A dichotomy is a set of two mutually exclusive, jointly exhaustive alternatives. Dichotomies are typically expressed with the words "either" and "or", like this: "Either the test is wrong or the program is wrong."
A false dichotomy is a dichotomy that is not jointly exhaustive (there are other alternatives), or that is not mutually exclusive (the alternatives overlap), or that is possibly neither. Note that the example given above is not mutually exclusive, since the test and the program could both be wrong. It's not jointly exhaustive either, since they could both be correct, but it could be a hardware error, a compiler error and so on.
A false dichotomy is typically used in an argument to force your opponent into an extreme position -- by making the assumption that there are only two positions.
Examples:
"If you want better public schools, you have to raise taxes. If you don't want to raise taxes, you can't have better schools." - A third alternative is that you could spend the existing tax money more efficiently.
"You're either part of the solution or part of the problem." - No room for innocent bystanders here.
"If you're not with us, you're against us." - Being neutral is not an option.
Forcing people to classify themselves as either "with us" or "against us", leads to the saying "An enemy of my enemy is my friend." While they may hate both of you.
The characteristic thing about the type of argument I have described above is the implicit, almost "sneaky", assumption that theory B is right — KevinB
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