noun

- a situation requiring a choice between equally undesirable alternatives.
- any difficult or perplexing situation or problem.
- Logic. a form of syllogism in which the major premise is formed of two or more hypothetical propositions and the minor premise is a disjunctive proposition, as “If A, then B; if C then D. Either A or C. Therefore, either B or D.”

noun

- a situation necessitating a choice between two equal, esp equally undesirable, alternatives
- a problem that seems incapable of a solution
- logic a form of argument one of whose premises is the conjunction of two conditional statements and the other of which affirms the disjunction of their antecedents, and whose conclusion is the disjunction of their consequents. Its form is if p then q and if r then s; either p or r so either q or s
- on the horns of a dilemma
- faced with the choice between two equally unpalatable alternatives
- in an awkward situation

1520s, from Late Latin dilemma, from Greek dilemma “double proposition,” a technical term in rhetoric, from di- “two” + lemma “premise, anything received or taken,” from root of lambanein “to take” (see analemma). It should be used only of situations where someone is forced to choose between two alternatives, both unfavorable to him. But even logicians disagree on whether certain situations are dilemmas or mere syllogisms.

see horns of a dilemma.