Connectionism, Analogicity and Mental Content
Consider a standard example of an analog computer: a scale model of a proposed
building, onto which light is shone in order to determine shadow patterns. In what sense is this
device mechanistically processing representations in a semantically coherent fashion? First, a
number of its component parts are representational: the light shone on the model represents
sunlight, the model building represents a planned real building, and the shadow patterns
generated represent the shadow patterns that would be produced by sunlight shining on the
actual building. Secondly, these representational vehicles enter into causal relations with one
another: the light shone on the model building causes specific kinds of shadow patterns to be
produced. Finally, and crucially, the causal relations that obtain between these representational
vehicles are semantically coherent: the content of the output representation (the shadow pattern)
is non-arbitrarily related to the contents of the input representations (the light and the model
building), in that sunlight falling at that angle on a real building of that shape would produce
that shadow pattern.
But from whence does this semantic coherence come? The operating principles in the
case of a scale model are obvious and straightforward. The model derives its computational
power from the similarities that exist between the representational elements of its material
substrate and the representational domain its computations are about. Specifically, the light
shone on the scale model behaves the same way as sunlight, and the shape of the model building
is the same as that of the proposed building. These similarities ensure that the physical relations
and hence causal dynamics of the “input” representational vehicles in the scale model (the light
and the model building) automatically track those between the objects in the represented
domain (sunlight and the proposed building), such that the “output” representational vehicle of
this analog device (the shadow pattern across the model) mirrors the behaviour of its
representational object in this domain (the shadow pattern that would occur in the real world).
While a scale model is a very simple analog computer, its operating principles exemplify
the basis of all analog computation. Baldly stated, analog computers compute by physically
manipulating “analogs” of their representational domains. A material substrate embodies an
analog of some domain when there is a structural isomorphism between them, such that
elements of the former (the representational vehicles) resemble aspects of the latter (the
representational objects).4 The resemblance relation here can come in different varieties. In the
case of the scale model, the relation is one of first order structural isomorphism, whereby the
relevant physical properties of the representational objects (sunlight, shape of the proposed
building, etc) are represented by equivalent physical properties of the representational vehicles
(the light source, the shape of the model building, etc.). But this particular requirement can be
relaxed without undermining resemblance. For example, we might suppose that certain
properties of representational objects can be represented by non-equivalent properties of
representational vehicles, as long as variations in the former are systematically mirrored by
corresponding variations in the latter. This gives us a notion of second order structural
isomorphism (see Palmer, 1978; and Shepard and Chipman, 1970). Whether the resemblance
relation is first or second order, however, its obtaining makes it possible for the material
substrate to behave in a semantically coherent fashion. That is, because its representational
vehicles resemble their representational objects, the causal relations between the former can
naturally reflect certain relations (causal or otherwise) between the latter (see Trenholme, 1994).
4 It’s important to stress the relevant isomorphism here is between representational vehicles and their objects, rather
than between the causal network of vehicles and certain relations (causal or otherwise) between their representational
objects. The latter is sometimes termed functional isomorphism (see, eg, Von Eckhardt, pp.206-14), and is another way of
construing semantically coherent processing. In all computations there is a functional isomorphism between
representational vehicles and their objects. The question, though, is how this functional isomorphism is generated. In
digital computation the isomorphism is imposed by syntactically applied rules. With analog computation, by contrast,
functional isomorphism is founded on structural isomorphism.