Skip to main content

Critical Thinking, Logic, and Argument: Chapter 14. Fallacies of Ambiguity

Critical Thinking, Logic, and Argument
Chapter 14. Fallacies of Ambiguity
    • Notifications
    • Privacy

“Chapter 14. Fallacies of Ambiguity” in “Critical Thinking, Logic, and Argument”

Chapter14Fallacies of Ambiguity

14.1 Introduction to Fallacies of Ambiguity

In part 1 of this book, we discussed in depth how important it is to have clear definitions for rational arguments. Language maps the kinds of things we talk about, and to reason about the world, we need a precise map. In order to avoid talking past each other and other issues, ambiguity of one’s ideas and terms must be addressed. Often, just by the nature of the language and phrases we use, ambiguity is present.

Ambiguity is the condition of having more than one interpretation or meaning.

When an expression or set of words is ambiguous, it can be used to convey more than one meaning, which means the others participating in a dialogue do not have a way of knowing which meaning is intended. All parties must use the same terms in the same ways for an argument to work. One resolves ambiguity either by adding background information that rules out all meanings except the intended one or by using a different phrase that lacks the ambiguity in question.

Fallacies of ambiguity are invalid because they contain words or phrases that can be understood in more than one way.

There are two basic ways in which ambiguity can arise in language. The first is lexical ambiguity or equivocation, in which a word or phrase has more than one definition and so can be understood in more than one way. Alternatively, two different words that look or sound the same may become confused and lead to fallacious inference. The second basic way ambiguity can arise is structural ambiguity or amphiboly, in which a string of words in a sentence have more than one legitimate grammatical interpretation and so can be understood in more than one way. Ambiguity can also creep into our language in terms of describing the kinds of things we are talking about and how we talk about them. We will examine six fallacies of ambiguity: the fallacies of equivocation, amphiboly, accent, composition, division, and hypostatization.

14.2 Equivocation

The fallacy of equivocation is due to lexical ambiguity. This means there is ambiguity about the meaning of a word or words. If we break down “equivocation” to its Latin roots, there’s “equi/voc/at/ion,” which is a noun that means speaking out equally or twice. Language is constantly changing, so it is important to check in on the meaning of words in our shared lexicon (meaning our vocabulary, which can be related to a person, a place, or a specific domain of knowledge or work).

Equivocation occurs in two main ways: When a key word is used in two or more senses in the same argument and the apparent success of the argument depends on the shift in meaning. Or, when two different words that look or sound the same may become confused and lead to fallacious inference (fig. 14.1).

Two simple diagrams sit side by side. Three colours are used to show relationships between the parts: blue, red, and yellow. The word “meaning 1” (blue) has a blue arrow pointing to the words “same word” (presented in yellow). The word “meaning 2” (red) also points to the words “same word” (yellow) but with a red arrow. Beside this is another set of words and arrows. The word “word 1” (blue) and the word “word 2” (red) are separated by a does-not-equal sign. Both word 1 (blue) and word 2 (red) have yellow arrows pointing the words “same meaning” (presented in yellow).

Figure 14.1 Two forms of equivocation. Artwork by Jessica Tang.

Before we get further into equivocation, we should briefly review syllogisms (covered in part 2, Chapter 8). A syllogism is a very general argument pattern that involves two premises, a conclusion, and three terms. There are many varieties of the syllogism pattern.

Examples of syllogisms

1. “Older than” syllogism

2. Syllogism of containment

3. “Greater than” syllogism

Hanna is older than Nasim.

Nasim is older than Joe.

_______________

Hanna is older than Joe.

Regina is in Saskatchewan.

Saskatchewan is in Canada.

_______________

Regina is in Canada.

Nine is greater than seven.

Seven is greater than four.

_______________

Nine is greater than four.

By now, you should be able to see that these arguments are valid. That is to say, if the premises are true, then the conclusion must also be true. What makes them valid? They have four common features that make them valid:

  1. 1. In each line, there are two terms connected by a relation (e.g., in the first one, the terms “Hanna” and “Nasim” are connected by the relation “_____ is older than _____”).
  2. 2. The two premises share a “middle term”: for example, in the first one, “Nasim” appears in both premises.
  3. 3. The relation is transitive. Transitivity is an ordering relation. A transitive relation, R, has the property that for every three things a, b, and c, to which R applies if a is R to b and b is R to c, then a is R to c.
  4. 4. Finally, the three terms are in the right places in the relation to make the conclusion valid.

We have reviewed how syllogistic arguments depend on transitivity in order to introduce a syllogistic fallacy of ambiguity, called the fallacy of four terms. What happens with equivocation is that a syllogism will look like it has three terms, but it will actually have four. Now if a syllogism uses a term equivocally or in two different senses, it can look valid. Consider the following example:

The argument:

Looks like this:

But is really this:

Only man is rational.

No woman is a man.

∴ No woman is rational.

Only As are Bs.

No C is an A.

∴ No C is a B.

Only As are Bs.

No C is a D.

∴ No C is a B.

