Chapter 4
Proof
Analysis of Arguments

1. Introduction

He who asserts must prove.  That is a basic rule in debate.  If you make a statement which is not readily acceptable to the listener, you must prove it.  You must show evidence.  You must explain why your evidence supports your statement.  In other words the proof consists of evidence and reasoning.  This whole process of your making a statement and proving it is called an argument or making an argument.

In any forensic events--debate, speech, or discussion, you must understand the nature of arguments in order to build logical arguments.  If you can correctly analyze arguments and find problems in illogical arguments, you can critically listen to speeches and read writings.  This ability is essential for both senders and receivers of messages in today's society in which vast amount of information is constantly transmitted.
This chapter introduces the basic structure of arguments and discuss some of the most frequently used methods of supporting one's claims in arguments.

2. Structure of Arguments

An argument consists of (1) a claim, or a conclusion that the speaker wants the listener to accept, (2) evidence, or data that the claim is based on, and (3) a warrant, or a reasoning process that bridges the gap between the claim and the evidence.  The figure below graphically show this structure.
 
 
 
 

[Claim] <---- (Warrant) ----[Evidence]
 
 
 
 

For illustration, let us analyze the following argument:

Japan's atomic power plants are likely to cause serious accidents because those in Three Mile Island and Chernobyl caused big accidents.

The three basic elements in this argument may be identified as:

claim:  Japan's atomic power plants are likely to cause serious accidents.

evidence: Atomic power plants in Three Mile Island and Chernobyl caused serious accidents.

warrant: Japan's atomic power plants are similar to those in Three Mile Island and Chernobyl.

In this example, it is relatively easy to identify the claim and evidence since they are explicitly stated in the argument.  But the warrant is more difficult to identify since it is hidden.  When we make this argument, we are filling the gap between the claim and the evidence in our brain.  If we cannot fill the gap, we will consider the argument illogical.  In ordinary language use including debate, it is quite common to find this kind of arguments in which one or two of the basic elements are not explicitly stated but rather implied.  When we hear or read such an argument, we can examine the strength of the argument by making implicit elements explicit.

3. Claims

Claims are propositions.  They are statements about facts, values, and policies that can be tested its validity.  In general, if a claim sounds implausible, you need stronger support to prove it.  If you find a claim difficult to be accepted by your audience, you will need stronger support.

4. Evidence

Evidence may be any kind of information that serves as a ground of your argument.  It can be a fact known to the participants in debate.  It can be a tangible object which demonstrates the truth of a claim.  In academic debate, however, evidence is usually quotations from published sources such as books and magazine articles.  This is because objectivity and fairness are important in academic debate.  If evidence is a commonly known fact, it is difficult to determine whether a particular information is "commonly" known.  If evidence is a personal testimony or a personal letter, it is difficult to validate the existence of such evidence.  If evidence is from published sources, it is always possible to go back to the original information to check its accuracy.
 There are three kinds of evidence often used in academic debate:

(1) facts

(2) statistics

(3) experts' opinions
 

There are several points to note so that you can find quality evidence and point to some problems in the opposing team's evidence.  You can ask following questions to examine the quality of evidence:

(1) Is evidence consistent with other evidence?

(2) Is evidence consistent within itself?

(3) Is the source of evidence competent?

(4) Is the statistics methodologically sound?

(5) Is the expert credible?
 

5. Warrants

It is often unlikely that you can find evidence which exactly shows your claim.  You must prove your claim with available evidence.  If there is a gap between the claim and the evidence, there is a inferential jump from the evidence to the claim.  A warrant is a justification which guarantees such a jump, or a bridge which connects the evidence and the claim.

Some warrants are processes of inference or rules in logic which are sound or unsound.  Some warrants are more substantive, i.e., they are claims that must be independently proven.  The following sections will discuss three common types of warrants.

5.1. Analogy
In our earlier example of an argument about atomic power plants, the claim that Japan's atomic power plants are likely to cause serious accidents based on the evidence that the atomic power plants in Three Mile Island and Chernobyl caused serious accidents.  The warrant "Japan's power plants are similar to those in Three Mile Island and Chernobyl" is not something everyone can readily accept.  This warrant of analogy must be proven separately.

In the warrant of analogy, those two compare phenomena must be similar in their "essential" features, "essential" in the sense of being relevant to the claim being made.  In the argument of atomic power plants above, those atomic power plants must be similar in their structures and safety measures so that the analogy about accidents will be valid.

5.2. Generalization
This is a logical process of making a generic statement based on a number of specific examples.  For example, in order to prove a claim "There is a defect in the brake installed in the cars Model X of Maker Y," you may be able to find evidence "Mr. A's Model X had a defect in its brake.  Ms. B's Model X also had a defect in its brake.  Mr. C, Ms. D, and Mr. E had Model Xs and they had defects in their brakes."  The warrant that justifies a jump from specific examples to a generalized conclusion is an assumption of regularity among the cars of the same model.  Usually we can assume that different cars of the same model have the same design and thus the same problem if any.

When we use the warrant of generalization, we should be careful about such factors as whether the quantity of examples is enough, whether such examples are typical to the group in question, and whether there are some serious counterexamples.

