postulate has 10 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. 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.
take as a given; assume as a postulate or axiom
“He posited three basic laws of nature”
(logic) a proposition that is accepted as true in order to provide a basis for logical reasoning
Synonyms, antonyms and the broader and narrower relations for postulate come from Princeton University’s WordNet. Full sources and licences.