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