“Chapter 18. Fallacies of Presumption” in “Critical Thinking, Logic, and Argument”
Chapter18Fallacies of Presumption
We will look at three fallacies of presumption. In sweeping generalization, the fallacy involves assuming that what is true in general applies even in special circumstances. In the fallacy of hasty generalization, the problem lies in assuming that the evidence on which the argument is based is sufficient to warrant the conclusion, when the evidence is unrepresentative or insufficient. And in the fallacy of bifurcation, one incorrectly assumes that the alternatives presented exhaust the field, when in fact other alternatives exist.
Fallacies of presumption are unsound because of unfounded or unproven assumptions embedded in them.
By smuggling in such presumptions, these fallacies give the impression of being valid arguments. The fallacies of presumption are pervasive and require special vigilance. There are some general reasons that fallacies of presumption are so deeply entrenched. One reason is that human beings often have epistemically inappropriate attractions to certain beliefs; in belief, we are a certain kind of “social conservative” and believe what others do often for no good reason at all other than that others believe them. We want to believe that certain ideas are true and tend to protect them from rational scrutiny by systematic inattention to relevant facts and by isolating them from counter-argument.
Prejudice and bigotry function largely through subtle processes of protection and defence against clear reasoning. We are also likely to believe what our parents and peers do, and not always for very good reasons. So we have various non-rational motives to engage in subtlety fallacious forms of reasoning that protect us from having to be critical and clear. Another reason that the fallacies of presumption are pervasive is that human beings have limitations of attention and focus. Human reasoning capacity is not a single unified process but a hodgepodge of special-purpose mental powers and mechanisms each having a natural history and origin that may be quite remote from their present functions. Being a critical thinker involves harnessing the uses of these separate capacities and minimizing the problems they pose for each other.
We have seen that a way to clarify and correct reasoning is to bring implicit processes of reasoning into our awareness by making them explicit; by doing this, we can ameliorate their deficiencies and perfect them. But we cannot make everything explicit because we cannot pay attention to everything at once. Most of the basic mechanisms of belief production work, automatically, and unless we have reason to distrust their reliability in a particular case, we pay very little attention to them and their presuppositions. We have already suggested that we become better reasoners by regimenting our belief-forming processes in a way that allows us to monitor how well they are working. For example, by becoming skilled at seeing argument patterns like modus ponens, we become more certain that our reasoning proceeds correctly, leaving us energy and attention for other aspects of our reasoning. Later in this chapter, we will see examples of reasoning failures that depend largely on inattentiveness to relevant information. But let us give an especially clear example right now, generally known as the conjunction problem.
The conjunction problem, in which subjects attribute higher probability to the truth of a sentence of form P-and-Q than to the sentence P (a result that is logically impossible), was first presented by A. Tversky and D. Kahneman in “Judgments of and by Representativeness” (in Judgment Under Uncertainty:Heuristics and Biases, ed. D. Kahneman, P. Slovic, and A. Tversky, pp. 84–98, Cambridge: Cambridge University Press, 1982) and is often presented as follows.
Subjects in the study were given the following paragraph:
Linda is thirty-one years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice and also participated in anti-nuclear demonstrations.
They were then asked to rank the following statements by their probability, using one for the most probable and eight for the least probable.
When a group of ordinary subjects with no background in probability and statistics was given this task, 89 percent judged that statement (h) was more probable than statement (f), despite the obvious fact that one cannot be a feminist bank teller without being a bank teller. When the same task was given to a group of graduate students in the decision science program of the Stanford Business School (students who were acquainted with statistics), 85 percent made the same judgment! This conclusion is striking because, as just mentioned, to be both a bank teller and a feminist, one must be a bank teller, so the choice that Linda is a bank teller cannot be less probable than the choice that she is both a bank teller and a feminist. Results of this sort are very robust and have been repeatedly confirmed by other researchers; it is referred to as the conjunction problem because subjects attribute higher probability to the truth of a sentence of form P-and-Q than to the sentence P, even though it is logically impossible for this to be true.
