The concept of innovation is making a successful comeback in philosophy, particularly with the qualifier "responsible" attached. This attachment of the qualification "responsible" reflects the idea that the concept of innovation has to be opened to new considerations, namely social, political and ethical concerns. Since the 18th century, innovation has been the object of economics and science of business and growth. This paper aims at testing the legitimacy of these attempts to open the concept and redefine it in terms other than those of economics. We start with a contextualization of the use of the term innovation, to see why it has been so strongly associated with the market, growth and business then we see what is at stake in opening it up to other considerations. We consider the limits of this opening and look at possible ways to attach other meanings to the concept, without losing significance by too much inclusion. The solution proposed is that instead of imposing new parameters and trying to shift the concept, we could keep the economic bias of the term, but challenge it with concerns expressed by people coming from the field of economics who are trying to propose an alternative framework for economics that would take into account other concerns, and in which responsible innovation could find a place.