Black-or-White Fallacy


  • Bifurcation
  • Black-and-White Fallacy
  • Either/Or Fallacy
  • False Dilemma
Type: Informal Fallacy


Gerda Reith is convinced that superstition can be a positive force. "It gives you a sense of control by making you think you can work out what's going to happen next," she says. "And it also makes you feel lucky. And to take a risk or to enter into a chancy situation, you really have to believe in your own luck. In that sense, it's a very useful way of thinking, because the alternative is fatalism, which is to say, 'Oh, there's nothing I can do.' At least superstition makes people do things."

Source: David Newnham, "Hostages to Fortune"



The problem with this fallacy is not formal, but is found in its disjunctive—"either-or"—premiss: an argument of this type is fallacious when its disjunctive premiss is fallaciously supported.


The Black-or-White Fallacy, like Begging the Question, is a validating form of argument. For example, some instances have the validating form:

Simple Constructive Dilemma:

Either p or q.
If p then r.
If q then r.
Therefore, r.

For this reason, this fallacy is sometimes called "false" or "bogus" dilemma. However, these names are misleading, since not all instances have the form of a dilemma; some instead take the following, also validating form:

Disjunctive Syllogism:

Either p or q.
Therefore, q.

Usually, the truth-value of premisses is not a question for logic, but for other sciences, or common sense. So, while an argument with a false premiss is unsound, it is usually not considered fallacious. However, when a disjunctive premiss is false for specifically logical reasons, or when the support for it is based upon a fallacy, then the argument commits the Black-or-White Fallacy.

One such logical error is confusing contrary with contradictory propositions: of two contradictory propositions, exactly one will be true; but of two contrary propositions, at most one will be true, but both may be false. For example:

It's hot today. It's not hot today.
It's hot today. It's cold today.

A disjunction whose disjuncts are contradictories is an instance of the Law of Excluded Middle, so it is logically true. For instance, "either it's hot today or it's not hot today." In contrast, a disjunction whose disjuncts are contraries is logically contingent. For example, "either it's hot today or it's cold today." If an arguer confuses the latter with the former in the premiss of an argument, they commit the Black-or-White Fallacy.


S. Morris Engel, With Good Reason: An Introduction to Informal Fallacies (Fifth Edition) (St. Martin's, 1994), pp. 140-142.

Analysis of the Example:

Fatalism is not the alternative to superstition; it is an alternative. Superstition involves acting in ways that are ineffective, whereas fatalism involves failing to act even in situations in which our efforts can be effective. Fortunately, there are other alternatives, such as recognizing that there are some things we can control and other things we cannot, and only acting in the first case.