# Dilemma

For other uses, see Dilemma (disambiguation).
"Between a rock and a hard place" redirects here. For other uses, see Between a Rock and a Hard Place (disambiguation).

A dilemma (Greek: δίλημμα "double proposition") is a problem offering two possibilities, neither of which is practically acceptable. One in this position has been traditionally described as "being on the horns of a dilemma", neither horn being comfortable. This is sometimes more colorfully described as "Finding oneself impaled upon the horns of a dilemma", referring to the sharp points of a bull's horns, equally uncomfortable (and dangerous).

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 incorrectly, it constitutes a false dichotomy, a fallacy.

## Types of dilemmas

Colorful names have been given to many types of dilemmas.

• Double bind: conflicting requirements ensure that the victim will automatically be wrong.
• Ethical dilemma: a choice between moral imperatives.
• Extortion: the choice between paying the extortionist and suffering an unpleasant action.
• Fairness dilemmas: when groups are faced with making decisions about how to share their resources, rewards, or payoffs.
• Hobson's choice: a choice between something and nothing; "take it or leave it".
• Morton's fork: choices yield equivalent, often undesirable, results.
• Prisoner's dilemma: An inability to coordinate makes cooperation difficult and defection tempting.
• Samaritan's dilemma: the choice between providing charity and improving another's condition, and withholding it to prevent them from becoming dependent.
• Sophie's choice: a choice between two persons or things that will result in the death or destruction of the person or thing not chosen.
• Zugzwang: One must move and incur harm when one would prefer to make no move (esp. in chess).

## Related terms

Several idioms describe dilemmas:

A dilemma with more than two forks is sometimes called a trilemma (3), tetralemma (4), or polylemma.

The errant spelling dilemna is often seen in common usage. It appears to have been taught in many areas of the United States and all over the world, including (but not limited to) France, England, Jamaica and Australia.[1][2][3] There is no prima facie reason for this substitution error and there is no erroneous parallel to be found with the word lemma, from which dilemma derives.

## Use in logic

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:

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

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."

There are also constructive dilemmas and destructive dilemmas.

### Constructive dilemmas

1. (If X, then Y) and (If W, then Z).
2. X or W.
3. Therefore, Y or Z.
4. All are possible but not

### 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.