1 00:00:02,740 --> 00:00:07,059 Now that we understand the distinction between sufficient conditions and 2 00:00:07,059 --> 00:00:11,378 necessary conditions, we need to ask how we can tell which conditions are 3 00:00:11,378 --> 00:00:14,620 necessary, and which conditions are sufficient. 4 00:00:14,620 --> 00:00:19,323 So we're going to have one pair of test for sufficient conditions, one pairs of 5 00:00:19,323 --> 00:00:23,604 tests for necessary conditions. For each of these we're going to have a 6 00:00:23,604 --> 00:00:27,885 positive test and a negative test. So for example, the negative test for 7 00:00:27,885 --> 00:00:32,529 sufficient conditions is going to tell you what's not a sufficient condition. 8 00:00:32,529 --> 00:00:36,870 And the positive test for sufficient conditions will tell you what is a 9 00:00:36,870 --> 00:00:40,729 sufficient conditions. One of these is going to be deductive and 10 00:00:40,729 --> 00:00:46,415 the other's going to be inductive. So let's go through these various tests 11 00:00:46,415 --> 00:00:50,673 one by one. First of all, you get the negative 12 00:00:50,673 --> 00:00:55,850 version of a sufficient condition test, which basically says. 13 00:00:55,850 --> 00:01:02,698 That something x is not a sufficient condition of something else. 14 00:01:02,698 --> 00:01:06,150 Why? If there is any case where x is present 15 00:01:06,150 --> 00:01:10,242 and y is absent. There don't have to be a lot of cases, 16 00:01:10,242 --> 00:01:13,576 just one. If there's any one case where x is 17 00:01:13,576 --> 00:01:17,971 present and y is absent. Then that shows you that x is not 18 00:01:17,971 --> 00:01:22,215 sufficient for y. This test is negative because it tells 19 00:01:22,215 --> 00:01:25,625 you what is not a sufficient condition for y. 20 00:01:25,625 --> 00:01:30,020 It does not tell you what is a sufficient condition for y. 21 00:01:30,020 --> 00:01:36,395 Basically it says if there's one case where X is present and Y is absent then 22 00:01:36,395 --> 00:01:42,444 that's a counter example of the generalization that whenever X is present 23 00:01:42,444 --> 00:01:47,022 Y is always present, because if Y is absent it's not present. 24 00:01:47,022 --> 00:01:53,725 So, we've now got basically an deductive arguement against the generalization that 25 00:01:53,725 --> 00:01:57,240 whenever X is present Y is present as well. 26 00:01:57,240 --> 00:02:01,261 And because it's deducted that means it's not defeasible. 27 00:02:01,261 --> 00:02:06,764 If you add other cases it doesn't matter. More information in the premises, the 28 00:02:06,764 --> 00:02:11,562 argument is still going to be valid. Because as long as you have one 29 00:02:11,562 --> 00:02:17,065 counterexample that shows that x is not sufficient for y because it's not the 30 00:02:17,065 --> 00:02:20,240 case that whenever x is present y is present. 31 00:02:20,240 --> 00:02:24,832 To see how this negative sufficient condition works, let's go through an 32 00:02:24,832 --> 00:02:27,447 example. Now the example we're going to talk 33 00:02:27,447 --> 00:02:30,434 about. Derives from the great comedy classic, 34 00:02:30,434 --> 00:02:34,888 airplane, with Lesly Neilson. So we have a link, that you can check 35 00:02:34,888 --> 00:02:40,303 out, if you want, and I warn you, there's some offensive parts of this comedy, and 36 00:02:40,303 --> 00:02:44,689 you all be ready for that. Partly, to avoid those essential parts, 37 00:02:44,689 --> 00:02:50,034 it also say that we can really get all the cases, straight, and specify them in 38 00:02:50,034 --> 00:02:53,598 the way we need to. We are going to use our own example. 39 00:02:53,598 --> 00:02:59,474 We are going to call it the banquet. So what happens, is that there are group 40 00:02:59,474 --> 00:03:04,157 of people who are eating together, and they eat a full meal. 41 00:03:04,157 --> 00:03:07,967 They have a soup course. They have a main course. 42 00:03:07,967 --> 00:03:11,680 They have some wine. Then they have dessert. 