Self-centred based explanations such as invisible-hand accounts look like armchair constructions with no relevance to the real world. Whether and how they nonetheless provide an insight into social reality is a puzzling matter. Philip Pettit's idea of self- interest virtually bearing on choices offers the prospect of a solution. In order to assess the latter we first distinguish between three variants of invisible-hand explanations, namely: a normative, an historical and a theoretical one. We then show that, while the model of virtual self-interest is a helpful gloss on each variant, it may not convincingly succeed, pace Pettit, in reconciling the economic mind with the common mind.