1 00:00:02,780 --> 00:00:05,845 Great. We can do course analysis, we can 2 00:00:05,845 --> 00:00:11,425 identify the premises and conclusions, we can put them in standard form. 3 00:00:11,425 --> 00:00:15,433 What's next? Well, the next step is take those parts 4 00:00:15,433 --> 00:00:20,228 and put them in a certain order, and fill in the missing gaps. 5 00:00:20,228 --> 00:00:21,564 We need to learn how to reconstruct arguments. 6 00:00:25,179 --> 00:00:29,148 Are you ready? Well, there are lots of ways to 7 00:00:29,148 --> 00:00:31,954 reconstruct. When you think about constructing a 8 00:00:31,954 --> 00:00:35,606 house, or a building. In order to construct a good building 9 00:00:35,606 --> 00:00:40,265 you've got know, what the goal is, what the standards of a good building are. 10 00:00:40,265 --> 00:00:43,350 The same thing goes for reconstructing arguments. 11 00:00:43,350 --> 00:00:49,747 In order to reconstruct an argument properly, you need to know what the 12 00:00:49,747 --> 00:00:54,729 standards are for reconstruction. We're trying to reconstruct it so as to 13 00:00:54,729 --> 00:00:58,464 meet those standards. Because the goal is not to reconstruct 14 00:00:58,464 --> 00:01:01,079 the argument in order to make it look bad. 15 00:01:01,079 --> 00:01:05,810 The point is going to be reconstruct arguments so as to make them look good. 16 00:01:05,810 --> 00:01:10,449 because by making your opponents look bad or silly, that doesn't do anybody any 17 00:01:10,449 --> 00:01:12,800 good. If you want to learn about their 18 00:01:12,800 --> 00:01:17,749 perspective, and you want to learn from their views, then you need to reconstruct 19 00:01:17,749 --> 00:01:21,276 their argument, so as to make it look as good as possible. 20 00:01:21,276 --> 00:01:25,359 And to do that, you need to know about the standards for arguments. 21 00:01:25,359 --> 00:01:28,700 That is the standards that make arguments good or bad. 22 00:01:28,700 --> 00:01:33,800 So what we're going to do this week is we're going to look first at some 23 00:01:33,800 --> 00:01:38,476 standards for our arguments, validity and soundness in particular, and 24 00:01:38,476 --> 00:01:43,749 they we're going to use those standards to develop a method called reconstruction 25 00:01:43,749 --> 00:01:46,835 or deep analysis, I'll explain those terms later. 26 00:01:46,835 --> 00:01:51,594 And then we are going to apply that methods to a few concrete examples, in 27 00:01:51,594 --> 00:01:56,674 order to be able to take a passage and take those premises and conclusions and 28 00:01:56,674 --> 00:02:01,625 fill them out and get a full fledged argument that if we've done it properly 29 00:02:01,625 --> 00:02:05,291 will be be as good as it can be, and that we can learn from. 30 00:02:05,291 --> 00:02:07,570 That's the goal. Now, 31 00:02:07,570 --> 00:02:12,394 because an argument consists of premises and a conclusion, and the premises are 32 00:02:12,394 --> 00:02:17,279 supposed to be related in the right way to the conclusion, there can be two main 33 00:02:17,279 --> 00:02:21,615 ways an argument can go wrong, two main vices of argument, you might say. 34 00:02:21,615 --> 00:02:26,256 The first is there might be something wrong with the premises. In particular, 35 00:02:26,256 --> 00:02:29,860 they might be false, or at least one of them might be false. 36 00:02:29,860 --> 00:02:34,986 Second, there might be something bad about the relation between the premises 37 00:02:34,986 --> 00:02:38,899 and the conclusion. The premises might fail to give a good 38 00:02:38,899 --> 00:02:43,351 reason for the conclusion. Now each of these problems is something 39 00:02:43,351 --> 00:02:48,275 that we need to avoid and when we do avoid them, we get the corresponding 40 00:02:48,275 --> 00:02:53,402 virtues mainly validity and soundness. And those are the two notions that we 41 00:02:53,402 --> 00:02:56,438 want to discuss in this lecture and the next. 42 00:02:56,438 --> 00:03:01,900 Let's begin with the relation between the premises and the conclusion. 43 00:03:01,900 --> 00:03:07,315 What kind of relation between the premises and the conclusion is good for 44 00:03:07,315 --> 00:03:11,414 an argument or makes an argument good? Well, that depends. 45 00:03:11,414 --> 00:03:14,927 Some arguments are deductive and others are not. 46 00:03:14,927 --> 00:03:18,660 So, let's focus for a moment on deductive arguments. 