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excogitation has 4 distinct synonyms spread across 1 of its 2 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.
thinking something out with care in order to achieve complete understanding of it
the creation of something in the mind
Synonyms, antonyms and the broader and narrower relations for excogitation come from Princeton University’s WordNet. Full sources and licences.