Read the case State v. Ransom (pp. 411-425). Consider your verdict. Prepare a document that expresses your deliberation that justifies your vote of guilty or not guilty. The goal is not simply a w

7 Analyzing Arguments

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When analyzing an argument, start with the conclusion. If you are trying to construct a compelling argument, first decide exactly what conclusion you want to establish. If you are evaluating someone else’s argument, first determine exactly what the argument is supposed to prove.

When you have picked out the conclusion, you can examine the structure of the argument in support of that conclusion. Consider this example.

We should not build more nuclear power plants in the United States. Nuclear power is a dangerous technology: We have already experienced several nuclear accidents, and nuclear accidents have the potential to be catastrophic; even if the operators are well trained and careful and make no errors and all safety features are incorporated into the design—which is unlikely—there is always the danger that a nuclear power plant might be the target of a terrorist strike, with terrible consequences for public safety. Furthermore, nuclear power places an unfair burden on future generations: While we gain the benefit of the electricity produced, we leave for future generations the legacy of dangerously radioactive spent nuclear fuel. It’s selfish and unfair to use a technology that benefits the present at the expense of future generations. Finally, we do not really need the increased power that more nuclear power plants would generate. Through careful conservation of energy—including strict requirements for energy-efficient appliances and equipment and automobiles and houses—we could reduce our power needs, and through greater use of solar and hydroelectric and wind power, we could substantially increase our supply of energy. So we should put an immediate stop to the building of new nuclear power plants.

Don’t worry right now about whether that is a good or a bad argument. Let’s just look at the structure of the argument. First: what’s the overall conclusion?

Argument Structure

Convergent Arguments

The overall conclusion is just this: No additional nuclear power plants should be built. (It is important to note the precise conclusion. It is not that there should be no use of nuclear power; this argument does not attempt to establish that all existing nuclear power plants should be closed.)

Next, what reasons are given in support of that conclusion?

Three main reasons are given for the conclusion: First, nuclear power plants are dangerous; second, use of nuclear power is unfair to future generations; third, the power from additional nuclear power plants is not essential.

The next consideration is this: What is the structure of the argument? How are the reasons related to each other, and how are the reasons related to the conclusion? In answering those questions, the first issue is, Do the reasons given hang together, or does each stand independently? If one of the reasons offered were found to be false, would that undermine the other reasons also? For example, if we should be convinced that nuclear power is not placing an unfair burden on future generations (the second reason is rejected), would that destroy the whole argument? Or would we still have to evaluate the other two reasons independently?

In this case, each of the three reasons stands or falls independently. Consider the first reason offered against additional nuclear power plants: Nuclear power is too dangerous. If you reject that reason (you decide that nuclear power is not excessively dangerous), what effect would that have on the other two reasons? None. You might still decide that no new nuclear power plants should be built on the grounds that (second reason) nuclear energy places an unfair burden on future generations, or on the grounds that (third reason) alternative energy sources and energy conservation are better ways of meeting our future energy needs. Or suppose you reject the second reason: You decide that spent nuclear fuel can be disposed of in such a manner that it does not unfairly burden future generations. You could not just stop at that point and reject the entire argument; instead, you would still have to decide whether the remaining reasons are sufficient to establish that additional nuclear power plants are undesirable. Don’t misunderstand: If an argument gives three independent reasons in support of a conclusion and one reason fails, then certainly that argument is not as strong as it would have been had all three reasons proved true. Nonetheless, the remaining reasons may still offer substantial support—perhaps sufficient support—even if one reason is rejected. (If additional nuclear power plants are very dangerous, unfair to future generations, and unneeded, those are certainly good grounds for rejecting the construction of additional nuclear power plants. But one might reasonably be convinced that it’s a bad idea to construct additional nuclear power plants strictly on the grounds that nuclear power plants are very dangerous. The first reason alone might be sufficient even if the other two were rejected. The first reason alone will not offer as much support for that conclusion as all three together, but it might suffice.)

Since there are independent reasons, each offering independent support for a conclusion on which they all converge from separate directions, this argument structure is often called a convergent argument type. In a convergent argument, the different reasons are independent of one another, and when one falls it does not take the others down with it. Our example convergent argument is diagrammed in Figure 7-1.

