Mind, Body, World- Foundations of Cognitive Science, 2013a

sense that they are digital: consistent with the neural all-or-none law (Levitan &
Kaczmarek, 1991; McCulloch & Pitts, 1943), as the rule either executes or does not.
In contrast, the continuous values of the activation functions used in connectionist
networks permit knowledge to be applied to varying degrees. From this perspective,
networks are analog, and are not digital.
Again, however, this context also does not successfully provide a mark of the
classical. First, one consequence of Church’s thesis and the universal machine is
that digital and analogical devices are functionally equivalent, in the sense that
one kind of computer can simulate the other (Rubel, 1989). Second, connectionist
models themselves can be interpreted as being either digital or analog in nature,
depending upon task demands. For instance, when a network is trained to either
respond or not, as in pattern classification (Lippmann, 1989) or in the simulation of
animal learning (Dawson, 2008), output unit activation is treated as being digital.
However, when one is interested in solving a problem in which continuous values
are required, as in function approximation (Hornik, Stinchcombe, & White, 1989;
Kremer, 1995; Medler & Dawson, 1994) or in probability matching (Dawson et al.,
2009), the same output unit activation function is treated as being analog in nature.
In conclusion, though the notion of explicit rules has been proposed to distinguish
classical models from other kinds of architectures, a more careful consideration
suggests that this approach is flawed. Our analysis suggests, however, that the
use of explicit rules does not appear to be a reliable mark of the classical. Regardless
of how the notion of explicit rules is defined, it appears that classical architectures
do not use such rules exclusively, and it also appears that such rules need to be part
of connectionist models of cognition.
7.8 The Cognitive Vocabulary
The goal of cognitive science is to explain cognitive phenomena. One approach to
such explanation is to generate a set of laws or principles that capture the regularities
that are exhibited by members that belong to a particular class. Once it is
determined that some new system belongs to a class, then it is expected that the
principles known to govern that class will also apply to the new system. In this
sense, the laws governing a class capture generalizations (Pylyshyn, 1984).
The problem that faced cognitive science in its infancy was that the classes of
interest, and the laws that captured generalizations about their members, depended
upon which level of analysis was adopted (Marr, 1982). For instance, at a physical
level of investigation, electromechanical and digital computers do not belong to the
same class. However, at a more abstract level of investigation (e.g., at the architectural
level described in Chapter 2), these two very different types of physical devices belong
to the same class, because their components are functionally equivalent: “Many of
348 Chapter 7