43 00:03:11,680 --> 00:03:14,680 And the meal goes pretty well until the end. 44 00:03:14,680 --> 00:03:18,165 Oh, that was great. I love the tomato soup. 45 00:03:18,165 --> 00:03:20,928 Yeah. This fish is to die for. 46 00:03:20,928 --> 00:03:24,514 Yeah and this wine, oh my gosh it's so good. 47 00:03:24,514 --> 00:03:29,892 I love the combination of both the fish and the red wine together. 48 00:03:29,892 --> 00:03:33,088 Yeah, it's so sad that the dinner is over. 49 00:03:33,088 --> 00:03:38,155 [SOUND] Oh man when I stood up, my stomach started hurting. 50 00:03:38,155 --> 00:03:40,415 Mine did too. Ohhhh, oh man. 51 00:03:40,415 --> 00:03:44,079 [SOUND] Oh, really? Yeah I think I'm dying. 52 00:03:44,079 --> 00:03:48,600 [COUGH] Ohhh, [COUGH] What's happening? You okay? 53 00:03:48,600 --> 00:03:52,030 Oh man what's making them all feel this way? 54 00:03:52,030 --> 00:03:58,313 The question is, what caused them to die? So we checked a number of different 55 00:03:58,313 --> 00:04:01,869 things, they weren't shot, they weren't stabbed. 56 00:04:01,869 --> 00:04:05,666 They were poisoned. Where was the poison? 57 00:04:05,666 --> 00:04:11,183 We checked their water glasses, and we checked for injection points, if somebody 58 00:04:11,183 --> 00:04:14,466 shot the poison through a seringe. None of that. 59 00:04:14,466 --> 00:04:19,145 So we figured the poison must have gotten to them through the food. 60 00:04:19,145 --> 00:04:24,452 And now, we need to look at all the different people who were at the banquet, 61 00:04:24,452 --> 00:04:30,039 and what each particular person ate at the banquet, in order to figure out which 62 00:04:30,039 --> 00:04:34,720 of these different food items was the one that killed them. 63 00:04:34,720 --> 00:04:39,440 So we have a little chart. Ann went to the banquet, Barney went to 64 00:04:39,440 --> 00:04:42,490 the banquet, and Cathy went to the banquet. 65 00:04:42,490 --> 00:04:48,246 So each of the rows on this chart indicates a different diner, a different 66 00:04:48,246 --> 00:04:53,225 person who ate at the banquet. And each of the columns indicates what 67 00:04:53,225 --> 00:04:56,955 they ate or drank. So one column is for the soup course. 68 00:04:56,955 --> 00:05:01,906 One column's for the main course. One column's for the wine, one's for the 69 00:05:01,906 --> 00:05:05,025 dessert. And then, of course, the last column to 70 00:05:05,025 --> 00:05:08,213 the right tells you whether they lived or died. 71 00:05:08,213 --> 00:05:13,503 And what we need to figure out is which of those food items or drinks is what 72 00:05:13,503 --> 00:05:17,165 caused their death. We're going to use the letter, y, to 73 00:05:17,165 --> 00:05:21,710 refer to the target feature, or the effect, the thing that is caused. 74 00:05:21,710 --> 00:05:27,915 And we're going to use the letter X to refer to the different candidates for the 75 00:05:27,915 --> 00:05:31,654 cause. And our question is, which candidate X is 76 00:05:31,654 --> 00:05:36,380 sufficient. For, the target Y. 77 00:05:36,380 --> 00:05:42,470 And the table with all the diners and all the courses, represents all of the data 78 00:05:42,470 --> 00:05:46,456 that we have available to us, to answer that question. 79 00:05:46,456 --> 00:05:49,840 So let's look first, at the very first course. 80 00:05:49,840 --> 00:05:53,960 The soup course. What does the soup course show us? 81 00:05:53,960 --> 00:05:58,820 Does it show us that anything is not sufficient for death? 82 00:05:58,820 --> 00:06:04,115 Yes. Shows tomato soup is not sufficient for 83 00:06:04,115 --> 00:06:05,039 death. Why? 84 00:06:05,039 --> 00:06:09,474 Because Anne had tomato soup and she didn't die. 85 00:06:09,474 --> 00:06:16,404 So it's not true that whenever you have tomato soup you die, since Anne had 86 00:06:16,404 --> 00:06:22,594 tomato soup and did not die. So that candidate X, tomato soup, is not 87 00:06:22,594 --> 00:06:29,524 sufficient for the target Y, death. Cathy shows the same thing, she shows the 88 00:06:29,524 --> 00:06:34,051 tomato soup is not sufficient for death. No. 89 00:06:34,051 --> 00:06:40,619 What do we learn from the main course? Do we learn that anything is not 90 00:06:40,619 --> 00:06:43,120 sufficient for death? Yes. 91 00:06:43,120 --> 00:06:47,336 We learned that chicken is not sufficient for death. 