If we look at the various contexts in which objectivity is pursued (scientific inquiry, social debates, policy decisions) we immediately realize that, by referring to this concept, there is often a chasm between what is ideally aimed at and what can be sensibly argued for and/or achieved in practice (different practices). In the first part of this article I will revisit the two main debates where the issue of objectivity has been traditionally raised and discussed: the real/constructed debate, and the fact/value debate. By retracing the general features of these two debates I will bring out what meaning of objectivity can be formulated for social science if we follow the epistemological limits and constraints set out by these debates. in t...