1 00:00:00,012 --> 00:00:04,912 In the last lecture, we talked about paradoxes of vagueness. 2 00:00:04,912 --> 00:00:11,744 Arguments that involve vague expressions that are apparently valid, the argument 3 00:00:11,744 --> 00:00:17,706 is apparently valid, and yet the premises are all apparently true, and the 4 00:00:17,706 --> 00:00:22,546 conclusion is apparently false. So, something is wrong with that 5 00:00:22,546 --> 00:00:25,133 argument. Either the argument contrary to 6 00:00:25,133 --> 00:00:30,223 appearences is not valid or the premises contrary to appearances are not all true 7 00:00:30,223 --> 00:00:33,622 or the conclusion contrary to appearances is not false. 8 00:00:33,622 --> 00:00:37,540 Today, we're not going to be talking about paradoxes of vagueness. 9 00:00:37,540 --> 00:00:40,725 We'll be talking about fallacies of vagueness. 10 00:00:40,725 --> 00:00:46,601 That's to say, bad arguments, arguments that are clearly bad that result from the 11 00:00:46,601 --> 00:00:51,350 use of vague expressions, but with these fallacies, we can explain, 12 00:00:51,350 --> 00:00:56,466 we already know how to explain what's wrong with the argument. 13 00:00:56,466 --> 00:01:01,495 Today, in particular, we'll be looking at three fallacies of vagueness, 14 00:01:01,495 --> 00:01:07,087 these are all different versions of what sometimes called a slippery slope 15 00:01:07,087 --> 00:01:10,622 argument. We're going to talk about conceptual 16 00:01:10,622 --> 00:01:15,276 slippery slope arguments, causal slippery slope arguments, and 17 00:01:15,276 --> 00:01:20,262 fairness slippery slope arguments. These are three arguments, all of them 18 00:01:20,262 --> 00:01:25,456 are bad and all of them result from the careless use of vague expressions. 19 00:01:25,456 --> 00:01:30,821 Let's start by talking about what we'll call a conceptual slippery slope 20 00:01:30,821 --> 00:01:35,070 argument. Now, in order to illustrate a conceptual 21 00:01:35,070 --> 00:01:41,558 slippery slope argument, I've drawn a picture here of my children's playroom. 22 00:01:41,558 --> 00:01:45,714 I'll explain to you what the different things are. 23 00:01:45,714 --> 00:01:52,743 This is my daughter's piano, right there, these are the shelves that their various 24 00:01:52,743 --> 00:01:59,241 toys and books are supposed to be on, and these things, right here are their 25 00:01:59,241 --> 00:02:04,391 various toys and books. Now, suppose I were to walk into this 26 00:02:04,391 --> 00:02:08,773 room one day on a typical day when it looks like this. 27 00:02:08,773 --> 00:02:13,305 I would tell my kids to clean up their room, to make it neat. 28 00:02:13,305 --> 00:02:16,985 Now, my kids are young and compliant as it is right now, 29 00:02:16,985 --> 00:02:22,320 and so, they would do what I tell them, but eventually, they won't be so young, 30 00:02:22,320 --> 00:02:27,111 and they won't be so compliant. And at that point, I can expect that they 31 00:02:27,111 --> 00:02:31,950 will offer the following argument in response to my enjoinder to clean up 32 00:02:31,950 --> 00:02:36,594 their room. They'll say, anyhow if they've studied 33 00:02:36,594 --> 00:02:40,114 some logic, they'll say, dad. Look, 34 00:02:40,114 --> 00:02:45,235 suppose we were to take any one of these toys or books, 35 00:02:45,235 --> 00:02:49,995 this one let's say, and, put it up on that shelf, 36 00:02:49,995 --> 00:02:57,336 would that improve our room? No, our room would still be as uninhabitable 37 00:02:57,336 --> 00:03:02,951 then as it is now. Suppose we were to take another one of 38 00:03:02,951 --> 00:03:07,204 these toys or books, this one let's say, 39 00:03:07,204 --> 00:03:13,874 and put it up on that shelf, would that improve our room? No, our room 40 00:03:13,874 --> 00:03:17,914 would still be as unihabitable as it is now. 41 00:03:17,914 --> 00:03:25,072 And what this shows is that you can't improve a room by simply taking one toy 42 00:03:25,072 --> 00:03:30,342 or book from the floor and putting it where it belongs. 