Are truth and other epistemic values such as accuracy, consistency, broad scope, simplicity and fruitfulness the most important values? This is a position that can be defended as long as one focusses on the outcomes of the scientific endeavour – mainly theories and models. If one also takes into account the social process that yields these outcomes, then a series of other values become not only important, but really constitutive of science: if one is not free to engage in scientific activity, for example, then there are no outcomes in the first place to be appraised invoking epistemic values. It seems that non-epistemic values such as freedom, honesty and integrity are also constitutive of the collective scientific endeavour. Do we possess an external criterion guaranteeing the priority of a single value or a set of values vis-à-vis the rest?