The first premise says that only As are Bs (which is the same as saying that if something is a B, then it is an A), and the second premise says that no Cis an A (which is the same as saying that if something is a C, then it is not an A); from these premises, it does follow logically that no C is a B. But since the two instances of “man” represent different terms in the two premises, we really have four terms A, B, C, and D and thus no middle term to tie the two premises together in a way that could support the conclusion.

A way to think about equivocation is that it blocks transitivity. If we are to take the premises seriously in this argument, the word “man” must mean human being in the first premise and male in the second. In short, although the two uses of “man” look the same, they are really different terms with different meanings. But the conclusion only follows from the premises if “man” is a single term having the same meaning in both premises so that it can tie them together.

We are hoping that no one would take such an argument seriously. The equivocation on the word “man” is obvious. And we hope no one would be deceived by an equivocation on the word “bank” (for example, in the phrases “bank of commerce” and “river bank”), since the two meanings are completely different. However, most words in the English language have more than one meaning, and in many cases, the meanings are closely related enough that it is easy to use them equivocally. Equivocation is especially likely when a key term in an argument is a figure of speech, a theoretical term, or a metaphor, and since many terms in our language are dead or dying metaphors, equivocation is a fairly common fallacy.

Examples of equivocation

  1. 1. The public is interested in choosing their own doctor, therefore it is in the public interest that people get to choose their own doctor.
  2. 2. Knowledge is power, and power corrupts, therefore knowledge corrupts.
  3. 3. The end of a thing is its purpose; death is the end of a thing, therefore death is the purpose of life.
  4. 4. “Sugar is an essential component to the human body” (an ad for sugar).
  5. 5. “Ask not what your country can do for you, but ask what you can do for your country” (John F. Kennedy [JFK]).

Example 1 shifts the meaning of “public interest.” The phrase often means something like public welfare; it also often means what the public desires, and even what the public takes an interest in. Clearly something could be in the public interest in one of these senses without being in the public interest in either of the others. Indeed, the questions “What are various sense of ‘public interest’?” and “How they are related?” are complex, subtle, and require study. Such questions constitute an important part of the subject matter of political studies. But here we can understand that just because it is of interest to the public doesn’t mean it is in the public’s best interest. There might be good reasons to allow people to choose their own doctor, but this isn’t justified by the very fact that it is of interest to the public. The workings of the public health care system have many competing interests and organizational structures to balance, one of which is public interest.

Example 2 uses “power” in ambiguous ways. Knowledge is power means that if you know more things, you have increased abilities in some domains (fig. 14.2). Is “increased power in some domains” the way that “power” is used in “power corrupts”? No. In the second sense, they mean something more like unchecked force or sovereign power. It is hard to clarify exactly how power is being used in both senses, but it is clear that the argument makes a serious mistake by concluding that knowledge is corrupting.

Example 3 uses “end” in two ways that are related, but only loosely. First, “end” is used in an ordinary way meaning the conclusion or ceasing to be of something. This is the sense of “death is the end of life.” But the second sense of “end” used in “the end of a thing is its purpose” refers to the use of “end” in the phrase “the ends justify the means.” This sense of “end” is unlike the sense of “end” used in terms of “the end” that shows on the screen at “the end” of a movie. Death is “the end” in that sense, but it is not clear that is is “the end” of life in the sense of its purpose. In fact, it is not at all clear that life has a purpose in that sense.

Example 4 uses “sugar” to mean both blood glucose and the refined commodity used in baking, tea, and so on. Here we might respond, “I know my body needs glucose to function, but that doesn’t mean I need literal sugar to function.” Example 5 shifts meaning for the term “country.” In one sense, it means government: “Ask not what your country can do for you.” And in another sense, it means nation, homeland, or community: “but what you can do for your country.” J.F.K. was not asking people to work for free for the government; he was asking people to orient themselves toward helping their communities rather than asking the government to help them. This is also a fallacy of bifurcation, which we discuss in Chapter 18.

A syllogism is presented: Knowledge is power (ability) / Power (force) corrupts / Conclusion: Knowledge corrupts. The words “power (ability)” and “power (force)” in each statement are presented inside blue boxes. A “blocked transitivity” label points to the “power (ability)” box of the first statement in the syllogism.

Figure 14.2 Equivocation. Artwork by Jessica Tang.

Another kind of equivocation comes from the misuse of relative terms, which have different meanings in different contexts. The word “tall” is a relative term in the sense that a tall man and a tall building are tall relative to different tallness measures. A tall man is a man who is tall for a man, whereas a tall building is a building that is tall for a building. Forms of argument that are valid for nonrelative terms may be invalid for relative terms. Thus “An elephant is an animal, therefore a gray elephant is a gray animal” is valid, but “An elephant is an animal, therefore a small elephant is a small animal” is invalid. This is because when we use the word “gray” about animals, it picks out pretty much the same range of tones (indeed colour terms are typically like this); size terms however pick out different ranges of size for different animals, since the normal size of an animal depends on what kind of animal it is. Actually, it is not always easy to tell when a term has a relative use (for example, we use the term “red” for a range of natural hair colours that lie completely outside of the usual range of “red”); we have to think about whether we are using the word in the same way across different cases. No one would be taken in by the argument about small elephants, as everyone knows that an elephant is not a small animal, but there are relative terms that can be used equivocally without obvious error. Words like “good,” “fun,” or “hot” (as advertisers use them) are especially easy to misuse because they are used in so many different but contextually relative ways that it is often easy to use them equivocally without noticing that one is doing so. Consider the example of labels reading “Light Olive Oil.” What is light about it?

