1 00:00:02,480 --> 00:00:05,866 Well welcome back. I've really missed you over the last 2 00:00:05,866 --> 00:00:10,421 couple of weeks when you've have been off with wrong meta learning about 3 00:00:10,421 --> 00:00:13,377 propopsitional logic and then categorical logic. 4 00:00:13,377 --> 00:00:16,640 And, I hope that you enjoyed that. It's very important. 5 00:00:16,640 --> 00:00:21,944 But in the next few weeks, we're going to turn to a different kind of argument. 6 00:00:21,944 --> 00:00:26,432 Because that type of logic is appropriate for deductive arguments. 7 00:00:26,432 --> 00:00:30,581 And what we're going to study instead is inductive arguments. 8 00:00:30,581 --> 00:00:34,797 Now, deductive arguments are given quite often throughout life. 9 00:00:34,797 --> 00:00:38,470 But inductive arguments are probably even more common. 10 00:00:38,470 --> 00:00:43,506 Whenever you want to figure out who committed a crime, we're talking about an 11 00:00:43,506 --> 00:00:48,221 inference of the best explanation. Then there are arguments from analogy, 12 00:00:48,221 --> 00:00:52,548 which happen quite often. Just think of all the analogies that you 13 00:00:52,548 --> 00:00:55,695 run into in life. And then we'll see statistical 14 00:00:55,695 --> 00:00:59,367 generalizations. Well, just think about all the polls and 15 00:00:59,367 --> 00:01:02,580 politics these days and statistical applications. 16 00:01:02,580 --> 00:01:07,628 Whenever you want to know how those generalizations tell you something about 17 00:01:07,628 --> 00:01:12,017 a particular person. And then we'll turn to causal reasoning. 18 00:01:12,017 --> 00:01:16,978 Well, causes are crucial to everything, from science to figuring out what made 19 00:01:16,978 --> 00:01:20,409 your car stop and decision-making and probability. 20 00:01:20,409 --> 00:01:25,364 So we've got a lot of things to cover. And the first thing that we need to do is 21 00:01:25,364 --> 00:01:29,328 to see the difference between inductive and deductive arguments. 22 00:01:29,328 --> 00:01:34,469 Because you've been focused for a couple of weeks with wrong about deductive 23 00:01:34,469 --> 00:01:37,442 arguments. And you need to understand what's the 24 00:01:37,442 --> 00:01:42,149 difference between those arguments and the ones that we're going to study over 25 00:01:42,149 --> 00:01:45,680 the next couple of weeks. In order to see that difference. 26 00:01:45,680 --> 00:01:49,911 I'm going to show you a little video. It's a video I made a few years ago, so 27 00:01:49,911 --> 00:01:53,272 you might notice that I was a little younger back then. 28 00:01:53,272 --> 00:01:58,395 Okay fair enough, but. I think this video will help you see what 29 00:01:58,395 --> 00:02:04,731 the difference is between inductive arguments and deductive arguments. 30 00:02:04,731 --> 00:02:08,636 Rainy days and Mondays always get me down. 31 00:02:08,636 --> 00:02:14,538 The sun will come out tomorrow. Let your bottom dollars out tomorrow. 32 00:02:14,538 --> 00:02:18,964 There'll be sun tomorrow, tomorrow. Wait a minute. 33 00:02:18,964 --> 00:02:21,921 Wait a minute. How do you know that? 34 00:02:21,921 --> 00:02:24,242 I heard a weather report. So what? 35 00:02:24,242 --> 00:02:28,627 They get it wrong all the time. Well maybe the sun won't come out 36 00:02:28,627 --> 00:02:31,851 tomorrow but at least it will come up tomorrow. 37 00:02:31,851 --> 00:02:36,688 So you say, but is that really true? How many of you agree that the sun will 38 00:02:36,688 --> 00:02:39,332 come up tomorrow morning? Of course. 