False Dilemma (Logical Fallacy)

Also Known as Black & White Thinking, False Dichotomy, Bifurcation Error.

Description of False Dilemma
A False Dilemma is a fallacy in which a person uses the following pattern of "reasoning":
1 .Either claim X is true or claim Y is true (when X and Y could both be false).
2. Claim Y is false.
3. Therefore claim X is true.

This "reasoning" is fallacious because if both claims could be false, then it cannot be inferred that one is true because the other is false. That this is the case is made clear by the following example:
1. Either 1+1=4 or 1+1=12.
2. It is not the case that 1+1=4.
3. Therefore 1+1=12.

In cases in which the two options are, in fact, the only two options, this line of reasoning is not fallacious. For example:
1. Bill is dead or he is alive.
2. Bill is not dead.
3. Therefore Bill is alive.

Examples of False Dilemma
1. “You’re either with us, or you support the terrorists.”
2. Bill: "Jill and I both support having prayer in public schools."
Jill: "Hey, I never said that!"
Bill: "You're not an atheist are you Jill?"