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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 impaled on the horns of a dilemma, neither horn being comfortable.

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:

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

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."

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.

- Cornelian dilemma
- Euthyphro dilemma
- Hedgehog's dilemma
- Platonia dilemma
- Prisoner's dilemma
- Scylla and Charybdis
- Security dilemma
- Stagflation
- Traveler's dilemma
- Warnock's Dilemma

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Last updated on Sunday October 05, 2008 at 10:46:20 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Sunday October 05, 2008 at 10:46:20 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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