Argument Analysis
4.4 Induction and Deduction
So far we have treated all arguments as a single class, defined by the use of premises to support a conclusion. But there are many different types of argument, different pat-terns of reasoning. These narrower classes have distinctive structures, and in later chap-ters we will learn specific methods for analyzing and evaluating them. It is important now, however, to understand the broad distinction between two basic types of argu-ment: induction and deduction.
The following arguments illustrate the difference:
A. A detective investigating a murder notices that nothing was taken from the victim’s wallet. He might reason as follows: (1) If robbery was the motive, the money would have been taken, but (2) the money was not taken, so (3) robbery was not the motive.
B. A scientist investigating an outbreak of disease examines a random sample of the vic-tims. She discovers (1) that all of them had recently eaten strawberries from California, and, as far as she can tell, (2) that the people in the sample had nothing else in com-mon. The scientist concludes (3) that something in the strawberries was causing the disease in all the victims.
Argument A is an example of a deductive argument. The conclusion (3) simply makes explicit the information implicit in premises 1 and 2. If those premises are true, they guarantee the truth of the conclusion: It would be impossible for the conclusion to be false. Argument B is an inductive argument. The conclusion is certainly supported by the premises, but it does not merely draw out the information contained in them.
The conclusion applies not just to the particular victims in the sample, but to all cases of the disease: The scientist is inferring that the strawberries (or food containing the same chemical elements) causes the disease in people she has not examined. Logicians sometimes describe this feature of induction by saying that it is ampliative: The conclu-sion amplifies—it goes beyond—what the premises state. As a result, the truth of the premises does not guarantee the truth of the conclusion; there is some possibility, how-ever small, that the conclusion is false.
b. People should be treated the same regardless of race and sex, but affirmative action programs require that people be treated differently depending on their race and sex. Such programs should therefore be abolished.
❋10. a. The government’s banning Muslim women from wear-ing a burqa in public spaces is detrimental to individual liberty.
Wearing the burqa is an instance
of religious expression, and freedom of religion is crucial to individual liberty.
b. The government’s banning Muslim women from wearing a burqa in public spaces is detri-mental to individual liberty. The ban is xenophobic in motiva-tion, it causes tension within the Muslim community, and it makes Muslim women feel uncomfortable.
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Both deductive and inductive arguments have certain common forms. We will ex-plore these forms in detail in Part 2 (Deductive Logic) and Part 3 (Inductive Logic). As a preview, let us consider a few of the more common ones.
Some deductive arguments have compound premises with more than one compo-nent proposition. Among the most common are those with premises of the form if p then q and p or q. Neither type of statement asserts the component propositions p and q as being true; what is asserted is a relationship between p and q. But in combination with other premises, such statements allow us to make deductive arguments. In the following examples, beginning with the detective’s argument, notice how the premises, if true, would guarantee the truth of the conclusion. (Instead of diagrams, we use the standard form for deductive arguments: The propositions are put on separate lines, with an underscore separating premises from conclusion.)
A. If robbery was the motive, then the victim’s money would have been taken.
The victim’s money was not taken.
Therefore, robbery was not the motive.
C. If robbery was the motive, then the victim’s money would have been taken.
If the victim’s money was taken, then the bills will have the perpetrator’s fingerprints.
Therefore, if robbery was the motive, then the bills will have the perpetrator’s fingerprints.
D. The motive for the murder was either robbery or vengeance.
The motive was not robbery.
Therefore, the motive was vengeance.
In each of these examples, the conclusion follows because of the repetition of the component propositions ( p and q). Another type of deductive argument involves non-compound statements, and the conclusion follows because of the repetition of subject and predicate terms in the statements. Here are a few examples of this type, beginning with an inference we discussed previously.
E. All water flows downhill.
All rivers in Taiwan are water.
Therefore, all rivers in Taiwan flow downhill.
F. Any driver convicted of three moving violations will have his or her license suspended.
Roxanne has been convicted of three moving violations.
Therefore, Roxanne will have her license suspended.
In all these forms of deductive argument, the conclusion simply makes explicit the information contained in premises, so there is no gap between premises and conclu-sion. If the premises are true, the conclusion must be true as well. If you accept the premises but deny the conclusion, you contradict yourself. This property is known as validity. A deductive argument is valid when it is impossible for the premises to be true and the conclusion false. If an argument is intended as deductive but does not meet this criterion, it is invalid. Suppose, for example, that our detective found that money was taken from the victim’s wallet and then reasoned as follows:
G. If robbery was the motive, then the victim’s money would have been taken.
The victim’s money was taken.
Therefore, robbery was the motive.
