chapter 3
A third common argument form is called hypothetical syllogism. "Hypo- thetical" is just another term for conditional. A syllogism is a deductive argument made up of three statements—two premises and a conclusion. (Modus ponens and modus tollens are also syllogisms.) In a hypothetical syllogism, all three statements are conditional, and the argument is always valid: If the ball drops, the lever turns to the right. If the lever turns to the right, the engine will stop. Therefore, if the ball drops, the engine will stop.
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An inductively strong argument is such that if its premises are true, its conclusion is probably or likely to be true. The structure of an inductively strong argument cannot guaran- tee that the conclusion is true if the premises are true—but the conclusion can be rendered probable and worthy of acceptance. (Here again, the structure and con- tent of an argument are distinct elements.) Because the truth of the conclusion cannot be guaranteed by the truth of the premises, inductive arguments are not truth-preserving.
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People often use hypothetical syllogisms to reason about causal chains of events. They try to show that one event will lead inexorably to a sequence of events, finally concluding in a single event that seems far removed from the first. This linkage has prompted some to label hypothetical syllogisms "chain arguments." There are two common argument forms that are not valid, though they strongly resemble valid forms. One is called denying the antecedent. For example: If Einstein invented the steam engine, then he's a great scientist. Einstein did not invent the steam engine. Therefore, he is not a great scientist.
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There's another common invalid form you should know about: affirming the consequent. Here's an instance of this form: If Buffalo is the capital of New York, then Buffalo is in New York. Buffalo is in New York. Therefore, Buffalo is the capital of New York. We represent this form like this: If p, then q. q. Therefore, p.
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To recognize an argument, you must be able to identify the premises and the conclusion. Indicator words such as because and since often signal the presence of premises, and words such as therefore and thus can point to a conclusion.
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What about this one: The use of marijuana should be legal because it's an act that brings pleasure to people's lives. To make this argument valid, we would need to add this premise (or one like it): "Any act that brings pleasure to people's lives should be legal." But this premise is hard to accept since many heinous acts—such as murder and theft— may bring pleasure to some people, yet few of us would think those acts should be legal. To try to make the argument strong, we might add this premise in- stead: "Some acts should be legal simply because they bring pleasure to peo- ple's lives." This premise is actually controversial in some quarters, but it at least is not obviously false. It also fits with the point of the argument. If we decide that the premise is neither plausible nor fitting, we would declare the argument beyond repair.
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When it comes to deductive and inductive arguments, the most important skills you can acquire are being able to identify them and determining whether they are good or bad.
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• Analyzing the structure of arguments is easier if you diagram them. Argu- ment diagrams can help you visualize the function of premises and conclu- sions and the relationships among complex arguments with several subarguments.
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• Arguments can come in certain common patterns, or forms. Two valid forms that you will often run into are modus ponens (affirming the anteced- ent) and modus tollens (denying the consequent). Two common invalid forms are denying the antecedent and affirming the consequent.
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AFFIRMING THE CONSEQUENT If p, then q. q. Therefore, p. EXAMPLE If the cat is on the mat, she is asleep. She is asleep. Therefore, she is on the mat
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An inductive argument that succeeds in providing probable—but not conclusive—logical support for its conclusion is said to be strong
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Arguments come in two forms: deductive and inductive. A deductive argu- ment is intended to provide logically conclusive support for a conclusion; an inductive one, probable support for a conclusion. Deductive arguments can be valid or invalid; inductive arguments, strong or weak. A valid argument with true premises is said to be sound. A strong argument with true prem- ises is said to be cogent.
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Not only that, but you can see that the unstated prem- ise is questionable, which is the case with many implicit premises. Not everyone would agree that anything raising the risk of death or injury should be banned, for if that were the case we would have to outlaw automobiles, airplanes, most pre- scription drugs, most occupations, and who knows how many kitchen appliances! Many unstated premises are like this one: They're controversial and therefore should not be left unexamined.
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The point of devising an argument is to try to show that a statement, or claim, is worthy of acceptance. The point of evaluating an argument is to see whether this task has been successful—whether the argument shows that the statement (the conclu- sion) really is worthy of acceptance. When the argument shows that the statement is worthy of acceptance, we say that the argument is good. When the argument fails to show that the statement is worthy of acceptance, we say that the argument is bad.
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Good inductive arguments are cogent. Bad inductive argu- ments are not cogent.
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Here are three more inductive arguments about some everyday concerns: Almost every computer I've purchased at an online store has been a dud. Therefore, the next computer I purchase at the same online store will likely be a dud. Maria's car broke down yesterday. When it broke down, it made the same noise and spewed the same stinky exhaust that it always does when it breaks down. Maria's car breaks down a lot. Her mechanic, who does excellent work, always says the same thing: The problem is the carburetor. Therefore, Maria's car trouble yesterday was probably due to a carburetor problem. Nine toddlers out of the thirty-two at the day care center have a cold. Therefore, probably every child there has a cold.
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Here's another example of this form: If science can prove that God is dead, then God is dead. Science cannot prove that God is dead. Therefore, God is not dead. Even if science cannot prove that God is dead, that in itself does not show that God is not dead. Perhaps God is dead even though science cannot prove it. In other words, it's possible for both premises to be true while the conclusion is false.
