Argument Analysis
4.2 Diagramming Arguments
4.2 Diagramming Arguments
We can think of the premises as the raw materials for an argument and the conclusion as the final product. To understand an argument, we need to know what happens in between—on the factory floor, so to speak. We need to analyze the inner workings of the argument, the individual steps that lead from premises to conclusion. Once we have analyzed the argument, we can go on to evaluate it: Is it a good argument? Does it pro-vide a good reason to accept the conclusion? Analysis and evaluation are the two basic tasks we are going to discuss in this chapter. We will begin with analysis in this section and move on to evaluation in later sections.
To analyze an argument, we can use a diagramming method that employs just two symbols but is flexible enough to handle arguments of any complexity. One symbol is an arrow pointing from premise to conclusion. This arrow represents a single step in reasoning—the relationship between a premise and the conclusion. Suppose you ar-gued against gun control on the ground that it would violate the right of self-defense.
Then your reasoning could be diagrammed as follows:
Restricting handgun ownership violates the right of self-defense.
The government should not restrict handgun ownership.
This is an extremely simple argument. It has a single premise, and there is a single step in the reasoning. So the structure of the argument is fully represented by a single arrow.
But what if there is more than one premise? Then we have a decision to make. In some cases, the premises are dependent on one another: Two or more premises work together to make a single argument for a conclusion. In other cases, the premises are independent: They do not work together; each one offers a separate line of support for the conclusion. These two patterns are diagrammed in different ways, so we have to decide which pattern is present in a given argument. To illustrate the distinction, let’s reexamine two arguments that we have already discussed.
The first is Ronald Reagan’s argument about politics and religion. In essence, he said: (1) politics depends on morality, and (2) morality depends on religion, therefore (3) politics depends on religion. This argument illustrates the first pattern—an argu-ment with dependent premises. Premises 1 and 2 must be combined in order to have an argument for 3. The premise that politics depends on morality, taken by itself, does not tell us anything about religion, so it doesn’t give us any reason to think that politics depends on religion. In the same way, the premise that morality depends on religion, taken by itself, does not tell us anything about politics, so again we would have no rea-son to think politics depends on religion. It is only when we put the premises together that we have an argument. We represent this fact by using a second symbol, the plus (+) sign, to join the premises. Using the numbers to stand for the individual propositions, we would diagram the argument like this:
1 + 2
3
We use a single arrow, drawn from the line joining the premises, to represent the fact that the premises together make up a single argument.
By contrast, consider the argument about the rule of law. In this case, the conclu-sion is stated first, so we give it the number 1. In diagramming arguments, it does not matter how we number the premises and conclusion, as long as we give each proposi-tion its own number. So it is easiest to number them in the order they are stated.
(1) The rule of law is a worthy ideal. To the extent that it can be achieved, (2) it allows people to know which actions will and will not get them in trouble with the law. (3) It is also fair in treating all people without discrimination.
This argument illustrates the second pattern: premises 2 and 3 independently support the conclusion. If the rule of law allows people to know the legal consequences of their actions, as stated in 2, that gives us some reason to think the rule of law is a worthy ideal, regardless of whether it is also fair. And the fairness of the rule of law, as stated in 3, provides a reason for considering it a worthy ideal, regardless of premise 2. So in diagramming this argument, we don’t use the plus sign. We use two arrows to join each premise to the conclusion separately:
2 3
1
► ►
To tell whether a set of premises is dependent or independent, we look at each prem-ise separately and ask whether the kind of support it offers to the conclusion depends on the other premises. A good way to pose the question is to suppose that the other premises are unknown or even false. If that would significantly affect the logical impact of the premise in question, then the relationship among the premises is one of mutual dependence, and a plus sign should be used in the diagram. In contrast, if the premise in question would still give us a reason for accepting the conclusion, then it is indepen-dent of the other premises and should be diagrammed with a separate arrow. The goal is to put together those premises that form a single line of thought and separate them from premises that represent distinct lines of thought. But this is not always easy. If the relationship between premises is unclear, it is a good idea to treat them as dependent.
As we learn more about specific types of argument, we’ll learn more about what sorts of premises must be combined to support a conclusion.
