1 00:00:00,012 --> 00:00:06,902 >> You'll remember that in the second unit of our course, we considered the rules 2 00:00:06,902 --> 00:00:12,473 that we can use to evaluate deductive arguments for validity. 3 00:00:12,473 --> 00:00:19,479 Now, Walter and I noticed that very few of the submitted arguments were deductive in 4 00:00:19,479 --> 00:00:25,461 form and there's a good reason for that. Most of the arguments that we give in 5 00:00:25,461 --> 00:00:29,350 everyday life are actually not deductive arguments. 6 00:00:29,350 --> 00:00:35,395 But there is a domain of reasoning where deductive arguments are common and useful. 7 00:00:35,395 --> 00:00:38,941 And that is in Mathematics and Computer Science. 8 00:00:38,941 --> 00:00:44,557 In particular, in disciplines that involve a lot of precision in reasoning, we 9 00:00:44,557 --> 00:00:50,232 frequently find deductive arguments. So, we're going to look at an example of 10 00:00:50,232 --> 00:00:54,609 those in a moment. But first, I want to consider a submitted 11 00:00:54,609 --> 00:00:59,805 deductive argument that was my personal favorite submission of all. 12 00:00:59,805 --> 00:01:05,856 And that was Ram's lecture series needs a mental health warning, submitted by 13 00:01:05,856 --> 00:01:10,089 Marjorie Forbes. Now, Marjorie's argument is a deductive 14 00:01:10,089 --> 00:01:14,301 argument that has three smaller deductive arguments in it. 15 00:01:14,301 --> 00:01:16,236 Let's look at those. Okay. 16 00:01:16,236 --> 00:01:20,017 So, premise one. There are over 30 million sheep in New 17 00:01:20,017 --> 00:01:25,202 Zealand, another 70 plus million in Australia, a few more in the UK, and so 18 00:01:25,202 --> 00:01:28,509 on. In short, there are many, many millions of 19 00:01:28,509 --> 00:01:32,808 sheep in the world. Now, from premise one, Marjorie draws the 20 00:01:32,808 --> 00:01:37,819 conclusion, that there are no fields large enough to hold all the sheep. 21 00:01:37,819 --> 00:01:43,765 Now, I should mention, if that conclusion is meant to be drawn deductively from 22 00:01:43,765 --> 00:01:48,747 premise one, we're going to need to add some more premises in there. 23 00:01:48,747 --> 00:01:53,498 In particular, we're going to need to add premises about the largest fields that 24 00:01:53,498 --> 00:01:58,389 there are, and we're going to need to add premises about the smallest condensation 25 00:01:58,389 --> 00:02:02,367 of sheet that we can arrange within a particular field, right? 26 00:02:02,367 --> 00:02:07,167 So, for instance, if you could condense each sheep down to a tiny little size, 27 00:02:07,167 --> 00:02:12,213 then you might be able to fit them into any number of fields that exist right now. 28 00:02:12,213 --> 00:02:16,503 But given that you can't do that, and given the fields that exist on the earth 29 00:02:16,503 --> 00:02:20,267 right now, there are no fields large enough to hold all the sheep. 30 00:02:20,267 --> 00:02:24,746 So, I think if we added a couple extra premises into that first step, then the 31 00:02:24,746 --> 00:02:29,787 first deductive argument, the first of the three deductive arguments in Marjorie's 32 00:02:29,787 --> 00:02:35,286 overall argument is going to be sound. It's going to be sound because the premise 33 00:02:35,286 --> 00:02:40,656 is true, I looked into it. And the conclusion is going to follow from 34 00:02:40,656 --> 00:02:46,571 the premise plus a couple of the other premises I mentioned that we're going to 35 00:02:46,571 --> 00:02:52,395 have to add in about the limited size of fields on the earth right now and about 36 00:02:52,395 --> 00:02:56,819 the limits to how tightly you can pack sheep into a field. 