92 00:06:47,336 --> 00:06:53,442 Because Ann has chicken and doesn't die. And what does Cathy tell us is not 93 00:06:53,442 --> 00:06:58,698 sufficient for death? The case of Cathy tells us that beef is 94 00:06:58,698 --> 00:07:03,641 not sufficient for death. So, now we have a whole list of things 95 00:07:03,641 --> 00:07:07,564 that have been ruled out as sufficient conditions. 96 00:07:07,564 --> 00:07:13,280 Tomato soup, chicken and beef. And what about the wine course? 97 00:07:14,300 --> 00:07:19,092 What does Ann tell us in the wine course? Tells us that white wine is not 98 00:07:19,092 --> 00:07:23,097 sufficient for death. And what does Kathy tell us in the wine 99 00:07:23,097 --> 00:07:25,986 course? Red wine is not sufficient for death. 100 00:07:25,986 --> 00:07:31,304 And notice that it's Ann and Kathy that are giving us all this information about 101 00:07:31,304 --> 00:07:36,491 what's not sufficient, and that's because they didn't die, so anything that they 102 00:07:36,491 --> 00:07:40,220 ate or drank cannot be sufficient for death. 103 00:07:40,220 --> 00:07:46,803 But Barney did die. So, the things that he ate and drank 104 00:07:46,803 --> 00:07:52,279 still might be sufficient for death. They're not ruled out by the negative 105 00:07:52,279 --> 00:07:57,088 sufficient condition test. Of course, tomato soup was ruled out by 106 00:07:57,088 --> 00:08:00,936 the other cases. And red wine was ruled out by Kathy. 107 00:08:00,936 --> 00:08:05,450 But still, what about fish? Could fish be sufficient for death? 108 00:08:05,450 --> 00:08:10,086 It's not ruled out, right? It's not ruled out by the negative 109 00:08:10,086 --> 00:08:16,500 sufficient condition test because there's no case in this data, where somebody eats 110 00:08:16,500 --> 00:08:21,137 fish and doesn't die. But does that mean that eating fish is 111 00:08:21,137 --> 00:08:26,469 sufficient for death? No, cause this is just the negative 112 00:08:26,469 --> 00:08:31,455 sufficient condition test. It tells you whats not sufficient, it 113 00:08:31,455 --> 00:08:35,000 doesn't tell you what is sufficient, okay. 114 00:08:35,000 --> 00:08:39,251 But still, you want to look at the rest of the chart and figure, is there 115 00:08:39,251 --> 00:08:42,410 anything else is not ruled out sufficient condition. 116 00:08:42,410 --> 00:08:48,361 Well pie is ruled out as a sufficient condition because Anne had pie, is still 117 00:08:48,361 --> 00:08:51,566 alive. Kathy shows that ice cream is not a 118 00:08:51,566 --> 00:08:56,755 sufficient condition for death. But cake still might be a sufficient 119 00:08:56,755 --> 00:09:02,860 condition for death, for all we've read. So now we've got two candidates, fish and 120 00:09:02,860 --> 00:09:06,828 cake still might be sufficient conditions for death. 121 00:09:06,828 --> 00:09:12,398 They're not ruled out by the negative sufficient condition test but that 122 00:09:12,398 --> 00:09:15,680 doesn't mean they are sufficient for death. 123 00:09:15,680 --> 00:09:21,115 In order to conclude that they are sufficient conditions for death, we need 124 00:09:21,115 --> 00:09:26,406 to apply not the negative sufficient conditions but instead the positive 125 00:09:26,406 --> 00:09:31,117 sufficient condition test. The positive sufficient condition test 126 00:09:31,117 --> 00:09:36,915 tells us when we have a good reason to believe that X is a sufficient condition. 127 00:09:36,915 --> 00:09:42,786 What makes its positive is it tells you that you have a reason to believe that X 128 00:09:42,786 --> 00:09:47,280 positively is a sufficient condition, unlike the negative test. 129 00:09:47,280 --> 00:09:52,358 It says that you have a good reason to believe that X is a sufficient condition 130 00:09:52,358 --> 00:09:55,406 of Y, if all of the following conditions are met. 131 00:09:55,406 --> 00:10:00,357 Now I want to warn you, there are going to be four conditions and they have to 132 00:10:00,357 --> 00:10:05,309 all be met in order for you to reach a positive conclusion, or be justified in 133 00:10:05,309 --> 00:10:09,690 reaching a positive conclusion that X is a sufficient condition of Y. 134 00:10:09,690 --> 00:10:12,867 Now, the first condition is pretty simple. 