1 00:00:00,012 --> 00:00:07,640 We've been talking about fallacies that result from the use of expressions that 2 00:00:07,640 --> 00:00:12,468 are vague. In other words, that signify something 3 00:00:12,468 --> 00:00:18,299 without precise boundaries. Now I want to talk about a different kind 4 00:00:18,299 --> 00:00:21,934 of fallacy, fallacies that result from the use of 5 00:00:21,934 --> 00:00:26,359 expressions that are not necessarily vague but ambigious. 6 00:00:26,359 --> 00:00:32,194 To say that an expression is ambigious is to say that it has different meanings, 7 00:00:32,194 --> 00:00:37,162 and there are 2 kinds of ambiguity that I want to distinguish. 8 00:00:37,162 --> 00:00:42,951 We'll call them semantic ambiguity and syntactic ambiguity. 9 00:00:42,951 --> 00:00:48,016 Let me start off by talking about semantic ambiguity. 10 00:00:48,016 --> 00:00:55,647 Semantic ambiguity is a kind of ambiguity that results when a single word means 11 00:00:55,647 --> 00:01:00,411 more than one thing. Consider the word bank. 12 00:01:00,411 --> 00:01:07,790 If I say Jill went down to the bank, I could mean two different things. 13 00:01:07,790 --> 00:01:15,338 I could mean Jill went down to the financial institution, or I could mean 14 00:01:15,338 --> 00:01:22,592 Jill went down to the edge of the river, because the word bank in English can mean 15 00:01:22,592 --> 00:01:28,150 either of those two things. It can mean a financial institution, or 16 00:01:28,150 --> 00:01:34,180 it can mean the edge of the river. Another example is if I say John became a 17 00:01:34,180 --> 00:01:38,663 cardinal. The word cardinal, in English, can be 18 00:01:38,663 --> 00:01:45,049 used to mean different things. It can be used to mean, rank in the 19 00:01:45,049 --> 00:01:49,645 Catholic hierarchy, just below the rank of pope, 20 00:01:49,645 --> 00:01:55,539 or it can be used to mean a baseball team that plays for St. 21 00:01:55,539 --> 00:01:59,666 Louis, or it can be used to mean a particular 22 00:01:59,666 --> 00:02:05,573 kind of bird, a red bird. So when I say John became a Cardinal, I 23 00:02:05,573 --> 00:02:13,042 could mean he was promoted to the rank of Cardinal from the rank of Archbishop, 24 00:02:13,042 --> 00:02:16,857 or I could mean that he was recruited to play for the St. 25 00:02:16,857 --> 00:02:20,597 Louis Cardinals. Or I could mean that he was magically 26 00:02:20,597 --> 00:02:25,617 turned from a person into a red bird. I've just given you some examples of 27 00:02:25,617 --> 00:02:30,435 words that are semantically ambiguous, that have multiple meanings, 28 00:02:30,435 --> 00:02:35,817 words like cardinal or bank. Another example of such a word is the 29 00:02:35,817 --> 00:02:40,317 word odd. Odd could mean strange, and it could also 30 00:02:40,317 --> 00:02:45,642 mean indivisible by two. An odd number is a number that's not 31 00:02:45,642 --> 00:02:50,677 divisible by two. Now here's an example of how the 32 00:02:50,677 --> 00:02:58,542 ambiguity in the word odd, the semantic ambiguity of odd, can give rise to a 33 00:02:58,542 --> 00:03:02,172 fallacy. Consider this argument. 34 00:03:02,172 --> 00:03:07,302 Premise 1, 6 is an odd number of legs for a horse. 35 00:03:07,302 --> 00:03:12,482 Most horses have four. Premise two. 36 00:03:12,482 --> 00:03:22,817 Odd numbers are not divisible by two. Therefore, conclusion, six is not 37 00:03:22,817 --> 00:03:26,212 divisible by two. Now, 38 00:03:26,212 --> 00:03:32,934 that conclusion is obviously false, but is this argument valid? I mean, if 6 39 00:03:32,934 --> 00:03:39,754 is an odd number, and odd numbers are not divisible by 2, doesn't it follow that 6 40 00:03:39,754 --> 00:03:46,616 is not divisible by 2? The only way to explain what's wrong with 41 00:03:46,616 --> 00:03:55,609 this argument is to point to the ambiguity in the word odd. When the word 42 00:03:55,609 --> 00:03:59,592 odd appears in premise 1, it means, strange. 