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illogicality has 3 distinct synonyms spread across 1 of its 1 sense. 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 logicality.
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.
Synonyms, antonyms and the broader and narrower relations for illogicality come from Princeton University’s WordNet. Full sources and licences.