39 00:02:39,332 --> 00:02:41,395 Definitely. Absolutely yes. 40 00:02:41,395 --> 00:02:45,039 Everybody knows that. Okay, so you all agree with her. 41 00:02:45,039 --> 00:02:50,425 But, do you really know that it's true? How could you show that the sun will come 42 00:02:50,425 --> 00:02:52,310 up tomorrow? I don't know. 43 00:02:52,310 --> 00:02:55,946 I'm just a kid. Wait I, I didn't mean to get you all 44 00:02:55,946 --> 00:02:58,530 upset. But there really is an issue here. 45 00:02:58,530 --> 00:03:03,470 The question is, how can you prove that the sun will come up tomorrow morning? 46 00:03:03,470 --> 00:03:08,730 Well here's one way that some people use, the conclusion is that the sun will come 47 00:03:08,730 --> 00:03:12,008 up tomorrow. The premise is yesterday the sun came up. 48 00:03:12,008 --> 00:03:14,970 The second premise the day before that the sun came up. 49 00:03:14,970 --> 00:03:19,225 The third premise the day before that the sun came up, then the day before that, 50 00:03:19,225 --> 00:03:23,372 then the day before that, and the day before that, and the day before that, and 51 00:03:23,372 --> 00:03:25,741 the day before that, and the day before that. 52 00:03:25,741 --> 00:03:29,027 Well that can get awfully long so we'll shorten the argument. 53 00:03:29,027 --> 00:03:33,335 The conclusion is still that the sun will come up tomorrow but the premises are 54 00:03:33,335 --> 00:03:37,590 just the sun came up yesterday and the sun came up everyday before that for an 55 00:03:37,590 --> 00:03:43,052 awfully long time. Now, is the argument valid? 56 00:03:43,052 --> 00:03:51,097 Yes or no? Right. 57 00:03:51,097 --> 00:03:55,979 It's not valid. An argument is valid if and only if it's 58 00:03:55,979 --> 00:04:00,314 not possible for the premises to be true and the conclusion false. 59 00:04:00,314 --> 00:04:05,634 But it is possible for these premises to be true and this conclusion to be false. 60 00:04:05,634 --> 00:04:10,757 Can you imagine how that would happen? One way would be if a meteor struck the 61 00:04:10,757 --> 00:04:14,829 Earth in the middle of the night and stopped it from spinning. 62 00:04:14,829 --> 00:04:20,150 Then the sun wouldn't rise tomorrow, . Now you're really freaking me out. 63 00:04:20,150 --> 00:04:24,933 Don't worry, that's extremely unlikely. However, it's possible. 64 00:04:24,933 --> 00:04:29,140 And that shows that the argument is not valid. 65 00:04:29,140 --> 00:04:33,160 The next question is, is this argument any good. 66 00:04:33,160 --> 00:04:36,122 An argument's good if it serves its purpose. 67 00:04:36,122 --> 00:04:41,240 The purpose of this argument, and many other arguments, is to provide reasons 68 00:04:41,240 --> 00:04:44,943 for its conclusion. So, do the premises in this argument 69 00:04:44,943 --> 00:04:47,569 provide reasons for its conclusion? Yes. 70 00:04:47,569 --> 00:04:52,285 Some philosophers deny this. But most people think that these premises 71 00:04:52,285 --> 00:04:56,933 provide good reasons for its conclusion. So let's assume that for now. 72 00:04:56,933 --> 00:05:00,841 What does that show? That shows that some arguments can be 73 00:05:00,841 --> 00:05:05,152 good, even if they're not valid. But don't generalize too quickly. 74 00:05:05,152 --> 00:05:09,666 There are other arguments that are no good, because they're invalid. 75 00:05:09,666 --> 00:05:15,987 Take Bub for example. Is it true, that every sophomore is a 76 00:05:15,987 --> 00:05:17,425 student? Yeah. 77 00:05:17,425 --> 00:05:19,619 Are you a sophomore? No. 78 00:05:19,619 --> 00:05:23,803 So you're not a student, right. Wrong, I, I am a student. 79 00:05:23,803 --> 00:05:29,215 Well then what's wrong with the argument? Every sophomore's a student, you're not a 80 00:05:29,215 --> 00:05:34,296 sophomore, so you're not a student. Well both the premises are true, but, the 81 00:05:34,296 --> 00:05:37,859 conclusion's false so the argument must be invalid. 82 00:05:37,859 --> 00:05:42,743 So you're telling me what makes that argument bad, is that it's invalid? 