14.3 Amphiboly

Not only can there be issues with the meaning of words, but there can be issues with the sentence construction itself in conveying meaning. We discussed in the introduction of this book that linguistic mastery is essential for reasoning since a lot of reasoning deals with tracing the consequences of our mastery of language—what follows from what has already been said or written? When we assert beliefs using statements, we must do so in a way that conveys meaning to those with whom we are dialoguing. This means, among other things, constructing grammatically correct sentences. If we don’t, we have a lexical ambiguity (like equivocation), but one that instead arises from a structural ambiguity.

The fallacy of amphiboly is when there is a structural ambiguity in the grammar of a sentence that the argument or claim depends on.

Structural ambiguity is usually due to poor grammatical construction. The rules of grammar typically work to determine a single meaning from a well-formed linguistic string—at least they do in the absence of background information that may overrule that interpretation. A statement is amphibolous when its meaning is unclear because of the loose or awkward way in which its words are combined, or because insufficient contextual information is supplied to decide which meaning is intended. Amphiboly is especially common in advertisements and news writing. Consider the following three sentences:

Examples of Amphiboly

  1. 1. Clean and decent dancing, every night except Sunday (pub sign).
  2. 2. We dispense with accuracy (druggist’s sign).
  3. 3. Killer says dead man was chasing him with drawn razor (headline).

In these three sentences, it is possible to find an unintended meaning as well as the intended meaning because of sloppy sentence construction. The rules of grammar weakly suggest that the unintended meaning is the correct one. Thus the pub sign suggests that the dancing on Sunday is indecent rather than that there is no dancing, which it obviously actually means. The druggist’s sign can be read to mean either that accuracy is dispensed with (or done without) or that drugs are dispensed accurately; clearly the second meaning is the intended one. And of course, dead men cannot chase people, even though that is what the rules of grammar suggests. These three cases are examples where the rules of grammar suggest one meaning but our background knowledge overrules that meaning. Each of these sentences could be rephrased so that the unintended meaning could be ruled out.

Now consider these sentences:

More Examples of Amphiboly

  1. 4. I heard about them at the bar.
  2. 5. The children were eating good cake and candy.
  3. 6. Mary and Frieda are visiting doctors.

In these three cases, one simply cannot tell the meaning without added information. We need more information even to know how the parts of the sentence fit together properly. Thus in sentence 4, we don’t know whether “at the bar” refers to the place where the speaker was when the speaker heard about them or where they were: Was I at the bar that I heard about them, or did I hear about what they did while they were at the bar?

In sentence 5, we don’t know whether it was candy and good cake that the children were eating, or whether both the cake and candy were good.

The explanation for this is quite straightforward. There is a rule in English grammar that says we can delete unnecessary words, and the sentence in 5 can be produced from that rule. Consider:

  1. 5a. The children were eating good cake and eating good candy.

By first deleting the second instance of “eating,” we get

  1. 5b. The children were eating good cake and good candy.

And then by deleting the second instance of “good,” we get

  1. 5. The children were eating good cake and candy.

But sentence 5 can also be produced by that rule from

  1. 5c. The children were eating good cake and eating candy.

The list goes on. The idea is that every time we delete words, we open the possibility that there will be ambiguous references amongst the elements of a sentence.

In sentence 6, the sentence either tells us that Mary and Frieda are doctors who are visiting or that they have gone to visit doctors. We need more information, for example, that “Mary and Frieda were not at the party that night. They were visiting doctors.”

These cases show a deep fact about language, which we explore throughout this course—that language comprehension is a knowledge-based process.

Two simple diagrams sit side by side. On the left side, the diagram presents the word “good” in red, with two red arrows pointing down to two different words: cake and candy. The words “cake” and “candy” are presented in blue with an addition symbol between them. The diagram on the right has the word “good” (in red) with a red arrow straight down to the word “cake” (in blue).

Figure 14.3 Example of lexical ambiguity. Artwork by Jessica Tang.

Merely knowing the meaning of words is not enough; we typically need knowledge of the world (of what is being talked about) in order to process a sentence grammatically to understand what is said. In fact, the two versions of “Mary and Frieda are visiting doctors” are really two different sentences with different grammatical structures that have the same surface appearance. It all depends on whether “visiting” is an adjective that modifies “doctor” or a verb telling us what Mary and Frieda are doing. Consider two more sentences:

More Examples of Amphiboly

  1. 7. Bill became disgusted with Fred at Mary’s party, so he went home in a funk.
  2. 8. Launching the ship with impressive ceremony, the admiral’s daughter smashed a bottle of champagne over her stern as she slid gracefully down the slipway.

