students there are have got to be in this region right here. That's the only region where there could be any Duke students given the two premises of our argument. In other words, all Duke students are animals. And that's just the conclusion of our syllogism. Remember, all Duke students are animals. So we just used the Venn diagram to explain why this syllogism, which is obviously valid, is valid. We explained why it is valid. It is valid because when you shade in the portion of the Duke student circle that's outside the human circle and you shade in the portion of the human circle that's outside the animal circle, the only place left over in the Duke student circle for there to be any Duke students is inside the animal circle. And so all Duke students are animals, as we all know. Now, here's a second syllogism. Let's consider this one. Some Duke students are humans. All humans are animals. Therefore, some Duke students are animals. Valid or not? Well, let's see. So, some Duke students are humans. How would we represent that information? Some Duke students are humans. What that means is that there's got to be something in this part of the circle of Duke students that's also in the circle of humans. But the first premise doesn't tell us where that thing would be. Would it be here or would it be here? Well, let's hedge our bets and draw it right here since we don't know. We'll draw it on the borderline of the animal circle since the first premise doesn't yet tell us whether it's here or here. The second premise said all humans are animals. Well, if all humans are animals, what that tells us is that there aren't any humans outside the animal circle. So, we can just shade in the part of the human circle that's outside the animal circle. Shade it in right there. But then notice, remember, we had to have an X inside our Duke student circle and our human circle inside the intersection. Well, it can't be in here because this is shaded in, which means there's nothing there. So, the only place it can be is right there. So, now we know that the X had to be over here. But once we put the X over there, which we have to, given the information in the two premises of our syllogism, what can we conclude? We can conclude that some Duke students are animals. And that's exactly what the conclusion of the syllogism is. That some Duke students are animals. Finally, oh, that should say example three, not example one. Finally, consider this syllogism. No Duke students are humans. All humans are animals. Therefore, no Duke students are animals. Okay. Now, how would we represent that using the Venn diagram? Well, no Duke students are humans. So, that means that we have to shade in the portion of the Duke student circle that's inside the human circle to show that there's nothing in there. Right? None of the Duke students are humans. Okay? All humans are animals. So, that means we have to shade in the portion of the human circle that's outside the animal circle. Right? Because there are no humans out there. All humans are animals. Right? And the conclusion was that no Duke students are animals. But wait a second. You can't read that off the diagram. There could be lots of Duke students over here who are animals. There could be all sorts of Duke students who are animals right there. They wouldn't be human. But there could still be plenty of Duke students that are animals. In other words, this third syllogism is not valid. And it's not valid for a reason that's made clear by the Venn diagram that we just looked at. The Venn diagram shows us that and explains why the inference, the syllogism, is not valid. Just because no Duke students are humans and all humans are animals, it doesn't follow that no Duke students are animals. Those premises leave it open that there are plenty of animal Duke students. They just wouldn't be the humans. So, in this lecture, I've tried to show how we can use Venn diagrams to predict that and to explain why syllogisms are valid or invalid, as the case may be. Next time, we'll apply these lessons to some examples that we've already looked at before, but that we weren't treating as syllogisms when we looked at them before. See you next time. In the last few lectures, we've seen how we can use Venn diagrams to predict that and to show why, explain why certain immediate categorical inferences and certain syllogisms are valid or invalid. Now, I'd like to make a point today about categorical logic, about categories in general. It might seem that the application of the method of Venn diagrams is really quite limited, because a lot of our statements aren't really about categories at all. They're about individuals, not categories. But I want to say that this is an example of how ordinary language can mislead us. If we think about precisely what it is that we're saying in a lot of the ordinary statements that appear to be about individuals, we'll see that, in fact, those ordinary statements really are about categories, not just about individuals. Let me give you an example to illustrate this point. Consider the statement, Mary owns a Ferrari. Now, that statement appears to be just about individuals. It doesn't appear to involve any categories, right? There's Mary, who, let's suppose, is a particular person that I'm talking about, like a co-worker of mine. Not that any of my co-workers would own a Ferrari, but suppose that Mary is a particular person, and we're talking about Mary's Ferrari, which is a particular car, and it seems that that statement is just claiming that the person, the particular person I'm talking about, owns that particular car. All right? There don't seem to be any categories involved at all. But wait a second. Compare the statement Mary owns a Ferrari to the statement, some of Mary's possessions are Ferrari cars. Now, that second statement notice is of the I form. It's of the form some F's, RGs. You're saying some things that fall into one category, the category of Mary's possessions, also fall into a second category, the category of Ferrari cars. Now, these two statements seem to amount to the same thing. When I say Mary owns a Ferrari, what I'm saying is true if and only if some of Mary's possessions are Ferrari cars. The information carried by one of those statements seems to be the same as the information carried by the other. So here's a case where to look at the language we were using when we said Mary owns a Ferrari, you would have thought, well, we're not talking about any categories there. So the method of then diagrams and all of this stuff about categorical logic is completely irrelevant to any argument we might make that uses the statement Mary owns a Ferrari either as a premise or as a conclusion. But in fact, that's not true. In fact, the statement that Mary owns a Ferrari is equivalent to the statement some of Mary's possessions are Ferrari cars, which is a statement of the I form some F surges. And so the categorical logic that we've been developing this week in the method of Venn diagrams actually can be used to study the validity of arguments where the statement Mary owns a Ferrari is included as one of the premises or as the conclusion. Because the statement Mary owns a Ferrari is just equivalent to a statement of the I form some of Mary's possessions or Ferrari cars. I want to say this phenomenon is very general. Not every statement is of the AI or O forms, but lots and lots of ordinary statements that we make are of one of those forms. Many more than ordinary language would suggest. So with that in mind, I want now to show how we can apply the categorical logic, how we can apply the lessons we learned concerning the validity of syllogisms and how we can use Venn diagrams to predict and explain the validity of syllogisms, how we can now apply those lessons to arguments that are syllogisms, but you wouldn't think that they are just to look at the language in which they're expressed. Okay, see next time. Today, we're going to talk about how you can use Venn diagrams to show that a particular inference is valid and to explain why it's valid. We're going to do that by considering the particular inferences, the particular arguments that we looked at at the beginning of last week when we were starting our unit on deductive logic. So let's look at those inferences right now. Remember the first one was the example that Walter gave back in week three, our argument about Mary. Premise one was Mary has a child who is pregnant. Premise two was only daughters can become pregnant. And so the conclusion of those two premises was therefore Mary has at least one daughter. Okay, now how do we represent the information contained in the premises of this inference using a Venn diagram? Well, let's begin by asking what are the categories that this inference that this argument brings into relation with each other is Mary one of the categories? Well, no, because Mary's not a category, Mary's an object, Mary's a thing. She's a particular thing. She's not a category. What is a category though, that's mentioned in this argument is Mary's children. And the information in the first premise is that the category of Mary's children includes something that is also in the category of pregnant people or pregnant beings. So we can visually represent that information as follows. The category of Mary's children includes something that's in the category of pregnant people. Right, so we don't know whether or not the category of Mary's children includes anything out here. But whether or not it includes anything out here, it's got to include something that's in this region. So do we draw an X? Well, let's wait a minute. Let's ask, where would we draw that X? Would we draw it here? Or would we draw it here? That's going to make a difference. That's going to make a difference where we draw it. So we don't yet know whether to draw the X in here or in here. We know though that the X is supposed to go somewhere in this football shaped region that's in the intersection of the category of Mary's children and the category of pregnant people. Maybe premise two will help us figure out where to draw that X. Let's see. So premise two says only daughters can become pregnant. So how do we visually represent the information that only daughters can become pregnant? Well, only daughters can become pregnant means that there can't be any pregnant people who are not daughters. So we have to shade out the circle, the portion of the circle of pregnant people, people that's outside the circle of daughters. Right? There can't be any pregnant people who are outside this circle. All the pregnant people are inside this circle. Okay, but remember, what did premise one tell us? Premise one told us that Mary has a child who is inside this circle. So here's what we know. Mary has a child who's inside the circle of pregnant people and anyone who's inside the circle of pregnant people must also be inside the circle of daughters. Well, so Mary's child who's inside the pregnant people circle must be right here. So that's where the X goes. So what we can figure out from just the first two premises, remember, I haven't relied on any information here other than the information given in premises one and two. What premises one and two tell us is that there's an X and it goes right here. Okay, but if the X goes right there, then what does that tell us? That tells us that at least one of Mary's children is a daughter. Mary has at least one daughter. Maybe she has more than one daughter, but we know based on the information contained in premises one and two, we can conclude that she has at least one daughter. We know that for sure based on the information contained in premises one and two. So if the information contained in premises one and two is correct, then Mary must have at least one daughter. And so the argument is valid. And the Venn diagram shows us that the argument is valid because once we visually represent the information contained in premises one and two, then we can simply read off the diagram that the conclusion is true. We can read off the diagram that Mary has at least one daughter. Okay, now let's see if we can apply this technique to the other arguments of the same form that we considered at the beginning of last week. Remember, we considered an argument concerning Terry. Premise one was Terry has a job in which she arrests people. Premise two was only police officers can arrest people. And the conclusion of those two premises was therefore at least one of Terry's jobs is as a police officer. Now, how would we visually represent the information contained in the premises? Well, let's consider premise one tells us that Terry's jobs includes a job in which she arrests people, right? So at least one of Terry's jobs has to be in this circle. Because whatever else it is that Terry does, she has a job in which she arrests people. So at least one of her jobs must be in this circle. And of course, it has to be in this circle because that's the circle of Terry's job. So at least one of Terry's jobs must be in this football shaped region right here in this intersection of the category of Terry's jobs and professionals who arrest people. That's what premise one tells us. But again, it doesn't tell us where that particular job of Terry's would be. Is it here? Or is it here? Right? Premise one doesn't give us that information. But what does premise two tell us? Well, remember premise two tells us that only police officers can arrest people. So how would we visually represent that? Only police officers can arrest people. That means that there's in the circle of professionals who arrest people, we have to shade in this part because there are no professionals who arrest people other than police officers. Only police officers arrest people. So we shade in that portion of the professionals who arrest people circle. And I remember what we learned from premise one was that Terry has a job in which she arrests people. So somewhere in this football shaped region, there has to be an X. But we know now that it can't be here. So the X must be here. So that's the information that we get from premises one and two. But notice, once we visually represent that information in our Venn diagram, then we can simply read off the Venn diagram that Terry has a job, at least one job in which she's a police officer. So at least one of Terry's jobs is as a police officer. And we can just read that off the Venn diagram once we've used the Venn diagram to represent the information contained in premises one and two. So the Venn diagram, again, can be used to represent the validity of the inference. And not only that, notice also that the Venn diagram for this inference is the same in the placement of its shading in its X's as the Venn diagram for the previous inference about Mary. Well, what does that tell us? That tells us that the two inferences, the two arguments are of the same form. They're of the same form. And you can see that by seeing that their Venn diagrams look the same. The only difference between the two Venn diagrams is the labeling of the circles is the categories, the specific categories involved in the arguments. Other than the specific categories involved in the arguments, the labeling of the circles, everything else is the same. The shading is in the same place, the X is in the same place. Okay. Now, can we apply this to our third argument about Robert? You'll remember this third argument that we considered of the same form at the beginning of week four at the beginning of our unit on deductive logic. Remember, we considered an argument that went like this. Premise one, Robert has a pet who is canine. Premise two, only mammals are canine. Conclusion, therefore at least one of Robert's pets is mammal. Okay, well, how would we visually represent the information contained in premises one and two of this argument? Here's how. At least one of Robert's pets is canine. So that means that whatever other pets Robert has, right, maybe Robert has some