1 00:00:02,420 --> 00:00:06,932 Now that we've seen which features distinguish inductive arguments from 2 00:00:06,932 --> 00:00:11,319 deductive arguments, we want to look at the different kinds of inductive 3 00:00:11,319 --> 00:00:16,207 arguments one by one. And the first two we're going to look at are moving up from 4 00:00:16,207 --> 00:00:21,158 a sample to a generalization, and then moving back down from the generalization 5 00:00:21,158 --> 00:00:24,166 to some kind of prediction in a particular case. 6 00:00:24,166 --> 00:00:28,240 Generalizations are all around us. Almost all movies have credits. 7 00:00:28,240 --> 00:00:34,818 Most popular bands have drummers. Many restaurants are closed on Mondays. 8 00:00:34,818 --> 00:00:40,118 three quarters of police officers are very nice people. 9 00:00:40,118 --> 00:00:43,955 Two thirds of books have chapters in them. 10 00:00:43,955 --> 00:00:48,158 Half of the people I know like to play sports. 11 00:00:48,158 --> 00:00:50,898 And my favorite of all, 87.2%. 12 00:00:50,898 --> 00:00:58,637 The statistics are made up on the spot. It should come as no surprise at all that 13 00:00:58,637 --> 00:01:01,610 there's so many generalizations filling our lives. 14 00:01:01,610 --> 00:01:06,425 Because generalizations can be extremely useful, especially when you need to make 15 00:01:06,425 --> 00:01:09,389 a decision. So, for example, if you're feeling a 16 00:01:09,389 --> 00:01:14,405 little nauseous, that is a little sick at your stomach, then you need to know 17 00:01:14,405 --> 00:01:19,751 whether most people who have symptoms of your sort have something serious enough 18 00:01:19,751 --> 00:01:24,238 that they need to go to a doctor. And they also need to know whether 19 00:01:24,238 --> 00:01:28,396 doctors can usually help people who have symptoms of that sort. 20 00:01:28,396 --> 00:01:33,808 All of those generalizations are relevant to whether or not you want to go to the 21 00:01:33,808 --> 00:01:38,440 doctor to see if you can get some help with your sick stomach. 22 00:01:38,440 --> 00:01:44,060 But then the problem is, how can we decide which generalizations to believe? 23 00:01:44,060 --> 00:01:49,084 Since there generalizations, and you pile all instances of certain sort, you can't 24 00:01:49,084 --> 00:01:52,681 check them all out. You have to take a sample of some sort. 25 00:01:52,681 --> 00:01:55,596 I mean, just imagine that your running a bakery. 26 00:01:55,596 --> 00:01:59,752 And, your making jelly doughnuts and you want to know whether the jelly doughnuts 27 00:01:59,752 --> 00:02:02,730 are filled with the right amount of jelly. 28 00:02:02,730 --> 00:02:07,418 You can make hundreds of jelly donuts. You're not going to tear them all apart 29 00:02:07,418 --> 00:02:11,980 and check every one for how much jelly they have in the middle, because then 30 00:02:11,980 --> 00:02:15,275 you'd have no donuts left to sell to your customers. 31 00:02:15,275 --> 00:02:19,584 Or imagine, that you want to buy a car. This time you're the customer. 32 00:02:19,584 --> 00:02:24,843 You want to buy a car and you need to know how often these cars had problems in 33 00:02:24,843 --> 00:02:28,074 the first year. Because if they have problems a lot 34 00:02:28,074 --> 00:02:31,940 during the first year, you don't want to buy that kind of car. 35 00:02:31,940 --> 00:02:36,546 But you don't want every car of that sort to been tested for the first year because 36 00:02:36,546 --> 00:02:41,152 then you can't buy a new car, you're only going to have a used car because they've 37 00:02:41,152 --> 00:02:45,445 all been used in the test. Or, imagine that you want to know what 38 00:02:45,445 --> 00:02:49,490 types of trees grew during a certain period of history. 39 00:02:49,490 --> 00:02:55,080 So, you look at the soil and you dig down, and you start looking for how many 40 00:02:55,080 --> 00:03:00,654 pollen grains there are, and a certain level that indicates a certain age. 41 00:03:00,654 --> 00:03:05,841 Well, you can't check every spot in the field because if you did that, you'd just 42 00:03:05,841 --> 00:03:10,551 be destroying the entire field. So, in these cases and many other cases, 43 00:03:10,551 --> 00:03:15,328 you just have to take samples. You can't test the whole class and then 44 00:03:15,328 --> 00:03:19,560 you have to generalize from the sample to the larger class. 