In 7, we have another kind of structural ambiguity that is called ambiguity of cross-reference. This occurs when a referring phrase refers back to something mentioned in the sentence, but it isn’t clear to what. To see that it is ambiguous, it is only necessary to see that the statement could be an answer either to the question “Why did Fred leave?” or the question “Why did Bill leave?” (fig. 14.4).

In example 8, while we know perfectly well what the speaker intends to say, the rules of grammar that we intuitively apply to the sentence suggest another reading; normally the word “her” in a sentence refers back to the nearest linguistically female object (in the sentence above, that would be the admiral’s daughter, not the ship). In this case, there is a mismatch between what the speaker intends to say and what grammar dictates.

Simple arguments that are amphibolous usually fool no one; they are simply funny or confusing. In speech situations, the speaker can wave her hands, point to things, and fix meaning in various non-linguistic ways, and the hearer can always ask the speaker what she means. But in writing, these opportunities to clarify meaning are not available, and so ambiguity in writing is a genuine and continuing danger. Amphiboly is most dangerous to understanding in extended passages of exposition or argument. Five or six sentences taken together may contain so much structural ambiguity that a reader doesn’t know what the writer means at all. This is unfortunately a common failing in student essays, and it is difficult to avoid because the author knows what she means, and it may not occur to her that grammar tells the innocent reader something else. There is only one sure way to avoid this problem. It is to construct each sentence with care and to make sure that enough context is provided to rule out all possible, or at least all the likely, unintended interpretations.

The following sentence appears: Bill became disgusted with Fred at Mary’s party, so he went home in a funk. The words “Bill,” “Fred,” and “he” all are presented in blue with blue boxes around them. Blue arrows point from “Bill” and “Fred” to “he.” A large blue question mark sits below the sentence.

Figure 14.4 Example of the ambiguity of cross-reference. Artwork by Jessica Tang.

14.4 Fallacy of Accent

A speaker’s tone of voice often conveys important information about background assumptions that the speaker makes and thus against which the meaning of an utterance is to be understood.

The fallacy of accent arises when there is an ambiguity of meaning because it is unclear where the stress should fall in a statement, or what tone of voice is intended.

Since tone of voice cannot be conveyed directly in writing, we need to find other ways to convey what the underlying assumptions are. Consider, for example, the difference accent makes in the following statements:

  1. 1. Did you steal the butter? (Assumption: Someone stole the butter.)
  2. 2. Did you steal the butter? (Assumption: You acquired it somehow.)
  3. 3. Did you steal the butter? (Assumption: You stole something.)

In sentence 1, the accent on “you” in the question suggests that the speaker believes that someone stole the butter and is asking you for the information of whether that someone is you. In sentence 2, the speaker presumably believes that you have acquired the butter by some means and is asking you whether you stole it as opposed to, say, bought it. In sentence 3, it appears that the speaker believes or presumes that you have stolen something and wants to know whether it was butter that you stole (perhaps with the implied expression of astonishment that if you were going to steal something, why didn’t you steal something valuable, say, a stereo system, instead).

These examples reveal something about important about communication. Remember that a statement is the use of a sentence to make a claim that can be true or false. So a statement is a public vehicle for expressing beliefs and making claims. But communication, whether it takes the form of argument or merely conversation, is more than just the making of claims that express beliefs. It’s a social process in which persons engage in a give and take of asking or answering questions, making assertions, and responding to one another.

There are two quite different ways in which conversations are more complicated than just claim-making. First, people can discuss topics and situations that they don’t think are actually real: they can discuss imaginary situations or situations that could have been real had some event in the past been different; they can discuss future events that have not and may never come to pass. In short, human beings can think and talk about a vastly larger range of possibilities than those that are believed to be actual. They can also disagree deeply about what the actual facts are, and so a conversation may often have the form of asking which of several possible situations the actual one is. Human beings live in a sea of possibilities that extend beyond the actual, partly because they can imagine things being different than they are and partly because, being ignorant of the truth, they must attempt to determine which possibilities are more likely to be true.

The second important way in which communication is more complicated than simple claim-making rests on the fact that, to a large degree, people understand the world by way of stories, narratives, scenarios, and scripts. A story organizes a set of claims, real or hypothetical, into a structure that makes sense in terms of normal human interests and concerns. We live largely in a human-centred world, in which our beliefs and indeed the very words we know refer us to ways of living with which we are familiar. Let us give you an example.

We tell you that Joe went to Wendy’s and had a burger. You have no trouble understanding that Wendy’s is the name of a restaurant, that Joe is someone we know, and that people typically go to restaurants to purchase and eat food. And so given your background knowledge of “what one does at a restaurant,” you interpret my statement as telling you that a person named Joe went to a particular restaurant because he was hungry and ordered and ate and paid for a burger. And of course, you know what a burger is, and so on. However, if you knew in addition that Joe had a friend named Wendy with whom he sometimes ate, you might be unsure of whether Joe went to Wendy’s, the restaurant, or to Wendy’s home to eat.