non canine pets, but at least one of Robert's pets must be in this circle. Well, that particular pet that we're talking about has to be in this circle. But of course, it also has to be in this circle because this is the circle of Robert's pets. So the pet must be in this football shaped region right here, the intersection of Robert's pets and canines. But where is it? Is it here or is it here? Well, now let's look at premise two. What do we find out from premise two? What we find out from premise two is that only mammals are canine. Okay, well, if only mammals are canine, then that means that there can't be any canines outside the circle of mammals, right? All the canines, whatever canines there are, are in this region right here. There aren't any canines outside the mammal circle. So we know that whatever canines there are have to be in this intersection right here of the circle of canines in the circle of mammals. And we also know that whatever that Robert has at least one pet in the circle of canines. Okay, well, if Robert has a pet in the circle of canines, and we also know that there's nothing in the circle of canines that's over here, then we know that Robert's pet, which has to be in this circle, right, this is the circle of Robert's pets, Robert's pet has got to be in here, right? The pet that we're talking about, the pet that's canine has got to be in there. Okay, so that's a way of visually representing the information contained in the in the two premises of our argument. But once we visually represent that information, we can just look at the diagram and read off the fact that at least one of Robert's pets is mammal. Because at least one of Robert's pets is inside the circle of mammals, right, inside the circle, which means that at least one of Robert's pets is mammal. But that's exactly what the conclusion says. And so this Venn diagram shows us that this argument about Robert is valid just as the arguments about Mary and Terry were valid. And furthermore, this argument about Robert is valid for the same reason as the arguments about Mary and Terry were valid. They're valid not because of their subject matter, right, the three arguments have completely different subject matters. They're valid because of their form. And their form is what's revealed by the Venn diagram. The form is what's in common to the three Venn diagrams. The placement of shading and X's in the Venn diagrams is their common form. And that's what explains why all three of the arguments are valid. Okay, see you next time. In the last few lectures, we've seen how we can use Venn diagrams to visually represent the information that's conveyed in A, E, I or O propositions. And we've also seen how there are different ways in ordinary language of expressing such propositions. Sometimes such propositions are expressed even by sentences that use individuals' names and don't explicitly mention categories. Today, I want to talk a bit more about that. I want to talk about the various ways in which, in English at least, and in many other natural languages, we can represent the information conveyed by A, E, I or O propositions using forms of language that we haven't yet discussed. So let's consider some examples. So consider propositions of the form not all F's or G's. We haven't talked about not all before. Well, when you say not all F's or G's, what exactly are you saying? Usually, when you say not all F's or G's, what you mean to be saying is that there are some F's that are not G's. In short, what you mean to be saying when you say not all F's or G's is usually a proposition of the O form. So how would you represent not all F's or G's? Well, all F's or G's, remember, would be represented by shading this out. That would be all F's or G's, but you're saying not all F's or G's. In other words, some F's are not G's. So instead of shade there, what you would do is put an X right there. There's some F, something out there that's not a G. It's outside the category of the G's. And for some examples, you might say not all geniuses take Corsera courses. In other words, some geniuses don't take Corsera courses. Or you might say not everything that Pat does is intended to annoy Chris. In other words, some of the things that Pat does, some of the things that fall into the category, things that Pat does, are intended to annoy Chris. That is to say they do fall into the category, things that are intended to annoy Chris. So those are both examples of statements of the form not all F's or G's. And they're both equivalent to a statement of the form some F's or not G's. Now consider statements of the form all F's are not G's. Well, when you say something of the form all F's or not G's, that's usually intended to convey that no F's are G's. In other words, it's usually intended to convey a proposition of the E form. So when you say no F's or G's, how do you represent that? Well, you represent it by shading in the intersection of the F's and the G's. And that's just to say that all F's are not G's. Right? If there are any F's at all, they've got to be out here. They've got to be outside the category of the G's. Some examples of statements like that. All Nobel Prize winners are not alcoholics. Right? You're saying if there are any Nobel Prize winners, they're outside the category of the alcoholics. Everything that Pat does is not designed to achieve victory. Again, you're saying that whatever falls into the category of things that Pat does, it is outside the category of things designed to achieve victory. Right? So if this is the category of Pat's actions, and this is the category of things designed to achieve victory, then when you say everything that Pat does is not designed to achieve victory, you're saying there's nothing in this intersection. Whatever Pat's actions are, they've got to be out here. Okay, finally, let's consider a statement of the form. Some F's are both G's and H's. If you say some F's are both G's and H's, what are you saying? Well, are you saying that there are some F's that are G's and some F's that are H's? Well, that's something you could say, of course. You could say some F's are G's and some F's are H's. You could say some men are tall and some men are short. But when you say some F's are both G's and H's, you're not saying that. You're saying that some F's are in this intersection of G's and H's. So some F's have got to be here. That's what you're saying. When you say some F's are both G's and H's. That's why you couldn't say, at least you couldn't truthfully say some men are both tall and short. There's no man who is both tall and short. But you could say there are some men who are both wealthy and happy. They're a man who is wealthy and who is happy. Other examples, some philosophers are both robotic and monotone. It's not just that there are some philosophers who are robotic and some philosophers who are monotone. There are actually some philosophers who are both robotic and monotone. Some of the things that Pat does are both intended to amuse and to provoke. It's not just that some of the things she does are intended to amuse and some of the things she does are intended to provoke. It's that some of the things she does are intended to do both amuse and to provoke. So if these are Pat's actions right here, and this is the category of things intended to amuse, and this is the category of things intended to provoke, then this last statement, some of the things that Pat does are both intended to amuse and to provoke, is saying that some of Pat's actions fall into this area right here, this intersection of things designed to amuse and things designed to provoke. But of course, since they're Pat's actions, they have to fall into this portion of the area right here. Okay, I hope I've given you a sense of the various ways in which ordinary language can express ideas that we can represent visually using Venn diagrams. Over the past couple of weeks, we've seen how we can use truth tables in Venn diagrams to predict and explain the validity of arguments. But the arguments that we've looked at are all arguments that are given in ordinary language that we can understand. But of course, not all arguments are like that. Some arguments are given in foreign languages that we don't understand, or they're given in technical languages that we don't understand. Could you use truth tables or Venn diagrams to predict and explain the validity of those arguments? Even those arguments that are given in languages that you don't yet understand? Well, today, I'm gonna show that you can. You can do that. And I'm gonna show it by giving some examples. So let's start with a simple but fanciful example. So suppose you're an anthropologist, you're a cultural anthropologist, you're studying some foreign culture, and you're trying to translate their language because their language has been here to fore untranslated. So you go in, and you're translating their language, you're figuring out what they mean by various words that they use. And you've translated most of their words, but there's this word they use, spook, and you haven't yet figured out what that means. And so you're observing their behavior. And finally, you come up with a hypothesis. And you're pretty confident of this hypothesis. Your hypothesis is that they use spook as a truth functional connective. And it's a truth functional connective that has this truth table. It connects two propositions to make a larger proposition. And that resulting proposition, p spook q, for whatever propositions p and q spook is connecting, that resulting proposition is gonna be true whenever p is true or whenever both p and q are false. So the only scenario in which p spook q is gonna be false is where p is false and q is true. So that's your hypothesis about what they mean by spook. Okay, now one day you hear one of the members of this foreign culture give an argument. And using the translation manual that you've developed, you translate their argument as follows. John is riding his bicycle. Spook, Jill is walking to the park. Premise to Jill is walking to the park. Therefore, John is riding his bicycle. Now, is this argument valid or invalid? Well, you can use the truth table for spook to figure out whether the argument is valid or invalid and also to see why. So, let's consider how the truth table would go, right? This is the truth table again for spook applied to the case that we're considering. Well, premise one tells us that John is riding his bicycle, spook, Jill is walking to the park. So, if premise one is true, then we're either in this scenario, in this scenario, or in this scenario. Premise two tells us that Jill is walking to the park. So, if premise two is true, then we're either in this scenario or in this scenario. Okay, so what do premises one and two put together? What do they tell us? Well, premises one and two tell us that, first of all, we're not in this scenario because in this scenario, it's not gonna be true that Jill is walking to the park. Again, premises one and two put together tell us that we're not in this scenario because in this scenario, it's not gonna be true that John is riding his bicycle, spook, Jill is walking to the park. Again, premises one and two tell us that we're not in this scenario, because in this scenario, it's not gonna be true that Jill is walking to the park. So if premises one and two are both true, that tells us that we've gotta be in this scenario. But in this scenario, it's gotta be true that John is riding his bicycle. And so using the truth table for spook, you can figure out that this argument is valid. And you can explain why it's valid. See? So you can use the truth table for a truth functional connective that you don't have any understanding of independently of the truth table for it, right? It's not a connective that you use in your language. You can just use the truth table to figure out that a particular argument is valid. Let's try that with a more complicated case. Okay. So now suppose you hear some member of this foreign culture arguing as follows, at least according to your translation. John is riding his bicycle spook. Jill is walking to the park or Frank is sick. Frank is not sick. John is not riding his bicycle. Therefore, Jill is walking to the park. Okay. Now is that argument valid or not? Okay. So let's look at this more complicated truth table. Okay. So premise three tells us that John is not riding his bicycle. So that tells us that we've got to be in one of these four scenarios. Premise two tells us that Frank is not sick. So that tells us that we've got to be in one of these four scenarios. And premise one tells us that John is riding his bicycle spook. Jill is walking to the park or Frank is sick. So that tells us that we've got to be in one of these scenarios right here. Okay. So based on that information, what can we figure out? Well, we can immediately figure out that we're not in one of these top four scenarios because in all of those top four scenarios, Frank is riding his bicycle, right? So premises one, two and three together rule out the top four scenarios. We can also figure out that we're not in scenarios five or seven because in scenarios five or seven, Frank is sick. So we can rule out those scenarios. And we can rule out the sixth scenario because in the sixth scenario, it's not true that John is riding his bicycle spook. Jill is walking to the park or Frank is sick. So based on the information that we get from premises one, two and three of the argument, we can deduce that we're in this last scenario. We've got to be in this last scenario. And in this last scenario, it's false that Jill is walking to the park. In other words, Jill is not walking to the park. But that's not what the conclusion of our argument says. So this argument, this more complex argument is not valid. And we can prove that as we just did using the truth table for spook and disjunction. Okay. Now, let me show how we can do the same thing with quantifiers. So imagine as you're translating this foreign language, you hear a word. It's always said in a high-pitched tone, an excited tone, jid. And you wonder, what does jid mean? Well, after watching the way they use that word, you come up with a hypothesis. Your hypothesis is that when they use the word jid, they're using a quantifier. And the quantifier works like this. When you say jid f are g, you're saying that there aren't any f that are outside the g category, but there is an f that's inside the g category. So this diagram represents, according to your hypothesis, this diagram represents what the members of this foreign culture mean by jid. Okay. So now, suppose you hear one of the members of this foreign culture give the following argument. Jid, giraffes or herbivores, you translate. Then they say jid, herbivores are mammals. And then they draw the conclusion there are some giraffes and all of them are mammals. Now, is that argument valid? Well, let's use the Venn diagram for jid to figure out whether or not it's valid. So the first premise says, jid, giraffes or herbivores. So, how do we represent that? Well, remember, we have to shade out the portion of the giraffe circle that's outside the herbivore circle, and we have to draw an x that's in the giraffe circle and in the herbivore circle. We don't know quite where to draw that x, so let's hedge our bets right now and draw it over here. Okay. The second premise, though, tells us that jid, herbivores are mammals. Now, how do we represent that? Well, remember, by the Venn diagram, we have to shade out that part of the herbivore circle that's outside the mammal circle and draw an x inside the herbivore circle that's also inside the mammal circle. Right, now we know that this x that we drew on the edge has to be inside the mammal circle, not outside the mammal circle. Okay, so we're gonna put this x right here on the edge of the mammal circle and the giraffe circle because we don't know specifically which one it's supposed to go