135 00:10:12,867 --> 00:10:18,835 It simply says, we have not found any case where x is present, and y is absent. 136 00:10:18,835 --> 00:10:24,725 Basically, it says, you've already passed the negative part of the sufficient 137 00:10:24,725 --> 00:10:28,755 condition test. You can't rule out x as a sufficient 138 00:10:28,755 --> 00:10:34,722 condition on the basis of any cases. The second part says that we've tested a 139 00:10:34,722 --> 00:10:39,605 wide variety of cases. Including cases where x is present, and y 140 00:10:39,605 --> 00:10:43,762 is absent. And the reason that we have to have this 141 00:10:43,762 --> 00:10:49,055 condition, is that, without it, we could reach really silly conclusions much too 142 00:10:49,055 --> 00:10:52,041 easily. For example, on the basis of the data 143 00:10:52,041 --> 00:10:56,384 that we looked at before. We could reach the conclusion that pea 144 00:10:56,384 --> 00:11:00,455 soup is sufficient. Because there wasn't a single person who 145 00:11:00,455 --> 00:11:05,138 had pea soup and didn't die. There can't be a case where somebody had 146 00:11:05,138 --> 00:11:10,500 pea soup and didn't die, if there isn't a case where somebody had pea soup. 147 00:11:10,500 --> 00:11:15,037 That's why we have to check cases where X is present. 148 00:11:15,037 --> 00:11:20,600 Similarly, imagine that the only case that we knew was Barney. 149 00:11:20,600 --> 00:11:23,390 Right? And that means that nobody lived. 150 00:11:23,390 --> 00:11:27,110 Everybody died. Well, if everybody dies then we don't 151 00:11:27,110 --> 00:11:32,763 have any cases where somebody had tomato soup and didn't die, or where somebody 152 00:11:32,763 --> 00:11:38,773 had fish and didn't die or where somebody had beef and didn't die or where somebody 153 00:11:38,773 --> 00:11:43,066 had cake and didn't die. Whatever they had they died because 154 00:11:43,066 --> 00:11:47,073 everybody died. So if everybody dies, it's really hard to 155 00:11:47,073 --> 00:11:53,560 tell which of the different candidates is the one that's really causing the death. 156 00:11:53,560 --> 00:11:59,034 So that's why we have to have some cases where X is present, that is where the 157 00:11:59,034 --> 00:12:04,719 candidate that we're testing is present. And other cases where the target feature, 158 00:12:04,719 --> 00:12:08,299 Y, is absent. And that's what the second part of the 159 00:12:08,299 --> 00:12:12,880 positive sufficient condition test tells you that you need. 160 00:12:12,880 --> 00:12:19,323 Those two clauses are pretty tricky, but the next ones more important and its also 161 00:12:19,323 --> 00:12:24,037 a little bit trickier. What it says is that, if there are any 162 00:12:24,037 --> 00:12:30,088 other features that are never present or y as absent, then we've tested cases 163 00:12:30,088 --> 00:12:34,410 where those other features are absent but x is present. 164 00:12:34,410 --> 00:12:40,199 this can be confusing but the basic idea is that if there are two competing 165 00:12:40,199 --> 00:12:46,062 hypothesis, two competing candidates for sufficient condition, and neither one is 166 00:12:46,062 --> 00:12:51,412 ruled out by the negative sufficient condition test, then need to look at 167 00:12:51,412 --> 00:12:54,930 cases that will decide between those hypothesis. 168 00:12:54,930 --> 00:13:00,280 Now in our example we saw that neither fish nor cake is ruled out as the 169 00:13:00,280 --> 00:13:04,613 sufficient condition. And if we want to decide whether it's 170 00:13:04,613 --> 00:13:07,960 fish or cake, this really is a sufficient condition. 