perceptiveness has 5 distinct synonyms spread across 3 of its 4 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. Its one recorded opposite is unperceptiveness.
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.
delicate discrimination (especially of aesthetic values)
“arrogance and lack of taste contributed to his rapid success”
Synonyms, antonyms and the broader and narrower relations for perceptiveness come from Princeton University’s WordNet. Full sources and licences.
the quality of insight and sympathetic understanding