43 00:03:30,342 --> 00:03:35,733 The room remains in a state of uninhabitability, 44 00:03:35,733 --> 00:03:42,584 even if you take one toy or book and put it back where it belongs. 45 00:03:42,584 --> 00:03:49,212 Now, right now, our room is in a state of uninhabitability, 46 00:03:49,212 --> 00:03:53,830 but you can't take it from being in a state of uninhabitability. 47 00:03:53,830 --> 00:03:58,984 You can't make it habitable by putting one toy or book where it belongs. 48 00:03:58,984 --> 00:04:04,244 So, even if we were to follow your instructions by putting one toy or book 49 00:04:04,244 --> 00:04:09,772 onto the shelf, and then putting another toy or book onto the shelf, and then 50 00:04:09,772 --> 00:04:15,742 putting another toy or book onto the shelf, it wouldn't change our room from a 51 00:04:15,742 --> 00:04:20,312 state of unhabitability to a state of habitability. 52 00:04:20,312 --> 00:04:27,190 So dad, following your directions would make no difference to the habitability of 53 00:04:27,190 --> 00:04:31,280 our room. That's what I imagine they'll be saying 54 00:04:31,280 --> 00:04:39,873 to me in a few years. Now, let's consider that argument for a 55 00:04:39,873 --> 00:04:46,338 moment. Premise one, the room is now 56 00:04:46,338 --> 00:04:51,712 uninhabitable. Premise two, 57 00:04:51,712 --> 00:05:24,740 you can't turn an uninhabitable room into a habitable one by picking up one thing. 58 00:05:24,740 --> 00:05:52,112 So the conclusion is picking up, things won't change the habitability of our 59 00:05:52,112 --> 00:05:59,339 room. Now, this argument looks a lot like one 60 00:05:59,339 --> 00:06:09,352 of the paradoxes of vagueness that we considered in the last lecture, but here 61 00:06:09,352 --> 00:06:16,057 is the difference. In this argument, premise two is not as 62 00:06:16,057 --> 00:06:23,539 obviously true as the second premise in the paradoxes of vagueness. 63 00:06:23,539 --> 00:06:31,147 In particular, if you think of habitability or uninhabitability as a 64 00:06:31,147 --> 00:06:37,646 matter of degree, then you can see where premise two goes wrong. 65 00:06:37,646 --> 00:06:45,731 Because, you can't turn a less habitable room into a slightly more habitable room 66 00:06:45,731 --> 00:06:52,132 by picking up one thing. If habitability is a matter of degree, 67 00:06:52,132 --> 00:06:56,909 then, we can see how premise two could be false. 68 00:06:56,909 --> 00:07:05,341 You can't make a somewhat uninhabitable room somewhat more habitable by picking 69 00:07:05,341 --> 00:07:10,912 up one thing. See, when we were using terms that seemed 70 00:07:10,912 --> 00:07:14,562 not to be a matter of degree, like bald for instance, 71 00:07:14,562 --> 00:07:18,012 either someone's bald or they're not bald or heap, 72 00:07:18,012 --> 00:07:21,162 either something is a heap or it's not a heap. 73 00:07:21,162 --> 00:07:26,712 In those cases, it might seem that there is no boundary line where you cross from 74 00:07:26,712 --> 00:07:31,862 being not bald into being bald or no boundary line where you cross from being 75 00:07:31,862 --> 00:07:36,142 not a heap into being a heap. But when we're dealing with something 76 00:07:36,142 --> 00:07:40,706 that's a matter of degree like habitability, then, you can change the 77 00:07:40,706 --> 00:07:43,842 degree of the relevant quantity by doing just one thing, 78 00:07:43,842 --> 00:07:49,040 like picking up one thing off the floor and putting it on the shelf. 79 00:07:49,040 --> 00:07:54,244 So in this case, the argument that they are giving, while valid, is only 80 00:07:54,244 --> 00:07:58,868 superficially sound. It's not really sound because premise two 81 00:07:58,868 --> 00:08:04,047 of that argument is not really true and that's why it's a bad argument. 82 00:08:04,047 --> 00:08:08,172 Not because it's not valid, but because it's not sound. 