1 00:00:02,120 --> 00:00:08,091 Last time we looked at sufficient condition tests, and they tell us what is 2 00:00:08,091 --> 00:00:13,494 or is not sufficient condition. We also need to know which factors or 3 00:00:13,494 --> 00:00:17,201 features or candidates are necessary conditions. 4 00:00:17,201 --> 00:00:21,989 So this time we're going to look at necessary condition tests. 5 00:00:21,989 --> 00:00:27,549 And as with sufficient conditions tests, there's going to be two of them. 6 00:00:27,549 --> 00:00:33,187 There's a negative necessary condition test that tells you what is not a 7 00:00:33,187 --> 00:00:39,519 necessary condition and then there'll be a positive necessary condition test that 8 00:00:39,519 --> 00:00:42,850 tells you what is. A necessary condition. 9 00:00:42,850 --> 00:00:46,997 So first, the negative necessary condition test. 10 00:00:46,997 --> 00:00:54,319 It says simply that X is not a necessary condition of Y if there is any case where 11 00:00:54,319 --> 00:01:00,318 X is absent and Y is present. Because to be a necessary condition, it 12 00:01:00,318 --> 00:01:04,250 has to be the case that whenever X is absent, 13 00:01:04,250 --> 00:01:08,928 Y is absent too. So, if there's even one case where X is 14 00:01:08,928 --> 00:01:15,478 absent and Y is present, that's a counter example to the universal claim that 15 00:01:15,478 --> 00:01:22,000 whenever, that is in all cases. Where X is absent, Y is absent, 16 00:01:22,000 --> 00:01:25,717 okay? So let's apply this to our data so far. 17 00:01:25,717 --> 00:01:31,969 Then let's look first just at the first three people and Barney and Cathy. 18 00:01:31,969 --> 00:01:36,869 You remember them from last time, they were at the banquet. 19 00:01:36,869 --> 00:01:44,538 Is pie a necessary condition of death? Well, is there a case where pie is absent 20 00:01:44,538 --> 00:01:50,351 and death is present. Yes, that means that pie is not a 21 00:01:50,351 --> 00:01:55,940 necessary condition of death. Which case shows us that, 22 00:01:55,940 --> 00:01:59,266 well it's Barney. Notice that it's not Ann. 23 00:01:59,266 --> 00:02:05,364 Some people get confused about this. But what Ann tells us is that pie is not 24 00:02:05,364 --> 00:02:10,353 sufficient for death. It's Barney that tells us that pie is not 25 00:02:10,353 --> 00:02:15,501 necessary for death because with Barney, you get death without pie. 26 00:02:15,501 --> 00:02:18,906 So pie was not necessary for Barney to die. 27 00:02:18,906 --> 00:02:25,004 So it's the cases of death that leave Barney out of these three, that tell us 28 00:02:25,004 --> 00:02:30,919 what's not necessary for death. Now the case of Barney also tells us 29 00:02:30,919 --> 00:02:35,050 there is another result its not necessary for death. 30 00:02:35,050 --> 00:02:37,621 Which one is that? Ice cream. 31 00:02:37,621 --> 00:02:43,254 because Barney also didn't have ice cream and he died, so he died without having 32 00:02:43,254 --> 00:02:46,961 ice cream. So ice cream is not necessary for death. 33 00:02:46,961 --> 00:02:52,743 So, what might be necessary for death? Tomato soup might be necessary for death, 34 00:02:52,743 --> 00:02:58,302 because out of these three cases there's nobody who dies without having tomato 35 00:02:58,302 --> 00:03:01,193 soup. Fish might be necessary for death, 36 00:03:01,193 --> 00:03:06,160 because out of these cases there's nobody who dies without having fish. 37 00:03:06,160 --> 00:03:10,071 Red wine might be necessary, and cake might be necessary. 38 00:03:10,071 --> 00:03:15,169 Because Barney's the only one who dies, all of those things still might be 39 00:03:15,169 --> 00:03:19,150 necessary for death. And the only way to rule out some of 40 00:03:19,150 --> 00:03:24,660 those candidates so as to narrow down the field, is to get more data. 41 00:03:24,660 --> 00:03:28,700 So remember Doug and Emily, our old friends from the banquet. 42 00:03:29,740 --> 00:03:35,460 What do they show us? Is cake necessary for death. 43 00:03:35,460 --> 00:03:45,080 No, because now we have a case of someone dying without eating cake namely Emily. 44 00:03:45,080 --> 00:03:51,504 And is fish necessary for death? Whoa, well both Emily and Barney had 45 00:03:51,504 --> 00:03:56,417 fish, so there's nobody who dies without having fish. 46 00:03:56,417 --> 00:04:03,975 So, so far for this data, it looks like fish still might be a necessary condition 47 00:04:03,975 --> 00:04:08,990 for death. So, since it survived this far, I guess 48 00:04:08,990 --> 00:04:14,140 we can conclude that fish is a necessary condition for death. 