dilemma -
A type of syllogism of the form "if A is true then B is true; if C is true then D is true; either A or C is true; therefore either B or D is true".
dilemma -
Offering to an opponent a choice between two equally unfavorable alternatives.
Wikipedia
A dilemma is a problem offering at least two solutions or possibilities, of which none is practically acceptable. One in this position has been traditionally described as "being on the horns of a dilemma", neither horn being comfortable, "between Scylla and Charybdis"; or "being between a rock and a hard place", since both objects or metaphorical choices are rough. This is sometimes more colorfully described as "Finding oneself impaled upon the horns of a dilemma", referring to sharp points of a bull's horns, each of which are equally uncomfortable.
OmegaWiki Dictionary
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dilemma A circumstance in which a choice must be made between two or more alternatives that seem equally undesirable.
