The mainstream view in cognitive science is that computation lies at the basis of and explains cognition. Our analysis reveals that there is no compelling evidence or argument for thinking that brains compute. It makes the case for inverting the explanatory order proposed by the computational basis of cognition thesis. We give reasons to reverse the polarity of standard thinking on this topic, and ask how it is possible that computation, natural and artificial, might be based on cognition and not (...) the other way around. (shrink)