49 00:04:14,140 --> 00:04:19,955 No way, because remember, this is just the negative necessary condition test. 50 00:04:19,955 --> 00:04:23,722 It tells us what is not a necessary condition. 51 00:04:23,722 --> 00:04:29,291 We still are not in a position to conclude, that fish is a necessary 52 00:04:29,291 --> 00:04:33,668 condition for death. For that, we'll need to look at the 53 00:04:33,668 --> 00:04:39,535 positive necessary condition test. The positive necessary condition test is 54 00:04:39,535 --> 00:04:45,559 just like positive sufficient condition test, except that you change the absent 55 00:04:45,559 --> 00:04:49,705 for present in the two positions throughout the test. 56 00:04:49,705 --> 00:04:53,357 So. It tells you that we have good reason to 57 00:04:53,357 --> 00:04:58,776 believe that x is a necessary condition of y if all of the following conditions 58 00:04:58,776 --> 00:05:02,163 are met. Now remember it's got to be all four that 59 00:05:02,163 --> 00:05:07,108 are met before you can reasonably conclude that it really is a necessary 60 00:05:07,108 --> 00:05:10,495 condition. And it's positive because it allows you 61 00:05:10,495 --> 00:05:13,950 to conclude positively it is a necessary condition. 62 00:05:13,950 --> 00:05:21,314 [SOUND] So first clause is that we've not found any case where X is absent and Y is 63 00:05:21,314 --> 00:05:24,716 present. Again it's just like the sufficient 64 00:05:24,716 --> 00:05:29,354 condition test except that we've changed absent for present. 65 00:05:29,354 --> 00:05:35,151 And what this is saying is that this particular candidate X, has passed the 66 00:05:35,151 --> 00:05:40,295 negative necessary condition test. And you got to do that, because if you're 67 00:05:40,295 --> 00:05:45,200 ruled out as a necessary condition, there can't be adequate reason to conclude. 68 00:05:45,200 --> 00:05:49,098 But you are a necessary condition, 'cause you've been ruled out. 69 00:05:49,098 --> 00:05:54,066 Second, you've tested a wide variety of cases, including cases where X is absent, 70 00:05:54,066 --> 00:05:58,590 and cases where Y is present. I mean after all, if nobody dies, you 71 00:05:58,590 --> 00:06:01,967 can't test to see what's necessary for death. 72 00:06:01,967 --> 00:06:05,568 You're not going to be able to have enough data. 73 00:06:05,568 --> 00:06:11,345 You're going to reach silly conclusions. So, we need to make sure we have a bunch 74 00:06:11,345 --> 00:06:17,347 of cases where X is absent, and a bunch of cases where Y is present or we're not 75 00:06:17,347 --> 00:06:21,323 going to have any reason at all. So, remember our data, 76 00:06:21,323 --> 00:06:25,674 what about tomato soup? Is tomato soup necessary for death? 77 00:06:25,674 --> 00:06:28,342 Well, it might be cause we didn't have any 78 00:06:28,342 --> 00:06:32,370 cases in the first three at least, where nobody drank tomato soup. 79 00:06:32,370 --> 00:06:35,401 So that would be a silly conclusion to reach. 80 00:06:35,401 --> 00:06:40,386 We need to look at cases where people didn't have tomato soup in order to 81 00:06:40,386 --> 00:06:45,641 determine whether the tomato soup really was necessary, to cause death in that 82 00:06:45,641 --> 00:06:48,470 case. Now the third, condition says that if 83 00:06:48,470 --> 00:06:53,522 there are any other features, that are never absent where Y is present, then 84 00:06:53,522 --> 00:06:57,430 we've tested cases where those other features are present, 85 00:06:57,430 --> 00:07:02,234 but X is absent. And the idea here is that you've got 86 00:07:02,234 --> 00:07:06,062 competing hypotheses. Some people might think that one 87 00:07:06,062 --> 00:07:11,048 candidate is a necessary condition for death and other people might think that 88 00:07:11,048 --> 00:07:15,781 another candidate is a necessary condition for death and some people might 89 00:07:15,781 --> 00:07:19,758 say, well I don't know which one, because neither ones ruled out. 90 00:07:19,758 --> 00:07:24,428 Well, if neither ones ruled out by the necessary test, then we need to have 91 00:07:24,428 --> 00:07:29,414 cases that decide between the competing candidates, the competing hypothesis to 92 00:07:29,414 --> 00:07:32,254 determine what really is necessary for death. 93 00:07:32,254 --> 00:07:37,791 So that means that, in our example, at least for the first three cases, and 94 00:07:37,791 --> 00:07:42,125 Barney and Cathy. Fish and red wine and tomato soup all 95 00:07:42,125 --> 00:07:45,508 still might be necessary conditions of death. 