Consider another example of a convergent argument. You are a juror in the burglary trial of Priscilla Prowler. The district attorney is endeavoring to prove that Ms. Prowler was indeed the villain who burglarized the Jones’ home, and he offers the following evidence in support of that conclusion: Three eyewitnesses independently identify Ms. Prowler as the person seen running from the Jones’ house carrying a crowbar on the night of the burglary; Ms. Prowler’s fingerprints are found inside the house; Ms. Prowler’s boyfriend testifies that she bragged to him about having “done the Jones job”; and when Ms. Prowler is apprehended she is wearing a diamond bracelet that was taken in the burglary, and Jones’ silver is found in the trunk of her car. That’s a rather strong case against Ms. Prowler. Now suppose that during the cross-examination of Ms. Prowler’s boyfriend it comes out that he and Priscilla had recently been spatting because he had discovered that Priscilla had been secretly seeing an old flame. As a result, you decide that the boyfriend is probably “out to get” Ms. Prowler, and you become convinced that his testimony—that Ms. Prowler bragged to him of doing the burglary—is unreliable. What effect will that have on your evaluation of the argument as a whole?

Not much, since this is a convergent argument offering independent reasons for the defendant’s guilt. The boyfriend’s testimony—if it is believable—would support the conclusion that Priscilla Prowler committed the burglary. The argument for her guilt is not quite as strong as it would be if the boyfriend’s testimony were believable. But failure of that one reason does not undermine the entire argument, for all the other reasons for the guilty verdict remain: They are not undermined by the failure of the boyfriend’s testimony. Even if we reject the boyfriend’s testimony, there are still some very strong independent reasons that point to a conclusion of guilty. However, the danger is that so much attention will be drawn to the failed reason that the remaining reasons in support of the conclusion will be ignored.

The famous British murder trial of Steinie Morrison (convicted in 1911 of the brutal murder of Leon Beron) offers a striking illustration of how one failed reason can overwhelm other independent reasons. Morrison’s defense barrister pointed out excellent reasons for reasonable doubt of the defendant’s guilt (and remember, the defense need only establish a reasonable doubt). The prosecution case rested heavily on the eyewitness identification of Morrison as the man seen with the murder victim shortly before the murder. It was established that the light was such that it would have been almost impossible to identify anyone under such conditions, and indeed the eyewitnesses admitted that they had seen newspaper photographs of the accused just prior to picking him out of a police lineup. The presiding judge’s doubts are clear in his summation to the jury:

Are you satisfied beyond reasonable doubt that that is the man ... ? Think for yourselves. With what certainty could you swear to a man whom you saw on a night like that, by the kind of light there was at those places? Can you feel certain that a man would not be mistaken? ... Are you so sure that they [the eyewitnesses] really took notice enough, that they had opportunity enough, to be able some days afterwards to swear with certainty to the man?1

Unfortunately for the defendant, two girls—who apparently had become attracted to the handsome defendant—testified that they had seen him at a show the evening of the murder. However, that alibi collapsed when under cross-examination it was shown that the girls could remember nothing from the show, could not recall the price of admission, and claimed to have bought tickets at curtain time for a show that had long been sold out. That was only a small part of the defense case and obviously had no connection with the weakness of the eyewitness testimony. Apparently, however, the jurors focused on the weak—almost certainly fabricated—alibi, and gave little attention to the remaining independent points that favored reasonable doubt. They deliberated half an hour and returned a verdict of guilty.

When examining arguments, first determine the conclusion: What is this argument supposed to prove? Then consider how the argument is structured: Are there several independent reasons given for the conclusion? If so, you will have to consider each reason on its own merits and not reject the whole argument because one reason is flawed.

Convergent arguments offer independent, free-standing reasons for the conclusion. In convergent arguments, if one reason is not convincing, perhaps another will be. But not all arguments have that form. In some arguments, the premises—the reasons given in support of the conclusion—are linked together like a chain, and if one link breaks, the entire argument fails: The linked argument is thus only as strong as its weakest link. In short, a linked argument is an argument in which the reasons given depend on one another for their strength. Separately, each premise offers little or no support for the conclusion; together, they may form a powerful argument.

