undecidable

The word undecidable describes something that cannot be settled with a definite yes-or-no answer. It is stronger than "hard to decide" or "still unanswered." If something is undecidable, the point is not simply that people have not solved it yet, but that, in the relevant system or setting, there is no way to reach a final decision.

This idea is especially important in mathematical logic and computer science. In those fields, an undecidable problem is one that cannot be resolved by the allowed rules or by any procedure that is supposed to work in every case. Gödel's work showed that in rich formal systems there are statements that can be neither proved nor disproved within the system itself. In computation, some decision problems are called undecidable because no algorithm can always determine the answer.

Outside technical subjects, the word is sometimes used more loosely. In philosophy, ethics, or ordinary conversation, it can describe a situation that seems impossible to settle in a final or fully satisfying way. A deeply personal moral dilemma, for example, may be described this way when each choice has serious costs and no single answer feels clearly right.

You might also see the word used for interpretation. A work of art, a philosophical question, or a legal issue may be called undecidable when no single reading can be established as the final one. In these broader uses, the word often suggests deep ambiguity rather than a formal proof.

So, while undecidable has a precise technical meaning in logic and computing, it also has a wider everyday use. In both cases, the core idea is the same: the matter cannot be brought to a final, definite decision.