83 00:08:08,172 --> 00:08:12,806 The second premise is not true because they're taking a matter of degree and 84 00:08:12,806 --> 00:08:15,572 treating it like it's not a matter of degree. 85 00:08:15,572 --> 00:08:19,476 So that's an example of a conceptual slippery slope argument. 86 00:08:19,476 --> 00:08:24,314 A conceptual slippery slope argument is an argument to the effect that a series 87 00:08:24,314 --> 00:08:29,263 of particular actions can't change the quality of the thing that we're concerned 88 00:08:29,263 --> 00:08:31,821 with, but typically, the problem with 89 00:08:31,821 --> 00:08:37,030 conceptual slippery slope arguments is that the second premise that they use, 90 00:08:37,030 --> 00:08:41,968 the premise that has this form is false because it takes something that's a 91 00:08:41,968 --> 00:08:46,166 matter of degree and treats it like it's not a matter of degree, 92 00:08:46,166 --> 00:08:50,552 like it's an either/or. So that's the conceptual slippery slope 93 00:08:50,552 --> 00:08:53,977 argument. Now, let's talk about the other kinds of 94 00:08:53,977 --> 00:08:58,502 slippery slope argument. We just talked about conceptual slippery 95 00:08:58,502 --> 00:09:03,227 slope arguments, and now, I want to turn to what we're going to call causal 96 00:09:03,227 --> 00:09:07,727 slippery slope arguments. A causal slippery slope argument is an 97 00:09:07,727 --> 00:09:12,949 argument concerning the effects of a possible course of action. 98 00:09:12,949 --> 00:09:19,113 Let me give you an example. Suppose I propose introducing a bill into 99 00:09:19,113 --> 00:09:24,182 our state legislature. A bill that would ban people from 100 00:09:24,182 --> 00:09:31,302 carrying military style arms, like say, bazookas or nuclear weapons 101 00:09:31,302 --> 00:09:37,501 onto college campuses. Now, I realize this bill is going to be 102 00:09:37,501 --> 00:09:44,434 received as a radical abrogation of freedom in many parts of the United 103 00:09:44,434 --> 00:09:48,912 States. And I can imagine a legislator saying the 104 00:09:48,912 --> 00:09:52,774 following thing, if you don't allow people to carry 105 00:09:52,774 --> 00:09:58,895 bazookas and nuclear weapons onto college campuses, what's the next thing that's 106 00:09:58,895 --> 00:10:03,588 going to happen? Well, the next thing that's going to happen is that 107 00:10:03,588 --> 00:10:09,264 legislators like you are going to try to take away our freedom to bring AK-47s 108 00:10:09,264 --> 00:10:14,654 onto college campuses and what happens after that? Well, before you know it, 109 00:10:14,654 --> 00:10:19,994 we're not going to be allowed to bring any machine guns onto college campuses. 110 00:10:19,994 --> 00:10:25,410 And before you know it, then, legislators are going to take away all our freedoms 111 00:10:25,410 --> 00:10:29,567 altogether. Okay? 112 00:10:29,567 --> 00:10:37,042 So, wow does this argument go? It goes, 113 00:10:37,042 --> 00:10:49,840 if this happens, namely we pass a bill denying people the right to carry 114 00:10:49,840 --> 00:10:57,256 bazookas or nuclear arms onto college campuses. 115 00:10:57,256 --> 00:11:20,272 If that happens, then some further thing of an even more radical nature will 116 00:11:20,272 --> 00:11:27,001 happen. And the argument is a series of premises, 117 00:11:27,001 --> 00:11:33,481 each one of which has this form. If the course of action that you're 118 00:11:33,481 --> 00:11:39,800 considering takes place, if you do this thing, then, some further 119 00:11:39,800 --> 00:11:44,597 thing of an even more radical nature will happen. 