1 00:00:02,900 --> 00:00:08,765 Another kind of inductive argument concerns causes or causal reasoning. 2 00:00:08,765 --> 00:00:13,060 Well, we think about causes all the time in everyday life. 3 00:00:13,060 --> 00:00:18,780 Suppose that all of a sudden, your computer screen goes black. 4 00:00:18,780 --> 00:00:23,635 Wow, what made that happen? Was it the Coursera website going down or 5 00:00:23,635 --> 00:00:28,968 is there some problem with your computer? Or was I just playing a trick on you? 6 00:00:28,968 --> 00:00:34,507 Well, you need to know that in order to figure out whether or not you need to get 7 00:00:34,507 --> 00:00:38,405 your computer fixed. Or suppose that, make a cup of coffee, 8 00:00:38,405 --> 00:00:43,699 I love a good cup of coffee. [SOUND] That's disgusting. 9 00:00:43,699 --> 00:00:47,374 What went wrong? What made it taste so bad? 10 00:00:47,374 --> 00:00:52,710 There must be something in the coffee that made it taste bad. 11 00:00:52,710 --> 00:00:56,910 But what was it? What caused that horrible taste? 12 00:00:56,910 --> 00:01:03,519 Or think about a court room, a law suit. Someone is found guilty of murder. 13 00:01:03,519 --> 00:01:08,925 Well, to be found guilty of murder, you have to show they are the one that caused 14 00:01:08,925 --> 00:01:12,169 the death. That their action, pulling the trigger, 15 00:01:12,169 --> 00:01:16,020 putting the poison in the food, whatever caused the death. 16 00:01:16,020 --> 00:01:21,088 And whether you send them to prison for a long time depends on that causal 17 00:01:21,088 --> 00:01:24,061 judgement. So, we got to get causal judgement 18 00:01:24,061 --> 00:01:28,099 straight. The causal judgements cannot be certain. 19 00:01:28,099 --> 00:01:32,816 We can't know with absolute certainty what causes what. 20 00:01:32,816 --> 00:01:38,470 It's just not like that in life. That's why we need inductive arguments in 21 00:01:38,470 --> 00:01:44,084 order to support these causal judgements that play such a big role in all of our 22 00:01:44,084 --> 00:01:45,674 lives. Okay. 23 00:01:45,674 --> 00:01:49,871 So, we need inductive arguments to support causal claims. 24 00:01:49,871 --> 00:01:54,666 But how does that work? To get straight on that, we need to think 25 00:01:54,666 --> 00:01:59,462 a little bit about causation. Causal claims are about individual 26 00:01:59,462 --> 00:02:02,310 events. One event causes another event. 27 00:02:02,310 --> 00:02:07,406 For example, my phone is off. But if I push this button on the bottom, 28 00:02:07,406 --> 00:02:12,259 then it turns on. Great. And if I push this button on the 29 00:02:12,259 --> 00:02:17,096 top, then it turns off. That particular event of me pushing the 30 00:02:17,096 --> 00:02:21,799 button on the bottom, turned it on. And the particular event of me turning, 31 00:02:21,799 --> 00:02:24,633 pushing the button on the top, turned it off. 32 00:02:24,633 --> 00:02:29,593 But behind that connection between the particular events lies a general rule. 33 00:02:29,593 --> 00:02:34,683 Every time I push a button on the bottom, it turns on and every time I push the 34 00:02:34,683 --> 00:02:39,547 button on the top, it turns off. If it didn't hold, as a general rule, it 35 00:02:39,547 --> 00:02:42,193 wouldn't be a causal relation, right? 36 00:02:42,193 --> 00:02:46,236 Every time I push the button on the bottom, it turns on. 37 00:02:46,236 --> 00:02:48,001 Now, not really. because look, 38 00:02:48,001 --> 00:02:52,338 if I push it now, something else happens. It doesn't turn on. 39 00:02:52,338 --> 00:02:56,749 I can keep pushing it. If it's already on, that won't turn it 40 00:02:56,749 --> 00:02:59,821 on. So, it's not true that every time I push 41 00:02:59,821 --> 00:03:05,149 the button on the bottom, it turns on. And it's not true that every time I push 42 00:03:05,149 --> 00:03:09,478 the button on the top, it turns off. It might be broken, for example. 