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Some of the more common argument patterns that you encounter are like this pattern—they're deductive, and they contain one or more conditional, or if-then, premises. The first statement in a conditional premise (the if part) is known as the antecedent. The second statement (the then part) is known as the consequent.
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Denying the antecedent is represented like this: If p, then q. Not p. Therefore, not q. You can see the problem with this form in the preceding argument. Even if the antecedent is false (if Einstein did not invent the steam engine), that doesn't show that he's not a great scientist because he could be a great scientist on account of some other great achievement. Thus, denying the antecedent is clearly an invalid pattern: It's possible for the premises to be true and the conclusion false.
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DENYING THE ANTECEDENT If p, then q. Not p. Therefore, not q. EXAMPLE If the cat is on the mat, she is asleep. She is not on the mat. Therefore, she is not asleep.
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Obviously, in this form it's possible for the premises to be true while the con- clusion is false, as this example shows. This pattern, therefore, is invalid. Finally, we come to a common argument form called disjunctive syllogism. It's valid and extremely simple: Either Ralph walked the dog, or he stayed home. He didn't walk the dog. Therefore, he stayed home. The symbolized form: Either p or q. Not p. Therefore, q.
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Sometimes you can see right away that an argument has a valid or invalid form. At other times, you may need a little help figuring this out, or you may want to use a more explicit test of validity. In either case, the counterexample method can help. With this technique you check for validity by simply devising a parallel argument that has the same form as the argument you're evaluating (the test argument) but has obviously true premises and a false conclusion. Recall that any argument having true premises and a false conclusion cannot be valid. So if you can invent such an argument that also has the same pattern as the test argument, you've proved that the test argument is invalid.
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The kind of support that a deductive argument can give a conclusion is absolute. Either the conclusion is shown to be true, or it is not. There is no sliding scale of truth or falsity. The support that an inductive argu- ment can provide a conclusion, however, can vary from weak to extremely strong.
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A fact that can further complicate the argument structure of a long passage is that complex arguments can sometimes be made up of simpler arguments (sub- arguments). For example, the conclusion of a simple argument can serve as a premise in another simple argument, with the resulting chain of arguments con- stituting a larger complex argument. Such a chain can be long. The complex ar- gument can also be a mix of both deductive and inductive arguments. Fortunately, all you need to successfully analyze these complex arguments is mastery of the elementary skills discussed earlier. Let's take a look at another long passage: Contemporary debates about torture usually concern its use in getting infor- mation from suspects (often suspected terrorists) regarding future attacks, the identity of the suspects' associates, the operations of terrorist cells, and the like. How effective torture is for this purpose is in dispute, mostly because of a lack of scientific evidence on the question. We are left with a lot of anecdotal accounts, some of which suggest that torture works, and some that it doesn't. People who are tortured often lie, saying anything that will make the torturers stop. On the other hand, in a few instances torture seems to have gleaned from the tortured some intelligence that helped thwart a terrorist attack. Is torture sometimes the right thing to do? The answer is yes: in rare situa- tions torture is indeed justified. Sometimes torturing a terrorist is the only way to prevent the deaths of hundreds or thousands of people. Consider: In Washington, D.C., a terrorist has planted a bomb set to detonate soon and kill a half million people. FBI agents capture him and realize that the only way to disarm the bomb in time is for the terrorist to tell them where it is, and the only way to get him to talk is to torture him. Is it morally permissible then to stick needles under his fingernails or waterboard him? The consequences of not torturing the terrorist would be a thousand times worse than torturing him. And according to many plausible moral theories, the action resulting in the best consequences for all concerned is the morally correct action. When we weigh the temporary agony of a terrorist against the deaths of thousands of innocents, the ethical answer seems obvious. The length of this passage might suggest to you that the argument within it is long and tangled. But that's not the case here. The conclusion is this: In rare situations torture is morally justified. The first paragraph just provides back- ground information; the second contains two premises. A paraphrase of the first premise would go something like this: In a ticking-bomb scenario, the conse- quences of not torturing a terrorist would be far worse than those of torturing him. The second premise says that the morally right action is the one that results in the best consequences for all concerned. Notice that these premises are depen- dent ones. The argument then looks like this: (1) In a ticking-bomb scenario, the consequences of not torturing a terrorist would be far worse than those of torturing him. (2) The morally right action is the one that results in the best consequences for all concerned. (3) Therefore, in rare situations torture is morally justified.
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And one in regular paragraph form: [Premise] If abortion is the taking of a human life, then it's murder. [Premise] It is the taking of a human life. [Conclusion] So it necessarily follows that abortion is murder. In each of these arguments, if the premises are true, the conclusion must be absolutely, positively true. It is impossible for the premises to be true and the conclusions false. The conclusion logically follows from the premises. And the order of the premises makes no difference.
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Any argument in the modus ponens form is valid—if the premises are true, the conclusion absolutely must be true. This means that if "If p, then q" and "p" are both true, the conclusion has to be true also. These facts, then, provide a way to quickly size up an argument. If it's in the form of modus ponens, it's valid, regardless of the content of the statements. Another common argument form is called denying the consequent, or modus tollens: If Austin is happy, then Barb is happy. Barb is not happy. Therefore, Austin is not happy. The form of modus tollens is: If p, then q. Not q. Therefore, not p. Like modus ponens, modus tollens is always valid. If the premises are true, the conclusion must be true. So any argument that's in the modus tollens pattern is valid.
