Structure Diagrams and Arguments in Ordinary Language

One way in which to be sure that you understand the meaning of an argument, and at the same time determine the quality of the inferences informing it, is to construct a structure diagram for it, showing its internal structure and indicating clearly the propositions and inferences that constitute it. Structure diagrams are to be combined with what you already know about the three criteria of cogent reasoning (relevance, strength and truth). The structure diagram will more easily and readily allow you to make determinations about the quality of the argument.

The Three Criteria for Cogent Reasoning

There are three conditions that an argument must meet to be considered worthy of your acceptance. First, the premises must be relevant to the conclusion. Second, there must be enough information to warrant the conclusion. Third, the information presented in the premises must be true, unambiguous, and warranted.

The relevance requirement is truly simple to understand. For an argument to have merit, the information offered in support of a conclusion must be relevant to the conclusion. The determination of relevance will be based primarily on your general experience and background knowledge. This might even be called your "world view." In an argument discussing the funding of sex education in elementary schools, it is probably irrelevant to point out in support of such an academic endeavor that your grandmother always said that it was good to discuss those issues with children. The issue at hand is funding, and though your grandmother may be right, it is irrelevant to a consideration of how much money is to be spent on it. Your grandmother's opinion could be relevant if the issue was whether sex education should be part of the curriculum in an elementary school, but even then it is questionable that her opinion (unless she is an expert on this issue) should count heavily in any such determination.

The strength requirement refers to the amount of information that is present in the premises that purport to provide support for the conclusion. If, for example, you are attempting to determine whether to take your car to a neighborhood mechanic to be repaired (and you have never met him before, nor has he worked on your car), asking friends, relatives, or co-workers about his qualifications as a mechanic could certainly be useful. But suppose that you ask a friend at work who tells you that the mechanic failed to fix his transmission, that he charged an outrageous amount of money simply to find out the nature of the problem with the car, and that he is unreliable. Is this enough information to make a decision concerning the acceptability of this mechanic to perform repairs to your car? Probably not. One person's opinion may be an accurate representation of the nature of things, but it could be that the person you asked has a 1971 Pinto, the mechanic charged $50.00 to remove the transmission, and informed your friend that the car wasn't really worth spending $500.00 on for a new transmission. If you had that background information, you would know that a 1971 Pinto was junk anyway, that $50.00 to remove an entire transmission is exceedingly inexpensive, and that the mechanic was not being unreliable; he was simply stating that he did not think that it would be worth the money to fix a car that wasn't worth the amount of money it would cost to fix it.

Add to this example, however, that you ask your brother who had his car repaired by that mechanic, you call the Better Business Bureau, the local chamber of commerce, and know 5 other people who have had their cars repaired by the mechanic in question. You find that the BBB has unfavorable reports about the mechanic, the chamber of commerce does not have him listed as a licensed mechanic in the city in which you live, and the other 5 people you asked about the quality of his work were dissatisfied with his services for a variety of reasons. With the weight of that evidence, you may be better off looking for a different mechanic.

Taking a different look at the mechanic example, suppose that the five people you ask about the quality of his work point out that he has a wife and 8 children to feed, he goes to church every Sunday, and his mother and father were recently killed in a plane crash. They suggest on the basis of this information that you hire him to repair your car. Those facts about his life are completely irrelevant to the quality of his work as a mechanic in general, and no matter how many people you ask about him, if this is all the information they give you, you will not benefit by having more instances of it. It is always inappropriate to ask for more irrelevant information.

Through the extensions of this example, it ought to be clear that the relevance requirement always takes precedence over the strength (amount of information) requirement. But further, these two requirements always take precedence over the "truth" requirement. The reason for this is complicated, but can be expressed clearly enough in the following examples.

Suppose that you are considering a mechanic (we'll use that example again for ease in explanation) to repair your car. You ask 5 people about the quality of his work, and they tell you that if you take your car to him, a quality job will be done. Assuming that you have faith in the opinions of the people you asked, and that the information they provide to you is relevant to a consideration of the expertise of the mechanic in question, and also assuming that 5 people are a sufficient number to ask in order to determine whether you ought to take your car to that mechanic, what else is to be considered?

What do your friends mean by the claim "a quality job will be done"? How did they say that? What tone was in their voices when they made that claim? Were they sarcastic? Were they sincere? Did they tell you what they meant by "quality"? Isn't that term unclear in itself? A Pinto owner might consider a quality job one that simply keeps the car running. A Jaguar owner might consider a quality job one that preserves the value of the car, and makes it run the way it did when it came off the showroom floor.

Assuming that your friends were not being snide and sarcastic when they told you he would do a quality job, and assuming that a quality job is what you are seeking, you have relevant and (probably) sufficient information to make a determination. But the truth requirement is much more difficult to satisfy. Sometimes it is not possible to research a claim completely to verify the truth of the claims that are made in support of a conclusion. There are cases in which a claim may be vague or ambiguous. There are cases in which the information provided in support of a claim is simply false. But no one can be expected to research every piece of information that is presented to him in every single decision to be made. It might be appropriate to expect such research to be done when deciding which candidate will receive your vote in the next election, but a simple decision probably does not require that much research or even that much care. This is not to imply that the decision concerning who will fix your car is not important, but there are usually more pressing concerns of the day. It would probably be a waste of your time to call the BBB, the chamber of commerce, and all of the people for whom the mechanic has repaired cars in order to make your decision. Ask a few people, find out what they mean by "quality", and decide what you will do.

