The word "logomachize" means to argue or dispute over words, language or meanings. Some possible antonyms for this word could include words like agree, concur, harmonize, conciliate or cooperate. These words describe actions or behaviors that involve finding common ground, working towards a shared goal, and avoiding unnecessary conflict. Other antonyms for logomachize could be words like elude, evade, or avoid, which describe a desire to escape or stay away from words or arguments altogether. Whatever antonym you choose, the idea is to describe a mindset and behavior that is focused on unity, collaboration, and peaceful interaction, rather than argumentation or debate.