45 00:03:19,560 --> 00:03:24,120 All of these generalizations from samples share a certain form. 46 00:03:24,120 --> 00:03:27,219 First, we look at one instance of the sample. 47 00:03:27,219 --> 00:03:31,727 We say that first F is G. That is the thing fats in the, fits in 48 00:03:31,727 --> 00:03:36,023 the class F, and has the property G. And we check another. 49 00:03:36,023 --> 00:03:39,475 The second F is also G, and the third F is also G. 50 00:03:39,475 --> 00:03:42,785 And all the rest of the Fs in the sample are G. 51 00:03:42,785 --> 00:03:47,732 So, we conclude that all Fs are G. Now notice that all in the conclusion 52 00:03:47,732 --> 00:03:52,770 means everything in the class of Fs. It doesn't only mean the ones in our 53 00:03:52,770 --> 00:03:56,014 sample. So we've started from premises that are 54 00:03:56,014 --> 00:04:00,431 only about the sample, which is only a part of the general class. 55 00:04:00,431 --> 00:04:06,021 And we've reached a conclusion about the whole class when we say that all Fs are 56 00:04:06,021 --> 00:04:09,315 G. Now, other arguments of the same general 57 00:04:09,315 --> 00:04:14,173 type are a little bit different. Because you don't always get complete 58 00:04:14,173 --> 00:04:17,227 uniformity. You don't always get all Fs or G. 59 00:04:17,227 --> 00:04:22,778 Sometimes you get the first F is G, and the second F is G, but the third F is not 60 00:04:22,778 --> 00:04:25,762 G. And the fourth F is G, and the fifth F is 61 00:04:25,762 --> 00:04:30,204 G, but the sixth F is not G. So you get, like, two-thirds of the Fs 62 00:04:30,204 --> 00:04:33,347 are G. And then, you reach the conclusion that 63 00:04:33,347 --> 00:04:38,194 two-thirds of all Fs are G. Again though, you've only looked at the 64 00:04:38,194 --> 00:04:42,528 Fs in the sample. You've only observed a small part of that 65 00:04:42,528 --> 00:04:48,036 total class of all Fs and you draw a conclusion that two-thirds of overall 66 00:04:48,036 --> 00:04:51,562 class, the whole class of Fs has that property, G. 67 00:04:51,562 --> 00:04:56,923 So, that's why you have a general, that's why it's called a generalization. 68 00:04:56,923 --> 00:05:02,432 You start from a smaller sample, and reach a conclusion about a much larger 69 00:05:02,432 --> 00:05:05,370 class. You generalize to the whole class. 70 00:05:05,370 --> 00:05:10,236 The fact that the argument moves from a small part of the class to the whole 71 00:05:10,236 --> 00:05:13,775 class shows that it's inductive. And what does that mean? 72 00:05:13,775 --> 00:05:18,010 Well first, is the argument valid? Think back to one of the examples. 73 00:05:18,010 --> 00:05:22,723 Almost all bands that I know of have drummers. Therefore, almost all bands 74 00:05:22,723 --> 00:05:26,080 have drummers. Well, is it possible that the premises 75 00:05:26,080 --> 00:05:29,308 are true and the conclusion false? Of course it is. 76 00:05:29,308 --> 00:05:34,408 Because maybe I only listen to bands that have drummers, but there are a lot of 77 00:05:34,408 --> 00:05:39,509 bands out there that don't have drummers, and I just didn't happen to listen to 78 00:05:39,509 --> 00:05:42,350 them. That is, they weren't part of my sample, 79 00:05:42,350 --> 00:05:44,608 okay? And is the argument defeasible? 80 00:05:44,608 --> 00:05:49,448 That means, that you can add further information to the premises and it'll 81 00:05:49,448 --> 00:05:54,094 make the argument much less strong. It might even undermine the argument 82 00:05:54,094 --> 00:05:56,998 totally. And of course, it could because you could 83 00:05:56,998 --> 00:06:01,128 give me all kinds of examples of bands that don't have drummers. 84 00:06:01,128 --> 00:06:05,839 And then, I would have to change my conclusion that almost all bands have 85 00:06:05,839 --> 00:06:10,090 drummers. So, this argument is defeasible. 