43 00:03:09,478 --> 00:03:12,560 There might be something wrong with the button. 44 00:03:12,560 --> 00:03:17,152 So, these generalizations behind causal reasoning only hold in certain 45 00:03:17,152 --> 00:03:20,300 circumstances, in a particularly restricted set of 46 00:03:20,300 --> 00:03:23,710 circumstances. And we'll have to think about that in 47 00:03:23,710 --> 00:03:28,236 order to get causation straight. But first, we want to look at general 48 00:03:28,236 --> 00:03:33,090 rules and how we're going to determine which general rules hold and which 49 00:03:33,090 --> 00:03:37,150 general rules don't hold. So, how can we test general principles? 50 00:03:37,150 --> 00:03:40,520 That's going to be the topic for this whole week. 51 00:03:40,520 --> 00:03:46,492 The big question is going to be which cases in the data do we need to look at 52 00:03:46,492 --> 00:03:52,624 and how do we know when we have enough data to really believe in a general 53 00:03:52,624 --> 00:03:56,969 principle? Well, the first thing we need to do is to 54 00:03:56,969 --> 00:04:02,947 draw an important distinction between two different types of general principles. 55 00:04:02,947 --> 00:04:08,627 Sometimes, we say that one thing is a sufficient condition for another thing. 56 00:04:08,627 --> 00:04:14,307 And that means basically that whenever you have the first thing, you're also 57 00:04:14,307 --> 00:04:19,164 going to have the second thing. But sometimes, we're going to claim that 58 00:04:19,164 --> 00:04:23,350 something is a necessary condition for the second thing. 59 00:04:23,350 --> 00:04:28,911 And basically again, that means that if you don't have the first thing, you're 60 00:04:28,911 --> 00:04:33,100 not going to have the second thing. And it's going to be crucial to 61 00:04:33,100 --> 00:04:38,517 distinguish sufficient conditions from necessary conditions because people 62 00:04:38,517 --> 00:04:42,128 confuse them all the time and we need to get them straight, 63 00:04:42,128 --> 00:04:45,234 get them straight. So, let's start with a very simple 64 00:04:45,234 --> 00:04:48,556 example. First, being a whale is sufficient for 65 00:04:48,556 --> 00:04:52,617 being a mammal. Well, that's because every whale is a 66 00:04:52,617 --> 00:04:57,387 mammal so if you got something that's a whale, you know you've got something 67 00:04:57,387 --> 00:04:58,760 that's a mammal, okay? 68 00:04:59,960 --> 00:05:03,697 But being a whale is necessary for being a sperm whale. 69 00:05:03,697 --> 00:05:06,890 If you're not a whale, you're not a sperm whale. 70 00:05:06,890 --> 00:05:10,220 You can't be a sperm whale without being a whale. 71 00:05:10,220 --> 00:05:15,316 So, being a whale is necessary for being a sperm whale but being a whale is 72 00:05:15,316 --> 00:05:19,936 sufficient for being a mammal. One way to illustrate this is to draw 73 00:05:19,936 --> 00:05:24,690 them into circles. So, if you know that there's a large 74 00:05:24,690 --> 00:05:30,754 group of mammals, that's a big circle? But within that is the set of whales, 75 00:05:30,754 --> 00:05:36,326 which is smaller than the mammals. But even within the whales circle, 76 00:05:36,326 --> 00:05:41,288 there's a set of sperm whales, then you know that being a whale is 77 00:05:41,288 --> 00:05:46,780 sufficient for being a mammal, because everything in the whale circle is in this 78 00:05:46,780 --> 00:05:50,325 mammal circle. And being a, a whale is necessary for 79 00:05:50,325 --> 00:05:55,747 being a sperm whale because everything that's not in the whale circle is also 80 00:05:55,747 --> 00:06:01,598 not in the sperm whale circle because the sperm whale circle is totally inside the 81 00:06:01,598 --> 00:06:05,080 whale circle, okay? 82 00:06:05,080 --> 00:06:09,758 Now, let's trying to formulate a definition of necessary and sufficient 83 00:06:09,758 --> 00:06:15,038 conditions a little more precisely. The definition for sufficient conditions 84 00:06:15,038 --> 00:06:20,251 and necessary conditions is a little different with events than it is with 85 00:06:20,251 --> 00:06:23,392 features. So, we're going to give you two different 86 00:06:23,392 --> 00:06:28,271 versions and you can really use the one that applies to the case in hand. 87 00:06:28,271 --> 00:06:33,818 We can define a sufficient condition by saying that F is a sufficient condition 88 00:06:33,818 --> 00:06:38,768 for G. If and only if, that is, just in case, 89 00:06:38,768 --> 00:06:48,040 whenever an event of type F happens, then an event of type G also happens. 