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Arguments come in two forms—deductive and inductive. A deductive argu- ment is intended to provide logically conclusive support for its conclusion. An inductive argument is intended to provide probable—not conclusive—support for its conclusion. A deductive argument that succeeds in providing such decisive logical sup- port is said to be valid; a deductive argument that fails to provide such support is said to be invalid.
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Both deductive and inductive arguments can be manipulated in various ways to yield new insights. For example, let's say that you have formulated a valid deductive argument, and you know that the conclusion is false. From these facts you can infer that at least one of the premises is false. Using this tack, you can demonstrate that a premise is false because in a valid argument it leads to an absurd conclusion. Or let's say that you've fashioned a valid argument, and you know that your premises are true. Then you can infer that the conclusion must be true—even if it's contrary to your expectations. Or maybe you put forth a strong inductive argument, and you know that the premises are questionable. Then you know that the conclusion also can't be trusted.
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By permission of the Jerry Van Amerongen and Creators Syndicate, Inc. In this diagram you can see that premises 3 and 4 are handled differently from premises 6 and 7. The reason is that some premises are independent and some are dependent. An independent premise offers support to a conclusion without the help of any other premises. If other premises are omitted or undermined in an argument, the support supplied by an independent premise does not change. We represent this fact in the diagram by drawing separate arrows from premises 6 and 7 to the conclusion. Premise 6 gives independent support to the conclusion, and premise 7 gives independent support to the conclusion. If we delete one of these premises, the support that the other one gives does not change. Premises 3 and 4 are dependent premises. They do depend on each other to jointly provide support to a conclusion. If either premise 3 or 4 is removed, the support that the remaining premise supplies is undermined or completely can- celed out. By itself, premise 3 ("Because if he did it, he would probably have blood stains on the sleeve of his shirt") offers no support whatsoever to the conclusion ("Colonel Mustard is the murderer"). And by itself, premise 4 ("The blood stains are tiny, but they are there") doesn't lend any support to the conclusion. But to- gether, premises 3 and 4 offer a good reason to accept the conclusion. We repre- sent dependent premises by joining them with a plus sign ("1") and underlining them, as in our diagram. Since dependent premises together act as a single prem- ise, or reason, we draw a single arrow from the combined premises ("3 1 4") to the conclusion. With the diagram complete, we can see clearly that two independent premises and one set of dependent premises provide support for the conclusion (statement 2).
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Deductive and Inductive Arguments • A deductive argument is intended to provide conclusive support for its conclusion. • A deductive argument that succeeds in providing conclusive support for its conclusion is said to be valid. A valid argument is such that if its premises are true, its conclusion must be true. • A deductively valid argument with true premises is said to be sound. • An inductive argument is intended to provide probable support for its conclusion. • An inductive argument that succeeds in providing probable support for its conclusion is said to be strong. A strong argument is such that if its premises are true, its conclusion is probably true. • An inductively strong argument with true premises is said to be cogent.
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In step 4, once you discover which kind of argument is intended, you will know that it is either invalid or weak (because in steps 2 and 3 we eliminated the possibility of a valid or strong argument). The only remaining task is to deter- mine whether the premises are true.1 Let's try out the four-step procedure on a few arguments. Consider this one: [Premise] Unless we do something about the massive AIDS epidemic in Africa, the whole continent will be decimated within six months. [Premise] Unfortu- nately we won't do anything about the AIDS epidemic in Africa. [Conclusion] It necessarily follows that the whole of Africa will be decimated within six months. Step 1 is already done for us; the premises and conclusion are clearly labeled. In step 2, we must ask, "Is it the case that if the premises are true, the conclusion must be true?" The answer is yes: If it's true that the AIDS epidemic in Africa will decimate the population in six months unless "we do something," and it's true that "we won't do anything," then the conclusion that Africa will be decimated in six months must be true. So this argument is deductively valid. To determine if it's sound, we would need to check to see if the premises are true. In this case, the first premise is false because, under current conditions, it would take longer than six months for the epidemic to decimate the whole continent. The other premise ("we won't do anything") is at least dubious since we can't predict the future. So what we have here is a deductively valid argument that's unsound—a bad argument.
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Keep in mind that in a disjunctive syllogism, either disjunct can be denied, not just the first one. These six deductive argument forms (four valid ones and two invalid ones) can help you streamline the process of argument evaluation. If you want to find out quickly if a deductive argument is valid, you can use these patterns to do that. (Remember, a good deductive argument has both a valid form and true prem- ises.) You need only to see if the argument fits one of the forms. If it fits a valid form, it's valid. If it fits an invalid form, it's invalid. If it doesn't fit any of the forms, then you need to find another way to evaluate the argument. The easiest way to regularly apply this form-comparison technique is to memorize all six forms so you can identify them whenever they arise.
