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A dilemma (Greek: δίλημμα "double proposition") is a problem offering two possibilities, neither of which is practically acceptable. One in this position has been traditionally described as "being on the horns of a dilemma", neither horn being comfortable. This is sometimes more colorfully described as "Finding oneself impaled upon the horns of a dilemma", referring to the sharp points of a bull's horns, equally uncomfortable (and dangerous).
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 incorrectly, it constitutes a false dichotomy, a fallacy.
Colorful names have been given to many types of dilemmas.
Several idioms describe dilemmas:
The errant spelling dilemna is often seen in common usage. It appears to have been taught in many areas of the United States and all over the world, including (but not limited to) France, England, Jamaica and Australia. There is no prima facie reason for this substitution error and there is no erroneous parallel to be found with the word lemma, from which dilemma derives.
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:
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." This is a rule of inference called Disjunction elimination.
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