The idea of social capital contains two opposite terms: (private) capital and (public) society. This duality is condemned to remain unsolved in the modern society. In fact, modernity uses knowledge as a productive force, and knowledge needs both these two sides: cognitive property (private rents and investments), on one hand; and social sharing (open access, cognitive reserves), on the other. Hence, social capital is a necessary feature of modern economy. We have utilized social capital in the last 30 year to overcome the crisis of fordist production. Small firms and industrial districts, in Italy, made a deep use of the social capital produced by history and tradition, and embedded in local systems. But today we are facing another problem: how to produce the new social capital that is needed for a post-fordist social organization of production. We are looking for a new form of modernity, suitable for a more complex world. And the social capital, that is to be produced in the future, ought to be designed to fit this more complex economy and society.