Bayesian models are often criticized for postulating computations that are computationally intractable (e.g., NP-hard) and therefore implausibly performed by our resource-bounded minds/brains. Our letter is motivated by the observation that Bayesian modelers have been claiming that they can counter this charge of “intractability” by proposing that Bayesian computations can be tractably approximated. We would like to make the cognitive science community aware of the problematic nature of such claims. We cite mathematical proofs from the computer science literature that show intractable (...) Bayesian computations, such as postulated in existing Bayesian models, cannot be tractably approximated. This does not mean that human brains do not (or cannot) implement the type of algorithms that Bayesian modelers are advancing, but it does mean that proposing that they do by itself does nothing to parry the charge of intractability, because the postulated algorithms are as intractable (i.e., require exponential time) as the computations they try to approximate. Besides our negative message for the community, our letter also makes a positive contribution by referring to a methodology that Bayesian modelers can use to try and parry the charge of intractability in a mathematically sound way. (shrink)