undecidable

This term carries a heavy weight of finality, suggesting that a lack of resolution is not due to a lack of effort or data, but is an inherent property of the problem itself. In general conversation, it describes a stalemate or a philosophical paradox where no amount of reasoning can produce a definitive answer.

In technical fields like mathematics and computer science, the word is a precise term of art. It describes a specific class of problems—such as the halting problem—where it has been mathematically proven that no algorithm can ever be written to provide a consistent yes-or-no answer for all possible inputs.