In an argument with independent premises, two (or more) arrows will converge on the conclusion. But can we have the opposite situation? Can we have arrows diverging from a single premise to two or more different conclusions? That is, can a single fact serve as evidence for more than one conclusion? Certainly—as we noticed earlier, the law of gravity implies that water flows downhill, but the law of gravity has many other implications: that the roof of a building needs to be supported, that a rocket needs a certain velocity to go into orbit around the earth, and so on. These would be distinct arguments, but because they rely on the same premise, we can combine them in a single diagram. If we numbered all these different propositions, starting with the law of grav-ity itself, the diagram would look like this:
4.2 Diagramming Arguments 75
2 3
1
4 …
In all the arguments we have examined so far, a given proposition served as either a premise or a conclusion, but not as both. But that’s only because we have been dealing with very simple arguments. In everyday thinking, as well as in science and other aca-demic subjects, we often find chains of inferences: A premise gives us evidence for a cer-tain conclusion, which in turn supports a further conclusion, and so on. Or conversely, we look for a premise to back up our position, and then look for a further premise to back up the first premise, and so on. For example, if someone opposes gun control on the ground that it violates the right of self-defense, we might ask: Why assume that people have such a right? The person might answer: Because people have a right to life, and therefore have a right to defend themselves. So we have four propositions to deal with:
1. People have a right to life.
2. People have a right to defend their lives.
3. Gun control violates the right of self-defense.
4. The government should not restrict gun ownership.
And the argument would be diagrammed.
2+3
4 1
STRATEGY
Diagramming Arguments1. An argument must have at least one prem-ise and one conclusion; use an arrow to represent the link between them.
2. A single conclusion may be supported by more than one premise; use a plus sign and a single arrow for dependent premises, convergent arrows for independent ones.
3. A single premise may support more than one conclusion; draw divergent arrows.
4. An argument may have more than one step, so that a given proposition can be both a conclusion (of one step) and a premise (of another step); use separate arrows to repre-sent each step, with the final conclusion on the bottom line.
This argument has two steps, and proposition 2 serves both as the conclusion of the first step and as a premise of the second. An argument can have any number of prem-ises, any number of steps.
Point 1 in the Strategy box is true of all arguments; indeed, it is true by the very definition of an argument. Points 2 through 4 describe the various ways in which ar-guments can differ in structure, and for each one we have a way of representing it in a diagram. So no matter how complex an argument is—no matter how many steps it has, or how many conclusions each premise supports, or how many premises support each conclusion—we should now be able to represent it in a diagram.
Now let’s use the diagramming method to construct an argument of our own.
Consider the proposition that extremely sarcastic people feel inadequate. Let’s see whether we can find an argument to support the claim. We might notice that chronic sarcasm, especially when it is not provoked, seems to express hostility. And why would someone express unprovoked hostility all the time? Isn’t it usually because the person feels inadequate in some way? Let’s write these ideas down in a list. And since the order in which we number the propositions in an argument is arbitrary, we’ll start with the conclusion this time:
1. Extremely sarcastic people feel inadequate.
2. Extreme sarcasm is a form of unprovoked hostility.
3. Unprovoked hostility results from feelings of inadequacy.
Sentences 2 and 3 are clearly dependent premises; neither one alone supports the con-clusion. So when we diagram the argument, we get:
2 + 3
1
Now suppose someone challenges us on premise 2—or suppose we ourselves wonder why it strikes us as true. Can we offer any further argument for it? After all, sarcasm can be playful and witty. It can be an indirect way of expressing fondness or any number of other feelings. Yes,we might answer, that’s true in small doses. But chronic and extreme sarcasm always seems to have the goal of undercutting or belittling another person.
And the desire to undercut someone, when it isn’t provoked, is a kind of hostility So now we have two further premises:
4. Extreme sarcasm is an effort to undercut someone.
5. The desire to undercut someone is a kind of hostility.
Like 2 and 3, these are dependent premises, so we can expand the diagram thus:
2 + 3
1 4 + 5
4.2 Diagramming Arguments 77
Now we have an argument in two steps. If we were to discuss the issue thoroughly, we would have to look for reasons to support premise 3, and we would want to consider other lines of evidence as well. The diagram would get more and more complex. But we would proceed in the same fashion, listing premises and adding them to the diagram as we go.
