Main Think Again: How to Reason and Argue
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PART II HOW TO ARGUE In gratitude to Stacey Meyers, Lisa Olds, Diane Masters, Dana Hall, and all of the unsung heroines who enable me to do what I want. 9 HOW TO EVALUATE ARGUMENTS AFTER WE IDENTIFY AN ARGUMENT along with its purpose and structure and fill it out with suppressed premises, we finally reach the time to evaluate it—that is, to ask whether it is any good. To call something good, as we saw, is to say that it meets the relevant standards. So, what are the relevant standards for arguments? One standard is pragmatic. Just as we call an advertisement good when it increases sales, because that is its purpose, so we call an argument good when it serves its intended purpose. If an argument is presented to persuade some audience, then it is good in this pragmatic way to the extent that it succeeds in persuading that audience. However, the argument might persuade only by tricking its audience into believing something that they have no real reason to believe. The argument might give no reason at all or only a very bad reason. Then it persuades without justifying. If we seek justification, understanding, and truth instead of only persuasion, then we hold arguments to a higher standard. We want arguments that provide good and adequate reasons or at least some real reason as opposed to a trick or misdirection. But then we need standards for determining when reasons are good in some epistemic sense that has to do with truth and justification instead of only belief or persuasion. That is the kind of standard and value that we discuss in this chapter. The particular relation to truth and justification that an arguer claims can be revealed by the argument’s form. Some arguers want their premises to guarantee their conclusions whereas others are happy with some evidence well short of any guarantee. On this basis, it is common to distinguish deductive from inductive forms of arguments, so we will follow that tradition, although we will s; ee that this distinction is problematic in some ways. WAS SHERLOCK HOLMES A MASTER OF DEDUCTION? Let’s start with a few simple examples. Imagine someone who argues like this: (I) Noel is a Brazilian. Therefore, Noel speaks Portuguese. This argument is clearly not valid, because Noel could easily be a Brazilian who does not speak Portuguese. Maybe Noel is a baby who is too young to speak any language or a recent immigrant who has not yet learned Portuguese. Despite these weaknesses, it is easy to add a single suppressed premise that makes this argument valid: (II) All Brazilians speak Portuguese. Noel is a Brazilian. Therefore, Noel speaks Portuguese. Now it is not possible for both premises to be true when the conclusion is false. If the conclusion is false because Noel does not speak Portuguese, then either Noel is not a Brazilian (in which case the second premise is false) or Noel is a Brazilian who does not speak Portuguese (in which case the first premise is false). This relation between its premises and conclusion makes argument (II) valid. Great, so it is valid! Does that make argument (II) any better than argument (I)? No. Adding the suppressed premise that turned invalid (I) into valid (II) simply shifted any doubts from the relation between the premises and conclusion in (I) to the first premise in (II). This shift merely raises the question of whether we should accept that added premise. What kind of evidence could support the premise that all Brazilians speak Portuguese? Maybe the speaker generalized from the Brazilians whom he knows. Then his argument might seem like this: (III) All Brazilians whom I know speak Portuguese. Noel is a Brazilian. Therefore, Noel speaks Portuguese. Unfortunately, now the argument is back to being invalid, because it is possible that I do not know Noel, who does not speak Portuguese even though he is a Brazilian. Another possibility is that the arguer read on Wikipedia that Brazilians speak Portuguese, and he assumed this meant all Brazilians. (IV) Wikipedia says that Brazilians speak Portuguese. Therefore, all Brazilians speak Portuguese. Noel is a Brazilian. Therefore, Noel speaks Portuguese. The last three lines are just like argument (II), so that second part is still valid. However, the inference from the first line to the second line is clearly not valid, because Wikipedia might be wrong or might have been referring only to Brazilians in general rather than to every single Brazilian, including babies and recent immigrants. This sequence of arguments teaches an important lesson. Argument (II)—repeated in lines 2–4 of (IV)—is the only one that is valid. By squeezing the argument into this stilted form, the speaker suggests that he intends argument (II) to be valid. After all, it is obviously valid, and it took effort to formulate it to be valid, so the speaker must have wanted it to be valid and to appear valid. In contrast, arguments (I), (III), and the first two lines of (IV) are all obviously invalid, so speakers would not formulate these arguments in this way if they intended these arguments to be valid. This contrast shows that some speakers intend their arguments to be valid, while others do not. That intention is the difference between deductive and inductive arguments. An argument is deductive if its proponent intends it to be valid. An argument is inductive if its proponent does not intend it to be valid. Thus, argument (II) is deductive, but arguments (I) and (III) are inductive. Argument (IV) combines an inductive argument in its first two lines with a deductive argument in its lines 2–4. It might seem odd to distinguish forms of arguments in terms of what their proponents intended. The reference to intention is needed, however, because of bad deductive arguments, like this: (V) All Brazilians speak Portuguese. All citizens of Portugal speak Portuguese. Therefore, all Brazilians are citizens of Portugal. If speakers were ever confused enough to give this invalid argument, then the fact that they put it in this form would suggest that they intended it to be valid. That intention explains why we would classify this argument as deductive, even though it is invalid and fallacious. This way of distinguishing deduction and induction shows why that distinction is important. Since deductive arguments are intended to be valid, it is fair to criticize them for being invalid. In contrast, the fact that an inductive argument is invalid is no criticism at all, because it is not intended to be valid. To criticize an inductive argument for being invalid is just as inappropriate as criticizing a rugby ball for failing as a football (or soccer ball), when the rugby ball was never intended for use in that other game. Although this notion of deduction is common among philosophers and logicians, others conceive of deduction very differently. Some people say that induction rises from particulars to generalizations. This characterization is inaccurate, because some inductive arguments run in the reverse direction, as we will see. Another potential source of confusion is Sir Arthur Conan Doyle, who described his fictional detective, Sherlock Holmes, as a master of the science of deduction because Holmes could draw conclusions from minor observations that others overlooked. In one story, Holmes glimpses a man on the street and immediately pegs him as “an old soldier . . . served in India . . . Royal Artillery.” How could he tell so much so quickly? “Surely, answered Holmes, “it is not hard to say that a man with that bearing, expression of authority, and sun-baked skin, is a soldier, is more than a private, and is not long from India . . . . He had not the cavalry stride, yet he wore his hat on one side, as is shown by the lighter skin on that side of his brow. His weight is against his being a sapper [a soldier who works on fortifications]. He is in the artillery.”1 These inferences are amazing, but are they deductive? Well, the arguments are clearly not valid, because it is possible that the man is an actor playing the part of an old artilleryman in India. Since their invalidity is so obvious, it is unlikely that anyone as smart as Holmes would have intended them to be valid. So these arguments are not deductive by our definition. That does not mean that the arguments are no good. Their brilliance is the point of the incident in the story. Still, instead of being a master of deduction, Holmes is a master of induction—in the philosophical sense of these terms. WHAT’S SO GREAT ABOUT DEDUCTION? Why did Conan Doyle misleadingly describe Sherlock Holmes as a master of deduction instead of induction? Perhaps to heap the highest possible praise on Holmes’s reasoning. Many people assume that deduction is somehow better than induction. The comparisons among arguments (I)–(V) should already make us skeptical of this assumption, but it is worth asking why so many people believe it. One reason for preferring deduction might be that it seems to achieve certainty by ruling out all possibilities. A valid argument excludes any possibility of a false conclusion when its premises are true. Another apparent advantage of deduction is that validity is indefeasible in the sense that if an argument is valid, then adding an extra premise can never make it invalid. (Just try it with argument (II).) Addition cannot invalidate validity. These features of deduction seem desirable if you want certainty. Unfortunately, you can’t always get what you want, according to philosophers Mick Jagger and Keith Richards. The appearance of certainty in deductive arguments is an illusion. The conclusion of a valid argument is guaranteed only if its premises are true. If its premises are not true, then a valid argument shows nothing. Hence, when we cannot be certain of its premises, a deductively valid argument cannot create certainty about its conclusion. An argument’s validity does rule out the option of believing the premises and denying the conclusion, but you still have several alternatives: You can either accept the conclusion or deny a premise. In argument (II) above, you can deny the conclusion that Noel speaks Portuguese as long as you give up either the premise that Noel is Brazilian or the other premise that all Brazilians speak Portuguese. The argument cannot tell you whether its own premises are true, so it cannot force you to accept its conclusion as long as you are willing to give up one of its premises. This point is ossified in the adage: “One person’s modus ponens is another person’s modus tollens.” Recall that modus ponens is the argument form “If x, then y; x; so y,” whereas modus tollens is the argument form “If x, then y; not y; so not x.” In modus ponens, the antecedent x is accepted, so the consequent y is also accepted. But in modus tollens, the consequent y is rejected, so the antecedent x is also rejected. The conditional “If x, then y” cannot tell us whether to accept its antecedent x and then apply modus ponens or instead to deny its consequent y and then apply modus tollens. Similarly, a valid argument cannot tell us whether to accept its premises and then accept its conclusion or instead to reject its conclusion and then also reject one of its premises. As a result, the valid argument by itself cannot tell us whether to believe its conclusion. We cannot easily give up either premise if both premises are certain or justified. However, all that shows is that the real force of a valid argument comes not from its validity but from the justifications for its premises. If my only reason to believe that all Brazilians speak Portuguese is that all Brazilians whom I know speak Portuguese, then it is hard to see why valid argument (II) is any better than invalid argument (III). The only real difference is that the uncertainty in argument (II) is about its first premise, whereas the uncertainty in argument (III) is about the relation of its premises to its conclusion. Neither form of argument avoids uncertainty. They simply locate that uncertainty in different places. For these reasons, we need to give up our quest for certainty.2 One way to curtail this impossible dream is to turn from deductive arguments to inductive arguments. Inductive arguments are not intended to be valid or certain. They do not try or pretend to rule out every contrary possibility. They admit to being defeasible in the sense that further information or premises can turn a strong inductive argument into a weak one. All of this might seem disappointing, but it is actually invigorating. The realization that more information could make a difference motivates further inquiry. A recognition of uncertainty