Chapter Five: Specifying

Clearness and precision usually go together, though one may be clear without being precise . . . or precise without being clear. . . . Ideally, clearness is precision with due courtesy for one’s audience.

—Brand Blanshard, Four Reasonable Men

Sydney Smith once described how two women used to lean out of their windows, on opposite sides of the street, and argue with each other. “They will never agree,” he said, “for they are arguing from different premises.”

—Lionel Ruby, The Art of Making Sense

When language is not specific enough, it too often gives rise to misunderstanding. An important part of the clarifying process is specifying—that is, paraphrasing in a way that narrows the range of possible things that an expression can mean, thus increasing the clarity of the argument. Perfectly specific language is not always achievable or even desirable, but increased specificity often makes it easier to understand an argument and thus to tell whether it is sound and conversationally relevant.

5.1 Semantic Ambiguity and the Fallacy of Equivocation

Ambiguity occurs when an expression has more than one possible meaning and it is not clear which meaning is intended. We will pay special attention to two types of ambiguity: semantic and syntactic.

At the height of the American Civil War, Abraham Lincoln gave a speech that included this parable:

The shepherd drives the wolf from the sheep’s throat, for which the sheep thanks the shepherd as a liberator, while the wolf denounces him for the same act as the destroyer of liberty. . . . Plainly the sheep and the wolf are not agreed upon a definition of the word liberty; and precisely the same difference prevails today among us human creatures, even in the North, and all professing to love liberty. Hence we behold the processes by which thousands are daily passing from under the yoke of bondage, hailed by some as the advance of liberty, and bewailed by others as the destruction of all liberty.

To the slave, illustrated by the sheep, liberty means “for each man to do as he pleases with himself, and the product of his labor,” Lincoln went on to explain. But to the slaveholder, illustrated by the wolf, liberty means “for some men to do as they please with other men, and the product of other men’s labor.” In Lincoln’s parable the word liberty is an example of semantic ambiguity—that is, it is a term that has more than one plausible meaning and it is not entirely clear which is intended. A semantically ambiguous term may be also described as equivocation, since different things are being called (. . . vocation) by the same (equi . . .) name.

Ambiguity exists only when there is lack of clarity about which meaning is intended; the mere presence of a term with more than one possible meaning does not count as ambiguity if the context makes it clear which is intended. Lincoln, for example, uses the word love in his parable, a word that can have a romantic or a nonromantic meaning. The context makes it clear that the romantic meaning is not intended (we don’t love liberty in that way!), so the term love is not semantically ambiguous in this passage.

When clarifying an argument, follow this simple guideline for any sort of ambiguity: eliminate the ambiguity—by paraphrasing with terms that are not ambiguous. This assumes there is enough information in the context for you to be confident that you can apply the principle of loyalty; if not, then apply the principle of charity.

5.1.1 Lexical Ambiguity

As we have seen, semantic ambiguity most often occurs when there is more than one meaning of a term and it is unclear which is intended. When the multiple meanings are due to different definitions of the term, this sort of semantic ambiguity is sometimes termed lexical ambiguity—indicating that a lexicon, or dictionary, might define the term in more than one way.

The notorious wit Dorothy Parker, for example, was laughing at the clownish antics of another guest at a dinner party. Her companion, an overeducated snob, was disdainful. “I’m afraid I can’t join in the merriment,” he said. “I can’t bear fools.” “That’s queer,” replied Parker. “Your mother could.”

Our pleasure in her quick riposte arises at least partly because the word bear is, if only for a moment, semantically ambiguous. Two of the word’s definitions are at issue. The snob’s remark, rendered unambiguous, would be “I can’t tolerate fools.” Parker’s would be, “Your mother could give birth to them.” (If Parker had concerned herself with disambiguation, she would not be remembered today as a humorist.)

More subtle examples are easy to find. Monetary measures, for example, sometimes mean something different depending on the year—and in some economies, depending on the month or the day! A dollar today is worth less than a dollar twenty years ago; so, a statement such as “Your house is worth a million dollars” might be ambiguous if it is unclear when it was uttered. The ambiguity of such statements is eliminated with qualifiers such as ‘in 2020 dollars.’”

