incorrect vs correctness

incorrect is not a noun while correctness is a noun.

Word	Noun	Adjective	Verb	Adverb
incorrect	No	Yes	No	No
correctness	Yes	No	No	No

incorrect (noun)	correctness (noun)
	conformity to fact or truth
	the quality of conformity to social expectations

incorrect (adjective)	correctness (adjective)
not correct; not in conformity with fact or truth
not in accord with established usage or procedure
characterized by errors; not agreeing with a model or not following established rules
(of a word or expression) not agreeing with grammatical principles