This argument is somewhat similar in form to argument A, so we would classify it as deductive, but it is invalid because the premises could be true and the conclusion false.
For example, the murderer might have killed for revenge but taken the money to cover his tracks. The following deductive arguments are likewise invalid:
H. The woman just appointed CEO at Megacorp is either very smart or very ambitious.
She is very ambitious.
Therefore she is not very smart.
I. All voters are citizens.
Some citizens are not taxpayers.
Therefore, some taxpayers are not voters.
A deductive argument is either valid or invalid. Validity does not come in degrees. It is either possible or impossible for the premises to be true and the conclusion false. In the first case the argument is invalid, period; in the second it is valid.
Inductive arguments also have various common forms. One common form is gener-alization: drawing a general conclusion about a class of things by observing a sample of the class. Inductive generalizations are pervasive in science as well as everyday common knowledge. For example, you know that fire burns, not because you have observed every case of fire burning, worldwide, but because you have observed enough cases to draw the general conclusion. Argument B given earlier is another example. From information about a sample of people who got sick after eating the strawberries, the scientist infers that any person who eats strawberries with the same chemical composition would get the disease.
Another kind of inductive argument moves in the opposite direction, drawing a conclusion about some particular thing or event from a generalization about that type of thing or event. For example:
J. Cold fronts usually bring rain.
A cold front is moving in.
Therefore, it will rain tomorrow.
If the first premise stated that all cold fronts bring rain, this would be a deductive argu-ment. But the premise says only that cold fronts usually bring rain, not that they always do, so it is possible for the conclusion to be false even if the premises are true. The argu-ment provides reasonably good support for the conclusion, depending on exactly what percentage of cold fronts bring rain, but the truth of the premises would not guarantee the truth of the conclusion.
Yet another common form of induction is called argument by analogy. We draw a conclusion about one thing because of its similarity to something else that we know more about. Here’s an example from pop music:
K. Lady Gaga is like Madonna in a lot of ways. She’s edgy and iconoclastic, she keeps reinventing her persona, she’s a talented performer and has a huge talent for self-promotion. Madonna has had a long and successful career, so Lady Gaga probably will, too.
The premises assert several points of similarity between the two singers. Together with the further premise that Madonna had a successful career, the similarities provide
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evidence for Lady Gaga’s future success, though the premises do not guarantee the truth of that conclusion. We use argument by analogy frequently in thinking about people, as in the example; in using history to predict future political and economic outcomes; and in problem-solving, when we compare the problem at hand to other problems that we know how to solve.
These forms of arguments illustrate the ampliative nature of induction. Even in a good inductive argument, the conclusion goes beyond the information given in the premises. The distinction between valid and invalid is therefore not applicable. Instead, we evaluate such arguments in terms of their strength. Unlike the qualitative distinc-tion between valid and invalid deductive arguments, inductive strength comes in de-grees. When the scientist in argument B infers that the strawberries caused the disease, the argument has some strength. But the victims might have had something else in common, something that the scientist has not yet checked out. Or the victims might have reacted to the strawberries for diverse, idiosyncratic reasons that would not apply to people in general. Thus the argument could be made stronger by examining more cases of the disease, by testing other possible factors and ruling them out, and by find-ing the underlyfind-ing mechanism by which somethfind-ing in the strawberries affects the body.
For induction, in other words, there is a continuum from relatively weak support to very strong support. As we move along the continuum by gathering more evidence, we increase the likelihood that the conclusion is true.
As we noted in the previous section, we evaluate arguments by two basic standards:
1. Are the premises true? 2. How well do the premises support the conclusion?
In logic, we are mainly concerned with the second standard. To meet that standard, a deductive argument must be valid; an inductive argument must be strong. We also have special terms for arguments that meet both standards. If a deductive argument is valid and its premises are true, we say that the argument is sound. If an inductive argument is strong and its premises are true, we say that it is cogent. In other words:
Deduction: Sound = Valid + True premises Induction: Cogent = Strong + True premises
Induction and deduction normally work together. Deductive arguments typically apply general knowledge that we have already acquired to new instances. But we first had to acquire that general knowledge by inductive reasoning. Each individual step in an argument will be either inductive or deductive, but the argument as a whole—the case for believing the conclusion is true—normally requires that the premises of any deductive step be supported by induction. In argument A, the detective’s deductive con-clusion rests on the premise that if robbery had been the motive, then something would have been taken from the victim’s wallet. How does the detective know this? He learned it by observing human nature in general and the behavior of criminals in particular.
On the basis of these observations, he drew the inductive generalization that people normally carry money in wallets, that thieves know this, and that robbery is a common motive for murder but not the only one.