In “What Pragmatism Means” American philosopher William James recounts a discussion with some friends about whether one of them was going around a squirrel. The squirrel was on the trunk of a tree; as one of James’s friends circled the tree the squirrel also circled the tree, keeping itself hidden behind the tree as the man circled. His friend had gone around the tree and the squirrel was on the tree—that much was certain. But had his friend gone around the squirrel? Here is James’s solution:

“Which party is right,” I said, “depends on what you practically mean by ‘going around’ the squirrel. If you mean passing from the north of him to the east, then to the south, then to the west, and then to the north of him again, obviously the man does go around him, for he occupies these successive positions. But if on the contrary you mean being first in front of him, then on the right of him, then behind him, then on his left, and finally in front again, it is quite as obvious that the man fails to go round him, for by the compensating movements the squirrel makes, he keeps his belly turned towards the man all the time, and his back turned away. Make the distinction, and there is no occasion for any further dispute.”

The term going around is not normally ambiguous in this way, since the two ways of going around usually amount to the same thing; I doubt that any dictionary would be so precise as to offer these as alternative definitions of the term. Nevertheless, it was this subtle lexical ambiguity that was baffling James’s friends.

5.1.2 Referential Ambiguity

Semantic ambiguity sometimes occurs not because a term has more than one definition, but because it has more than one referent—that is, because there is more than one thing that might plausibly be picked out by a term. This sort of semantic ambiguity is sometimes called referential ambiguity. It is said that Croesus, the king of Lydia in the 6th century b.c., consulted the oracle at Delphi about whether to attack Cyrus and the Persians. The oracle pronounced, “If Croesus went to war with Cyrus, he would destroy a mighty kingdom.” Croesus charged ahead, was swiftly crushed by Cyrus, and returned bitterly to the oracle to complain. The ancient Greek historian Herodotus offered this analysis of the situation:

But regarding the prophecy that was given to him, Croesus should not complain about it. He should have sent and asked whether the god spoke of Croesus’s or Cyrus’s kingdom. But Croesus did not understand what was said, nor try to; so he should blame only himself now.

In the oracle’s pronouncement there was no confusion about how to define the word kingdom; but it was unclear to which kingdom it referred, and on that account the term was semantically ambiguous.^[1] (There is another term that could possibly be referentially ambiguous in the same utterance of the oracle: in he would destroy a mighty kingdom, the pronoun he could refer to Cyrus or Croesus.)

Proper names sometimes get us into the same trouble. In my graduate student days I often worked as a teaching assistant in introductory philosophy courses that enrolled hundreds of students. A professor lectured to the multitude; the teaching assistants taught the same students in smaller groups and graded their work. Early one quarter we met with the professor to coordinate our grading of an assignment. Another TA and I discovered that we had each received work from an Eloi Castro: same name, similar handwriting, similar quality of work. Aha! He was trapped in the old undergraduate trick of turning in work to more than one TA, so that he could find out who was the easier grader and switch to that TA’s section. We set out to confront him . . . only to find that there were two Eloi Castros. One name, two people who could be referred to by it, and insufficient information to make the distinction resulted in semantic ambiguity.

The English language often uses italics, underlining, or quotation marks to avoid referential ambiguities. These conventions, unfortunately, are not entirely standard and are useless in spoken English. But they can be helpful. Consider these sentences:

David Copperfield is highly entertaining.
David Copperfield is highly entertaining.

Which sentence refers to the groundbreaking illusionist? Only the second sentence can do so; this is made clear by the convention of italicizing titles but not italicizing personal names. (The first sentence, however, could still be ambiguous, since it could be the title of the Dickens book or of one of the dozen or so film adaptations.) But this convention, we have seen, is not entirely regular; underlining or quotation marks are sometimes substituted for italics, depending on the sort of title and the medium (in handwriting, for example, we normally use a combination of quotation marks and underlining; some newspapers use quotation marks exclusively).

Sometimes we wish to use words to talk about words. To do this, we must employ the word we’re talking about; for example:

Life is short.

After all, it’s only four letters. But I might express the same words to talk about life; for example:

Life is short.

After all, it’s only four score years.

The difference between these two sentences is commonly termed the use-mention distinction. Ordinarily, we use words—as in the second sentence. But when we talk about the word itself (rather than what the word talks about), then we mention it—as in the first sentence. When it is unclear which we are doing, the lack of clarity has to do with whether the word is or is not referring to itself; thus, it can count as referential ambiguity. This ambiguity is usually eliminated by the use of either italics or quotation marks to indicate the mention of a word; thus, the ambiguity occurs more often in speech than in writing. (Since in this text I am using italics rather than quotation marks to indicate that a word is being mentioned, there is still a possible ambiguity in the first sentence—you might wonder whether I mean to say that a certain word or a certain historic newsmagazine is short.)