90 00:06:48,040 --> 00:06:54,688 And to put it more appropriately for features, we can say that anything that 91 00:06:54,688 --> 00:06:59,200 has the feature F will also have the feature G. 92 00:06:59,200 --> 00:07:04,244 So, in our whale example, anything that's a whale is also a mammal. 93 00:07:04,244 --> 00:07:10,376 Anything that has the feature of being a whale also has the feature of being a 94 00:07:10,376 --> 00:07:14,101 mammal. So, being a whale is sufficient for being 95 00:07:14,101 --> 00:07:18,214 a mammal. We can do the same thing with necessary 96 00:07:18,214 --> 00:07:22,367 conditions, but you got to put the negations in there. 97 00:07:22,367 --> 00:07:27,617 That's the only difference. F is a necessary condition for G, if and 98 00:07:27,617 --> 00:07:33,245 only if, that is just in case, whenever an event of type f F does not 99 00:07:33,245 --> 00:07:37,960 happen, then an event of type G also does not happen. 100 00:07:37,960 --> 00:07:44,761 By putting a negation on both sides, you turn it into a necessary condition. 101 00:07:44,761 --> 00:07:51,744 And for features, we can say, anything that does not have F, the feature F, does 102 00:07:51,744 --> 00:07:59,002 not have the feature G." So, back to our whale example, anything that is not a 103 00:07:59,002 --> 00:08:05,667 whale is not a sperm whale. So, being a whale is necessary for being 104 00:08:05,667 --> 00:08:12,025 a sperm whale. And that's how our definitions work. 105 00:08:12,025 --> 00:08:18,266 Now, since you took propositional logic a few years, [LAUGH] few years, a few weeks 106 00:08:18,266 --> 00:08:26,998 ago with Ram it might help to think of this as equivalent to the propositional 107 00:08:26,998 --> 00:08:31,107 forms. So, you can think of F is sufficient for 108 00:08:31,107 --> 00:08:37,182 G, is like if F then G, or F horseshoe G. It's not really quite the same. 109 00:08:37,182 --> 00:08:41,112 It's different because you need quantifiers. 110 00:08:41,112 --> 00:08:45,221 But if you think of it that way, it won't hurt. 111 00:08:45,221 --> 00:08:51,921 And then, to say the F is necessary for G, it's kind of like saying, if not F, 112 00:08:51,921 --> 00:08:56,640 then not G. Or in symbols, not F horseshoe not G. 113 00:08:56,640 --> 00:09:01,182 And thinking of it along those lines is, is again, not quite right because there 114 00:09:01,182 --> 00:09:05,667 are no quantifiers, but it's close enough and it might help you understand the 115 00:09:05,667 --> 00:09:09,520 distinction between sufficient conditions and necessary conditions. 116 00:09:09,520 --> 00:09:14,563 The same concepts apply in causal examples but they're a little bit 117 00:09:14,563 --> 00:09:18,346 trickier to apply. And the main reason is that word, 118 00:09:18,346 --> 00:09:23,835 whenever because it's a quantifier and it applies to a restricted domain of 119 00:09:23,835 --> 00:09:27,284 discourse. And you don't know what that means 120 00:09:27,284 --> 00:09:32,365 because we haven't studied that yet. But the point is that it only holds 121 00:09:32,365 --> 00:09:36,741 whenever in a certain range of cases, not just any old case. 122 00:09:36,741 --> 00:09:42,000 So, to get the clear about that let's, let's look at an example. 