Subjects conclude that option (h) is more likely than option (f) because the biographical sketch they are given fits the stereotype of being a feminist more closely than being a bank teller. When subjects compare the likelihood of two scenarios, they typically use stereotypical likeness or fit as a measure. (Recall our discussion of stereotype in Chapter 13.) Some researchers have seen this as evidence that people are not good at measuring probabilities, but of course this does not fit the facts; the students at Stanford Business School did badly, and they may be presumed to be very good at measuring probabilities. What seems more likely is this: the subjects in the experiment implicitly make the reasonable assumption that the eight choices they are given form a coherent classification of the possibilities (a set that has genuine alternatives to each other) and so “is a bank teller” is implicitly taken to mean “is just a bank teller” (i.e., is a bank teller who is not a feminist). But the eight choices are not genuine alternatives. The researchers have rigged the choices so that they do not form a coherent set of alternatives; the set violates the conditions of being both exclusive and exhaustive. As a result of what is normally a reasonable assumption—that they have been given a genuine set of alternatives—the subjects don’t even notice that the two alternatives (h) and (f) stand in the relation of P-and-Q and P; they are just oblivious to that feature of the set.
We can draw two lessons from this study beyond noticing that participants reasoning using stereotypical likeness. The first is that it is very important when one is considering a set of alternatives for comparison that they are genuine alternatives for purposes of comparison. One cannot notice everything when thinking about a problem, so one should begin by setting the problem up as clearly as possible. Second, when one engages in an argument with others, it is important to be as charitable and clear as possible. In a psychological experiment, it may be acceptable to ask a trick question of the subjects to see whether they catch on, but in ordinary decision-making where you are trying to find out the truth, using trick questions would be a fallacy (as in the fallacy of complex question) and would simply cause others to reason badly. Let us now return to a discussion of the fallacies of presumption.
In fallacies of presumption, the facts relevant and necessary for the argument are not correctly and clearly represented in the premises. In this chapter, we deal specifically with how generalizations and other statements misconstrue relevant features of claims.
18.1 Sweeping Generalization (Fallacy of Accident)
Generalizations are commonly used in reasoning. Some generalizations are grounded in or explained by natural processes governed by causal laws of nature; other generalizations are probabilistic or dependent on local features of a subclass. There are typically exceptions even to strong generalizations, which makes reasoning using generalizations non-monotonic, which just means they can be overturned by evidence.
A generalization is a statement made about a property of all or most members of a class.
We used generalizations with categorical logic when we made universal statements, such as with A statements and E statements. These rules, however, were without exception. Often if we add information, it will cancel the force of a generalization. Laws and rules, like generalizations, have boundary conditions beyond which the rule does not apply. For example, the legal system of precedent is a system of figuring out like cases and whether generalizations hold over various differences.
The fallacy of sweeping generalization is committed when an argument that depends on the application of a generalization or rule to a particular case is improper because a special circumstance (accident) makes the rule inapplicable to that particular case.
In general, when we express general rules or universal laws, we do not state the boundary conditions of these rules or universal laws. This is due partly to the fact that to do so would be cumbersome and lengthy. But it is also often due to the fact that while we agree on the general characteristics of the concept, we may disagree about where to draw boundaries, or else we are not exactly sure ourselves where the boundaries lie. So to state the boundary conditions would be itself controversial and potentially arbitrary. Take the right of free speech. Most people would agree that this right guarantees freedom of religious and political beliefs (at least under ordinary conditions) and that it does not guarantee the freedom to yell “Fire!” in a crowded theatre. But there is considerable social disagreement about whether a person has the right to advocate overthrowing the government or to use obscenities in public. So although we might all agree that everyone has the right of free speech (and all agree that certain things are not covered by the right), there may be no generally agreeable way to state all the boundary conditions on the right. The fallacy of sweeping generalization violates a boundary condition on the application of the rule. Let’s look at some examples:
Example 1 uses a generalization “Everyone has a right to advance their ideas” and applies it to the religious views of public officials. Is this an appropriate application of a rule or generalization? Can you think of a boundary condition that makes this “sweeping”? The generalization cannot be applied to certain public officials because it is a condition of their holding legitimate office that they refrain from using that office as a platform for their own views. So the fact that you are talking about judges and public officials creates a special circumstance or “accident” that blocks the inference.
