1 00:00:03,000 --> 00:00:09,314 Generalizations are not much use if you can't apply them back to particular 2 00:00:09,314 --> 00:00:13,798 cases. It rains about 35% of the days in North 3 00:00:13,798 --> 00:00:14,881 Carolina. Great. 4 00:00:14,881 --> 00:00:18,851 But, is it going to rain tomorrow? That's what I want to know. 5 00:00:18,851 --> 00:00:21,810 I don't want to know the general statistic. 6 00:00:21,810 --> 00:00:26,574 I want to to know about tomorrow because I got to decide whether to go on a 7 00:00:26,574 --> 00:00:31,107 picnic. 65% of the snakes in this area are 8 00:00:31,107 --> 00:00:32,315 poisonous. Great. 9 00:00:32,315 --> 00:00:37,903 But I want to know whether the one I'm stepping on right now is poisonous. 10 00:00:37,903 --> 00:00:41,260 I don't want to know the general statistic. 11 00:00:41,260 --> 00:00:45,570 So, we need some way to take these generalizations and apply them down to 12 00:00:45,570 --> 00:00:50,000 particular cases, and that's the job of a form of argument we're going to call 13 00:00:50,000 --> 00:00:54,372 application of a generalization. Not a great name, but they're usually 14 00:00:54,372 --> 00:00:58,682 called statistical syllogisms. And that's an even worse name because 15 00:00:58,682 --> 00:01:03,055 they're not really necessarily statistical in the mathematical sense 16 00:01:03,055 --> 00:01:07,871 because they don't have to have numbers in them. And they're also not syllogisms 17 00:01:07,871 --> 00:01:13,258 like the categorical syllogisms that you studied back in the section on deductive 18 00:01:13,258 --> 00:01:16,300 arguments. So we're going to call them applications 19 00:01:16,300 --> 00:01:19,659 of generalizations, and they just happen all the time. 20 00:01:19,659 --> 00:01:23,250 They really do. You might say, for example, I almost 21 00:01:23,250 --> 00:01:27,098 never like horror movies. And that's a horror movie. 22 00:01:27,098 --> 00:01:31,772 So I don't want to go to it. I'm, because I'm not going to like it. 23 00:01:31,772 --> 00:01:35,952 Or you might say, I don't want to invest in that restaurant because 80% of 24 00:01:35,952 --> 00:01:39,840 restaurants fail during the first two or three years. 25 00:01:39,840 --> 00:01:44,812 And so, this is a restaurant that's new, it's probably going to fail, too. 26 00:01:44,812 --> 00:01:50,230 Or, how about this one. Most people who are on the track team are 27 00:01:50,230 --> 00:01:54,678 pretty thin. Now, you know there's some exceptions to 28 00:01:54,678 --> 00:01:58,120 that, like the people who throw shot put. That's what I used to do. 29 00:01:59,240 --> 00:02:02,163 But still, it's true that most of them do. 30 00:02:02,163 --> 00:02:05,800 And so if you know that Sally is on the track team, 31 00:02:05,800 --> 00:02:10,863 that's all you know about her. Then, you got some reason to believe that 32 00:02:10,863 --> 00:02:15,284 Sally is probably thin. She might throw the shot put, but there 33 00:02:15,284 --> 00:02:20,489 many more people on the track team who run and jump, and they're going to be 34 00:02:20,489 --> 00:02:25,506 thin if they're any good at it. so, although it might be wrong, it's a 35 00:02:25,506 --> 00:02:29,785 pretty good bet that Sally's thin if she's on the track team. 36 00:02:29,785 --> 00:02:34,977 And that's the kind of argument that we're going call an application of a 37 00:02:34,977 --> 00:02:37,408 generalization. Here's my favorite. 38 00:02:37,408 --> 00:02:41,801 Am I wearing shoes right now? You can't see, can you? 39 00:02:41,801 --> 00:02:47,056 Maybe I am, maybe I'm not. But most professors wear shoes when 40 00:02:47,056 --> 00:02:52,528 they're teaching a class. Walter is a professor who's teaching a 41 00:02:52,528 --> 00:02:56,101 class. So, Walter is probably wearing shoes 42 00:02:56,101 --> 00:02:59,249 right now. That's an application of a 43 00:02:59,249 --> 00:03:03,417 generalization. It has the same form as the other 44 00:03:03,417 --> 00:03:09,156 examples that we saw before. To see that form, we can substitute 45 00:03:09,156 --> 00:03:13,128 variables for the terms in the English argument. 