Dilemma

A dilemma (Greek: δίλημμα "double proposition") is a problem offering two possibilities, neither of which is unambiguously acceptable or preferable. One in this position has been traditionally described as "", 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:

A dilemma with more than two forks is sometimes called a trilemma (3), tetralemma (4), or more generally a polylemma.

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:

${\displaystyle A\vee B,A\Rightarrow C,B\Rightarrow C,\vdash C}$

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." This is a rule of inference called Disjunction elimination.

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