Example 2 uses the generalization that we have a right to own property (which, of course, is true but is very limited—not everyone can own a nuclear reactor, human persons, a tiger, and so on; we have special social processes and limits in place for different types of ownership). When we look at how Mary is a violent psychopath, this doesn’t undermine her right to own property in general, but we might be able to make a good argument that we can take away specifically her weapons.
Example 3 gives us cause for concern. What is healthy and safe for someone in normal health is not necessarily healthy or safe for someone with special health problems. Let us not sweep over George’s special circumstances.
The fallacy of sweeping generalization isn’t really concerned with the truth of the conclusion. We can see from these examples that what makes sweeping generalization a fallacy is not that the blocked conclusions are false per se but rather that you cannot correctly draw the inference given the information you have. It might be that cross-country skiing would be good for George, and even because of his heart condition. Still, the argument is a fallacy because one cannot infer that what is generally healthful will be healthful for a person with a heart condition.
Just because something is a generally accepted rule doesn’t mean that there aren’t legitimate times when that rule doesn’t apply.
When we make a generalization, we often have some information that allows us to make a reasonable inference given that information, but additional information can block that inference. Always ask whether the application is sweeping over a relevant difference. You hear that Pierre is from Quebec, so you might wonder whether he speaks English. Then you hear that he is a professor of English literature, and your prior wonder is no longer reasonable. Or your neighbours ask if you can look after their child for a while and you agree; had you known that they planned a six-month holiday in France, you would rethink your agreement.
18.2 Hasty Generalization (Converse Accident)
This fallacy is the reverse of the one above and is sometimes called the converse fallacy of accident, over generalization, or secundum quid (which in Latin means “in a certain respect”—to indicate that what is true “in a certain respect” need not be true in all relevant respects). It consists in arguing incorrectly from a special case to a general rule. Often the reason we overgeneralize is that we draw a conclusion from an evidential sample that is either is too small or biased and therefore not representative of the target population.
The fallacy of hasty generalization is committed when an argument that develops a general rule does so in an improper way because it reasons from a special case (accident) to a general rule.
One common form of hasty generalization occurs where the issue in question is complex and there are arguments on both sides. Although it is invalid, people often select only the arguments that are favourable to their own opinions and present them as though they were all that there was to say on the matter. Of course, if one’s objective is only to convince another person, this strategy may be effective. But as a piece of reasoning that establishes the truth (or even the probability of truth) of a conclusion, the method is fallacious.
Example 1 commits the fallacy of hasty generalization because the states of California, Florida, and Maine are all coastal states and most states are not, thus they do not represent an unbiased sample of “all Americans” with respect to spending time near the ocean. As a result, they represent a special case of Americans from which the conclusion cannot be legitimately drawn.
In example 2, the arguer takes the rare case when an accident is made worse by a seat belt and makes a rule ignoring the overwhelming majority of cases where seat belts are more helpful. So they are “special” cases (in fact, they are exceptions to the general rule) and cannot support the generalization that wearing seat belts is more dangerous than going without.
One way to combat a hasty generalization is to think of a “just because” statement. So, you can think that just because there was a special case that happened doesn’t mean it is statistically common enough to ground the creation of a rule.
Example 3 is a hasty generalization because wartime is a special circumstance, during which it is widely (although not universally) agreed that some peacetime rights can be temporarily ignored. Whatever one’s view on the conclusion, this fact blocks the generalization made in the argument.
18.3 Difference Between Hasty and Sweeping Generalization
Both hasty and sweeping generalizations deal with the relationship between generalizations and special cases (rules and boundary conditions).
In the above image (fig. 18.1), you have a relevantly similar group to which a specific rule applies. The line between the group members and the members in special circumstances represents the different conditions that block the application of the rule. Imagine the group members are “cars on the road” and the rule is the speed limit. But the vehicles in special circumstances are ambulances. They do not have to follow the speed limit (when they are actively responding to an emergency). So their special circumstances block the application of the rule.
Figure 18.1 A group with a rule and the special case where it doesn’t apply. Artwork by Jessica Tang.