also brings humility and openness to contrary evidence and competing positions. These are advantages of inductive arguments. HOW STRONG ARE YOU? Since inductive arguments by definition do not aim at validity, what do they aim at? The answer is strength. An inductive argument is better if its premises provide stronger reasons for its conclusion. Satisfied? I hope not. You should be asking, “But what is strength? It is a relation between premises and conclusion, but how can we tell when one reason or argument is stronger than another? And what makes it stronger?” No answer has achieved consensus. The notion of inductive strength is still highly controversial, but one natural way to think about strength is as probability. On this view, the strength of an inductive argument is (or depends on) the conditional probability of its conclusion, given its premises. An inductive argument is stronger when the probability of its conclusion, given its premises, is higher. To understand this standard of strength, we need to learn a little about conditional probability. Imagine an area of India where it rains one out of five days in general, but it rains four out of five days during monsoon season. What is the probability that it will rain there on Gandhi’s birthday? That depends on the date of Gandhi’s birthday. If you have no idea when Gandhi’s birthday is, it is reasonable to estimate this probability as one out of five or 0.20. But suppose you discover that Gandhi’s birthday is during the monsoon season in this area of India. With that extra information, it now becomes reasonable to estimate the probability of rain on Gandhi’s birthday as four out of five or 0.80. This new figure is the conditional probability of rain on Gandhi’s birthday in this area, given that his birthday is during the monsoon season in that area. The application to inductive arguments is straightforward. Consider this argument: Our parade will occur on Gandhi’s birthday in that area. Therefore, it will rain on our parade. This argument is neither valid nor deductive, so it makes sense to evaluate it by the inductive standard of strength. The premise by itself gives no information about when Gandhi’s birthday is, so the conditional probability of the conclusion, given the premise, is 0.20. That argument is not very strong, since it is more likely than not that it won’t rain there then, given only the information in the premises. But now let’s add a new premise: Our parade will occur on Gandhi’s birthday in that area. Gandhi’s birthday is during monsoon season in that area. Therefore, it will rain on our parade. The argument is still not valid, but it is stronger, because the conditional probability of the conclusion, given the premise, has risen to 0.80. The extra information in the new premise increases the probability. All of this is common sense. If you do not know when Gandhi’s birthday is, the first argument is not a strong reason to reschedule the parade. But when someone adds, “That’s during monsoon season!” then it makes sense to reschedule the parade, unless you like walking in the rain.3 HOW DO I INDUCE THEE? LET ME COUNT THE WAYS What is in the grab bag of inductive arguments? Let’s reach deep into the bag and see what comes out. Imagine that you want to open a restaurant, and you have chosen a location in Edinburgh, but you have not yet decided whether to serve Ethiopian food or Turkish food, your chef’s two specialties. The success of the restaurant depends on how many people in the neighborhood like each kind of food. To answer this crucial question, you ask random people in the neighborhood and discover that 60% like Turkish food but only 30% like Ethiopian food. You conclude that these same percentages hold throughout the whole neighborhood. This inference is a statistical generalization that argues from premises about the small sample that you tested to a conclusion about a larger group. Such generalizations are inductive arguments because they are not intended to be valid. The tested sample clearly might not match the whole neighborhood. Next you need to test items for your menu. You decide to try them out on friends and neighbors, but you do not want to test Turkish food on people who do not like it, since they won’t come to your restaurant anyway. You wonder whether your neighbor to the south of your restaurant likes Turkish food. You don’t know anything special about him, so you conclude that he probably has a 60% chance of liking Turkish food. This argument can be called a statistical application, because it applies a generalization about the whole population to an individual. It is inductive, because it is clearly not valid. It could underestimate the probability if, for example, your neighbor happens to be Turkish. Finally, your restaurant opens, but nobody shows up. Why not? The explanation cannot be that people in the neighborhood do not like Turkish food, since 60% do. The explanation cannot be that your prices are too high or that your dishes taste bad, because potential customers do not know your prices or quality yet. The explanation cannot be lack of advertising, because you have big banners, a fancy website, and advertisements in local papers. Then you hear that someone has been spreading rumors that your restaurant is filled with cockroaches. Who? Nobody else would have a motive, so you suspect the owner of the older restaurant across the street. This conclusion is supported by an inference to the best explanation. It is also an inductive argument, because its premises give some reason to believe your conclusion, but your suspicions could still be wrong. Although discouraged, you regain hope when you remember the story of another Turkish restaurant that had a rough first month but then later became extremely popular as soon as people tried it. That other restaurant is a lot like yours, so you conclude that your restaurant will also probably take off soon. This argument from analogy is inductive, because it is clearly not valid but does give some reason for hope. Luckily, your restaurant turns into a huge success. Customers pile in. What attracts them to your restaurant? To find out, you lower your prices a little, but that has no effect on turnout. Then you check your records to see which dishes customers order more often, but nothing sticks out. Your curiosity is piqued, so you drop items off your menu one by one and observe changes in the clientele. There is a big drop in customers when you take kokoreç off the menu. Kokoreç consists of lamb or goat intestines wrapped around seasoned hearts, lungs, and kidneys. You had no idea that local people like offal so much, but your experiment supports the conclusion that this dish is what causes people to come to your restaurant. This causal reasoning is inductive, because it is possible that something else is the cause, so the argument is not valid, but it still gives you some reason to believe its conclusion. Accordingly, you put kokoreç back on your menu. All goes well until your restaurant is robbed. The only witness reports that the robber drive off in a Fiat. Only a small percentage (2%) of cars in Edinburgh are Fiats, so the witness’s report is surprising, and you wonder whether to trust it. You and the police estimate that this witness in these lighting conditions will identify a Fiat correctly around 90% of the time and will misidentify another kind of car as a Fiat around 10% of the time. That sounds pretty good, but then (using Bayes’s theorem) you calculate that the probability of this report being accurate is less than one in six.4 It is five times more likely that the witness misidentified another car as a Fiat. This argument exemplifies reasoning about probability. This story could go on, but it already includes six kinds of inductive arguments: statistical generalization, statistical application, inference to the best explanation, argument from analogy, causal reasoning, and probability. Each of these forms of argument is common in many areas of everyday life. Each has its own standards and can be performed well or poorly. Each has special fallacies associated only with it. Instead of surveying them all, I will focus on a few of the most important kinds of inductive argument.5 HOW CAN DATES AND POLLS GO SO WRONG? Profiling and stereotypes are anathema to many people. Police are supposed to choose whom to stop or arrest by observing what those people do instead of what they look like or where they are. In everyday life, many people aspire to Martin Luther King’s vision: “I have a dream that my four little children will one day live in a nation where they will not be judged by the color of their skin, but by the content of their character.”6 We all hope to be treated as individuals rather than as members of groups. Despite these hopes and dreams, all of us often use stereotypes about groups to predict how other individuals will act. Marketing experts use generalizations about groups to predict which customers will buy their products, as with our Turkish restaurant. Doctors use risk factors—which include group membership—to recommend medications and operations. Insurance agents charge individual clients on the basis of whether they belong to groups that cost insurers expensive payments. Universities decide which applicants to admit on the basis of their grades. We hope that these professionals will not judge customers, patients, clients, or applicants by the color of their skin, but they also do not base their decisions on the content of their character. They can’t, because they do not know the content of their character. In many contexts, it is hard to see how we could do without stereotypes. If I do not know someone at all but I need to make a fast decision, then the only information I can use is what I can observe quickly. For example, if a stranger in a public bar talks casually with me for a few minutes and then offers to buy me a drink or dinner, then I need to decide whether to trust this stranger. What is he up to? As we saw, Sherlock Holmes might be able to induce a great deal about this stranger, but most of us have no choice but to rely on a few inaccurate generalizations based on our limited experience. We all do it, whether or not we accept the stranger’s offer. These cases depend on arguments up and down. First, they generalize up from premises about a sample of a group to a conclusion about the group as a whole. Second, they apply the resulting generalization back down to a conclusion about the individual. These two stages can be described as generalization and application. Generalization Each of these forms of argument introduces numerous complexities and complications. Even the most sophisticated reasoning of this sort can go badly wrong. Just recall the surprising mistakes made by political polls in the Brexit vote in the United Kingdom and also the 2016 presidential election in the United States. In those cases, even professional statisticians with tons of data were way off base. To avoid such errors and to fully understand statistical generalizations and applications, we all need to take several courses in statistics and probability, and then we need to gather big data of high quality. Who has the time? Luckily, a simple example can illustrate a few common methods and mistakes without going into technical detail. Imagine that you are seeking a male life partner who will play golf with you, and you are curious about online dating websites. You go onto one site, randomly pick ten potential dates, and ask each of them how often he played golf in the last six months. Only one of them reports having played golf at all in the last six months. You reason that only 10% of your sample played golf in the last six months, so around 10% of people who use online dating services play golf. This argument is a statistical generalization, because it runs from a premise about a sample (the ten you asked) to a conclusion about the whole group (people who use online dating sites). On the next day, someone else who uses the site contacts you. You decide not to reply, because you reason like this: “This person uses an online dating website, and only 10% of online dating website users play golf, so this person probably does not play golf—or, more precisely, there is only a 10% chance that this person played golf in the last six months.” This argument is a statistical application because it applies premises that include a generalization about the whole group to a conclusion about this particular user. Both of these arguments are inductive, because they are clearly not valid. It is possible that only 10% of your sample plays golf, but many more people