A nonclassical framework for cognitive science

David Marr provided a useful framework for theorizing about cognition within classical, AI-style cognitive science, in terms of three levels of description: the levels of (i) cognitive function, (ii) algorithm and (iii) physical implementation. We generalize this framework: (i) cognitive state transitions, (ii) mathematical/functional design and (iii) physical implementation or realization. Specifying the middle, design level to be the theory of dynamical systems yields a nonclassical, alternative framework that suits (but is not committed to) connectionism. We consider how a brain's (or a network's) being a dynamical system might be the key both to its realizing various essential features of cognition - productivity, systematicity, structure-sensitive processing, syntax - and also to a non-classical solution of (frame-type) problems plaguing classical cognitive science.