Hypothetical argument

HYPOTHETICAL SYLLOGISMS

Hypothetical thinking involves “If . . . then . . .” reasoning. According to some psychologists, the mental model for hypothetical thinking is built into our brain and enables us to understand rules and predict the consequences of our actions. We’ll be looking at the use of hypothetical reasoning in ethics in greater depth in Chapter 9. Hypothetical arguments are also a basic building block of computer programs.

A hypothetical syllogism is a form of deductive argument that contains two premises, at least one of which is a hypothetical or conditional “if . . . then” statement.

Hypothetical syllogisms fall into three basic patterns: modus ponens (affirming the antecedent), modus tollens (denying the consequent), and chain arguments.

Modus Ponens

In a modus ponens argument, there is one conditional premise, a second premise that states that the antecedent, or if part, of the first premise is true, and a conclusion that asserts the truth of the consequent, or the then part, of the first premise. For example:

Premise 1: If I get this raise at work, then I can pay off my credit-card bill.

Premise 2: I got the raise at work.

Conclusion: Therefore, I can pay off my credit-card bill.

A valid modus ponens argument, like the one above, takes the following form:

If A (antecedent), then B (consequent).

A.

Therefore, B.

Sometimes the term then is omitted from the consequent, or second, part of the conditional premise:

If the hurricane hits the Florida Keys, we should evacuate.

The hurricane is hitting the Florida Keys.

Therefore, we should evacuate.

Modus ponens is a valid form of deductive reasoning no matter what terms we substitute for A and B. In other words, if the premises are true, then the conclusion must be true. Thus:

If Barack Obama is president, then he was born in the United States.

Barack Obama is president.

Therefore, he was born in the United States. C

In this case, the first premise is true because the U.S. Constitution requires that the president be “a natural born citizen.” Therefore, the argument is a sound argument.

It is important not to deviate from this form in a modus ponens argument. If the second premise affirms the consequent (B) rather than the antecedent (A), the argument is invalid and the conclusion may be false, even though the premises are true.

If Oprah Winfrey is president, then she was born in the United States.

Oprah Winfrey was born in the United States.

Therefore, Oprah Winfrey is president.

But of course, as we all know, Oprah Winfrey is not president of the United States. This deviation from the correct form of modus ponens is known as the fallacy of affirming the consequent.

Modus Tollens

In a modus tollens argument, the second premise denies the consequent, and the conclusion denies the truth of the antecedent:

If A (antecedent), then B (consequent).

Not B.

Therefore, not A.

Here is an example of a modus tollens argument:

If Morgan is a physician, then she has graduated from college.

Morgan did not graduate from college.

Therefore, Morgan is not a physician.

Like modus ponens, modus tollens is a valid form of deductive reasoning. No matter what terms we substitute for the antecedent (A) and consequent (B), if the premises are true, then the conclusion must be true. If we change the form by changing the first premise to read “If not A, then B,” we commit the fallacy of denying the antecedent.

Chain Arguments

Chain arguments are made up of three conditional propositions—two premises and one conclusion— linked together. A chain argument is a type of imperfect hypothetical syllogism since it may contain more than three propositions.

If A, then B.

f B, then C.

Therefore, if A, then C.

The following is an example of a chain argument:

If it rains tomorrow, then the beach party is canceled.

If the beach party is canceled, we’re having a party at Rachel’s house.

Therefore, if it rains tomorrow, we’re having a party at Rachel’s house.

Just as some arguments by elimination are syllogisms and others are not, we can have a longer chain argument that is still a deductive argument but not a syllogism because it has more than two premises. For example:

If A, then B.

If B, then C.

If C, then D.

Therefore, if A, then D.

Here is an example of a chain argument with three premises:

If you don’t go to class, you won’t pass the final exam.

If you don’t pass the final exam, then you won’t pass the course.

If you don’t pass the course, then you won’t graduate this year.

Therefore, if you don’t go to class, you won’t graduate this year.

A chain argument is valid if it follows the form of using the consequent of the previous premise as the antecedent in the next premise, and so on, with the conclusion using the antecedent from the first premise (A) and the consequent in the last premise (D).

Glossary:

hypothetical syllogism : A deductive argument that contains two premises, at least one of which is a conditional statement.

modus ponens: A hypothetical syllogism in which the antecedent premise is affirmed by the consequent premise.

modus Tollens: A hypothetical syllogism in which the antecedent premise is denied by the consequent premise.

chain arguments: A type of imperfect hypothetical argument with three or more conditional propositions linked together.

