*dilemma*

n. [ L. dilemma, Gr. &unr_;; di- = di`s- twice + &unr_; to take. See Lemma. ] 1. (Logic) An argument which presents an antagonist with two or more alternatives, but is equally conclusive against him, whichever alternative he chooses. [ 1913 Webster ]

☞ The following are instances of the dilemma. A young rhetorician applied to an old sophist to be taught the art of pleading, and bargained for a certain reward to be paid when he should gain a cause. The master sued for his reward, and the scholar endeavored to elude his claim by a dilemma. “If I gain my cause, I shall withhold your pay, because the judge's award will be against you; if I lose it, I may withhold it, because I shall not yet have gained a cause.” “On the contrary, ” says the master, “if you gain your cause, you must pay me, because you are to pay me when you gain a cause; if you lose it, you must pay me, because the judge will award it.” Johnson. [ 1913 Webster ]

2. A state of things in which evils or obstacles present themselves on every side, and it is difficult to determine what course to pursue; a vexatious alternative or predicament; a difficult choice or position. [ 1913 Webster ]

A strong dilemma in a desperate case!
To act with infamy, or quit the place. Swift. [ 1913 Webster ]

Horns of a dilemma, alternatives, each of which is equally difficult of encountering. [ 1913 Webster ]