who use online dating services play golf. It is also possible that 10% of people who use online dating services play golf, but it is much more likely that this individual plays golf. Because these possibilities are so obvious, this argument is probably not intended to be valid. How strong are these inductive arguments? That depends on the probability of the conclusion given the premises. To assess that, we need to ask a series of questions to determine how each argument could go astray. The first question to ask about the generalization is whether its premise is true. Did only one out of your sample of ten play golf in the last six months? Even if only one reported playing golf then, maybe more of them played golf, but they chose to ignore that question; or maybe they played golf but forgot about it; or maybe they denied playing golf because they thought you were asking your question in order to weed out dates who play golf too often. People on online dating sites are not always trustworthy. What a surprise! The second question is whether your sample is big enough. It is better to ask ten than to ask only three, but it would be better yet to ask a hundred, although it would take a long time to gather such a large sample. A sample of ten, thus, gives your argument some strength, but not much. Whether it is strong enough depends on how much is at stake. If the sample is too small, then the argument commits a fallacy called hasty generalization. The third question is whether your sample is biased. A sample is biased when the percentage of the sample with the feature you are seeking is significantly higher or lower than the percentage of the whole group with that feature. Notice that even a large sample (such as 100 or 1,000 online daters) can be biased. This bias could occur if most golfers use a different online dating website, which reduces the number of golfers who use the website that you are sampling. Then you should not use your sample to draw any conclusion about how many people who use online dating services in general play golf. Even if you are interested only in this particular website, your sample might be biased if your application mentioned that you play golf, and the website used this information to suggest possible contacts. Then the names that you received might include many more golfers than is representative of the website as a whole. Or the website might send you only names of local users, and you might live in an area with fewer (or more) golfers than other areas. Another way to bias your sample is by asking leading or misleading questions. The percentage of affirmative answers would probably have been much higher if you had asked, “Would you ever be willing to play golf?” and much lower if you had asked, “Are you fanatical about golf?” To avoid this way of pushing your results in one direction or the other, you asked, “How often did you play golf in the last six months?” This apparently neutral question still might have hidden biases. If you ask it in April, many golfers in snowy climates will not have played golf in six months, even though they will play as much as they can after the snow melts and their courses open. To avoid this problem, you should have asked about a full year. Or maybe they really do like to play golf, but they have nobody to play golf with, so they are also looking for a partner who plays golf. Then you should have asked whether they want to play golf. The results of generalizations are often affected by the questions used to gather a sample. Overall, every inductive generalization from a sample needs to meet several standards. First, its premises must be true. (Duh! That is obvious, but people often forget it.) Second, its sample must be large enough. (Obvious again! But people rarely bother to ask how big the sample was.) Third, its sample must not be biased. (Bias is often less clear, because it is hidden in the sampling methods.) You will be fooled less often if you get in the habit of asking whether all three standards are met whenever you encounter or give an inductive generalization. Application The next kind of induction applies generalizations back down to individuals. Our example was this argument: “This person uses an online dating website, and only 10% of online dating website users play golf, so this person probably does not play golf.” How strong is this argument? As always, the first question that you need to ask is whether its premises are true. If not (and if you should know this), then this argument does not give you a strong reason to believe the conclusion. But let’s assume that the premises are true. You also need to ask whether the percentage is high (or low) enough. Your argument would provide a stronger reason for its conclusion if its premise cited 1% instead of 10% and a weaker reason for its conclusion if its premise cited 30% instead of 10%. And if its premise were that 90% of online daters play golf, then it could provide a strong reason for the opposite conclusion that this person probably does play golf. These numbers affect the strength of this kind of inductive argument. Another kind of mistake is more subtle and quite common. What if the person who contacts you on the dating website contacted you because your profile on the dating website mentioned golf? Add that 80% of users who contact people because their profiles mention golf are themselves golfers. We can build this new information into a conflicting statistical application: This person contacted you because your profile mentioned golf, and 80% of users who contact people because their profiles mention golf are themselves golfers, so this person probably does play golf—or, more precisely, there is an 80% chance that this person plays golf. Now we have statistical applications with opposite conclusions. The first said that this person probably does not play golf. The second says that this person probably does play golf. Which is more accurate? Which should we trust? The crucial difference to notice is that these arguments cite different classes, called reference classes. The first argument cites percentages within the class of online dating website users, whereas the second cites percentages within the class of those special online dating website users who contact people because their profiles mention golf. The latter class is smaller and a proper subset of the former class. In cases like this, assuming that the premises are true and equally justified, the argument with the narrower reference class usually provides a stronger reason, because its information is more specific to the case at hand. Conflicting reference classes are often overlooked by people who apply generalizations to individual conclusions. This mistake combined with the fallacy of hasty generalization lies behind a great deal of stereotyping and prejudice. We all depend on generalizations and stereotypes in some cases, but mistakes about disadvantaged and vulnerable ethnic, racial, and gender groups can be especially harmful. A bigot might run into one stupid, violent, or dishonest member of an ethnic group. Every group has bad apples. The bigot then hastily generalizes to the conclusion that everyone in that ethnic group is similarly stupid, violent, or dishonest. Then the bigot meets a new member of that ethnic group, and applies the hasty generalization. The bigot concludes that this new individual is also stupid, violent, or dishonest, without considering the fact that this new individual also has other features that indicate intelligence, pacifism, and honesty. The bigot’s small sample and failure to consider such narrower conflicting reference classes show how bad reasoning can play a role in originating and maintaining prejudice. Bad reasoning is not the whole story, of course, since emotion, history, and self-interest also fuel bigotry, but we still might be able to reduce some prejudice to some degree by avoiding simple mistakes in inductive arguments. WHY DID THAT HAPPEN? Our next form of inductive reasoning is inference to the best explanation. It might be the most common form of all. When a cake does not rise, the baker needs to figure out the best explanation of this catastrophe. When a committee member does not show up for a meeting, colleagues wonder why. When a car does not start in the morning, its owner needs to find the best explanation in order to figure out which part to fix. This kind of inductive argument is also what detectives (like Sherlock Holmes) use to catch criminals. Detectives infer a conclusion about who did it because that conclusion provides the best explanation of their observations of the crime scene, the suspects, and other evidence. Many crime dramas are, in effect, long inferences to the best explanation. Science also postulates theories as the best explanation of observed results in experiments, such as when Sir Isaac Newton postulates gravity to explain tides or paleontologists hypothesize a meteor to explain the extinction of the dinosaurs. These arguments share a certain form: (1)Observation: Some surprising phenomenon needs to be explained. (2)Hypothesis: A certain hypothesis explains the observations in (1). (3)Comparison: The explanation in (2) is better than any alternative explanation of the observations in (1). (4)Conclusion: The hypothesis in (2) is correct. In our examples, the observations in (1) are the cake not rising, the colleague missing the meeting, the car not starting, the crime occurring, the tides rising, and the dinosaurs disappearing. Each argument then needs a set of competing hypotheses to compare plus some reasons to prefer one of those explanations. Inferences to the best explanation are clearly not valid, since it is possible for the conclusion (4) to be false when the premises (1)–(3) are all true. That lack of validity is, however, a feature rather than a bug. Inferences to the best explanation are not intended to be valid, so it is unfair to criticize them for failing to be valid—just as it would be unfair to criticize a bicycle for failing to work in the ocean. Inferences to the best explanation still need to meet other standards. They can go astray when any of their premises is false. Sometimes an inference to the best explanation is defective because the observation in premise (1) is not accurate. A detective might be misled when he tries to explain the blood on the car seat, when the stain is really beetroot juice. An inference to the best explanation can also go astray when the hypothesis in premise (2) does not really explain the observation. You might think that your car did not start because it was out of fuel when actually the starter did not even begin to turn over, and lack of fuel cannot explain that observation, since the starter does turn over when it is out of fuel (but not when the electrical system fails). Perhaps the most common problem for inferences to the best explanation is when premise (3) is false either because a competing hypothesis is better than the arguer thinks or because the arguer overlooked an alternative hypothesis that provides an even better explanation. You might think that your colleague missed the meeting because she forgot, when really she was hit by a car on the way to the meeting. Such mistakes can lead to regret and apologies. Overall, some inferences to the best explanation can provide strong reasons to believe their conclusions, as when a detective provides evidence beyond a reasonable doubt that a defendant is guilty. In contrast, other inferences to the best explanation fail miserably, such as when beetroot juice is mistaken for blood. In order to determine how strong an inference to the best explanation is, we need to look carefully at each premise and also at the conclusion. Hussein’s Tubes Let’s try this with a controversial example. Some of the most important inferences to the best explanation lie behind political decisions, such as the decision by the United States to start the Iraq war. In his testimony before the United Nations Security Council on February 5, 2003, United States Secretary of State Colin Powell gave this argument: Saddam Hussein is determined to get his hands on a nuclear bomb. He is so determined that he has made repeated covert attempts to acquire high-specification aluminum tubes from eleven different countries . . . . There is controversy about what these tubes are for. Most U.S. experts think they are intended to serve as rotors in centrifuges to enrich uranium. Other experts, and the Iraqis themselves, argue that they are really to produce the rocket bodies for a conventional weapon, a multiple rocket launcher . . . . First, it strikes me as quite odd that these