47 00:03:18,660 --> 00:03:24,864 In deductive arguments, the conclusion is supposed to follow from the premises, but 48 00:03:24,864 --> 00:03:28,722 what does that mean? I mean, what does it mean for a 49 00:03:28,722 --> 00:03:34,700 conclusion to follow from the premises? That's a really hard notion to pin down. 50 00:03:34,700 --> 00:03:39,311 So what logicians usually do and, and what we're going to do, is focus instead 51 00:03:39,311 --> 00:03:43,383 on the notion of validity. And the idea is that a deductive argument 52 00:03:43,383 --> 00:03:46,318 is trying to structure itself so that it's valid. 53 00:03:46,318 --> 00:03:50,989 And we'll explain what validity is, but for now, I want to emphasize that we're 54 00:03:50,989 --> 00:03:55,541 only talking about deductive arguments. There's going to be another class of 55 00:03:55,541 --> 00:04:00,092 arguments called inductive arguments that we'll get to later in this course, 56 00:04:00,092 --> 00:04:02,607 where they don't even pretend to be valid. 57 00:04:02,607 --> 00:04:06,800 They don't even pretend that the conclusion follows from the premises. 58 00:04:06,800 --> 00:04:12,770 But just for simplicity, let's focus on deductive arguments now, and the idea is 59 00:04:12,770 --> 00:04:19,180 that the deductive argument should be structured in such a way that it's valid. 60 00:04:19,180 --> 00:04:22,477 Then the next question is what's validity? 61 00:04:22,477 --> 00:04:28,366 Let's start with a simple example. Suppose that you know Mary but you don't 62 00:04:28,366 --> 00:04:34,001 know her children. However you do know that she has one 63 00:04:34,001 --> 00:04:39,858 child who is pregnant. And you also know that only daughters can 64 00:04:39,858 --> 00:04:44,796 become pregnant. So you have all that you need to know in 65 00:04:44,796 --> 00:04:52,080 order to draw a further conclusion, namely, Mary has at least one daughter. 66 00:04:52,080 --> 00:04:57,900 So here's the argument. Mary has a child who is pregnant. 67 00:04:57,900 --> 00:05:03,565 Only daughters can become pregnant, therefore, Mary has at least one 68 00:05:03,565 --> 00:05:07,623 daughter. Now, if you think about it, there's just 69 00:05:07,623 --> 00:05:14,472 no way, no possibility that both of those premises are true and the conclusion is 70 00:05:14,472 --> 00:05:18,566 false. That is the feature that we're going to 71 00:05:18,566 --> 00:05:23,154 call validity. More generally, we can define validity in 72 00:05:23,154 --> 00:05:30,245 an argument so that an argument is valid if and only if, it's not possible for the 73 00:05:30,245 --> 00:05:34,840 premises to be true and the conclusion false. 74 00:05:34,840 --> 00:05:39,708 That is, it's not possible for there to be a situation where both of those hold, 75 00:05:39,708 --> 00:05:44,330 that is a situation where the premises are true and the conclusion is also 76 00:05:44,330 --> 00:05:48,625 false. Now that might strike you as a pretty 77 00:05:48,625 --> 00:05:52,436 simple notion. But actually that little word possible is 78 00:05:52,436 --> 00:05:55,975 a problem. How do you tell what's possible or what's 79 00:05:55,975 --> 00:05:59,504 not possible? Well, there's no mechanical solution to 80 00:05:59,504 --> 00:06:04,252 that and we'll struggle with that a little bit throughout this course. 81 00:06:04,252 --> 00:06:08,999 But for now, since we're right at the start, let's think of it this way. 82 00:06:08,999 --> 00:06:12,390 Is there any way for you to tell a coherent story? 83 00:06:12,390 --> 00:06:16,152 Where the premises are true and the conclusion is false. 84 00:06:16,152 --> 00:06:20,653 Can you describe a situation with that combination of truth values? 85 00:06:20,653 --> 00:06:25,960 That is, the premises being true and the conclusion false in the same situation. 86 00:06:25,960 --> 00:06:31,201 If you can tell a coherent story with that combination then it's possible and 87 00:06:31,201 --> 00:06:35,769 the argument is not valid. But if there is no way to tell a coherent 88 00:06:35,769 --> 00:06:41,076 story where the premises true and the conclusion is false, then the argument is 89 00:06:41,076 --> 00:06:45,342 valid. Now let's try that test on our example. 