1 00:00:00,012 --> 00:00:07,169 Today we're going to talk about a second way in which you can refute an argument. 2 00:00:07,169 --> 00:00:14,480 The second way of refuting an argument is something that we would call reductio ad 3 00:00:14,480 --> 00:00:19,209 absurdum. What is reductio ad absurdum? Let me give 4 00:00:19,209 --> 00:00:24,585 you an example. Contrary to what most people believe, it 5 00:00:24,585 --> 00:00:32,196 is actually impossible for a person to walk from 1 location to another location. 6 00:00:32,196 --> 00:00:38,004 Let me explain why. Imagine that this is the distance between 7 00:00:38,004 --> 00:00:42,650 any two locations. Now suppose a person starts at this 8 00:00:42,650 --> 00:00:48,723 location right here and they want to walk over to the location over here. 9 00:00:48,723 --> 00:00:54,361 How are they going to do that? Well in order to do that they first have 10 00:00:54,361 --> 00:01:00,425 to traverse half of that distance. But, in order to traverse half of that 11 00:01:00,425 --> 00:01:04,371 distance. They first have to traverse half of that 12 00:01:04,371 --> 00:01:10,302 distance or a quarter of the total. But in order to do that, they first have 13 00:01:10,302 --> 00:01:15,092 to traverse half of that distance, or an eighth of the total. 14 00:01:15,092 --> 00:01:21,981 And in order to do that they first have to transverse half of that distance or a 15 00:01:21,981 --> 00:01:27,179 16th of the total. Now notice, this process could go on and 16 00:01:27,179 --> 00:01:33,092 on indefinitely before they can pass through any distance at all. 17 00:01:33,092 --> 00:01:39,187 They have to pass through half that distance, and that goes on forever, so no 18 00:01:39,187 --> 00:01:44,447 one can ever get started. Since no one can ever get started, no one 19 00:01:44,447 --> 00:01:50,837 can ever traverse any distance at all, and so, it's impossible, for any person, 20 00:01:50,837 --> 00:01:54,917 to walk from any one location, to any other location. 21 00:01:54,917 --> 00:02:01,585 Quid est demonstrandum. What you just witnessed, was an example, 22 00:02:01,585 --> 00:02:07,759 of a reducteo ad absurdam. I was giving an argument for a particular 23 00:02:07,759 --> 00:02:12,768 conclusion. The conclusion that it's impossible, for 24 00:02:12,768 --> 00:02:17,932 any person to walk from one location to another location. 25 00:02:17,932 --> 00:02:22,796 And then, someone proved, simply by walking from one location to another 26 00:02:22,796 --> 00:02:26,549 location, that the conclusion of my argument was false. 27 00:02:26,549 --> 00:02:31,635 The conclusion of my argument had to be false since someone actually did walk 28 00:02:31,635 --> 00:02:36,647 from one location to another location. In a reductio ad absurdum you refute 29 00:02:36,647 --> 00:02:41,882 someones argument by showing that the conclusion of that argument is false. 30 00:02:41,882 --> 00:02:48,327 But what does that tell you that the conclusion of someone's argument is 31 00:02:48,327 --> 00:02:52,197 false. Well it could tell you one of two things. 32 00:02:52,197 --> 00:02:58,946 Either the argument is not valid or if the argument is valid then 1 or more of 33 00:02:58,946 --> 00:03:02,537 the premises must be false. Here's why. 34 00:03:02,537 --> 00:03:06,265 If the argument. What that means is that there's no 35 00:03:06,265 --> 00:03:10,900 possible way for all of the premises of that argument to be true while the 36 00:03:10,900 --> 00:03:14,775 conclusion is false. But if the conclusion is false, and the 37 00:03:14,775 --> 00:03:19,623 argument is valid than that means that there's no possible way for all of the 38 00:03:19,623 --> 00:03:24,142 premises of that argument to be true. So one or more of the premises. 39 00:03:24,142 --> 00:03:28,079 Must be false. Now in the argument that I was giving a 40 00:03:28,079 --> 00:03:33,973 moment ago for the false conclusion that it's impossible for any person to walk 41 00:03:33,973 --> 00:03:40,110 from one location to another location, is it clear that one or more of the premises 42 00:03:40,110 --> 00:03:43,527 I was using was false? Well, no, it's not. 43 00:03:43,527 --> 00:03:48,957 Because I wasn't entirely explicit about what premises I was using. 44 00:03:48,957 --> 00:03:54,077 I was sneaky about that. So until I make explicit what premises I 45 00:03:54,077 --> 00:04:00,932 was using just the fact that you can do a reductio ad absurdum of my argument 46 00:04:00,932 --> 00:04:05,407 doesn't tell you whether any of the premises I was using was false. 47 00:04:05,407 --> 00:04:09,957 Maybe all of the premises were true, but the argument wasn't valid. 