This paper explores a line of argument against the classical paradigm in cognitive science that is based upon properties of non-linear dynamical systems, especially in their chaotic and near-chaotic behavior. Systems of this kind are capable of generating information-rich macro behavior that could be useful to cognition. I argue that a brain operating at the edge of chaos could generate high-complexity cognition in this way. If this hypothesis is correct, then the symbolic processing methodology in cognitive science faces serious obstacles. (...) A symbolic description of the mind will be extremely difficult, and even if it is achieved to some approximation, there will still be reasons for rejecting the hypothesis that the brain is in fact a symbolic processor. (shrink)