Practical reasoning is exactly what it sounds like. It is for practical use. And even though it is probably not the case that you will ever be asked to provide a structure diagram of an editorial in the newspaper, the ability to analyze the structure of an argument can keep you more fully informed and more critical of claims that are made.

Arguments can be made to "sound good" even when they have very little merit. Chapter 11 of Chaffee’s text (and Flew’s How to Think Straight) is filled with informal fallacies. Some of them can be quite convincing. That is, they can make you change your mind, they can make you perform an action based on a decision. For example, the fallacious form of argumentation known as argumentum ad baculum is very convincing. If someone tells you that you could find yourself in an uncomfortable situation unless you pay protection money, you might feel compelled to pay the money. But the fact that someone can make you act does not imply that the reasoning used in order to do it was "good." Obviously, it worked. But the fact that someone can make you do something, or make a decision, does not make that person right. Most people, I think, will look at an example like this and claim that they would never be taken in by such a claim. Maybe not. But the point is that someone may think that might makes right. And only an awareness of the fallacious nature of such reasoning can make it clear to such a person that it does not "make right." Consider this. People tell their children that they must be good because Santa Claus will bring them nothing for Christmas if they don't. This is an argument, believe it or not.

Structure Diagrams

The structure of the argument can be represented in the following way. Take each claim that is made in the reasoning, number the propositions, and place the conclusion under the premise(s).

1. Santa Claus will bring you nothing for Christmas if you do not behave.

2. \You must be good.

The structure of the argument is given below.

(1)

(2)

The premise is proposition 1. The conclusion is proposition 2. The structure type is a "serial inference." A serial inference is one in which a conclusion follows directly from one premise (or from a series of premises and intermediate conclusions).

(I think it is obvious that you really don't need a structure diagram for such a simple argument, and you can see the problem in the reasoning without it. It may be that children ought to be good even if they don't get presents. (If this were a good argument, wouldn't it apply to Buddhist children, children in China, and Jewish children, who may not celebrate the holiday associated with the fictional figure used as a "club" for a reason?) The point here is simply to illustrate how structure diagrams are constructed.)

The inference is the "move" from (1) to (2). An inference is a psychological process in which a reason is offered and a conclusion is made on the basis of it. That is not something that an argument does; it is, instead, something that people do. Thus, even though an inference is a part of an argument, making inferences is the intellectual process by which conclusions are drawn.

Steps in Argument Diagram Construction

1. The first step in the construction of a structure diagram is to determine the main conclusion (MC). The MC is, by definition, the final point in the argument; it is the point at issue, the statement that someone is attempting to verify through the use of other claims.

2. The second step is to determine the function of the other statements informing the argument. There are two considerations. First, some statements are basic premises (BP). Others are intermediate conclusions (IC). A basic premise is, by definition, unsupported. It is a statement assumed to be true. It is the point at which an argument begins. An intermediate conclusion is both a premise and a conclusion at the same time. An intermediate conclusion is a claim made on the basis of at least one other (either a BP or an IC [or both, in rare instances]), which leads either to another IC or the MC.

3. The third step is to identify the inferences in the argument. Inferences are the intellectual "moves" between premise(s) and conclusion(s). They are the parts of the argument that can be fallacious. Statements can be either true or false, they can be questionable or ambiguous or vague, but statements are never the subject of fallacies of reasoning. Only inferences can involve fallacies.

4. The fourth step is to consider the three criteria of cogent reasoning and determine, for each inference, the quality of that inference.

5. The fifth step is to determine the quality of the argument as a whole, including consideration of the quality of the individual inferences, and whether the claims made in the argument are true or unambiguous, whether they need support, or whether they are simply false.

Types of Structure Diagrams

1. Serial Inference. This is an inference in which a single reason is given in support of a conclusion or conclusions. Its general format is such that a BP leads to an MC, or a BP to an IC, or a BP to an IC to an MC.

2. Convergent Inference. This is an inference that is actually a combination of two (or more) serial inferences. Its general format is such that, for example, two BPs lead to the MC independently of each other.

3. Divergent Inference. A divergent inference is one in which a reason leads to more than one conclusion. For example, one BP leads to two different ICs. This is, in fact, a case of there being two separate inferences. It is, in essence, the opposite of a convergent inference in form, but its analog in the sense that in such an inference, there is a series of serial inferences united by a common statement.

4. Dependent Premise Inference (Linked). This is an inference form in which a conclusion is reached such that the premises are not independent of each other, i.e., the conclusion would not follow without the two (or more) pieces of information being considered one.

Generic Format of Structure Diagrams

Serial

Convergent

BP1 BP2

Divergent

MC1 MC2

Dependent Premise

BP1 + BP2

Combination (any combination is possible)

IC + BP

IC1 IC2