5.3. Cause-Effect
If there is a causal relationship between the evidence and the claim, the warrant is of cause-effect.  There are two kinds of cause-effects inference.  One type of inference is that you have evidence to show the existence of cause.  You can prove the claim that shows the effect of that cause.  The other type is the inference to the opposite direction.  If you have evidence to show the effect, you can infer the existence of the cause that brought about that effect.  If the relation ship is one-to-one, the both directions of inference are warranted.  But if the relationship is not one-to-one, you need a caution.

Suppose that a causal warrant has already been proven that says, "habitual smoking causes lung cancer."  If you have evidence "Mr. A is a habitual smoker," you can support your claim "Mr. A will probably develop lung cancer."  On the other hand, you cannot prove the claim "Mr. B is a habitual smoker" based on the evidence "Mr. B had lung cancer."  For there are other possible causes of lung cancer.

In a policy proposition, causal warrants are often used in proving solvency (the plan would solve the problem).  This needs caution.  If the proposition is to prohibit smoking and the problem in the status quo is lung cancer.  The elimination of smoking would not solve all the lung cancers.  Habitual smokers like Mr. A above may have already inhaled enough carcinogens so it is too late for such people.  Lung cancer caused by other factors is also outside the solvency.  The affirmative can only solve lung cancers which may be caused in the future because of relatively new exposure to smoke.

You can sometimes use statistical "correlation" between the two phenomena whose "causality" cannot be proven.  Correlation is weaker than causality but you can still build many of the arguments in debate based on such a relation.

5.4. Sign
The warrant of sign is concerned with relationships between two effects of the same cause or between something and its symptoms.  This relationship works when two things almost always occurs at the same time but they do not have a causal relationship.  For example, when you see falling leaves, you may infer that birds will be flying away.  Both phenomena are the effects of the same cause, i.e., some climatic change toward winter.  Another example of a sign relationship may be found between freedom of speech and democracy.  We may argue that we will find democracy in country X when we find freedom of speech guranteed over there.

5.5. Authority
In dealing with complex and difficult issues in science and technology as well as in society, we may not be able to analyze them by ourselves and construct arguments based on raw data.  We often rely on explanations and opinions of experts in respective fields.  In academic debate, debaters also often resort to testimony of authorities.  For example, in order to prove a claim that "smoking causes lung cancer," a debaer may quote as evidence Professor X at National Cancer Research Institute in saying "smoking causes lang cancer."  The warrant here is that Professor X is believable in talking about smoking and cancer because he is an expert in the field.

When we use this warrant of authority, we must be careful about the authority's expertise and bias.  An expert in one field is not necessarily an expert in another field; when an economics professor is talking about the safety of atomic power plants, he won't be considered an expert (unless there is a reason to believe otherwise).  Politicians and government officials may be experts in government policies but we must always be aware of their political and ideological biases.  An engineer in a power company may be an expert in the safety of atomic power plants but he is likely to have bias because of his company's interests.  A university professor in nuclear engineering may also have a bias.  He may be a firm belief in nuclear energy and this may skew his testimony about it.

Sometimes, we find "unwilling witness" who testifies against his supposed interests.  For example, a researcher in a tobacco company comes out and confesses that cigarette smoking is actually harmful to out health.  Since he is speaking against his bias, this evidence is considered strong.  (Of course, he may have his hidden motive; he may be bullied in his company and wants to ruin the reputation of its products.)

6. Nature of Proof in Debate

It is advisable to note that "proof" in debate is different from "proof" in mathematics or in categorical logic.  The proof in debate is a matter of "probable truth."  You only need to show that your claim is probably true based on your evidence and warrant.  Even if there is on counterexample to your proof, it will not destroy the whole of your argument.

You must avoid strong statements such as "My proof is perfect" or "The opponent's argument is completely wrong."
 

Exercise

Identify CLAIM, EVIDENCE, and WARRANT in each of the arguments below.  Note that one or two of the three elements are implicit in many arguments.  Are there any problems in the arguments?  How can you improve the arguments?

1. Japanese women control their family's finance because my mother says she gets my father's whole salary and gives him monthly allowance.  My sister says the same thing.  Several of my friends say their mothers do so too.

2. Japanese women's employment opportunities are more limited than those of men's because a survey conducted by the Ministry of Labor shows that 20 % of the new female college graduates are unemployed while only 2 % of male graduates are unemployed.

3. Japan's atomic power plants are likely to cause serious accidents because those in Three Mile Island and Chernobyl caused big accidents.

4. The affirmative team says that Japan should stop further construction of atomic power plants.  If we do not construct any more atomic power plants, Japan will suffer from electricity shortage.

5. Japan will not invade other countries any more because Prime Minister Obuchi says that Japan does not have any intention to do so.

6. Professor Ichikawa's research has found that the higher than normal rate of leukemia is observed among the people living within the 10 km of atomic power plants

7. Dams in Japan attract many tourists because we usually find many tourists appreciating colorful autumn leaves in dam sites.

8. If marijuana is illegal, cigarettes should also be illegal because both are harmful and addictive.