Part of the reason that you make these background assumptions is that human beings are creatures that periodically need food; we live in a culture in which food can be purchased at restaurants; people often go to restaurants, and on and on. All this background knowledge gives you the resources to understand the point and significance of a great variety of human stories.

If we told you instead that Joe went to Wendy’s and had a baby, you would bring different knowledge structures or scripts to bear. “Had a baby” means “gave birth to a baby.” People do not give birth to babies at restaurants, except by accident in very unusual circumstances. You will take “Joe” to refer to the person who gave birth, and so on. As a result of this, the meaning that a sentence has in an argument or conversation is more finely grained than the fact or proposition to which it refers.

The factual meaning of a statement plays a certain role in the story or narrative that is being told. Because you have a general sense of how narratives unfold, you will know what questions to ask regarding a situation under discussion and how to interpret the answers. Although these two dimensions of conversation are quite different, in practice we understand the meanings of utterances made in conversation in the same ways. We recognize certain cues as imposing constraints on what sorts of information is relevant to the conversation, and we can make these constraints explicit by laying out certain statements as relevant background information or presuppositions of the conversation. If our knowledge of the presuppositions is not adequate to determine what is meant, we ask questions. The questions we ask will themselves presuppose some background assumptions, and the answers we receive will fill out the background assumptions we need to know to see how the person with whom we are talking envisions the situation under discussion. We can put the point simply by saying that facts by themselves are inadequate; they provide information only as answers to questions.

To return to the three sentences we began with, the claim “I stole the butter” provides quite different information depending on which question was asked. In response to question 1, it provides the information that it was I who stole the butter; in response to question 2, it provides the information that it was by theft that I acquired the butter; and in response to question 3, it says what it was that I stole: butter.

The misuse of accent can often deceive, as is the case when someone tells a woman that her husband wasn’t out with Betty last night (in the attempt to lead her to believe that her husband was out with some other woman), or when a child tells his father that he only ate some of the cookies in the package when he ate all but one.

A fallacy of accent rests upon mistaking the intended accent of a premise and thereby deriving a conclusion incompatible with the intent of the premise.

Fallacies of accent are often used by newspaper writers who deliberately take quotations out of context to distort their meaning or write in large headlines “Revolution in France,” and then in smaller type “Feared by Authorities If Inflation Continues to Rise.” Movie magazines and supermarket tabloids are common places to find examples of abuse of accent.

Examples of the Fallacy of Accent

  1. 1. Who was Frankie seen with at the Gilded Nickel while wife Lona cries at home?
  2. 2. The commandment says, “Thou shalt not covet thy neighbour’s wife,” so men should only covet wives of those living outside the neighbourhood.

Example 1 requires a lot of questions, the first of which is, What facts can be ascertained from the question? What do we actually know about Frankie and Lona? Not much, though we might feel like we do from how the question implies a story. It might imply there’s an affair going on, but we don’t know that. Consider that it could be the case that Lona asked Frankie to pick up a friend at the Gilded Nickel. While picking up the friend at the Gilded Nickel, Frankie and the friend are seen. At the same time, Lona is at home preparing dinner, cutting onions that make her cry as a result.

Example 2 is making a similar mistake in drawing a conclusion. It understands the issue with coveting to be about it being the neighbour’s wife, not that it is anyone outside of the marriage at all.

Although the fallacy of accent is connected with distortion, it reveals something important about the way language works. Language comprehension is deeply dependent upon background information. We are active seekers for information that will confirm or disconfirm our hypotheses. To understand what people say, we need to see their sentences as part of structured conversations that presuppose both shared information between speaker and hearer and shared interpretations of that information. Writing is more anonymous than speaking, and the author loses control of the context. People who write for a living are very familiar with the need to set a context for the reader and know that the reader cannot know what is being talked about without this help. The lesson for critical thinking is this: when you write about a subject, you need to give the reader clear cues about the assumptions that you are making.

14.5 Fallacy of Composition

The fallacies of composition and division are closely related to each other, fallacies of division being the reverse of those of composition. These two fallacies are fallacies of ambiguity because they draw conclusions through ambiguous relations between parts and wholes. We often do reason from parts to wholes or from wholes to parts, but everything depends on the kind of thing we are reasoning about. We will look at fallacies of composition first. The term “fallacy of composition” is applied to two related types of invalid argument.

The fallacy of composition is when one argues invalidly from the properties of the parts of a whole to the properties of the whole itself, and when one reasons invalidly from properties of a member to properties of a class.

In the first, one reasons fallaciously from the properties of the parts of a whole to the properties of the whole itself. For example, from the fact that every part of a machine is light, it does not follow that the machine is light. Of course, such a machine will be lighter than a similar one made of heavy parts, but the machine may be composed of a great many parts and so be very heavy. Similarly from the fact that every sentence in a book is well written, it does not follow that the book is well written. Such patterns are not always fallacious; some properties have what is called compositional heredity.