37 00:02:56,819 --> 00:03:02,925 Okay, so the first of Marjorie's 3 deductive arguments is sound, not just 38 00:03:02,925 --> 00:03:07,407 valid but also sound. Now, how about the second one? 39 00:03:07,407 --> 00:03:11,935 Well, she says, I can see sheep. I take her word for it. 40 00:03:11,935 --> 00:03:17,991 Therefore, there are definitely sheep. Now, valid or not valid? 41 00:03:17,991 --> 00:03:22,435 Well, it depends on how you use the verb, to see. 42 00:03:22,435 --> 00:03:28,721 Sometimes, we use the verb, to see, as what's called a success term. 43 00:03:28,721 --> 00:03:36,381 You can't see something that isn't there. If I say, oh, I saw Stacey in the office 44 00:03:36,381 --> 00:03:40,752 this morning. You could rightly object to me on one 45 00:03:40,752 --> 00:03:45,560 interpretation of see. You couldn't have seen Stacey, she wasn't 46 00:03:45,560 --> 00:03:50,040 there, she was home in bed. But sometimes, we use the verb, to see, in 47 00:03:50,040 --> 00:03:54,201 a broader sense. Sometimes, we use the verb, to see when we 48 00:03:54,201 --> 00:03:59,357 say that someone sees pink elephants. Let's say, when they've had too much to 49 00:03:59,357 --> 00:04:02,061 drink. Or Macbeth saw a dagger when he was 50 00:04:02,061 --> 00:04:06,559 hallucinating early on in the Shakespeare play that bore his name. 51 00:04:06,559 --> 00:04:11,542 When we use see in that sense, it doesn't follow from the fact that you can see 52 00:04:11,542 --> 00:04:16,901 sheep, that there are definitely sheep. But if we're using sheep in the narrower 53 00:04:16,901 --> 00:04:20,724 of those two senses as a success term, then it does follow. 54 00:04:20,724 --> 00:04:25,755 From the premise that you can see sheep, it does follow that there are definitely 55 00:04:25,755 --> 00:04:28,418 sheep. And so, using the verb, to see, in that 56 00:04:28,418 --> 00:04:33,459 narrower sense, if it's true that Marjorie can see sheep, then it definitely follows 57 00:04:33,459 --> 00:04:38,621 that there are sheep, okay? So, the second of her three deductive 58 00:04:38,621 --> 00:04:45,815 arguments is also valid at least on one interpretation of the verb to see, and if 59 00:04:45,815 --> 00:04:52,253 her premise is true, it's also sound. But is Marjorie three for three? 60 00:04:52,253 --> 00:04:57,958 I'm afraid not. Consider her third deductive argument. 61 00:04:57,958 --> 00:05:06,089 There's an otter at the door wearing a white coat, therefore, I need to lie down. 62 00:05:06,089 --> 00:05:12,442 Now, is that argument valid or not? Well, if there really is an otter at the 63 00:05:12,442 --> 00:05:18,202 door wearing a white coat, what I should do is call a zoologist or call the news 64 00:05:18,202 --> 00:05:24,142 reporter because that would be a really one of a kind event, if there was an otter 65 00:05:24,142 --> 00:05:29,649 at the door wearing a white coat. I bet it's the first time in history that 66 00:05:29,649 --> 00:05:33,949 an otter has been at a person's door wearing a white coat. 67 00:05:33,950 --> 00:05:38,792 Well, maybe not the first time, maybe some practical joker has arranged it to happen 68 00:05:38,792 --> 00:05:41,627 in the past. But it would be a very rare event that 69 00:05:41,627 --> 00:05:44,962 there would be an otter at the door wearing a white coat. 70 00:05:44,963 --> 00:05:49,419 From the fact that there's an otter at the door wearing a white coat, nothing 71 00:05:49,419 --> 00:05:51,960 whatsoever follows about what I need to do. 72 00:05:51,960 --> 00:05:54,478 In fact, it doesn't even follow that I exist. 73 00:05:54,478 --> 00:05:59,044 There might be an otter at the door wearing a white coat, even though I've 74 00:05:59,044 --> 00:06:03,604 been vaporized a minute ago, and so there's an otter at the door wearing a 75 00:06:03,604 --> 00:06:07,188 white coat, but it doesn't follow that I need to lie down. 76 00:06:07,188 --> 00:06:11,856 It doesn't follow that I need anything because it's consistent with there being 77 00:06:11,856 --> 00:06:15,892 an otter at the door wearing a white coat that I don't even exist. 