1 00:00:00,012 --> 00:00:04,183 . >> You'll remember that in the second unit 2 00:00:04,183 --> 00:00:10,135 of our course, we considered the rules that we can used to evaluate deductive 3 00:00:10,135 --> 00:00:15,789 arguments for validity. Now, Walter and I noticed that very few of 4 00:00:15,789 --> 00:00:20,286 the submitted arguments were deductive in form. 5 00:00:20,286 --> 00:00:25,461 And there's a good reason for that. Most of the arguments that we give in 6 00:00:25,461 --> 00:00:29,350 everyday life are actually not deductive arguments. 7 00:00:29,350 --> 00:00:35,395 But, there is a domain of reasoning where deductive arguments are common and useful. 8 00:00:35,395 --> 00:00:38,941 And that is in mathematics and computer science. 9 00:00:38,941 --> 00:00:44,642 In particular, in disciplines that involve a lot of precision and reasoning, we 10 00:00:44,642 --> 00:00:50,317 frequently find deductive argumnets. So we're going to look at an example of 11 00:00:50,317 --> 00:00:54,713 those in a moment. But first, I want to consider a submitted 12 00:00:54,713 --> 00:00:59,889 deductive argument that was my personal favorite submission of all. 13 00:00:59,889 --> 00:01:05,637 And that was, Rom's lecture series needs a mental health warning, submitted by 14 00:01:05,637 --> 00:01:09,865 Marjorie Forbes. Now Marjorie's argument is a deductive 15 00:01:09,865 --> 00:01:14,302 argument that has three smaller deductive arguments in it. 16 00:01:14,302 --> 00:01:17,374 Let's look at those. Okay so, premise one. 17 00:01:17,374 --> 00:01:22,565 There are over 30 million sheep in New Zealand, another 70 plus million in 18 00:01:22,565 --> 00:01:25,516 Australia, a few more in the UK, and so on. 19 00:01:25,516 --> 00:01:29,971 In short, there are many, many millions of sheep in the world. 20 00:01:29,971 --> 00:01:35,773 Now from premise one, Marjorie draws the conclusion that there are no fields large 21 00:01:35,773 --> 00:01:40,697 enough to hold all the sheep. Now, I should mention, if that conclusion 22 00:01:40,697 --> 00:01:45,638 is meant to be drawn deductively from premise one, we're going to need to add 23 00:01:45,638 --> 00:01:50,231 some more premises in there. In particular, we're going to need to add 24 00:01:50,231 --> 00:01:53,682 premises about the largest fields that there are. 25 00:01:53,682 --> 00:01:58,953 And we're going to need to add premises about the smallest condensation of sheep 26 00:01:58,953 --> 00:02:02,642 that we can arrange within a particular field, right? 27 00:02:02,642 --> 00:02:07,384 So, for instance, if you could condense each sheep down to a tiny little size, 28 00:02:07,384 --> 00:02:12,246 then you might be able to fit them in any number of fields that exist right now. 29 00:02:12,246 --> 00:02:16,668 But, given that you can't do that, and given the fields that exist on the Earth 30 00:02:16,668 --> 00:02:20,505 right now, there are no fields large enough to hold all the sheep. 31 00:02:20,505 --> 00:02:25,011 So I think if we add a couple extra premises into that first step, then the 32 00:02:25,011 --> 00:02:30,336 first deductive argument, the first of the three deductive arguments in Marjorie's 33 00:02:30,336 --> 00:02:35,700 overall argument, is going to be sound. It's going to be sound because the premise 34 00:02:35,700 --> 00:02:37,605 is true. I looked into it. 35 00:02:37,605 --> 00:02:43,663 And the conclusion is going to follow from the premise, plus a couple of the other 36 00:02:43,663 --> 00:02:49,448 premises I mentioned, that we're going to have to add in about the limited size of 37 00:02:49,448 --> 00:02:55,144 fields on the Earth right now, and about the limits to how tightly you can pack 38 00:02:55,144 --> 00:02:59,832 sheep into a field. Okay, so the first of Marjorie's three 39 00:02:59,832 --> 00:03:04,791 deductive arguments is sound, not just valid, but also sound. 40 00:03:04,791 --> 00:03:10,086 Now, how about the second one? Well, she says, I can see sheep. 