correctness

noun

1. Freedom from error: accuracy, accurateness, exactitude, exactness, preciseness, precision, rightness. See correct/incorrect.
2. Correspondence with fact or truth: accuracy, exactitude, exactness, fidelity, truth, veraciousness, veracity, veridicality, verity. See true/false.
3. Conformity to recognized standards, as of conduct or appearance: comeliness, decency, decentness, decorousness, decorum, properness, propriety, respectability, respectableness, seemliness. See usual/unusual.

The noun has 2 meanings:

Meaning #1: conformity to fact or truth
  Synonym: rightness
  Antonym: incorrectness (meaning #2)

Meaning #2: conformity to social expectations
  Antonym: incorrectness (meaning #1)