I address whether neural networks perform computations in the sense of computability theory and computer science. I explicate and defend
the following theses. (1) Many neural networks compute—they perform computations. (2) Some neural networks compute in a classical way.
Ordinary digital computers, which are very large networks of logic gates, belong in this class of neural networks. (3) Other neural networks
compute in a non-classical way. (4) Yet other neural networks do not perform computations. Brains may well fall into this last class.

According to the dominant computational approach in cognitive science, cognitive agents are digital computers; according to the alternative approach, they are dynamical systems. This target article attempts to articulate and support the dynamical hypothesis. The dynamical hypothesis has two major components: the nature hypothesis (cognitive agents are dynamical systems) and the knowledge hypothesis (cognitive agents can be understood dynamically). A wide range of objections to this hypothesis can be rebutted. The conclusion is that cognitive systems may well be dynamical systems, (...) and only sustained empirical research in cognitive science will determine the extent to which that is true. (shrink)

It will always remain a remarkable phenomenon in the history of philosophy, that there was a time, when even mathematicians, who at the same time were philosophers, began to doubt, not of the accuracy of their geometrical propositions so far as they concerned space, but of their objective validity and the applicability of this concept itself, and of all its corollaries, to nature. They showed much concern whether a line in nature might not consist of physical points, and consequently that (...) true space in the object might consist of simple [discrete] parts, while the space which the geometer has in his mind [being continuous] cannot be such. (shrink)

There are different ways to present a Presidential Address to the APA; the one I have chosen is simply to report on work that I am doing right now, on work in progress. I am going to present some of my further explorations into the computational model of the mind.\**.

Cognitive theories have expressed their components using an artificial symbolic language, such as first-order predicate logic, and the atoms in such representations are non-decomposable letter strings. A neural theory merely demonstrates how to implement a classical symbol system using neurons: this is actually an argument against the importance of the neural description. The fact that symbol systems are physically instantiated in neurons becomes a mere implementational detail, since there is a direct way to translate from the symbolic description to the (...) more neurally plausible one. It might then be argued that, while the neural aspects of the theory identify how behavior arises, they are not fundamentally important for understanding that behavior. Classical symbol systems would continue to be seen as the right kinds of description for psychological processes. (shrink)