48 00:04:09,957 --> 00:04:15,307 The argument afforded some way of having all the premises be true, even when the 49 00:04:15,307 --> 00:04:19,320 conclusion is false. So, until we see the argument laid out 50 00:04:19,320 --> 00:04:24,513 more carefully, we can't tell from the fact that the conclusion of the argument 51 00:04:24,513 --> 00:04:29,683 is false, whether that shows that one or more of the premises of the argument is 52 00:04:29,683 --> 00:04:32,853 false. One of the useful things about laying out 53 00:04:32,853 --> 00:04:37,827 arguments carefully, is that then, when you find out that the conclusion is 54 00:04:37,827 --> 00:04:41,662 false, that can tell you what lessons you should learn. 55 00:04:41,662 --> 00:04:44,914 About the truth or false hood of the premises. 56 00:04:44,914 --> 00:04:50,212 Let's try to be more careful in spelling out the argument that I gave for the 57 00:04:50,212 --> 00:04:55,227 conclusion that it's impossible for anyone to traverse any distance by 58 00:04:55,227 --> 00:05:03,473 walking. So, one way of spelling out that argument 59 00:05:03,473 --> 00:05:11,672 is like this, premise, there is no distance. 60 00:05:11,672 --> 00:05:33,542 That can be traversed first before traversing any other distance. 61 00:05:33,542 --> 00:05:57,526 And it might seem that from that premise I concluded there is no distance that can 62 00:05:57,526 --> 00:06:07,728 be traversed at all. Now, stated that way the argument seems 63 00:06:07,728 --> 00:06:16,557 clearly invalid. So, from the fact that the conclusion is 64 00:06:16,557 --> 00:06:20,248 false. We don't learn anything, about the truth 65 00:06:20,248 --> 00:06:24,675 or falsehood, of the premise. The premise could be true, or it could be 66 00:06:24,675 --> 00:06:27,528 false. In fact, as it happens, the premise is 67 00:06:27,528 --> 00:06:29,892 true. There is no distance that can be 68 00:06:29,892 --> 00:06:33,059 traversed, before traversing any other distance. 69 00:06:33,059 --> 00:06:37,618 because no matter what distance you traverse, you first have to traverse half 70 00:06:37,618 --> 00:06:40,162 of it. Alright, so the premise is true. 71 00:06:40,162 --> 00:06:44,868 But the conclusion is false, and that shows that the argument is invalid. 72 00:06:44,868 --> 00:06:50,050 So the fact that someone was able to do a reductio ad absurdem of the conclusion of 73 00:06:50,050 --> 00:06:54,777 this argument doesn't tell us anything about the truth or falsehood of the 74 00:06:54,777 --> 00:06:59,625 premise that I used in this argument. But there are other arguments that are 75 00:06:59,625 --> 00:07:06,878 valid And so when someone is able to do a reductio ad absurdum of their conclusion, 76 00:07:06,878 --> 00:07:11,895 that does show that one or more of the premises is false. 77 00:07:11,895 --> 00:07:18,567 Let me give you an example of those. Suppose someone says to you, I am lying 78 00:07:18,567 --> 00:07:23,151 to you right now. Now, you might make the following 79 00:07:23,151 --> 00:07:27,234 argument. Premise. 80 00:07:27,234 --> 00:07:49,712 Every statement is either true or false. And from that generalization. 81 00:07:49,712 --> 00:08:15,092 It follows that the particular statement that you just heard is either. 82 00:08:15,092 --> 00:08:21,458 True or false. But the particular statement that you 83 00:08:21,458 --> 00:08:28,202 just heard is the statement, I am lying to you right now. 84 00:08:28,202 --> 00:08:36,386 Now, this is a valid argument. The argument from the premise 1 to the 85 00:08:36,386 --> 00:08:41,270 conclusion 2. But is the conclusion 2 true? Well 86 00:08:41,270 --> 00:08:47,680 consider again the statement you just heard: I'm lying to you right now. 87 00:08:47,680 --> 00:08:53,484 Is that statement either true or false? Well, suppose it's true. 88 00:08:53,484 --> 00:09:00,532 So when the person said, I'm lying to you right now, what they were saying to you 89 00:09:00,532 --> 00:09:07,541 Was true, but if what they were saying to you was true, then they weren't lying to 90 00:09:07,541 --> 00:09:12,098 you right now. But if they weren't lying to you right 91 00:09:12,098 --> 00:09:16,482 now, then what they were saying to you, was false. 92 00:09:16,482 --> 00:09:20,442 But if what they were saying to you was false. 93 00:09:20,442 --> 00:09:28,405 Then the rule line to you right now and so what they were saying to you was true. 94 00:09:28,405 --> 00:09:36,368 So if that statement is true then it must be false, and if its false then it must 95 00:09:36,368 --> 00:09:43,389 be true So, it can't be either true or false, because if it's one, it has to be 96 00:09:43,389 --> 00:09:50,877 the other as well, and that's impossible. A statement can't be both true and false. 97 00:09:50,877 --> 00:09:58,007 So, their statement, I am lying to you right now, can't be either true or false. 