If referential ambiguity arises because the arguer has failed to use the appropriate indicators—or because the argument is spoken, not written—then be sure to eliminate the ambiguity by introducing these conventions into your clarification of the argument. Not all referential ambiguity can be eliminated by such conventions. When necessary, supplement the ambiguous term with an unambiguous name or a definite description that uniquely picks out the intended item; for example:

For Eloi Castro, substitute The Eloi Castro who is a student of Andrew Hsu’s.
For David Copperfield, substitute The Dickens novel David Copperfield

5.1.3 Elliptical Ambiguity

“I heard you finally finished your book last summer. I never knew you were such a slow reader!” In this remark finished is, if only briefly, semantically ambiguous. But it is not because of two different definitions or because of two different things it might refer to. It is because of two possible expressions that have been omitted. At first we assume that you finished writing it and later that you finished reading it. Since such omissions are termed ellipses, this sort of confusion is best termed elliptical ambiguity. Eliminate the ambiguity by supplying the omitted expressions—instead of I finished my book last summer, write I finished reading my book last summer.

5.1.4 The Fallacy of Equivocation

Eliminating ambiguity puts you in a better position to tell whether a premise is true, since it puts you in a better position to tell what the premise means. But it can also help you avoid disasters in assessing the logic of an argument. Good logic means that the conclusion follows from the premises, quite apart from whether the premises are true. Here’s a “textbook” example, expressed in standard clarifying format.

At a glance, not only does each individual premise look plausible, but also the logic looks good—that is, it looks as though the conclusion follows from the premises. It appears as though the argument is sound. But how could a sound argument have such a silly conclusion? The answer is that the argument is not sound, but only appears to be. This appearance of soundness is created because an ambiguous expression shifts its meaning from its first use to its second use. The first premise is plausible only if man means human (i.e., “mankind”), but the second premise is plausible only if it means male. This is an example of the broad fallacy of ambiguity—when an argument appears to be successful because of an ambiguous expression that shifts in meaning. More specifically, this is the fallacy of equivocation—that is, a fallacy of ambiguity in which the ambiguity is a semantic one.

The paraphrase of the No woman is rational argument, thus, is not yet complete, because we must eliminate the ambiguity. There is no context provided for this argument, thus no way of determining exactly what the arguer means. The question I must ask, according to the principle of charity, is What paraphrase would make the argument the most reasonable? There are two ways of doing this. One way is to make the premises of the argument as reasonable as possible. Call this the reasonable-premises approach. Here is such a paraphrase (the disambiguated term is in italics):

The premises seem reasonable, but the conclusion does not follow from the premises. Eliminating the ambiguity in this way makes it clear that the argument is unsound.

The other way of doing it is to make the logic of the argument as reasonable as possible. Call this the reasonable-logic approach. You could then eliminate the ambiguity in this way:

Or you could adopt this variation:

Each of these paraphrases produces an argument that is logically successful but each has a false premise (in the former version, No woman is human; in the latter, Only males are rational).

While either the reasonable-premises or the reasonable-logic approach is acceptable, I recommend the reasonable-premises approach. Recall from Chapter 3 that one way of thinking about the principle of charity was to ask, What might I have meant if I had uttered these words? Making the premises reasonable comes closer to answering this question. I don’t offer a rigid rule here because once the ambiguity is eliminated, arguments that commit a fallacy of ambiguity will typically prove to be defective regardless of which approach is adopted. As we saw in the example above, if you disambiguate for reasonable premises, the logic will typically be ridiculously bad; but if you disambiguate for reasonable logic, the premises will typically be preposterous.

No one is fooled by the No woman is rational argument. But much subtler ones abound. Several years ago a major university was trumpeting a 25 percent increase in the size of its library holdings during a four-year interval, catapulting it to the rank of third-largest among the nation’s university libraries. Various publications reported an account that might be clarified as follows:

It seems doubtful that the university would be lying about the premises (it would be too easy for someone to publicly embarrass the school); and the conclusion apparently follows—mathematically and thus logically—from the premises. But there nevertheless is a problem; two different definitions of the term volume are being used. While browsing through the stacks of this university’s main research library, someone overheard one library worker comment to another that they had for the first time begun including free government publications in their count. If this is so, then volume is semantically ambiguous, and the argument is better clarified as follows (using the reasonable-premises approach):

With the elimination of ambiguity for both occurrences of volume, the appearance of logical success is gone.

