If you are on the horns of a dilemma, you have to make a difficult choice between two alternatives. I find myself on the horns of a dilemma — whichever option I take, I'm going to disappoint someone. The police were on the horns of a dilemma. The girl appeared to be telling the truth, but it was her word against that of three officials. Note: In logic, a dilemma is a situation where an argument leads to two choices which are both undesirable. In the Middle Ages, a dilemma was traditionally represented as an animal with two horns such as a bull.