We provide a new approach to how, why and with what results people think about opposing or paradoxical categories. Using a two-part laboratory study, we found differences in whether people in China and the US categorized attempts to outperform others as an instance of both competition and cooperation. We call membership in both categories in a paradox integrative categorization. We found that Chinese were more likely than in the US to engage in integrative categorization, and that the cultural difference was mediated by differences in lay dialecticism. Finally, we showed behavioral effects: integrative categorization predicted peoples cooperative behavior after they experienced others attempt to outperform them.