Affirming a Disjunct

1 Affirming a Disjunct

Also known as the fallacy of the alternative disjunct, false exclusionary disjunct, affirming one disjunct, the fallacy of the alternative syllogism, asserting an alternative, improper disjunctive syllogism, or the fallacy of the disjunctive syllogism.

You have two choices with Obama. You either believe that he is a man of Christ, or you think he’s a liar.

Penn Jillette

Taken as mutually exclusive choices, these alternatives leave out someone who believes both. The related fallacy of affirming a disjunct occurs when someone accepts one option and concludes, without justification, that the other must be false.

Affirming a disjunct occurs when someone makes the false assumption that if one of two options presented in an “either/or” statement is true, the other must be false—even though the “or” does not specifically rule out both being true simultaneously. This mistake resembles the unwarranted contrast fallacy. Let’s begin by considering a straightforward example:

Either Madison likes cats or she likes dogs. I know she likes cats. Therefore, she doesn’t like dogs.

This argument is flawed because it fails to account for the possibility that Madison likes both cats and dogs. Here’s the example mapped out in logical form.

	Example	Logic
Premise 1	Madison likes cats or she likes dogs.	A or B.
Premise 2	Madison likes cats.	A.
Conclusion	Madison doesn’t like dogs.	Not B.

Take another everyday illustration: I either really love chocolate, or I have no will power. I really love chocolate, so I must have will power. This affirms the first option and denies the second. But loving chocolate is compatible with having no will power, so the conclusion does not follow.

As you can infer from the table above, this fallacy is caused by an ambiguity in the English word or. Because context makes the meaning clear in everyday usage, you might never have thought about this ambiguity before, but you actually use the word or in two very distinct ways. One type is “inclusive,” and the other is “exclusive.” Since this difference is the key to understanding the fallacy, let’s take a moment to explore it.

When you were a child, your mother probably had a hard time convincing you to eat your vegetables. At some point, she likely said, “Either you eat your veggies or you’re not getting dessert.” Chances are, you diligently ate your vegetables and your mother brought out dessert a short while later. But why did you understand your mom’s statement as a bargain? What made it clear that if one event happened (i.e., eating your vegetables), then the other would not (i.e., not getting dessert)? The answer lies in your belief that your mother was using an exclusive or.

Now, suppose that you ate your vegetables, but your mom failed to provide dessert. You’d approach her and complain, “Mom you promised dessert if I ate my vegetables!” But what if she responded, “No, I didn’t, Sweetie. I said, ‘Either you eat your veggies or you’re not getting dessert.’ You ate your veggies and you didn’t get dessert, so my statement is truthful. You really should listen more carefully.”

Aside from ensuring that you’ll never again eat your vegetables in exchange for dessert, what has your mother taught you? Well, she has given you a valuable lesson in the difference between two types of or.

The distinction becomes clearer when we spell out the possible cases. On the one side, there is the inclusive or. This is the or used in classical logic. Take the basic proposition “Either A or B.” If this proposition is using an inclusive or, it is true in three circumstances:

1. A is true and B is false.
2. B is true and A is false.
3. Both A and B are true.

Therefore, if your mother intended to use this inclusive or, her statement would have been true in three situations:

1. You eat your veggies and get dessert.
2. You do not eat your veggies and do not get dessert.
3. You eat your veggies and do not get dessert.

Unlucky for you, it was this third possibility that played out. A search system could use inclusive or for a query such as “apple or banana” to return results containing “apple,” results containing “banana,” and results containing both “apple” and “banana.” Another example: I either go to bed, or I watch TV. I will go to bed. Therefore, I will not watch TV. It’s perfectly possible to go to bed and watch TV at the same time—a fact many of us confirm nightly. The “or” simply doesn’t exclude doing both.

Exclusive or is quite different. It is true only in two circumstances:

1. A is true and B is false.
2. B is true and A is false.

If both A and B are true, then an exclusive or statement is false. If a search system used this form of or, it would return results that had the word “apple” and results that had the word “banana,” but it would exclude results that had both “apple” and “banana.”

To sum up, for inclusive or, there is an implicit or both that follows the statement. However, for exclusive or, there is an implicit but not both that follows the statement.

The opening quotation presents the alternatives as exclusive: “You have two choices with Obama. You either believe that he is a man of Christ, or you think he’s a liar.” But someone could believe that Obama is both a man of Christ and a liar. Inferring that one belief rules out the other would commit the fallacy.

Importantly, not every or statement can fall prey to this fallacy. Consider the following argument:

Either George Washington is dead or alive. George Washington is dead. Therefore, he is not alive.

This argument is valid because the alternatives are mutually exclusive. It differs from the standard disjunctive syllogism, which denies one disjunct to establish the other. The two possibilities are mutually exclusive. When someone is dead, they are not alive, and when someone is alive, they are not dead. In formal logic, if the choices really are mutually exclusive, deducing that the other choice must be false is perfectly valid. The fallacy only arises when the options can both be true but are treated as if they cannot.

Before using one option to rule out another, ask what establishes that they cannot both be true. The word or alone does not establish that.