trilemma

noun

1. 1.A circumstance in which a choice must be made between three options that seem equally undesirable or, put another way, in which a choice must be made among three desirable options, only two of which are possible at the same time.
2. 2.An argument containing three alternatives, jointly exhaustive either under any condition(s) or under all condition(s) consistent with the universe of discourse of that argument, that each imply the same conclusion.