86 00:06:10,090 --> 00:06:12,620 Does that mean that it can't be strong? No. 87 00:06:12,620 --> 00:06:16,295 It could still be strong. It could come in different types of 88 00:06:16,295 --> 00:06:19,308 strength. How would you get a stronger argument or 89 00:06:19,308 --> 00:06:23,465 a weaker argument in this case, while you can have a larger or smaller 90 00:06:23,465 --> 00:06:25,936 sample. If I take a very large sample, the 91 00:06:25,936 --> 00:06:29,912 argument's going to be stronger. If I take a very small sample, the 92 00:06:29,912 --> 00:06:34,190 argument's going to be weaker. So it's not like validity, which is on or 93 00:06:34,190 --> 00:06:35,937 off. It's either valid or not. 94 00:06:35,937 --> 00:06:40,697 Instead, the strength of the argument comes in degrees depending on how big the 95 00:06:40,697 --> 00:06:44,130 sample is. Now, does that mean that since it can't 96 00:06:44,130 --> 00:06:48,571 be valid, it can only be strong to a certain degree that it's no good? 97 00:06:48,571 --> 00:06:53,655 No. Because it's an inductive argument. Inductive arguments don't even try to be 98 00:06:53,655 --> 00:06:56,358 valid, they don't even pretend to be valid. 99 00:06:56,358 --> 00:07:01,507 That's not what they're supposed to be. And sob you can't criticize this argument 100 00:07:01,507 --> 00:07:05,755 by saying it's not valid. It's doing everything that it's supposed 101 00:07:05,755 --> 00:07:08,716 to do if it provides you with a strong reason, 102 00:07:08,716 --> 00:07:11,870 and a strong enough reason for the conclusion. 103 00:07:11,870 --> 00:07:16,666 That's what an inductive argument is supposed to do so if this argument does 104 00:07:16,666 --> 00:07:21,145 it, [SOUND] it's a good argument. Then, even if inductive arguments, 105 00:07:21,145 --> 00:07:26,179 including generalizations from samples, don't have to be valid. Tthey still do 106 00:07:26,179 --> 00:07:30,086 need to be strong. And so, we need to figure out how to tell 107 00:07:30,086 --> 00:07:35,120 when a generalization from a sample is a strong argument, when it provides a 108 00:07:35,120 --> 00:07:39,888 strong reason for the conclusion. And to really answer that question, you 109 00:07:39,888 --> 00:07:43,266 got to turn to statistics an area of mathematics. 110 00:07:43,266 --> 00:07:48,498 And learn how to analyze the data much more carefully than we'll be able to do 111 00:07:48,498 --> 00:07:51,976 here. But even mentioning the name statistics 112 00:07:51,976 --> 00:07:56,811 raises fear in some people. Mark Twain is famous for having said, 113 00:07:56,811 --> 00:08:01,427 there are three kinds of lies. There are lies, there are damn lies, and 114 00:08:01,427 --> 00:08:05,877 there's statistics. He actually gives credit to Israeli for 115 00:08:05,877 --> 00:08:11,401 having said it first. But the point is that statistics, are even worse than damn 116 00:08:11,401 --> 00:08:15,107 lies, you can't trust them at all, or so Mark Twain says. 117 00:08:15,107 --> 00:08:20,422 But on the other hand, some people say, statistics, that's math. It's all about 118 00:08:20,422 --> 00:08:25,891 numbers, you can't question that. Here's one example of somebody who 119 00:08:25,891 --> 00:08:31,234 suggests such a position. There's still one thing that's 120 00:08:31,234 --> 00:08:34,529 irrefutable, and that is the numbers. 121 00:08:34,529 --> 00:08:38,816 Numbers don't lie. You can't parse pull numbers. 122 00:08:38,816 --> 00:08:41,173 They're infallible. Okay, fine. 123 00:08:41,173 --> 00:08:43,856 He knows that statistics aren't infallible. 124 00:08:43,856 --> 00:08:47,973 He's just being sarcastic. But there are many people who put a lot 125 00:08:47,973 --> 00:08:50,593 of faith in the numbers and in statistics. 126 00:08:50,593 --> 00:08:55,645 They seem to think that you always have to trust it when a statistician comes up 127 00:08:55,645 --> 00:08:58,951 with an answer. And we're going to learn that neither of 128 00:08:58,951 --> 00:09:02,944 these views is correct. It's not true that statistics are always 129 00:09:02,944 --> 00:09:07,747 worse than damn lies, and it's also not true that the numbers are irrefutable. 130 00:09:07,747 --> 00:09:10,180 The truth lies somewhere in the middle.