into. Oh, but wait, we do, and here's why we do. Remember that when we drew the x on the border of the mammal circle and the herbivore circle right here inside the giraffe circle, we weren't sure if that x was supposed to go in here or in here. Now we know that this x is supposed to go in here. So maybe there are also herbivore mammals that are not giraffes, but what we can definitely conclude from premises one and two is that there are herbivore mammals that are giraffes. So we know that there's an x that's supposed to go in this region right here. There's an x in that region right here, and then this whole region is shaded out. There's nothing in this whole region. That's what we know from premises one and two using the Venn diagram for jid. Excuse me, for jid. Okay, now let's apply that to our argument. Well, what does our argument say? It says there are some giraffes and all of them are mammals. But that's exactly what we can read off from the Venn diagram that we just constructed, right? If you look at the Venn diagram that we just constructed, there's an x that's inside the giraffe circle and inside the mammal circle and every part of the giraffe circle that's outside the mammal circle is shaded out. So there aren't any giraffes that are not mammals. Okay, so we just figured out that this argument is valid and we figured it out even though our only understanding of jid was from the Venn diagram that we constructed. Now, I have another question. Given this Venn diagram, how would you translate jid into English? Well, often people use the word all to mean the same thing that jid means according to this Venn diagram. People speaking ordinary English use the word all to mean precisely this quantifier, right? When they use the word all, they often mean that there are things in the category that they're modifying by all. Like if I say all ravens are birds, often what I'm understood to mean is there actually are some ravens and all the ravens there are are birds. So there are some things in the F circle but they're all inside the G circle. There are some things in the circle of ravens, let's say, but they're all also inside the circle of birds. There are no ravens outside the bird circle but there are ravens inside the bird circle. That's often what people would understand me to mean if I said all ravens are birds. Now, we've been using the quantifier all, we've been understanding the quantifier all in a different way so that it doesn't imply that there actually are members of the category that's being modified by all. So the way we've been using the quantifier all, if you say all ravens are birds, all you mean is there aren't any ravens that are not birds. But that's not the same as saying there are ravens and all of them are birds. So it looks like we can use the Venn diagram for JIT to translate that quantifier in a foreign language into a familiar quantifier from ordinary English. Well, welcome back. I've really missed you over the last couple of weeks when you've been off with raw meta learning about propositional logic and then categorical logic. And I hope that you enjoyed that, it's very important. But in the next few weeks, we're gonna turn to a different kind of argument because that type of logic is appropriate for deductive arguments. And what we're going to study instead is inductive arguments. Now, deductive arguments are given quite often throughout life, but inductive arguments are probably even more common. Whenever you wanna figure out who committed a crime, we were talking about an interest of the best explanation. Then there are arguments from analogy which happened quite often just think of all the analogies that you run into in life. And then we'll see statistical generalizations. Well, just think about all the polls and politics these days and statistical applications. Whenever you wanna know how those generalizations tell you something about a particular person. And then we'll turn to causal reasoning. Well, causes are crucial to everything from science to figuring out what made your car stop and decision-making and probability. So we got a lot of things to cover. And the first thing that we need to do is to see the difference between inductive and deductive arguments. Because you've been focused for a couple of weeks with Rahm about deductive arguments. You need to understand what's the difference between those arguments and the ones that we're gonna study over the next couple of weeks. In order to see that difference, I'm gonna show you a little video. It's a video I made a few years ago. So you might notice that I was a little younger back then. Okay, fair enough. But I think this video will help you see what the difference is between inductive arguments and deductive arguments. Rainy days and Mondays always get me down. The sun will come out tomorrow But your bottom dollar that tomorrow will be sun tomorrow, tomorrow Wait a minute, wait a minute. How do you know that? I heard a weather report. So what? They get it wrong all the time. Well, maybe this one won't come out tomorrow but at least it'll come up tomorrow. So you say, but is that really true? How many of you agree that the sun will come up tomorrow morning? Of course, definitely. Absolutely, yes. Everybody knows that. Okay, so you all agree with her but do you really know that it's true? How could you show that the sun will come up tomorrow? I don't know, I'm just a kid. Wait, I didn't mean to get you all upset but there really is an issue here. The question is, how can you prove that the sun will come up tomorrow morning? Well, here's one way that some people use. The conclusion is that the sun will come up tomorrow. The premise is yesterday the sun came up. The second premise, the day before that the sun came up. The third premise, the day before that the sun came up. Then the day before that, then the day before that, and the day before that, and the day before that, and the day before that, and the day before that. Well, that can get awfully long so we'll shorten the argument. The conclusion is still that the sun will come up tomorrow but the premises are just the sun came up yesterday and the sun came up every day before that for an awfully long time. Now is the argument valid? Yes or no? Right. It's not valid. An argument is valid if and only if it's not possible for the premises to be true and the conclusion false. But it is possible for these premises to be true and this conclusion to be false. Can you imagine how that would happen? One way would be if a meteor struck the earth in the middle of the night and stopped it from spinning. Then the sun wouldn't rise tomorrow. Now you're really freaking me out. But don't worry, that's extremely unlikely. However, it's possible and that shows that the argument's not valid. The next question is, is this argument any good? An argument's good if it serves its purpose. The purpose of this argument and many other arguments is to provide reasons for its conclusion. So, do the premises in this argument provide reasons for its conclusion? Yes, some philosophers deny this, but most people think that these premises provide good reasons for its conclusion. So let's assume that for now. What does that show? That shows that some arguments can be good even if they're not valid. But don't generalize too quickly. There are other arguments that are no good because they're invalid. Take Bub, for example. Is it true that every sophomore is a student? Yeah. Are you a sophomore? No. So you're not a student, right? Wrong. I am a student. Well, then what's wrong with the argument? Every sophomore is a student. You're not a sophomore, so you're not a student. Well, both the premises are true, but the conclusion's false, so the argument must be invalid. So you're telling me that what makes that argument bad is that it's invalid. Yep. Good job. Now, we've got a puzzle. Some arguments are bad because they're invalid, whereas other arguments are good even though they're invalid. How can that be? Simple. There are two kinds of arguments, deductive and inductive. Deductive arguments are bad when they're invalid. Inductive arguments can be good even though they're invalid. Why? Because deductive arguments are intended to be valid, whereas inductive arguments are not intended to be valid. The crucial point is that there are different kinds of standards for evaluating arguments. Deductive standards ask whether an argument is valid or invalid. Inductive standards ask whether an argument is strong or weak. There's several important differences between these standards. First, deductive validity is all or nothing. An argument is either valid or not. It can't be partly valid or a little valid anymore than a woman can be a little pregnant. Inductive strength, in contrast, comes in degrees. An argument is stronger when it gives more and better reasons for its conclusion. So an argument can be very weak when the reasons it gives for its conclusion are very weak or it can be moderately strong when it gives moderately strong reasons for its conclusion or it can be very strong when it gives very strong reasons for its conclusion. Since inductive strength comes in degrees, we can't simply ask whether an argument is strong. We need to ask whether it's strong enough. That depends on the context and the values at stake. It's like you've got your cooking lesson? Yeah! One of the most important things in cooking is to make sure that whatever it is you're cooking is done. When people cook cakes the way they normally test it for being done is they take a straw or a piece of bamboo and they stick it in the middle of the cake. It comes up with raw dough, it's not done, but if it comes up clean like this, that means it's done. Well, at least in that spot, but if you want to make sure that it's done throughout the whole cake, then you have to test other spots as well. So much for that. Now, when you're cooking turkey, you could use the same method. You could stick in a straw or a piece of bamboo and see whether any pink juice comes out. If it comes out pink, then it's not done. But if it comes out clean, then the turkey's done. See any pink juice? No. Then it must be done. Let's try a piece. But you wouldn't want to do that with turkey because you can get very sick from uncooked turkey. That's why most of the time they build a pop up meat thermometer right into the turkey to make sure that nobody eats uncooked turkey. But this is not a cooking class. The point here is simply that whether an argument is strong enough depends on what's at stake. When there's a lot to lose, we demand better reasons and stronger arguments. Context is also important in another way. Additional information from the context can weaken an inductive argument. That is, it can change it from strong to weak. In technical language, the inductive standard of strength is called defeasible or non-monotonic. In contrast, the deductive standard of validity is indefensible or monotonic. That means that no matter what premises you add to a valid argument, it will still be valid. Go ahead. Try. Here's an example. If Joe is a sophomore, then Joe is a student. Joe is not a student, so Joe is not a sophomore. And any premise you want to that argument, and it will still be valid, which shows that the deductive standard of validity is indefensible. In contrast, the inductive standard of strength is defeasible. If you add additional premises or additional information, it can make a strong argument weak. Consider a courtroom. I'm sure it was him. He was only 10 feet away from me. I saw him do it. I'm sure it was him. I saw him with my own eyes. I'd like to cross-examine this witness. Are you positive that it was the defendant sitting right there, or could it have been his identical twin brother who is entering the courtroom right now? It could have been. I can't tell him apart. Now I would like to recall the first witness. Let me remind you that you're still under oath. Can you tell the difference between those two gentlemen? No, they look like the same person to me. Now there's at least a reasonable doubt, isn't there? What was very strong evidence becomes much weaker when we add the new evidence about the identical twin. That is an example of the defeasibility of inductive standards. Although tricky, it's important to classify arguments as inductive or deductive because it affects whether they're good or bad. An inductive argument might not be valid, but it can still be good, for example. The sum came up yesterday, it came up every day for thousands of years, therefore it will come up tomorrow. That's a good argument, even though it's invalid, because it's not intended to be valid. This is just one instance of a general rule that you shouldn't criticize something for not being what it's not supposed to be. This book can be a good book, even though it's no good as a frisbee. Similarly, an inductive argument can be a good argument, even if it's not valid, if it's not intended to be valid. That is, if it's an inductive argument. This point undermines many common mistakes about inductive arguments. Many people think that inductive arguments are somehow inferior to deductive arguments because they're not valid. But that can't be right, because it's easy to take any inductive argument and turn it into a deductive argument. For example, most of Joe's friends are seniors, so Joe must be a senior too. Well, we can make that argument valid simply by adding a conditional premise. If most of Joe's friends are seniors, then Joe is a senior too. But that just shifts all the doubts about the inductive argument into doubts about the conditional premise. So it hasn't really made us more sure of whether Joe is a senior. Our definition of induction also undermines a second common mistake. Many people believe that induction always takes us from the particular to the general. But no matter how many people say that, it's just plain wrong. Inductive generalization is one kind of inductive argument, but it's not the only kind. In fact, we are going to study five different types of inductive arguments. To see the differences between these arguments, let's do a simple experiment. Excuse me, we're testing a new type of lemonade here. Could you help us out? Sure. Thank you. First, could you try one from that cup? That's pretty good. Great. Now, could you try this second cup, please? Oh, that's terrible. Your reaction suggests that you don't like that. Well, obviously, you put dishwashing liquid in there. How do you know that? Well, it tastes like soap. Is that why you spit it out? Well, I didn't spit out the first one, did I? You might be interested to know that you agree with over 90% of the people we've tested so far. They all like our lemonade better than dishwashing liquid. That's great. And if you take it back to your dorm and try this test on your friends, I bet they'll like our lemonade too. Well, of course they would. Listen, this is stupid. I'm out of here. This experiment would be stupid if it were intended to show something about lemonade. But all it's supposed to show is the differences among the different kinds of inductive arguments. Our next step will be to look at each of these kinds of induction in more detail. Now that we've seen which features distinguish inductive arguments from deductive arguments, we want to look at the different kinds of inductive arguments one by one. And the first two we're going to look at are moving up from a sample to a generalization and then moving back down from the generalization to some kind of prediction in a particular case. Generalizations are all around us. Almost all movies have credits. Most popular bands have drummers. Many restaurants are closed on Mondays. Three quarters of police officers are very nice people. Two-thirds of books have chapters in them. Half of the people I know like to play sports. And my favorite of all, 87.2% of statistics are made up on the spot. It should come as no surprise at all that there's so