The author identifies a Law of Requisite Cognitive Capacity in human communication, conflict resolution, and cooperation solicitation. Based on Ashby's Law of the Requisite Variety and Jaques's theory of cognitive capacity and by combining the author's previous work on the cognitive model of improving communication efficiency, a quantitative limitation for people to understand each other can be identified. On the Jaquesian Cognitive Capacity Strata, it is necessary for the person on a higher stratum to make extra efforts to explain/ translate his/her mental model for the person (or P-individual) on a lower stratum, using the language/mental model available at the lower stratum. Without such explanation/translation, the person on a lower stratum cannot cognize the mental model being used and will misunderstand, therefore effective communication cannot be achieved. The existence of such limitation explains a number of interesting social and organizational phenomena.