90 00:06:45,342 --> 00:06:51,155 Mary has a child who is pregnant. Only daughters can be pregnant. 91 00:06:51,155 --> 00:06:57,851 Therefore, Mary has a daughter. So is there any way to tell a coherent 92 00:06:57,851 --> 00:07:03,953 story where the two premises are true? That is, where Mary has a child who is 93 00:07:03,953 --> 00:07:09,733 pregnant, and only daughters can be pregnant, but the conclusion is false. 94 00:07:09,733 --> 00:07:13,266 Mary does not have a daughter. Well, just try. 95 00:07:13,266 --> 00:07:17,040 Suppose Mary has only one child and it's a son. 96 00:07:17,040 --> 00:07:20,139 There's the conclusion that's false. Good. 97 00:07:20,139 --> 00:07:23,616 What about that? But then, is that son pregnant? 98 00:07:23,616 --> 00:07:28,378 Well, if the son is not pregnant then the first premise's false. 99 00:07:28,378 --> 00:07:31,553 Mary doesn't have a child who is pregnant. 100 00:07:31,553 --> 00:07:37,524 But if the son is pregnant somehow, don't ask me how, but if the son is pregnant 101 00:07:37,524 --> 00:07:43,496 then the second premise's not true. It can't be true that only daughters can 102 00:07:43,496 --> 00:07:48,259 be pregnant because this child is a son. Okay, 103 00:07:48,259 --> 00:07:51,065 what if Mary has two children? Try that. 104 00:07:51,065 --> 00:07:55,452 Try to tell the story that way. Mary has a daughter and a son. 105 00:07:55,452 --> 00:07:58,863 Now she's got a child who is pregnant, the daughter, 106 00:07:58,863 --> 00:08:02,306 and only daughters can be pregnant, but she has a son. 107 00:08:02,306 --> 00:08:05,229 Wait a minute, she's got a son and a daughter. 108 00:08:05,229 --> 00:08:10,620 So now the conclusion's true, because she does have a daughter even though she also 109 00:08:10,620 --> 00:08:12,511 has a son. Oh, oh, wait. 110 00:08:12,511 --> 00:08:18,153 How about this one? What if Mary has a child who is 111 00:08:18,153 --> 00:08:23,457 biologically female but sees himself as a male? 112 00:08:23,457 --> 00:08:31,808 And so she sees that child as a male, but that child is pregnant, because after 113 00:08:31,808 --> 00:08:38,705 all, they're biologically female. Now are the premises true and the 114 00:08:38,705 --> 00:08:42,956 conclusion false? Does that story make sense? 115 00:08:42,956 --> 00:08:47,980 Wait a minute. Either her child is a daughter or her 116 00:08:47,980 --> 00:08:53,295 child is a son. Now if it's a daughter and its pregnant, 117 00:08:53,295 --> 00:08:56,483 no problem. The conclusion's true. 118 00:08:56,483 --> 00:09:03,633 If it's a son, because that child sees himself as a male, then you've got a 119 00:09:03,633 --> 00:09:06,253 choice. Well, what about the first premise? 120 00:09:06,253 --> 00:09:10,597 The first premise is going to be true. She does have a child, who is pregnant, 121 00:09:10,597 --> 00:09:14,312 but what about the second premise, only daughters can be pregnant. 122 00:09:14,312 --> 00:09:16,998 Wait a minute. If that really is a son, if we're 123 00:09:16,998 --> 00:09:21,399 going to call that a son, then it's not true that only daughters can be pregnant. 124 00:09:21,399 --> 00:09:25,006 So now the second premise is false. So try it again. 125 00:09:25,006 --> 00:09:31,260 Try it with, you know, sex changes, and try it with Hermaphrodites tell the story 126 00:09:31,260 --> 00:09:37,356 any way you want about Mary's children. And there's no way that both premises 127 00:09:37,356 --> 00:09:41,340 come out true when the conclusion is false. 128 00:09:41,340 --> 00:09:46,751 That shows that the argument is valid. It might be just that we can't imagine 129 00:09:46,751 --> 00:09:49,702 the coherent story, which makes it invalid. 130 00:09:49,702 --> 00:09:55,184 But the fact that we've tried hard and looked at all the possibilities we can 131 00:09:55,184 --> 00:10:00,666 think of at least gives us a good reason to think that this argument is valid. 132 00:10:00,666 --> 00:10:04,953 Now some people like to think of it in the reverse direction. 133 00:10:04,953 --> 00:10:09,240 They say, let's imagine that the conclusion is false, and then, 134 00:10:09,240 --> 00:10:14,277 If it has to be the case, that at least one of the premises is false, the 135 00:10:14,277 --> 00:10:19,665 argument is valid. Then you can define the validity as, is necessarily the case 136 00:10:19,665 --> 00:10:24,773 that if the conclusion is false one of the premises is false, or in every 137 00:10:24,773 --> 00:10:29,951 possible situation, if the conclusion's false one of the premises is false. 