1 00:00:02,840 --> 00:00:08,068 Perhaps the most common kind of inductive argument is called an inference to the 2 00:00:08,068 --> 00:00:11,748 best explanation. And to understand this kind of argument 3 00:00:11,748 --> 00:00:16,718 we need to think way back to the first week when we discussed the difference 4 00:00:16,718 --> 00:00:21,882 between justification and explanation. If somebody uses an argument to justify a 5 00:00:21,882 --> 00:00:27,175 conclusion then they're trying to give a reason to believe that the conclusion is 6 00:00:27,175 --> 00:00:29,693 true. And maybe you didn't believe that 7 00:00:29,693 --> 00:00:35,269 conclusion before you heard the argument. But if somebody gives an argument. 8 00:00:35,269 --> 00:00:39,480 To explain, the conclusion. Then they're taking it for granted, that 9 00:00:39,480 --> 00:00:43,883 the thing they're explaining is true. An they're trying to, understand. 10 00:00:43,883 --> 00:00:47,264 Why it's true. An the argument is supposed to help us 11 00:00:47,264 --> 00:00:52,602 understand, why it's true. The weird thing about an inference to the 12 00:00:52,602 --> 00:00:56,199 best explanation is it really combines these two. 13 00:00:56,199 --> 00:01:01,997 It uses the argument to justify belief in the conclusion, that is to give you a 14 00:01:01,997 --> 00:01:07,869 reason to believe that it's true, and yet a premise of the argument is that, that 15 00:01:07,869 --> 00:01:12,660 conclusion explains a phenomenon that you took for granted. 16 00:01:12,660 --> 00:01:16,358 Inferences to the best explanation are extremely common. 17 00:01:16,358 --> 00:01:21,047 For example, almost every detective story uses an inference to the best 18 00:01:21,047 --> 00:01:23,615 explanation. Just imagine that there are three 19 00:01:23,615 --> 00:01:26,018 suspects. And you know that one of those three 20 00:01:26,018 --> 00:01:29,361 suspects must have done it. Because the door wasn't jimmied open. 21 00:01:29,361 --> 00:01:31,920 So, whoever got into the room must have had a key. 22 00:01:31,920 --> 00:01:34,271 And there are only three people who had keys. 23 00:01:34,271 --> 00:01:36,987 But one of'em couldn't have been the one who did it. 24 00:01:36,987 --> 00:01:40,904 Because she has really small feet. And the footprints outside the door were 25 00:01:40,904 --> 00:01:43,307 really large and so it couldn't have been her. 26 00:01:43,307 --> 00:01:47,329 And the second person couldn't have done it because they have an alibi on the 27 00:01:47,329 --> 00:01:50,724 other side of the town. So it must have been the third person who 28 00:01:50,724 --> 00:01:54,121 did it. You notice what you did is, you can't 29 00:01:54,121 --> 00:01:59,120 explain why the door wasn't jimmied by the person who got in. 30 00:01:59,120 --> 00:02:03,313 Because. there were no marks, and that means that 31 00:02:03,313 --> 00:02:07,554 the best explanation, that must be that the person that did it, had a key. 32 00:02:07,554 --> 00:02:11,855 And the best explanation why the footprints were so large, is that it was 33 00:02:11,855 --> 00:02:16,450 a large person who wore large shoes. And the best explanation of why the alibi 34 00:02:16,450 --> 00:02:21,116 would place the person on the other side of town was that they were being honest. 35 00:02:21,116 --> 00:02:25,606 Assuming it's not their brother or they're not the kind of person who would 36 00:02:25,606 --> 00:02:28,855 lie, or so on. So the best explanation of why the jewels 37 00:02:28,855 --> 00:02:33,463 are missing from the room, or why there's a dead body in the room, is that this 38 00:02:33,463 --> 00:02:38,399 third suspect is the one who did it. So all the, detective stories work like 39 00:02:38,399 --> 00:02:41,373 that. It's almost always an inference to the 40 00:02:41,373 --> 00:02:45,260 best explanation. The best explanation is, he's the one who 41 00:02:45,260 --> 00:02:48,217 did it. One implication of this, is that no 42 00:02:48,217 --> 00:02:53,689 matter what Sherlock Holmes says, the form of reasoning that he was using was 43 00:02:53,689 --> 00:02:57,100 inductive reasoning, not deduction, as he claimed. 44 00:02:57,100 --> 00:03:01,840 It's not only detective novels. It's also science abuses inference to the 45 00:03:01,840 --> 00:03:05,347 best explanation. Take for example the greatest murder 46 00:03:05,347 --> 00:03:08,270 mystery in history. What killed the dinosaurs? 47 00:03:08,270 --> 00:03:12,240 Well some people think that mammals eating their eggs, 48 00:03:12,240 --> 00:03:16,137 not a chance. That doesn't explain why they were also 49 00:03:16,137 --> 00:03:21,578 mass extensions in the oceans, where the mammals weren't eating their eggs. 50 00:03:21,578 --> 00:03:25,770 Well some people think that, the best explanation is that. 51 00:03:25,770 --> 00:03:30,239 There were big volcanic eruptions in Southern India. 52 00:03:30,239 --> 00:03:37,202 That seems pretty unlikely too, because the volcanoes that we know didn't put out 53 00:03:37,202 --> 00:03:42,360 enough material to kill things all the way around the world. 