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Let's say that you are confronted with this argument: If crime is increasing, then our nation has abandoned God. Our nation has abandoned God. Therefore, crime is increasing. And to check this test argument, you come up with this parallel argument: If George is a dog, then he is warm-blooded. George is warm-blooded. Therefore, he is a dog. This argument has the same pattern as the previous one—but the premises are true, and the conclusion is false. So the test argument is invalid. You may have already guessed that it is an instance of affirming the consequent. The counterexample method, though, works not just for the deductive forms we've discussed but for all deductive forms. (We will discuss other deductive forms in upcoming chapters.) Consider another counterexample test. The argument in question is: If Jackson drinks a lot of orange juice, he will get better. He didn't drink a lot of orange juice. Therefore, he will not get better. And the parallel argument is: If horses could fly, they would be valuable. But horses cannot fly. Therefore, horses are not valuable. The argument to be tested is, of course, an example of denying the anteced- ent, and the counterexample method shows it to be invalid.
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Let's see how this procedure works on the following selection: The Case for Discrimination Edgardo Cureg was about to catch a Continental Airlines flight home on New Year's Eve when he ran into a former professor of his. Cureg lent the professor his cell phone and, once on board, went to the professor's seat to retrieve it. Another passenger saw the two "brown-skinned men" (Cureg is of Filipino descent, the professor Sri Lankan) conferring and became alarmed that they, and another man, were "behaving suspiciously." The three men were taken off the plane and forced to get later flights. The incident is now the subject of a lawsuit by the ACLU. Several features of Cureg's story are worth noting. First, he was treated unfairly, in that he was embarrassed and inconvenienced because he was wrongly suspected of being a terrorist. Second, he was not treated unfairly, because he was not wrongly suspected. A fellow passenger, taking account of his apparent ethnicity, his sex and age, and his behavior, could reason- ably come to the conclusion that he was suspicious. Third, passengers' anxieties, and their inclination to take security matters into their own hands, increase when they have good reason to worry that the authorities are not taking all reasonable steps to look into suspicious characters themselves. . . . Racial profiling of passengers at check-in is not a panacea. John Walker Lindh could have a ticket; a weapon could be planted on an unwitting 73-year-old nun. But profiling is a way of allocating sufficiently the resources devoted to security. A security system has to, yes, discriminate—among levels of threat. [National Review, July 1, 2002] In this example, the author has given us a break by alluding to the conclusion in the title: Discrimination by racial profiling is a justified security measure. Notice that this conclusion is not explicitly stated in the text but is implied by various remarks, including "A security system has to, yes, discriminate." Given this conclusion, we can see that the entire first paragraph is background information—specifically, an example of racial profiling. The first premise is implicit. We glean it from the comments in the second paragraph: Racial profil- ing is a reasonable response in light of our legitimate concerns about security. The second premise is explicit: Profiling is a way of allocating sufficiently the resources devoted to security. Laid out in neat order, this argument looks like this: (1) Racial profiling is a reasonable response in light of our legitimate concerns about security. (2) Profiling is a way of allocating sufficiently the resources devoted to security. (3) Therefore, discrimination by racial profiling is a justified security measure.
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Logical validity or logical strength is an essential characteristic of good argu- ments. But there is more to good arguments than having the proper structure. Good arguments also have true premises. A good argument is one that has the proper structure—and true premises. Take a look at this argument: All pigs can fly. Vaughn is a pig. Therefore, Vaughn can fly. The premises of this argument are false—but the conclusion follows logically from those premises. It's a deductively valid argument with all the parts in the right place—even though the premises are false. But it is not a good argument. A good argument must have true premises, and this argument doesn't. A deductively valid argument that has true premises is said to be sound. A sound argument is a good argument, which gives you good reasons for accepting its conclusion.
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Now examine this one: Security officer Jones lied on her employment application about whether she had a criminal record. Security officer Jones will do a lousy job of screening passengers for weapons. The sentence "Security officer Jones will do a lousy job of screening passen- gers for weapons" is the conclusion here. To try to make this argument valid, we would need a premise like "Any security officer at La Guardia airport who has lied on his or her employment application about having a criminal record will do a lousy job of screening passengers for weapons." This premise fits the point of the argument, but it isn't plausible. Surely it cannot be the case that any security officer who has lied will do a lousy job of screening. A more plausible premise is "Most security officers at La Guardia airport who have lied on their employment applications about having a criminal record will do a lousy job of screening pas- sengers for weapons." This premise will do, and this is now a good argument— assuming that the other premise is true.
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Now let's analyze this one: [Premise] This week, under pressure from the American Civil Liberties Union, the school board rescinded its policy of allowing school-sponsored public prayers at football games. [Premise] All the school board members agreed with the policy change. [Premise] And a memo from the board was circulated to all students, teachers, and coaches declaring that there will be no more public prayers at football games. [Conclusion] Let's face it, the days of public prayers at our school football games are over. From step 2 we can see that even if this argument's three premises are all true, the conclusion can still be false. After all, even if everything described in the premises happens, there still could be a public prayer at a football game (perhaps because of some mistake or an act of protest on the part of school-prayer advocates). So the argument can't be deductively valid. But if we go through step 3, we can see that if all the premises are true, the conclusion is likely to be true, making the argument inductively strong. If the premises are true, the argument would be cogent.