Consider this example. The defendant is charged with murder, and the question is whether the defendant is actually the person who committed the drive-by shooting of the victim (i.e., there is no question of self-defense or insanity or accidental death; the only question is the identity of the person who did the deed). One of the arguments given by the prosecution is as follows:

White Jaguar automobiles are quite unusual in this area. The defendant owns a white Jaguar, and the car from which the fatal shots were fired has been identified by several witnesses as a white Jaguar. Therefore, there is some reason to think that the defendant is guilty of the drive-by murder.

Would that be sufficient reason to find the defendant guilty? Certainly not. Especially not when we consider that the prosecution bears the burden of proof and must do more than establish that the defendant might be guilty, or even that the defendant is probably guilty. The prosecution must prove the defendant’s guilt beyond a reasonable doubt, and this argument doesn’t come close. But leave that issue aside for a moment and look at the structure of the argument. We have three reasons, all supporting (though not establishing) the conclusion that the defendant is guilty. How do they support that conclusion? Not independently. Suppose we discover that the witnesses were lying and that the fatal shots were fired from a red van rather than from a white Jaguar. If the premise that the shots were fired from a white Jaguar falls, it brings the whole argument down with it: The other premises—the defendant owns a white Jaguar, and white Jaguars are rare—are now useless in trying to establish the guilt of the defendant. Or suppose we find that the defendant does not own (or have access to) a white Jaguar: Again, if that single link is broken, the entire linked argument fails. Or suppose that white Jaguars are not rare, but instead are the most popular car in that particular area: Again, the argument collapses. (If you have trouble seeing that, imagine that the testimony is that the fatal shots were fired from a car, and the defendant owns a car; since car ownership is hardly rare, that fact will lend no support to the claim that the defendant is the murderer.) So in this case—as in all linked arguments—the premises stand or fall together. If we are diagramming an argument, we need a special way of showing that. In the diagram of the convergent argument, the different independent lines are shown converging along separate paths toward the conclusion. With linked arguments, we want to show the premises joined as a team or unit, all of which together lead to the conclusion. So we might diagram the argument (as in Figure 7-2) with the premises linked by one line, and another line drawn from the link to the conclusion.

So now you know that it is essential to first pick out the conclusion, and you can distinguish the premises from the conclusion, and also distinguish among convergent and linked arguments. That’s a good start at analyzing arguments and enough to handle most arguments quite effectively. But arguments can and do get more complicated, and it’s important to be able to deal with that complexity; in fact, it’s in dealing with the complex arguments that argument diagrams are most useful.

Look back at the first example: the argument about nuclear power. That argument was actually considerably more complex than our diagram indicated. The argument, you’ll recall, goes like this:

We should not build more nuclear power plants in the United States. Nuclear power is a dangerous technology: We have already experienced several nuclear accidents, and nuclear accidents have the potential to be catastrophic; even if the operators are well trained and careful and make no errors and all safety features are incorporated into the design—which is unlikely—there is always the danger that a nuclear power plant might be the target of a terrorist strike, with terrible consequences for public safety. Furthermore, nuclear power places an unfair burden on future generations: While we gain the benefit of the electricity produced, we leave for future generations the legacy of dangerously radioactive spent nuclear fuel. It’s selfish and unfair to use a technology that benefits the present at the expense of future generations. Finally, we do not really need the increased power that more nuclear power plants would generate. Through careful conservation of energy—including strict requirements for energy-efficient appliances and equipment and automobiles and houses—we could eliminate some power requirements, and through greater use of solar and hydroelectric and wind power, we could substantially increase our supply of energy. So we should put an immediate stop to the building of new nuclear power plants.

The exact conclusion of that argument is that we should build no new nuclear power plants. In overall structure it is a convergent type of argument: Three distinct and independent reasons are given in support of that conclusion. First, nuclear power is too dangerous; second, nuclear power use is unfair to future generations; and third, additional nuclear power is not necessary. That’s as far as we went in analyzing the argument, but there’s still a lot further to go. The most obvious next step in analyzing that argument is to ask, Are the reasons given in support of the conclusion relevant to the conclusion? That is, do they actually support the conclusion? If they are true, do they make the conclusion more likely to be true? We have already examined relevance in an earlier chapter, so you can determine that the reasons given are relevant. But another question immediately arises: If the reasons given are true, then they will support the conclusion; but why should we accept the reasons given for the conclusion? That is, are the reasons given actually true?

