The logical fallacy of false dichotomy or false choice occurs when one provides only two (or a few) answers to a question, giving the illusion that these choices exhaust all possibilities, when in fact they don't. Some examples include:
- In fact, both may be wrong.
- This ignores other possibilities, such as "legend".
- You're either with us or against us.
- I might not stand in your way, but cannot actively support your course of action.
- Theism = Belief in one or more gods
- Atheism = "A" + "Theism" = Lacking + (Belief in one or more gods)
As one cannot simultaneously lack belief and believe, this is an example of a valid dichotomy.