In this paper we argue that transparency, just as explanation, can be defined at different levels of abstraction. We criticize recent attempts to identify the explanation of black box algorithms with making their decisions (post-hoc) interpretable. These approaches simplify the real nature of the black boxes and risk misleading the public about the normative features of a model. We propose a new form of transparency, that consists in explaining the artifact as an intentional product, that serves a particular goal, or multiple goals (Daniel Dennet’s design stance), and that provides a measure of the extent to which such goal is achieved, and evidence about the way that measure has been reached. We call such idea of transparency ‘design publicity’. We argue that design publicity can be more easily linked with the justification of the use and of the design of the algorithm, and of each individual decision following from it. Finally, we argue that when models that pursue justifiable goals (which may include fairness as avoidance of bias towards specific groups) to a justifiable degree are used consistently, the resulting decisions are all justified even if some of them are (unavoidably) based on incorrect predictions. For this argument, we rely on John Rawls’s idea of procedural justice applied to algorithms conceived as institutions.