In the original argument, some reasons were given in support of those reasons. That is, there are subarguments within the larger argument, and the subarguments are arguments in favor of the premises of the overall argument. For example, look at the third reason given for the conclusion: We do not really need the increased power that additional nuclear power plants would generate. That is a key premise in support of the overall conclusion; but it in turn is the conclusion of a subargument. The subargument is thus:

We do not need the increased power that more nuclear power plants would generate. Through careful conservation of energy—including strict requirements for energy-efficient appliances and equipment and automobiles and houses—we could eliminate some power requirements, and through greater use of solar and hydroelectric and wind power, we could substantially increase our supply of energy.

The conclusion of that subargument is that the increased power that more nuclear power plants would generate is not needed. Two reasons are offered in support of that conclusion: First, conservation practices could reduce our demand for energy, and second, other nonnuclear power sources could supply all the power we need. There you have a subargument within the larger argument; that is, you have a sort of miniargument in support of one of the reasons that supports the overall conclusion. And notice that the conclusion of the subargument functions as a premise in the overall argument. Notice also that each of the other two reasons given in support of the overall conclusion is in turn supported by subarguments, and that each of those reasons—while functioning as a premise in the overall argument—is the conclusion for its respective subargument.

With the added detail, the diagram for the overall argument becomes a bit more complicated, but taken step by step, it should not be confusing. The basic diagram, shown in Figure 7-3, remains the same.

To that basic diagram we add diagrams of each subargument. For example, the diagram of the third subargument is shown in Figure 7-4. And the second subargument is a linked argument; its diagram is shown in Figure 7-5. Now we put them together, with the conclusion of each subargument operating as a premise for the overall argument (Figure 7-6).

Piece of cake, right?

By examining and diagramming the above argument and subarguments, you can see that some of the reasons given in the argument are in turn supported by other reasons (are supported by further subarguments). But being of an inquiring and reflective nature, you no doubt asked, What about the reasons in the subargument? What supports them? For example, consider the claim that alternative soft energy sources are readily available: Why should I accept that? Shouldn’t there be a further argument—a subsubargument—to support that reason?

The answer is that there could be such a subsubargument—and perhaps there should be. In any case, it should be noted that arguments can be pushed to many different levels: The conclusion that no new nuclear power plants should be built can be supported by the claim that additional nuclear power is not needed, and that claim can be supported by the claim that alternative soft energy sources are readily available, and that claim could be supported by data on solar energy, and those data could be supported by claims about the reliability of the research studies that generated the data, and so on. At some point, of course, we must stop: when we reach some obvious fact, when we reach some assertion that everyone accepts, when we reach an assumption that is accepted as true for the purposes of this particular argument, or when we run out of energy and decide not to press any further back for support. Exactly under what conditions premises should be accepted as true, when assumptions are and are not reasonable, and what degree and type of justification should be demanded for premises are all important questions that will be examined in later chapters.

In some cases, a linked argument can be one of the convergent elements in a larger convergent argument. For example, consider the following argument in favor of physician-assisted suicide:

We should legalize physician-assisted suicide for terminally ill patients who wish to hasten their deaths. First, it is psychologically important that people have as much control over their situations as possible, and being able to control the process of one’s death gives some terminally ill patients a very satisfying and powerful sense of control. Furthermore, excruciating pain is always undesirable, and some forms of disease cause excruciating pain that can only be relieved by death. And finally, competent people should have the right to make their own decisions about their lives and deaths.

In this argument, the overall structure is convergent. There are three convergent lines leading to the conclusion: the first is the argument concerning control, the second the argument about pain, and the third the claim concerning rights. But the first and second of these convergent lines are linked arguments. The diagram for that argument is shown in Figure 7-7.