46 00:03:13,128 --> 00:03:17,927 So we can substitute the letter F for the reference class, 47 00:03:17,927 --> 00:03:22,380 which is the set of professors who are teaching. 48 00:03:22,380 --> 00:03:29,218 Then, we can substitute the letter G for what's called the attribute class, which 49 00:03:29,218 --> 00:03:35,628 is the people who are wearing shoes. Then, we can substitute the letter a, 50 00:03:35,628 --> 00:03:41,270 usually in lower case, for the individual that we're talking about. 51 00:03:41,270 --> 00:03:45,220 In this case, that individual is me, Walter. 52 00:03:45,220 --> 00:03:52,286 And we can substitute X% for the quantifier if it's most, or almost all, 53 00:03:52,286 --> 00:03:57,178 or something like that, then X% takes its place. 54 00:03:57,178 --> 00:04:04,517 And then, the form of the argument that I just gave about wearing shoes is simply 55 00:04:04,517 --> 00:04:09,771 that X% of F or G, a is F, therefore a is probably G. 56 00:04:09,771 --> 00:04:16,204 Notice that this application of a generalization moves in the opposite 57 00:04:16,204 --> 00:04:20,140 direction from the generalization from a sample. 58 00:04:20,140 --> 00:04:25,750 May I start off saying, well, X% of the f's in the sample are G. 59 00:04:25,750 --> 00:04:30,608 So, X% of f's are G. And that's generalization from a sample. 60 00:04:30,608 --> 00:04:37,223 But then, we take the generalization in that conclusion, and use it as a premise 61 00:04:37,223 --> 00:04:42,196 in a, in an application. So we say, X% of Fs are G, a is F, 62 00:04:42,196 --> 00:04:47,274 therefore, a is probably G. And that's why I said that we're going to 63 00:04:47,274 --> 00:04:53,992 study up to generalizations and then down from generalizations in this part of the 64 00:04:53,992 --> 00:04:57,585 course. And when they work together, we can use 65 00:04:57,585 --> 00:05:03,210 information about the sample to reach a conclusion about the individual. 66 00:05:03,210 --> 00:05:08,373 Image is pretty useful. Notice also that these applications of 67 00:05:08,373 --> 00:05:14,285 generalizations are inductive. They share all the features of inductive 68 00:05:14,285 --> 00:05:17,533 arguments. First of all, they're invalid. 69 00:05:17,533 --> 00:05:23,779 Because it's possible for the premises to be true and the conclusion false. 70 00:05:23,779 --> 00:05:28,320 That is, it's possible that X% of F are G, a is in F, 71 00:05:28,320 --> 00:05:34,710 but it's not true that a is probably G. There might be no chance at all that a is 72 00:05:34,710 --> 00:05:35,760 G. Second, 73 00:05:35,760 --> 00:05:39,271 applications of generalizations are defeasible. 74 00:05:39,271 --> 00:05:45,173 You can add additional information to the premises that make the argument very 75 00:05:45,173 --> 00:05:48,759 weak, and like, completely undermine the argument. 76 00:05:48,759 --> 00:05:54,362 For example, even if you know that Walter's a professor and most professors 77 00:05:54,362 --> 00:05:59,815 wear shoes while they're teaching, a little bit of additional information 78 00:05:59,815 --> 00:06:05,717 might show you that it's just not true that Walter is wearing shoes while he's 79 00:06:05,717 --> 00:06:08,536 teaching. By the way, I'm going to, well, you'll 80 00:06:08,536 --> 00:06:13,480 have to decide for yourself whether I'm really putting my shoes back on now. 81 00:06:13,480 --> 00:06:20,789 But the third feature of inductive arguments is that, They're strong or