Computationalist theories of mind require brain symbols, that is, neural events that represent kinds or instances of kinds. Standard models of computation require multiple inscriptions of symbols with the same representational content. The satisfaction of two conditions makes it easy to see how this requirement is met in computers, but we have no reason to think that these conditions are satisfied in the brain. Thus, if we wish to give computationalist explanations of human cognition, without committing ourselvesa priori to a (...) strong and unsupported claim in neuroscience, we must first either explain how we can provide multiple brain symbols with the same content, or explain how we can abandon standard models of computation. It is argued that both of these alternatives require us to explain the execution of complex tasks that have a cognition-like structure. Circularity or regress are thus threatened, unless noncomputationalist principles can provide the required explanations. But in the latter case, we do not know that noncomputationalist principles might not bear most of the weight of explaining cognition. Four possible types of computationalist theory are discussed; none appears to provide a promising solution to the problem. Thus, despite known difficulties in noncomputationalist investigations, we have every reason to pursue the search for noncomputationalist principles in cognitive theory. (shrink)