Definition

Also called Manicheanism, Black-and-White Thinking, Black-or-White Fallacy, Bifurcation, Bogus Dilemma, or Either/Or fallacy in gs.

A False Dilemma is a fallacy in which a person uses the following pattern of "reasoning":

• Either claim c1 is true (resp. false) or claim c2 is true (resp. false), when c1 and c2 could both be false (resp. true).
• Claim c1 is false (resp. true).
• Therefore claim c2 is true (resp. false).

This line of "reasoning" is fallacious because if both claims could be false (resp. true), then it cannot be inferred that one is true (resp. false) because the other is false (resp. true). Besides, there may be three, four or more other possibilities that have not been considered. This fallacy is based on the misuse of Aristotle's so-called premise of the excluded middle.

Examples

Either 1+1=3 or 1+1=4. It is not the case that 1+1=4. Therefore 1+1=3.
As you know, 1+1 equals neither 3 nor 4 but 2.

Either you're for us or against us.
As said by Nazi Germany; fallacious since there are neutral countries.

America: love it or leave it.
"Change it" could be a third possibility.

Counter-examples

In gs, some people incorrectly believe that an either/or form is necessarily fallacious. This is not correct.

Bill is dead or he is alive. Bill is not dead. Therefore Bill is alive.
Please, no Schrödinger quantum wit of the kind (dead+alive)/sqrt(2).

Either you're for us or against us.
As said of war on international terrorism, since there is little possible middle ground.

Advices

If you must use an either/or form, check that there are no other relevant possibilities and consider some of them carefully before.
If your opponent uses an either/or form, check if there are no other relevant possibilities and point them out.
Extensional orientation is a way to overcome a tendency to abusively use such forms.