they 82 00:06:20,789 --> 00:06:25,974 can be strong. They can vary in strength. So even if I don't have shoes on, it's 83 00:06:25,974 --> 00:06:31,160 still might be a fairly strong argument that almost all professors wear shoes 84 00:06:31,160 --> 00:06:35,348 while they're teaching. Walter's a professor and he is teaching, 85 00:06:35,348 --> 00:06:40,267 therefore he probably has shoes on. That can be strong before you get that 86 00:06:40,267 --> 00:06:44,456 additional information. Before you see my feet without shoes on. 87 00:06:44,456 --> 00:06:49,641 and now that you don't way whether I've got shoes on, it can still be a strong 88 00:06:49,641 --> 00:06:55,030 argument. So we have arguments that are not valid, 89 00:06:55,030 --> 00:06:59,109 and they're defeasible, and they vary in strength. 90 00:06:59,109 --> 00:07:05,853 And that makes them inductive arguments. So, how do we tell when an application of 91 00:07:05,853 --> 00:07:11,681 a generalization really is strong. That is, when does it provide strong 92 00:07:11,681 --> 00:07:16,196 reasons for the conclusion. Now, the first standard should be 93 00:07:16,196 --> 00:07:19,862 obvious. It's the same for generalizations, from samples. 94 00:07:19,862 --> 00:07:22,728 The premises have to be true and justified. 95 00:07:22,728 --> 00:07:28,193 If it's not true that I'm a professor, or if it's not true that I'm teaching, or if 96 00:07:28,193 --> 00:07:33,192 you have no reason to believe, you're not justified in believing that I'm a 97 00:07:33,192 --> 00:07:38,325 professor or I'm teaching, then the argument that we've been looking at can't 98 00:07:38,325 --> 00:07:43,390 give you a good reason to believe that I'm wearing shoes because I just don't 99 00:07:43,390 --> 00:07:46,590 fall under the classes that we're talking about. 100 00:07:46,590 --> 00:07:52,530 Secondly, a standard that's specific to these kinds 101 00:07:52,530 --> 00:07:59,264 of arguments is that the strength of the argument varies with how big X is. 102 00:07:59,264 --> 00:08:02,138 If X is 99%,. so 99% of F's are G's, 103 00:08:02,138 --> 00:08:07,525 and a is an F, that's a pretty strong argument that this 104 00:08:07,525 --> 00:08:10,080 a is a G. But if it's 60%,. 105 00:08:10,080 --> 00:08:14,813 then it's not a very strong argument. So, 99 is going to be stronger than 90, 106 00:08:14,813 --> 00:08:19,813 which is stronger than 80, which is stronger than 70, which is stronger than 107 00:08:19,813 --> 00:08:22,280 60. And the strength of the inductive 108 00:08:22,280 --> 00:08:25,600 argument can vary as the percentage X varies. 109 00:08:25,600 --> 00:08:31,448 But notice that if X is 10%,, then it becomes pretty strong argument for the 110 00:08:31,448 --> 00:08:36,219 opposite conclusion. If only 10% of professors wear shoes when 111 00:08:36,219 --> 00:08:40,375 they're teaching, and I am a professor who is teaching. 112 00:08:40,375 --> 00:08:44,720 Then, it's pretty likely that I'm not wearing shoes. 113 00:08:44,720 --> 00:08:48,421 And that's stronger than if it's twenty and 30 and 40. 114 00:08:48,421 --> 00:08:53,562 And when you get close to the middle, the 50%,, if 50% of professors wear shoes 115 00:08:53,562 --> 00:08:58,497 when they're teaching, and I'm a professor, then you can't really reach a 116 00:08:58,497 --> 00:09:02,884 conclusion one way or the other about whether I'm wearing shoes. 117 00:09:02,884 --> 00:09:05,832 At least, not on the basis of that evidence. 118 00:09:05,832 --> 00:09:08,505 Not on the basis of that argument, okay? 119 00:09:08,505 --> 00:09:13,509 So, a second standard for assessing applications of generalizations is to 120 00:09:13,509 --> 00:09:21,251 figure out what the percentage is. But another crucial feature of 121 00:09:21,251 --> 00:09:26,986 applications of generalization is that there can be conflicting reference 122 00:09:26,986 --> 00:09:29,968 classes. So, it might be true that 95% of 123 00:09:29,968 --> 00:09:33,333 professors wear shoes when they're teaching. 