54 00:03:42,360 --> 00:03:48,544 So, they think of the best explanation of what killed the dinosaurs is that a giant 55 00:03:48,544 --> 00:03:51,971 meteor hit in the Yucatan Peninsula, in Mexico. 56 00:03:51,971 --> 00:03:57,560 And that produced lots of soot in the atmosphere that killed the dinosaurs. 57 00:03:57,560 --> 00:04:02,302 As well as many other species at the time but luckily, not mammals. 58 00:04:02,302 --> 00:04:05,823 And so, we now have a best explanation in science. 59 00:04:05,823 --> 00:04:09,129 And a lot a scientific theories work that way. 60 00:04:09,129 --> 00:04:14,590 As a matter of fact, the point of most scientific theories is to provide, the 61 00:04:14,590 --> 00:04:17,896 best explanation of the experimental data. 62 00:04:17,896 --> 00:04:22,280 that has been observed by scientists throughout the world. 63 00:04:23,296 --> 00:04:28,936 And of course, we also use inference of best explanation in our everyday lives, 64 00:04:28,936 --> 00:04:32,335 to try to figure out what's going on around us. 65 00:04:32,335 --> 00:04:35,227 Here's an example. Whoa, what was that. 66 00:04:35,227 --> 00:04:40,300 A drop of water just hit my head. There must be a leak in the roof. 67 00:04:40,300 --> 00:04:43,778 Now that is an inference to the best explanation. 68 00:04:43,778 --> 00:04:47,753 Starts with an observation, of the water hitting my head. 69 00:04:47,753 --> 00:04:51,586 Then I think about, why the water would be coming down. 70 00:04:51,586 --> 00:04:57,193 And the best explanation I can come up with, is that there's a leak in the roof. 71 00:04:57,193 --> 00:05:00,530 So I conclude that there is a leak in the roof. 72 00:05:00,530 --> 00:05:06,103 Notice that this argument uses an explanation but it runs in the opposite 73 00:05:06,103 --> 00:05:11,978 direction from an ordinary explanation. In an explanation, the premises explain 74 00:05:11,978 --> 00:05:17,100 the conclusion and the conclusion describes the phenomenon that was 75 00:05:17,100 --> 00:05:20,715 observed. When there is a leak in the roof, water 76 00:05:20,715 --> 00:05:25,234 drops through the roof. When water comes through the roof, it 77 00:05:25,234 --> 00:05:29,000 drops onto whatever is in its way. I am in its way. 78 00:05:29,000 --> 00:05:36,280 Therefore, water drops onto me. This explains that. 79 00:05:36,280 --> 00:05:42,026 In contrast, an inference to the best explanation works in the opposite 80 00:05:42,026 --> 00:05:45,425 direction. The conclusion is what does the 81 00:05:45,425 --> 00:05:49,553 explaining. The premises are what get explained, and 82 00:05:49,553 --> 00:05:54,976 the point is to justify belief in the conclusion, not to explain it. 83 00:05:54,976 --> 00:05:59,913 Water drops onto me. Leak in the roof might explain why water 84 00:05:59,913 --> 00:06:03,879 drops onto me? No better explanation is available. 85 00:06:03,879 --> 00:06:07,920 Therefore, there must be a leak in the roof. 86 00:06:07,920 --> 00:06:14,211 Notice that the conclusion of the left argument is a premise, of the right 87 00:06:14,211 --> 00:06:18,463 argument. And, the conclusion of the right argument 88 00:06:18,463 --> 00:06:22,034 is part of a premise, of the left argument. 89 00:06:22,034 --> 00:06:26,742 So, the form is different. The function is different as well. 90 00:06:26,742 --> 00:06:32,207 In the explanation on the left we start out already knowing that the conclusion 91 00:06:32,207 --> 00:06:35,486 is true. In the interest to the best explanation 92 00:06:35,486 --> 00:06:40,473 on the right, we argue that the conclusion is probably true because it is 93 00:06:40,473 --> 00:06:45,060 the best explanation of the observation in the first premise. 94 00:06:45,060 --> 00:06:50,801 That's why we call it an inference to the best explanation. 95 00:06:50,801 --> 00:06:54,012 Is this argument valid? Yes or no? 96 00:06:54,012 --> 00:07:00,142 Right, it's not valid. Because it's possible for the premises to 97 00:07:00,142 --> 00:07:06,661 be true and the conclusion false. Now does it's invalidity make the 98 00:07:06,661 --> 00:07:08,900 argument bad? Yes or no? 99 00:07:09,940 --> 00:07:13,828 Right. It does not make it bad, because an 100 00:07:13,828 --> 00:07:19,020 inductive argument can be good, even if it's invalid. 101 00:07:19,020 --> 00:07:26,285 The next question's a bit trickier. Remember that an argument is defeasible 102 00:07:26,285 --> 00:07:31,128 if further information can make the argument weak. 103 00:07:31,128 --> 00:07:35,100 So, is this argument defeasible? Yes or no? 104 00:07:36,340 --> 00:07:40,398 Right. It is defeasible because further 105 00:07:40,398 --> 00:07:44,768 information could make this argument weak. 106 00:07:44,768 --> 00:07:49,555 So what? Does its defeasibility mean that this 107 00:07:49,555 --> 00:07:56,319 argument was weak even before we got that additional information? 108 00:07:56,319 --> 00:07:58,100 Yes or no? No. 109 00:07:58,100 --> 00:08:05,011 Because inductive arguments can be strong, even though they are defeasible. 110 00:08:05,011 --> 00:08:12,110 So now we know that this argument is invalid, and is defeasible but it still 111 00:08:12,110 --> 00:08:14,445 might be strong and good.