tubes are manufactured to a tolerance that far exceeds U. S. requirements for comparable rockets. Maybe Iraqis just manufacture their rockets to a higher standard than we do, but I don’t think so. Second, we actually have examined tubes from several different batches that were seized clandestinely before they reached Baghdad. What we notice in these different batches is a progression to higher and higher levels of specification . . . . Why would they continue refining the specifications? Why would they go to all the trouble for something that, if it was a rocket, would soon be blown into shrapnel when it went off? . . . These illicit procurement efforts show that Saddam Hussein is very much focused on putting in place the key missing piece from his nuclear weapons program, the ability to produce fissile material.7 Of course, I do not endorse this argument. There are many reasons to doubt its premises and conclusion, especially given what we learned later. My goal is only to understand it. The most natural way to understand Powell’s argument is as an inference to the best explanation. He mentions a surprising phenomenon that needs to be explained and compares three potential explanations of that phenomenon, so his argument fits cleanly into the form above: (1*)Observation: Saddam Hussein made repeated covert attempts to acquire high-specification aluminum tubes that were increasingly refined. (2*)Hypothesis: Hussein’s desire to produce fissile material and use it to make a nuclear bomb could explain why he made the attempts described in (1*). (3*)Comparison: The explanation in (2*) is better than any alternative explanation of the observations in (1*), including Hussein’s reported desire to produce conventional rocket bodies and higher standards in Iraqi manufacturing. (4*)Conclusion: Hussein desires to produce fissile material for a nuclear bomb. Powell adds more to back up his premises, but let’s start with the central argument (1*)–(4*). Reconstructing the argument in this form should reveal or clarify how its premises work together to provide some reason to believe its conclusion. But how strong is that reason? To assess the strength of the argument, we need to go through the premises and conclusion carefully. Premise (1*) raises several questions. How high were the specifications of the tubes that Hussein tried to obtain? How do we know that he insisted on such high specifications? How many attempts did he make? How long ago? Were they covert in the sense of being hidden from everyone or only from the United States? Why did he hide them? Although such questions are important, Powell could probably answer them, and he does cite evidence of Hussein’s attempts in other parts of his testimony, so it makes sense here to focus attention on his other premises. Premise (2*) adds that the phenomena in (1*) can be explained by Hussein’s desire to produce fissile material for a nuclear bomb. This makes sense. People who desire to make fissile material will want to acquire what is necessary to make it, and high-specification aluminum tubes were needed to produce fissile material. Indeed, the high specifications were needed only for fissile material of the kind used in nuclear bombs, and there would be little use for this kind of fissile material except in making nuclear bombs. At least that is what Powell assumes. The most serious problems arise in premise (3*). This premise compares Powell’s preferred explanation in (2*) with two competitors: a desire to produce conventional rocket bodies and higher Iraqi standards in manufacturing rockets. Powell focuses on rocket bodies because that explanation was offered by Hussein himself. Still, Powell’s argument would fail if any other explanation was as strong as Powell’s preferred explanation in (2*), so we need to consider both alternatives. Powell criticizes the alternative explanation in terms of conventional rockets by asking rhetorical questions: “Why would they continue refining the specifications? Why would they go to all the trouble for something that, if it was a rocket, would soon be blown into shrapnel when it went off?” His point here is that the explanation in terms of conventional rockets fails to explain the continual refinements because rockets do not require these refinements, whereas his preferred explanation in terms of nuclear bombs succeeds in explaining these additional observations. Its ability to explain more observations is what is supposed to make his explanation better. This increased explanatory power is a common ground for preferring one explanation to another. Suppose that the hypothesis that Gregor killed Maxim explains why the boot prints outside the murder scene are size 14, because Gregor wears size 14 boots, but this hypothesis cannot explain why those boot prints have their distinctive tread pattern, because Gregor does not own any boots with that tread pattern. Then that explanation is not as good as the hypothesis that Ivan killed Maxim, if Ivan wears size 14 and also owns boots with that distinctive tread pattern. We prefer hypotheses that explain more. Powell is simply applying this general principle to the case of aluminum tubes. This argument is still subject to many objections. Critics could deny or doubt that Iraq did continue refining the specifications, in which case there would be no need to explain this. Or they could reply that these continual refinements were needed for conventional rockets, so the alternative hypothesis does explain the observations. To avoid these objections, Powell needs background arguments that are not included in the quoted passage. Still, even without delving deeper, our reconstruction has pinpointed at least two issues for further exploration. The other alternative that Powell mentions is that “Iraqis just manufacture their rockets to a higher standard than we do.” Here Powell seems to have his tongue in his cheek. That is why he thinks all he needs to say in response is simply, “I don’t think so.” This sarcastic assurance seems to build on the assumption that US manufacturing is at least as precise as Iraqi manufacturing. That assumption might be obvious to this audience, but it is striking that Powell does not explicitly give any reason to favor his own explanation above this alternative. It need not always be a problem to ignore or dismiss an alternative explanation without argument. Some alternative explanations are so clearly inadequate that they do not deserve any effort at refutation. Every inference to the best explanation would need to be irritatingly long in order to deal with every fool alternative. Nonetheless, this failure to argue against an alternative does reduce the potential audience for the argument. It cannot reach anyone with any inclination to accept this alternative explanation. The most serious weakness in Powell’s argument lies not in the alternatives he does mention but in the alternatives he does not mention. This problem pervades inferences to the best explanation. Just recall any murder mystery in which a new suspect appears after the detectives thought that they had already solved the case. The same kind of possibility can undermine Powell’s argument, but here the suspects are hypotheses. To refute his argument, all Powell’s opponents need to produce is one other viable hypothesis that explains the relevant data at least as well as Powell’s. Notice that opponents do not have to produce a better alternative. If all they want to show is that he has not justified his conclusion, then all they need to show is that there is one alternative at least as good as his. If two alternative explanations tie for top place, then Powell’s argument cannot determine which of the top two is correct. In that case, Powell’s opponents win, because he is the one who is trying to argue for one of them over the other. Still, it might be hard to come up with even one decent alternative. Maybe Hussein was controlled by aliens who eat fissile material, but he did not want any for himself. You cannot falsify that alternative hypothesis if there is no way to detect the presence of such aliens. Nonetheless, these aliens would violate well-established laws of physics, so we have plenty of reason to dismiss this hypothesis as silly. A little more realistically, maybe Hussein had OCD (obsessive-compulsive disorder), and that is why he continually demanded more refined tubes. However, he did not show symptoms of OCD in other areas of his life, so there is no independent evidence that he had this mental disorder (though maybe he had others, such as narcissism). Hypotheses like these are clearly not even decent explanations. What we really need for a realistic explanation to be as good as Powell’s is some common and plausible motive that would make Hussein seek more and more refined aluminum tubes. Well, maybe he wanted to use these tubes in some innocent kind of manufacturing. Maybe, but that hypothesis lacks explanatory power—it cannot explain much—until we make it more specific. What kinds of products are such refined tubes needed to manufacture? The hypothesis that Hussein was planning to use the tubes to manufacture some other product also cannot explain why Hussein mentioned only conventional rockets in his defense. And Powell already rejected the rocket hypothesis. Thus, it is at least not easy to come up with any explanation that is as good as Powell’s. Of course, this difficulty might be due to my (and your?) lack of knowledge about rockets, fissile material, and Iraqi manufacturing. Even if we cannot come up with any viable alternative, there still might be some explanation that is as good as Powell’s. Nonetheless, in the absence of any such alternative, Powell’s argument does give some reason to believe his conclusion. Other problems arise, however, when we look closely at that conclusion. The conclusion of an inference to the best explanation is supposed to be the same as the hypothesis that explains the observations. However, people who use this form of argument often make subtle changes in their conclusions. That happens here. First, Hussein’s attempts to acquire the tubes occurred in the past. What explains these attempts is a desire at the past time when those attempts were made. However, the conclusion is about the present: Hussein desires—not desired—to produce fissile material for a nuclear bomb. Powell exchanged “s” for “d”! Moreover, the present tense is essential. Powell wants to justify invading Iraq soon after his testimony. His argument would not work if Hussein used to desire fissile material in the past but no longer has that desire at present. Thus, Powell at least owes us some reason to believe that Hussein has not changed. Similarly, what if Hussein still desires fissile material for a nuclear bomb, but he has little or no chance of getting any of what he desires? The Rolling Stones are right again: You can’t always get what you want. Then the conclusion that Hussein wants fissile material for nuclear bombs would hardly be enough to justify invading Iraq. A lot of other world leaders want nuclear bombs, but the United States is not justified in invading all of them. An invasion could be justified only if it would avoid some harm or danger, but a mere desire for nuclear bombs without any chance of fulfilling that desire would not be harmful or dangerous—or at least not harmful or dangerous enough to justify invasion. Thus, Powell also owes us some reason to believe that Hussein has a significant chance of getting nuclear bombs. These gaps show that Powell’s argument is at best incomplete. As always, my job here is not to determine whether he was correct, much less whether the United States was justified in invading Iraq. I doubt it, partly because of what we have learned in intervening years, but that does not matter in this context. My goal is only to understand Powell and his argument better. Admitting these gaps in his argument is completely compatible with admitting that his argument still achieves something: it gives us some reason to believe the conclusion that Hussein desired to produce fissile material for a nuclear bomb. As with many arguments, we understand the argument more fully if we recognize both its accomplishments and also its limits. This example also teaches other lessons. Powell’s argument shows that inferences to the best explanation can have important effects even when they are incomplete or worse. Like other arguments, inferences to the best explanation can persuade without justifying. We all need to learn how to evaluate inferences to the best explanation in order to avoid such mistakes and all of their accompanying costs. CONCLUSION Rules to