many generalizations filling our lives because generalizations can be extremely useful, especially when you need to make a decision. So for example, if you're feeling a little nauseous, that is a little sick at your stomach, then you need to know whether most people who have symptoms of your sort have something serious enough that they need to go to a doctor. And they also need to know whether doctors can usually help people who have symptoms of that sort. All of those generalizations are relevant to whether or not you want to go to the doctor to see if he can get some help with your sick stomach. But then the problem is how can we decide which generalizations to believe? Since they're generalizations and they apply to all instances of a certain sort, you can't check them all out. You have to take a sample of some sort. I mean just imagine that you're running a bakery and you're making jelly donuts and you want to know whether the jelly donuts are filled with the right amount of jelly. You've made hundreds of jelly donuts. You're not going to tear them all apart and check everyone for how much jelly they have in the middle because then you have no donuts left to sell to your customers. Or imagine that you want to buy a car. This time you're the customer. You want to buy a car and you need to know how often these cars had problems in the first year because if they have problems a lot during the first year you don't want to buy that kind of car. But you don't want every car of that sort to have been tested for the first year because then you can't buy a new car. You're only going to have a used car since they've all been used in the tests. Or imagine that you want to know what types of trees grew during a certain period of history. So you look at the soil and you dig down and you start looking for how many pollen grains there are at a certain level that indicates a certain age. Well you can't check every spot in the field because if you did that you'd just be destroying the entire field. So in these cases and many other cases you just have to take samples. You can't test the whole class and then you have to generalize from the sample to the larger class. All of these generalizations from samples share a certain form. First we look at one instance of the sample. We say that first F is G. That is the thing that fits in the class F and has the property G. Then we check another. The second F is also G and the third F is also G and all the rest of the F's in the sample are G. So we conclude that all F's are G. Now notice that all in the conclusion means everything in the class of F's. It doesn't only mean the ones in our sample. So we've started from premises that are only about the sample which is only a part of the general class and we've reached a conclusion about the whole class when we say that all F's are G. Now other arguments of the same general type are a little bit different because you don't always get complete uniformity. You don't always get all F's are G. Sometimes you get the first F is G and the second F is G but the third F is not G and the fourth F is G and the fifth F is G but the sixth F is not G. So you get like two-thirds of the F's are G and then you reach the conclusion that two-thirds of all F's are G. Again though you've only looked at the F's in the sample. You've only observed a small part of that total class of all F's and you draw a conclusion that two-thirds of the overall class the whole class of F's has that property G. So that's why you have a general that's why it's called a generalization. You start from a smaller sample and reach a conclusion about a much larger class. You generalize to the whole class. The fact that the argument moves from a small part of the class to the whole class shows that it's inductive and what does that mean? Well first is the argument valid. Think back to one of the examples. Almost all bands that I know of have drummers therefore almost all bands have drummers. Well is it possible that the premises are true and the conclusion false? Of course it is because maybe I only listen to bands that have drummers but there are a lot of bands out there that don't have drummers and I just didn't happen to listen to them. That is they weren't part of my sample. Okay and is the argument defeasible? That means that you can add further information to the premises and it'll make the argument much less strong. It might even undermine the argument totally. And of course it could because you could give me all kinds of examples of bands that don't have drummers and then I would have to change my conclusion that almost all bands have drummers. So this argument is defeasible. Does that mean that it can't be strong? No. It could still be strong. It can come in different types of strength. How would you get a stronger argument or a weaker argument in this case? Well you can have a larger or a smaller sample. If I take a very large sample the argument's going to be stronger. If I take a very small sample the argument's going to be weaker. So it's not like validity which is on or off. It's either valid or not. Instead the strength of the argument comes in degrees depending on how big the sample is. Now does that mean that since it can't be valid it can only be strong to a certain degree? That it's no good? No. Because it's an inductive argument. Inductive arguments don't even try to be valid. They don't even pretend to be valid. That's not what they're supposed to be. And so you can't criticize this argument by saying it's not valid. It's doing everything that it's supposed to do if it provides you with a strong reason and a strong enough reason for the conclusion. That's when an inductive argument is supposed to do. So if this argument does it it's a good argument. But even if inductive arguments including generalizations from samples don't have to be valid they still do need to be strong. And so we need to figure out how to tell when a generalization from a sample is a strong argument. When it provides a strong reason for the conclusion. I don't really answer that question. You got to turn to statistics and the area of mathematics and learn how to analyze the data much more carefully than we'll be able to do here. But even mentioning the name statistics raises fear in some people. Mark Twain is famous for having said there are three kinds of lies that are lies, they're damn lies, and they're statistics. He actually gives credit to Disraeli for having said it first. But the point is that statistics are even worse than damn lies. You can't trust him at all. We're still Mark Twain says. But on the other hand some people say statistics that's math. It's all about numbers. Can't question that. Here's one example of somebody who suggests such a position. There's still one thing that's irrefutable and that is the numbers. Numbers don't lie. They can't parse poll numbers. They're infallible. Okay, fine. He knows that statistics aren't infallible. He's just being sarcastic. But there are many people who put a lot of faith in the numbers and in statistics. They seem to think that you always have to trust it when a statistician comes up with an answer. And we're going to learn that neither of these views is correct. It's not true the statistics are always worse than damn lies and it's also not true that the numbers are irrefutable. The truth lies somewhere in the middle. So now we really got to face that crucial question. How can we tell when a generalization from a sample is a good argument? We're not going to be able to do a lot of mathematical statistics here. That would take a whole course and you ought to take one that's useful, it's important, it's interesting. Definitely worth taking a course on statistics. But all we're going to be able to do here is look at some really common errors that people make. So you won't be misled in these obvious ways. It won't so much help you do statistical studies of your own but it will help you avoid getting fooled by people who cite statistical studies for conclusions that you might not want to believe. To illustrate these problems I did a little survey. I happen to love chocolate chip cookies. Now not all chocolate chip cookies are equally good. Some of them I think have too few chips. You need a lot of chocolate chips. But you don't want too many because then it's just a bunch of chocolate and you don't get the dough, the butter, the sugar. That stuff's good too. So you want just the right balance here. You want I would say in a say a three inch diameter cookie you want about 10 to 12 chocolate chips. And there happened to be five bakeries in my hometown that serve chocolate chip cookies. So I went and got 10 chocolate chip cookies from each of the five bakeries and counted the chocolate chips in the cookies. And I found out that 80 percent of the chocolate chip cookies that I bought from Bakery A had 10 to 12 chips in them. So I conclude that 80 percent of the chocolate chip cookies from Bakery A have 10 to 12 chocolate chips in them. Now that sounds like a pretty good argument, doesn't it? I mean I cut a sample 20 or 30 but turns a pretty good number for a sample. So you ought to believe that conclusion, right? There's nothing wrong with that argument, is there? Well what's the problem? The problem is I'm lying. I didn't buy a single cookie. I didn't do this survey. What does that show you? That shows you that one problem for statistical generalizations from samples is that the premises have to be true. Kind of obvious. And what it shows is that just like a valid argument's no good unless it's also sound when it's a deductive argument, similarly what would be a strong argument if the premises were true is no good if the premises aren't true. But also like deductive arguments it's not enough for the premises to be true. What if I counted, I really did buy the cookies and I really did count, but I missed a bunch of them because I was going so fast or I couldn't count the chocolate chips very well because they were all like all melted together or maybe I got the cookies from Bakery A mixed up with the cookies from Bakery B or Bakery C or Bakery D then I just made a mistake when I was counting the cookies. Then it turns out the premises of the argument of the generalization from the sample those premises are false but not because I'm lying rather because I didn't count well. So I'm unjustified and of course it doesn't help if I'm justified if you're not justified you're not going to have any reason to believe this about the cookies unless not only did I count them accurately and carefully and reliably but you have reason to believe that I did so. So the general point is simply that when you face a generalization from a sample then the premises have to be true and justified so the first question you ought to ask about any generalization from a sample is are the premises true and are they justified? Next let's assume that I'm honest I'm not lying and I count carefully and thoroughly so I don't make a mistake and I'm just if I'm believing that I haven't made a mistake I go to all five of the bakeries and I buy a cookie from each bakery and I count the chips in the cookies that I bought and it turns out that the cookie from Bakery A has 11 chips in it and the cookies from Bakery B, Bakery C, Bakery D, Bakery E they all have less than 10 chips in them so now I can do two of these generalizations from samples right? I can say well 100% of the cookies that I sampled from Bakery A have between 10 and 12 chips therefore 100% of the cookies from Bakery A have between 10 and 12 chips but 0% of the cookies I sampled from Bakery B have 10 to 12 chips so 0% of the cookies from Bakery B have 10 to 12 chips. What's wrong with that argument? I hope it's pretty clear the problem is you can't generalize from just one cookie. The cookies aren't made in a totally mechanical way where they count the chips before they put in the cookies then you can't know that every cookie is the same and if you can't know that every cookie is the same then you can't generalize from one cookie alone to all the cookies in the bakery. You might have gotten one that happened to have 11 chips when all the others cookies in the bakery had less than 10 or for the other bakeries for BCDE you might have gotten a cookie that had less than 10 when actually they all all the rest of the cookies in the store had between 10 and 12. So when you generalize from such a small sample from a sample that's too small then it's called the fallacy of hasty generalization and it's so obvious that it's hard to believe but it's actually often committed. It's a very common fallacy you know your next door neighbor will buy a new car and it breaks down and you say ah kind of car is no good or you meet somebody from Sweden and this person from Sweden likes football and so you say ah people from Sweden like football and people just constantly generalize from extremely small samples in order to form generalizations that guide their behavior in everyday life. Sometimes they're right but a lot of times they're wrong. That's when you have the fallacy of hasty generalization. To avoid that fallacy we need to ask a second question about generalizations from samples namely we have to ask is the sample large enough? I notice the samples come in varying sizes from just one item to almost the whole set and so the question that we have to ask first is is it large but it's not clear what that means but we really want to know is is it large enough because sometimes a very small sample can be plenty big just imagine that you come across an apple tree and you want to find out whether the apples off that tree float in the water so you bring in a tub of water you pull off an apple off the tree and you put it in the tub and it floats. Now you can generalize that all the apples or maybe almost all the apples off that tree will float in water. One is a big enough sample in that case now why is that? It's because you have background information from biology that the apples on that tree are going to be very similar to each other because of how they arose and so sometimes a single instance is going to be enough even if it's not enough when we're counting chips and chocolate chip cookies. The other point about the sample being large enough that you need to keep in mind is that whether it's large enough depends on what the stakes are. If you're testing a bunch of parachutes to see if they work you better not just check a few even 10 is not enough like we use for the chocolate chip cookies you want to check every parachute to make sure that it's packed properly and it's going to work or you're going to have disaster when they fail. But what about chocolate chip cookies? Suppose you take a sample of 10 and it turns out that that sample is not really representative. Big deal! It's other nine chips or 13 chips you know it's just not that serious an issue. So a sample can be large enough for something that doesn't matter like chocolate chip cookies without being large enough for something that really does matter like whether parachutes are packed properly. So whether the sample is large enough depends on the background information that's what the apple case showed us and also on what's at stake that's what the parachute case showed us. Next let's assume that I'm not lying the count's accurate you're justified in believing it's accurate and the sample's big enough all that is settled right so what I did was I went into the five bakeries and I turned to the person behind the counter and I said I'm doing this little survey because I got to figure out which place I want to buy my chocolate chip cookies in town and and I want to find out whether how many of your cookies have between 10 and 12 chocolate chips so could you sell me 10 chocolate cookies and I'm going to do my survey so then I take 10 cookies from each of the five bakeries and I bring them home and I count them and sure enough from bakery A we found that 80 percent