The importance of the Stability Problem in neurocomputing is discussed, as well as the need for the study of infinite networks. Stability must be the key ingredient in the solution of a problem by a neural network without external intervention. Infinite discrete networks seem to be the proper objects of study for a theory of neural computability which aims at characterizing problems solvable, in principle, by a neural network. Precise definitions of such problems and their solutions are given. Some consequences (...) are explored, in particular, the neural unsolvability of the Stability Problem for neural networks. (shrink)

The commentary is presented in three sections. Section 1 presents a brief summary of the main theses in Cummins' paper. In section 2, I argue that this analysis is not peculiar to cognition, and that in fact, a similar, more general analysis has been given [3] in fundamental areas of inquiry, hitherto independent of cognitive science. Finally, in section 3, it is argued that, if this general form of Cummins' analysis is correct, it calls for a profound re‐evaluation of our (...) conception of science. (shrink)