Cogitating on means to think deeply about something. The antonyms for cogitating on are not considering, ignoring, neglecting, disregarding or dismissing. When we do not consider a subject deeply, we are failing to cogitate on it. Ignoring or dismissing an idea means that we are not giving it the attention it deserves, and we are not contemplating it deeply. Neglecting or disregarding an idea is also showing a lack of interest in cogitating on it. It is always important to give thought and to be open to cogitating on ideas in order to gain a better understanding of them.