of the cookies that I bought from bakery A have 10 to 12 chips and so I conclude that 80 percent of the cookies that are made in bakery A have 10 to 12 chips and that seems like a pretty good argument doesn't it it's got a big enough sample if you don't believe that let's say it's 20 cookies there's still something wrong there's something wrong with that argument what's wrong with that argument well I told the guy behind the counter that I was doing this survey to figure out where I was going to buy my chocolate chip cookies so if he wants me to buy chocolate chip cookies from his cookie shop or his bakery then he's going to look in the counter for the 10 cookies that look like they have about 10 to 12 chips in them so it might be no surprise that 80 percent of the cookies that I sampled have 10 to 12 chips because he picked out the ones that did this is called the problem of bias sampling sometimes the sample that you take is not representative of the whole because it's biased in a certain way in this case it was biased by the person behind the counter and what he knew about what I was doing and what his motives were in trying to get me to buy from his shop but the fallacy of bias sampling is something we have to watch out for and what we need to do then to avoid this fallacy is to ask a third question about all generalizations from samples we want to know whether premises are true and justified we want to know whether the sample is large enough we also have to ask is the sample biased in any way that's going to weaken the argument it might seem that the fallacy of bias sampling is so obvious that nobody who was careful and any good at what they were doing would ever commit that mistake but actually people do it all the time some of the top pollsters in history have done it the most famous example was Franklin Delano Roosevelt who was running for president in 1936 against Alf Landon and the literary digest did a poll that took just tons of data I can't remember how many tens of thousands of letters they sent out in this poll and they reached the conclusion from their poll that Alf Landon was going to win 56 to 44 but that's not the way it turned out turned out that Roosevelt won 62 to 38 they were way off they weren't even close so what was going on with that well they needed to get addresses of people to send the survey to and what did they use for that they used a phone book but back then remember this is 1936 a lot of people didn't have phones and in particular poor people didn't have phones and people who lived in rural areas didn't have phones and it was those poor people and people who lived in rural areas that love Franklin Roosevelt because of the new deal and all the policies that he had put in that helped them out so they voted for him and he won by a landslide and the prediction had gone the other way and it's all because of biosampling and the same problem continues today many pollsters especially when they want to do a really quick poll will call up people on their phones but there are lots of restrictions and lots of problems with that for one thing you're not supposed to do polls on cell phones but a lot of young people only have cell phones and don't have landlines so that means that young people are going to be underrepresented in the sample and even if they have a landline well they often have caller ID and they know it's a pollster so they don't answer so you get very low response rates and some studies have found that women tend to answer the phone more than men so you get samples skewed in that direction so what do you do when you get a biased sample like this well if you know it's been biased in these ways then you try to correct for that that's where the pollsters don't all agree they correct in different ways because think about it suppose at this time you got a lot more people from the liberal party than you did last time that might mean that your sample is skewed but it might mean that there's just more people that have moved over to the liberal party or to the conservative party either way how do you know the proper way to correct so as to get an accurate answer and different polling organizations use different techniques and that explains why very often the polls reach quite different results about who's ahead in an election another reason my polls often reach different results is that some pollsters are dishonest I know it comes as a shock but it's true and pollsters can sometimes reach the conclusions that they want to reach by slanting their questions so the fourth question that we want to ask about any generalization from samples is was the question slanted in some way which means was phrased in a way that made it more likely to reach one result rather than a conflicting result so how does this happen well a simple way to do it is to word the question in such a way that people are going to feel bad about giving a certain answer so for example if you want to find out how many people in a certain society think that it's it's wrong to experiment in scientific experiments on animals then you can always ask one question if you want one answer and another question if you want another answer so what about this one suppose they say is it okay to kill a mouse in order to save a human I think most people are going to say yes and then they're going to say ah so they those people who gave that answer they actually support scientific experiments on mice to save human lives therefore they support animal experimentation if you want to reach the other result in your poll then you can say should scientists torture animals in their experiments nobody wants to say they're gonna be for torture so they're going to say no scientists shouldn't do that and then you can conclude ah so most people are against animal experimentation because animal experimentation is torturing animals in fact you can go a little further you could say should scientists stop torturing animals in their experiments it's like should when did you stop beating your wife it presupposes that they are torturing animals and then people who say of course they should stop it I didn't even realize they were doing it well you're just guaranteeing the result in your poll by the way you ask the question another way to slant your questions in a poll is to give the survey participants limited options so in one example the New York Times magazine reported a poll by the Doris Day Animal League where they said 51 percent of the people we surveyed think that chimpanzees should be treated about the same as children but what happened in the survey was they were only given four options they could say chimpanzees should be treated like property or they should be treated a lot like children or they should be treated like adult humans or you're not sure well notice that given those options you don't want to say chimps are like property because you can just destroy your property if you want if you've got an old car and you want to tear it to bits with a sledgehammer that's up to you and they're not like adult humans because we don't think they should be given schooling and so on or votes or so on so you're pretty much left with either saying you're not sure and you feel like well I should have thought about this a little bit see most people were saying 51 percent were saying that chimpanzees ought to be treated similar to children so by limiting the options to a list where all the other options were undesirable for one reason or another the pollsters can get you to pick the option that they want you to pick and then the next trick is you report the conclusion right they actually didn't say the 51 percent said that chimpanzees should be treated similar to children they said that the survey showed that primates should be treated the same as children they changed chimpanzees to primates which includes a lot of very small primates that aren't nearly as intelligent and close to us as chimps are and they also said it's not similar to children the same as children so you can also slap the poll not by playing around with the question but by playing around with the way you report the conclusion of the survey so those are some of the tricks that people use in order to reach a predetermined result and to fool you into believing that their poll results are reliable and we saw other mistakes that people make even when they're not trying to fool you so what you need to do is to keep your eye on all those you need to ask these questions that i've emphasized throughout this lecture namely you guys see are the primates true and justified is the sample large enough is the sample biased in some way and have the questions or the conclusion been reported in a slanted way and there's a lot more to learn about statistics and again i want to emphasize to be useful to take a statistics course people ought to know more about statistics but we can't go into all of those details here still if you can just avoid these few simple mistakes that i've been talking about then you can avoid being misled in a number of situations in everyday life generalizations are not much use if you can't apply them back to particular cases it rains about 35 percent of the days in north carolina great but is it going to rain tomorrow that's what i want to know i don't want to know the general statistic i want to know about tomorrow because i got to decide where they're going to picnic 65 percent of the snakes in this area are poisonous great but i want to know whether the one i'm stepping on right now is poisonous i don't want to know the general statistic so we need some way to take these generalizations and apply them down to particular cases and that's the job of a form of argument we're going to call application of a generalization not a great name but they're usually called statistical syllogisms and that's an even worse name because they're not really necessarily statistical in the mathematical sense because they don't have to have numbers in them and they're also not syllogisms like the categorical syllogisms that you studied back in the section on deductive arguments so we're going to call them applications of generalizations and they just happen all the time they really do you might say for example i almost never like horror movies and that's a horror movie so i don't want to go to it because i'm not going to like it or you might say i don't want to invest in that restaurant because 80 percent of restaurants fail during the first two or three years and so this is a restaurant that's new it's probably going to fail too or how about this one most people who are on the track team are pretty thin now you know there's some exceptions to that the people who throw shot put that's what i used to do but still it's true that most of them do and so if you know that sally is on the track team and that's all you know about her then you've got some reason to believe that sally is probably thin she might throw the shot put but there are many more people on the track team who run and jump and they're going to be thin if they're any good at it so although it might be wrong it's a pretty good bet that sally's thin if she's on the track team and that's the kind of argument that we're going to call an application of a generalization here's my favorite am i wearing shoes right now can't see can you maybe i maybe i'm not but most professors wear shoes when they're teaching a class walter is a professor who's teaching a class so walter is probably wearing shoes right now that's an application of a generalization and it has the same form as the other examples that we saw before to see that form we can substitute variables for the terms in the english argument so we can substitute the letter f for the reference class which is the set of professors who are teaching then we can substitute the letter g for what's called the attribute class which is the people who are wearing shoes then we can substitute the letter a usually in lower case for the individual that we're talking about in this case that individual is me walter and we can substitute x percent for the quantifier if it's most or almost all or something like that then x percent takes its place and then the form of the argument that i just gave about wearing shoes is simply that x percent of f are g a is f therefore a is probably g notice that this application of a generalization moves in the opposite direction from the generalization from a sample we might start off saying x percent of the f's in the sample are g so x percent of f's are g and that's generalization from a sample but then we take the generalization in that conclusion and use it as a premise in an application so we say x percent of f's are g a is f therefore a is probably g and that's why i said that we're going to study up to generalizations and then down from generalizations in this part of the course and when they work together we can use information about the sample to reach a conclusion about the individual which is pretty useful notice also that these applications of generalizations are inductive they share all the features of inductive arguments first of all they're invalid because it's possible for the premises to be true and the conclusion false that is it's possible that x percent of f are g a is an f but it's not true that a is probably g there might be no chance at all that a is g second applications of generalizations are defeasible you can add additional information to the premises that make the argument very weak they might completely undermine the argument for example even if you know that walters a professor and most professors wear shoes while they're teaching a little bit of additional information might show you that it's just not true that walter is wearing shoes while he's teaching by the way i'm gonna well you'll have to decide for yourself whether i'm really putting my shoes back on now but the third feature of inductive arguments is that they're strong or they can be strong they can vary in strength so even if i don't have shoes on it still might be a fairly strong argument that almost all professors wear shoes while they're teaching walters a professor and he's teaching therefore he probably has shoes on that can be strong before you get that additional information before you see my feet without shoes on and now that you don't know whether i've got shoes on it can still be a strong argument so we have arguments that are not valid and they're defeasible and they vary in strength and that makes them inductive arguments so how do we tell when an application of a generalization really is strong that is when does it provide strong reasons for the conclusion now the first standard should be obvious it's the same for generalizations from samples the premises have to be true and justified if it's not true that i'm a professor or if it's not true that i'm teaching or if you have no reason to believe you're not justified in believing that i'm a professor or i'm teaching then the argument that we've been looking at can't give you a good reason to believe that i'm wearing shoes because i just don't fall into the classes that we're talking about secondly a standard that's specific to these kinds of arguments is that the strength of the argument varies with how big x is if x is 99 percent so 99 percent of f's are g's and a is an f that's a pretty strong argument that this a is a g but if it's 60 percent then it's not a very strong argument so 99 is going to be stronger than 90 which is stronger than 80 which is stronger than 70 which is stronger than 60 and the strength of the inductive argument can vary as the percentage x varies now notice if x is 10 percent then it becomes a pretty strong argument for the opposite conclusion if only 10 percent of professors wear shoes when they're teaching and i'm a professor who's teaching then it's pretty likely i'm not wearing shoes and that's stronger than if it's 20 and 30 and 40 and when you get close to the middle