Today we're going to talk about how to refute an argument, by using counterexamples. So what's a counterexample and how does it help to refute an argument? A counter example is an example that runs counter to some generalization, and thereby shows that the generalization that's false. Now counterexamples can be used to refute an argument that contains a generalization, either as one of its premises or as its conclusion. So, if the argument contains a generalization as its conclusion, and the counterexample shows that the generalization is false, then in effect what the counter example does is show that the argument reaches a false conclusion. If the argument contains a generalization as one of it's premises, then the counterexample shows that that premise of the argument is false. But either way, the counterexample shows that the argument is unsuccessful, either because the argument has a false a premise or because its conclusion is false. Okay. So what are some examples of counterexamples? Well, let's start by considering this argument. Premise one, you should always treat others the same way that you would like to be treated yourself. Premise two, I would not like anyone to change my diapers. So conclusion, I should not change the baby's diapers. Now, this argument appears to be valid. Furthermore, I can assure you, premise two is true. So if premise one is also true, then it looks like I have a good argument for why I shouldn't change the baby's diapers. I should get someone else to do it. But is premise one true? Well, premise one sounds familiar enough. You should always treat others the same way that you would like to be treated yourself. That's something we frequently hear people say but that can't be precisely true. After all I would like to be treated as an adult but that doesn't mean that I should treat my children as adults right? So if the generalization is that you should always treat others the same way that you would like to be treated yourself that generalization is false. It's false even though I would like to be treated as an adult, it doesn't mean I should treat my children as adults. I shouldn't treat my children as adults because they're not adults, but I am. Now that doesn't meant that I should baby my children. But I shouldn't treat them the same way that I would like to be treated myself. I shouldn't treat them as if they're adults. Okay, so that's a counter example to premise one. And that counterexample shows that premise one stated in the way that it's stated here, you should always treat others the same way that you would like to be treated yourself. Premise one stated in that way is false and so this argument does not work. This argument does not succeed in showing that I should not change the baby's diaper, first the reason it doesn't succeed is because one of its premises is false. Now, premise one might seem to be true, but if it seems to be true, that's only because something very similar to premise one is true. What's similar to premise one that is true is the claim that you should usually typically often treat others the same way that you would like to be treated yourself. Now those claims are true you should usually treat others the same way that you'd like to be treated yourself. But that doesn't mean that you should always treat others the way you'd like to be treated yourself. That general claim about how you should always behave. That claim is false, and our counterexample shows it. There's an example of the use of counterexample to refute an argument. Let's consider another example. Consider this argument. Premise one, if it's wrong for all of us to perform a particular action then it's wrong for any of us to perform that action. Premise two, it's wrong for all of us to try to take the last piece of bread on the table. So conclusion it's wrong for any of us to try to take the last piece of bread on the table, you could imagine this situation. Let's say, a bunch of us are sitting around the dinner table eating dinner. There's a basket of bread in the middle of the table and we've been bit by bit reaching in to take out pieces of bread. And now there's only one piece of bread left in the basket and there are a bunch of us sitting around the table. Well it would be wrong for all of us to jump up and grab that piece of bread and start fighting over it. That would be wrong. That would be completely unacceptable. But just because that would be unacceptable, does that mean that none of us is allowed to go and eat that last piece of bread? Well, no. That seems like a preposterous conclusion. I mean, if all of us have to sit there just staring at that last piece of bread and none of us is allowed to eat it, well, then that's wasting food. That's not an acceptable conclusion. So, it's gotta be okay for one of us to take that last piece of bread even though it's not okay for all of us to try to take that last piece of bread. So here's an example where It's okay for one person to do something even though it's not okay for everyone simultaneously to do that thing. It's okay for one, it's not okay for everyone. So that's a counterexample to the generalization that occurs in premise one of our argument. So this argument is not a successful argument. This argument does not prove that it's wrong for any of us to try to take the last piece of bread on the table. And the reason it doesn't prove that is not because the argument is fallacy. The reason it doesn't prove that is because premise one of the argument is false. Premise one of the argument states a general claim. And that general claim that it states does not true. Well, that might be true that it's usually wrong for anyone to perform an action that is wrong for everyone to perform. It's not true that it's always wrong for anyone to perform an action that it's wrong for everyone to perform. And in fact I just gave a counter example to that generalization. It's not wrong for what one person to take a piece of bread, the last piece of bread on the table even though it would be wrong for everyone to try to take that piece of bread simultaneous. Okay, so there's another example of an argument that we can refute by means of counter example. We can use a counter example to show that premise one of that argument is false, and so the argument is unsuccessful. Finally, let's consider this third case. Premise one, breaking the law is almost always wrong. Premise two, double parking is breaking the law. So conclusion, double parking is almost always wrong. Now, can we refute this argument by means of counterexample? Well, There's no counter example to premise two. Premise two is simply true, double parking is breaking the law. That's part of what's involved in double parking. When you double park, you are breaking the law. Well what about premise one? Breaking the law is almost always wrong. Is there a counter example to that? No. There's no counter example to premise one that's stated. If premise one were to say breaking the law is always wrong, then we could produce a counter example to premise one. Sometimes, it's an emergency. You have no choice but to double park. You need to do something very quickly. It's not wrong to double park in that situations especially not if you're doing it in just a few seconds. It's not wrong to double park, and yet you're breaking the law because there's a law against double parking. So if premise one were to say breaking the law is always wrong, then there would be a counterexample to premise one. But premise one doesn't say that. Premise one says that breaking the law is almost always wrong. Now how to you produce a counterexample to a claim of the form almost always? Well the answer is you don't, because even if you produce an example of a case where breaking the law is not wrong, that still doesn't show that it's false, that breaking the law is almost always wrong. Maybe breaking the law is almost always wrong but just not in the case that you produced. So you can't produce a counterexample to a generalization of the form, breaking the law is almost always wrong. That generalization might be false, but you can't show that it's false by using a counterexample. Okay, so we cannot refute this argument by means of counterexample. That's not to say that this is a good argument. In fact, this third argument is not a good argument. But we can't show that it's not a good argument by using a counter example. So sometimes counterexample can succeed in refuting an argument, and sometimes it can't. It depends on whether the argument contains a generalization to the effect that something always happens or something is true in all cases. If the argument contains a generalization like that, an unexceptional generalization, a generalization without any room for exceptions, then the counter example can be used to refute that generalization. But if a generalization is phrased in such a way that it admits of exceptions, like if a generalization talks about what almost always happens or about what usually happens, about what typically happens, then we can't refute that generalization by means of counterexamples. Okay, so we can look at examples of counterexamples in the exercises that follow. See you next time.
