Mediation is becoming increasingly important in our societies. But isn't it still a little vague? What is it that resists our thought? Are we not better prepared to think of the figure of the Judge who «decides» the trial from the outside, by his sole authority? Rather than that of the Mediator engaging in a process from which the conflict can be «resolved»? François Jullien proposes a series of concepts to shed light on the logic of mediation and the art of operating, such as “situational potential”, “bias”, “initiation” or “viability”; or even “gap”, “between” and “de-coincidence”. To the "compromise" of concession and half-measures so often invoked, should we not prefer the com-possible – that is a possible one open to the parties in conflict – thus freeing up a fruitful path ?