124 00:09:33,333 --> 00:09:37,845 But, I'm not just any old professor. I'm an online professor. 125 00:09:37,845 --> 00:09:41,515 This course is online and that's very different. 126 00:09:41,515 --> 00:09:47,786 Because most professors will wear shoes when they teach because students will see 127 00:09:47,786 --> 00:09:51,450 their bare feet. But you can't see my bare feet. So, 128 00:09:51,450 --> 00:09:57,191 maybe, it turns out, that a lot of online professors are really not wearing shoes 129 00:09:57,191 --> 00:10:00,764 when they teach. So, that's a conflicting reference class. 130 00:10:00,764 --> 00:10:05,068 It's a different reference class that conflicts because it points to a 131 00:10:05,068 --> 00:10:08,402 different conclusion than the original reference class. 132 00:10:08,402 --> 00:10:12,100 The original reference class was professors who are teaching. 133 00:10:12,100 --> 00:10:16,693 The conflicting reference class is online professors who are teaching, 134 00:10:16,693 --> 00:10:21,812 or professors who are teaching online. When you run into conflicting reference 135 00:10:21,812 --> 00:10:26,668 classes, as a general rule, what you ought to do is look at the smallest of 136 00:10:26,668 --> 00:10:30,474 those reference classes. because that's usually going to give you 137 00:10:30,474 --> 00:10:35,395 a better estimate of how likely it is that this individual has the general 138 00:10:35,395 --> 00:10:39,000 attribute. That is, how likely it is that a is G. 139 00:10:39,000 --> 00:10:44,530 So, if you want to know whether Walter is wearing shoes, you shouldn't look at the 140 00:10:44,530 --> 00:10:49,290 broad class of all professors. But should instead, look at the narrow 141 00:10:49,290 --> 00:10:55,100 class of online professors, if the course that he's teaching right now is an online 142 00:10:55,100 --> 00:10:58,181 course. But there's a problem that you might run 143 00:10:58,181 --> 00:11:01,405 into also. As you get a narrower, narrower reference 144 00:11:01,405 --> 00:11:06,273 class, you sometimes just don't have enough data to figure out what the exact 145 00:11:06,273 --> 00:11:09,624 percentage is. How do you know what the percentage of 146 00:11:09,624 --> 00:11:13,480 professors who are teaching online is, that are wearing shoes? 147 00:11:13,480 --> 00:11:17,273 How many of them are wearing shoes? I've never seen a survey. 148 00:11:17,273 --> 00:11:20,497 I've seen lots of professors give regular lectures, 149 00:11:20,497 --> 00:11:23,594 but you rarely see the feet of online professors. 150 00:11:23,594 --> 00:11:28,400 So, you might not have enough information to apply that generalization. 151 00:11:28,400 --> 00:11:33,901 So, while the narrower reference class of two reference classes that conflict can 152 00:11:33,901 --> 00:11:38,588 be more accurate, it can also be problematic if you don't have enough 153 00:11:38,588 --> 00:11:43,955 information to support the premise. That says that a certain percentage of that 154 00:11:43,955 --> 00:11:46,807 class, that F, have the general attribute G. 155 00:11:46,807 --> 00:11:51,766 The fallacy of overlooking conflicting reference classes can be a little 156 00:11:51,766 --> 00:11:56,589 confusing, but it's very important. So, let's look at another example, and 157 00:11:56,589 --> 00:11:59,510 this time let's focus on a medical example. 158 00:11:59,510 --> 00:12:06,353 Let's suppose that 90% of the people with a certain condition, a certain medical 159 00:12:06,353 --> 00:12:11,291 condition, a certain illness, die. And Bob has that illness. 