18.4 Difference Between Hasty and Sweeping Generalization and Composition and Division
Students sometimes confuse the fallacies of hasty generalization and sweeping generalization respectively with the fallacies of composition and division. Hasty generalization improperly generalizes from an unusual specific case, whereas composition involves an inference from the possession of a feature by every member of a class (or part of a greater whole) to the possession of that feature by the entire class (or whole). So the difference is between “this X is Y, therefore all Xs are Y” and “Every X in G is Y, therefore G is Y.” For the fallacy of composition, the central fact is that even when something can be truly said of each and every individual member, it does not follow that the same can be truly said of the whole class. Similarly, division involves an inference from the possession of some feature by an entire class (or whole) to the possession of that feature by each of its individual members (or parts), and this differs from sweeping generalization, which mistakenly applies a general rule to an atypical specific case (fig. 18.2).
Figure 18.2 Difference between hasty and sweeping generalization. Artwork by Jessica Tang.
Fallacy | Example | Explanation |
|---|---|---|
Division | The old have many health problems. Martha is old. ___________ So: Martha has many health problems. | “Many health problems” is a feature of a group that cannot be divided down to an individual such as Martha. “Many” is vague and is likely speaking to a statistical average, which of course means there is a distribution of health indicators within that group. |
Sweeping generalization | Poodles are popular dogs. Ditzy is a poodle who bites people. ___________ So: Ditzy is a popular dog. | Poodles as a group are popular, this is for certain. But Ditzy, who is a poodle, bites people, which acts against their popularity. Thus we cannot take the rule that poodles are popular and apply it to Ditzy. Ditzy’s biting blocks the application of the rule. |
Composition | Every player on the team is excellent. ___________ So: The team is excellent. | Here a property of each player is attributed to the team as a whole. This is fallacious because, as many fans of team sports will tell you, teams have dynamics that are different from the abilities of each individual player. |
Hasty generalization | Emil, the star centre of the team, is excellent. ___________ So: The team is excellent. | Notice how Emil is identified as a “star centre.” This is a special circumstance that blocks the inference to a generalization about the team. |
18.5 The Fallacy of Bifurcation
The fallacy of bifurcation is sometimes called the either-or fallacy, false dichotomy, “excluded middle,” or false dilemma. Bifurcation is the fallacy of treating a distinction or classification as exclusive and exhaustive of the possibilities when in fact other alternatives exist. Here the arguer presents two exclusive options to force a choice in the dialogue partner. Another way to explain this false choice is to say that this fallacy confuses contraries with contradictories.
Two statements are contradictories if the first is false then the second is true and vice versa. With two contradictory statements, one is always true and the other false. But contrary statements don’t always have opposing truth values. Contraries can both be false. (Recall we discussed contraries in our discussion of categorical logic, Chapter 11.) You might remember this from our discussion of inclusive versus exclusive “or” with the disjunctive syllogism. Student papers often suffer from the fallacy of bifurcation. Often a paper will have the argument form that either A or B is true, and since A is false, B must be true. If A and B are only contraries and there are other possibilities (C, D, . . . , etc.), the effect is that the paper as a whole fails, even though the individual arguments may be acceptable.
Let us look at the difference between a contrary and a contradictory:
- 1. (Contradictory) Either a human is alive, or he is not (can’t have someone be alive and dead at the same time).
- 2. (Contrary) Either it is Wednesday, or it is Thursday (can’t be both Wednesday and Thursday at the same time).
For 1, ask yourself, can both statements be true? Can some be alive and not alive? No. But 2 should hit differently at this point. Let’s ask the same questions: Can they both be true? Can it be Wednesday and Thursday at the same time? No. But can they both be false? Yes, because whenever it is Sunday, Monday, Tuesday, Friday, or Saturday, both statements are false.
The fallacy of bifurcation is when an arguer treats a distinction of classification as exclusive and exhaustive of the possibilities when in fact other alternatives exist. In this fallacy, one confuses contraries with contradictories.
Have you ever heard the phrase “You can’t be a little bit pregnant,” implying that you are either pregnant or you are not pregnant? This is because the statements “you are pregnant” and “you are not pregnant” cannot both be true (they are contradictory). But there are other uses of “or” in life that are much more forgiving. I (Kristin) like to think about my years as a waitress. Breakfast specials often have a complex array of “ors” operating. You can have eggs, bacon, or sausage (both are possible!) and hash browns and toast or pancakes (all three are possible, but it costs extra!).
