An either/or fallacy, sometimes called false dichotomy, occurs when the arguer mistakenly reason from two alternatives, one claimed to be bad (that is, to be avoided) so that we ought to choose the other alternative. Put differently, an either/or fallacy consists of mistakenly assuming that there are only two possible solutions to some problem or that solving some problem consists of choosing between only two alternatives.
Thus, in either/or fallacy or false dichotomy, the argument develops by showing that one of the alternatives is false or unacceptable and then concludes that the other must be true.
Let us consider the example below.
Example 1
As I see it, either we enforce the death penalty or we eventually find the convicted murderer out on parole. We cannot have murderers going free, so we had better start enforcing the death penalty.
The example above has this from:
Either we enforce the death penalty or we eventually find the convicted murderer out on parole.
We cannot have murderers going free.
Therefore, we must enforce the death penalty.
The form of the argument is as follows:
Either P or Q
Not Q
Therefore, P
If one is familiar with a disjunctive proposition in symbolic logic, one may notice that the argument above is a valid argument form. Hence, the either/or fallacy or false dichotomy does not consist in the use of an invalid argument form. Rather, it consists in a false premise, that is, the premise that says that there are only two alternatives available in addressing the problem or, as in the case of the example above, the death penalty or parole for murderers.
Let us consider another example.
Example 2
President George W. Bush: If you are not with us, then you are against us.
We heard this famous line of the former president of the United State George W. Bush during his war against the Al Qaida. In his attempt to force the governments in the world to support him, he argued that if they are not with him, they are against him. Of course, it does not always follow that if one is not in favor of a particular idea, then he is against it. For sure, if one nation is not on the side of President George W. Bush in his war against the Al Qaida, it does not necessarily follow that it is against Bush.
The following examples below will further illustrate the either/or fallacy or false dichotomy.
Example 3
Either we give in to these terrorists’ demands and jeopardize the lives of thousands of Americans or we refuse and risk the lives of the hostages. Well, I for one will not risk the lives of the Americans all over the world. So, we must not give in to these terrorists.
Example 4
The idea of deliberately causing trauma, deliberately injuring the head of a living baboon, is extremely distasteful. But if we are not allowed to continue this research, then we will simply not learn how to treat human beings with head injuries. It is unfortunate, but it must be done.