This paper scrutinizes two research programs that advocate respectively for the existence of a universal moral grammar and a predisposition to moralize behaviours with certain contents. It focuses on how the arguments commonly used to ground each program fare at relevant contemporary research in cognitive science and how well they meet constructivist arguments proposed by Jesse Prinz and Kim Sterelny, among others. We argue that there is little evidence that our moral judgements follow the model of principles and parameters. At the same time, ‘ease of learning’ suggests that the human brain is somehow prepared to learn moral rules.