Last time we looked at sufficient condition tests and they tell us what is or is not a sufficient condition. But we also need to know which factors or features or candidates are necessary conditions. So this time, we're going to look at necessary condition tests. And as with sufficient condition tests, there's going to be 2 of them. There's a negative necessary condition test that tells you what is not a necessary condition, and then there will be a positive necessary condition test that tells you what is A necessary condition. So first, the negative necessary condition test. It says simply that x is not a necessary condition of y, if there's any case where x is absent and y is present. Because to be a necessary condition it has to be the case that whenever, x is absent, y is absent too. So if there is even one case, where X is absent and Y is present, that's a counterexample to the universal claim that whenever, that is in all cases X's. Where x is absent, y is absent, okay? So let's apply this to our data so far. But let's look first, just at the first 3 people Ann, Barney, and Cathy. You remember them from last time, they were at the banquet. Is pie a necessary condition of death, well, is there a case where pie is absent and death is present? Yes. That means that pie is not a necessary condition of death. Which case shows us that? Well, it's Barney. Notice that it's not and. Some people get confused about this, but what and tells us is that pie is not sufficient for death. It's Barney that tells us that pie is not necessary for death because with Barney, you get death without pie. So pie was not necessary. For Barney to die. So it's the cases of death that made Barney out of these 3 to tell us what's not necessary for death. Now, the case of Barney also tells us that another dessert is not necessary for death. Which one is that? Ice cream. because Barnie also didn't have ice cream, and he died, so he died without having ice cream, so ice cream is not necessary for death. So, what might be necessary for death? Tomato soup might be necessary for death, because out of these 3 cases, there's nobody who dies without having tomato soup. Fish might be necessary for death. because out of these cases, there's nobody that dies without having fish. Red wine might be necessary. And cake might be necessary. Because Barney's the only one who dies, all of those things still might be necessary for death. And the only way to rule out some of those candidates so as to narrow down the field. Is to get more data. So remember Doug and Emily, our old friends from the banquet. What do they show us? Is cake necessary for death? No, because now we have a case where someone died without eating cake. Namely, Emily. And is fish necessary for death? Oh, well both Emily and Barney had fish. So there is nobody that dies without having fish. So, so far on this data. It looks like fish still might be a necessary condition for death. So, since it's survived this far, I guess we can conclude that fish is a necessary condition for death. No way, because remember, this is just the negative necessary condition test. It tells us what is not a necessary condition. We still are not in a position to conclude that fish is a necessary condition for death. For that, we'll need to look at the positive necessary condition test.