160 00:12:11,291 --> 00:12:14,929 So, it looks very likely that Bob will die. 161 00:12:14,929 --> 00:12:21,166 And this is an application of the generalization about people with this 162 00:12:21,166 --> 00:12:25,614 illness. But now, let's suppose we find out that 163 00:12:25,614 --> 00:12:32,480 most people catch this illness when they're old, but Bob is quite young. 164 00:12:32,480 --> 00:12:37,179 So, it turns out that young people with this illness usually survive. 165 00:12:37,179 --> 00:12:43,759 As a matter of fact, only about 20% of the people with this illness, who get it 166 00:12:43,759 --> 00:12:50,025 when they're young, die from the illness. If Bob is young and has this illness, so 167 00:12:50,025 --> 00:12:55,560 now we can rethink, well he probably won't die from the illness. 168 00:12:55,560 --> 00:13:01,468 But, wait a minute. We now have another conflicting reference class because Bob 169 00:13:01,468 --> 00:13:06,165 has a heart condition. And it turns out that even young people, 170 00:13:06,165 --> 00:13:11,999 when they catch this illness, if they have a heart condition, they usually die. 171 00:13:11,999 --> 00:13:17,453 As a matter of fact, 80% of the people with this illness, who have a heart 172 00:13:17,453 --> 00:13:20,938 condition and are young, die from this illness. 173 00:13:20,938 --> 00:13:26,392 So Bob, who is young and has this illness, and also has a heart condition 174 00:13:26,392 --> 00:13:32,168 will probably die from this illness. But wait a minute, it turns out that 175 00:13:32,168 --> 00:13:37,023 there's a new treatment. And of the people who are given this 176 00:13:37,023 --> 00:13:42,135 treatment, only about 30% of them die even if they are young, with this 177 00:13:42,135 --> 00:13:47,704 illness, with a heart condition. And Bob lives in an area where he can get 178 00:13:47,704 --> 00:13:51,596 the treatment. So now, it looks like there's only 30% 179 00:13:51,596 --> 00:13:54,876 chance that Bob will die from this illness. 180 00:13:54,876 --> 00:13:59,760 So what's happening here is as we get more and more information, 181 00:13:59,760 --> 00:14:04,620 the likelihood of Bob dying from this illness starts out really high and then 182 00:14:04,620 --> 00:14:07,860 it goes low. And then it goes high again, and then it 183 00:14:07,860 --> 00:14:11,412 goes low again. And it goes back and forth as we get more 184 00:14:11,412 --> 00:14:17,140 information. And then the question arises, 185 00:14:17,140 --> 00:14:22,010 which of these different generalizations should we use to figure out how likely it 186 00:14:22,010 --> 00:14:27,377 is that Bob will die from the illness? The answer here, as with most cases of 187 00:14:27,377 --> 00:14:33,226 conflicting reference classes, is that we ought to look at the narrowest class that 188 00:14:33,226 --> 00:14:35,659 we can. because if we know that there's a 189 00:14:35,659 --> 00:14:40,326 treatment and Bob is young, and he has a heart condition, and he also has this 190 00:14:40,326 --> 00:14:45,174 illness, and we put all of that together and compare him to other people who are 191 00:14:45,174 --> 00:14:49,780 young with this illness and a heart condition who can get the treatment, and 192 00:14:49,780 --> 00:14:54,507 look at how many of them have died in order to form an estimate of how likely 193 00:14:54,507 --> 00:14:57,053 it is that Bob will die from this illness. 194 00:14:57,053 --> 00:15:01,538 So, we always want to look at the narrowest reference class that we can in 195 00:15:01,538 --> 00:15:05,720 order to get the best estimate of the probability in the conclusion. 