Later in the book you will be expected to follow each clarification with a full-fledged evaluation. One important thing to note when you evaluate the logic of an argument like this is that it has committed the fallacy of equivocation.

In general, it is a good idea to be especially attentive when an argument’s premises seem plausible and the conclusion seems to follow from the premises, yet the conclusion strikes you as preposterous. There are many reasons this can happen. The preposterous conclusion might even be true! Nevertheless, in such cases look hard for a fallacy of ambiguity. It is often the culprit.

5.2 Syntactic Ambiguity and the Fallacy of Amphiboly

Newspaper columnist Jack Smith puzzled over the following passage he found in a book called The Christian Couple:

We discovered . . . that good sex doesn’t happen automatically. The pleasure and fulfillment of sex involves more than two people sleeping together in the same bed.

The columnist adds: “The question that arises, of course, is how many people does it take in a bed to make good sex?”

The phrase more than two people sleeping together in the same bed is ambiguous, but not because it includes an expression with more than one meaning. (The term sleeping together can be semantically ambiguous, but not here.) The puzzle is whether the author is saying that good sex requires more than two people or that good sex requires more than sleeping together in the same bed. The problem is strictly a grammatical one: whether more than modifies two or sleeping. This is syntactic ambiguity—the sort of ambiguity that occurs when the terms of an expression have more than one plausible grammatical relationship to one another, and when this results in lack of clarity about what the expression means. It is also called amphiboly, from a Greek word for a special net that could be cast on both sides of the boat, thereby catching twice as many fish—or meanings.

The guideline for paraphrasing syntactic ambiguity is the same as for semantic ambiguity: when there is syntactic ambiguity, and when it is possible to tell from the context what the arguer probably intended, then eliminate the ambiguity by rewriting the offending expression in an unambiguous way. Sometimes it requires only a comma or a reorganization of the phrases in the sentence. Our initial example might be paraphrased in the following way:

Pleasure and fulfillment in sex involves two people doing more than sleeping together in the same bed.

A syntactic ambiguity in the United States Constitution was the focus of much debate in the early years of the history of America. Article I, Section 8, sometimes known as the “general welfare clause,” states:

The Congress shall have power to lay and collect taxes, duties, imposts and excises, to pay the debts and provide for the common defence and general welfare of the United States.

Supporters of a strong central government argued that provide for the . . . general welfare was the object of the infinitive to . . . collect taxes. On this interpretation, taxes were to be collected, in part, to provide for the general welfare. But supporters of strong states and a weaker central government argued that provide for the . . . general welfare was simply another thing that Congress was empowered to do—it was to collect taxes, it was to pay debts, and it was to provide for the general welfare. As evidenced today by ever higher tax bills, the supporters of the first interpretation won. And they do seem to offer the more plausible interpretation of the text. Otherwise, we would expect a comma after debts and the repetition of the word to in front of provide, indicating it is the next distinct item in the series. Further, the sentence is more logical if the first part of it (about collecting taxes) is understood as providing the means to meet the objectives of the second half (about paying debts and providing for the general welfare). We could eliminate the ambiguity by rewriting it thus:

The Congress shall have power to lay and collect taxes, duties, imposts and excises, the purpose of which is to pay the debts and provide for the common defence and general welfare of the United States.

Syntactic and semantic ambiguity sometimes combine their fuzzy forces. The magazine Free Inquiry publishes advertisements in its back pages. In one issue, a page of ads includes the following:

“Free promotional albums” for Barry Publications
“Free brochure and travel directions” for Villa Vegetarian Holistic Retreat
“One free copy” of a booklet called Biblical Inerrancy
“Free information” on making homemade booklets
“Free details” on how to be “stronger, smarter, happier, richer, more confident and respected (guaranteed!)”

In their midst, there is a large ad announcing,

“FREE ATHEIST PRISONERS, Prisoner Atheist League of America. . . .”

When I first saw the ad, I momentarily took free as an adjective (as it is in all the other ads) modifying prisoners. Noticing the absurdity—why would they want to send me an atheist prisoner for free?—I shifted to seeing free as a verb—an imperative, telling the reader what to do to the prisoners—to set them free. This is syntactic ambiguity, since it has to do with lack of clarity regarding the grammatical construction of the phrase. The expression, however, is semantically ambiguous as well; when free is used here as an adjective, it is in the sense of not requiring any payment; when used here as a verb it is in the sense of enjoying personal liberty. Both ambiguities could be eliminated, of course, with a paraphrase such as this:

Liberate atheist prisoners.

