D defs.my
Entry 2 senses Webster, 1913

Dilemma

/dī-lĕmʹə or dĭ-lĕmʹə/ · Di·lem·ma · IPA /daɪˈlɛmə/
01 n. An argument which presents an antagonist with two or more alternatives, but is equally conclusive against him, whichever alternative he chooses.
  1. 1.
    An argument which presents an antagonist with two or more alternatives, but is equally conclusive against him, whichever alternative he chooses.(Logic)
  2. 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.
    “A strong dilemma in a desperate case! To act with infamy, or quit the place.” Swift.
Phrases & compounds
Horns of a dilemma — alternatives, each of which is equally difficult of encountering.