96 00:07:45,508 --> 00:07:51,746 And to figure out which one really is, we want to look at a case of somebody that's 97 00:07:51,746 --> 00:07:57,458 fish and red wine, but not tomato soup, somebody who has fish and tomato soup, 98 00:07:57,458 --> 00:08:03,170 but not red wine and somebody who has tomato soup and red wine but not fish. 99 00:08:03,170 --> 00:08:09,054 So we need to do more research. Now luckily, again lucky for us but not 100 00:08:09,054 --> 00:08:14,013 for them, we have additional people who came to the banquet. 101 00:08:14,013 --> 00:08:19,309 It had just those combinations, namely Fred, Gertrude and Harold. 102 00:08:19,309 --> 00:08:23,260 Fred had fish and red wine but not tomato soup. 103 00:08:23,260 --> 00:08:27,473 Gertrude had fish and tomato soup, but not red wine. 104 00:08:27,473 --> 00:08:31,851 And Harold had tomato soup and red wine, but not fish. 105 00:08:31,851 --> 00:08:36,807 So, what does Fred tell us? What does this case rule out as a 106 00:08:36,807 --> 00:08:41,543 necessary condition. It tells us that tomato soup is not a 107 00:08:41,543 --> 00:08:46,799 necessary condition for death, because Fred died without having tomato soup. 108 00:08:46,799 --> 00:08:49,883 He had leek soup instead, and no tomato soup. 109 00:08:49,883 --> 00:08:54,719 What does Gertrude tell us? What does this case rule out as necessary 110 00:08:54,719 --> 00:08:58,598 condition? Nothing, why? Because Gertrude didn't 111 00:08:58,598 --> 00:09:01,941 die. And it's only the cases where people die 112 00:09:01,941 --> 00:09:06,733 that can rule out necessary conditions. What about Harold? 113 00:09:06,733 --> 00:09:10,709 What does Harold tell us? Same thing, Harold didn't die so he 114 00:09:10,709 --> 00:09:14,090 doesn't rule out anything as a necessary condition, 115 00:09:14,090 --> 00:09:20,265 okay. Gertrude might show us that fish is not a sufficient condition for death, we 116 00:09:20,265 --> 00:09:26,365 already talked about that in the last lecture but since Gertrude and Harold are 117 00:09:26,365 --> 00:09:32,084 alive and don't die, they can't rule out candidates as necessary conditions. 118 00:09:32,084 --> 00:09:37,955 So, so far, it looks like fish might be necessary but not sufficient for death, 119 00:09:37,955 --> 00:09:41,615 given this set of data with Ann through Harold. 120 00:09:41,615 --> 00:09:47,310 It also looks like red wine. Still might be necessary but not 121 00:09:47,310 --> 00:09:49,900 sufficient for death. So. 122 00:09:49,900 --> 00:09:57,037 Is it reasonable to conclude that both of these features, both of these candidates 123 00:09:57,037 --> 00:10:00,780 are necessary and not sufficient for death. 124 00:10:00,780 --> 00:10:03,968 No, not yet. because remember there's a fourth 125 00:10:03,968 --> 00:10:07,934 condition. And the fourth condition says that we've 126 00:10:07,934 --> 00:10:14,311 tested enough cases of various kinds that are likely to include a case where X is 127 00:10:14,311 --> 00:10:18,600 absent and Y is present, if there is any such case. 128 00:10:18,600 --> 00:10:23,124 And as with the positive sufficient condition test, this is going to require 129 00:10:23,124 --> 00:10:28,207 background knowledge about what kinds of things might or not be causally relevant, 130 00:10:28,207 --> 00:10:32,360 might or might not be necessary in sufficient conditions for death. 131 00:10:32,360 --> 00:10:36,784 It's going to be defeasible. It's not going to be valid, because it's 132 00:10:36,784 --> 00:10:40,818 an inductive argument. But still, we can get pretty good reason 133 00:10:40,818 --> 00:10:44,723 to believe that something's a necessary condition for death. 134 00:10:44,723 --> 00:10:47,586 If we have enough cases with enough variety. 135 00:10:47,586 --> 00:10:52,140 And that's what this positive necessary condition test is telling you. 136 00:10:52,140 --> 00:10:55,980 What kinds of cases you need. What kind of variety you need. 137 00:10:55,980 --> 00:11:01,687 Of course, the more cases and the more the variety, the stronger the reason, 138 00:11:01,687 --> 00:11:07,626 because inductive arguments come in degrees but we've got at least some good 139 00:11:07,626 --> 00:11:13,589 reason when these conditions are met. But if we've got both fish and red wine 140 00:11:13,589 --> 00:11:17,840 as being necessary but not sufficient for death. 141 00:11:17,840 --> 00:11:23,190 Well, what is sufficient for death? That's what we'll have to talk about in 142 00:11:23,190 --> 00:11:24,420 the next lecture.