43 00:03:59,592 --> 00:04:06,332 6 is a strange number of like for a horse to have. 44 00:04:06,332 --> 00:04:09,807 It's not a normal number of legs for a horse to have. 45 00:04:09,807 --> 00:04:14,657 But, when the word odd appears in premise 2, it has a different meaning. 46 00:04:14,657 --> 00:04:19,132 It means indivisible by 2. And so of course, it's true, just by the 47 00:04:19,132 --> 00:04:24,772 definition of odd in this second meaning, that odd numbers are not divisible by 2. 48 00:04:24,772 --> 00:04:31,170 So, premise one is true, given the correct understanding of odd. 49 00:04:31,170 --> 00:04:38,752 Premise two is true given the correct understanding of odd for premise two But 50 00:04:38,752 --> 00:04:43,452 the argument is not valid because the meaning of odd in this premise is 51 00:04:43,452 --> 00:04:46,852 different from the meaning of odd in that premise. 52 00:04:46,852 --> 00:04:51,352 That's how the ambiguity in the word odd can give rise to a fallacy, 53 00:04:51,352 --> 00:04:56,137 can give rise to bad reasoning that might appear to be valid. 54 00:04:56,137 --> 00:05:02,409 In the examples of symantic ambiguity that we've looked at so far, examples 55 00:05:02,409 --> 00:05:09,063 concerning the word odd, or cardinal, or bank, you have a single word in English 56 00:05:09,063 --> 00:05:15,874 that has completely different meanings. But there are other examples of symantic 57 00:05:15,874 --> 00:05:22,573 ambiguity where a single word can mean 2 different categories, and one of those 58 00:05:22,573 --> 00:05:27,744 categories is broader than the other and includes the other. 59 00:05:27,744 --> 00:05:33,374 Let me give you an example of what I'm talking about to illustrate. 60 00:05:33,374 --> 00:05:38,462 Consider the word drug. Sometimes when we use the word drug, 61 00:05:38,462 --> 00:05:46,835 we're referring to any kind of drug whatsoever, legal or illegal, licit or 62 00:05:46,835 --> 00:05:51,858 illicit. But other times when we use the word 63 00:05:51,858 --> 00:06:00,295 drug, we're only referring to illegal or illicit drugs. So in the example that I 64 00:06:00,295 --> 00:06:06,805 just gave, one category that's signified by the word drug is broader than, and 65 00:06:06,805 --> 00:06:12,181 includes, the other category that's signified by the word drug. 66 00:06:12,181 --> 00:06:17,379 Because illicit drugs. are a subcategory of the broader category 67 00:06:17,379 --> 00:06:21,551 of all drugs. So that's a kind of semantic ambiguity, 68 00:06:21,551 --> 00:06:26,892 and that kind of semantic ambiguity can also give rise to fallacies. 69 00:06:26,892 --> 00:06:30,512 Consider this example. Premise 1, our company. 70 00:06:31,632 --> 00:06:39,962 you might say to a perspective employee, our company cannot hire drug users. 71 00:06:39,962 --> 00:06:44,751 Premise 2, Walter, you might find out, takes 72 00:06:44,751 --> 00:06:46,950 aspirin. Premise 3. 73 00:06:46,950 --> 00:06:52,142 Aspirin is a drug. And now from those 3 premises, 74 00:06:52,142 --> 00:06:59,089 it might look like you can validly conclude, our company cannot hire Walter. 75 00:06:59,089 --> 00:07:05,905 Now, that argument might look valid, because if Walter takes aspirin and 76 00:07:05,905 --> 00:07:11,298 aspirin is a drug, then it looks like Walter is a drug user. 77 00:07:11,298 --> 00:07:17,539 And if our company cannot hire drug users, then our company cannot hire 78 00:07:17,539 --> 00:07:21,946 Walter. But even though that argument might look 79 00:07:21,946 --> 00:07:23,545 valid, it's not, 80 00:07:23,545 --> 00:07:28,827 and here's why. When premise 3 says that aspirin is a 81 00:07:28,827 --> 00:07:35,032 drug, it's using the word drug to mean the broad category of drugs, 82 00:07:35,032 --> 00:07:42,902 the category that includes not just illegal or illicit drugs, but all drugs. 