When the apparent success of an argument is due to a shift in the meaning of a syntactically ambiguous expression, the argument commits the fallacy of amphiboly. You should indicate this in your evaluation of the argument.

5.3 Generality

In everyday language, terms like ambiguous, general, and vague are often used interchangeably to indicate imprecision or lack of specificity. But in this text (to avoid ambiguity, excessive generality, and unnecessary vagueness) we will for the most part use them in quite different and more precise ways.

Generality is present when a term allows for degrees. Suppose you ask your instructor how you are doing in class and she replies, “You’re doing just fine.” Fine in this case is general; for it can cover a range extending from average to superior, and there is nothing in your instructor’s reply to suggest precisely where in that range she is placing your performance.

Generality of this sort usually serves some useful everyday purpose. Bald and brown, for example, can be general in this way. If I am told to meet a bald man in a brown suit on the corner of LeConte and Westwood, I normally don’t regret not knowing precisely how many hairs he has on his head, nor the suit’s precise shade of brown expressed in the wavelength of the reflected light. Replacing the general terms with more precise ones would make the task of identification harder, not easier. So language is well served by its enormous stock of general terms. Not only is fine often general, but generality is often fine.

5.3.1 Generality and the Fallacy of Equivocation

Generality, nevertheless, can sometimes produce problems in reasoning. Consider the statement:

People who are incompatible should not live together.

Without any context we simply cannot decide whether it is true or false, due to the generality of both incompatible and live together. How incompatible? Living how intimately together? Slide both of them to one extreme and the statement is obviously true (people who can’t stand one another shouldn’t try to share their entire lives). But slide them to the other extreme and it is obviously false (people who have different personality types could still live peaceably in the same house).

So generality, as the previous example suggests, can sometimes result in semantic ambiguity. If fine can cover a range from average to superior, then it can be used to mean average and it can be used to mean superior. Those are two different meanings, and an argument whose apparent success depends on a shift from one to the other commits the fallacy of equivocation.

Generality usually does not result in semantic ambiguity. You’re doing fine typically just means You’re somewhere in the range of acceptability—I really don’t know or care where. This isn’t precise, but it is as precise as it needs to be; there aren’t two different meanings here, thus no ambiguity and no lack of clarity. Conversely, semantic ambiguity is usually the result of something other than generality (lexical, referential, or elliptical confusion for example). Suppose you describe a fabric as fine, and I’m not sure whether you mean that its quality is high or that it is closely woven and lightweight. That is semantic ambiguity of the lexical sort. The two meanings are different in kind, not merely in degree, and thus the ambiguity has nothing to do with generality.

When generality does result in semantic ambiguity, it is especially important to eliminate it. Consider Plato’s famous argument that all wrongdoing is a result of ignorance—that if we just knew more, we would never do anything wrong. Here is one way of characterizing Plato’s argument:^[2]

It is obvious that none of us wants to do evil if we know that it is evil. And, of course, to do wrong is to do evil. So, by the same token, none of us desires to do wrong if we know that it is wrong.

A preliminary clarification of the argument might look something like this.

What makes the argument seem to succeed is the generality of the term wrong. Wrong covers all of the abhorrently wrong offenses that are covered by the term evil (thus, while evil is itself general, its generality doesn’t contribute to the problem here), but it also covers less abhorrently wrong offenses, such as jaywalking and white lies, that are not encompassed by evil. We are persuaded by premise two only when we take it to mean the more extreme wrongs, but the conclusion is intended to cover the entire range of wrongs. It is plausible, then, to say that the generality of wrong results in semantic ambiguity in both 2 and C and leads the argument into the fallacy of equivocation. A much better clarification would eliminate the ambiguity, as follows:

It is now clear that the premises cannot support the conclusion—that the logic of the argument is unsuccessful.

Usually you should leave generality alone. But on those infrequent occasions when it does present a problem, and when there is information in the context that suggests a more precise way of paraphrasing it, paraphrase it so as to be more specific.

