impossibleness

State of unachievability

The state or quality of being impossible.

This is a rare and awkward formation; impossibility is the standard noun for this concept.

The sheer impossibleness of the task overwhelmed him works grammatically but sounds stilted compared to the impossibility of the task.

infeasibility

impracticability

Impossibility of execution

inoperability · unsustainability · unmanageability · nonviability · inaccessibility · unattainability · insurmountability · intractability

obstruction

barrier

Obstruction preventing passage

blockade · insurmountability · impassability · impenetrability · obstruction · deadlock · impasse · stalemate · roadblock · bottleneck

absurdity

inconceivability

Inability to be grasped mentally

incredibility · unfathomability · incomprehensibility · illogicality · irrationality · absurdity · ludicrousness · ridiculousness · outrageousness · unbelievability

hopelessness

futility

Lack of purpose

resignation · defeatism · despondency · pessimism · fatalism · discouragement · dejection · desolation · gloom · inevitability

Opposites
achievability

impossiblenesspossibility

State of being achievable

achievability · attainability · feasibility · doability · practicability

logical/conceptual coherence

impossiblenesspossibility

State of being achievable

conceivability · plausibility · imaginability · logical consistency · coherence

Family

possible, impossible, possibly, possibility, impossibly, impossibility, impossibilities, unpossible, impossibles

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Used worldwide · Timeless · Abstract · Everyday, not technical · Rated G