A dilemma (Greek δί-λημμα "double proposition") is a problem offering at least two solutions or possibilities, of which none are practically acceptable; one in this position has been traditionally described as "being on the horns of a dilemma", neither horn being comfortable; or "being between a rock and a hard place", since both objects or metaphorical choices being rough.

The dilemma is sometimes used as a rhetorical device, in the form "you must accept either A, or B"; here A and B would be propositions each leading to some further conclusion. Applied in this way, it may be a fallacy, a false dichotomy.

In formal logic, the definition of a dilemma differs markedly from everyday usage. Two options are still present, but choosing between them is immaterial because they both imply the same conclusion. Symbolically expressed thus:

$A\; \backslash vee\; B,\; A\; \backslash Rightarrow\; C,\; B\; \backslash Rightarrow\; C\; \backslash vdash\; C$

Which can be translated informally as "one (or both) of A or B is known to be true, but they both imply C, so regardless of the truth values of A and B we can conclude C."

Horned dilemmas can present more than two choices. The number of choices of Horned dilemmas can be used in their alternative names, such as two-pronged (two-horned) or dilemma proper , or three-pronged (three-horned) or trilemma, and so on.

Constructive dilemmas--

1. (If X, then Y) and (If W, then Z).

2. X or W.

3. Therefore, Y or Z.

Destructive dilemmas--

1. (If X, then Y) and (If W, then Z).

2. Not Y or not Z.

3. Therefore, not X or not W.

Named dilemmas

• Cornelian dilemma
• Euthyphro dilemma
• Hedgehog's dilemma
• Platonia dilemma
• Prisoner's dilemma
• Scylla and Charybdis
• Security dilemma
• Stagflation
• Traveler's dilemma
• Warnock's Dilemma
• Catch-22 (logic)

See also

• Coordination game
• Dharmasankat
• Dilemma story
• False dilemma
• Paradox
• Tetralemma
• Trilemma