As a verb, to mediate is to help two or more sides in a conflict find a solution or agreement. As an adjective (less common), mediate can mean being in the middle or acting as a go‑between.
From Late Latin “mediatus” meaning 'placed in the middle', from “medius” 'middle'. It first meant to be in a middle position or to act through an intermediary. The modern sense of conflict resolution grew from this idea of being a middle person.
To mediate is literally to 'middle‑ize' a conflict—step into the space between and change what happens there. It’s a cousin of 'medium', 'median', and 'immediate' (which originally meant 'without anything in the middle').
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