11.2: The Either/Or Fallacy

Disjunctions

Earlier, we encountered a type of compound statement called a conditional. In this module, we will be concerned with a second kind of compound sentence; it’s called a disjunction.

A disjunction is an “either/or” sentence. It claims that (at least) one or the other of two alternatives is the case. For example:

1. Either the butler did it, or the witness for the defense is lying.
2. Either I have a throat infection, or I have the flu.
3. “‘Hey,’ I said, ‘When you [write novels], do you sort of make it up, or is it just, you know, like what happens?”’ [Martin Amis, Money]
4. We will either balance the federal budget this year, or we will stand by and watch our country go broke sometime in the next quarter century.
5. Either the dead simply cease to exist and have no perceptions of anything, or else they go on to a better life after death. [Socrates, from Plato’s dialogue, the Apology]

The two simpler sentences that make up a disjunction are called disjuncts. The order of the disjuncts in a disjunction doesn’t matter (you can reverse their order, and the resulting disjunction will mean the same thing as the original disjunction). The first sentence in the list above says that either the butler did it or the witness for the defense is lying. So, it will be true if the butler did do it or if the witness is lying. And it will be false if both these disjuncts is false.

The Either/Or Fallacy

We commit the either/or fallacy when we assume that there are fewer alternatives than there are, typically two. When this happens, we mistakenly suppose that a disjunction is true when it is false. The either/or fallacy gets its name from the fact that we act as though either the one alternative is true or else the other alternative is, though in fact there are more than just these two alternatives. In such cases, we have overlooked some third alternative. For example, in sentence 1. (about the butler), we may have overlooked the possibility that the witness made an honest mistake (maybe her eyesight isn’t what it used to be).

The either/or fallacy goes by a variety of names. It is sometimes called the false dilemma fallacy, the black and white fallacy, or the fallacy of false alternatives. It often results from what is called all-or-none thinking.

These names reflect the nature of the fallacy. For example, talk of black or white thinking suggests a tendency to think in extremes, to see things as definitely one way or else definitely the other, without any room in between for various shades of gray. And talk of all-or-none thinking suggests a tendency to believe that things must be all one way or all another (when in fact the truth may lie somewhere in the middle). Let’s see how some of the sentences in the list above might involve the either/or fallacy.

1. Either the butler did it, or the witness for the defense is lying.

As we noted above, the butler may be innocent, and the witness may simply be mistaken for some reason or another.

2. Either I have a throat infection or I have the flu.

Perhaps I have correctly narrowed the possibilities down to these two, in which case the disjunction is true. But I may have jumped to the conclusion that I have one or the other of these infirmities, when it fact it is only my allergies acting up again (perhaps the pollen count has been high lately).

3. “‘Hey,’ I said, ‘When you [write novels], do you sort of make it up, or is it just, you know, like what happens?”’ [Novelist] “Neither” [Martin Amis, Money, p. 87]

Here John Self, a character in Martin Amis’s novel, Money, asks a novelist whether he just makes everything up or whether it he writes about things that have really happened. The novelist replies that he doesn’t do either of the two. Real life events give him lots of ideas, but he is constantly changing them in his imagination as he writes. The novelist is pointing out, in his oneword response (‘Neither”), that Self is committing the either/or fallacy.

4. Either the dead simply cease to exist and have no perceptions of anything, or else they have a good life after death.

Socrates asserts this disjunction in an argument which concludes that death is nothing to fear. He seems to overlook the possibility that there is life after death, but that it will be unpleasant.

Examples of the Either/Or Fallacy

Since the either/or fallacy makes things look simpler than they really are, it makes for pithy, memorable slogans. You will be familiar with some of the following examples:

• America: Love it or Leave it.
• You are either part of the solution or you are part of the problem.
• You are either with us or against us.

Another common pair of slogans several decades ago were:

• “Better dead than red.” (a favorite of proponents of the arms race at the height of the cold war), and
• “Better red than dead.” (a favorite of their opponents)

Both these slogans rested on the assumption that there were only two alternatives: either we engage in an escalating arms race with the Soviet Union, or they will crush us. Such claims often do make a point, but snappy slogans by themselves rarely make for good reasoning.

More Complex Examples of the Either/Or Fallacy

Many examples of the either/or fallacy can be more difficult to spot. For example, one frequently hears the following sorts of claims in current debates over policy issues.

1. Either we keep teaching the Western Canon (the great literary and philosophical works of the Western world), or we just let each professor teach whatever junk they want.
2. We either must institute the death penalty, or we will have to live with the same people committing terrible crimes over and over (each time they are released from prison).

