Connectionism, Analogicity and Mental Content
automatically, without human intervention. The first step in Turing’s imagining, however, was
to consider not how such a machine could be constructed, but what such a machine had to do.
Turing asked: what, from an objective point of view, occurs when we perform a mathematical
calculation? His answer was: we write a sequence of symbols on a piece of paper. But not just
any old sequence of symbols. Our behaviour constitutes “computing” only when the later
symbols in the sequence are systematically related to the earlier ones, the precise relation
depending on the kind of mathematical operation being performed. For example, in the case of a
simple arithmetical calculation, such as adding two numbers together, the third symbol we write
refers to a number that is the sum of the two numbers denoted by the first and second symbols
we have written. Seen from this perspective, a computation is a process that produces a
mathematically coherent sequence of symbols, where this is a sequence in which later symbols bear
comprehensible mathematical relations to earlier ones. This is the general idea about
computation that is embodied in Turing’s work.
That computational processes are mathematically coherent sequences of symbols is not
an idea that originated with Turing, of course. This is just Turing’s analysis of calculational
procedures with which we are all familiar. The idea that did originate with Turing is the more
specific one about how to construct a machine that performs such computations, that
automatically generates such a sequence of symbols. That is, Turing’s great achievement wasn’t
that he told us what computational processes are; his achievement was to show us one way that
these processes could be mechanised (more about which in the next section).
Distinguishing between these two ideas is important, for the following reason. Once it is
clear that the conception of computation that Turing employed in his work is quite distinct from
his more specific idea as to how computational processes could be mechanised, it is possible to
investigate the former independently of the latter (something that is sorely lacking in most
contemporary discussions in this area). When this is done, it quickly becomes apparent that even
this general conception of computation is too restrictive, and can be liberalised along two
dimensions: one concerning the entities over which computational processes are defined; the
other the systematic relations that obtain between these entities.
First, there seems to be no reason, even in the context of mathematical calculation, to
restrict computation to sequences of symbols. Geometric proofs, for example, use a combination
of symbols and nonsymbolic diagrams. And when we step outside the field of mathematics to
consider the vast range of calculations we routinely perform in other domains (remembering all
the while that it was to our calculational capacities that Turing looked for the conception of
computation he employed), it is obvious that our deliberations engage all manner of
nonsymbolic representational entities (such as when we draw a picture to determine whether A
is taller than C when you are told that B is taller than C but shorter than A),. What seems
essential to computation, therefore, is not that it implicates symbols as such, but that
representational vehicles of some kind are employed, be these vehicles symbolic or nonsymbolic.
Second, there seems to be no reason to restrict the systematic relations between these
representational vehicles to those characterisable in mathematical terms. The computational
process at the centre of Fodor’s discussion of Turing, for example, is deductive inference, where
the systematic relation that obtains between later symbols (the conclusion) and earlier ones (the
premises) is truth preservation. And there are other kinds of representational relations that are
exploited in computation. Consider, as another example, the calculation we perform when using
a street map to determine the best route across a city. One of the crucial things in this case, as we
work out a route by tracing our finger across the map, is that the relations between the map’s
representational vehicles (the black lines that represent streets, the red dots that represent traffic
lights, and so forth) accurately reflect the relations between the map’s representational objects
(the streets, the traffic lights, and so on). In the end, perhaps the best we can say is that the