Live By NOW YOU KNOW SOMETHING ABOUT why we need arguments, what arguments are, how to analyze them, how to evaluate them, and how to catch fallacies. What next? First, admit your limits. This short book has barely scratched the surface. You have seen some purposes of arguments, some words in arguments, some valid forms of argument, some kinds of induction, and some fallacies. That is a lot to have covered, but please do not imagine that you know it all. Nobody does. Second, learn more. To understand arguments and reasons fully will take a lifetime. In addition to exploring further kinds of arguments,1 we all need to know more about language (our shared means of communication), science (including psychology and economics), mathematics (especially statistics and probability), and philosophy (which explores our basic assumptions and values). There is much more to study. Third, keep practicing. The only effective way to learn how to identify, analyze, evaluate, and avoid fallacies in arguments and reasons is to practice, practice, and practice again. The best way to practice is with other people, and the best people to practice with are people who disagree with you but sincerely want to understand you and to be understood by you. If you can find such partners, you are lucky. Treasure them and use them. Fourth, construct your own arguments. When you want to think about an important issue, construct the best argument that you can on both sides of that issue. (For example, if you want to decide whether to buy a larger car or a smaller car, spell out the reasons on both sides, such as greater comfort in a larger car, and less environmental impact from a smaller car. And if you can vote in an election, specify the reasons for and against each candidate, such as more focus on issues that matter to you or less ability to get anything done.) After laying out your reasons in discursive form, do a close analysis and a deep analysis of your own argument and evaluate its validity and strength. If you do this honestly, you will gain a better understanding of your beliefs, your values, and yourself. Then ask a friend, colleague, or opponent to analyze and evaluate your arguments, and return the favor. This exchange will help you both understand each other better. Fifth, use your skills. When? Throughout your daily life, including Internet chats, political debates, and other contexts where polarization and incivility run rampant. Don’t simply declare what you believe. Give arguments. Don’t let others merely announce their positions. Ask questions about their reasons. Don’t interrupt. Listen carefully to their answers. Don’t attack opponents too soon. Interpret them charitably. Don’t insult or abuse opponents. Be civil and respectful. Don’t commit fallacies. Be critical of your own reasoning. Don’t think that you have all the answers. Be humble. Sixth, teach others. The skills that you have learned are not widely enough shared, so share them widely. One method involves explicit training or lengthy discussions about argumentation, but that is not the only way. You can also teach others simply by pointing out problems as they arise in informal contexts. When one person interrupts another, you can ask, “What were you saying before you were interrupted?” When someone calls an opponent crazy or stupid, you can say, “I don’t think you are crazy. I want to understand your point of view.” When a speaker presents a bad argument, you can specify precisely what is bad about it. When they present a good argument, you can say why it is good. We too often let teaching opportunities like these slip by. We cannot always follow these rules. It takes too long to practice or to construct and listen to arguments on every issue. Nobody has that much patience or time. Moreover, not every circumstance is right for teaching, and not every audience is amenable to learning. Even incivility is sometimes justified. Nonetheless, we could all benefit from following these rules more than we do now. So let’s get started. 11 HOW TO REFUTE ARGUMENTS MANY PEOPLE TALK AS IF all you need to do to refute a position is simply deny it or say anything at all in reply to it. Such talk is too loose. Monty Python taught that “argument is not just contradiction” or denial. Even if you go beyond denial and say something in reply, not every response is a refutation. For example, suppose a theist argues, “God exists, because nothing else could explain the existence of the Universe.” An atheist cannot refute that argument simply by saying “No, God does not exist” or “I do not believe in God” or “That’s stupid.” The same goes for the other side. If an atheist argues, “Evil exists, so God does not,” a theist cannot refute that argument simply by saying “God does exist” or “I believe in God” or “That’s silly.” These simple responses are not refutations. To refute an argument, you need to give an adequate reason to doubt that argument. We saw that some arguments give reasons that justify belief in their conclusions, whereas other arguments give reasons that explain phenomena. In contrast, refutations give reasons to doubt other arguments. Thus, refutation is a new purpose of arguments in addition to justification and explanation. The reasons supplied by refutations are reasons to doubt rather than reasons to believe. To refute a theist’s argument that God exists, atheists do not have to show that God does not exist. All atheists need is an adequate reason to doubt that the theist’s argument provides enough reason to believe that God does exist. Similarly, theists can refute an atheist’s argument against God without giving any reason to believe that God does exist. All the theist needs is an adequate reason to doubt that the atheist’s argument shows that God does not exist. Refutation can lead to doubt and suspension of belief in both directions. Many people who refute arguments do go on to deny those arguments’ conclusions. That additional move results in part from the discomfort of admitting, “I don’t know.” Many atheists who refute arguments for God conclude that God does not exist, partly because they do not want to end up as a wishy-washy agnostic. For similar reasons, many theists who refute arguments against God jump to the conclusion that God exists. That additional claim does not, however, follow from the refutation alone. All that the refutation by itself supports is doubt, not belief. What does it mean to doubt an argument? It means simply to doubt that the argument gives enough reason to believe its conclusion. This doubt can be directed at different parts of the argument. According to our definition of arguments, an argument includes premises and a conclusion and presents the premises as a reason for the conclusion, so a refutation has three main targets to aim at. First, refutations can give reasons to doubt one or more premises. Second, refutations can give reasons to doubt the conclusion. Third, refutations can give reasons to doubt that the premises provide adequate support for the conclusion. We will survey these forms of refutation in turn. DOES THE EXCEPTION PROVE THE RULE? The first way to refute an argument is to cast doubt on its premises. This task can be accomplished either by giving some reason to believe that the premise is not true or by finding some fallacy in the strongest argument for that premise. We will focus here on one common method of refuting premises, namely, providing counterexamples. Suppose that a business owner argues, “Higher taxes always reduce employment, so we need to keep taxes low.” One way to raise doubts about this argument is to give a reason to doubt or deny its premise that higher taxes always reduce employment. That’s easy. Just point to one time when taxes went up to a high level without employment going down. That one counterexample is enough to show that higher taxes do not always reduce employment. But is this refutation strong? Not if the opponent has an easy reply. To respond, all the arguer needs is a guarding term: “Fine, so high taxes do not always reduce employment. Still, they usually do—almost always.” A single counterexample cannot raise doubts about this guarded premise. The arguer can claim that this counterexample is the exception that proves the rule in the sense that its exceptional features show that the rule holds in normal cases (rather than in the original sense of this slogan, which was that the exception tests the rule). That response is not the end of the discussion, however. As soon as the arguer admits an exception, it raises the question of whether the case under discussion is more like the rule or more like the exception. If we are trying to determine whether “we need to keep taxes low” (as the conclusion claims), then we need to figure out whether our current circumstances are more like the exceptional period when taxes go up and employment does not go down or more like the usual periods when taxes go up and employment does go down. It is not enough to give a single counterexample and then stop thinking. That further issue will not be easy to settle, but it should not be ignored. The same goes for every counterexample. Many religious and cultural traditions espouse something like the golden rule: “Do unto others as you would have them do unto you” (Matthew 7:12). It is easy to think up counterexamples to this esteemed principle. It is not wrong for judges to sentence murderers to prison, even though the judges would want not to be sentenced to prison themselves. It is not right for sadomasochists to whip their victims, even if they would like to be whipped themselves. Examples like these raise doubts about the golden rule, but how could its defenders respond? The obvious point about sadomasochists is that their (non-masochistic) victims do not consent to being whipped, whereas sadomasochists would like being whipped only in ways and at times to which they consent. Thus, the golden rule still holds if we apply it only to the act of whipping without consent. Nobody likes to be the victim of that. In the other counterexample, the judge would not like to be sentenced to prison even if she deserved it because she was guilty of a crime. However, the judge would presumably admit that punishing her would be fair in those circumstances. If so, then we can avoid this counterexample by reformulating the golden rule like this: “Do unto others as it would be fair for them to do to you.” What is wrong is then determined by what is fair instead of what you happen to like. The problem is that this reformulation of the golden rule cannot be applied to cases without determining in advance what is fair in those cases. That makes it hard to see how this rule could function as a basic principle of morality. When a counterexample casts doubt on a premise that an argument depends on, the counterexample raises doubts about whether the argument provides adequate reason for its conclusion. After all, if the premise is false, the argument fails. That is how counterexamples to premises can refute arguments. Nonetheless, the conclusion could still be true. Moreover, the argument still might succeed if it can be reformulated in a way that avoids the counterexample and still provides a strong enough reason for the conclusion. Thus, this form of refutation, like all others, is inconclusive. It moves the discussion forward instead of ending it. IS THIS ABSURDITY MADE OF STRAW? The second way to refute an argument is to cast doubt on its conclusion. If a refutation shows that a conclusion is false, then there must be something wrong with the argument for that conclusion. At least it cannot be sound. This kind of refutation might not reveal specifically what is wrong with the argument, but it can still show that something went wrong somewhere in the argument. We know that we took a wrong turn somewhere if we end up in a ditch. The strongest refutations of this flavor are reductio ad absurdum—they reduce the conclusion to absurdity. The clearest absurdities are outright contradictions. If someone gives reasons to believe that China has the largest number of citizens, an opponent could reply, “That’s absurd. Just wait a minute, and it will have more. If China had one more citizen, then it would have an even larger number of citizens, so the number that it used to have cannot be the largest number.” It is contradictory to claim that any number is the largest number. This reductio ad absurdum obviously rests on a misinterpretation. What the arguer meant was not that the number of citizens in China is the largest of all numbers but only that China has a larger number of citizens than any other country. When a refutation misinterprets