unsolvability

Cannot be resolved

Unsolvability is the quality of having no solution.

In mathematics and logic, it refers specifically to problems that can be proven impossible to solve—not merely difficult, but demonstrably beyond resolution: Turing proved the unsolvability of the halting problem.

More loosely, it describes any situation that seems to have no way out: the apparent unsolvability of the conflict.

impossibility

intractable

Impossible to manage

hopeless · impossible · unattainable · unachievable · infeasible · unrealizable · unworkable · impervious · unbreakable · futility

enigma

mystery

Something unexplained or unknown

paradox · unfathomable · inexplicable · incomprehensible · indecipherable · inscrutable · cryptic · impenetrable · opaque · bafflement

impasse

deadlock

Mutual blocking, no progress

quagmire · logjam · bottleneck · cul-de-sac · morass · mire · blockage · stuck · paralysis · stagnation

philosophy

incompleteness

State of lacking parts

unknowable · indeterminate

complexity

convoluted

Excessively complex or twisted

knotty · thorny · entangled · perplexing · complicated · intricate · abstruse · multifaceted · layered · recursive

Opposites
problem resolution potential

unsolvabilitysolvability

Capacity for resolution

resolvability · decidability · solubility · tractability · answerability

epistemic tractability

unsolvabilitytractability

Readiness to be guided

computability · decidability · solvability · calculability · provability

Family

solve, solvable, solvability, unsolvable, solver, solves, solved, solving, solution

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Used worldwide · Timeless · Abstract · Rated G