196 00:15:07,400 --> 00:15:11,119 But then, there's a problem. There might not be very many people, 197 00:15:11,119 --> 00:15:14,758 remember it's a new treatment. So there are not very many people who are 198 00:15:14,758 --> 00:15:16,881 young, who have this illness to begin with. 199 00:15:16,881 --> 00:15:19,560 Remember, most of the people with the illness are old. 200 00:15:19,560 --> 00:15:24,415 And the treatment's new so it hasn't been tried on very many young people. 201 00:15:24,415 --> 00:15:28,417 And, of course, young people don't often have heart conditions. 202 00:15:28,417 --> 00:15:33,666 So, it might be very difficult to find enough people who are like Bob in all the 203 00:15:33,666 --> 00:15:39,111 essential respects in order to determine whether or not Bob will probably die from 204 00:15:39,111 --> 00:15:42,326 this illness. So there's a kind of a tension here. 205 00:15:42,326 --> 00:15:47,706 More information gives us more accuracy, but only if we have enough information to 206 00:15:47,706 --> 00:15:52,890 be justified in trusting the premises of the application that we're looking at. 207 00:15:52,890 --> 00:15:59,606 And that's one of the tricks in figuring out how to estimate whether or not Bob is 208 00:15:59,606 --> 00:16:05,190 likely to die from the illness. The same points apply to all kinds of 209 00:16:05,190 --> 00:16:09,155 examples. You know, if you want to know the climate 210 00:16:09,155 --> 00:16:15,143 in the area, that's going to be a generalization about days around here in 211 00:16:15,143 --> 00:16:18,637 this time of year. But if you want to know the weather 212 00:16:18,637 --> 00:16:22,712 tomorrow, you need to apply it. And then, you're going to need to look at 213 00:16:22,712 --> 00:16:25,349 specifically what the weather was yesterday. 214 00:16:25,349 --> 00:16:29,664 Specifically, what the humidity is. The more information you can build in, 215 00:16:29,664 --> 00:16:33,260 the better estimate of what the weather's going to be tomorrow. 216 00:16:33,260 --> 00:16:37,243 Or, if you want to bet our sports team. You say, well, they're a very good team, 217 00:16:37,243 --> 00:16:40,120 they won most of their games in the last five years. 218 00:16:40,120 --> 00:16:44,380 But wait a minute, there'll be other players left and now its not likely that 219 00:16:44,380 --> 00:16:47,091 they're going to win. But wait a minute, they got new players 220 00:16:47,091 --> 00:16:50,355 that are even better. That makes it more likely they are going 221 00:16:50,355 --> 00:16:53,066 to win. And again, the information can make the 222 00:16:53,066 --> 00:16:57,271 probability go low and then high, and then low and then high, and you have to 223 00:16:57,271 --> 00:17:01,974 get the most specific information you can to get the most accurate estimate of how 224 00:17:01,974 --> 00:17:05,863 likely it is that this team will win. But, you might not have enough 225 00:17:05,863 --> 00:17:11,436 information about this team with these players under these circumstances because 226 00:17:11,436 --> 00:17:15,220 there just hasn't been enough cases for you to observe. 227 00:17:15,220 --> 00:17:20,014 So, as with the medical example, it's going to be a tension between wanting the 228 00:17:20,014 --> 00:17:25,065 most precise, the most smallest reference class among the different conflicting 229 00:17:25,065 --> 00:17:28,773 reference classes. And yet, you need premises that you have 230 00:17:28,773 --> 00:17:31,650 enough information that you can justify them. 231 00:17:31,650 --> 00:17:36,712 And if you can reach that perfect point. Where you've got enough information to 232 00:17:36,712 --> 00:17:40,557 justify the premises. But that premise is specific enough so 233 00:17:40,557 --> 00:17:44,145 that it has all the relevant information about the case, 234 00:17:44,145 --> 00:17:48,374 that's when we're going to have the best outcome on our applications of 235 00:17:48,374 --> 00:17:49,400 generalizations.