With a little thought, we can see that there are more than two alternatives in each case. But when we hear such claims in conversation, they often go by so fast, and may be asserted with such confidence, that we don’t realize how much they oversimplify the situation.

The either/or fallacy is often committed alongside the straw man fallacy. For when we simplify someone’s views into two easily attacked alternatives, we typically substitute a weakened version of their view for the view that they really hold.

Clashes of Values

Many of the difficult moral and political issues of our day involve clashes of values. Virtually all of us think that the following values are important:

1. Freedom (liberty)
2. Security
3. Majoritarianism (majority rule, i.e., democracy)
4. Equal opportunity
5. Community moral standards

For example, virtually all of us believe that democracy, the rule of the many, is a good thing. But democracy can be in tension with other values, most obviously, individual rights and liberties. A majority can tyrannize a minority just as much as a dictator can. For example, until the 1960s, poll taxes and other public policies made it almost impossible for African Americans in many parts of this country to vote (and gerrymandering and other manifestations of institutionalized racism continue to contribute to the disenfranchisement of people of color today).

Freedoms, or liberties, are in tension with other values. Giving people a great deal of freedom can make our lives less secure in various ways. Indeed, various types of liberty can even be in tension with each other. Unlimited freedom of the press may infringe on a person’s right to have a fair trial, for example, or violate people’s rights to privacy.

Most of us think that it is also important to make sure that everyone in our country (especially children) have a decent standard of living (enough food to survive, basic medical care, etc.). But the two values, freedom to spend one’s money as one likes, and helping others, are in tension, because in our society the only way to ensure that everyone has a reasonable standard of living is to tax people and redistribute the money to people who don’t have enough of it (in the form of food stamps, welfare payments, etc.).

In such cases, it may be tempting to pose the issues in terms of two stark alternatives: freedom (to keep what one owns) vs. everyone having a reasonable standard of living. These cases are difficult, because both values are important to most of us. But there is a definite tension between them, and finding satisfactory ways to reconcile them is difficult.

Disjunctions in the Guise of Conditionals

Disjunctions can be restated as conditionals. For example, we can restate the claim: “Either you are part of the solution or you are part of the problem” as the conditional:

• If you are not part of the solution, then you are part of the problem.

And we can restate the claim: “Either I have a throat infection or I have the flu,” as the conditional:

• If I don’t have a throat infection, then I have the flu.

If I assert either of these conditionals, I may be just as guilty of the either/or fallacy as if I had asserted the original disjunction, but it is harder to spot this fallacy when we are dealing with a conditional. If you come across the claim:

• If we don’t balance the federal budget this year, then we will have to stand by and watch our country go broke sometime in the next twenty-five years.

It may be far from obvious that this passage involves the either/or fallacy. To see that it does, we must see that it is just another way of saying, “We will either balance the federal budget this year, or we will stand by and watch our nation go broke sometime in the next twenty-five years.”

Finally, we should note that the either/or fallacy could be involved if someone said that there were only three alternatives when in fact there were four. Indeed, the fallacy is committed whenever someone claims that there are fewer alternatives than there are.

Why it’s Easy to Commit the Either/Or Fallacy

1. It takes less energy and imagination to suppose that there are only two alternatives than to try to figure out whether there are additional possibilities.
2. Language is full of simple opposites—good vs. bad, right vs. wrong, us vs. them—and this can encourage us to think in oversimplified terms.
3. It is easier to persuade others to accept our view about something if we can convince them that the only alternative is a very extreme position. So, characterizing the situation in terms of a limited number of options often makes it easier to defend our position.
4. Prejudices and stereotypes can make it easier to think in all-ornone fashion (we will return to this in a later chapter). For example, extremists of various sorts tend to see issues in very simple terms; it is either us or them. For this reason, such people are often unwilling to compromise.
5. There are two kinds of deductively valid arguments that involve disjunctions, and below we will see how these sometimes encourage us to commit the either/or fallacy.

Safeguards

There may only be two alternatives in any given case, and there are certainly issues on which we should not be willing to compromise. But we shouldn’t assume this without considering the matter. Here are some safeguards against the either/or fallacy.

1. When you encounter a disjunction (or a conditional), consider the possibilities. Has the other person overlooked some genuine alternatives?
2. Avoid the temptation to think in extremes. Difficult issues rarely have simple solutions, so we need to at least consider a range of options.
3. Be especially wary if someone argues that the only alternative to their position is some crazy-sounding, extreme view.

Arguments involving Disjunctions

There are two kinds of arguments that involve disjunctions. They are relevant here, because when we use them, it can be easy to commit the either/or fallacy.

In Chapter 3, we studied conditional arguments. Here we will learn about two kinds of disjunctive arguments, two important argument forms or formats that involve disjunctions.