5.4 Vagueness

Suppose you are still looking for the bald man in the brown suit on the corner of LeConte and Westwood. You finally do spot a man and you wonder whether his hair is thin enough for him to count as bald; you then see that his suit is a sort of khaki color, and you wonder if it counts as brown. You could count each hair (if he would let you); that would eliminate any worry about the generality of the term bald—but that wasn’t your worry, for you would still be no closer to deciding whether he is bald. And you could measure the wavelengths of the light reflected from his suit (if you had the equipment), but you would be no closer to deciding whether the suit was brown. For the new problem we face with the terms bald and brown is not their generality, but their vagueness—that is, the lack of a strictly defined boundary between what has the property and what does not. The man is not only on the corner of two streets, but he is also on the border of two vague terms; and, given the way I have described him, the surprising result is that there may be no correct answer to whether he is bald or whether his suit is brown.

Vague terms like bald and brown can be understood as having quantitatively fuzzy borders—their borders are fuzzy because there is no precise number (which specifies either the number of hairs or the length of the light waves) that marks off items that have the property from those that do not. But other vague terms have qualitatively fuzzy borders. Terms that have nothing to do with quantities—say, game or religion—can be vague because there is no fixed set of criteria for their application. Some games have winners and losers (but then there is the “telephone game” of whispering a phrase from one person to the next to see how the phrase changes). Some games have definite rules (but then there is peek-a-boo). Some games are played for fun (but then there is professional football). Some games are social activities (but then there is solitaire). Perhaps the best we can do is list the typical criteria and then call something a game if it satisfies several of them. Games seem to have what the philosopher Wittgenstein called a “family resemblance” to one another, without having a single set of unifying conditions that applies to all games. The result is that the term game can be vague; there can be borderline cases—circus tightrope walking, for example—that don’t satisfy enough criteria to be definitely in or definitely out of the family of games.

Vagueness, like generality, exists because it can be useful; adopting terminology with more precise borders could make life difficult. First, it could make our concepts more complicated than they need to be. Consider the term skinny. The concept is easy to grasp. But what would it take to make the border between skinny and not skinny more precise? Skinniness has something to do with weight relative to height, so the more precise notion must include the notions of weight, of height, and of some formula that produces a proportional relationship between the two. We would not be able to teach our children the more precise term until they reached junior high school! Second, greater precision could make it more difficult to apply the concept. A quick glance tells you if someone is skinny (unless it is a borderline case); but measuring height and weight and calculating the ratio is hard enough to do to make you wonder whether you really care. And third, greater precision could make our concepts too rigid. A skinny person 100 years ago might not, at exactly the same height and weight, count as a skinny person today. The more precise term would have lost its value to us; but as circumstances change, so can our vague concepts.

Note that even terms that we ordinarily assume to be precise can have beneficially vague uses. A 12 1/8-inch gasket is not a foot long, and if substituted where a foot-long gasket is called for could allow leaks and lead to disaster; but no one would ever object that a 12 1/8-inch hot dog was not a foot long. In short, practicality demands vagueness.

5.4.1 How to Settle Border Disputes

Vagueness rarely needs to be eliminated when you paraphrase an argument. But it is something you should be aware of in your own reasoning. Sometimes we care very much which side of a vague border something falls on. In such cases, instead of arguing for a more precise border, it is often better to forget the border and ask the following two practical questions: Why do I care which side of the border it falls on? and, only then, What considerations directly bear on what I care about?

Suppose I am trying to establish the minimal annual income that would constitute the clear borderline for poverty. But let’s say that what I really care about—my reason for trying to establish the borderline—is whether a family should be eligible for benefits provided by a charitable foundation that I run. I can then focus entirely on the kinds of needs that the foundation wishes to satisfy and the sorts of resources the foundation has. If a fixed threshold for annual income is needed, I can decide it on that basis—say, we want to enhance early childhood education in a certain neighborhood and I conclude that we have enough money to help the families in the neighborhood with an income lower than $25,000 per year. Thus, the distracting question of a borderline for poverty simply drops out. Or suppose I am the basketball coach and am trying to decide whether a particular student trying out for my team is a good player; my problem is that he is good in some ways, not so good in others, and I can’t decide. Perhaps what I should focus on instead is whether the things he can do are things that my team needs; in that way, I can ignore the distracting question of fixing the borderline for being a good player.

5.4.2 The Fallacy of Arguing from the Heap

Vagueness normally causes no trouble unless it is exploited by one of
two fallacious styles of argumentation. One of these is the fallacy of arguing from the heap, which mistakenly concludes that, because fuzzy borders can take longer to pass, they are impassable. Here is a simple example:

If something is not a heap of sand, then adding one grain of sand will not make it a heap of sand. Therefore, no matter how many grains of sand you add, a layer of sand will not become a heap of sand.