Evaluating Hypothetical Syllogisms for Validity

Not all hypothetical syllogisms are laid out in standard syllogistic form. If an argument isn’t already in standard form, put it in standard form with the conditional premise first and the conclusion last. In the case of a chain argument, begin by listing the premise containing the antecedent from the conclusion. In 1758, Ben Franklin offered this bit of wisdom in his famous Poor Richard’s Almanac: For want of a Nail the Shoe was lost; For want of a Shoe the Horse was lost; For want of a Horse, the Rider was lost, being overtaken and slain by the enemy; For want of Care about the Horse-Shoe Nail, the Rider is lost. Let’s test the validity of Franklin’s argument by writing it out as a hypothetical syllogism, in this case a chain argument:

If a nail is missing (A), then the horseshoe will be lost (B).

If the horseshoe is lost (B), then the rider is lost (C).

If the nail is missing (A), then the rider is lost (C).

By rewriting this as a hypothetical syllogism, we can see that it is a valid argument. In some cases, it may be too awkward to restate each use of the antecedents and consequents using the exact same language as in Franklin’s argument. In these cases, it is acceptable to use everyday language as long as the meaning remains the same each time it is used. Otherwise, the argument commits the fallacy of equivocation.

A hypothetical syllogism is valid if it follows one of the forms discussed in this chapter—modus ponens, modus tollens, or chain argument. If you are uncertain whether a hypothetical syllogism is valid, you can also try substituting different terms for those used in the argument under evaluation.

Not all valid arguments are sound. As we noted earlier, a deductive argument can be valid by virtue of its form but still be unsound because one of the premises is false. Rewording arguments in ordinary language in the form of a hypothetical syllogism can help you expose the faulty premises. Suppose you are looking for a new cell phone and find two models that seem to suit your needs—a Sony and a Motorola. Both have similar features, but the Sony costs more than the Motorola. So you think: The Sony cell phone costs more, so it should be the better phone. I think I’ll buy the Sony. Putting your argument in the form of a hypothetical syllogism, we have this:

If a product is expensive, then it must be good.

This brand of cell phone is expensive.

Therefore, it must be good.

However, the first premise is false. Not all expensive products are good, nor are all inexpensive products of poor quality. Therefore, this is an unsound argument. Unfortunately, many people fall for this line of reasoning. Indeed, some clever marketers have found that when they increase the price of certain items, such as jewelry or clothing, it actually sells better!

Putting an argument in the form of a hypothetical syllogism can be helpful in clarifying what’s at stake. Consider this argument from the abortion debate:

If a being is a person (A), then it is morally wrong to kill that being except in self-defense (B).

The fetus is a person (A).

Therefore, it is morally wrong to kill the fetus except in self-defense (B).

HIGHLIGHTS

VALID FORMS OF HYPOTHETICAL SYLLOGISMS

Modus Ponens

Modus Tollens

Chain Argument

If A, then B.

If A, then B.

If A, then B.

A.

Not B.

If B, then C.

Therefore, B.

Therefore, not A.

Therefore, if A, then C.

Judith Jarvis Thomson, in her essay “A Defense of Abortion” (which we will read at the end of Chapter 9), recognizes the strength of this type of deductive reasoning and acknowledges that she must accept the conclusion if she accepts the premises as true. She also realizes that the only way to reject this argument—since it is a valid argument—is to show that one of the premises is false and there- fore the argument is unsound. Otherwise, she must accept the conclusion. Since she can’t prove that the fetus is not a person, she tentatively accepts the second premise as true. Instead, she questions the first premise, arguing that there may be circumstances when we can kill another person for reasons other than self-defense.

Hypothetical arguments are common in everyday reasoning. In addition to being used in promises and ultima- tums (see “Critical Thinking in Action: Empty Promises: If This, Then That—Making Promises and Threats” on page 249), they can be used to spell out the outcomes of certain choices you make in your life: for example, the necessary antecedents you’ll need to graduate from college or go on graduate school.

Exercise 8-3

#3. Think of an issue or goal that is important in your life. Write a hypothetical syllogism related to the issue or goal. Evaluate the syllogism for validity and soundness.

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