83 00:07:42,902 --> 00:07:49,127 But when premise 1 says, our company cannot hire drug users, presumably the 84 00:07:49,127 --> 00:07:55,607 word drug in that premise is being used to mean the narrower category of drugs, 85 00:07:55,607 --> 00:07:59,072 the category of illegal, or illicit drugs. 86 00:07:59,072 --> 00:08:05,797 So, even though this argument might look valid, it really is invalid, because the 87 00:08:05,797 --> 00:08:12,357 word drug in premise 1 means something different than, and something narrower 88 00:08:12,357 --> 00:08:18,312 than, the word drug in premise 3. The fallacious argument that we just 89 00:08:18,312 --> 00:08:24,602 considered helps us to appreciate how widespread semantic ambiguity is in our 90 00:08:24,602 --> 00:08:29,765 language. For instance, consider a variation of 91 00:08:29,765 --> 00:08:35,496 that fallacious argument. Suppose I say, premise 1, 92 00:08:35,496 --> 00:08:40,582 our company cannot hire drug users. Premise 2, 93 00:08:40,582 --> 00:08:45,412 Walter uses marijuana as a wall decoration. 94 00:08:45,412 --> 00:08:54,949 Now, from those 2 premises, it might seem that we can validly conclude our company 95 00:08:54,949 --> 00:09:01,681 cannot hire Walter. But again, this argument is invalid, 96 00:09:01,681 --> 00:09:07,002 and it's invalid because the meaning of use. 97 00:09:07,002 --> 00:09:18,562 In this premise, is the narrower than the meaning of use in this premise. 98 00:09:18,562 --> 00:09:26,627 Here in premise 1, where I say, our company cannot hire drug users, what I 99 00:09:26,627 --> 00:09:33,574 mean is our company cannot hire people who use drugs in the way that they're 100 00:09:33,574 --> 00:09:39,280 designed to be used. So for instance, people who use marijuana 101 00:09:39,280 --> 00:09:45,491 to get high or who use amphetamines to achieve a rush. 102 00:09:45,491 --> 00:09:54,969 But in premise 2, I'm using the verb use in a much more unspecific way when I say 103 00:09:54,969 --> 00:10:00,132 Walter uses marijuana as a wall decoration. 104 00:10:00,132 --> 00:10:05,500 Well, he is using it, but he's not using it in the way that 105 00:10:05,500 --> 00:10:10,926 it's designed to be used. He's using it in some other way. 106 00:10:10,926 --> 00:10:18,022 So, while it might be true that Walter uses marijuana as a wall decoration, 107 00:10:18,022 --> 00:10:25,388 that doesn't make him a drug user in the specific sense of use as is shown in 108 00:10:25,388 --> 00:10:30,059 premise 1. So he's not a drug user just by virtue of 109 00:10:30,059 --> 00:10:37,218 using marijuana as a wall decoration. So the verb to use here means something 110 00:10:37,218 --> 00:10:42,051 more specific, more narrow than what it means here. 111 00:10:42,051 --> 00:10:46,690 And so this argument, contrary to initial appearances, 112 00:10:46,690 --> 00:10:50,860 is not valid. This is another example of a fallacy that 113 00:10:50,860 --> 00:10:56,492 results from semantic ambiguity. And to see just how widespread semantic 114 00:10:56,492 --> 00:11:02,772 ambiguity is, at least in the English language, notice that every single word 115 00:11:02,772 --> 00:11:06,785 in this sentence is semantically ambiguous. 