Here’s one more example before we turn to some exercises:

Alice should be found not guilty, because Alice did not rob the Key West Convenience Store at 10:00 p.m. on August 9. In the first place, she had no motive. Certainly she did not need money: Her parents are quite wealthy, and her personal checking account contained over $8,000 on the day of the robbery. Furthermore, such a crime would be completely out of character for the defendant. She is a gentle, nonviolent individual. Her character is shown by the testimony of her biology professor (who spoke of her adamant refusal to harm a frog in her biology laboratory), the testimony of the director of Meals-on-Wheels (who testified that she had—for over 3 years—been a dedicated volunteer for their program of providing hot meals to the elderly and disabled), and by the testimony of three of her friends (who noted that she is fiercely opposed to firearms, refused to even hold a pistol shown her by a friend, and refuses on principle to attend violent movies). This is not the sort of person who takes a pistol into a convenience store and robs it at gunpoint. And finally, Alice could not have been the robber because she was not in Key West when the crime was committed. She could not have been in Key West, because at 9:30 p.m. on August 9 she was in Miami, and there is no way to get from Miami to Key West in half an hour. There’s no doubt she was in Miami at the time, for a professor at the University of Miami testified that he talked with Alice at 9:30 p.m. on the night of August 9 while waiting in line to get popcorn at a movie theater in Miami. And he could not have been mistaken, because he recognized her from two seminars she had taken with him at the university. Also, the usher at the theater remembered seeing her there.

The basic structure of this argument is convergent. The first strand of the argument (Figure 7-8) contains a convergent subargument to prove that Alice had no motive. The second strand of the overall convergent argument ends in the conclusion (the subconclusion) that armed robbery is out of character for Alice. That conclusion is supported by a convergent (sub)argument, as shown in Figure 7-9. The third part of the overall convergent argument is diagrammed in Figure 7-10. The third reason for the conclusion that Alice did not rob the Key West Convenience Store is the claim that Alice was not in Key West at the time of the robbery. That is in turn the conclusion of a linked subargument (if Miami were only 2 minutes from Key West, the sighting of Alice in Miami would carry no weight; and of course if Alice was not in Miami, it would make no difference how far Miami was from Key West). And there is another subargument (this time a convergent argument) in support of one of the linked premises: Alice was in Miami because her professor saw her in Miami and the usher saw her in Miami. Those two premises are convergent (even if the usher’s testimony is mistaken, the professor’s testimony would independently support the subconclusion that Alice was in Miami).

Now it’s just a matter of putting all these arguments together. The resulting diagram is shown in Figure 7-11. The diagram might look formidable at first glance; but taken step by step, there’s really nothing difficult about it.

As you check your diagram of an argument to see if the pieces are in the right place, start from the most basic premises and work your way up. At each step, ask yourself: Does this premise support the claim above it? Does it make sense to use this as a reason in support of the statement immediately above it? For example, check the line of argument running from “Alice’s parents are wealthy” up to “Alice should be found not guilty.”

Is it diagrammed correctly? Well, does it make sense to say, “Alice’s parents are wealthy” and therefore “Alice did not need money”? Yes, of course. (And it would not make sense to say “Alice is gentle and nonviolent,” so therefore “Alice did not need money”; so if you had the argument diagrammed in that form, working upward would tip you off to your mistake.) Likewise, it makes sense to say, “Alice did not need money,” so therefore “Alice had no motive for the robbery.” And the next step also works: “Alice had no motive for the robbery,” so “Alice did not rob the Key West Convenience Store.” (Of course that’s not a conclusive reason for thinking Alice did not do the robbery, but certainly it’s a reason.) And the final step also works: “Alice did not rob the Key West Convenience Store,” and therefore “Alice should be found not guilty.” One note of caution as you check your argument diagram by moving up the ladder: You may come to a point at which the underlying premise does not support the next step, and yet your diagram of the argument is still correct. In that case, you have the correct diagram for a fallacious argument: an argument that commits the fallacy of irrelevant reason.

Of course this is not the end of argument analysis. We still must decide whether the premises are in fact true, and whether the premises—even if they are true—provide adequate support for the conclusion. And there is another essential step in analyzing arguments: determining what assumptions are embedded in the argument. That’s the task of the next section.

