There are two distinct approaches to Bayesian modelling in cognitive science. Black-box approaches use Bayesian theory to model the relationship between the inputs and outputs of a cognitive system without reference to the mediating causal processes; while mechanistic approaches make claims about the neural mechanisms which generate the outputs from the inputs. This paper concerns the relationship between these two approaches. We argue that the dominant trend in the philosophical literature, which characterizes the relationship between black-box and mechanistic approaches to (...) Bayesian cognitive science in terms of the dichotomy between instrumentalism and realism, is misguided. We propose that the two distinctions are orthogonal: black-box and mechanistic approaches to Bayesian modelling can each be given either an instrumentalist or a realist interpretation. We argue that the current tendency to conflate black-box approaches with instrumentalism and mechanistic approaches with realism stems from unwarranted assumptions about the nature of scientific explanation, the ontological commitments of scientific theories, and the role of abstraction and idealization in scientific models. We challenge each of these assumptions to reframe the debates over Bayesian modelling in cognitive science. (shrink)