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

were provided earlier in this chapter, in the discussion of carving pattern spaces into
decision regions and the determination that output unit activities could be interpreted
as being conditional probabilities.
That computational analysis is possible for both connectionist and classical
cognitive science highlights one similarity between these two approaches. The
results of some computational analyses, though, reveal a more striking similarity.
One debate in the literature has concerned whether the associationist nature
of artificial neural networks limits their computational power, to the extent that
they are not appropriate for cognitive science. For instance, there has been considerable
debate about whether PDP networks demonstrate appropriate systematicity
and componentiality (Fodor & McLaughlin, 1990; Fodor & Pylyshyn, 1988;
Hadley, 1994a, 1994b, 1997; Hadley & Hayward, 1997), two characteristics important
for the use of recursion in classical models. However, beginning with the mathematical
analyses of Warren McCulloch (McCulloch & Pitts, 1943) and continuing
with modern computational analyses (Girosi & Poggio, 1990; Hartman, Keeler, &
Kowalski, 1989; Lippmann, 1989; McCulloch & Pitts, 1943; Moody & Darken, 1989;
Poggio & Girosi, 1990; Renals, 1989; Siegelmann, 1999; Siegelmann & Sontag, 1991),
we have seen that artificial neural networks belong to the class of universal machines.
Classical and connectionist cognitive science are not distinguishable at the computational
level of analysis (Dawson, 1998, 2009).
Let us now turn to the next level of analysis, the algorithmic level. For classical
cognitive science, the algorithmic level involves detailing the specific information
processing steps that are involved in solving a problem. In general, this almost always
involves analyzing behaving systems in order to determine how representations are
being manipulated, an approach typified by examining human problem solving
with the use of protocol analysis (Ericsson & Simon, 1984; Newell & Simon, 1972).
Algorithmic-level analyses for connectionists also involve analyzing the internal
structure of intact systems—trained networks—in order to determine how they
mediate stimulus-response regularities. We have seen examples of a variety of techniques
that can and have been used to uncover the representations that are hidden
within network structures, and which permit networks to perform desired inputoutput
mappings. Some of these representations, such as coarse codes, look like
alternatives to classical representations. Thus one of classical cognitive science’s
contributions may be to permit new kinds of representations to be discovered and
explored.
Nevertheless, algorithmic-level analyses also reveal further similarities between
connectionist and classical cognitive science. While these two approaches may propose
different kinds of representations, they still are both representational. There
is no principled difference between the classical sandwich and the connectionist
sandwich (Calvo & Gomila, 2008). Furthermore, it is not even guaranteed that the
Elements of Connectionist Cognitive Science 201