171 00:13:07,960 --> 00:13:13,014 Then what we need to look at is a case where fish is present, but cake is not. 172 00:13:13,014 --> 00:13:16,230 And a case where cake is present, but fish is not. 173 00:13:16,230 --> 00:13:22,167 We can't be sure from the first three cases because we don't have that 174 00:13:22,167 --> 00:13:27,938 combination of fish and cake. So we have to do a little more research. 175 00:13:27,938 --> 00:13:33,541 And luckily for us, not for them of course because one of them dies. 176 00:13:33,541 --> 00:13:38,391 So luckily for us Doug and Emily were also at the banquet. 177 00:13:38,391 --> 00:13:43,242 And Doug had tomato soup, beef, red wine and cake and lived. 178 00:13:43,242 --> 00:13:48,260 Emily had tomato soup, fish, red wine, pie and poor Emily died. 179 00:13:48,260 --> 00:13:54,545 The crucial thing here is that Doug had cake but not fish, and Emily had fish but 180 00:13:54,545 --> 00:13:58,192 not cake. Now, did these cases help us determine 181 00:13:58,192 --> 00:14:04,245 whether cake is sufficient for death? Yes, because one of these new cases rules 182 00:14:04,245 --> 00:14:07,660 out cake as a sufficient condition of death. 183 00:14:07,660 --> 00:14:12,697 Which one does that? Well it's Doug, because by the negative 184 00:14:12,697 --> 00:14:19,271 sufficient condition test, Doug had cake and didn't die, so that shows you the 185 00:14:19,271 --> 00:14:25,333 cake is not sufficient for death. Now does Emily rule out anything as a 186 00:14:25,333 --> 00:14:30,660 sufficient condition for death? No. 187 00:14:31,760 --> 00:14:33,924 Why not? Well, because she died. 188 00:14:33,924 --> 00:14:39,914 And if somebody dies they can't rule out something that's sufficient condition for 189 00:14:39,914 --> 00:14:43,017 death. Cases of death can't rule out what's 190 00:14:43,017 --> 00:14:48,862 sufficient for death, because to rule it out, you need a case where the candidates 191 00:14:48,862 --> 00:14:51,802 present and the targets not present. Okay? 192 00:14:51,802 --> 00:14:57,425 So the cases that rule out something as a sufficient condition of death are going 193 00:14:57,425 --> 00:15:02,225 to be the cases without death. Anyway, fish still might be a sufficient 194 00:15:02,225 --> 00:15:06,270 condition for death. So fish seems to be the only remaining 195 00:15:06,270 --> 00:15:11,481 candidate because we ruled out cake. So fish is the only remaining candidate 196 00:15:11,481 --> 00:15:15,595 for a sufficient condition, at least among those on the list. 197 00:15:15,595 --> 00:15:19,778 Now, we can conclude fish is a sufficient condition for death. 198 00:15:19,778 --> 00:15:22,348 Right? No, because remember, I told you, I 199 00:15:22,348 --> 00:15:25,474 warned you, there could be four conditions. 200 00:15:25,474 --> 00:15:31,502 We need all those conditions to be met in order for us to be, reasonably conclude 201 00:15:31,502 --> 00:15:35,298 that something sufficient in this one more to come. 202 00:15:35,298 --> 00:15:39,020 But why do we need more? The answer really is that. 203 00:15:39,020 --> 00:15:44,791 We don't know whether all the different features that might of caused the death 204 00:15:44,791 --> 00:15:48,903 are on our list. We've only looked at the soup course, the 205 00:15:48,903 --> 00:15:53,520 main course, the wine and the dessert. It might be something else. 206 00:15:53,520 --> 00:15:59,003 So we need to add one more clause. This last positive clause to our positive 207 00:15:59,003 --> 00:16:03,836 sufficient condition test. Namely that we've tested enough cases of 208 00:16:03,836 --> 00:16:09,824 various kinds that are likely to include a case where x is present and y is absent 209 00:16:09,824 --> 00:16:16,502 if there is any such case. So this cause is obviously going to be 210 00:16:16,502 --> 00:16:19,643 hard to apply. Right, it's not mechanical. 211 00:16:19,643 --> 00:16:23,122 How do we know that whether we've tested enough cases of various kinds? 212 00:16:23,122 --> 00:16:26,993 We have to know what kinds of things can cause death, and which kinds of things 213 00:16:26,993 --> 00:16:30,679 that can't cause death. That's going to depend on background 214 00:16:30,679 --> 00:16:35,620 conditions, background knowledge, right? We need to know something about potential 215 00:16:35,620 --> 00:16:38,584 causes of death, what can and cannot cause death. 