123 00:09:42,000 --> 00:09:47,118 Striking this match, [SOUND] this match right here, 124 00:09:47,118 --> 00:09:50,804 right, is sufficient for lighting it. 125 00:09:50,804 --> 00:09:54,886 [SOUND] So, when I strike it, I light it, okay? 126 00:09:54,886 --> 00:10:01,546 And striking the match on a rough surface is necessary for lighting it because if I 127 00:10:01,546 --> 00:10:06,700 strike it [SOUND] on a surface that's not rough, it doesn't light. 128 00:10:06,700 --> 00:10:12,019 So now, we know that striking it is sufficient and striking on a rough 129 00:10:12,019 --> 00:10:16,502 surface is necessary but wait a minute, that can't be right. 130 00:10:16,502 --> 00:10:20,530 It can't be true that whenever you strike the match, 131 00:10:20,530 --> 00:10:26,172 it lights because we know that when you strike it on a surface that's not rough, 132 00:10:26,172 --> 00:10:30,121 it doesn't light. So, how do we get that striking [SOUND] 133 00:10:30,121 --> 00:10:35,834 it is sufficient for lighting it when we know that if you strike it on the wrong 134 00:10:35,834 --> 00:10:40,771 place [SOUND] it's not going to light? And the answer is that when we say 135 00:10:40,771 --> 00:10:46,454 whenever we strike it, we're taking for granted that we're talking about a normal 136 00:10:46,454 --> 00:10:51,291 match, maybe just this one, with the right chemicals on the end, and we're 137 00:10:51,291 --> 00:10:56,665 talking about striking it, we're talking about striking it in a certain way at a 138 00:10:56,665 --> 00:11:00,024 certain place. So, when we're saying whenever, we're 139 00:11:00,024 --> 00:11:05,856 saying, whenever we strike it [SOUND] on that surface then, it will light. 140 00:11:05,856 --> 00:11:12,644 I mean, for example, if you were to take [SOUND] the match, and you were to start 141 00:11:12,644 --> 00:11:17,830 with a regular match but then dip it in the coffee, 142 00:11:17,830 --> 00:11:26,070 [SOUND] that still tastes horrible, then it won't light when you strike it 143 00:11:26,070 --> 00:11:30,909 because it's wet. So, in causal cases, you're always saying 144 00:11:30,909 --> 00:11:36,955 that within the certain range of circumstances it will hold. 145 00:11:36,955 --> 00:11:44,620 Whenever in those circumstances you strike the match, it will light and the 146 00:11:44,620 --> 00:11:49,600 same point holds for necessary conditions. So, 147 00:11:49,600 --> 00:11:56,224 this match, this box, rough surface, it's not lighting. 148 00:11:56,224 --> 00:12:01,818 Well, why not? Because if you don't strike the match, it 149 00:12:01,818 --> 00:12:03,683 won't light, right? 150 00:12:03,683 --> 00:12:06,480 No, that's not right either. 151 00:12:06,480 --> 00:12:11,349 because if you take another match and you light it, 152 00:12:11,349 --> 00:12:16,529 then look, I can light this match without striking 153 00:12:16,529 --> 00:12:21,881 it. So, it turns out that necessary 154 00:12:21,881 --> 00:12:28,475 conditions and sufficient conditions in causal cases have to be understood as 155 00:12:28,475 --> 00:12:33,464 holding, as a general rule within appropriate circumstances. 156 00:12:33,464 --> 00:12:40,312 And that means that we have to change our definition of necessary conditions and 157 00:12:40,312 --> 00:12:46,823 sufficient conditions to make that clear. To be strictly true then, we need to 158 00:12:46,823 --> 00:12:52,150 qualify the definition with the phrase in normal circumstances. 159 00:12:52,150 --> 00:12:59,020 And the in normal circumstances tell us how the term, whenever, applies. 160 00:12:59,020 --> 00:13:05,720 So then, F is a sufficient condition for G, if and only if, 161 00:13:05,720 --> 00:13:12,709 in normal circumstances, whenever G happens, G also happens. 162 00:13:12,709 --> 00:13:20,060 Or, in normal circumstances, anything that's an F is also an G. 163 00:13:21,260 --> 00:13:25,020 And the same hold for the necessary condition. 