Around 1184, Alan de Lille composed a sermon addressed to Europe's knights (Ad milites) as part of a treatise on the art of preaching (Ars praedicandi). In it, Alan condemned the felonious and violent behavior of Western warriors and reproached them for their mistreatment of the poor and the Church—the very groups that knights ought to protect in an ideal Christian society. According to Alan, such actions must cease and knightly behavior must be reformed. Using scriptural precedent, he encouraged knights to consider their spiritual welfare by articulating a difference between internal and external military service. Knights, if they wish to be soldiers of God, must wield both temporal and spiritual arms: the former to protect the Church and their homelands, the latter to combat the enemies of their souls. Balance between the two was essential since external service (earthly combat) was empty and meaningless without its internal counterpart (spiritual combat). By ensuring the proper equilibrium, knights could fulfill their assigned role in the world while actively working to ensure their own salvation.
Computing a proper equilibrium of a bimatrix game