This fallacy can be considered a variation on the fallacy of Suppressed Evidence. By leaving out important possibilities, the argument is also leaving out relevant premises and information which would lead to better evaluation of the claims.
Usually, the False Dilemma fallacy takes this form:
- 1. Either A or B is true. A is not true. Therefore, B is true.
As long as there are more options than A and B, then the conclusion that B must be true cannot follow from the premise that A is false. This makes an error similar to that found in the fallacy of Illicit Observation. One of the examples of that fallacy was:
- 2. No rocks are alive, therefore all rocks are dead.
We can reword it to:
- 3. Either rocks are alive or rocks are dead.
Whether phrased as an Illicit Observation or as a False Dilemma, the error in these statements lies in the fact that two contraries are presented as if they were contradictories. If two statements are contraries, then it is impossible for both of them to be true, but it is possible for both to be false. However, if two statements are contradictories, it is impossible for them to both be true or both be false.
Thus, when two terms are contradictories, the falsehood of one necessarily implies the truth of the other. The terms alive and lifeless are contradictories - if one is true, the other must be false. However, the terms alive and dead are not contradictories; they are, instead, contraries. It is impossible for both to be true of something, but it is possible for both to be false - a rock is neither alive nor dead because "dead" assumes a prior state of being alive.
Example #3 is a False Dilemma fallacy because it presents the options alive and dead as the only two options, on the assumption that they are contradictories. Because they are actually contraries, it is an invalid presentation.