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 "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.
Chicken or egg: which is first of two things, each of which presupposes the otherDouble bind: conflicting requirements ensure that the victim will automatically be wrong.Ethical dilemma: a choice between moral imperatives.Extortion: the choice between paying the extortionist and suffering an unpleasant action.Hedgehog's dilemma: the desire for intimacy going unfulfilled due to accompanying substantial mutual harm.Fairness dilemmas: when groups are faced with making decisions about how to share their resources, rewards, or payoffs.Hobson's choice: a choice between something and nothing; "take it or leave it".Mesh Fencer: relates to a difficult commercial choice where neither option is cost effective but a decision has to be made.Morton's fork: choices yield equivalent, often undesirable, results.Prisoner's dilemma: an inability to coordinate makes cooperation difficult and defection tempting.Samaritan's dilemma: the choice between providing charity and improving another's condition, and withholding it to prevent them from becoming dependent.Sophie's choice: a choice between two persons or things that will result in the death or destruction of the person or thing not chosen.Traveler's dilemma: you could make the best move possible to win the game according to its rules. But in doing so, you forfeit almost the entire value of a lost suitcase full of antiques of which you are the owner.Zugzwang: one must move and incur harm when one would prefer to make no move (esp. in chess).Several idioms describe dilemmas:
"Damned if you do, damned if you don't""Between Scylla and Charybdis""Lesser of two evils""Between a rock and a hard place", since both objects or metaphorical choices are rough."Between the devil and the deep blue sea""Out of the frying pan, into the fire"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:
A ∨ B , A ⇒ C , B ⇒ C , ⊢ 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.
There are also constructive dilemmas and destructive dilemmas.
1. (If X, then Y) and (If W, then Z).2. X or W.3. Therefore, Y or Z.1. (If X, then Y) and (If W, then Z).2. Not Y or not Z.3. Therefore, not X or not W.