to 50 percent if 50 percent of professors wear shoes when they're teaching and i'm a professor then you can't really reach your conclusion one way or the other about whether i'm wearing shoes at least not on the basis of that evidence not on the basis of that argument okay so a second standard for assessing applications of generalizations is to figure out what the percentage is but another crucial feature of applications of generalizations is that there can be conflicting reference classes so it might be true that 95 percent of professors wear shoes when they're teaching but i'm not just any old professor i'm an online professor this course is online and that's very different because most professors wear shoes when they teach because the students will see their bare feet but you can't see my bare feet so maybe it turns out that a lot of online professors are really not wearing shoes when they teach so that's a conflicting reference class it's a different reference class that conflicts because it points to a different conclusion than the original reference class the original reference class was professors who are teaching the conflicting reference class is online professors who are teaching or professors who are teaching online when you're running the conflicting reference classes as a general rule what you ought to do is look at the smallest of those reference classes because that's usually going to give you a better estimate of how likely it is that this individual has the general attribute that is how likely it is that a is g so if you want to know whether walter is wearing shoes you shouldn't look at the broad class of all professors but should instead look at the narrow class of online professors if the course that he's teaching right now is an online course but there's a problem that you might run into also as you get a narrower narrower reference class you sometimes just don't have enough data to figure out what the exact percentage is how do you know what the percentage of professors who are teaching online is that are wearing shoes how many of them are wearing shoes i've never seen a survey i've seen lots of professors give regular lectures but you rarely see the feet of online professors so you might not have enough information to apply that generalization so while the narrower reference class of two reference classes that conflict can be more accurate it can also be problematic if you don't have enough information to support the premise that says that a certain percentage of that class that f have the general attribute g the fallacy of overlooking conflicting reference classes can be a little confusing but it's very important so let's look at another example and this time let's focus on a medical example let's suppose that 90 percent of the people with a certain condition certain medical condition a certain illness die and bob has that illness so looks very likely that bob will die and this is an application of the generalization about people with this illness but now suppose we find out that most people catch this illness when they're old but bob is quite young so it turns out that young people with this illness usually survive matter of fact only about 20 of the people with this illness who get it when they're young die from the illness if bob is young and has this illness so now we can reach the conclusion you probably won't die from the illness but wait a minute we now have another conflicting reference class because bob has a heart condition and it turns out that even young people when they catch this illness if they have a heart condition they usually die as a matter of fact 80 percent of the people with this illness who have a heart condition and are young die from this illness so bob who is young and has this illness and also has a heart condition will probably die from this illness but wait a minute it turns out that there's a new treatment and of the people who are given this treatment only about 30 of them die even if they're young with this illness with a heart condition and bob lives in an area where he can get the treatment so now it looks like there's only a 30 chance that bob will die from this illness so what's happening here is is we get more and more information the likelihood of bob dying from this illness starts out really high and then it goes low and then it goes high again and then it goes low again and it goes back and forth as we get more information and then the question arises which of these different generalizations should we use to figure out how likely it is that bob will die from the illness the answer here as with most cases of conflicting reference classes is that we ought to look at the narrowest class that we can because if we know there's a treatment and bob is young and he has a heart condition and he also has this illness and we put all that together and compare him to other people who are young with this illness and a heart condition who can get the treatment and look at how many of them have died in order to form an estimate of how likely it is that bob will die from this illness so we always want to look at the narrowest reference class that we can in order to get the best estimate of the probability in the conclusion but then there's a problem there might not be very many people remember it's a new treatment so they're not very many people who are young who have this illness to begin with remember most of the people with the illness are old and the treatment's new so it hasn't been tried on very many young people and of course young people don't often have heart conditions so it might be very difficult to find enough people who are like bob in all the essential respects in order to determine whether or not bob will probably die from this illness so there's a kind of attention here more information gives us more accuracy but only if we have enough information to be justified in trusting the premises of the application that we're looking at and that's one of the tricks in figuring out how to estimate whether or not bob is likely to die from the illness the same points apply to all kinds of examples no if you want to know the climate in the area that's going to be a generalization about days around here in this time of year but if you want to know the weather tomorrow you need to apply it and then you're going to need to look at specifically what the weather was yesterday specifically what the humidity is the more information you can build in the better estimate of what the weather is going to be tomorrow or if you want a better sports team you say well they're a very good team they've won most of their games in the last five years but wait a minute maybe all their players left and now it's not likely that they're going to win but wait a minute they got new players that are even better that makes it more likely they're going to win and again the information can make the probability go low and then high and then low and then high and you have to get the most specific information you can to get the most accurate estimate of how likely it is that this team will win but you might not have enough information about this team with these players under these circumstances because they just haven't been enough cases for you to observe so as with the medical example it's going to get tension between wanting the most precise the most smallest reference class among the different conflicting reference classes and yet you need premises that you have enough information that you can justify them and if you can reach that perfect point where you've got enough information to justify the premises but that premise is specific enough so that it has all the relevant information about the case that's when we're going to have the best outcome for applications of generalizations perhaps the most common kind of inductive argument is called an inference to the best explanation and to understand this kind of argument we need to think way back to the first week when we discuss the difference between justification and explanation if somebody uses an argument to justify a conclusion then they're trying to give a reason to believe that the conclusion is true and maybe you didn't believe that conclusion before you heard the argument but if somebody gives an argument to explain the conclusion then they're taking it for granted that the thing they're explaining is true and they're trying to understand why it's true and the argument is supposed to help us understand why it's true or the weird thing about an inference to the best explanation is it really combines these two it uses the argument to justify belief in the conclusion that is to give you a reason to believe that it's true and yet a premise of the argument is that that conclusion explains a phenomenon that you took for granted inferences to the best explanation are extremely common for example almost every detective story uses an inference to the best explanation just imagine that there's three suspects and you know that one of those three suspects must have done it because the door wasn't jimmied open so whoever got into the room must have had a key and there are only three people who had keys but one of them couldn't have been the one who did it because she has really small feet at the footprints outside the door were really large and so it couldn't have been her and the second person couldn't have done it because they have an alibi on the other side of town so it must have been the third person who did it and notice what you did is you can't explain why the door wasn't jimmied by the person who got in because there were no marks and that means that the best explanation or that must be that the person who did it had a key and the best explanation why the footprints were so large was that it was a large person who wore large shoes and the best explanation of why the alibi would place the person on the other side of town was that they were being honest assuming it's not their brother they're not the kind of person who would lie or so on so the best explanation of why the jewels are missing from the room or why there's a dead body in the room uh is that this third suspect is the one who did it so all the detective stories work like that it's almost always an inference to the best explanation the best explanation is he's the one who did it and one implication of this is that no matter what Sherlock Holmes says the form of reasoning that he was using was inductive reason not deduction as he claimed but it's not only detective novels it's also science that uses inference the best explanation take for example the greatest murder mystery in history what killed the dinosaurs well some people think that it was mammals eating their eggs not a chance that doesn't explain why there were also mass extensions in the oceans for the mammals weren't eating their eggs but some people think that the best explanation is that there were big volcanic eruptions in southern india that seems pretty unlikely too because the volcanoes that we know didn't put out enough material to kill things all the way around the world so they think that the best explanation of what killed the dinosaurs is that a giant meteor hit in the Yucatan Peninsula in mexico and that produced lots of soot in the atmosphere that killed the dinosaurs as well as many other species at the time but luckily not mammals and so we now have a best explanation in science and a lot of scientific theories work that way as a matter of fact the point of most scientific theories is to provide the best explanation of all the experimental data that has been observed by scientists throughout the world and of course we also use inference the best explanation our everyday lives to try to figure out what's going on around us here's an example whoa what was that drop of water just hit my head there must be a leak in the roof now that is an inference to the best explanation starts with an observation of the water hitting my head then i think about why the water would be coming down and the best explanation i can come up with is that there's a leak in the roof so i conclude that there is a leak in the roof notice that this argument uses an explanation but it runs in the opposite direction from an ordinary explanation in an explanation the premises explain the conclusion and the conclusion describes the phenomenon that was observed when there is a leak in the roof water drops through the roof when water comes through the roof it drops onto whatever is in its way i am in its way therefore water drops on to me this explains that in contrast an inference to the best explanation works in the opposite direction the conclusion is what does the explaining the premises are what get explained and the point is to justify belief in the conclusion not to explain it water drops on to me a leak in the roof would explain why water drops on to me no better explanation is available therefore there must be a leak in the roof notice that the conclusion of the left argument is a premise of the right argument and the conclusion of the right argument is part of a premise of the left argument so the form is different the function is different as well in the explanation on the left we start out already knowing that the conclusion is true in the inference to the best explanation on the right we argue that the conclusion is probably true because it is the best explanation of the observation in the first premise that's why we call it an inference to the best explanation is this argument valid yes or no right it's not valid because it's possible for the premises to be true and the conclusion falls now does its invalidity make the argument bad yes or no right it does not make it bad because an inductive argument can be good even if it's invalid the next question is a bit trickier remember that an argument is defeasible if further information can make the argument weak so is this argument defeasible yes or no right it is defeasible because further information could make this argument weak so what does its defeasibility mean that this argument was weak even before we got that additional information yes or no no because inductive arguments can be strong even though they are defeasible so now we know that this argument is invalid and it's defeasible but it still might be strong and good we've learned that inferences to the best explanation are inductive arguments they're not valid and they are defeasible but still they might be strong and good arguments they might give you good reasons to believe their conclusions great they might be sure but how do you tell whether they really are strong arguments and good arguments we need standards for determining when an inference to the best explanation is a good argument and to understand those standards we're going to view another skit made by my students a few years ago it's time for class whoa where is everybody it's me it's monday isn't it yeah first day of the week remember the weekend hmm the weekend yeah i remember vaguely good times but now it's back to work it's monday but what time is it 12 and 15 well isn't that one class is supposed to start here's the start of a good explanation there are surprising circumstances that need to be explained maybe my watch is fast it has been giving me some trouble lately do you check yours oh i don't wear a watch i just ask you what i need to know the time great so i'm your designated timekeeper kind of but there's usually a clock around one right there okay so we know it's 11 15 right in any inference to the best explanation it's crucial to get an accurate picture of what you're trying to explain in this case if it were 11 10 instead of 11 15 then the explanation would be different or there might be nothing at all to explain so where is everybody well maybe everybody else is late after all the professor does show up a few minutes late he told me that he doesn't like to start teaching right away because it isn't like when he's talking