Computational power of cognition

The debate concerning the computational powers of the various manifestations of neural networks continues without the benefit of a common theoretical foundation. This paper addresses the question of relative computational power in five categories; the Turing machine, the digital computer, the neural network, physical systems, and the mind/brain. The explicit and implied decisions one makes when assuming an equivalence or a difference in power between these elements are discussed. Initially a motivation for the study of computational power is presented which begins with the apparent failure of the Turing test to resolve certain aspects of the mind/machine dilemma. The classical arguments concerning the capabilities and limitations of each of the five categories of computing devices are summarized in an attempt to separate the logically-valid positions from those based on emotional appeal.