We’ve been talking about the structure of arguments and how to get from premises to conclusions. But there’s another question, of course: How do we get the premises in the first place? There are lots of sources, and we’ll be examining some of them: eyewitness testimony, for example. But not all premises require further justification. Sometimes we simply agree to an assumed premise—everyone participating in the discussion accepts the premise as true, implicitly or explicitly—and then we go on from there.

It is sometimes said—usually in an oracular voice, as if imparting an ageless truth—that one should never assume anything. Balderdash. We couldn’t function without assumptions. When I drive through a green light I assume that the drivers for whom the light is red will stop. (If I refused to make that assumption and stopped to check, I would get rear-ended by the cars following me.) When I read a scientific report, I assume that the scientist has not deliberately faked the reported data. (If I felt I had to personally check all the results before I could profitably read a scientific report, I should certainly not read many.) When the weatherperson reports a severe blizzard in Minneapolis, I assume that he or she is honestly reporting from reliable sources, and I assume that the accompanying video of Minnesotans under the snow was not taken in Anchorage during 1979. (Sometimes, unfortunately, such trust is misplaced. Fox News has run inaccurate video reports—such as claiming that a video of a large crowd came from a Sarah Palin book signing event, when in fact it came from a McCain–Palin rally during McCain’s presidential campaign. When that happens, we legitimately lose confidence in that source.) When scientists do research, they operate from many givens that are not brought into question by that particular research project. Research on lasers, for example, might make use of our knowledge of the speed of light—without testing what we believe to be the actual speed of light. (Of course if the research goes badly, one might then critically examine the underlying assumptions.)

Consider this argument:

We should ban the manufacture and sale of lead-based paints. Think about what happens when you paint your house or apartment. You paint over the paint that was there, and eventually your paint is painted over, until the result is a thick coat of lead-based paint that ultimately begins to peel and flake. The small children in the house pick at the paint, then put their fingers—or even flakes of paint—into their mouths. Through these and other events, a substantial portion of the lead may ultimately end up in the children, and thus in their bloodstreams. And when that happens, the children suffer from lead poisoning, which may cause mental retardation, nervous disorders, blindness, and even death. Therefore, lead-based paints should be banned.

That seems to me a good argument. In fact, it is essentially the argument that brought about the ban of lead-based paint in most countries. But it contains a crucial assumption that is left unstated. It is a perfectly legitimate assumption, and it is so obvious and widely accepted that it is almost impossible to pick out. You may be able to find several unstated assumptions in that argument; but the most basic assumption—or at least the most basic unstated assumption—is quite difficult to detect. Have a go at it before you peek at the next paragraph.

The assumption is: We don’t want children to suffer mental retardation, nervous disorders, blindness, or death. Now that is hardly a controversial assumption; in fact, it is because it is so universally accepted that it is both difficult to detect and unnecessary to state. (If we added to the argument “And we do not wish children to go blind or die,” that would strike most people as belaboring the obvious.)

And remember the argument about Alice not being guilty? The main reason was that the crime was committed in Key West, and Alice was in Miami at the time.

Alice could not have been the robber, since Alice was not in Key West when the crime was committed. She could not have been in Key West, because at 10:00 p.m. on August 9 she was in Miami.

But that involves an essential (unstated) assumption: It is impossible for someone to be in two different places at the same time. That is hardly an assumption that needs to be noted or supported: No further evidence or expert testimony is required to back it up. (That is not to say that it is never disputed: Some “psychics” claim to be in at least two different places—maybe more—simultaneously, through out-of-body experiences. Still, the assumption that if Alice was in Miami, then she was not in Key West at the same time seems a safe and legitimate one.) And the moral of the story is a simple one: Assumptions are sometimes perfectly legitimate.

We often make explicit assumptions—sometimes when we are in fact doubtful of their truth—in order to consider what would follow from them:

• “Assuming that the track remains very muddy, which horse do you think is more likely to win the Kentucky Derby?”

• “If we assume that the inflation rate will be low during the next year, what do you think will be the average increase in industrial wages?”

In some cases, it is useful to assume things that one believes are false in order to show that even if they were true a certain conclusion still would not follow:

• “Look, even assuming that Richard Nixon knew nothing about the Watergate break-in before it occurred, he still deserved to be impeached for helping to cover it up.”