a claim in order to make it look absurd, although it is not really absurd when interpreted correctly, the argument attacks a straw man or a straw person. The best response to this trick is simply, “That’s not what I meant.” Real cases are usually subtler. In June of 2017, a member of the Israeli parliament pushed for a bill that would have required all professors to give equal time to any position that any student wanted to be discussed. The goal was to enable conservative students to require their liberal professors to consider the conservative side of controversial issues so that students would not be brainwashed toward liberalism. That goal might seem reasonable, but the law would quickly lead to absurdity. Just imagine a course on neuroscience, whose professor emphasizes the role of the hippocampus in memory. One student says that memory might instead be lodged in the temporal pole. Another suggests that it could be the cingulate. A third suggests the striatum. And so on for every part of the brain. The proposed law requires the professor to give equal time to all of these possibilities. That would be absurd for two reasons. First, there is little evidence linking memory to those other parts of the brain, so what is the professor supposed to discuss? Second, it would take every minute of every class to discuss all of these possibilities, so the course could never proceed to other topics in neuroscience. These absurdities can be cited to refute anyone who argues, “Every student opinion deserves equal consideration, so professors should give equal time to any position that any student wants to discuss.” Does this refutation attack a straw man? That is not clear. On the one hand, the proponents of the law were probably thinking of positions in politics rather than neuroscience. If so, these advocates might be able to avoid absurdity by restricting the law to political issues somehow. On the other hand, it is not always clear which issues are political, so proponents of the law might have meant to include debates about politically controversial positions in history and science, such as global warming, the origins of life and the Earth, the efficacy of torture, the causes of certain wars, and so on. If the law covered all of these issues as well, then any student could stop professors from discussing any of them simply by advocating an endless number of alternative views with nothing to recommend them (except the student’s desire to avoid an impending test). That threat shows that the law would effectively prevent professors from discussing any topic within its scope. Is that absurd? I think so, but maybe that’s just because I am a professor. If that result is what proponents of the law want, then they might not see it as absurd. One lesson from this example is that absurdity is sometimes in the eye of the beholder. Not so in the case of outright contradiction, but often in real cases. Does that mean that reductios cannot refute any real arguments? No, but it does reveal that those refutations will work only for limited audiences. This refutation cannot work against extremists who hold that professors should not be able to discuss any controversial issues. Nonetheless, it can still work for moderates who think that professors should be able to discuss the main alternative positions on a controversial issue without spending equal time on every possibility that any student might like to bring up for whatever reason. This case reinforces my earlier point that arguments will never satisfy anyone whose standards are too high, such as those who seek certainty; but they can still be very useful for people with reasonable goals, such as justifying their conclusion to reasonable moderates with open minds. WHAT IS JUST LIKE ARGUING . . . ? The third way to refute an argument is to give reasons to doubt that its premises provide adequate support for its conclusion. This variety of refutation targets defects in the relationship between premises and conclusion rather than in the premises or conclusion themselves. We saw examples in our discussion of fallacies. Equivocation occurs when a word has a different meaning in the conclusion than it had in a premise. Ad hominem arguments and appeals to authority used premises about believers to support conclusions about their beliefs. And arguments beg the question when their premises are not independent of their conclusions—that is, when premises and conclusion are too closely related. The relation between premises and conclusion can also be defective in other arguments that do not fit the patterns of standard fallacies. How can we tell whether that relation is defective? The most direct method is to look closely at the argument itself and assess it for validity (if it is deductive) or for strength (if it is inductive). Recall that inductive strength is the conditional probability of the conclusion given the premises. That probability is often hard to calculate or even estimate, so this method has its limits. Another method is less direct but sometimes easier to apply: Try to construct a parallel argument that mirrors the form of the argument being assessed and has obviously true premises and an obviously false conclusion. If opponents admit that the premises are true and the conclusion is false, then this parallel argument can reveal something defective in the relation between the premises and conclusion in the original argument being assessed. In other words, when someone presents an argument, critics respond, “That’s just like arguing in this parallel way” where the parallel argument has an obvious defect. The original argument can then be defended only by showing that it does not share the same defect. Martin Luther King Jr. deployed this strategy in his “Letter from Birmingham Jail.” He had been jailed for marching in favor of racial equality and civil rights. His jailors and critics argued that he should not have marched because this protest would inspire his opponents to violently attack him and other marchers. King replied, “In your statement you asserted that our actions, even though peaceful, must be condemned because they precipitate violence. But can this assertion be logically made? Isn’t this like condemning the robbed man because his possession of money precipitated the evil act of robbery?” In this case, King’s critics argued, “The marchers precipitate violence, so they must be condemned.” He replied, in our terms, “That’s just like arguing that the robbery victim’s possession of money precipitated robbery, so the robbery victim must be condemned.” Pretty powerful reply, right? But what is going on? King does not deny the truth of the premise that the marchers precipitate violence. They do. King also does not argue that the conclusion is false. That could not be shown by switching the subject to robbery. Indeed, King’s reply might seem irrelevant. How could talking about robbery show anything about marches? The key lies in the form of the arguments. Because they share a similar form, if one is defective in its form, so is the other. The parallel argument about robbery is supposed to move from a true premise that the robbery victim’s acquisition of money precipitated robbery to a false conclusion that this victim should be condemned. That movement shows that there must be some defect in the relation between premises and conclusion in the argument about robbery. If the argument about marches has the same form and the same relation between its premises and its conclusion, then the relation between premises and conclusion in the argument about marches must also be defective. This reply does not attempt to show that the conclusion of the argument about marches is false. It still might be true that the marchers ought to be condemned. All King has shown is that this one argument is not enough to support that conclusion. He casts doubt on one argument without arguing for the opposite. Moreover, he casts only some doubt. He does not prove beyond any question that the argument fails. His critics still have several moves available. First, King’s critics can accept the conclusion that the robbery victim should be condemned. If that conclusion is true, then the parallel argument is not obviously defective, so this refutation fails to reveal a defect in the original argument. But this reply seems implausible in this case. Second, King’s critics can deny the premise that the robbery victim’s possession of money precipitated the robbery. If the robbery victim hid his money, as most people do, then the robber would not know whether he had money, so he would have robbed this victim even if he had had no money with him. Since possessing money is not necessary for him to be robbed, his possession of money might not be what causes or precipitates the robbery. This reply is perhaps more plausible but still problematic. Third, King’s critics can point out differences between the supposedly parallel arguments. The robbery victim did not know that he would be robbed, but King did know that his opponents would attack violently. The robbery victim presumably hid his possessions to avoid robbery, whereas King marched in the open and hid nothing. He wanted publicity. King cannot deny these differences between the supposedly parallel arguments, but he could deny that these differences make a difference. One way to test what makes a difference is to add premises to each argument. King’s critics could reply, “Fine, we spoke too quickly. But our main point still holds: The marchers knowingly and publicly precipitate violence, so they must be condemned.” To refute this revised argument, King would need to say, “That’s just like arguing that the robbery victim’s possession of money knowingly and publicly precipitated robbery, so the robbery victim must be condemned.” The problem is that this new premise is clearly false, so this new argument does not move from true premises to a false conclusion. As a result, it cannot reveal anything defective in the relation between this premise and this conclusion. As always, the discussion can continue. The point here is only that an attempt to refute an argument by saying “That’s just like arguing . . . ” works only if the supposedly parallel argument has true premises and a false conclusion and only if the arguments really are parallel. All of that needs to be shown for the refutation to work. It is not enough to say, “That’s just like arguing . . . ” unless it really is like arguing. . . . When this method of refutation is applied properly, it can be used to uncover many kinds of fallacies. Here are a few examples with varying degrees of strength: The Fallacy of Composition Argument: If one person doubles her income, then she will be better off. Therefore, if all people double their incomes, then they will all be better off. Refutation: That’s like arguing that if I stand up at a concert, then I will see better; so, if the entire audience stands up at a concert, then they will all see better. Lesson: What holds for parts might not hold for the whole. The Fallacy of Division Argument: North Korea is an aggressive country, and you are from North Korea, so you must be aggressive. Refutation: That’s like arguing that North Korea is a mountainous country, and you are from North Korea, so you must be mountainous. Lesson: What holds for the whole might not hold for parts. False Dichotomy Argument: You are either with us or against us, and you are not yet fully committed to our cause, so you must be our enemy. Refutation: That’s like arguing that you are either with Fiji or against Fiji, and you are not yet fully committed to Fiji, so you must be an enemy of Fiji. Lesson: People can be neutral—neither for nor against. False Equivalence Argument: There is some argument for adopting this policy, but there is also some argument against it and in favor of an alternative; so both sides are reasonable, and it is unreasonable to favor one over the other. Refutation: That’s like arguing that there is some argument for jumping off this building (how thrilling!), and there is also some argument against jumping off (how deadly!); so both choices are reasonable, and it is unreasonable to favor one over the other. Lesson: Not all arguments and reasons are equivalent. Some are better than others. (The same point holds when there are experts on both sides.) Appeal to Ignorance Argument: You can’t prove that there were weapons of mass destruction in Iraq, so there must have been none. Refutation: That’s like arguing that you can’t prove that there are tiny spiders in this room, so there must not be any tiny spiders in this room. Lesson: There might have been lots that