Because our language is full of opposites, we have a strong tendency to bifurcate and argue either (the first) . . . or (the second). But many situations do not present us with opposites like this. In fact, most opposites are not genuine contradictories but simply contrast classifications. Take “weak” and “strong” for example. Quite apart from the fact that there are different respects in which things can be weak or strong, it is quite possible for something to be neither weak nor strong in whatever respect one considers. Weak and strong represent boundary cases between which there is a normal range. Thus one cup of coffee could be weak, another normal, and a third strong.
Example 1 is definitely trying to sell us something with a false choice. These are presented as one or the other, but really, a person might not own one or want to own one.
Example 2 presents “cheap” and “good” as contradictory, but they are really contraries. Other options exist, so the argument is fallacious.
Example 3 is very common among political speeches and rhetoric. Here the speaker has used an “or” between two terms, “safety” and “freedom,” when the two are not even contraries.
Like many fallacies we will discuss, a good place to look for the fallacy of bifurcation is the editorial page of the newspaper. Letters to the editor are also frequently fallacious in this way. A good example is President’s Bush’s famous November 20012 claim that “You’re either with us or with the enemy.” In short, the fallacy of bifurcation is easy to identify because an assertion is made that there are only two possibilities when there are three or more (or at least the arguer hasn’t provided a reason to think otherwise).
Key Takeaways
- • Fallacies of presumption are unsound because of unfounded or unproven assumptions embedded in them.
- • The fallacy of sweeping generalization is committed when an argument that depends on the application of a generalization or rule to a particular case is improper because a special circumstance (accident) makes the rule inapplicable to that particular case.
- • The fallacy of hasty generalization is committed when an argument that develops a general rule does so in an improper way because it reasons from a special case (accident) to a general rule.
- • The fallacy of bifurcation is when an arguer treats a distinction of classification as exclusive and exhaustive of the possibilities when in fact other alternatives exist. In this fallacy, one confuses contraries with contradictories.
Exercises
Identify Fallacies of Presumption (and Ambiguity)
Identify the fallacies of presumption, and explain why they are the particular fallacies you identify and what is wrong with them. Note: There are also examples of composition and division mixed in.
- 1. Each oil company is perfectly free to set its own price for gas, so there can be nothing wrong with all the oil companies getting together to fix a common price for gas.
- 2. Diamonds are rarely found in this country, so be careful not to misplace your wedding ring.
- 3. The New Democratic Party was booted out of government in the last provincial election in Saskatchewan, so the New Democratic MLA Pat Atkinson must have lost her race here in Saskatoon Broadway.
- 4. Traffic accidents are on the increase. Collisions between Model T Fords are traffic accidents, therefore collisions between Model T Fords are on the increase.
- 5. Yes, I know Mike had surgery, but that was a month ago, and he should have recovered by now. The point is that his term paper ought to have been in by now. That’s enough to show me that nobody can ever count on Mike to do his work.
- 6. Anyone who cares about their appearance would never wear sweatpants. I just picked up Marcia from the gym, and she is wearing sweatpants, so we can see she has chosen not to care about her appearance.
- 7. Marcia loves pepperoni and olives, and she is crazy about butterscotch swirl ice cream, so she is sure to love the pepperoni and olive butterscotch swirl sundae you made her.
- 8. Consider why you should accept Jesus into your heart as your personal saviour. Do you want to go to hell? You have a choice, salvation or endless suffering. If you accept Jesus and change your life, you will be saved. If you don’t, you will go to hell.
- 9. Terminally ill people in hospital are often given morphine drips when they are in pain, so morphine must be a good pain reliever for my headache.
- 10. Dogs are harmless companions, therefore this 110-pound Cane Corso that hasn’t eaten in a week is harmless.
- 11. Athletes are physically fit, so this strong-man competition winner should be able to run a 40-kilometre marathon.
- 12. Birds can fly, so penguins can fly.
- 13. In life, you either choose to dedicate yourself to your family or your career. You choose.
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