116 00:11:06,785 --> 00:11:13,927 I've just shown you how the word user is semantically ambiguous and the word drug 117 00:11:13,927 --> 00:11:18,873 is semantically ambiguous, but so too is the word hire. 118 00:11:18,873 --> 00:11:25,961 When you hire someone, do you hire them as a full-time employee, or does hiring a 119 00:11:25,961 --> 00:11:33,322 contractor count as hiring them? Cannot. What do you mean when you say our company 120 00:11:33,322 --> 00:11:40,738 cannot hire drug users? They're legally prohibited from doing so? It's physically 121 00:11:40,738 --> 00:11:47,224 impossible for them to do so? It's morally impermissible for them to do 122 00:11:47,224 --> 00:11:50,752 so? Cannot can mean different things. 123 00:11:50,752 --> 00:11:55,212 Company. What is a company? Is it a corporation, 124 00:11:55,212 --> 00:11:59,682 or is it the people that we're hanging out with, 125 00:11:59,682 --> 00:12:08,569 the people whose company we keep? And finally our, what do I mean by our? 126 00:12:08,569 --> 00:12:18,096 Our is a first person plural pronoun, but does the first person plural extend 127 00:12:18,096 --> 00:12:25,466 just to me and a few other people, or does it extend much more widely than 128 00:12:25,466 --> 00:12:32,985 that? All of these words, every single one of them, is semantically ambiguous. 129 00:12:32,985 --> 00:12:39,768 And so, each one of them can give rise to the kind of fallacy that we've described 130 00:12:39,768 --> 00:12:43,483 so far. Let's call that kind of fallacy a fallacy 131 00:12:43,483 --> 00:12:48,832 of equivocation. Now that we've looked at fallacies of 132 00:12:48,832 --> 00:12:52,842 equivocation that arise from semantic ambiguity. 133 00:12:52,842 --> 00:12:58,522 Let's look at fallacies of equivocation that arise from a different kind of 134 00:12:58,522 --> 00:13:02,062 ambiguity, a kind of ambiguity that we'll call 135 00:13:02,062 --> 00:13:06,342 syntactic ambiguity. Sometimes it's called amphiboly. 136 00:13:06,342 --> 00:13:10,587 Now the second kind of ambiguity, syntactic ambiguity, 137 00:13:10,587 --> 00:13:15,082 isn't an ambiguity in the meaning of any particular word. 138 00:13:15,082 --> 00:13:21,416 Rather, it's an ambiguity in the grammar of a whole phrase or sentence. 139 00:13:21,416 --> 00:13:26,059 Let me give you an example of what I'm talking about. 140 00:13:26,059 --> 00:13:33,125 Consider the sign that was common in the United States during World War II, that 141 00:13:33,125 --> 00:13:39,679 said Save Soap and Waste Paper. Now what does that sign mean? Well, one 142 00:13:39,679 --> 00:13:47,471 way of understanding it is as saying that we should save soap but we should waste 143 00:13:47,471 --> 00:13:52,089 paper. Now that is one way of understanding the 144 00:13:52,089 --> 00:13:58,232 sign, but it's probably not what the sign was supposed to mean. 145 00:13:58,232 --> 00:14:04,679 There's no reason why anyone would make a sign telling you to waste paper during 146 00:14:04,679 --> 00:14:08,885 wartime. So that's one interpretation of the sign, 147 00:14:08,885 --> 00:14:12,397 but it's not a very likely interpretation. 148 00:14:12,397 --> 00:14:18,451 A much likelier interpretation of the sign is that it's telling you to save 149 00:14:18,451 --> 00:14:25,121 soap, and also to save waste paper, paper that you've already used and that you 150 00:14:25,121 --> 00:14:30,280 were going to throw away. The sign is telling you not to throw it 151 00:14:30,280 --> 00:14:36,593 away, but to save it, because presumably that waste paper can be turned into 152 00:14:36,593 --> 00:14:41,782 something useful. So that's another way of interpreting the 153 00:14:41,782 --> 00:14:45,452 sign. It's telling you to save waste paper, 154 00:14:45,452 --> 00:14:50,927 but what's different between those two interpretations? The first 155 00:14:50,927 --> 00:14:57,031 interpretation, where the sign tells you to waste paper, and the second 156 00:14:57,031 --> 00:15:01,794 interpretation where the sign tells you to save waste paper. 