At the very heart of polemos, the conflict which rules the world, the philosophy of Heraclitus suggests the possible existence of a specific dialogical alchemy, able to turn the lead of opposition into the gold of cooperation. Not in spite of war, but – as delicate as the premise could be judged – thanks to it. This article translates this intuition to the specific context of international relations. Referring to the theory of argumentation (from Aristotle to some recent developments of the informal logic), it redefines war as a “convergent eristic syllogism” and recognizes the validity of the heraclitean harmoniè, provided that the logic of armed conflict remains dependent on its enunciative context, itself shaped by the tragic rationality constitutive of any political opposition.