120 00:11:44,597 --> 00:11:50,772 If you pass this bill, prohibiting people from carrying bazookas and nuclear 121 00:11:50,772 --> 00:11:56,202 weapons onto college campuses, then imagine what will happen next. 122 00:11:56,202 --> 00:12:02,197 What will happen next is that some bill will pass prohibiting students from 123 00:12:02,197 --> 00:12:08,000 carrying AK-47s into their classrooms and what happens if a bill is passed 124 00:12:08,000 --> 00:12:14,065 prohibiting students from carrying AK-47s into their classrooms? Well, next thing 125 00:12:14,065 --> 00:12:18,654 you know, no machine guns will be allowed on college campuses. 126 00:12:18,654 --> 00:12:24,742 And if that happens, then next thing you know, we won't have any freedoms at all. 127 00:12:24,742 --> 00:12:31,615 So the conclusion of the argument is a conclusion to the effect that if we 128 00:12:31,615 --> 00:12:36,312 pursue the course of action that you're proposing, 129 00:12:36,312 --> 00:12:42,452 then the eventual end result will be a loss of all of our freedoms. 130 00:12:42,452 --> 00:12:48,732 That's the form that the conclusion takes and the premises all take this form right 131 00:12:48,732 --> 00:12:51,670 here. They all take the form of saying, 132 00:12:51,670 --> 00:12:56,338 if we pursue the course of action that you're considering now, 133 00:12:56,338 --> 00:13:01,367 then some further thing of an even more radical nature will result. 134 00:13:01,367 --> 00:13:08,022 And each premise takes that same form and describes a further thing of an even more 135 00:13:08,022 --> 00:13:13,790 and more and more radical nature untill we get something of an unacceptably 136 00:13:13,790 --> 00:13:17,874 radical nature, like the loss of all of our freedoms. 137 00:13:17,874 --> 00:13:22,542 Now, that's an example of a causal slippery slope argument. 138 00:13:22,542 --> 00:13:28,277 And again, the argument is valid, there's no possible way that the premises could 139 00:13:28,277 --> 00:13:33,767 all be true, while the conclusion is false or in any case, the argument can be 140 00:13:33,767 --> 00:13:38,517 designed so as to be valid. There's no obstacle to such an argument 141 00:13:38,517 --> 00:13:44,030 being valid, but the problem with the argument is typically not that it's 142 00:13:44,030 --> 00:13:50,869 invalid but rather that it's unsound, that one or more of the premises taking 143 00:13:50,869 --> 00:13:55,663 this form is not true. So suppose we do pass a bill that 144 00:13:55,663 --> 00:14:03,422 prohibits students from carrying bazookas or nuclear weapons onto college campuses? 145 00:14:03,422 --> 00:14:10,337 Is that really going to result in a prohibition against carrying AK-47s onto 146 00:14:10,337 --> 00:14:16,852 college campuses? Not necessarily. I have to tell you, I don't see it. 147 00:14:16,852 --> 00:14:24,292 Just because students aren't allowed to carry bazookas and nuclear weapons onto 148 00:14:24,292 --> 00:14:30,315 college campuses doesn't mean that some further thing of an even more radical 149 00:14:30,315 --> 00:14:34,982 nature like prohibiting them from carrying AK-47s onto college campuses 150 00:14:34,982 --> 00:14:39,123 would result from that. I mean, maybe, legislatures would just 151 00:14:39,123 --> 00:14:43,696 stop at prohibiting the use of bazookas and nuclear weapons or even the 152 00:14:43,696 --> 00:14:48,363 possession of bazookas and nuclear weapons on college campuses and they 153 00:14:48,363 --> 00:14:52,542 wouldn't proceed to anything of an even more radical nature. 154 00:14:52,542 --> 00:14:58,587 They would still allow students to carry AK-47s onto college campuses as they 155 00:14:58,587 --> 00:15:02,583 pleased, so long as they were licensed of course. 156 00:15:02,583 --> 00:15:08,967 So, typically, the problem with a causal slippery slope argument is not that it's 157 00:15:08,967 --> 00:15:15,482 invalid but rather that it's unsound because one or more premises of this form 158 00:15:15,482 --> 00:15:18,571 is not true. So far, we've talked about conceptual 159 00:15:18,571 --> 00:15:22,506 slippery slope arguments and causal slippery slope arguments. 