98 00:09:58,007 --> 00:10:03,693 It's got to be neither. But if their statement, I am lying to you 99 00:10:03,693 --> 00:10:10,470 right now is neither true nor false, then the conclusion of this argument right 100 00:10:10,470 --> 00:10:16,981 here conclusion two is false and, if conclusion two is false, then since the 101 00:10:16,981 --> 00:10:23,157 argument from one to two is a valid argument, the premise one Must also be 102 00:10:23,157 --> 00:10:28,952 false because there's no way for a valid argument to be one in which the premise 103 00:10:28,952 --> 00:10:34,332 is false and the conclusion true. So premise 1 is false and we just proved 104 00:10:34,332 --> 00:10:39,292 it's false by doing the reductio ad adsurdum on the conclusion 2. 105 00:10:39,292 --> 00:10:44,890 Now so far in this lecture we've looked at two different reductio ad absurdum 106 00:10:44,890 --> 00:10:47,985 arguments. The first one was very simple. 107 00:10:47,985 --> 00:10:53,394 It was a reductio ad absurdum that consisted in someone's walking from one 108 00:10:53,394 --> 00:10:59,063 point to another, thereby proving That the conclusion of the argument that I was 109 00:10:59,063 --> 00:11:02,747 giving was false. They proved it just by walking from one 110 00:11:02,747 --> 00:11:06,553 point to another. That's all they needed to do to prove it. 111 00:11:06,553 --> 00:11:11,126 But the other reductio ad absurdum argument, that we just considered a 112 00:11:11,126 --> 00:11:13,626 moment ago. Was much more elaborate. 113 00:11:13,626 --> 00:11:18,768 It consisted in an argument to the effect that, if a statement that you just heard, 114 00:11:18,768 --> 00:11:22,411 I'm lying to you right now, is true, then it must be false. 115 00:11:22,411 --> 00:11:27,120 And if it's false, then it must be true. So it can't be either true or false, 116 00:11:27,120 --> 00:11:30,122 because if it were either one, it would have to. 117 00:11:30,122 --> 00:11:34,718 To be both, and that's impossible. Now that's a more complicated argument. 118 00:11:34,718 --> 00:11:38,527 That isn't as simple as just walking from one place to another. 119 00:11:38,527 --> 00:11:42,872 So sometimes giving a reductio ad absurdem argument can be very simple. 120 00:11:42,872 --> 00:11:46,279 It can be as simple as walking from one place to another. 121 00:11:46,279 --> 00:11:51,027 Other times, it can be very complicated. It can involve lots of steps Also, 122 00:11:51,027 --> 00:11:56,602 Reductio ad absurdum arguments sometimes don't tell us anything about the truth of 123 00:11:56,602 --> 00:12:01,527 the premises of the arguments, whose conclusions they prove to be false. 124 00:12:01,527 --> 00:12:06,952 That was the case in our first argument. We didn't learn anything about the truth 125 00:12:06,952 --> 00:12:11,927 of the premises I was using in my argument, because the argument, itself, 126 00:12:11,927 --> 00:12:15,577 wasn't valid. All we learned was that the conclusion, 127 00:12:15,577 --> 00:12:19,611 itself, was false. But we didn't learn whether the premises 128 00:12:19,611 --> 00:12:22,818 were false. But sometimes reductio out of certain 129 00:12:22,818 --> 00:12:27,758 arguments can teach us that the premises of the argument whose conclusion was 130 00:12:27,758 --> 00:12:32,940 proven to be false are themselves false. That's a case where we can prove that the 131 00:12:32,940 --> 00:12:38,193 conclusion of a valid argument is false. If the argument is valid, then a reductio 132 00:12:38,193 --> 00:12:41,907 of its conclusion. Discredits its premises because there's 133 00:12:41,907 --> 00:12:46,729 no way that the premises could be true if the conclusion is false and the argument 134 00:12:46,729 --> 00:12:49,817 is valid. So reductio ad absurdum arguments come in 135 00:12:49,817 --> 00:12:53,260 different kinds. Some are simple, some are complicated, 136 00:12:53,260 --> 00:12:58,189 some tell us something about the truth of the premises of the argument that they're 137 00:12:58,189 --> 00:13:02,837 targeting and some don't. But in all cases, reductio ad absurdum, 138 00:13:02,837 --> 00:13:08,202 can be an effective tool for refuting someone's argument, for showing that 139 00:13:08,202 --> 00:13:13,572 someone's argument doesn't succeed, doesn't succeed in demonstrating the 140 00:13:13,572 --> 00:13:18,057 truth of its conclusion. In the next lecture, we'll talk about 141 00:13:18,057 --> 00:13:21,962 straw men and false dichotomies. These are pitfalls. 142 00:13:21,962 --> 00:13:25,248 That can befall any attempt at reductio ad abusrdum. 143 00:13:25,248 --> 00:13:29,042 And these are also ways of refuting someone else's argument. 144 00:13:29,042 --> 00:13:31,043 We'll talk about those next time.