More familiar are claims like Just one small dessert won’t make me fat and Just one white lie won’t make me a liar. The premises are true; but the tempting conclusions—No number of small desserts will make me fat; No number of white lies will make me a liar—do not follow.

The problem is the small size of the increment—a grain of sand, a small dessert, a white lie—that has been chosen. It is not large enough by itself to bridge the gap between those things that definitely are on one side of the fuzzy border and those that definitely are on the other side. It is nevertheless an increment; if something is not a heap of sand, even though adding one grain of sand may not make it a heap, it does make it more like a heap.

5.4.3 The Slippery Slope Fallacy

A second fallacy that exploits vagueness is the slippery slope fallacy; this is the fallacy of mistakenly concluding that because fuzzy borders can be harder to see, they are nonexistent. Such an argument might start with the same premise:

If something is not a heap of sand, then adding one grain of sand will not make it a heap of sand.

But now the conclusion is this:

Therefore, there is ultimately no difference between a heap of sand and a layer of sand.

Such arguments have been used to support conclusions such as There is no difference between amateurs and professionals; There is no difference between plants and animals; and There is no difference between sanity and insanity.

Suppose you are perfectly sane and for no identifiable reason become just a bit more careful about locking the doors and setting the alarms before going to bed at night. That certainly doesn’t make you insane. And if you go a step further and begin to glance on the floor of the backseat before getting into your car, there is still no reason to doubt your sanity. A slippery slope argument would conclude that, given that these small increments make no difference in your sanity, there is no difference between a sane and insane person.

The same trick used by the argument from the heap is now being exploited to a different end. An increment is chosen that is too small to bridge the gap between something that definitely has the property (say, sanity) and something that definitely does not—but this time, with the conclusion that this shows there is no difference between having it and not having it. It is, nevertheless, an increment, and it does make a difference.

5.5 Emptiness

Robespierre headed the Reign of Terror for a time during the French Revolution and sent thousands of “enemies of the state” to the guillotine. When his political opponents accused him of counting his personal enemies as enemies of the state, Robespierre responded,

I deny the accusation, and the proof is that you still live.

Dropping the attitude indicator and the argument indicator, a preliminary clarification of his argument might be this:

The clarified argument is easy to understand in the context of my introductory story. But removed from context and placed alone, the statements are empty—that is, we know how the words in them are defined, but we have no idea to what they refer. (This is a referential problem but is not referential ambiguity, since we do not have too many referents to decide among, we have too few—zero.) Who is you? What is the accusation? We must, without any context, evaluate such an argument as neither sound nor unsound but as undecidable.

The clarified argument is the argument you will evaluate. But, empty as they are, these sentences cannot be evaluated. It is probably more appropriate to call such sentences formulas rather than statements; we would have just as much information if the argument were paraphrased as follows:

A much better paraphrase would be this:

(For simplicity I have not supplied the obvious implicit premise, namely, Robespierre does not allow the enemies of the state to live.)

Whenever possible, give your paraphrased statements enough content so they can be evaluated. If the contextual information is simply not there, the worst that can happen is that you clarify it emptily and evaluate it as undecidable. Be careful not to introduce emptiness yourself when clarifying the argument.

5.6 Summary of Chapter Five

Ambiguity, generality, vagueness, and emptiness are some ways in which an argument can lack specificity. Although any lack of specificity can potentially interfere with your ability to tell whether premises are true or whether the logic of an argument is good, ambiguity is by far the most problematic and should always be eliminated, when possible, in your paraphrase.

Semantic ambiguity, or equivocation, occurs when it is not clear which of two or more meanings is intended by a term. Some varieties of semantic ambiguity are: lexical ambiguity, when the intended definition of a term is not clear; referential ambiguity, when it is not clear which item a term is intended to pick out; and elliptical ambiguity, when it is not clear which expression has been omitted. When a shift from one such meaning to another accounts for the apparent success of an argument, that argument commits the fallacy of equivocation.

Syntactic ambiguity, or amphiboly, occurs when it is unclear which of two or more grammatical constructions is intended by an expression. When a shift from one grammatical construction to another accounts for the apparent success of an argument, that argument commits the fallacy of amphiboly.

