trilemma

A trilemma is a term used to describe a problem that involves choosing among three options, where the options are mutually incompatible or mutually exclusive, so that satisfying all three at once is impossible or highly undesirable. The word derives from the roots tri- (three) and lemma (premise or proposition). It extends the idea of a dilemma, which involves two alternatives.

In practice, a trilemma refers to a three-way trade-off in which selecting one option rules out one or both of the others, often forcing a compromise. The concept is used to illustrate how pursuing one goal may undermine others and why decision-makers must prioritize among competing objectives.

Examples of trilemmas appear in multiple fields. In international economics, the impossible trinity states that a country cannot simultaneously maintain a fixed exchange rate, free capital movement, and an independent monetary policy; only two of the three can be sustained. In distributed computing, the CAP theorem describes a trilemma among consistency, availability, and partition tolerance, indicating that a system must sacrifice at least one of these properties under network partitions.

The term is employed to clarify policy choices, design constraints, and philosophical challenges, highlighting that some goals are incompatible and that prioritization is often necessary. While everyday usage may describe three options as a dilemma, the trilemma frame emphasizes the three-way constraint and the resulting trade-offs inherent in complex systems.