The antonyms for the word "cogitates on" include disregard, neglect, ignore, dismiss, and overlook. These words indicate a lack of attention or consideration, rather than thoughtful contemplation. When we disregard something, we are actively choosing not to think about it. Neglect and ignore suggest a similar lack of engagement, while dismiss indicates a decision to reject something without serious consideration. Overlook implies a failure to notice, which could be accidental or intentional. In any case, these antonyms suggest a lack of mental engagement with a topic or idea, contrasting with the active mental effort involved in cogitating on something.