83 00:05:42,743 --> 00:05:43,799 Yep. Good job. 84 00:05:43,799 --> 00:05:47,890 Now we've got a puzzle. Some arguments are bad because they're 85 00:05:47,890 --> 00:05:52,444 invalid, whereas other arguments are good even though they're invalid. 86 00:05:52,444 --> 00:05:56,531 How can that be? Simple, there are two kinds of arguments, 87 00:05:56,531 --> 00:06:01,307 deductive and inductive. Deductive arguments are bad when their 88 00:06:01,307 --> 00:06:04,718 invalid. Inductive arguments can be good even 89 00:06:04,718 --> 00:06:06,611 though their invalid. Why? 90 00:06:06,611 --> 00:06:12,715 Because deductive arguments are intended to be valid, whereas inductive arguments 91 00:06:12,715 --> 00:06:17,613 are not intended to be valid. The crucial point is that there are 92 00:06:17,613 --> 00:06:21,682 different kinds of standards for evaluating arguments. 93 00:06:21,682 --> 00:06:26,505 Deductive standards ask whether an argument is valid or invalid. 94 00:06:26,505 --> 00:06:31,177 Inductive standards ask whether an argument is strong or weak. 95 00:06:31,177 --> 00:06:35,999 There are several important differences between these standards. 96 00:06:35,999 --> 00:06:39,240 First, deductive validity is all or nothing. 97 00:06:39,240 --> 00:06:43,954 An argument is either valid or not. It can't be partly valid or a little 98 00:06:43,954 --> 00:06:47,360 valid, anymore than a woman can be a little pregnant. 99 00:06:47,360 --> 00:06:51,680 Inductive strength, in contrast, comes in degrees. 100 00:06:51,680 --> 00:06:57,980 An argument is stronger when it gives more and better reasons for its 101 00:06:57,980 --> 00:07:01,384 conclusion. So an arguement can be very weak, when 102 00:07:01,384 --> 00:07:05,860 the reasons it gives for its conclussion are very weak, or can be moderately 103 00:07:05,860 --> 00:07:10,571 strong when it gives moderately strong reasons for its conclussion, or it can be 104 00:07:10,571 --> 00:07:14,457 very strong, when it gives very strong reasons for its conclussion. 105 00:07:14,457 --> 00:07:18,756 Since inductive strength comes in degrees, we can't simply ask, whether an 106 00:07:18,756 --> 00:07:23,173 arguement is strong, we need to ask whether it's strong enough, that depends 107 00:07:23,173 --> 00:07:27,825 on the context and the values at stake. Psyched about your cooking lesson? 108 00:07:27,825 --> 00:07:30,203 Yeah! One of the most important things in 109 00:07:30,203 --> 00:07:34,940 cooking, is to make sure that whatever it is you're cooking is done. 110 00:07:34,940 --> 00:07:40,337 When people cook cakes, the way they normally test it for being done, is they 111 00:07:40,337 --> 00:07:45,876 take a straw or a piece of bamboo and they stick it in the middle of the cake. 112 00:07:45,876 --> 00:07:49,001 If it comes up with raw dough it's not done. 113 00:07:49,001 --> 00:07:52,694 If it comes up clean, like this, that means it's done. 114 00:07:52,694 --> 00:07:57,310 Well, at least in that spot. If you want to make sure that it's done, 115 00:07:57,310 --> 00:08:02,140 throughout the whole cake, then you have to test other spots as well. 116 00:08:05,040 --> 00:08:12,041 Whoa, what are you doing? So much for that. 117 00:08:12,041 --> 00:08:16,567 Now, when you're cooking turkey, you could use the same method. 118 00:08:16,567 --> 00:08:22,428 You could stick in a straw or a piece of bamboo and see whether any pink juice 119 00:08:22,428 --> 00:08:26,138 comes out. If it comes out pink, then it's not done. 120 00:08:26,138 --> 00:08:29,700 But, if it comes out clean, then the turkeys done. 121 00:08:32,755 --> 00:08:34,763 See any pink juice? No. 122 00:08:34,763 --> 00:08:37,560 Then it must be done. Let's try a piece. 123 00:08:41,440 --> 00:08:46,740 There. . 