we did not see, because they are hard to find, even when they are there. False Cause (or post hoc ergo propter hoc) Argument: Our economy improved right after he became president, so he helped our country a lot. Refutation: That’s like arguing that our economy improved right after my daughter was born, so she helped our country a lot. Lesson: The timing might be a coincidence. More generally, correlation does not imply causation. None of these refutations is conclusive. In each case, defenders of the argument could claim that (a) the premise in the refutation is false, (b) the conclusion in the refutation is true, or (c) the argument in the refutation is not really parallel to the original argument, because they differ in some relevant respect. Such attempts at refutation still shift the burden of proof to the defender of the argument, so even inconclusive refutations can make progress. They do not end the discussion, but that is not their purpose. Their goal is to rule out simple mistakes, and they can do that. When arguers succeed in defending their arguments against refutations by parallel reasoning, they usually need to complicate their arguments and add qualifications. The refutation shows that the original argument without the qualifications oversimplified the issues. The revised argument reveals complexities and subtleties that the original overlooked. Refutation can thereby improve discussions without ending them. 8 HOW TO COMPLETE ARGUMENTS IN THE PREVIOUS CHAPTER, we saw how to analyze arguments by looking closely at crucial words. This technique of close analysis helps readers locate argument parts—premises and conclusions—that are given explicitly in the text. Even after such close analysis, we still need to arrange these elements of the argument into an intelligible order and then complete this structure by inserting additional premises that are assumed but not stated openly. This method is called deep analysis. Close and deep analysis can be combined to produce argument reconstruction. The goal of this chapter is to explain deep analysis and illustrate argument reconstruction. First, however, we need to define the standard of validity that will guide these methods. WHICH ARGUMENTS ARE VALID? When non-philosophers call an argument valid, they often mean simply that it is good. The word “valid” is then an evaluative term. In contrast, when philosophers (including logicians) call an argument valid, they mean something entirely different that does not imply either that the argument is good or that it is bad. The notion of validity as it is understood by philosophers concerns the relation between the premises and conclusion in an argument. An argument is valid in this technical, philosophical sense when and only when it is not possible for there to be any situation in which all of its premises are true and its conclusion is false. This definition is also equivalent to defining an argument as valid if and only if at least one of its premises must be false in every possible situation where its conclusion is false. You can think about validity in either of these ways, depending on which formulation makes the most sense to you. Either way, it is crucial that the definition is about possibility rather than actuality. Whether an argument is valid does not depend on whether its premises or conclusion actually happen to be true. All that matters is whether a certain combination—true premises and a false conclusion—is impossible (in which case the argument is valid) or possible (in which case the argument is invalid).1 As a result, some arguments with true premises and a true conclusion are still not valid. Consider “All citizens of Egypt are less than a kilometer tall, all citizens of Egypt breathe air, so all animals that breathe air are less than a kilometer tall.” These premises and conclusion are all true. Nonetheless, this argument is still not valid because it is possible for the premises to be true when the conclusion is false. Just imagine a possible world where some giraffes grow to more than a kilometer tall. This evolution is possible, and it would make the conclusion false, but both premises could still be true if citizens of Egypt remained just like they are in the actual world. This possibility is enough to show that the argument is not valid in the technical sense of philosophers, despite the three truths it contains. On the other hand, some valid arguments have false premises and a false conclusion. For example, “All sushi chefs are women, all women play cricket, so all sushi chefs play cricket” is a silly argument, because both premises and its conclusion are false. Despite all of this falsity, it is valid in the technical sense, because it is not possible for its premises to be true when its conclusion is false. If it is false that all sushi chefs play cricket, then there must be some sushi chef who does not play cricket. That sushi chef must be either a woman or not a woman. If that sushi chef is not a woman, then the first premise (“All sushi chefs are women”) is false. And if that sushi chef is a woman, then the second premise (“All women play cricket”) is false, since we are assuming that she does not play cricket. There is no possibility of a combination where both premises are true and the conclusion is false. That makes the argument valid in this technical sense (even though it is a very bad argument in other ways). To determine whether an argument is valid, one method is to try your best to imagine or describe a situation in which the premises are true and the conclusion is false. If you can describe a situation with this combination of truth values, then the argument is not valid. Of course, you need to be sure that your description really is coherent. You might not notice some incoherence in the description, so you need to look carefully. Still, if you can describe a situation with this combination of truth values that seems coherent after close inspection, that apparent coherence is some reason to believe that the argument is not valid. On the other hand, suppose you fail to find a coherent description with that combination of truth values. Your failure might show only your lack of imagination instead of the validity of the argument. Still, if you tried hard enough, and you could not imagine any situation that makes the premises true when the conclusion is false, that is some reason to believe that the argument is valid. Trying to describe a coherent situation that combines true premises with a false conclusion is, therefore, a useful start in the absence of any more technical method. The best way to master this technique is to discuss cases with friends, who might be able to imagine possibilities that you overlook. WHEN IS VALIDITY FORMAL? Some arguments are valid because of their specific words or sentences. The argument “My pet is a tiger, so my pet is a cat” is valid, because it is not possible to be a tiger without being a cat. However, this validity is destroyed if we substitute certain other words, such as in “My pet is a tapir, so my pet is a dog.” Thus, what makes the original argument valid is the (semantic) meanings of its words—“tiger” and “cat.” In contrast, other arguments are valid by virtue of their form. Consider “My pet is either a tiger or a tapir. My pet is not a tiger. Therefore, my pet is a tapir.” If the conclusion is false (my pet is not a tapir), and the second premise is true (my pet is not a tiger), then the first premise has to be false (my pet is not either a tiger or a tapir). Thus, this argument is valid. Moreover, it remains valid no matter which words are substituted for “tiger” and “tapir” as well as “My pet.” This argument is also valid: “Your pet is either a dog or a pig. Your pet is not a pig. Therefore, your pet is a dog.” So is this one: “My country is either at war or in debt. My country is not at war. Therefore, my country is in debt.” In every case with this form, it is not possible for the conclusion to be false in circumstances where the premises are both true. Thus, this argument is valid by virtue of its form. This argument form is called denying a disjunct (because the “either” and “or” propositions are called disjuncts) or process of elimination (because the second premise eliminates one of the alternatives in the first premise). It is useful to remember a few other argument forms that are formally valid as well as a few that are not valid by virtue of their form but are often mistakenly thought to be valid. The variables “x” and “y” can be replaced by any sentence as long as the same sentence replaces the same variable wherever that variable occurs. These argument forms are valid: Modus Ponens: If x, then y; x; so y. Modus Tollens: If x, then y; not y; so not x. These argument forms are invalid: Affirming the Consequent: If x, then y; y; so x. Denying the Antecedent: If x, then y; not x; so not y. (These names are derived from calling the “if” clause the antecedent and the “then” clause the consequent in an “if . . . , then . . . ” proposition, which is also called a conditional or hypothetical.) Here are two more valid argument forms: Hypothetical Syllogism: If x, then y; if y, then z; so, if x, then z. Disjunctive syllogism: Either x or y; if x, then z; if y, then z; so, z. If you think about these argument forms and replace their variables with any sentences of your own choice, then you should be able to see which of these forms are valid and why. Formal methods (including truth tables) have been developed for showing validity by virtue of propositional form. Other methods (such as Venn diagrams, truth trees, matrices, and proofs) have also been developed for showing validity by virtue of some non-propositional forms. We will not go into those details here.2 What matters here is only to gain some initial rough feel for which arguments are valid and when their forms make them valid. WHAT MAKES ARGUMENTS SOUND? Even formal validity is not enough to make an argument good or valuable. Consider this argument: “If the Amazon is the largest river in the world, then it has the largest fish in the world. The Amazon does not have the largest fish in the world. Therefore, the Amazon is not the largest river in the world.” This argument has the form modus tollens, so it must be formally valid. However, its conclusion is false, because the Amazon is in fact the largest river in the world. So, how can its conclusion be false when it is valid? The answer is simply that its first premise is false. The largest fish do not live in the largest river. What makes arguments good is not only validity but soundness. A sound argument is defined as an argument that both is valid and also has all true premises. This definition guarantees that every sound argument has a true conclusion. Its validity ensures that it cannot have true premises and a false conclusion. Thus, the truth of its premises entails that its conclusion cannot be false. That makes soundness valuable. WHAT ARE YOU ASSUMING? These notions of validity and soundness are useful for determining when an argument depends on an assumption that it does not state explicitly. This happens often. While you and I are scheduling a business meeting in 2019, you might say, We should not schedule it for June 4, because that is the last day of Ramadan. This is all you need to say in order to move our conversation to other possible dates, if you know that we both assume that some people whom we want at the meeting will refuse to meet on the last day of Ramadan. If we add that assumption, then we get a longer argument: Some people whom we want at the meeting will refuse to meet on the last day of Ramadan. We ought not to schedule the meeting on a date on which some people whom we want at the meeting will refuse to meet. Therefore, we ought not to schedule the meeting on the last day of Ramadan. June 4 is the last day of Ramadan in 2019. Therefore, we should not schedule our meeting for June 4, 2019. A single sentence has grown into five sentences in two stages. What could possibly justify our putting so many words into your mouth? How can we tell whether you really do assume the extra premises in the larger argument? The answer relies on validity. It is fair to ascribe these extra assumptions to you, even though you did not say them, because they are needed in order to make your argument valid. Without the implicit assumption that “We ought not to schedule the meeting on the last day of Ramadan,” it is hard to see how your explicit premise “That [June 4] is the last day of Ramadan” gives any reason for your explicit conclusion “We should not schedule it [our meeting] for June 4.” Adding the extra