Decidableness

Part of speech: noun

Definitions

1. The state or quality of being capable of reaching a clear and definite conclusion or decision; the property of resolvability in a matter or problem; the characteristic of being determinable without ambiguity
2. The condition in which a problem or question can be conclusively solved or settled; the attribute allowing a firm judgment to be made; the trait of having a clearly definable outcome or answer
3. The feature of something that permits an unambiguous resolution or determination; the degree to which an issue can be conclusively decided; the aspect of being definitively ascertainable or settled

Etymology: "Decidableness" is "decidable" plus the suffix "-ness", which turns an adjective into a noun for a state or quality. "Decidable" comes from "decide," itself from Latin "decidere," meaning "to cut off" or "to cut short," from "de-" (off) and "caedere" (to cut). The sense of settling a dispute was drawn from that image of cutting a matter off or ending it. "Decidable" was formed in English from "decide" with the suffix "-able," meaning capable of being done. In logic and mathematics it describes a problem for which an algorithm can determine, in finitely many steps, whether a statement is true or false. The idea became central to 20th-century mathematics, especially after Alonzo Church and Alan Turing showed in the 1930s that some problems have no such method. Because "decidableness" is a rare noun formed by adding a suffix, it appears mostly in technical writing about logic and computation, where it names the property rather than the process of deciding.

Synonyms: decisiveness, resoluteness, determination

Antonyms: indecisiveness, uncertainty