students walk in oh that makes me mad so maybe they're coming in later because they don't want to have to wait around for him to start talking it's one of those vicious circles okay maybe that's it but then some students should start showing up so let's just wait and see okay that's enough if people were coming they'd be here by now i mean the professor's been late but he's never been this late and refutes bob's explanation by pointing out new facts that falsify bob's hypothesis that all the students are late a good explanation has to be compatible with all of the facts not just the particular ones that it's trying to explain bob's hypothesis can't be the best explanation of why the students aren't there at 11 15 if they're still not there by noon well that brings us right back to where we started why isn't anybody else here you're guessing as good as mine well well my guess is that everybody else is here we just can't see or hear them i bet they're laughing at us right now i bet the professor is up there jabbering away right now like he always does yeah well i hope this material is not on the test congratulations you proved me wrong your guess is not as good as mine why humans can't become invisible how do you know have you ever seen it no they're invisible that's why i've never seen it okay but the laws of physics don't allow humans to become silent and invisible and dismisses bob's new hypothesis because it's not conservative it conflicts with well established prior beliefs in physics if you start believing that humans can become invisible you'll have to give up everything you know about how light and matter work besides if they were here the seats wouldn't be popped up like this nope because besides being invisible and silent these students are also weightless no smell either okay so there is no way to tell whether or not their students here you're catching up but the laws of physics still don't allow people to be weightless invisible and silent well the laws of physics are based on observation and there is no way these students can be observed at all the laws of physics can apply to something that can't be observed or these students so then nothing could possibly tell whether or not there are students in these chairs exactly hey ed we're here live with an unidentifiable unobservable student what's it like to be unobservable okay back to you ed pretty sweet huh no it is not sweet the only reason why your idea isn't falsified is because it's not falsifiable if you can't prove it then it's useless i mean you might as well say there's invisible elephants floating around and rejects bob's new explanation on the grounds that it's not falsifiable it's compatible with anything that could possibly happen but that means that it can't explain why one thing happens rather than another it's completely empty i was just joking this is a philosophy class after all okay i don't mind jokes but let's get serious it's not helping us with our problem why isn't anybody here speaking of joking maybe they're all playing a trick on us maybe they decided not to show up okay but why would they do that is it april fools day no it's january oh well then i don't know why they're tricking us they just are okay i can't believe that unless you can tell me why they would be so silly and it's criticizing bob's new explanation because it's not deep it's shallow because it depends on a principle that is not itself explained and needs to be explained i guess the professor just decided to cancel class because he didn't feel like teaching today maybe but then other students wouldn't know so they would be here unless he emailed the entire class then they would know did you check your email recently about an hour ago then maybe he emailed us in the past hour i guess i mean that would explain why nobody's here some professors do cancel class at the last minute but not him i think he's too strict i've had five classes with him and he's never cancelled class at the last minute if you miss even one class in this course you will will fade fade fade so maybe this time it's different yeah maybe the sun didn't rise either way it's totally out of character Ann's point is that Bob's new explanation is ad hoc. It applies only to the very circumstances that it was invoked to explain, and it doesn't apply to other cases. That means that it lacks power and breadth. Okay, but I've got it. Classes must have been canceled for some reason. What reason? Maybe it's a holiday. Okay, what holiday? I... Martin Luther King. That's it! It's Martin Luther King Day! That would explain it. I mean nobody goes to class but a fool on a holiday. Hi, I'm here. I guess that makes us both fools. Yeah. So I guess that's why he didn't send the note, because he figured no one would come here. I bet he wrote it down in the syllabus. It also explains why no one's in the whole classroom building. Bob's new explanation works because it has all of the virtues that the other explanations lack. It's powerful, broad, deep, simple, conservative, and not falsified and yet falsifiable. Those virtues make his explanation good, or in his words, so weak. You're right. You know, I think there's some kind of ceremony today with the president of the college and some big hot shot from Washington, from Martin Luther King Day. So probably that's where the whole class is. That's why they're not here. Maybe, but even if there weren't a ceremony, the fact that it's Martin Luther King Day would explain why nobody's here, so you don't really need to add anything else. Ann rejects Bob's newest explanation because it's not modest. It commits him to more matters of fact than are needed to explain the observations at hand. So I guess the holiday explains it all. Oh, not really. We still don't know why that big head keeps popping in on the side. That's one that I can't figure out myself. That guy looks like this kid who used to babysit me when I was younger. This whole exchange can be seen as a single argument that takes the form of a long inference to the best explanation. The first premise is an observation. Nobody else is in the room. The second premise is an explanation. The hypothesis that class was canceled because of the holiday plus accepted facts and principles gives a suitably strong explanation of the observation in premise one, namely the observation that nobody else is in the room. Premise three is a comparison. No other hypothesis provides an explanation nearly as good as the holiday hypothesis in premise two. And the conclusion is that the holiday hypothesis in premise two is true. The most controversial premise is probably premise three. It says that no other explanation provides nearly as good an explanation as the holiday hypothesis. To justify this premise, we need to compare other possible explanations. And that's exactly what the two students do throughout the skit. Their discussion can then be summarized in this background argument that supports premise three. The hypothesis that the other students are late is falsified by the passing of time. The hypothesis that the other students are invisible is not conservative. The hypothesis that the other students are undetectable is not falsifiable. The hypothesis that the other students are playing a joke is not deep. The hypothesis that the professor skipped class is not powerful or broad. The hypothesis that the other students are at a ceremony is not modest. No other hypothesis seems plausible. Therefore, no other hypothesis provides an explanation nearly as good as the holiday hypothesis in premise two. Even if the other explanations are inadequate, the inference of the best explanation fails unless the holiday hypothesis succeeds at explaining why there's nobody else in the room. Premise two claims that the holiday hypothesis does explain why there's nobody else in the room. So we need to analyze why it succeeds. And to do that, we can look at another background argument. The holiday hypothesis explains why nobody else is there because if classes were canceled because of the holiday, then nobody else would be there. That is, nobody else would be in the room at the usual time. The holiday hypothesis is also broad because it explains other actual observations, such as the observation that the whole building is empty. The holiday hypothesis is also powerful because it applies to many separate cases. For example, it explains why students won't be there on future holidays. The holiday hypothesis is also falsifiable because two students might find out that classes were not canceled for the holiday. The holiday hypothesis is not falsified because the two students do not actually find out that classes were not canceled for the holiday. And similarly for other ways to falsify the hypothesis. The holiday hypothesis is also conservative because it does not conflict with any prior well-established beliefs. The holiday hypothesis is also deep because it does not depend on any assumptions that need but lack independent explanation. So the holiday hypothesis explains why nobody else is there and it's broad, powerful, falsifiable, but not falsified, conservative, deep. Therefore, the holiday hypothesis plus accepted facts and principles gives a suitably strong explanation of why nobody else is in the room. These two background arguments use a common list of virtues that are usually called explanatory virtues. In general, one explanation is better or stronger than another if it has more of these virtues. When you understand these explanatory virtues, then you've mastered inference to the best explanation. Right? Right. Now we can go on and look at other kinds of inductive argument. In the previous lecture, we saw one example of inference to the best explanation, but it might help to go through just one more. I told you that detectives often use inference to the best explanation to figure out who committed the crime. One really neat example of this kind of argument was provided by some students in the first offering of this course. Just check out the video that they made. I think I'm going to go for a run. Philip and Mackenzie are sleeping. Work up an appetite. I might dig into some of those cookies later. That was a good run. I think I'm going to have some cookies. What? Oh man, that was a brand new day. The dish broke. And I was wondering if you heard anything or if you had anything to do with it. No, I just woke up. You didn't hear? Huh. I wonder how this could have happened. You didn't feel any earthquake. Did you or something? Well, I suggest that perhaps it was Timmy. You know, come to think of it, I'm looking at this counter and I'm seeing a dumb cat's hair. I think we found our answer. Timmy did it. Philippa? Timmy. Timmy, what do you have to say for yourself? Love that video, didn't you? Great production values. He's ready for Hollywood. The actors, Emmys. Oh man, whatever you hired professionals. And the argument was good too. First of all, it was really clear. I mean, you know exactly why they think Timmy did it. The structure was really good. You start with a phenomenon that needs to be explained, namely, the dish was broken on the floor and you look for alternative explanations and you compare those different explanations and the best explanation is that Timmy did it. Okay, so what are the competing explanations? Well, Mackenzie might have done it, but she denied it and she wouldn't lie to her parents. She looked so innocent, at least I thought so. We'll see whether other people agree. And the other possibility is an earthquake that nobody felt an earthquake and they probably would have felt an earthquake so that's no good. Maybe Philippa did it. Wait a minute. I don't know if you noticed that little box. Philippa sleeps like a log and he got back at 7.45. That's when the dish was broken. She didn't come down till 9.45 and she's sleeping like a log. How could she have done it? So we've got different hypotheses that are being considered and he's looking for the best one. So what makes it best is not just that those other hypotheses have things that rule them out, but also that this hypothesis has a lot of positive support for it. One thing is nice is that he found the hair on the counter. That was crucial because now the hypothesis that Timmy did it explains not just the dish but also the hair on the counter and that's a sign of a good explanation that it explains not just the particular things but it's powerful and broad. It applies to other things as well and explains other phenomenon that need to be explained. So overall, I think there's pretty good reason to think that Timmy did it. And the kicker that proves it all is that the cat confessed. You heard it yourself. The cat said, Of course the argument could be stronger because inductive strength comes in degrees but the fact that it could be stronger doesn't mean it's no good. You can get a pretty good reason by ruling out the most plausible hypotheses even if there are few that you didn't quite get to in presenting your argument. And sure enough, in the discussion forums some students pointed out weaknesses which amounted to looking at these different hypotheses as possible explanations of the data. A lot of students seem to suspect Mackenzie. Here's one of them. Joe writes, Hi Kevin. While watching the interrogation of Mackenzie, I got the feeling she was hiding something. She had means, motive, and opportunity. I think in order to add to the strength of the inductive argument that she's innocent she should volunteer for a lie detector test. And then he goes on. I suspect that Timmy was framed considering how minorities and the poor are treated in the justice system I recommend that he remain silent until he secures representation. Well, I don't know about the second half of that but with regard to Mackenzie there's an interesting point to notice here. Joe doesn't know Mackenzie and he doesn't trust her. Thinks she looks suspicious. But Kevin, he knows Mackenzie. He lives with her. He spent a lot of time with her. And he trusts her. So we have a nice example of how an inductive argument might be strong for one person and not for the other person. Because Kevin has this background information that Mackenzie's trustworthy. Whereas Joe doesn't have that background information. So the argument that Kevin gave in the very short form in which it occurred might be good enough for him because of his background knowledge about Mackenzie's trustworthiness. Whereas it's not good enough for Joe because Joe doesn't have that background knowledge. And that's just a fact about inductive arguments in general that they might be strong for some people and not so strong for other people. And we could make the argument even stronger by looking at other explanations. So what about Philippa? Well, she sleeps like a log but maybe she was sleepwalking and knocked the cookies over when she was sleepwalking. What about Kevin himself? How come he's getting off the hook? Maybe he did it when he came back from running because he had sweat in his eyes and didn't notice it and didn't hear the plate drop because he was so tired. Maybe there was a burglar who came in and while they were stealing things they knocked the cookies over and that made noise and so they got scared and ran away. Maybe it was Santa Claus. He has been known to eat cookies that are left down on the counter for him. Maybe it was ghosts. There's all kinds of possible explanations and you could drive yourself crazy trying to rule out every possible explanation. So at a certain point you have to decide when is the argument strong enough? And that depends on what you're going to do with it. Now I've said I think this is a good argument. I think Timmy did it. The confession really is the kicker but I'm not ready to give Timmy capital punishment. I'm not ready to banish Timmy from the house. There's some steps that would just be too harsh in response to this amount of evidence. However, I do think that the evidence is strong enough