discernment has 11 distinct synonyms spread across 5 of its 5 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
the cognitive condition of someone who understands
“he has virtually no understanding of social cause and effect”
delicate discrimination (especially of aesthetic values)
“arrogance and lack of taste contributed to his rapid success”
the mental ability to understand and discriminate between relations
the trait of judging wisely and objectively
“a man of discernment”
Synonyms, antonyms and the broader and narrower relations for discernment come from Princeton University’s WordNet. Full sources and licences.