41 00:03:10,086 --> 00:03:15,476 I take her word for it. Therefore, there are definitely sheep. 42 00:03:15,476 --> 00:03:21,932 Now, valid, or not valid? Well, it depends on how you use the verb, 43 00:03:21,932 --> 00:03:26,002 to see. Sometimes we use the verb, to see, as 44 00:03:26,002 --> 00:03:32,808 what's called a success term. You can't see something that isn't there. 45 00:03:32,808 --> 00:03:39,054 If I say, oh, I saw Stacy in the office this morning, you could rightly object to 46 00:03:39,054 --> 00:03:44,229 me, on one interpretation of see, you couldn't have seen Stacy. 47 00:03:44,229 --> 00:03:47,226 She wasn't there. She was home in bed. 48 00:03:47,226 --> 00:03:51,126 But sometimes, we use the verb, to see, in a broader sense. 49 00:03:51,126 --> 00:03:56,708 Sometimes we use the verb, to see when we say that someone sees pink elephants, 50 00:03:56,708 --> 00:03:59,843 let's say, when they've had too much to drink. 51 00:03:59,843 --> 00:04:04,905 Or Macbeth saw a dagger when he was hallucinating early on in the Shakespeare 52 00:04:04,905 --> 00:04:09,172 play that bore his name. When we use see in that sense, it doesn't 53 00:04:09,172 --> 00:04:14,189 follow from the fact that you can see sheep that there are definitely sheep. 54 00:04:14,189 --> 00:04:19,200 But if we're using sheep in the narrower of those two senses, as a success term, 55 00:04:19,200 --> 00:04:23,037 then it does follow. From the premise that you can see sheep, 56 00:04:23,037 --> 00:04:26,117 it does follow that there are definitely sheep. 57 00:04:26,117 --> 00:04:31,081 And so, using the verb, to see, in that narrower sense, if it's true that Marjorie 58 00:04:31,081 --> 00:04:35,135 can see sheep, then it definitely follows that there are sheep. 59 00:04:35,135 --> 00:04:42,314 Okay, so the second of her three deductive arguments is also valid, at least on one 60 00:04:42,314 --> 00:04:48,658 interpretation of the verb, to see. And if her premise is true, it's also 61 00:04:48,658 --> 00:04:52,237 sound. But is Marjorie three for three? 62 00:04:52,238 --> 00:04:57,911 I'm afraid not. Consider the third deductive argument. 63 00:04:57,911 --> 00:05:05,861 There's an otter at the door wearing a white coat, therefore, I need a lie down. 64 00:05:05,861 --> 00:05:12,378 Now, is that argument valid, or not? Well, if there really is an otter at the 65 00:05:12,378 --> 00:05:18,010 door wearing a white coat, what I should do is call a zoologist or call the news 66 00:05:18,010 --> 00:05:24,170 reporter, because that would be a really one-of-a-kind event, if there was an otter 67 00:05:24,170 --> 00:05:29,644 at the door, wearing a white coat. I bet it's the first time in history that 68 00:05:29,644 --> 00:05:33,923 an otter has been at a person's door wearing a white coat. 69 00:05:33,924 --> 00:05:38,248 Well, maybe not the first time. Maybe some practical joker has arranged it 70 00:05:38,248 --> 00:05:41,697 to happen in the past. But it would be a very rare event, that 71 00:05:41,697 --> 00:05:45,050 there would be an otter at the door wearing a white coat. 72 00:05:45,051 --> 00:05:49,507 From the fact that there's an otter at the door wearing a white coat, nothing 73 00:05:49,507 --> 00:05:52,048 whatsoever follows about what I need to do. 74 00:05:52,048 --> 00:05:54,654 In fact, it doesn't even follow that I exist. 75 00:05:54,654 --> 00:05:59,040 There might be an otter at the door wearing a white coat, even though I've 76 00:05:59,040 --> 00:06:03,143 been vaporized a minute ago. And so, there's an otter at the doorway 77 00:06:03,143 --> 00:06:07,168 wearing a white coat, but it doesn't follow that I need a lie down. 78 00:06:07,168 --> 00:06:11,718 It doesn't follow that I need anything, because it's consistent with there being 79 00:06:11,718 --> 00:06:15,813 an otter at the doorway wearing a white coat that I don't even exist. 