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A dilemma (Greek δί-λημμα "double proposition") is a problem offering at least two solutions or possibilities, of which none are practically acceptable. One in this position has been traditionally described as "being on the horns of a dilemma", neither horn being comfortable, "between Scylla and Charybdis"; or "being between a rock and a hard place", since both objects or metaphorical choices are rough.

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.

See also








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