160 00:15:22,506 --> 00:15:27,194 Now, I'd like to talk about a third kind of slippery slope argument that we'll 161 00:15:27,194 --> 00:15:29,848 call the fairness slippery slope argument. 162 00:15:29,848 --> 00:15:34,712 We call it the fairness slippery slope argument, because it's a kind of argument 163 00:15:34,712 --> 00:15:40,457 that's typically given in the service of showing that a particular policy is fair 164 00:15:40,457 --> 00:15:43,772 or unfair. Let me give you an example that hits 165 00:15:43,772 --> 00:15:48,177 pretty close to home. See, although I teach at the University 166 00:15:48,177 --> 00:15:53,217 of North Carolina at Chapel Hill, my family and I live in Durham, North 167 00:15:53,217 --> 00:15:56,618 Carolina. The city next door to Chapel Hill. 168 00:15:56,618 --> 00:16:02,020 we live right by Duke University. Now there are many nice things about 169 00:16:02,020 --> 00:16:06,994 living close to Duke University. Unfortunately, it means living in 170 00:16:06,994 --> 00:16:13,461 proximity to a lot of people who attend Duke University and part of the problem 171 00:16:13,461 --> 00:16:19,495 with that has to do with their taste for heavy metal music. 172 00:16:19,495 --> 00:16:27,137 You see, a lot of Duke students love to play their heavy metal music at a very 173 00:16:27,137 --> 00:16:32,594 high volume and this presents us with a predictable challenge. 174 00:16:32,594 --> 00:16:36,732 On the one hand, we like to sleep at night when we can. 175 00:16:36,732 --> 00:16:42,917 On the other hand, we have to consider the rights of our Duke student neighbors, 176 00:16:42,917 --> 00:16:49,305 they like to play their loud heavy metal. They like to play their loud heavy metal 177 00:16:49,305 --> 00:16:54,589 music, we like to sleep. What's a fairer solution? Well, some of 178 00:16:54,589 --> 00:16:59,985 our Duke student neighbors have been inclined to argue as follows. 179 00:16:59,985 --> 00:17:05,729 It's fair to allow neighbors to play their music at 50 decibels, that's a 180 00:17:05,729 --> 00:17:11,241 totally reasonably volume. Right now, I am probably speaking to you 181 00:17:11,241 --> 00:17:15,522 in a volume that's maybe a little over 50 decibels. 182 00:17:15,522 --> 00:17:21,437 Allowing your neighbors to play their music at 50 decibels, that's certainly 183 00:17:21,437 --> 00:17:25,016 fair. There should be no legal restrictions on 184 00:17:25,016 --> 00:17:30,782 playing your music at 50 decibels. Now, adding a single decibel of volume, 185 00:17:30,782 --> 00:17:36,890 could that change the fairness of the arrangement? Could it be fair to allow 186 00:17:36,890 --> 00:17:42,750 your neighbor to play their music at 50 decibels, but not at 51 decibels? 187 00:17:42,750 --> 00:17:48,494 It hardly seem right, I mean, after all, the human ear probably can't even 188 00:17:48,494 --> 00:17:53,714 distinguish 50 decibals from 51 decibals. If I were to play those two volumes to 189 00:17:53,714 --> 00:17:58,693 you, the same sound of both of those two volumes, you probably couldn't tell which 190 00:17:58,693 --> 00:18:01,239 was which because they're so close together. 191 00:18:01,239 --> 00:18:05,704 If you can't discriminate between 50 decibels and 51 decibels, then the 192 00:18:05,704 --> 00:18:10,696 difference between 50 decibals and 51 decibels can't possibly make a difference 193 00:18:10,696 --> 00:18:16,859 to whether it's fair to allow your neighbors to play music at that volume. 194 00:18:16,859 --> 00:18:23,677 But if adding a single decibel doesn't change the fairness of the arrangement, 195 00:18:23,677 --> 00:18:30,261 then it's going to be fair to allow your neighbors to play their music at 51 196 00:18:30,261 --> 00:18:32,991 decibels. And again, if adding a single decibel 197 00:18:32,991 --> 00:18:36,912 doesn't change the fairness of the arrangement, it's going to be fair to 198 00:18:36,912 --> 00:18:40,101 allow your neighbors to play their music at 52 decibels. 