10.1: Relevance

In reasoning and argumentation, it is important to stay focused on the topic at issue. This means giving reasons or pieces of evidence that are relevant to the topic. This sounds easy, but a great deal of bad reasoning occurs because we don’t stay focused on the issues.

Relevance is important in all communication, even when we are not constructing arguments or trying to persuade other people. In a normal conversation, each person typically says things that are relevant to the general topic and to what the other person has been saying. Slight departures from relevance are alright but conversing with someone who keeps bringing in irrelevant points is difficult.

A statement is not relevant all by itself, in isolation from anything else. Relevance instead involves a relationship between one statement and another. So, a premise can be relevant to one conclusion, but completely irrelevant to others. It is irrelevant if it simply doesn’t bear on the truth or falsity of the conclusion, if it is independent of it, if it does not affect it one way or the other.

Examples of Relevance

1. The premise that there have been multiple credible allegations against him is relevant to the conclusion that Supreme Court Justice Bret Kavanaugh has committed sexual assault.
2. The premise that Wilbur has failed his first two exams in Chemistry 1113 is relevant to the conclusion that he will fail the course.
3. The premise that the death penalty deters murder is relevant to the claim that we should retain capital punishment for murder.
4. The premise that the death penalty does not deter murder is relevant to the claim that we should retain capital punishment for murder.

Examples of Irrelevance

1. The fact that President Donald Trump believed he was innocent of any wrongdoing is not relevant to claims about Kavanaugh’s guilt or innocence.
2. When a reporter asks a politician a tough question, the politician often gives a long response that really doesn’t answer the question at all. Here the politician acts as though what they are saying supports their position, but it may be completely irrelevant to it. This happens when they put a “spin” on things that shifts the focus from the real issue to something else.
3. Many advertisements use celebrity endorsements. Often, the fact that a famous person endorses a product is altogether irrelevant to the claim that it’s a good product. For example, the fact that Michael Jordan plugs a certain cologne isn’t likely to be relevant to the conclusion that it’s a good cologne.
4. In everyday conversations, people are often at “cross purposes,” they “talk past each other.” This can occur when they think they are discussing the same claim or issue, but in fact the two of them are concerned with somewhat different issues. In such cases, the things each person says in support of their own views may seem irrelevant to the other person.

Relevance vs. Other Concepts

Relevance is Not the Same as Truth

A premise can be true, but irrelevant to a give conclusion.

Example: it is true that Bret Kavanaugh has a certain astrological sign, but this is irrelevant to the claim that he is guilty of sexual assault (or that he would be a good justice).

Irrelevance is Not the Same as Falsity

A premise can be false, but still be relevant to a given conclusion. To say that it is relevant is to say that if it were true, it would make the conclusion more (or less) likely to be true.

Example: The claim gun owners are less likely to die from gun violence than non-gun owners is false. But it is relevant to the claim that we should not make it harder for people to acquire guns.

Relevance is Not the Same as Importance

An important claim can be irrelevant to a give conclusion.

Example: It is a very important fact that many people were murdered in the Boston Marathon Bombing, but this is irrelevant to the conclusion that the Tsarnaev brothers planted the bombs.

An unimportant claim can be relevant to a conclusion.

Example: The fact that there are over ten thousand blades of grass in Rodney’s lawn isn’t very important to anyone, but it is highly relevant to the claim that there are over nine thousand blades of grass in his lawn.

Relevance is Not the Same as Conclusive Support

Relevance comes in degrees. Some premises are highly relevant to a given conclusion, others are somewhat relevant, and yet others are completely irrelevant. So, to say that a premise is relevant to a conclusion is not to say that it provides conclusive support for the conclusion.

Example: The claim that John had been involved in a long-running feud with the murder victim is relevant to the conclusion that he committed the crime. But it does not prove that John was the murderer.

Relevance Can be Positive or Negative

Any claim that provides evidence for, or against, some other claim is relevant to it. It has positive relevance if it supports it or counts in favor of it. It has negative relevance if it makes it less likely or counts against.

Example: The claim that John’s fingerprints are on the murder weapon is relevant to the conclusion that he committed the crime. It makes it more likely, and so has positive relevance for this conclusion.

Example: The claim that John was seen in another state at the time of the murder is also relevant to the conclusion that he committed the crime. It makes it less likely, and so has negative relevance for this conclusion.

Irrelevant Claims are Independent of One Another

If two claims are irrelevant to each other they are sometimes said to be independent of each other. The truth-value of one has no effect, influence, or bearing on the truth-value of the other. Knowing that one is true (or false) tells you nothing whatsoever about whether the other is true (or false). Irrelevance is a two-way street: if one thing is irrelevant to a second, the second is also irrelevant to the first.

Example: If you are flipping a fair coin, the chances that it will land heads on any given flip is 1/2. The outcomes of successive flips are independent of each other, so the outcome on the previous flip is irrelevant to what you’ll get on the next flip.

Example: If you and your spouse are going to have a child, the chances that it will be a girl are very nearly 1/2. The outcomes of successive births are independent of each other, so the sexes of your previous children are irrelevant to the sex of your next child.

Exercises on Relevance

1. Write a sentence or two explaining why each of the following claims is either relevant or irrelevant to the claim that Florida should abolish the death penalty.
   1. Innocent people have sometimes been executed.
   2. Statistics show that the death penalty deters (decreases) murder.
   3. Some people really enjoy watching executions.
   4. Statistics show that the death penalty does not deter murder.
   5. Executions make the warden sick to his stomach.
2. Say whether the members of the following pairs of statements are positively relevant, negatively relevant, or simply irrelevant to each other, and explain why.
   1. The President resigns. The Vice President becomes President.
   2. Jesse “The Body” Ventura is elected President in the next election. I roll a 3 on the first roll of a die.
   3. Jesse “The Body” Ventura is elected President in the next election. The economy goes south.
   4. I get a head on the next flip on a coin. I get a head on the flip after that.
   5. I pass all the exams in this course. I pass the course itself.
   6. I miss a lot of classes. I pass the course.
   7. There are many valuable things about sports. Names of sports teams like “Redskins” aren’t demeaning to Native Americans.
3. Give two premises that are relevant (in the sense discussed in class and in the text) to the following conclusions. Then give two premises that are irrelevant.
   1. We should not shelter-in-place during the Covid-19 pandemic.
   2. President Trump should have been impeached.
   3. I’ll probably not get an “A” in my chemistry course.

Answer

1. Write a sentence or two explaining why each of the following claims is either relevant or irrelevant to the claim that we should abolish the death penalty in Florida.
   1. Innocent people have sometimes been executed.
      • Relevant (various analyses possible, but you need to defend your answer)
   2. Statistics show that the death penalty deters murder.
      • Relevant (various analyses possible, but some analysis needed). Note that relevance can be either positive (supporting a view) or negative (weakening the case for it).
   3. Some people really enjoy watching executions.
      • Irrelevant (various analyses possible, but some analysis needed).
   4. Statistics show that the death penalty does not deter murder.
      • Relevant (various analyses possible, but some analysis needed). Note that relevance can be either positive (supporting a view) or negative (weakening the case for it).