Approximating Bayes? On the role of approximations in Bayesian cognitive science

Approximations have come to occupy a central role within Bayesian cognitive science. Many cognitive scientists view current approximation-based models as showing that the mind approximates Bayesian inference. In this paper I interrogate this idea, asking what it means to claim that the mind approximates one computation by executing another. I look at three possible interpretations of such claims, finding problems with each. I argue that this poses challenges to one central rationale for the Bayesian approach, and to its top-down methodology.