78 00:06:15,892 --> 00:06:23,400 But If we interpret statement 5 as expressing not a fact, as reporting not a 79 00:06:23,400 --> 00:06:31,507 fact, but rather as reporting a belief that Marjorie has, then we can understand 80 00:06:31,507 --> 00:06:36,067 this argument as much stronger. Here's what I mean. 81 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. 82 00:06:40,990 --> 00:06:46,126 Or suppose that I believe that there is an otter at the door wearing a white coat. 83 00:06:46,126 --> 00:06:51,265 But if I'm in either of those two psychological states, if it seems to me 84 00:06:51,265 --> 00:06:56,659 that as if there is an otter at the door wearing a white coat or I believe that 85 00:06:56,659 --> 00:07:01,879 there is an otter at the door wearing a white coat, then I shouldn't call a 86 00:07:01,879 --> 00:07:05,446 zoologist and I shouldn't call a news reporter. 87 00:07:05,446 --> 00:07:10,299 I should call a psychiatrist, because I need help. 88 00:07:10,299 --> 00:07:18,170 So, if premise 5 reports a fact, then nothing whatsoever about me follows from 89 00:07:18,170 --> 00:07:22,128 that fact. But if premise 5 reports a psychological 90 00:07:22,128 --> 00:07:26,947 state that I'm in, let's say, it's appearing to me as if there's an otter at 91 00:07:26,947 --> 00:07:32,161 the door or my believing that there's an otter at the door, if premise 5 reports a 92 00:07:32,161 --> 00:07:37,375 psychological state that I'm in, then it might very well follow from my being in 93 00:07:37,375 --> 00:07:43,030 that psychological state. That I need to call a psychiatrist, I need 94 00:07:43,030 --> 00:07:49,686 to lie down, I need to have my guns taken away from me, and so on, and so forth. 95 00:07:49,686 --> 00:07:55,836 So, of the three arguments, the first one is not just valid, but also sound. 96 00:07:55,836 --> 00:08:02,341 The second one, if the verb, to see, is interpreted in the narrow sense where it's 97 00:08:02,341 --> 00:08:08,840 a success verb, then the second argument is definitely valid and if Marjorie can 98 00:08:08,840 --> 00:08:14,526 see sheep, it's also sound. The third argument, unfortunately, not 99 00:08:14,526 --> 00:08:19,429 sound and not valid. And the reason why it's not valid is 100 00:08:19,429 --> 00:08:25,918 because from the fact that there's an otter at the door wearing a white coat, 101 00:08:25,918 --> 00:08:31,942 nothing whatsoever follows about me. Because I might not even exist if there's 102 00:08:31,942 --> 00:08:37,108 an otter at the door wearing a white coat. But I think what Marjorie might have had 103 00:08:37,108 --> 00:08:42,100 in mind when she wrote premise 5, was it seems to me as if there is an otter at the 104 00:08:42,100 --> 00:08:46,232 door wearing a white coat. And that premise, that it seems to me as 105 00:08:46,232 --> 00:08:51,342 if there is an otter at the door wearing a white coat, then something definitely does 106 00:08:51,342 --> 00:08:54,993 follow about me. Of course, nothing can seem to me to be 107 00:08:54,993 --> 00:08:59,415 anyway, unless I do exist. And if something seems to me to be a 108 00:08:59,415 --> 00:09:03,826 particularly strange way, then that suggests that I need help. 109 00:09:03,826 --> 00:09:09,442 So, if premise 5 was intended to say, it seems to me, or I believe there's an otter 110 00:09:09,442 --> 00:09:14,967 at the door wearing a white coat, then that premise really does support though 111 00:09:14,967 --> 00:09:20,067 it's not clear to me at all that it entails, but it does support that I need 112 00:09:20,067 --> 00:09:23,762 to lie down. So, I want to thank Marjorie for one of 113 00:09:23,762 --> 00:09:28,366 the few deductive argument submissions that we got in the posts. 114 00:09:28,366 --> 00:09:33,115 And now, I want to consider another deductive argument submission.