Connectionist models purport to model cognitive neuropsychology by means of adaptive linear algebra applied to point neurons. Cognitive processing by neuronal flows is offered as a viable alternative. Finally, neural nets fail Hempel's test of empirical and systematic import. Yet this trifle is the key to a real difficulty for the connectionist approach.
Connectionist models are asymptotic.
They converge as time t approaches infinity. This may hold no problem for a digital computer operating at microsecond rates, but it is a real problem for a model of neuropsychological processes that must be realized in neurobiological real-time, something of the order of a few hundred milliseconds at most, if indeed it is to represent a cognitive process. This may seem to have more significance for mathematics than cognitive theory, but if a full-fledged computational model for cognition is the goal of connectionism, then, lacking the symmetric difference, connectionism falls short. This lacuna further affects the topological structure of connectionism in a critical way. The connectionist model purports to provide a realization of the nodes and edges of information processing psychology.