Disjunctive Syllogism

1. Either the butler did it or the witness is lying.
2. The witness isn’t lying (she’s as honest as the day is long).
3. So (3) The butler did it.

Arguments having this form are called disjunctive syllogisms. All arguments with this form are deductively valid. They involve a simple process of elimination; one premise says that there are only two possibilities and the second premise eliminates one of the two. This leaves only one possibility as the conclusion.

Disjunctive syllogisms have the form:

1. Either A or B.
2. But A is not true.
3. So, (3) B is true.

Constructive Dilemmas

Socrates gives the following argument for the conclusion that death is nothing to fear (Plato reports the argument in his dialogue the Apology).

1. Either the dead simply cease to exist and have no perceptions of anything, or else they go on to a better life after death.
2. If the dead simply cease to exist, then death is nothing to fear [it would be like a long, restful sleep].
3. If the dead go on to a better life, then death is nothing to fear.
4. So, (4) Death is nothing to fear.

In the first premise, we narrow the range of alternatives down to two. Then, even if we don’t know which of the two is the case, we claim (in premise 2) that if the first alternative is true, then such and such follows. We repeat this strategy, adding (in premise 3) that if the second alternative is true, then (the same) such and such follows. So, if either of them is true, such and such must follow (in this case, that death is nothing to fear).

Constructive dilemmas have the form:

1. Either A or B
2. If A, then C
3. If B, then C
4. So (4) C

All arguments with this form are deductively valid.

Disjunctive Arguments and the Either/Or Fallacy

When we encounter either type of disjunctive argument, we should ask whether its disjunctive premise is true, or whether we have an either/or fallacy. Such fallacies are especially easy to overlook in such contexts because the argument may be good in several ways that lead us to overlook the false disjunctions. Particularly:

1. Both sort of arguments is always deductively valid,so the formal reasoning is correct.
2. All the premises other than the disjunction may well be true.
3. The person giving the argument may spend a lot of time defending the non-disjunctive premises. This may focus our attention on them, leading us to overlook potential problems with the disjunction. In Socrates’ argument about death, for example, a lot of time might be spent defending the claim that an eternal sleep is not to be feared, and this may lead us to overlook problems with the first, disjunctive, premise.

Exercises

When you encounter a disjunction (or a conditional) it is always worth asking whether it commits the either/or fallacy. Thought is required; we want to be alert to the possibility that this fallacy has been committed, but we don’t want to jump too quickly to the conclusion that it has been.

In each of the following passages, determine whether the either/or fallacy has been committed or not. In those cases where it has (a) say precisely how it has been committed, and (b) explain what might be done to strengthen the argument so that it doesn’t commit this fallacy.

1. Mother to son: “Are you going to college, or are you going to be a bum like the Jones boy?”
2. “Hallmark. When you care enough to send the very best.”
3. Either a positive integer is even or else it is odd.
4. Roseanne: “How bad is it? I mean, are we going to have to eat cat food, or just the kids?”
5. If you can’t beat ’em, join ’em.
6. If God doesn’t exist, then anything is permitted.
7. We obviously cannot legalize recreational drugs, as some people recommend. For if drugs aren’t illegal, we will be encouraging people to use them. And it is clear that drugs are extremely dangerous. So, it’s better to live with the current situation than to try to change things in this extreme sort of way.
8. We will either balance the federal budget this year, or we will stand by and watch our country go broke sometime in the next quarter century.
9. Either there is a God, or there isn’t.
10. Either the dead simply cease to exist and have no perceptions of anything, or else they go on to a better place after death.
11. Either we keep teaching the Western Canon (the great literary and philosophical works or the Western world), or we just let each professor teach whatever garbage they like.
12. Either we must institute the death penalty, or we will have to live with the same people committing terrible crimes over and over (each time they are released from prison).
13. Polling questions and opinion surveys often require you to select from a restricted set of alternatives (e.g., should we increase defense spending or should we lower it?). Give examples, either ones that you have encountered or ones that you construct, which illustrate this.

Answer

2. This is a nice advertising hook. The conditional, “When you care enough to send the very best, you send Hallmark,” is equivalent to the disjunction, “Either you don’t care enough to send the best, or you send Hallmark.” So, if you send any card that isn’t a Hallmark card, you really don’t care much about the person you send it to (you louse). This commits the either/or fallacy.

3. This does not commit the either/or fallacy. There really are only two alternatives here. A positive integer must be one or the other. The claim here is perfectly true, and it doesn’t involve any fallacy whatsoever.

5. The key to working this is to note that the conditional here is equivalent to the disjunction: Either you beat them or you join them.