157 00:15:01,794 --> 00:15:07,877 What's different between those two interpretations is that they each provide 158 00:15:07,877 --> 00:15:14,148 a different grammar for the sentence. The first interpretation, Save Soap and 159 00:15:14,148 --> 00:15:19,787 Waste Paper understands the verb to save as applying only to soap, 160 00:15:19,787 --> 00:15:26,736 whereas the second interpretation, Save Soap and Waste Paper, interprets the verb 161 00:15:26,736 --> 00:15:31,942 to save as applying not just to soap, but also to waste paper. 162 00:15:31,942 --> 00:15:36,612 It's not that the verb to save means something different in the two 163 00:15:36,612 --> 00:15:40,654 interpretations. The verb to save means exactly the same 164 00:15:40,654 --> 00:15:44,983 thing in the two interpretations. It's just that in the first 165 00:15:44,983 --> 00:15:48,289 interpretation, save is applied only to soap, 166 00:15:48,289 --> 00:15:54,242 and in the second interpretation, save is applied both to soap and to waste paper. 167 00:15:54,242 --> 00:15:58,030 That's the difference between the two interpretations. 168 00:15:58,030 --> 00:16:03,369 So it's a difference not in the meaning of the word save, it's a difference in 169 00:16:03,369 --> 00:16:08,271 the grammar that's assigned to the sentence by the two interpretations. 170 00:16:08,271 --> 00:16:11,435 So that's an example of syntactic ambiguity. 171 00:16:11,435 --> 00:16:14,808 Here's another example of syntactic ambiguity. 172 00:16:14,808 --> 00:16:20,822 Consider the sentence first uttered by Paul Benacerraf, as far as I know. 173 00:16:20,822 --> 00:16:26,357 Only Sons Marry Only Daughters. Now what does that sentence mean? Well, 174 00:16:26,357 --> 00:16:31,290 there are two ways of understanding what it means, at least two ways. 175 00:16:31,290 --> 00:16:37,199 One is that male children who are only children who have no siblings marry 176 00:16:37,199 --> 00:16:42,395 female children who are only children, who have no siblings. 177 00:16:42,395 --> 00:16:46,364 That's one way of understanding what it means. 178 00:16:46,364 --> 00:16:52,762 Another way of understanding what it means is that the only people who marry 179 00:16:52,762 --> 00:16:58,782 daughters are sons and the only people who marry sons are daughters. 180 00:16:58,782 --> 00:17:05,782 Those are two different interpretations of that sentence, but they don't differ 181 00:17:05,782 --> 00:17:11,703 in the meaning that they assign to the word son or daughter or marry. 182 00:17:11,703 --> 00:17:17,447 They differ in the grammar that they assign to the sentence, Only Sons Marry 183 00:17:17,447 --> 00:17:21,786 Only Daughters. On the first interpretation, only sons 184 00:17:21,786 --> 00:17:27,903 should be understood as a single phrase referring to a certain class of boys and 185 00:17:27,903 --> 00:17:33,883 only daughters should be understood as a single phrase referring to a certain 186 00:17:33,883 --> 00:17:39,474 class of girls. In the second interpretation, only, 187 00:17:39,474 --> 00:17:45,752 should be understood as applying to what follows it. 188 00:17:45,752 --> 00:17:54,752 Only sons marry only daughters, and only daughters marry only sons. 189 00:17:54,752 --> 00:18:00,192 So, the two interpretations differ, not in the meaning that they assign to any 190 00:18:00,192 --> 00:18:05,607 particular word, but in the grammar that they assign to the whole sentence. 