• “Even assuming that all the Sandinistas are doctrinaire Marxists, it still doesn’t follow that we should support groups like the Contras who commit terrorist acts against the civilian population of Nicaragua.”

• “Even if it were true that the tobacco companies really want to curb teenage smoking, it still would not be a good idea to leave efforts to reduce underage smoking to the discretion of the tobacco industry.”

In short, assumptions are not the enemy. Assumptions may be wrong, of course. In the case of science, if we try to duplicate a scientist’s findings and consistently find it impossible to do so, we may eventually conclude that we were mistaken in assuming that that particular scientist was reporting data honestly. If we run experiments and our results constantly conflict with our predictions, we may eventually come to believe that some of our operating assumptions were mistaken. We do occasionally find that we operated on mistaken assumptions; when that occurs we reject that assumption and try again, but we do not reject all assumptions.

So it is legitimate and probably essential to operate from some assumptions. The goal is not to eliminate all assumptions; rather, the point is to recognize the assumptions being made, especially the key ones.

While we’re on the subject of unstated assumptions, this may be a good time to talk about enthymemes, which is just a classy name for a common phenomenon. An enthymeme is an argument that contains a premise that is regarded as so obvious that it need not be stated. We’ve looked at a couple already: the argument about Alice not being in Key West because she was in Miami (the obvious unstated premise is that if she is in Miami, then she can’t simultaneously be in Key West); and the argument about the hazards of lead-based paint, with its unstated premise that the damage and death of small children should be prevented.

My grandmother was fond of enthymemes. When I was a boy, when my grandmother thought “my eyes were bigger than my stomach,” and that I had taken more food on my plate than I was likely to eat, she would rebuke me with one of her favorite sayings: “If you eat all that, then I’m the Queen of Sheba.” Since it was obvious that my grandmother was not the Queen of Sheba, her conclusion was clear: “You’re not going to eat all that.”

Grandmothers aren’t the only source of enthymemes. “Either I’ve got the best used-car deals in town, or my name’s not Honest Bill Barton. So come on down to Honest Bill’s Used Cars, ‘cause Honest Bill is dealin’, darlin’.” Well, it doesn’t take a rocket scientist to figure out that the conclusion of Honest Bill’s argument is that “I’ve got the best used-car deals in town,” and that the unstated premise in this enthymeme is, My name is Honest Bill Barton. (Honest Bill’s argument is valid; whether it’s sound is a very different question.)

In order to combat the mistaken assumption that assumptions are typically false, and should always be shunned, we have examined some legitimate and useful assumptions. But, of course, some assumptions are false (such as the common assumption that it is always wrong to make assumptions) or at least are controversial. Such illegitimate assumptions cause problems, and they are not infrequent.

In uninspired mystery novels, the chief inspector assumes that the foul murder was committed by either the duke or the cook; and in such cases, you can be confident that the villain is the duchess, or perhaps the butler, but certainly not the suspects who were assumed to be the only alternatives. And when the president of the university announces that the university must either cut classes or raise tuition, that may also be a false assumption: perhaps cutting salaries or reducing overhead should also be considered. When one of your fellow jurors announces that the defendant must be guilty, because she did not testify in her own behalf, that juror is operating from a common but false assumption: that the defendant must prove her innocence.

The problem is not with assumptions as such; assumptions are often legitimate. Nor is there a special problem with unstated assumptions. In the earlier examples, the assumption that Alice could not be in two places at the same time and the assumption that we do not want children to die are both left unstated, but they are so obvious and acceptable that they do not require statement. The problem is with controversial assumptions: assumptions that are false or at least require further support. Such controversial assumptions are particularly insidious when left unstated.

For example, many of the purveyors of pain-relief medications tout their products as extra strength. Anacin®4 runs a catchy little commercial in which “the Anacin difference” is strongly emphasized: The two standard aspirin tablets contain a total of 650 milligrams of aspirin; but each tablet of Anacin contains 400 milligrams of aspirin, for a total dose of 800 milligrams if two are taken. The announcer in the commercial points out this difference, and then asks the shopper which she plans to take when she next has a headache; the answer, of course, is that she plans to take Anacin and get the extra pain relief, the Anacin difference of an extra 150 milligrams of aspirin.

