A dilemma (Greek δί-λημμα "double proposition") is when two solutions or possibilities are present. If both solutions are undesirable or impossible, this may put a person on the horns of a dilemma, neither outcome is comfortable.
The dilemma is sometimes put as a choice "you must accept either A, or B". Here A and B are each leading to some undesirable conclusion.
In formal logic, the definition of a dilemma differs from everyday usage. Two options are still present, but choosing between them is immaterial because they both imply the same conclusion. Symbolically expressed thus:
This 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
Questions and Answers
Q: What is a dilemma?
A: A dilemma is when two solutions or possibilities are present, and both outcomes are undesirable or impossible.
Q: How is a dilemma expressed in formal logic?
A: In formal logic, the definition of a dilemma differs from everyday usage. Two options are still present, but choosing between them is immaterial because they both imply the same conclusion. This can be symbolically expressed 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."
Q: Are there different types of dilemmas?
A: Yes, there are constructive and destructive dilemmas. Constructive dilemmas involve if-then statements that lead to two possible conclusions while destructive dilemmas involve two choices that each lead to an undesirable outcome.
Q: How many choices does a horned dilemma have?
A: Horned dilemmas can present more than two choices - the number of choices determines their alternative names such as two-pronged (two-horned) or three-pronged (three-horned).
Q: What does it mean to be on the horns of a dilemma?
A: To be on the horns of a dilemma means that neither outcome is comfortable - it's an unpleasant situation where you must choose between two undesirable options.
Q: What do constructive dilemmas involve?
A: Constructive dilemmas involve if-then statements that lead to two possible conclusions.