138 00:10:29,951 --> 00:10:34,010 We can apply this new account of validity to the same old example. 139 00:10:34,010 --> 00:10:38,260 It's got to be the case that if Mary doesn't have a daughter, 140 00:10:38,260 --> 00:10:42,976 then she doesn't have a child who is a pregnant, or else there are at least some 141 00:10:42,976 --> 00:10:45,806 children who are pregnant who are not daughters. 142 00:10:45,806 --> 00:10:50,641 So notice in this case you're reasoning back from the falsehood of the conclusion 143 00:10:50,641 --> 00:10:53,471 to at least one of the premises has to be false. 144 00:10:53,471 --> 00:10:57,893 whereas in the earlier definition you were saying it's not possible in the 145 00:10:57,893 --> 00:11:02,021 situations where the premises are true for the conclusion to be false. 146 00:11:02,021 --> 00:11:04,867 You can look at it either way, either direction. 147 00:11:04,867 --> 00:11:09,940 Just pick the one that works for you and go with that definition, because in the 148 00:11:09,940 --> 00:11:14,695 end, the two definitions are equivalent. It's just a matter of what's going to 149 00:11:14,695 --> 00:11:19,070 help you understand which arguments are valid and which ones are not. 150 00:11:19,070 --> 00:11:24,254 In addition to understanding what validity is, it's also very important to 151 00:11:24,254 --> 00:11:29,018 understand what validity is not. A lot of people get confused by the 152 00:11:29,018 --> 00:11:34,343 notion of validity in this context, because they're thinking that to call an 153 00:11:34,343 --> 00:11:37,495 argument valid must be to call it good, right? 154 00:11:37,495 --> 00:11:42,880 You call a driver's license valid when it's good in the eyes of the law. 155 00:11:42,880 --> 00:11:45,672 But that's not what we're talking about here. 156 00:11:45,672 --> 00:11:50,822 The notion of validity is getting used by logicians here as a technical notion and 157 00:11:50,822 --> 00:11:55,352 it's very, very, very important to remember that to call an argument valid 158 00:11:55,352 --> 00:11:59,089 is not to call it good. For some arguments, like deductive 159 00:11:59,089 --> 00:12:03,233 arguments the invalid might be necessary for them to be good. 160 00:12:03,233 --> 00:12:07,920 But it's not enough and we'll see a lot of examples of that later on. 161 00:12:07,920 --> 00:12:13,354 The second point about what validity is not is that validity does not depend on 162 00:12:13,354 --> 00:12:17,905 whether the premises and the conclusion are actually true or false. 163 00:12:17,905 --> 00:12:23,136 Instead it depends on what's possible whether there is a certain combination, 164 00:12:23,136 --> 00:12:27,640 true premises and a false conclusion, it's even possible. 165 00:12:27,640 --> 00:12:34,097 So, whether the premise is actually true in the actual world is not what's at 166 00:12:34,097 --> 00:12:37,954 issue. And we can see this, by seeing that some 167 00:12:37,954 --> 00:12:42,063 arguments with false premises can still be valid. 168 00:12:42,063 --> 00:12:46,760 And some arguments with true conclusions can be invalid. 169 00:12:46,760 --> 00:12:53,375 So let's look at some examples of that. Indeed there four possibilities. 170 00:12:53,375 --> 00:13:00,549 because remember, the conclusion could be true or false, and the premises could be 171 00:13:00,549 --> 00:13:07,020 all true or at least one false. So we've got four possibilities. 172 00:13:07,020 --> 00:13:10,050 And all of those are possible except for one. 173 00:13:10,050 --> 00:13:15,505 The one combination that's not possible for valid arguments is true premises and 174 00:13:15,505 --> 00:13:19,344 a false conclusion. But if you've got true premises and a 175 00:13:19,344 --> 00:13:22,509 true conclusion, it might be valid, it might not. 176 00:13:22,509 --> 00:13:27,762 If you've got false premises and a true conclusion it might be valid, it might 177 00:13:27,762 --> 00:13:30,591 not. If you got false premises and a false 178 00:13:30,591 --> 00:13:33,420 conclusion, it might be valid, it might not. 179 00:13:33,420 --> 00:13:38,949 So let's look at some examples each of those possibilities in order to better 