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

For example, mushrooms that were assigned to Cluster 2 had an odour that
was either almond or anise, which is represented by the network’s five hidden units
adopting a particular vector of activities. These activities serve as a condition that
causes the network to assert that the mushroom is edible.
By interpreting a hidden unit vector in terms of condition features that are
prerequisites to network responses, Dawson et al. (2000) discovered an amazing
relationship between the clusters and the set of productions in Table 4-5. They
determined that each distinct class of hidden unit activities (i.e., each cluster) corresponded
to one, and only one, of the productions listed in the table. This mapping
is provided in the last column of Table 4-5. In other words, when one describes the
network as generating a response because its hidden units are in one state of activity,
one can translate this into the claim that the network is executing a particular
production. This shows that the extra output learning translated the classical algorithm
into a network model.
The translation of a network into a production system, or vice versa, is an
example of new wave reductionism (Bickle, 1996; Endicott, 1998). In new wave
reductionism, one does not reduce a secondary theory directly to a primary theory.
Instead, one takes the primary theory and constructs from it a structure that is
analogous to the secondary theory, but which is created in the vocabulary of the
primary theory. Theory reduction involves constructing a mapping between the
secondary theory and its image constructed from the primary theory. “The older
theory, accordingly, is never deduced; it is just the target of a relevantly adequate
mimicry” (Churchland, 1985, p. 10).
Dawson et al.’s (2000) interpretation is a new wave intertheoretic reduction
because the production system of Table 4-5 represents the intermediate structure
that is analogous to the decision tree of Table 4-4. “Adequate mimicry” was established
by mapping different classes of hidden unit states to the execution of particular
productions. In turn, there is a direct mapping from any of the productions back
to the decision tree algorithm. Dawson et al. concluded that they had provided an
exact translation of a classical algorithm into a network of value units.
The relationship between hidden unit activities and productions in Dawson
et al.’s (2000) mushroom network is in essence an example of equivalence between
symbolic and subsymbolic accounts. This implies that one cannot assume that classical
models and connectionist networks are fundamentally different at the algorithmic
level, because one type of model can be translated into the other. It is possible
to have a classical model that is exactly equivalent to a PDP network.
This result provides very strong support for the position proposed by Vera and
Simon (1993). The detailed analysis provided by Dawson et al. (2000) permitted
them to make claims of the type “Network State x is equivalent to Production y.”
Of course, this one result cannot by itself validate Vera and Simon’s argument. For
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