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Definition of rightness : 1. Straightness; as, the rightness of a line.
2. The quality or state of being right; right relation.

Synonyms:

worth, justness, chastity, nicety, virtue, rightfulness, rectitude, probity, faithfulness, righteousness, worthiness, refinement, subtlety, uprightness, ethicalness, ethic, shade, justice, correct, accurateness, purity, duty, propriety, excellence, honor, goodness, ethicality, virtuousness, right, nuance, morality, appropriateness, integrity, good

exactness, accuracy, precision, faultlessness, preciseness, rigor, correctness, exactitude, strictness

authenticity, veracity, definiteness, matter-of-factness, fact, gospel, verity, proof, honesty, truth, absoluteness, axiom, certainty

Usage examples:

• Katharsis is indeed not the mark of Tragedy alone, although in Tragedy it has a very great relative intensity; it is ultimately only a designation for the specific aesthetic pleasure, to which I can give no better name than the oft- repeated one of triumphant acquiescence in the rightness of relations. - "The Psychology of Beauty", Ethel D. Puffer.
• He was a constant worker in planting the first seeds of the moral rightness of the cause, the crusader whose faith clarified the fundamental religious background inherent in good government. - "Frank H. Nelson of Cincinnati", Warren C. Herrick.
• With some real though limited talent as an artist, she had the touch of instinct, the sense of rightness, and the drive to be unsatisfied with anything but what was right. - "The Way of Decision", M. C. Pease.