180 00:13:38,949 --> 00:13:44,337 understand the relation between premises and conclusion that exist when the 181 00:13:44,337 --> 00:13:48,236 argument is valid. It's hard to give examples with true 182 00:13:48,236 --> 00:13:53,199 premises or false conclusion, or any these other combinations when the 183 00:13:53,199 --> 00:13:57,594 truth is controversial. So we're going to have a really simple 184 00:13:57,594 --> 00:14:02,699 example, and we're going to start just by stipulating what the facts are. 185 00:14:02,699 --> 00:14:06,740 We're going to assume that all Ford cars have four tires, 186 00:14:06,740 --> 00:14:12,600 but some Ford cards do not have four doors. 187 00:14:12,600 --> 00:14:19,458 We're also going to assume that Henry's car is a Ford that has four doors. 188 00:14:19,458 --> 00:14:25,760 And Jane's car is a Chrysler that has only two doors, not four doors. 189 00:14:25,760 --> 00:14:30,586 And we're just going to take those facts for granted and assume that that's the 190 00:14:30,586 --> 00:14:35,037 situation we're talking about, and then we can give examples of all the 191 00:14:35,037 --> 00:14:40,648 combinations that we discussed before. Let's begin with true premises and a true 192 00:14:40,648 --> 00:14:44,107 conclusion. So, here's an example of that sort. 193 00:14:44,107 --> 00:14:49,180 All Fords have four doors. Henry's car is a Ford, therefore, Henry's 194 00:14:49,180 --> 00:14:52,640 car has four doors. Is the first premise true? 195 00:14:52,640 --> 00:14:57,164 Yes, that's what we are assuming, that's one of our assumptions. 196 00:14:57,164 --> 00:14:59,426 Is the second premise true? Yes. 197 00:14:59,426 --> 00:15:03,877 That's another one of our assumptions. Is the conclusion true? 198 00:15:03,877 --> 00:15:06,723 Yes. So they're all true and now is the 199 00:15:06,723 --> 00:15:10,810 argument valid? Is it possible that all Fords have four 200 00:15:10,810 --> 00:15:14,094 doors? Henry's car is a Ford and yet it's not 201 00:15:14,094 --> 00:15:18,317 true that Henry's car has a four doors. I mean, just think about it. 202 00:15:18,317 --> 00:15:22,027 How would that happen? Well, for the conclusion to be false, it 203 00:15:22,027 --> 00:15:25,806 would have to not have four doors. Suppose it has two doors. 204 00:15:25,806 --> 00:15:29,265 Well then, either it's not a Ford or there's some Ford, 205 00:15:29,265 --> 00:15:32,916 namely Henry's Ford, that only has two doors and not four 206 00:15:32,916 --> 00:15:35,734 doors. So, there's just no coherent story you 207 00:15:35,734 --> 00:15:40,537 can tell where the premises of this argument are true and the conclusion's 208 00:15:40,537 --> 00:15:43,484 false. Or in reverse, if you start off with the 209 00:15:43,484 --> 00:15:48,608 assumption that the conclusion's false. You can tell from that, that at least one 210 00:15:48,608 --> 00:15:54,280 of the premises has to be false as well. Nonetheless. 211 00:15:54,280 --> 00:15:59,788 There are other examples, where the premises are true, and the conclusion is 212 00:15:59,788 --> 00:16:03,900 true, but the argument is not valid, instead it's invalid. 213 00:16:03,900 --> 00:16:08,894 Here's an example of that combination. All Ford cars have four tires. 214 00:16:08,894 --> 00:16:13,227 Henry's car, has four tires. Therefore, Henry's car is a Ford. 215 00:16:13,227 --> 00:16:16,973 Now, in this new argument, are all the premises true? 216 00:16:16,973 --> 00:16:21,159 Yes, the first premise says, all Ford cars have four tires. 217 00:16:21,159 --> 00:16:26,669 And that's true by our assumptions. Second premises Henry's car has four 218 00:16:26,669 --> 00:16:32,468 tires and that's also true by our assumptions and is the conclusion true? 219 00:16:32,468 --> 00:16:37,076 Yes our assumptions also tells that Henry's car is a Ford. 220 00:16:37,076 --> 00:16:42,875 But is it possible, is there any way to tell a coherent story where those 221 00:16:42,875 --> 00:16:46,370 premises are true and the conclusion is false? 222 00:16:46,370 --> 00:16:50,740 Yes, absolutely. All that has to happen is that Jane and 223 00:16:50,740 --> 00:16:55,093 Henry switch cars. Then the first premises can be true 224 00:16:55,093 --> 00:17:01,265 because all four cars have four tires, and the second premise is going to be 225 00:17:01,265 --> 00:17:07,519 true, because Henry's car has four times, of course now it's a Chrysler, because he 226 00:17:07,519 --> 00:17:11,182 got it from Jane, but the conclusions can be false. 