that we can guide our action with it at least in ways that don't have a lot of cost. So for example, my suggestion to Kevin and his entire family is don't put the cookies on the edge of the counter. I mean, if Timmy's going to knock them off then you don't want them knocked off. You've got to accept some responsibility yourself and this argument can be good enough to guide our action about where to put the cookies on the counter, when to leave them out and when not to leave them out even if it's not good enough to justify capital punishment. So one thing that we need to think about in assessing not just how strong an argument it is but whether it's strong enough is what are we going to do with it and what are the costs incurred if we're wrong. Another very common kind of inductive argument is an argument from analogy. We'll see that these arguments from analogy are very closely related to inferences to the best explanation. But first we've got to ask what's an analogy? An analogy is basically a comparison between two things. It points out similarities between those two things. And analogies are given all the time. For example, a poet might say her eyes were like emeralds. Well, in what way were they like emeralds? They might have had the same color. They might have shimmered like emeralds. They might have been valuable like emeralds. And the analogy, her eyes were like emeralds, doesn't really tell you exactly which respect her eyes resembled emeralds. But that's part of the point. When you're writing poetry, you want to stimulate creative comparisons and analogies so that readers of the poem can think about it in their own way. And the same thing holds for other analogies in other areas. But because it's not very specific, some people think that analogies are just no good at all in arguments. Actually, though, we use analogies in arguments all the time. Here's an example from public policy. It built a transportation system in the city of Houston, Texas. It worked pretty well. And then the planners in the city of Phoenix, Arizona were wondering what kind of public transportation system to build there. And they reasoned like this. They said Phoenix is a lot like Houston in many ways. Large population, hot during the summer, many, many people, and large area. So they said Phoenix resembles Houston in a lot of ways. This type of transportation system worked in Houston, so it'll probably work well in Phoenix also. Now, what about law? Lots of legal decisions are based on analogies, too, because common law systems, at least, follow precedent. When judges decide a case one way at one point, then later on, other judges are supposed to make similar decisions. So you can say, for example, the Supreme Court declared that segregated public high schools are unconstitutional in the United States. Colleges are a lot like high schools, so segregated public colleges are also unconstitutional in the United States. And then med schools are a lot like colleges. So segregated public medical schools are also unconstitutional in the United States. And that's the way the legal system evolves by drawing analogies among the different cases that come up within that jurisdiction. This form of argument in law might seem to be a real problem because you don't say exactly what the similarities are. But actually, it's very useful because it is predictable if you know that segregated high schools have been declared unconstitutional. You pretty much know that judges are going to find colleges unconstitutional, too, if they're segregated. And it also gives flexibility so that judges can see when they're going too far, they say, well, that precedent's different, and they distinguish the precedents. So by resting legal reasoning on arguments from analogy, they gain both predictability and also flexibility in the legal system. So arguments from analogy can be pretty useful. Fine, but policies and laws are all about norms and values. What about science and hard facts? Well, scientists use analogies, too. For example, scientists at one point didn't know what was at the center of the earth, but they found a bunch of meteors and meteorites that had a high iron content much higher than the content of iron in the crust of the earth. So they reasoned the earth must be like these other meteors and meteorites, so it must have a similar amount of iron in it because they were produced in the same way in the history of the universe. But that means there must be a similar amount of iron in the earth. If it's not in the crust, where could it be? It must be down in the core. So they figured probably the core of the earth has a lot of iron in it. That's just one example. But scientists actually use analogies a lot. And if you don't believe me, go read some psychological studies of scientific reasoning. But we're going to focus on an example from art history. Just imagine that you're going through the attic and you find an old painting. It looks a lot like a painting by the famous impressionist Cézanne. And if it is by Cézanne, it's worth an awful lot. But you've got to figure out whether this painting is by Cézanne. How do you figure it out? Because Cézanne didn't sign it. He didn't sign a lot of his paintings. Well, what you do is you look at other Cézanne paintings and try to figure out whether they're similar. And if you're not an expert, you'd probably better check with an expert and have them do it. But they're going to do the same thing. They're going to compare this painting to a lot of other paintings that we know are by Cézanne. And then you can reason like this. This painting has a certain kind of brush work and coloring and so on and so on, subject matter, whatever. Other paintings by Cézanne have very similar brush work and color patterns and topic and so on. Those other paintings are definitely by Cézanne. We know that. Therefore, this painting is probably by Cézanne as well. Now that's an argument from analogy. This argument from analogy shares a certain form with the other arguments from analogy that we discussed before. And we can pick out that form by substituting letters for the English words in the English argument. For example, we can substitute the letter A for the subject. That is the topic of the argument, the painting that we don't know whether it's a Cézanne or not. And we can substitute the letters B, C and D for the similar objects that are also Cézanne paintings. And we can substitute the letters P, Q and R for the similarities between the paintings that we know are by Cézanne and the one that we're not sure of. And then we can substitute the letter X for that particular property of being by Cézanne. And when you substitute all those letters for the English words, then the argument simply says that object A has properties P, Q and R. And objects B, C and D also have those properties P, Q and R. And B, C and D also have the property X. So the subject, object A, probably also has the property X. Namely, this painting is by Cézanne, probably. Of course, since this argument only tries to show that the conclusion is probably true, it's an inductive argument. It's not valid. It's possible for the premises to be true and the conclusion false. Namely, this painting might resemble all those other paintings in those respects, and yet it's not by Cézanne. Secondly, the argument's defensible. You can get some additional information that makes it really look like a bad argument. For example, you could turn the painting over and on the back, you find the signature of a different artist, like Seraf. And then you realize this isn't by Cézanne at all. But nonetheless, the argument can be strong. It can always be stronger because there can be more similarities and more important similarities. But it can be a strong argument and a good argument because it's inductive, so it doesn't even try or pretend to be valid. How can we tell when an argument for an analogy really does give us a strong reason to believe the conclusion? What are the standards by which we measure how strong the argument is and how strong the reasons are? Well, one of them should be obvious. Of course, the premises have to be true and justified, like in any argument. A standard that's relevant here is that when there are more important analogies, then it provides a stronger reason. Because some analogies are just totally unimportant. The painting is square. Other paintings by Cézanne are square. Therefore, this is by Cézanne. Well, that's ridiculous, right? Because lots of painters use square candles. But something that's important that's going to be specific to Cézanne, a very idiosyncratic, is going to be more important for this type of argument. Secondly, when there are more analogies, because we don't know exactly which one is the one that's important. That's the point of an argument from an analogy. You draw the analogy without knowing exactly which respect is the crucial one. So the more analogies that you have, the more likely you're going to hit on the ones that are crucial. So if it's not just brushwork, it's also the type of paint that was used. It's also the color scheme that was used. It's also the geometric shapes. It's also the subject matter. It's a particular mountain that's close by where Cézanne lived, and he painted a lot of that mountain and on and on and on. The more analogies, the more likely that some of them are going to be the crucial ones, and therefore the stronger the argument is, and the stronger reason it gives you to believe that this particular painting is by Cézanne. But of course, there are always going to be some disanalogies as well, because Cézanne didn't paint the same thing over and over again, exactly the way he did the first time. The fewer disanalogies, the stronger the argument. There'll always be some, or there wouldn't be much of an argument there. It would be exactly the same painting. But the fewer disanalogies, and the less important those disanalogies are, then the stronger the argument is going to be. Next, the objects that you're comparing, because they're similar in various respects, that is the other paintings that we know are by Cézanne. If they're quite diverse, then that means that you have similarities among a diverse group. They all share these particular properties, and that means that Cézanne continued to use those features throughout all the different types of paintings that he did, and that means that it's going to be a stronger reason to believe that this painting is by Cézanne. Finally, the conclusion is weaker. You could say, therefore, this painting is definitely by Cézanne. It couldn't be anybody else. Well, that's kind of crazy, right? But if you say it's probably by Cézanne, but it has some chances by Cézanne, maybe you want to check it further, then you're weakening the conclusion, and that can make the argument stronger. So in all of these different ways, we can assess how strong the argument from analogy is by looking at the respects in which the objects are analogous, the diversity among the objects that are analogous, the strength of the conclusion, and so on and so on. And that's how we assess an argument from analogy for strength. I want to close with one more example that raises interesting questions about the relationship between arguments from analogy and inferences to the best explanation. It concerns the pressing issue of whether Neanderthals were cannibals. Now, it's not a pressing issue for most people, but it is a very pressing issue for people who study Neanderthals. And so it's quite a breakthrough when they found some bones in a cave that they knew was inhabited by Neanderthals. In that cave, next to what looked like a fire pit, there were bones of deer with markings of a certain sort that looked like they had been cutting the meat off the bone. And they also found bones of humans in that cave where they had been cutting, where they had similar markings. And they argued, since the bones have similar markings, and these bones, the bones of the deer, were probably cut up for food, well, the human bones were probably also cut up for food. So they reached the conclusion that at least sometimes Neanderthals ate humans. What's interesting is that there are two ways to reconstruct this argument. First, you can reconstruct it as an argument from analogy. The bones of the humans were found in this location with these kinds of markings. And the bones of deer were also found in this location with these kinds of markings. That the deer were cut up for food, therefore the humans were probably also cut up for food. Now that sounds like an argument from analogy when you think about it that way. But you can also reconstruct the argument as an inference to the best explanation. The bones of the humans had these markings on them, and were in this location. How do you explain that? The best explanation of why they have these particular kinds of markings is that they were cut up for food. Therefore the humans were probably cut up for food as well. Now notice that both reconstructions of the argument make the argument look okay. And so it's not clear which tells you the real structure of the argument that the author was trying to give. And that means that arguments from analogy and inferences of the best explanation are actually very closely related. And sometimes you can take an argument and reconstruct it either way. It's not going to affect very much how strong the argument is, but it might affect how you see the argument working. And the big difference is that when you do an argument from analogy, you don't have to specify exactly which respect is important. So you can point out lots of analogies and hope that you hit the one that really matters. Whereas when you're doing an inference to the best explanation, then you have to pick out the specific property that gives you the explanation of the phenomenon that you observe. So it forces you to get a little bit more specific than with an argument from analogy. But otherwise, these two arguments are clearly very closely related. And they're basically two different ways to argue for similar conclusions. For example, in this case, with the argument from analogy, you don't know whether it's the location next to the fire or the types of markings, or maybe there's several different types of markings, and they're all the same, but you don't know which ones are the ones that indicate how it was killed and which markings indicate how it was cut up to be eaten. And an argument from analogy can leave all that vague and just think that probably one of those similarities justifies the conclusion that the humans were cut up to be eaten. But if you're going to give an inference to the best explanation, then you're saying that these markings, for example, diagonal markings on leg bones, might suggest that they cut that up in a certain way because that's how they prepared the deer meat, and they were used to preparing deer meat that way. So they used similar cutting techniques when they were preparing human meat. And you've got an explanatory story that's much more specific than a mere analogy, but it also commits you to a lot, so it might be questionable in various ways. So when you look at an argument like this, you've got to decide which way to reconstruct the argument as an argument from analogy or as an inference to the best explanation. And the general rule is one that we saw long ago in the early weeks of this course. If you really want to understand an argument, you want to understand your opponents or you want to have a better argument for yourself, then you try to make the argument look as good as possible. So when you face a particular example like the Neanderthal example, you have to decide, is this argument going to be better if I reconstruct it as an argument from analogy, or is it going to be better if I reconstruct it as an inference to the best explanation. And the best reconstruction is going to be the one that makes the argument look best.