undecidability

This term operates across two distinct registers: the general legal or social context and the specialized technical context of logic and computer science. In general usage, it describes a state of uncertainty or a stalemate where a conclusion cannot be reached because the evidence is balanced or insufficient. It carries a connotation of frustration or an impasse.

In theoretical computer science and mathematics, the term is a precise technical descriptor. It refers to a proven impossibility rather than a temporary lack of knowledge. When used in this sense, it describes a property of a problem—such as the halting problem—that is logically impossible to solve with a general algorithm, regardless of the computing power available.