227 00:17:11,182 --> 00:17:15,472 Henry's car is not a Ford because Ford and Chrysler are different companies. 228 00:17:15,472 --> 00:17:19,875 So, if he switches cars with Jane and he has a Chrysler then he doesn't have a 229 00:17:19,875 --> 00:17:21,760 Ford. His car is not a Ford. 230 00:17:21,760 --> 00:17:27,469 Okay, so now you've got a situation where the premises are true and conclusion 231 00:17:27,469 --> 00:17:30,763 false. It's not the actual situation but its a 232 00:17:30,763 --> 00:17:35,008 possible situation. You can tell a coherent story with the 233 00:17:35,008 --> 00:17:40,571 premises true and conclusions false and that tells you that the argument is 234 00:17:40,571 --> 00:17:43,791 invalid. Next, let's consider an example with 235 00:17:43,791 --> 00:17:51,852 false premises and a true conclusion. Premise one, all Fords have four doors. 236 00:17:51,852 --> 00:17:59,760 Premise two, Henry's car is a Ford. Conclusion, Henry's car has four doors. 237 00:17:59,760 --> 00:18:04,709 Is the first premise true? No, it's not true that all Ford's have 238 00:18:04,709 --> 00:18:08,920 four doors. Our assumptions tell us that. 239 00:18:08,920 --> 00:18:12,090 Second, is Henry's car a Ford? That's true. 240 00:18:12,090 --> 00:18:16,497 So one of the premises is false and the other one's true. 241 00:18:16,497 --> 00:18:21,445 That means they're not all true. And the conclusion, is that true? 242 00:18:21,445 --> 00:18:25,400 Yes, it is true that Henry's car has four doors. 243 00:18:25,400 --> 00:18:30,418 But remember, the fact that that's actually the case doesn't tell us wether 244 00:18:30,418 --> 00:18:34,031 or not is valid. So, is it valid? That depends on wether 245 00:18:34,031 --> 00:18:38,940 it's possible for the premises to be true and a conclusion false. 246 00:18:38,940 --> 00:18:43,592 Premises aren't actually true, but is there a possible story that you could 247 00:18:43,592 --> 00:18:48,307 tell that would be coherent where the premises are true and the conclusions 248 00:18:48,307 --> 00:18:50,416 false? That's the test of validity. 249 00:18:50,416 --> 00:18:55,593 So let's apply it to this case. We'll just imagine, that, the 250 00:18:55,593 --> 00:19:00,372 conclusion's false, that Henry's car does not have four 251 00:19:00,372 --> 00:19:05,381 doors. It's only got two doors. Then, there are really only two 252 00:19:05,381 --> 00:19:09,280 possibilities, either it's a ford or it's not a Ford. 253 00:19:09,280 --> 00:19:13,037 If it is a Ford, then the first premise is false. 254 00:19:13,037 --> 00:19:17,060 It's not true that all Fords have four doors. 255 00:19:17,060 --> 00:19:21,989 But if Henry's car is not a Ford, then, the second premise is false, because it 256 00:19:21,989 --> 00:19:26,849 says that Henry's car is a Ford. So, there's no coherent way in which it 257 00:19:26,849 --> 00:19:32,525 could possibly be true that both of these premises are true and the conclusion is 258 00:19:32,525 --> 00:19:37,994 false so this argument's valid and notice that, that shows that an argument can 259 00:19:37,994 --> 00:19:40,970 valid, even though it's got a false premise. 260 00:19:40,970 --> 00:19:46,162 Now, you might be thinking to yourself this is crazy how can an argument be 261 00:19:46,162 --> 00:19:49,069 valid when one of it's premises are false? 262 00:19:49,069 --> 00:19:52,980 An argument's no good when it's premises are false. 263 00:19:52,980 --> 00:19:56,732 Notice what that does. That confuses the notion of valid. 264 00:19:56,732 --> 00:20:00,685 Like in a valid driver's license where to be vaild is good. 265 00:20:00,685 --> 00:20:04,705 With the technical notion of validity that we're using here. 266 00:20:04,705 --> 00:20:09,664 The technical notion of validity that we're using here has to do with the 267 00:20:09,664 --> 00:20:12,947 relation between the premises and the conclusion. 268 00:20:12,947 --> 00:20:16,297 And in particular, it has to do with possibilities, 269 00:20:16,297 --> 00:20:19,580 and not with the actual falsehood of the premise. 