216 00:16:38,584 --> 00:16:43,339 And we need to take that for granted in applying this last cause, so it's not 217 00:16:43,339 --> 00:16:47,073 going to be simple at all. But if we do know that there has to be 218 00:16:47,073 --> 00:16:50,929 some sufficient condition. I mean after all, people just don't die 219 00:16:50,929 --> 00:16:54,251 for no reason. And if we know that nothing else could be 220 00:16:54,251 --> 00:16:58,522 a sufficient condition, because maybe we checked the water and we looked for 221 00:16:58,522 --> 00:17:01,784 syringe marks and there were no bullet holes and so on. 222 00:17:01,784 --> 00:17:06,708 Then we have to have at least some reason to believe that the sufficient condition 223 00:17:06,708 --> 00:17:10,030 must be somewhere among the features that we're testing. 224 00:17:10,030 --> 00:17:12,601 Some people might say it's something else. 225 00:17:12,601 --> 00:17:17,378 After all, could be, I've got an idea. It could be the fact that both Barney and 226 00:17:17,378 --> 00:17:20,011 Emily both have the letter E in their name. 227 00:17:20,011 --> 00:17:22,950 But, you know that's not going to cause their death. 228 00:17:22,950 --> 00:17:25,767 That's just common sense, background knowledge. 229 00:17:25,767 --> 00:17:29,686 We looked at their glasses. There was no poison in their glasses. 230 00:17:29,686 --> 00:17:34,156 So, we have at least some reason to believe that the sufficient condition 231 00:17:34,156 --> 00:17:37,646 must lie somewhere among the features that we're testing. 232 00:17:37,646 --> 00:17:42,624 Now, this argument is not deductive. If something fails in negative sufficient 233 00:17:42,624 --> 00:17:47,483 condition test, then it's valid to conclude that, that candidate is not a 234 00:17:47,483 --> 00:17:53,466 sufficient condition for that target. But if something passes the positive 235 00:17:53,466 --> 00:17:58,106 sufficient condition test, then the argument's not valid. 236 00:17:58,106 --> 00:18:04,404 It's possible still that this is not sufficient and that argument, namely an 237 00:18:04,404 --> 00:18:10,619 application of the positive sufficient condition test, can be undermined by 238 00:18:10,619 --> 00:18:14,513 future data. It's defeasible like all inductive 239 00:18:14,513 --> 00:18:18,491 arguments. For example, we haven't mentioned Fred, 240 00:18:18,491 --> 00:18:24,585 Gertrude and Harold yet. And what do they show? 241 00:18:24,585 --> 00:18:32,045 Well wait a minute, Gertrude. Shows that fish is not sufficient after 242 00:18:32,045 --> 00:18:35,092 all. Notice that all the data before Fred, 243 00:18:35,092 --> 00:18:40,549 seem to a point of conclusion, that fish, was sufficient for death, but it just 244 00:18:40,549 --> 00:18:46,076 take ones more case, go through, to show that fish is not really sufficient for 245 00:18:46,076 --> 00:18:49,620 death afterall. That shows that it is an inductive 246 00:18:49,620 --> 00:18:53,589 argument, and that means that its going to be diffusible. 247 00:18:53,589 --> 00:18:58,550 Still, of'course, the inductive argument, can be strong, if w have enough. 248 00:18:58,550 --> 00:19:03,139 Data, we've looked at enough cases. And our background knowledge really is 249 00:19:03,139 --> 00:19:05,905 reliable. So, we're not saying that inductive 250 00:19:05,905 --> 00:19:09,740 arguments are no good, but the point is that their defeasible. 251 00:19:09,740 --> 00:19:14,280 Their going to be better when we've got more data, when our background 252 00:19:14,280 --> 00:19:19,160 assumptions are more reliable. And strength then is going to be a matter 253 00:19:19,160 --> 00:19:23,023 of degree and can go from slightly strong to very strong. 254 00:19:23,023 --> 00:19:27,700 In this case, because of Gertrude, we know that fish is not sufficient. 255 00:19:27,700 --> 00:19:32,331 So I have to think more about what still could be sufficient. 256 00:19:32,331 --> 00:19:35,140 But first, let's ask what's necessary.