premise makes the argument valid, for it is not possible that both premises are true and the conclusion is false in the same situation. The new premise thereby explains why the original premise was a reason for the original conclusion. This addition then raises the question of why we should accept the new premise. After all, even if the argument with this premise is valid, that validity by itself does nothing to show that its conclusion is true unless its premises are true. What we need is soundness, not just validity. So, we need to ask: Why not schedule the meeting on the last day of Ramadan? One potential reason is that a meeting on that day would violate some religious rule. However, whether a meeting violates a religious rule depends on the kind and time of the meeting. Moreover, even if our meeting would violate a religious rule, this fact by itself would not support the conclusion that we ought not to meet on that date unless religious rules determine what we ought to do. Some people might accept this rule, but atheists and secular humanists would reject it, and they might be everyone in the group that is meeting. Thus, this extra premise would make the argument questionable and unable to reach this audience. We do not need to endorse any religious rule in order to agree that a meeting does not go well when the right people do not show up. That is a reason why we do not want to schedule a meeting for a date when crucial people would refuse to show up. Therefore, if we know that some people whom we want at the meeting will refuse to meet on the last day of Ramadan, that gives us a reason not to schedule the meeting on that date. This reason is captured by the initial premises in the longer argument, and its premises are acceptable to a wider audience than the alternative premises that cite a religious rule. Moreover, this premise is strong enough to make the resulting argument valid, since it is not possible for its conclusion to be false when its premises are true. These features speak in favor of the secular interpretation of this argument. It is unfair to saddle arguers with stronger assumptions when weaker assumptions would make their arguments better. The goal of filling out assumptions in arguments is not to make the arguers look silly or stupid. The goal is instead to understand their point of view and learn from it. For this purpose, we need to make arguments look as good as possible, since then they teach us more. We still might end up disagreeing, but we cannot conclude that there is no good argument for a position unless we have looked at the best possible argument for that position. All of this together explains why it is fair to ascribe the extra premises and the longer argument to someone who explicitly asserts only the shorter original sentence. Implicit premises like these are often called suppressed, perhaps because the arguer supposedly suppressed an inclination to assert them openly. In general, we should ascribe suppressed premises to an arguer only if they are necessary to make the original argument valid, and only if the arguer would view the added premises as true and hence the longer argument as sound. In this way, validity and soundness are essential standards for completing arguments by adding suppressed premises. To call a premise suppressed might seem to disparage it as sneaky. However, the term “suppressed” here is not a negative evaluation. Everyone suppresses premises, and it is hard to see how we could (or why we would) avoid doing it. It is often legitimate for arguers to suppress premises. Indeed, it is often bad not to suppress premises. Just look at how much longer our completed argument is than the original sentence. If we had to spell out every assumption whenever we gave any argument, then it would take a very long time to say much at all. Suppressing premises promotes efficiency in communication. Other arguers use this defensible tool for nefarious purposes. They try to fool fools by suppressing the most dubious premises in their arguments. Imagine a used car dealer who argues, “You should purchase five years of service from my dealership, because then you will not need to pay for repairs.” He is suppressing the premise that you should buy whatever will avoid repair expenses. He never comes out and asserts that extra premise, because you could question it if he did. Nonetheless, he still does need that premise in order to make his argument valid. The problem is that this suppressed premise raises crucial issues that the dealer is trying to hide. How much does the service contract cost? How likely is the car to need repairs? How expensive will the repairs be? And, of course, why is he selling you a car that is so likely to need such expensive repairs? His trick is to steer you away from those questions by focusing your attention on other premises instead of the questionable one. To avoid getting fooled by such tricks, it is useful to fill out all of the suppressed premises in an argument. That exercise will make you less likely to overlook a dubious premise that the arguer is hiding. DO THESE METHODS SCALE UP? An extended example can illustrate how close analysis and deep analysis work together in argument reconstruction. Here is one example from the opening of an unsigned article entitled “New Approaches Needed to Address Rise of Poor Urban Villages in the Pacific”: New approaches are needed to address the challenge of rising urban dwellers in the Pacific who live in poor-quality housing with inadequate provision for basic services in settlements known as “urban villages,” a new Asian Development Bank (ADB) report says. “There has been a rapid rise of urban villages in recent years due to increased poverty and the negative impacts of climate change,” said Robert Jauncey, head of ADB’s Pacific Subregional Office in Suva, Fiji. “These informal or unplanned settlements are often neglected and excluded from the government’s planning system, so we need to rethink approaches to urban management and development to include urban villages in the mainstream policies, strategies, projects, and programs.” The report, entitled The Emergence of Pacific Urban Villages—Urbanization Trends in the Pacific Islands, defines urban villages as native and traditional communities and village-like settlements in urban areas that display common characteristics: association with certain ethnic groups, strong socio-cultural ties, land tenure based on custom, heavy reliance on the informal economy, and persistence of subsistence activities. Urban village dwellers often live in hardship and poverty, and are stereotyped with negative traits.3 What we need to determine is whether this passage includes an argument, where that argument is located in the passage, what it is, what purpose it serves, and how it is structured. Those tasks require careful attention to detail. We will work backward through the text. Without Argument Consider the second paragraph first. Does that paragraph give any argument? No. It gives the title of the report, perhaps so that readers can look it up. Then it defines what an urban village is, presumably so readers will know what the article is about. Then it describes the lives of urban villagers. The evaluative words in this paragraph might make readers think of an argument: Urban villagers face “hardship and poverty” as well as “negative” stereotypes. Therefore, someone needs to help them. That argument seems implicit. However, the paragraph does not explicitly give that argument or any other. We can tell this by applying our definition of argument and looking for argument markers. Just ask where the premise and conclusion are. Justification Next consider the last sentence of the first paragraph. The argument marker “so” indicates that an argument does occur in this sentence. However, this argument is quoted from Jauncey, so the author of the article does not assert this argument. Jauncey does. Perhaps the author of the article wants to preserve neutrality as a news reporter. Or maybe the author agreed with Jauncey. After all, the article never suggests any doubts about what Jauncey (or the ADB) said. In any case, we can see that at least Jauncey is giving an argument, so let’s try to reconstruct it. The word “so” is a conclusion marker that tells readers that what comes before is a reason for what follows: Urban villages are often neglected and excluded from government planning. Therefore, we need to rethink approaches to urban management and development to include urban villages in the mainstream policies, strategies, projects, and programs. The last instance of the little word “to” is also an argument marker if it can be interpreted as “in order to,” which is plausible. This reason marker indicates that what follows it is a reason for what comes before, so we might reconstruct the whole argument like this: We need to include urban villages in the mainstream policies, strategies, projects, and programs. Urban villages are often neglected and excluded from government planning. Therefore, we need to rethink approaches to urban management and development. Now we have two premises and one conclusion. What is the purpose of this argument? It is often hard to tell precisely what someone intends, and arguers are no exception. Still, Jauncey seems to be trying to persuade or convince his audience that his conclusion is true—that we need to rethink urban management in certain ways. He presumably believes that many in his audience did not have that belief before he spoke. They thought that urban management was going fine, at least in this area, or they did not think about it at all. So, he was trying to change their beliefs. But that is not all, we can assume. He probably also wanted them to believe his conclusion not arbitrarily but on the basis of reason. That is why he did not simply assert the conclusion but instead presented an argument that gave reasons for the conclusion. Hence, he was trying not only to persuade but also to justify his audience’s belief in his conclusion. To see how this argument is supposed to serve that purpose, we need to fit these premises and conclusion into a structure that shows how they work together to justify its conclusion. The presence of two argument markers might seem to suggest that each premise provides a separate reason for the conclusion. On that interpretation, there are two distinct arguments: (1) Urban villages are often neglected and excluded from government planning. Therefore, we need to rethink approaches to urban management and development. (2) We need to include urban villages in the mainstream policies, strategies, projects, and programs. Therefore, we need to rethink approaches to urban management and development. Each of these arguments needs a suppressed premise to make it valid. In particular, the first argument needs a suppressed premise like this: “We need to rethink any approach to urban management that neglects and excludes urban villages.” But that suppressed premise is close to the explicit premise in the second argument: “We need to include urban villages in the mainstream policies, strategies, projects, and programs.” Similarly, the second argument needs a suppressed premise something like this: “Current approaches to urban management and development do not already include urban villages.” But that suppressed premise is close to the explicit premise of the first argument. This search for suppressed premises thus reveals that the two premises are supposed to work together (not separately) to justify the conclusion. Each depends on the other. This structure can be called joint. To see how these premises work together, first we need to clarify the terms. In particular, the first premise refers to “government planning,” the second premise instead mentions “mainstream policies, strategies, projects, and programs,” and the conclusion says “approaches to urban management and development.” Writers often vary their wording in inessential ways to avoid the appearance of repetition. However, such unimportant variations can obscure the structure of the argument. If these three phrases describe different things, then it is hard to see how a premise about one could adequately support a conclusion about another. Then the argument would make no sense. In order to show how the argument works, then, we need to relate these phrases somehow. One option is to add a premise that identifies them: “Mainstream policies, strategies, projects, and programs as well as urban management and development are government planning.” This sentence might seem true, but it is verbose. For simplicity, I will instead replace them all with a si