80 00:06:15,813 --> 00:06:23,541 But, if we interpret statement five as expressing not a fact, as reporting not a 81 00:06:23,541 --> 00:06:31,380 fact, but rather as reporting a belief that Marjorie has, then we can understand 82 00:06:31,380 --> 00:06:36,067 this argument as much stronger. Here's what I mean. 83 00:06:36,067 --> 00:06:40,990 Suppose it seems to me as if there's an otter at the door wearing a white coat. 84 00:06:40,990 --> 00:06:45,792 Or suppose I believe that there's an otter at the door wearing a white coat. 85 00:06:45,792 --> 00:06:51,342 Well, if I'm in either of those two psychological states, if it seems to me as 86 00:06:51,342 --> 00:06:57,150 if there's an otter at the door wearing a white coat, or if I believe that there's 87 00:06:57,150 --> 00:07:03,046 an otter at the door wearing a white coat, then I shouldn't call a zoologist, and I 88 00:07:03,046 --> 00:07:09,410 shouldn't call a news reporter. I should call a psychiatrist, because I 89 00:07:09,410 --> 00:07:14,333 need help. So, if premise five reports a fact, then 90 00:07:14,333 --> 00:07:19,432 nothing whatsoever about me follows from that fact. 91 00:07:19,432 --> 00:07:23,831 But if premise five reports a psychological state that I'm in, let's 92 00:07:23,831 --> 00:07:28,913 say, it's appearing to me as if there's an otter at the door, or my believing that 93 00:07:28,913 --> 00:07:33,838 there's an otter at the door. If premise five reports a psychological 94 00:07:33,838 --> 00:07:38,942 state that I'm in, then it might very well follow, from my being in that 95 00:07:38,942 --> 00:07:43,202 psychological state, that I need to call a psychiatrist. 96 00:07:43,202 --> 00:07:47,743 I need to lie down. I need to have my guns taken away from me, 97 00:07:47,743 --> 00:07:52,834 and so on and so forth. So, of the three arguments, the first one 98 00:07:52,834 --> 00:07:58,576 is not just valid but also sound. The second one, if the verb, to see, is 99 00:07:58,576 --> 00:08:04,750 interpreted in the narrow sense, where it's a success verb, then the second 100 00:08:04,750 --> 00:08:10,727 argument is definitely valid. And, if Marjorie can see sheep, it's also 101 00:08:10,727 --> 00:08:14,581 sound. The third argument unfortunately, not 102 00:08:14,581 --> 00:08:19,429 sound and not valid. And the reason why it's not valid is 103 00:08:19,429 --> 00:08:26,021 because, from the fact that there's an otter at the door wearing a white coat, 104 00:08:26,021 --> 00:08:31,582 nothing whatsoever follows about me. Because I might not even exist if there's 105 00:08:31,582 --> 00:08:36,572 an otter at the door wearing a white coat. But I think what Marjorie might have had 106 00:08:36,572 --> 00:08:41,382 in mind when she wrote premise five, was, it seems to me as if there's an otter at 107 00:08:41,382 --> 00:08:45,728 the door wearing a white coat. And from that premise, that it seems to me 108 00:08:45,728 --> 00:08:49,962 as if there is an otter at the door wearing a white coat, then something 109 00:08:49,962 --> 00:08:54,684 definitely does follow about me. Of course, nothing can seem to me to be 110 00:08:54,684 --> 00:08:59,181 any way, unless I do exist. And if something seems to me to be a 111 00:08:59,181 --> 00:09:03,751 particularly strange way, then that suggests that I need help. 112 00:09:03,751 --> 00:09:09,537 So, if premise five was intended to say it seems to me, or I believe there's an otter 113 00:09:09,537 --> 00:09:15,147 at the door wearing a white coat, then that premise really does support, though 114 00:09:15,147 --> 00:09:20,332 it's not clear to me at all that it entails, but it does support that I need a 115 00:09:20,332 --> 00:09:23,732 lie down. So, I want to thank Marjorie for one of 116 00:09:23,732 --> 00:09:28,391 the few deductive argument submissions that we got in the posts. 117 00:09:28,391 --> 00:09:33,140 And now, I want to consider another deductive argument submission.