A property F is compositionally hereditary with regard to a whole if and only if when every part of the whole has property F, then the whole does as well.

But whether a property has compositional heredity depends on what kind of property it is. Thus if all the parts of a machine are made of iron, then the whole machine is also made of iron. The property of being iron is, so to speak, an absolute property of a thing, and its attribution to a thing is context independent: if all its parts have that property the whole does as well. By contrast, the property of being heavy is a relative property. When we judge that something is heavy, we take that thing to be heavy for an object of that kind (i.e., in relation to other objects of that kind). We saw in the discussion of relative terms, as used in a syllogism in Chapter 8, that a light elephant (which is light for an elephant) is not light for an animal, as even a very light elephant is heavy compared to many other animals. The class of comparison for a relative term typically varies from part to whole, so a relative term will not generally have compositional heredity. Consider the following fallacious inference regarding a hockey team: “Every player on the team is a superstar and a great player, so the team is a great team.” The term “great” is a relative term, and so its application is dependent upon the context given by the comparison class. Consider the features that make a player great (relative to other players), and compare that with the features that make a team great—there is no need to think that if a set of players have great-making characteristics for an individual player they will form a team that has great-making characteristics for a team. A team must, for example, have players whose skills complement and balance those of other players; a team composed entirely of terrific goaltenders will not be a good team (fig. 14.5).

In the second type of fallacy of composition, one reasons incorrectly from the properties possessed by the individual members of a class or collection to the properties possessed by the class or collection itself. When we talk about the properties of collections or groups, we do so in two quite different ways that are not marked by a difference in grammar. There is no grammatical difference between “Dogs are mammals” and “Dogs are variable in size,” but the properties of being a mammal and being variable in size are attributed to the class of dogs in quite different ways.

The members of a class can, as a class, have properties distributively (so that each member of the class has that property—i.e., every dog is a mammal).

Or:

The members of a class can, as a class, have properties collectively (so that the class as a whole has that property but not its members—dogs do not individually have the property of being variable in size).

Again, in “Rodents have four feet,” we predicate the property of having four feet to rodents distributively (each rodent has four feet), but in “Rodents are widely distributed over the earth,” we predicate the property of being widely distributed over the earth to rodents collectively. We certainly do not intend to say that each and every rodent is widely distributed over the earth. This gives us a kind of test for distinguishing the two uses. Can we preserve the truth of the sentence if we replace the general term (applying to the whole class) by a phrase referring to each and every member of that class? For example, in “Cows are mammals,” we can say “Each and every cow is a mammal” and say the same thing so the property of being a mammal is predicated of the class of cows distributively. But in “Cows are found in many countries,” we cannot say “Each and every cow is found in many countries” and say the same thing because the predicate applies to the class of cows collectively only. The fallacies of composition and division involve ambiguity in the way predicates apply to general terms. Consider an example:

On the left side of the figure is the title “compositional heredity,” and on the right side is the title “fallacy of composition.” A thin line separates the two columns. Everything that appears in the left-hand column is red, and everything in the right-hand column is blue. At the bottom of the left-hand column is a series of dashes with the words “iron machine parts” above. Two lines point up from either end of the dashes. These two lines converge and point toward the words “whole machine is on.” At the bottom of the right-hand column, a series of dashes appears with the words “great hockey players” above. Two lines, which start at either end of the dashes, converge and point up to the words “team as a whole is great.”

Figure 14.5 Example of compositional heredity (iron) and the fallacy of composition (greatness). Artwork by Jessica Tang.

  • P1: Atoms are so small they are invisible.
  • P2: My arm is composed of atoms.
  • _______________
  • C: So my arm (is so small it) is invisible.

This foolish argument commits the fallacy of composition. It assumes that a predicate (is so small that it is invisible) that applies to a subject distributively (each and every) applies collectively (all the atoms in my arm).

14.6 Fallacy of Division

The phrase “fallacy of division” is also applied to two related types of fallacious arguments that are the reverse of the two above. The first kind consists of reasoning invalidly from the properties of a whole to the properties of its parts.

The fallacy of division is when one argues invalidly from the properties of the whole itself to properties of a part, and when one reasons invalidly from properties of a class to properties of a member.

“Exxon is a very important company, and Bill Speed is an official at Exxon, therefore Bill Speed is very important” is an instance of the fallacy of division.

A property F is divisionally hereditary with respect to some whole if and only if whenever the whole has property F, then its parts do as well.

We should note that there are special self-referential properties that are context independent but are not compositionally or divisionally hereditary. For example, every part of some whole X has the property of being a part of X, but X doesn’t have this property. And similarly, every whole X has the property of being the whole of X, and no part of X has that property.

None of this discussion of fallacies of division and composition should lead anyone to believe that the part/whole relationship is easy to decipher. Philosophers have an area of philosophy dedicated to the metaphysics and ontology of parts and wholes called mereology.1 If you are interested in how parts are determined or if wholes are the sum of their parts, maybe you are interested in mereology!