124 00:08:46,740 --> 00:08:52,175 But you wouldn't want to do that with turkey because you can get very sick from 125 00:08:52,175 --> 00:08:56,047 uncooked turkey. That's why most of the time they build a 126 00:08:56,047 --> 00:09:01,211 pop up meat thermometer right into the turkey to make sure that nobody eats 127 00:09:01,211 --> 00:09:05,600 uncooked turkey [SOUND] But this is not a cooking class. 128 00:09:05,600 --> 00:09:11,050 The point here is simply that whether an argument is strong enough depends on 129 00:09:11,050 --> 00:09:14,824 what's at stake. When there's a lot to loose we demand 130 00:09:14,824 --> 00:09:21,190 better reasons and stronger arguments. Context is also important in another way. 131 00:09:21,190 --> 00:09:26,818 Additional information from the context can weaken an inductive argument. 132 00:09:26,818 --> 00:09:30,288 That is, it can change it from strong to weak. 133 00:09:30,288 --> 00:09:35,454 In technical language, the inductive standard of strength is called 134 00:09:35,454 --> 00:09:40,543 defeasible, or non-monotonic. In contrast, the deductive standard of 135 00:09:40,543 --> 00:09:46,557 validity is indefeasible, or monotonic. That means that, no matter what premises 136 00:09:46,557 --> 00:09:50,489 you add to a valid argument, it will still be valid. 137 00:09:50,489 --> 00:09:52,880 Go ahead, try. Here's an example. 138 00:09:52,880 --> 00:09:56,235 If Joe is a sophomore then Joe is a student. 139 00:09:56,235 --> 00:10:00,407 Joe is not a student, so Joe is not a sophomore. 140 00:10:00,407 --> 00:10:05,645 Add any premise you want to that argument, and it will still be valid. 141 00:10:05,645 --> 00:10:10,806 Which shows that the deductive standard of validity is indefeasible. 142 00:10:10,806 --> 00:10:15,436 In contrast, the inductive standard of strength is defeasible. 143 00:10:15,436 --> 00:10:20,826 If you add additional premises or additional information, it can make a 144 00:10:20,826 --> 00:10:24,241 strong argument weak. Consider a courtroom. 145 00:10:24,241 --> 00:10:28,870 I'm sure it was him. He was only ten feet away from me, I saw 146 00:10:28,870 --> 00:10:32,084 him do it. I'm sure it was him, I saw him with my 147 00:10:32,084 --> 00:10:35,299 own eyes. I'd like to cross examine this witness. 148 00:10:35,299 --> 00:10:39,270 Are you positive that it was the defendant sitting right there? 149 00:10:39,270 --> 00:10:42,358 Or, could it have been his identical twin brother? 150 00:10:42,358 --> 00:10:49,294 Who is entering the courtroom right now. It could have been. 151 00:10:49,294 --> 00:10:54,492 I can't tell them apart. Now I would like to recall the first 152 00:10:54,492 --> 00:10:57,644 witness. Let me remind you that you're still under 153 00:10:57,644 --> 00:11:01,157 oath. Can you tell the difference between those 154 00:11:01,157 --> 00:11:02,400 two gentlemen? No. 155 00:11:02,400 --> 00:11:07,957 They look like the same person to me. Now, there's at least a reasonable doubt, 156 00:11:07,957 --> 00:11:11,054 isn't there? What was very strong evidence becomes 157 00:11:11,054 --> 00:11:15,142 much weaker when we add the new evidence about the identical twin. 158 00:11:15,142 --> 00:11:19,045 That is an example of the defeasibility of inductive standards. 159 00:11:19,045 --> 00:11:23,319 Although tricky, it's important to classify arguments as inductive or 160 00:11:23,319 --> 00:11:26,416 deductive. Because it affects whether they're good 161 00:11:26,416 --> 00:11:29,883 or bad. An inductive argument might not be valid 162 00:11:29,883 --> 00:11:34,544 but it can still be good. For example, the sun came up yesterday, 163 00:11:34,544 --> 00:11:39,724 it came up every day for thousands of years therefore, it will come up 164 00:11:39,724 --> 00:11:43,100 tomorrow. That's a good argument even though it's 165 00:11:43,100 --> 00:11:46,218 invalid because it's not intended to be valid. 