Is the brain an effective Turing machine or a finite-state machine?

A theorem presented by Hornik, Stinchcombe, and White (1989) suggested the possibility that connectionist networks could be effectively Turing machines. Levelt (1990) argued that the theorem of Hornik et al. only implies that networks are finite-state machines and are therefore not capable of generating the very unlimited productivity of symbol systems. Yet it can be argued that all real machines, including the brain, are finite-state machines. If so, no real machine actually possesses the very unlimited productivity of symbol systems. So any model of actual behaviour should capture the limitations on productivity inherent in the situation. Thus connectionist networks can be valuable models in psychology, precisely because they are finite-state machines.