EXERCISE 4.2
A. For each of the following arguments, you are given the structure of the diagram; fill in the numbers at the appropriate places.
❋ 1. (1) I shouldn’t go home this week-end not only because (2) I have too much studying to do, but also (3) because I can’t afford the trip.
( ) ( )
( )
2. (1) Cheating on schoolwork is wrong because (2) it is dishonest.
( )
( )
3. (1) Cheating on schoolwork is wrong because (2) it means rely-ing on someone else’s knowledge, whereas (3) the purpose of educa-tion is to learn how to rely on your own knowledge.
( ) ( )
( ) +
❋ 4. (1) Regular exercise strengthens muscles, (2) strengthens the car-diovascular system, and (3) lowers cholesterol. For all those reasons, (4) one should exercise regularly.
( ) ( ) ( )
( )
5. Since (1) my car won’t start, (2) I will have to take the bus, so (3) I need to take exact change for the fare.
( )
( )
( )
B. In each of the following arguments, identify the conclusion. Then determine whether the premises are dependent or independent.
❋1. (1) To be a lawyer, you need to be good at keeping track of details, and (2) Lenny is terrible at that, so (3) he shouldn’t go into law.
2. (1) Molly is a very bright child.
(2) She began speaking on her first birthday, whereas (3) most children do not begin to speak until later.
C. Diagram each of the following arguments. (For further practice, diagram the ex-amples in Exercise 4.1 on pages [71–72] that you have determined are arguments.)
❋ 1. Annette must be wealthy. Last week she bought a diamond choker for her ocelot.
2. That movie was terrible. The plot was incoherent, the theme was trite, and the acting was not very good.
3. Johnson finished his last project in only 4 days. Because he’s such an efficient worker, he deserves a promotion.
❋ 4. I don’t think it would be a good idea to take the American Revolution course this term, because it conflicts with a course I need for my major, and my sched-ule would have more balance if I took a science course instead.
5. Everyone needs to understand how the structure of language can affect the way we think. But since this is
difficult to appreciate in the case of our native language, it is valuable to study a foreign language.
6. Key West, the southernmost city in the continental United States, is located at the tip of the Florida peninsula. This means not only that it enjoys year-round warm weather, but also that it is vulner-able to Caribbean hurricanes.
❋ 7. Business conditions will im-prove over the next year, and when they do so, corporate profits will increase. Increasing profit levels will drive up stock prices. So I am confident that investing in the stock market is a good idea.
8. Government regulation tends to delay the introduction of new drugs. If a drug is harmful, regula-tors get blamed for approving it;
3. (1) At the trial, Harris said he was in Milwaukee that night, but (2) he later told me that he was in Chicago. One way or another, then, (3) he is a liar.
❋4. (1) Edward prefers Frigidaire to Amana. (2) Edward always buys Frigidaire appliances, even though (3) the Amana store is cheaper and (4) closer to his home.
5. (1) Thomas Jefferson had a pro-found effect on America, inasmuch as (2) he drafted the Declaration of Independence, (3) served as ambas-sador to France during a crucial period in the young country’s history, and (4) negotiated the Louisiana purchase.
6. (1) We cleaned out all the water that flooded the basement before and (2) all the windows were shut the last time it rained. (3) Now there’s
water in the basement again, so (4) there must be a leak somewhere.
❋7. (1) Governor Baldacci originally told the press that a civil union was an appropriate alternative to gay marriage. (2) He has since signed a bill to legalize gay mar-riage, which means that (3) he changed his mind.
8. (1) When a pencil is put into water, it remains straight. (2) But our eyes perceive it as bent. Therefore, (3) our senses are flawed.
9. (1) The military must invade the city. (2) It needs supplies, and (3) if it moves ahead without tak-ing the city, there will be enemies both behind and in front of it.
❋ 10. (1) He sat next to me in class today, and (2) the other day he smiled when I ran into him at the library.
(3) I think he is interested in me.