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Now let's apply this procedure to a few arguments: If the Fed lowers interest rates one more time, there will be a deep recession. I'm telling you there's going to be a deep recession. The first step is to see if there's a credible premise that would make the argument valid. We can see right away that one premise will do the trick: "The Fed has lowered interest rates again." Adding it to the argument will supply the needed link between the existing premise and the conclusion. We also can see that our new premise is plausible (the Fed has lowered interest rates again) and seems to fit with the point of the argument (to prove that there will be a recession). Our resulting argument, though, is probably not a good one be- cause the premise about the effect of the Fed's lowering interest rates is dubious.
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Now, consider this argument: (1) The famous trial lawyer Clarence Darrow (1857-1938) made a name for himself by using the "determinism defense" to get his clients acquitted of serious crimes. (2) The crux of this approach is the idea that humans are not really responsible for anything they do because they cannot choose freely—they are "determined," predestined, if you will, by nature (or God) to be the way they are. (3) So in a sense, Darrow says, humans are like wind-up toys with no control over any ac- tion or decision. (4) They have no free will. (5) Remember that Darrow was a renowned agnostic who was skeptical of all religious claims. (6) But Darrow is wrong about human free will for two reasons. (7) First, in our moral life, our own commonsense experience suggests that sometimes people are free to make moral decisions. (8) We should not abandon what our commonsense experience tells us without good reason—and (9) Darrow has given us no good reason. (10) Second, Darrow's determinism is not confirmed by science, as he claims—but actually conflicts with science. (11) Modern science says that there are many things (at the subatomic level of matter) that are not determined at all: (12) They just happen. Indicator words are scarce in this argument, unless you count the words "first" and "second" as signifying premises. After we number the statements consecutively, draw a wavy line under the conclusion, underline the premises, and cross out extraneous statements, the argument looks like this: (1) The famous trial lawyer Clarence Darrow (1857-1938) made a name for him- self by using the "determinism defense" to get his clients acquitted of serious crimes. (2) The crux of this approach is the idea that humans are not really re- sponsible for anything they do because they cannot choose freely—they are "de- termined," predestined, if you will, by nature (or God) to be the way they are. (3) So in a sense, Darrow says, humans are like wind-up toys with no control over any action or decision. (4) They have no free will. (5) Remember that Darrow was a renowned agnostic who was skeptical of all religious claims. (6) But Darrow is wrong about human free will for two reasons. (7) First, in our moral life, our own commonsense experience suggests that sometimes people are free to make moral decisions. (8) We should not abandon what our commonsense experience tells us without good reason—and (9) Darrow has given us no good reason. (10) Second, Darrow's determinism is not con- firmed by science, as he claims—but actually conflicts with science. (11) Modern science says that there are many things (at the subatomic level of matter) that are not determined at all: (12) They just happen. To simplify things, we can eliminate several statements right away. State- ments 1 through 4 are just background information on Darrow's views. State- ment 5 is irrelevant to the argument; his agnosticism has no logical connection to the premises or conclusion. Statement 12 is a rewording of statement 11. After this elimination process, only the following premises and conclusion (statement 6) remain: (6) But Darrow is wrong about human free will for two reasons. (7) First, in our moral life, our commonsense experience suggests that some- times people are free to make moral decisions. (8) We should not abandon what our commonsense experience tells us without good reason. (9) Darrow has given us no good reason. (10) Darrow's determinism is not confirmed by science, as he claims—but actu- ally conflicts with science. (11) Modern science says that there are many things (mostly at the subatomic level of matter) that are not determined at all. The question is, how are these premises related to the conclusion? Well, prem- ises 7, 8, and 9 are dependent premises supporting the conclusion. Taken sepa- rately, these premises are weak, but together they constitute a plausible reason for accepting statement 6. Premise 10 directly supports the conclusion, and it in turn is supported by premise 11.
