Evolutionary explanations offer convincing accounts of the origin of ethics but seem to undermine the prospects of its objective foundation. On the basis of these explanations, Sharon Street and others have argued that the claim to objectivity is misplaced insofar as it commits to moral realism or it should be reinterpreted otherwise (e.g. contingent on shared values). By contrast, I argue that evolutionary explanations challenge any meta-ethics that is indifferent to the temporal dimension of normativity and, in particular, finitude as a dimension of contingency. While I share some of the premises of the anti-realist argument, I deny that they compel us to accept deflated conceptions of objectivity, e.g. in terms of intersubjective agreement or reflective endorsement. In fact, such deflationary strategies bear heavy epistemic costs and are vulnerable to the objection of bootstrapping. In contrast to debunking arguments, I suggest that evolutionary accounts of the origin of ethics provide support for a strong understanding of ethical objectivity, which requires (i) independence of practical subjects' comprehensive views, interests, and preferences; (ii) rational validity, and (agreement in judgment); (iii) authority that does not rest on power position, or rational compliance. In the main part of the paper, I offer a constructivist account of rational justification, which meets these requirements. Finally, I attempt to show that the evolutionary concept of exaptation may be of help in characterizing the sort of adjustments available to constructivism, as an alternative to bootstrapping strategies.