270 00:20:19,580 --> 00:20:24,740 So what we have to ask ourselves is, what would happen if it really were true? 271 00:20:24,740 --> 00:20:31,156 That all Fords have four doors is not true in the actual world, but we're 272 00:20:31,156 --> 00:20:37,134 concerned with possibility. And if all Fords did have four doors, and 273 00:20:37,134 --> 00:20:42,760 if Henry's car was a Ford, then it would have to have four doors. 274 00:20:42,760 --> 00:20:49,382 So, that possibility of the premise being true, even though it's not, is what's 275 00:20:49,382 --> 00:20:54,420 crucial for determining validity. Because it's not possible for the 276 00:20:54,420 --> 00:20:57,333 premises to be true, and the conclusion false. 277 00:20:57,333 --> 00:21:00,116 That makes it valid in our technical sense. 278 00:21:00,116 --> 00:21:04,905 Even if it's not valid, in the common sense notion of validity as goodness, 279 00:21:04,905 --> 00:21:08,336 we're not saying that the argument's a good argument. 280 00:21:08,336 --> 00:21:12,543 We're saying that it meets this technical definition of validity. 281 00:21:12,543 --> 00:21:16,426 That logicians use. Now the only combination of truth values 282 00:21:16,426 --> 00:21:20,827 in premise and conclusion, that you cannot get with a valid argument 283 00:21:20,827 --> 00:21:23,870 is to have true premises, an a false conclusion. 284 00:21:23,870 --> 00:21:27,020 So here's an example of that. Premise one, 285 00:21:27,020 --> 00:21:36,680 some Ford cars do not have four doors. Premise two, Henry's car is a Ford. 286 00:21:36,680 --> 00:21:41,900 Conclusion, Henry's car does not have four doors. 287 00:21:41,900 --> 00:21:47,444 The premises by our assumptions are both true and the conclusion is false and it's 288 00:21:47,444 --> 00:21:53,056 not valid because it's easy to see how it might be possible for the premises to be 289 00:21:53,056 --> 00:21:55,896 true and the conclusion false. It's simple. 290 00:21:55,896 --> 00:22:00,967 Even if some Ford's don't have four doors, Henry's car is one of the Ford's 291 00:22:00,967 --> 00:22:05,902 that does have four doors, and then both the premises can be true and the 292 00:22:05,902 --> 00:22:09,312 conclusions false. So that's how you can get an invalid 293 00:22:09,312 --> 00:22:12,333 argument with true premises and a false conclusion. 294 00:22:12,333 --> 00:22:14,940 But you don't [LAUGH] really even need that. 295 00:22:14,940 --> 00:22:17,488 Look. Every argument that has, true premises 296 00:22:17,488 --> 00:22:19,917 and a false conclusion, has to be invalid. 297 00:22:19,917 --> 00:22:24,538 Because if it does in fact actually have true premises and a false conclusion, 298 00:22:24,538 --> 00:22:28,745 then it's possible, for it to have true premises and a false conclusion. 299 00:22:28,745 --> 00:22:33,711 So you can know right off the bat that every argument with true premises and a 300 00:22:33,711 --> 00:22:37,975 false conclusion is invalid. What you can't know is for the other 301 00:22:37,975 --> 00:22:41,057 combinations. Then you have to think of what is 302 00:22:41,057 --> 00:22:43,812 possible instead of simply what is actual. 303 00:22:43,812 --> 00:22:48,797 So far we've only looked at arguments with all and some and we've looked at 304 00:22:48,797 --> 00:22:53,626 Henry and Ford and Chrysler and so on. But the same points are going to apply to 305 00:22:53,626 --> 00:22:56,862 lots of different arguments with very different forms. 306 00:22:56,862 --> 00:23:04,601 So lets look at one example of that. Premise one, David, is either a swimmer 307 00:23:04,601 --> 00:23:09,266 or a golfer. Premise two, David, is a swimmer, 308 00:23:09,266 --> 00:23:14,420 therefore, conclusion, David is not a golfer. 309 00:23:14,420 --> 00:23:20,680 Okay, is it possible for the premises to be true and the conclusion false? 310 00:23:20,680 --> 00:23:27,024 How could you tell a coherent story where both premises are true and the conclusion 311 00:23:27,024 --> 00:23:29,215 is false? Just think about it. 312 00:23:29,215 --> 00:23:32,010 How could that happen? Oh I've got it! 313 00:23:32,010 --> 00:23:35,382 He could be both a swimmer and a golfer, like me. 314 00:23:35,382 --> 00:23:38,895 I play golf, and I also swim, and lots of people do. 315 00:23:38,895 --> 00:23:44,234 Now of course, if you have or, and you say something like he's either male or 316 00:23:44,234 --> 00:23:49,223 female, maybe you can't have both. But with swimming and golfing you can 317 00:23:49,223 --> 00:23:54,492 just be both a swimmer and also a golfer. And then the premises can be true when 318 00:23:54,492 --> 00:23:59,270 the conclusion is false, which shows that this argument is not valid. 