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These logical relationships can be diagrammed like this: Now read this one: As the Islamic clerics cling to power in Iran, students there are agitating for greater freedom and less suppression of views that the clerics dislike. Even though ultimate power in Iran rests with the mullahs, it is not at all certain where the nation is headed. Here's a radical suggestion: The Islamic republic in Iran will fall within the next five years. Why do I say this? Because the majority of Iranians are in favor of democratic reforms, and no regime can stand for very long when citizens are demanding access to the political process. Also, Iran today is a mirror image of the Soviet Union before it broke apart—there's widespread dissatisfaction and dissent at a time when the regime seems to be trying to hold the people's loyalty. Every nation that has taken such a path has imploded within five years. Finally, the old Iranian trick of gaining support for the government by fomenting hatred of America will not work anymore because Iran is now trying to be friends with the United States. When we number the statements and underline the indicators, we get this: (1) As the Islamic clerics cling to power in Iran, students there are agitating for greater freedom and less suppression of views that the clerics dislike. (2) Even though ultimate power in Iran rests with the mullahs, it is not at all certain where the nation is headed. Here's a radical suggestion: (3) The Islamic republic in Iran will fall within the next five years. Why do I say this? (4) Because the majority of Iranians are in favor of democratic reforms, (5) and no regime can stand for very long when citizens are demanding access to the political process. (6) Also, Iran today is a mirror image of the Soviet Union before it broke apart—there's wide- spread dissatisfaction and dissent at a time when the regime seems to be trying to hold the people's loyalty. (7) Every nation that has taken such a path has imploded within five years. (8) Finally, the old Iranian trick of gaining support for the government by fomenting hatred of America will not work anymore (9) because Iran is now trying to be friends with the United States. And here's the passage with the premises and conclusion underlined and the extraneous material crossed out: (1) As the Islamic clerics cling to power in Iran, students there are agitating for greater freedom and less suppression of views that the clerics dislike. (2) Even though ultimate power in Iran rests with the mullahs, it is not at all certain where the nation is headed. Here's a radical suggestion: (3) The Islamic republic in Iran will fall within the next five years. Why do I say this? (4) Because the majority of Iranians are in favor of democratic reforms, (5) and no regime can stand for very long when citizens are demanding access to the political process. (6) Also, Iran today is a mirror image of the Soviet Union before it broke apart—there's widespread dis- satisfaction and dissent at a time when the regime seems to be trying to hold the people's loyalty. (7) Every nation that has taken such a path has imploded within five years. (8) Finally, the old Iranian trick of gaining support for the government by fomenting hatred of America will not work anymore (9) because Iran is now trying to be friends with the United States. The conclusion is statement 3, and the premises are statements 4 through 9. The first two statements are extraneous. Statements 4 and 5 are dependent prem- ises, and so are statements 6 and 7. Statements 8 and 9 constitute an argument that gives support to the passage's conclusion. Statement 8 is the conclusion; statement 9, the premise. Notice also that the sentence "Why do I say this?" is not diagrammed at all because it's not a statement. The diagram of this argument is as follows: By the time you work through the diagramming exercises in this chapter, you will probably be fairly proficient in diagramming arguments of all kinds. Just as important, you will have a better appreciation of how arguments are built, how they're dissected, and how you can judge their value in a penetrating, systematic way.
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A deductively valid argument is such that if its premises are true, its conclusion must be true. That is, if the premises are true, there is no way that the conclusion can be false.
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Diagramming Arguments Most of the arguments we've looked at so far have been relatively simple. When arguments are more complex (in real life they usually are!), you may find it increas- ingly difficult to sort out premises from conclusions and argument parts from non- argumentative background noise. If you can visualize an argument's structure, though, the job gets much easier. That's where argument diagramming comes in.
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• Sometimes you also have to ferret out implicit, or unstated, premises. Find- ing implicit premises is a three-step process.
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A good inductive argument must also have true premises. For example: Scientific studies show that 99 percent of dogs have three eyes. So it's likely that the next dog I see will have three eyes. This is an inductively strong argument, but it's not a good argument because its premise is false. When inductively strong arguments have true premises, they are said to be cogent.
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An inductive argument that fails to provide such support is said to be weak.
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Here's the symbolized version: If p, then q. If q, then r. Therefore, if p, then r.
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Assessing Long Arguments The general principles of diagramming can help you when you have to evaluate arguments that are much longer and more complicated than most of those in this chapter. Some arguments are embedded in extended passages, persuasive essays, long reports, even whole books. In such cases, the kind of detailed argument dia- gramming we use to analyze short passages won't help you much. In very lengthy works, our five-step diagramming procedure would be tedious and time-consuming—if not maddening. But the general approach used in the proce- dure is relevant to longer arguments.
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Here's a simple deductively valid argument: All dogs have fleas. Bowser is a dog. So Bowser has fleas. And here's a golden oldie. All men are mortal. Socrates is a man. Therefore, Socrates is mortal.
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Earlier we discussed the importance of being familiar with argument patterns, or forms, the structures on which the content is laid. The point was that know- ing some common argument forms makes it easier to determine whether an argument is deductive or inductive. But being familiar with argument forms is also helpful in many other aspects of argument evaluation. Let's take a closer look at some of these forms. Since argument forms are structures distinct from argument content, we can easily signify different forms by using letters to represent statements in the argu- ments. Each letter represents a different statement in much the same way that letters are used to represent values in a mathematical equation. Consider this argument: If the job is worth doing, then it's worth doing well. The job is worth doing. Therefore, it's worth doing well. We can represent this argument like this: If p, then q. p. Therefore, q. Notice that the first line in the argument is a compound statement—it's com- posed of at least two constituent statements, which are represented in this case by p and q. So we have three statements in this argument that are arranged into an argument form, one that is both very common and always valid. We can plug any statements we want into this form, and we will still get a valid argument. The premises may be true or false, but the form will be valid.
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See what you think of this one: [Premise] If you act like Bart Simpson, you will be respected by all your classmates. [Premise] But you don't act like Bart Simpson. [Conclusion] It follows that you will not be respected by all of your classmates. This argument flunks the tests in steps 2 and 3: It is not deductively valid, and it is not inductively strong. But it does resemble a deductive argument in two ways. First, it displays a pattern of reasoning that can, at first glance, seem deduc- tive. Actually, it uses an argument pattern that is always deductively invalid (called denying the antecedent, an argument form we will look at shortly). This alone should be evidence enough that the argument is indeed deductive but in- valid. But it also contains an argument indicator phrase ("it follows that") that suggests an attempt at a deductive form.