164 00:13:25,020 --> 00:13:32,480 F is a necessary condition for G, if and only if, just in case, or that's what 165 00:13:32,480 --> 00:13:38,665 this means is that in normal circumstances, whenever F does not 166 00:13:38,665 --> 00:13:43,499 happen, G does not happen. Or for features, 167 00:13:43,499 --> 00:13:50,710 in normal circumstances, for normal cases, anything that's not an F is also 168 00:13:50,710 --> 00:13:54,998 not a G. Now, of course, what counts as normal 169 00:13:54,998 --> 00:14:01,918 circumstances is going to be a tricky term that, that changes from case to 170 00:14:01,918 --> 00:14:06,303 case. And this definition applies in a lot of 171 00:14:06,303 --> 00:14:11,321 different kinds of cases. We already saw one case. 172 00:14:11,321 --> 00:14:15,494 That's the conceptual case. So, let's look at that first. 173 00:14:15,494 --> 00:14:19,060 Being a whale is sufficient for being a mammal. 174 00:14:19,060 --> 00:14:24,295 Now notice, being a whale is not necessary for being a mammal because 175 00:14:24,295 --> 00:14:27,785 there are lots of mammals that aren't whales, 176 00:14:27,785 --> 00:14:34,337 like sea otters. And being a whale is necessary for being 177 00:14:34,337 --> 00:14:41,230 a sperm whale, but it's not sufficient for being a sperm whale because there are 178 00:14:41,230 --> 00:14:46,215 lots of whale that are not sperm whales, okay? 179 00:14:46,215 --> 00:14:51,978 So, that's a conceptual case. Now, we saw a causal case. 180 00:14:51,978 --> 00:14:56,640 Striking this match is sufficient for lighting it. 181 00:14:56,640 --> 00:15:03,070 And striking this match on a rough surface is necessary for lighting it, 182 00:15:03,070 --> 00:15:07,179 okay? But it also have the same distinction in 183 00:15:07,179 --> 00:15:13,080 the, in other kinds of cases. Here's a moral example. 184 00:15:13,080 --> 00:15:18,457 Torturing someone just for fun is sufficient for doing something wrong 185 00:15:18,457 --> 00:15:22,395 because torturing somebody just for fun is always wrong. 186 00:15:22,395 --> 00:15:29,448 You shouldn't do it, period or at least so, someone, my client, I think so at 187 00:15:29,448 --> 00:15:34,427 least. And doing something wrong is necessary 188 00:15:34,427 --> 00:15:39,115 for being punishable. And notice that torturing for fun is not 189 00:15:39,115 --> 00:15:43,500 necessary for doing something wrong because you can do wrong without 190 00:15:43,500 --> 00:15:44,962 torturing for fun, okay? 191 00:15:44,962 --> 00:15:49,601 And doing something wrong is not sufficient for being punishable because 192 00:15:49,601 --> 00:15:52,970 you ought to get a fair trial before you're punished. 193 00:15:52,970 --> 00:15:57,863 If you do something wrong and didn't get a fair trial, you're not ready to be 194 00:15:57,863 --> 00:16:00,723 punished yet. but notice, I've now make some 195 00:16:00,723 --> 00:16:04,357 controversial claims here. Some people might say that doing 196 00:16:04,357 --> 00:16:08,116 something wrong is not really necessary for being punishable. 197 00:16:08,116 --> 00:16:12,859 Sometimes, we ought to punish people even when they didn't do something wrong. 198 00:16:12,859 --> 00:16:16,864 So, when you get into the moral realm, it's going to be a little more 199 00:16:16,864 --> 00:16:19,760 controversial and that shouldn't be surprising. 200 00:16:19,760 --> 00:16:24,810 In any case, the main point here is that we're trying to understand the claims 201 00:16:24,810 --> 00:16:30,265 that are being made and in particular to distinguish the claim that something is 202 00:16:30,265 --> 00:16:33,970 sufficient from the claim that, that thing is necessary, 203 00:16:33,970 --> 00:16:37,374 okay? Distinguishing sufficient conditions from 204 00:16:37,374 --> 00:16:42,951 necessary conditions is crucial because if you mess these up, you'll make all 205 00:16:42,951 --> 00:16:47,152 kinds of mistakes in arguments. So, let's do a few examples, 206 00:16:47,152 --> 00:16:53,163 a few exercises in order to be sure that you understand that before we look at the 207 00:16:53,163 --> 00:16:57,220 test for sufficient conditions and necessary conditions.