The second kind of fallacy of division consists in reasoning from the properties of a class or collection of things to the properties the members of that class or collection. Reasoning from “This vase is part of a very valuable collection of antiques” to “This vase is very valuable” is an example of that fallacy. Obviously, a collection can be made valuable by having a few very valuable members together with a large number of members of moderate value. Reasoning from “Dogs are common, and Japanese Spaniels are dogs” to “Japanese Spaniels are common” is equally fallacious, as the property of being common is true of dogs only as a class or collectively and does not imply that every (kind of) dog is common (fig. 14.6). The old riddle “Why do white sheep eat more than black sheep?” turns on a fallacy of division. The answer, “Because there are more of them,” treats collectively what seemed to be referred to distributively in the question. The fallacy of division consists in assuming (wrongly) that a predicate that applies collectively must also apply distributively.

On the left side of the figure is the title “divisional heredity” and on the right side is the title “fallacy of division”: a thin line separates the two columns. Everything that appears in the left-hand column is red and everything in the right-hand column is blue. In the left-hand column, the words “whole machine is iron” have two lines that begin on either side of the phrase: they point down and converge to point at a single dash among the many dashes that run along the bottom of the column. The statement “individual parts are iron” sits below the dashes. In the right-hand column, the phrase “dogs are common” has two lines on either side that point down and converge on a single dash in the middle of the many dashes that run along the bottom of the column. A dash to the left of centre at the bottom of the right-hand column has an arrow that points down to the phrase: “Japanese spaniels are common.”

Figure 14.6 Example of divisional heredity (iron) and the fallacy of division (commonness). Artwork by Jessica Tang.

Here are two examples:

  • P1: The people in this class are half female.
  • P2: Jack is in this class.
  • ∴ Jack is half female.

Here the predicate “is half female” is predicated on the members of the class collectively, not distributively (it is not true that each and every member of the class is half female!). This might seem silly, but statistical reasoning is often flawed in just this way. Consider this example:

  • P1: University graduates make 70 percent more per year than non-graduates.
  • P2: Kofi is a university graduate.
  • ∴ Kofi makes 70 percent more per year than non-university graduates.

The problem with this reasoning is that averages are made up of a wide variety of individuals, thus we cannot “divide” the average onto particular individuals. We need to pay attention to the relevant features of the individual that differentiate their place in the group. For example, Bill Gates (billionaire inventor of Microsoft) does not have a college degree, and it isn’t uncommon to meet a barista with a college degree averaging a yearly income of about $30,000 CAD/year. What these outliers suggest is the heterogeneity of members in a group, thus a group property cannot be divided onto individual members. And in our example above, we have no reason to believe Kofi makes 70 percent more than non-college grads by the very fact of what the average college grad makes.

14.7 Fallacy of Hypostatization

When we discussed language and definition, we talked about how successful communication requires that both people are using the same terms in the same way. Further, when discussing classification, we talked about how classification systems have embedded knowledge about the world. To put these two things together, we have to use words with the same meaning in the same way about the same things. What if the thing in question we are talking about is much more difficult to classify? Consider the difference between classifying Legos by colour and classifying virtues. They are quite different. That is because “virtue” is an abstract quality of humans or actions while Legos picks out physical items in the world. The fallacy of hypostatization confuses the abstract and concrete difference. Hypostatization is a big word meaning to treat something as real. An abstract word designates a general quality such as virtue or roundness. While roundness exists only in the particular objects that are round, we can talk about it without reference to the individual objects that possess roundness.

The fallacy of hypostatization consists of regarding an abstract word or a metaphor as if it were a concrete one.

The fact that we can talk about general qualities adds greatly to the power of our language and enables us to talk about things such as truth, goodness, and beauty; it also creates potential dangers. We may make the mistake of assuming that because we can refer to general qualities, they name specific individual entities. We may be misled, for example, into thinking that in addition to individual red Lego pieces there are also separate entities such as redness and Legoness. We are not likely to commit many intellectual errors talking about redness, but many general terms that are easy to misuse get their meaning by a similar kind of abstraction.

Think of the terms “science” and “the state.” We are likely to use these terms without any sense of ambiguity or unclarity, and yet it would be a mistake to think that these terms referred to discrete objects in the world. When we say things like “Science is on the march” or “The state opposes anarchy,” it sounds as though we are saying something with determinate truth conditions. But these statements are metaphors and have no clear truth conditions. If they do not have clear truth conditions, then we cannot form cogent arguments and solid conclusions.

However, we often forget this and thus talk and think as though there really are such entities as science or the state or nature that act and think. Often hypostatization takes the form of personification, as in the case of “Nature favours the survival of the fittest.” Here the statement invites us to think that nature is a person, or at least person-like, and that it guides or directs the process of evolution.

Examples of Hypostatization

  1. 1. Whenever the state butts into private enterprise, it makes a mess of things.
  2. 2. The government has a hand in every business and the other in every person’s pocket. We should limit government pickpocketing.
  3. 3. These issues give Canada a black eye.

Example 1 uses “the state” as if it were a concrete thing that can “butt” into people’s private enterprises. Whatever intrusions particular areas of government might have, the state as a concrete entity cannot take on such actions as “butting into” enterprise.