The Anacin commercial contains a very important unstated assumption. What is it? (Leave aside the fact that by simply taking three generic-brand aspirin tablets of 325 milligrams each, you could get more aspirin for less money than by taking two 400-milligram Anacin tablets.) In trying to detect the unstated assumption in the commercial, first ask, What is the conclusion of the commercial’s argument? With the conclusion in view, it may be easier to detect the tricky unstated assumption.

The conclusion is just that two 400-milligram tablets of Anacin (aspirin) will be more effective in relieving headache than two 325-milligram tablets of aspirin. The unstated assumption is that 800 milligrams of aspirin will provide more effective headache relief than will 650 milligrams of aspirin. That sounds like an innocent enough assumption; but in fact it is false. Clinical studies on the effects of different dosages indicate that at 650 milligrams of aspirin, the dose–response curve levels off markedly. In other words, most people will not get more effective headache relief by taking 800–1,000 milligrams of aspirin than by taking 650 milligrams. A seemingly insignificant and unstated assumption turns out to be crucial for establishing the conclusion that Anacin is better: It is a crucial assumption, and it is false.5 (Though the 800 mg dose won’t relieve your headache any better than the standard 650 mg, there is one significant difference: the 800 mg dose is more likely to cause nausea.)

We typically operate under basic assumptions that shape the way we think about our world and our society. For example, our debate over national economic policies may take place within a controlling, unexamined framework of assumptions about distribution of wealth, rights to profits, and control of capital, and those invisible assumptions may tightly constrain the sorts of options and changes that can be considered. In another instance, a Senate committee might examine scrupulously the most effective method of distributing the limited supply of childhood vaccinations, but remain unaware of the structural assumptions that allow the pharmaceutical industry to control prices and limit supply; examination of those key assumptions might eliminate the problem of how to deal with vaccine shortages. The university’s animal research committee may scrutinize new ways of ventilating cages and reducing the suffering of research animals, while remaining blind to their basic operating assumption that it is acceptable to use animals for research. The slaveowner may examine whether working conditions and living quarters could be improved, while being unable to see the monstrous controlling assumption of the legitimacy of slavery. And Ptolemaic astronomers may develop elaborate and elegant accounts of planetary motion, while leaving unexamined the controlling assumption that the Earth is stationary. Good critical thinking often involves reasoning from assumptions, but the best critical thinking also requires the ability to critically examine those assumptions, including the most basic social and institutional assumptions of our society.

In scientific research—as in other areas of thought—it is the unrecognized assumptions that are most troublesome. Those assumptions are likely to be embedded in the questions posed by the scientific investigator. For example, eighteenth- and nineteenth-century biologists asked what purpose was served by the existence of such a variety of species. Darwin recognized that the assumption that such variety had to be explained in terms of purposes was questionable, and he was able to develop his mechanistic theory of natural selection by abandoning talk of purposes. Many researchers of the seventeenth and eighteenth centuries endeavored to discover what leaves the object when it is burned (What does the fire “consume” when something is “consumed by fire”?). The assumption was so natural and pervasive that it led to the development of an elaborate theory of phlogiston: Phlogiston was supposed to be the combustible material in an object, which was removed when the object burned. But by questioning that assumption, Lavoisier was able to recognize oxygen as a distinct gas and thus laid the foundation for modern chemical theory.

Assumptions can be legitimate and acceptable in the right setting, and they can be misleading and suffocating in the wrong setting. When someone tries to slip in as an assumption a point that is critical to an argument and that is also a point that might be doubted by some parties to the argument, assumptions are being used in a misleading way (more about that in Chapter 13 on begging the question). But when assumptions are used to specify some points of agreement (perhaps tentative or hypothetical or local or conditional agreement) so that attention can be focused on the key issues being contested, assumptions can do valuable work. It’s impossible to argue about everything at once. If the assumptions that are operating are clearly spelled out and agreed upon, it may be possible to focus attention on the key issues. And assumptions need not be carved in stone: Today’s assumption can be critically examined—and perhaps rejected—tomorrow.