191 00:18:05,607 --> 00:18:10,812 Those are some examples of syntactic ambiguitiy, and there are plenty of 192 00:18:10,812 --> 00:18:14,047 others. And, now I want to show how syntactic 193 00:18:14,047 --> 00:18:19,564 ambiguity can result in fallacy just as semantic ambiguity can. 194 00:18:19,564 --> 00:18:26,673 Here's an example of how a fallacy of equivocation can result from syntactic 195 00:18:26,673 --> 00:18:30,109 ambiguity. Consider this argument. 196 00:18:30,109 --> 00:18:34,705 Premise 1, this is a headline I remember seeing 197 00:18:34,705 --> 00:18:38,060 once. Police cannot stop gambling. 198 00:18:38,060 --> 00:18:42,978 Premise 2, if you cannot stop gambling, you should 199 00:18:42,978 --> 00:18:47,537 seek therapy. Now it might appear that from those two 200 00:18:47,537 --> 00:18:53,524 premises, you could validly conclude police should seek therapy, 201 00:18:53,524 --> 00:19:00,598 but in fact, that argument is not valid. That argument is a fallacy of 202 00:19:00,598 --> 00:19:09,792 equivocation, because in premise 2, when premise 2 says you can cannot stop 203 00:19:09,792 --> 00:19:16,521 gambling, what that means is if you cannot stop yourself from gambling, then 204 00:19:16,521 --> 00:19:21,276 you should seek therapy. Alright, there's no reason why you should 205 00:19:21,276 --> 00:19:26,598 seek therapy just because you are incapable of stopping other people from 206 00:19:26,598 --> 00:19:29,845 gambling. If I want to stop other people from 207 00:19:29,845 --> 00:19:35,590 gambling, but I am unable to do so, that's no reason for me to seek therapy. 208 00:19:35,590 --> 00:19:41,698 So premise 2 says if you cannot stop yourself from gambling, then you should 209 00:19:41,698 --> 00:19:45,861 seek therapy. But when premise 1 said police cannot 210 00:19:45,861 --> 00:19:52,217 stop gambling, did that premise mean the police could not stop themselves from 211 00:19:52,217 --> 00:19:57,296 gambling? I doubt it. I think it meant that the police cannot 212 00:19:57,296 --> 00:20:02,840 stop other people from gambling. Police cannot stop the practice of 213 00:20:02,840 --> 00:20:06,352 gambling from taking place in our society. 214 00:20:06,352 --> 00:20:12,462 So I think the phrase, cannot stop gambling, has a different interpretation 215 00:20:12,462 --> 00:20:18,057 in premise 1 than it does in premise 2. And now notice, even though it's a 216 00:20:18,057 --> 00:20:24,037 different interpretation for that phrase, the difference in interpretation is not 217 00:20:24,037 --> 00:20:29,692 the result of any semantic ambiguity. The word gambling means the same thing in 218 00:20:29,692 --> 00:20:34,682 the two interpretations, the word stop means the same thing in the two 219 00:20:34,682 --> 00:20:39,929 interpretations, and the word cannot means the same thing in the two 220 00:20:39,929 --> 00:20:44,641 interpretations. What differs in the two interpretations 221 00:20:44,641 --> 00:20:50,349 is not the meaning of any particular word that's used in that phrase, 222 00:20:50,349 --> 00:20:56,201 but it's the grammar of the phrase. Who is it who cannot be stopped from 223 00:20:56,201 --> 00:21:02,610 gambling, according to the phrase? Is it the police themselves, or is it someone 224 00:21:02,610 --> 00:21:08,915 else? So, premise 1 should be understood to mean that the police can't stop others 225 00:21:08,915 --> 00:21:13,247 from gambling. Premise 2, that phrase should be used to 226 00:21:13,247 --> 00:21:18,721 mean that if you cannot stop yourself from gambling, then you should seek 227 00:21:18,721 --> 00:21:22,390 therapy. And so the conclusion the police should 228 00:21:22,390 --> 00:21:27,211 seek therapy does not follow validly from those two premises. 229 00:21:27,211 --> 00:21:32,744 This argument is an example of a fallacy of equivocation that results from 230 00:21:32,744 --> 00:21:34,294 syntactic ambiguity.