irresolvable

Irresolvable is an adjective meaning not able to be resolved, settled, or explained. It is used for problems, disputes, questions, or contradictions that cannot be solved within the available information, rules, or constraints. In practice, an issue described as irresolvable may be one that resists current methods or lacks a determinate outcome under a given framework. The term often conveys a sense of impasse rather than mere difficulty, suggesting that any proposed solution would violate some constraint or lead to a contradiction.

Etymology and variations: The word derives from the prefix ir- meaning not, attached to resolvable, meaning capable of being resolved. It is formed in English from Latin roots related to resolvere, to loosen or to solve. A less common variant is irresoluble, which shares the same meaning and is sometimes encountered in older or formal texts.

Usage and contexts: Irresolvable is commonly used in philosophy, logic, and policy or legal debates to describe disputes with no satisfactory settlement under the given premises. In mathematics or computer science, it may describe problems that have no solution under specified axioms or constraints. In ordinary language, it can describe situations that reach an impasse or paradox where a clear resolution appears unattainable.

See also: unsolvable, insoluble, irresolution, deadlock, paradox.