166 00:11:46,218 --> 00:11:51,165 This is just one instance of a general rule that you shouldn't criticize 167 00:11:51,165 --> 00:11:54,757 something for not being what it's not supposed to be. 168 00:11:54,757 --> 00:11:59,840 This book can be a good book even though, , it's no good as a Frisbee. 169 00:11:59,840 --> 00:12:03,700 Similarly an argument can be a good argument. 170 00:12:03,700 --> 00:12:07,293 Even it it's not valid. It's not intended to be valid. 171 00:12:07,293 --> 00:12:12,177 That is, if it's an inductive argument. This point undermines many common 172 00:12:12,177 --> 00:12:17,743 mistakes, about inductive arguments, many people think that inductive arguments are 173 00:12:17,743 --> 00:12:23,241 somehow inferior to deductive arguments, because they're not valid, but that can't 174 00:12:23,241 --> 00:12:26,568 be right. Because it's easy to take any inductive 175 00:12:26,568 --> 00:12:29,758 argument and turn it into a deductive argument. 176 00:12:29,758 --> 00:12:34,781 For example, most of Joe's friends are seniors, So, Joe must be a senior too. 177 00:12:34,781 --> 00:12:39,940 Well, we can make that argument valid simply by adding a conditional premise. 178 00:12:39,940 --> 00:12:44,810 If most of Joe's friends are seniors, then Joe is a senior too. 179 00:12:44,810 --> 00:12:50,850 But that just shifts all the doubts about the inductive argument into doubts about 180 00:12:50,850 --> 00:12:55,580 the conditional premise. So, it hasn't really made us more sure of 181 00:12:55,580 --> 00:12:59,728 whether Joe is a senior. Our definition of induction also 182 00:12:59,728 --> 00:13:05,477 undermines the second common mistake. Many people believe that induction always 183 00:13:05,477 --> 00:13:08,680 takes us from the particular to the general. 184 00:13:08,680 --> 00:13:12,686 But no matter how many people say that, it's just plain wrong. 185 00:13:12,686 --> 00:13:18,006 Inductive generalization is one kind of inductive argument, but it's not the only 186 00:13:18,006 --> 00:13:20,568 kind. In fact, we're going to study five 187 00:13:20,568 --> 00:13:25,963 different types of inductive arguments. To see the differences between these 188 00:13:25,963 --> 00:13:29,635 arguments, let's do a simple experiment. . 189 00:13:29,635 --> 00:13:35,972 Excuse me we're testing a new type of lemonade here could you help us out? 190 00:13:35,972 --> 00:13:40,511 Sure thank you. First could you try one from that cup? 191 00:13:40,511 --> 00:13:44,023 That's pretty good. Great, glad to hear it. 192 00:13:44,023 --> 00:13:49,075 Now could you try the second cup please? Oh that's terrible! 193 00:13:49,075 --> 00:13:53,186 Your reaction suggests that you don't like that. 194 00:13:53,186 --> 00:13:57,640 Well obviously, you put dish washing liquid in there. 195 00:13:57,640 --> 00:14:01,579 How do you know that? Well it tastes like soap. 196 00:14:01,579 --> 00:14:06,565 Is that why you spit it out. Well, I didn't spit out the first one, 197 00:14:06,565 --> 00:14:09,852 did I? You might be interested to know that you 198 00:14:09,852 --> 00:14:13,402 agreed with over 90% of the people we've tested so far. 199 00:14:13,402 --> 00:14:17,479 They all liked our lemonade better than dishwashing liquid. 200 00:14:17,479 --> 00:14:21,226 That's great. And if you take it back to your dorm, and 201 00:14:21,226 --> 00:14:25,762 try this test on your friends, I bet they'll like our lemonade too. 202 00:14:25,762 --> 00:14:28,918 Well, of course they would. Listen, this is stupid. 203 00:14:28,918 --> 00:14:32,268 I'm out of here. This experiment would be stupid, if it 204 00:14:32,268 --> 00:14:35,111 were intended to show something about lemonade. 205 00:14:35,111 --> 00:14:39,830 But all it's supposed to show is the differences among the different kinds of 206 00:14:39,830 --> 00:14:44,013 inductive arguments. Our next step will be to look at each of 207 00:14:44,013 --> 00:14:46,621 these times of induction in more detail.