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Sometimes arguments not only are faulty but also have a few pieces missing. Prem- ises (and sometimes even conclusions)—material needed to make the argument work—are often left unstated. These implicit premises, or assumptions, are essential to the argument. Of course, certain assumptions are frequently left unsaid for good reason: They are obvious and understood by all parties to the argument, and bore- dom would set in fast if you actually tried to mention them all. If you wish to prove that "Socrates is mortal," you normally wouldn't need to explain what mortal means and that the name Socrates does not refer to a type of garden tool. But many argu- ments do have unstated premises that are not only necessary to the chain of reason- ing but also must be made explicit to fully evaluate the arguments. For instance: The easy availability of assault rifles in the United States has increased the risk of death and injury for society as a whole. Therefore, assault rifles should be banned. Notice that there is a kind of disconnect between the premise and the conclu- sion. The conclusion follows from the premise only if we assume an additional premise, perhaps something like this: "Anything that increases the risk of death and injury for society as a whole should be banned." With this additional prem- ise, the argument becomes: The easy availability of assault rifles in the United States has increased the risk of death and injury for society as a whole. Anything that increases the risk of death and injury for society as a whole should be banned. Therefore, assault rifles should be banned.
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Such implicit prem- ises should never be taken for granted because, among other things, they are often deliberately hidden or downplayed to make the argument seem stronger. Be aware, though, that many times the problem with an ar- gument is not unstated premises, but invalid or weak structure. Consider this:If Tariq works harder, he will pass his calculus course. But he will not work harder, so he will not pass calculus. This argument is invalid; the conclusion does not follow from the premises. Like most invalid arguments, it can't be salvaged without altering it beyond what is clearly implied. It's just a bad argument. The same goes for weak arguments. They usually can't be fixed up without adding or changing premises gratuitously. Remember, the point of articulating unstated premises is to make explicit what is already implicit. Your job as a critical thinker is not to make bad arguments good; that task falls to the one who puts forth the argument in the first place. To make sure that your investigation of implicit premises is thorough and reasonable, work through the following three-step process.
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The best way to learn how to assess long passages is to practice, which you can do in the following exercises. Be forewarned, however, that this skill de- pends heavily on your ability to understand the passage in question. If you do grasp the author's purpose, then you can more easily paraphrase the premises and conclusion and uncover implicit statements. You will also be better at telling extraneous stuff from the real meat of the argument. (Also see Appendix D: Critical Thinking and Writing.)
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In logic, valid is not a synonym for true. A deduc- tively valid argument simply has the kind of logical structure that guarantees the truth of the conclusion if the premises are true
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"Logical structure" refers not to the content of an argument but to its construction, the way the premises and conclusion fit together. Because of the guarantee of truth in the conclusion, deductively valid arguments are said to be truth-preserving.
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• Assessing very long arguments can be challenging because they may con- tain lots of verbiage but few or no arguments, and many premises can be implicit. Evaluating long arguments, though, requires the same basic steps as assessing short ones: (1) Ensure that you understand the argument, (2) locate the conclusion, (3) find the premises, and (4) diagram it to clarify logical relationships.
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• Evaluating an argument is the most important skill of critical thinking. It involves finding the conclusion and premises, checking to see if the argu- ment is deductive or inductive, determining its validity or strength, and discovering if the premises are true or false.
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Here's another one: Anyone who craves political power cannot be trusted to serve the public interest. Senator Blowhard can't be trusted to serve the public interest. As stated, this argument seems like a rush to judgment because the first premise concerns anyone who craves power, and suddenly Senator Blowhard is denounced as untrustworthy. Something's missing. What we need is another premise connecting the first premise to the conclusion: "Senator Blowhard craves political power." Now let's plug the implicit premise into the argument: Anyone who craves political power cannot be trusted to serve the public inter- est. Senator Blowhard craves political power. He can't be trusted to serve the public interest.
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Note, however, that deductively valid arguments can have true or false prem- ises and true or false conclusions. Specifically, deductively valid arguments can have false premises and a false conclusion, false premises and a true conclusion, and true premises and a true conclusion. A valid argument, though, cannot have true premises and a false conclusion—that's impossible. See for yourself: False Premises, False Conclusion All dogs have flippers. All cats are dogs. Therefore, all cats have flippers. False Premises, True Conclusion Bowser is a cat. All cats are mammals. Therefore, Bowser is a mammal. True Premises, True Conclusion Bowser is a dog. All dogs are mammals. Therefore, Bowser is a mammal.
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A deductively invalid version of these arguments might look like this: All dogs are mammals. All cows are mammals. Therefore, all dogs are cows. If Socrates has horns, he is mortal. Socrates is mortal. Therefore, Socrates has horns.
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The following is a suggested four-step procedure for answering these questions. We will be elaborate it on here and in later chapters. Step 1. Find the argument's conclusion and then its premises. Use the tech- niques you learned in Chapter 1. You'll have plenty of chances to hone this skill in upcoming chapters. Step 2: Ask: Is this the case that if the premises are true the conclusion must be true? If the answer is yes, treat the argument as deductive, for it is very likely meant to offer conclusive support for its conclusion. The argument, then, is deductively valid, and you should check to see if it's sound. If the answer is no, proceed to the next step. Step 3. Ask: Is it the case that if the premises are true, its conclusion is probably true? If the answer is yes, treat the argument as inductive, for it is very likely meant to offer probable support for its conclusion. The argument, then, is inductively strong, and you should check to see if it's cogent. If the answer is no, proceed to the next step. Step 4. Ask: Is the argument intended to offer conclusive or probable support for its conclusion but fails to do so? If you reach this step, you will have already eliminated two possibilities: a valid argument and a strong one. The remaining options are an invalid argument or a weak one. So here you must discover what type of (failed) argument is intended.