Generality is present when a term allows for degrees. It sometimes results in semantic ambiguity and in such cases should be eliminated in favor of more specific language.

Vagueness exists when there is no strictly defined boundary between what has a property and what does not; when something falls into this fuzzy area, there may be no correct answer to whether the term applies to it. Vagueness can tempt us to think that the border is either impassable (the fallacy of arguing from the heap) or nonexistent (the slippery slope fallacy). Such temptations should be resisted.

Emptiness occurs when there is not enough contextual information to allow for any judgment about whether a claim is true or false. You should be careful not to inadvertently introduce it into an argument’s clarification.

5.7 Guidelines for Chapter Five

• Eliminate lexical ambiguity by replacing or qualifying the ambiguous terms with unambiguous definitions.
• Eliminate referential ambiguity by using conventions such as italics, underlining, or quotation marks and, if necessary, by supplementing the ambiguous terms with names or definite descriptions.
• Eliminate elliptical ambiguity by supplying the omitted expression.
• If the apparent success of an argument depends on a shift in the meaning of a semantically ambiguous term, you should say in your evaluation that the argument commits the fallacy of equivocation. (You will also need to point out that it has either false premises or bad logic.)
• Eliminate syntactic ambiguity by rewriting the ambiguous sentences in an unambiguous way. If the apparent success of an argument depends on a shift in the meaning of a syntactically ambiguous expression, you should say in your evaluation that the argument commits the fallacy of amphiboly. (You will also need to point out that it has either false premises or bad logic.)
• Generality is usually unproblematic and even useful. When it does cause confusion, paraphrase with more specific terms.
• If you do need a precise border for a vague term, ask instead why it is you want a precise border and what it is that would address what you want.
• If an argument contends that a border cannot be crossed because its vagueness takes it longer to cross the border, evaluate it as committing the fallacy of arguing from the heap.
• If an argument contends that a border does not exist because its vagueness makes it hard to see the border, evaluate it as committing the fallacy of the slippery slope.
• Do not include empty sentences in your clarification if you can avoid it. Include in your clarified argument the minimal contextual information that is necessary for evaluation.

5.8 Glossary for Chapter Five

Ambiguity—occurs when an expression has more than one possible meaning and it is not clear which meaning is intended.

Elliptical ambiguity—semantic ambiguity in which lack of clarity regarding the meaning is due to an expression that has been omitted.

Empty—a statement that in a normal context would have clear referents for all its terms, but is in a context that provides the audience with no idea of what at least one of its terms refers to.

Fallacy of ambiguity—committed by an argument that appears to be successful because of an ambiguous expression that shifts in meaning; the fallacy of equivocation and the fallacy of amphiboly are two varieties.

Fallacy of amphiboly—a fallacy of ambiguity that goes wrong because of syntactic ambiguity.

Fallacy of arguing from the heap—the fallacy of mistakenly concluding that, because fuzzy borders can take longer to pass, they are impassable.

Fallacy of equivocation—a fallacy of ambiguity that goes wrong because of semantic ambiguity.

Generality—possessed by a term that allows for degrees.

Lexical ambiguity—semantic ambiguity in which the competing meanings are due to different definitions of a term (thus lexical, indicating that a lexicon, or dictionary, might define the term in more than one way).

Referential ambiguity—semantic ambiguity in which more than one thing might plausibly be picked out, or referred to, by a term.

Semantic ambiguity—a term that has more than one plausible meaning and it is not clear which is intended. Also called equivocation, since different things are being called (. . . vocation) by the same (equi . . .) name.

Slippery slope fallacy—mistakenly concluding that because fuzzy borders can be harder to see, they are nonexistent.

Specifying—paraphrasing in a way that narrows the range of possible things that an expression can mean, so as to increase the clarity of an argument.

Syntactic ambiguity—the sort of ambiguity that occurs when the terms of an expression have more than one plausible grammatical relationship to one another, and when this results in lack of clarity about what the expression means. (Also called amphiboly, from a Greek word for a special net that could be cast simultaneously on both sides of the boat, thereby catching twice as many fish—or meanings.)

Use-mention distinction—the difference between the expression of a word to refer to the word itself—in which case the word is, strictly speaking, merely being mentioned, not used—and the other more ordinary expressions of the word, when it is being used. Confusion about this distinction can cause the sort of semantic ambiguity we have termed referential ambiguity.

Vagueness—the lack of a strictly defined boundary between what has a property and what does not have it.