199 00:18:40,101 --> 00:18:44,171 And again, if adding a single decibel doesn't change the fairness of the 200 00:18:44,171 --> 00:18:48,365 arrangement, then it's going to be fair to allow your neighbors to play their 201 00:18:48,365 --> 00:18:55,377 music at 53 decibals, and so on. But if that's all true, then it's got to 202 00:18:55,377 --> 00:19:02,096 be fair to play, to allow your neighbors to play their music at 150 decibals, 203 00:19:02,096 --> 00:19:10,285 which is the volume of a loud which is the volume of a loud airplane, 204 00:19:10,285 --> 00:19:18,031 so, that doesn't seem right, and yet, it seems to follow from these two premises. 205 00:19:18,031 --> 00:19:26,192 Once again, we have an apparently valid argument from apparently true premises, 206 00:19:26,192 --> 00:19:33,760 for a conclusion which while it might be approved by many of our Duke student 207 00:19:33,760 --> 00:19:38,627 neighbors, my family and I would regard as false. 208 00:19:38,627 --> 00:19:42,992 So, what should we say about this argument? 209 00:19:42,992 --> 00:19:51,566 Well, again, the thing to say about this argument is that since fair in it's 210 00:19:51,566 --> 00:20:00,299 ordinary usage is a vague expression. What we need to do is give it a precise 211 00:20:00,299 --> 00:20:05,566 definition. [SOUND] A precise definition would make 212 00:20:05,566 --> 00:20:09,894 premise to talse. It would make premise two false, because 213 00:20:09,894 --> 00:20:14,795 if we define the fairness of this situation precisely, if we said there's a 214 00:20:14,795 --> 00:20:20,061 precise decibel level and it's fair to allow your neighbors to play their music 215 00:20:20,061 --> 00:20:25,158 at or below that decibel level but not above that decibel level, if we define 216 00:20:25,158 --> 00:20:30,570 fairness precisely in that way, then, premise two would be false and so 217 00:20:30,570 --> 00:20:34,642 this argument, while valid would be unsound. 218 00:20:34,642 --> 00:20:41,462 So, we need a way to define fairness for this situation precisely, and we have a 219 00:20:41,462 --> 00:20:44,942 way of doing that. It's called the law. 220 00:20:44,942 --> 00:20:52,431 The law can define ordinary concepts, like fairness, in a precise way, or 221 00:20:52,431 --> 00:20:59,023 anyhow, precisely enough so as to falsify premises like this. 222 00:20:59,023 --> 00:21:07,434 According to the law, there is an upper level of noise that people are allowed to 223 00:21:07,434 --> 00:21:11,932 make. Making any more noise than that is unfair 224 00:21:11,932 --> 00:21:15,517 to your neighbors. Less noise is fine. 225 00:21:15,517 --> 00:21:22,742 So, the law is an instrument for making precise some of the vague concepts that 226 00:21:22,742 --> 00:21:27,902 we use in ordinary life, vague concepts like fairness, 227 00:21:27,902 --> 00:21:32,996 and by making those concepts precise in their application to particular 228 00:21:32,996 --> 00:21:38,111 situations, we can avoid bad arguments like the kind that my family and I 229 00:21:38,111 --> 00:21:43,373 frequently find ourselves confronted with by our intelligent Duke student 230 00:21:43,373 --> 00:21:46,658 neighbors. Today we've studied some of the fallacies 231 00:21:46,658 --> 00:21:51,292 of vagueness, the bad arguments that typically result from the use of vague 232 00:21:51,292 --> 00:21:54,552 expressions. These are all slippery slope arguments 233 00:21:54,552 --> 00:21:59,204 and they've come in three forms that we've considered, conceptual slippery 234 00:21:59,204 --> 00:22:04,140 slope arguments, causal slippery slope arguments, and fairness Slippery slope 235 00:22:04,140 --> 00:22:07,253 arguments. In the next lecture, we're going to 236 00:22:07,253 --> 00:22:12,493 consider fallacies that arise from the incautious use of other expressions, 237 00:22:12,493 --> 00:22:17,986 ambiguous expressions, expressions that carry with them more than one meaning. 238 00:22:17,986 --> 00:22:19,138 See you next time.