Example 2 gives the government a metaphorical body—hands to pickpocket. But very few of us carry our money in our pockets anymore. There’s also a kind of equivocation here between taking something from a pocket and literal pickpocketing. A pickpocket breaks the rules of a society against stealing, whereas the government collects taxes with the consent of the public (in an ideal social contract). In any case, the two are not equivalent even if the government had hands!

Example 3 gives Canada a face. This is an interesting rhetorical flourish that might mean that the government has made a moral transgression. But we would need to actually explain the “bruised eye” in concrete terms if we were to try to establish a claim about the government of Canada’s behaviour.

Hypostatization is a danger to clear thinking because it blurs the distinction between metaphor and literal truth.

Fortunately, the dangers of hypostatization can be circumvented. Ask what specific claims are being made by a sentence and whether they are adequately supported by evidence. In short, attempt to replace the metaphorical associations of the claim with literal commitments. When you come to a sentence that resists replacement, like “The state is the march of God through history,” avoid it like the plague.

Key Takeaways

  • • Ambiguity is the condition of having more than one interpretation or meaning. Arguments with fallacies of ambiguity are invalid because they can be understood in more than one way.
  • • Equivocation occurs when a key word is used in two or more senses in the same argument and the apparent success of the argument depends on the shift in meaning. Or, two different words that look or sound the same may become confused and lead to fallacious inference. Equivocation blocks transitivity.
  • • The fallacy of amphiboly is when there is a structural ambiguity in the grammar of a sentence that the argument or claim depends on. We need more information in order to properly interpret the sentences.
  • • The fallacy of accent arises when there is an ambiguity of meaning because it is unclear where the stress should fall in a statement or what tone of voice is intended. Arguments require statements that express claims. If a statement’s meaning varies depending on where one puts an accent, it is too ambiguous to use in an argument.
  • • To adequately deal with the ambiguity of claims, we need opportunities to ask questions to fill in background assumptions to understand claims.
  • • The fallacy of composition is when one argues invalidly from the properties of the parts of a whole to the properties of the whole itself and when one reasons invalidly from properties of a member to properties of a class. The fallacy of composition improperly assumes compositional heredity.
  • • The fallacy of division is when one argues invalidly from properties of the whole itself to properties of a part and when one reasons invalidly from properties of a class to properties of a member. The fallacy of division improperly assumes divisional heredity.
  • • The fallacy of hypostatization consists of regarding an abstract word or a metaphor as if it were a concrete one. It is misleading because it makes something appear as if an indeterminate term is a discrete entity.

Exercises

Ambiguity Practice

Identify the following fallacies of ambiguity and explain why the fallacy demonstrated undermines the argument.

  1. 1. Our X-ray unit will give you an examination for tuberculosis and other diseases, which you will receive free of charge.
  2. 2. The apartment building Neetu lives in is just huge! She must have an enormous apartment!
  3. 3. Whenever the state butts into private affairs, it makes a mess of things.
  4. 4. The owners of this laundromat should be arrested for indecency! Look at the sign over the washers: “People using washers must remove their clothes when the machines stop.”
  5. 5. The font so generously donated by the Smith family will be placed at the east end of the church. Babies may now be baptized at both ends.
  6. 6. The MPs from Saskatchewan must have done a very good job last session because Parliament achieved a lot of good work.
  7. 7. The cost for the government to pay for the health care of a sick person is just a few thousand dollars a year on average. So health care can’t be a big factor in the national budget.
  8. 8. Doctor: “I’m not sure what the disease you have is, but frankly I think it is due to drinking.” Patient: “That’s okay. I will come back when you are sober.”
  9. 9. Don’t let worry make you depressed and angry—let the church help!
  10. 10. Politician: “You may be wondering whether you should vote for me or my opponent. This is, of course, a difficult and weighty question of public morality, but you may wish to consider that at least I have remained faithful to my wife.”
  11. 11. The only way our company will be successful is if every single one of us works as hard as possible.
  12. 12. People are always saying that the right wing is off base on the economy. That can’t be true. They are always on the right side of the issue.
  13. 13. Very improbable events happen all the time. Whatever happens all the time is a very probable event. Therefore, very improbable events are very probable events.
  14. 14. The bald eagle is disappearing. This bird is a bald eagle, so it must be disappearing.
  15. 15. The government needs to fight poverty.
  16. 16. I’m not saying he stole the money, but I am saying he “borrowed” it.
  17. 17. Let’s take this problem by the horns and destroy it once and for all.
  18. 18. I checked every piece of machinery in the plane, and they all look new, therefore the plane is working like a new plane.

1https://plato.stanford.edu/entries/mereology/

Next Chapter
Chapter 15. Fallacies of Emotional Bias
PreviousNext
Powered by Manifold Scholarship. Learn more at
Opens in new tab or windowmanifoldapp.org
Manifold uses cookies

We use cookies to analyze our traffic. Please decide if you are willing to accept cookies from our website. You can change this setting anytime in Privacy Settings.