Dilemma

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For other uses, see Dilemma (disambiguation).

A dilemma (Greek δί-λημμα "double proposition") is a problem offering two solutions or possibilities, in particular two solutions neither of which is acceptable. The two options are often described as the horns of a dilemma, neither of which is comfortable.

The dilemma is sometimes used as a rhetorical device, in the form "you must accept either A, or B"; here A and B would be propositions each leading to some further conclusion. Applied in this way, it may be a fallacy, a false dichotomy.

In formal logic, the definition of a dilemma differs markedly from everyday usage. Two options are still present, but choosing between them is immaterial because they both imply the same conclusion. Symbolically expressed thus:

$A \vee B, A \Rightarrow C, B \Rightarrow C \vdash C$

Which can be translated informally as "one (or both) of A or B is known to be true, but they both imply C, so regardless of the truth values of A and B we can conclude C."

Horned dilemmas can present more than two choices. The number of choices of Horned dilemmas can be used in their alternative names, such as two-pronged (two-horned) or dilemma proper , or three-pronged (three-horned) or trilemma, and so on.

Constructive dilemmas--

1. (If X, then Y) and (If W, then Z).

2. X or W.

3. Therefore, Y or Z.

Destructive dilemmas--

1. (If X, then Y) and (If W, then Z).

2. Not Y or not Z.

3. Therefore, not X or not W.