profundity has 7 distinct synonyms spread across 4 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 superficiality.
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.
wisdom that is recondite and abstruse and profound
“the anthropologist was impressed by the reconditeness of the native proverbs”
intellectual depth; penetrating knowledge; keen insight; etc
“the depth of my feeling”
the intellectual ability to penetrate deeply into ideas
the quality of being physically deep
“the profundity of the mine was almost a mile”
Synonyms, antonyms and the broader and narrower relations for profundity come from Princeton University’s WordNet. Full sources and licences.