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• Using the counterexample method can help you determine whether a de- ductive argument is valid or invalid.
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SYMBOLIZED VERSION Either p or q. Not p. Therefore, q. EXAMPLE Either we light the fire or we will freeze. We will not light the fire. Therefore, we will freeze.
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So exactly when should we try to ferret out an unstated premise? The obvious answer is that we should do so when there appears to be something essential missing—an implied, logical link between premises and conclusion that is not a com- monsense, generally accepted assumption.
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When you have to evaluate a very long passage, you're almost always faced with three obstacles: 1. Only a small portion of the prose may contain statements that serve as the premises and conclusion. (The rest is background information, reiterations of ideas, descriptions, examples, illustrations, asides, irrelevancies, and more.) 2. The premises or conclusion may be implicit. 3. Many longer works purporting to be filled with arguments contain very few arguments or none at all. (It's common for many books—even best sell- ers—to pretend to make a case for something but to be devoid of genuine arguments.) Fortunately, you can usually overcome these impediments if you're willing to put in some extra effort. The following is a four-step procedure that can help. Step 1. Study the text until you thoroughly understand it. You can't locate the conclusion or premises until you know what you're looking for—and that requires having a clear idea of what the author is driving at. Don't attempt to find the conclusion or premises until you "get it." This understanding entails having an overview of a great deal of text, a bird's-eye view of the whole work. Step 2. Find the conclusion. When you evaluate extended arguments, your first task, as in shorter writings, is to find the conclusion. There may be several main conclusions or one primary conclusion with several subconclusions (as de- picted in some of the previous argument diagrams). Or the conclusion may be nowhere explicitly stated but embodied in metaphorical language or implied by large tracts of prose. In any case, your job is to come up with a single conclusion statement for each conclusion—even if you have to paraphrase large sections of text to do it. Step 3. Identify the premises. Like the hunt for a conclusion, unearthing the premises may involve condensing large sections of text into manageable form— namely, single premise statements. To do this, you need to disregard extraneous material and keep your eye on the "big picture." Just as in shorter arguments, premises in longer pieces may be implicit. At this stage you shouldn't try to in- corporate the details of evidence into the premises, though you must take them into account to fully understand the argument. Step 4. Diagram the argument. After you identify the premises and conclu- sion, diagram them just as you would a much shorter argument.
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Diagramming Arguments: Step by Step 1. Underline all premise or conclusion indicator words, such as "since," "therefore," and "because." Then number the statements. 2. Find the conclusion and draw a wavy line under it. 3. Locate the premises and underline them. 4. Cross out all extraneous material—redundancies, irrelevant sentences, questions, exclamations. 5. Draw the diagram, connecting premises and conclusions with arrows showing logical connections. Include both dependent and independent premises.
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Let's turn our first two deductively valid arguments into inductively strong arguments: Most dogs have fleas. Therefore, Bowser, my dog, probably has fleas. Ninety-eight percent of humans are mortal. Socrates is human. Therefore, Socrates is likely to be mortal. Notice that in the first argument, it's entirely possible for the premise to be true and the conclusion false. After all, if only most dogs have fleas, there is no guarantee that Bowser has fleas. Yet the premise, if true, makes the conclusion probably true. Likewise, in the second argument it is possible that even if 98 percent of humans are mortal and Socrates is human, the conclusion that Socrates is mortal could be false. But the premises, if true, make it likely that the conclusion is true.
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So the obvious questions here are: When you come face to face with an argu- ment to evaluate, (1) how can you tell whether it's deductive or inductive, and (2) how can you determine whether it gives you good reasons for accepting the con- clusion (whether it's sound or cogent)?
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Step 1. Search for a credible premise that would make the argument valid, one that would furnish the needed link between premise (or premises) and con- clusion. Choose the supplied premise that a. is most plausible and b. fits best with the author's intent. The first stipulation (a) means that you should look for premises that are either true or, at least, not obviously false. The second stipulation (b) means that prem- ises should fit—that is, at least not conflict—with what seems to be the author's point or purpose (which, of course, is often difficult to discern). If the premise you supply is plausible and fitting (with author's intent), use it to fill out the argument. If your supplied premise is either not plausible or not fitting, go to step 2. Step 2. Search for a credible premise that would make the argument as strong as possible. Choose the supplied premise that fulfills stipulations a and b. If the premise you supply is plausible and fitting, use it to fill out the argument. If your supplied premise is either not plausible or not fitting, consider the argument beyond repair and reject it. Step 3. Evaluate the reconstituted argument. If you're able to identify a credible implicit premise that makes the argument either valid or strong, assess this revised version of the argument, paying particular attention to the plausibility of the other premise or premises.
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