In this paper we want to affirm the desiring-social-change that we find in practices presently represented by theorists and policy-makers as examples of ‘social entrepreneurship’ (SE). We do this as an attempt to intensify the presence of the social and sociality in today's discourse on the entrepreneurship–society relationship. SE, as all entrepreneurship practices, operates by social and economic forces (limiting ourselves to those here), and generates social and economic outcomes (amongst others). Its second half, however, dominates the concept of SE, and our analysis seek to remedy this imbalance by focusing on the social productivity of entrepreneurship, on entrepreneurship desiring social change. We suggest ‘public entrepreneurship’ might grasp this as a more balanced concept that will also support a more precise analysis of the entrepreneurship–society relationship.