319 00:23:59,270 --> 00:24:04,985 Now let's try this other example which is a lot like the last one, but it's 320 00:24:04,985 --> 00:24:10,395 different in an important way. Premise one, David is either a swimmer or 321 00:24:10,395 --> 00:24:13,748 a golfer. Premise two, David is not a swimmer, 322 00:24:13,748 --> 00:24:18,894 therefore conclusion, David is a golfer. Is there any way? 323 00:24:18,894 --> 00:24:23,027 Is it possible? Is there anyway to tell a coherent story 324 00:24:23,027 --> 00:24:28,020 where, the premises are true and the conclusion is false? 325 00:24:28,020 --> 00:24:31,974 We know. Well just think about it, the four 326 00:24:31,974 --> 00:24:35,265 possibilities. Suppose that David is both a swimmer and 327 00:24:35,265 --> 00:24:38,376 also a golfer. Well then the conclusion's true, right? 328 00:24:38,376 --> 00:24:42,864 So you can't have two premises and a false conclusion because then in that 329 00:24:42,864 --> 00:24:48,677 case then the conclusion is true. Now, suppose that David is a golfer, but 330 00:24:48,677 --> 00:24:53,100 he's not a swimmer. Well again, the conclusion's true. 331 00:24:53,100 --> 00:24:57,522 So that's not a case where the premise's is true and the conclusion's false. 332 00:24:57,522 --> 00:25:01,712 but suppose he's not a golfer but he is a swimmer Well wait a minute. 333 00:25:01,712 --> 00:25:06,368 In that case the second premise is wrong, because it says, he's not a swimmer and 334 00:25:06,368 --> 00:25:09,336 we're, in this story, imagining that he is a swimmer. 335 00:25:09,336 --> 00:25:12,420 Now suppose that he's neither a swimmer nor a golfer. 336 00:25:12,420 --> 00:25:16,261 Well then the conclusion is false, and that second premise is true. 337 00:25:16,261 --> 00:25:19,578 But wait a minute, now the first premise is false, because 338 00:25:19,578 --> 00:25:22,779 the first premise says, he either a swimmer or a golfer. 339 00:25:22,779 --> 00:25:25,700 In this story it's saying that he's neither. 340 00:25:25,700 --> 00:25:31,019 So, those are the four possibilities and there's none of them where the premises 341 00:25:31,019 --> 00:25:36,272 are true and the conclusions false. So it's not possible for the premises to be 342 00:25:36,272 --> 00:25:41,520 true and conclusions to be false in this case, so this argument is valid. 343 00:25:41,520 --> 00:25:46,097 And did you notice something? I didn't make assumptions like in Henry, 344 00:25:46,097 --> 00:25:50,873 and the Ford, and the Chrysler, because we don't need to know whether David 345 00:25:50,873 --> 00:25:55,782 really is a swimmer or a golfer. We don't need to know the actual facts of 346 00:25:55,782 --> 00:25:59,695 the world at all. We could tell that this argument is valid 347 00:25:59,695 --> 00:26:02,880 without knowing what kinds of sports David does. 348 00:26:02,880 --> 00:26:07,305 And that shows you that whether an argument is valid or not depends on 349 00:26:07,305 --> 00:26:11,917 what's possible, not on what's actual. because you can know that the argument's 350 00:26:11,917 --> 00:26:17,027 valid, even if you don't know whether in the actual world he's a swimmer or golfer 351 00:26:17,027 --> 00:26:19,770 or neither or both or one but not the other. 352 00:26:19,770 --> 00:26:22,813 We haven't been through all of the possibilities, 353 00:26:22,813 --> 00:26:27,534 but we have seen that you can have invalid arguments with true premises and 354 00:26:27,534 --> 00:26:30,974 true conclusions, and you can have valid arguments with 355 00:26:30,974 --> 00:26:36,052 false premises and true conclusions, and we've got a little table that shows 356 00:26:36,052 --> 00:26:40,396 us the other possibilities. Instead of going through all of those 357 00:26:40,396 --> 00:26:43,938 other possibilities myself, I think it'd be better, if. 358 00:26:43,938 --> 00:26:47,547 You did a few exercises, and that'll, make sure that you 359 00:26:47,547 --> 00:26:53,093 understand this notion of validity before we go on and try to show how validity is 360 00:26:53,093 --> 00:26:54,497 related to soundness.