As another example, consider an argument we diagrammed earlier: that extreme sarcasm is a form of unprovoked hostility, which results from feelings of inadequacy.
This argument would best be construed as deductive. To make its deductive character clear, we might formulate it as follows:
All extremely sarcastic people are acting from unprovoked hostility.
All people who act from unprovoked hostility feel inadequate.
Therefore, all extremely sarcastic people feel inadequate.
In this argument as stated, the conclusion necessarily follows from the premises. Now suppose that we want to provide evidence for the second premise. We might consider the people we know who tend to act from hostility. If they all tend to feel inadequate, then we have some inductive evidence for the generalization about human psychology.
We could strengthen the evidence by doing psychological experiments that use larger samples of people and objective measures for hostility and inadequacy. But the evidence would still be inductive because it involves a generalization from the sample of people in the experiment to the class of all humans.
Conversely, inductive arguments often involve deductive steps, at least implicitly. In argument B given earlier, the scientist looking for a common factor among the victims of the disease probably did not ask whether they all rooted for the same baseball team.
Why not? Because she knows that only biochemical processes in the body cause disease;
being a Yankees fan is not a biochemical process, so it could not cause the disease.
That’s a deductive inference.
EXERCISE 4.4
Determine whether each of the following arguments is inductive or deductive. If it is deductive, is it valid or invalid?
SUMMARY
Induction and Deduction1. A deductive argument attempts to show that its conclusion makes explicit the infor-mation implicit in the premises, so that the conclusion must be true if the premises are.
2. A deductive argument is either valid or invalid. If it is valid, then it is impossible for all of its premises to be true and its conclu-sion to be false. Otherwise it is invalid. If it is valid and all of its premises are true, the argument is sound.
3. An inductive argument attempts to show that the conclusion is supported by the
premises even though the conclusion amplifies—it goes beyond—what the premises state.
4. Inductive arguments have degrees of strength, and a given argument can be strengthened or weakened through ad-ditional evidence. If the argument is strong and all of its premises are true, it is cogent.
Deduction: Sound = Valid + True premises Induction: Cogent = Strong + True premises
❋1. No Greek philosopher taught in a university, but some Greek philosophers were great thinkers.
Therefore, some great thinkers have not taught in a university.
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2. Barbara is a liberal. She’s a strong advocate of environmentalism, and most environmentalists are liberals.
3. All Romans are Italians; all Italians are Europeans; so Romans are Europeans.
❋4. Two flowers of the same cultivar were planted in adjacent plots. The first was fertilized with Miracle-Gro and it flourished; the second was not and it didn’t. Therefore, Miracle-Gro stimulates plant growth.
5. If a triangle has angles of 30° and 60°, then its third angle is 90°. If an angle in a triangle is 90°, then it is a right triangle. So if a triangle has angles of 30° and 60°, then it is a right triangle.
6. Thanks to St. Patrick, no snake lives in Ireland. Since snakes are reptiles, that means no reptiles live in Ireland.
❋7. Xavier is a student at Orchard College, where 80% of students complete their undergraduate de-gree within 5 years. So Xavier has a good chance of getting his degree.
8. No machine is capable of perpet-ual motion, because every machine is subject to friction, and nothing that is subject to friction is capable of perpetual motion.
9. Either Jesus was telling the truth when he said he was the son of God or he was insane. But he wasn’t insane, so he was actually the son of God.
❋ 10. The plan to build a new fac-tory does not have a provision for construction delays, so its cost estimates are likely to be too low.
Experienced contractors know
that most building projects on this scale do have delays, which add to the expense of the project.
11. If the tectonic plates under the Atlantic Ocean are moving apart, there will be volcanic activity in Iceland—and there is volcanic ac-tivity there. So the tectonic plates are separating.
12. Everything we know about was created at a certain point in time, as a result of causes that existed before. So the universe itself must have been created by a being that existed before the universe.
❋ 13. The fossil record shows that certain dinosaurs, like birds, were capable of winged flight. Although the birds that exist today are dif-ferent in many ways, they do share a number of anatomical features with that class of dinosaurs, including scales, hollow bones, expanded pneumatic sinuses in the skull, 3-fingered opposable hands, and 4-toed feet. We can conclude that birds evolved from those dinosaurs.
14. Either health care is a right or it is something that individuals have to earn. Since health care is some-thing that has to be earned, it isn’t a right.
15. The economic crisis of 2008–2009 is like the panic of 1873 in that it was caused by a bubble in real estate, after which banks severely tightened their lending practices, and both consumers and busi-nesses were hobbled by the inabil-ity to get loans. The recession of the 1870s lasted more than 3 years, so today’s economy will likely take that long to recover.