Minds and Computers : An Introduction to the Philosophy of Artificial Intelligence

particular instantiation of the system. For two systems to be isomor-
phic to each other, they must be formally equivalent. This does not
mean, however, that every isomorphism of a formal system must
assign all and only the same values to variables. In fact, this will very
rarely be the case.
When doing Exercise 8.1, you were instantiating various isomor-
phisms of the formal system [ADD] in order to ascertain the function
which the program computes. In each case, you assigned di
fferent
values to the initial input variables.
Further, if we take two isomorphisms of [ADD], both of which
were assigned identical initial values, and then compare the contents
of registers at di
fferent stages in their operations, we will see different
values being held in each register. The operations of each system,
however, are still formally equivalent – they are still isomorphisms of
[ADD].
Now consider the system [MIND]. This must be an extraordinarily
complex system with very, very many variables. Presumably, every
instantiation of [MIND] is bound to be in a distinct stage of oper-
ation. Presumably also, every instantiation of [MIND] will begin with
(albeit perhaps slightly) distinct assignments of values to variables.
Hence it should come as no surprise that any two given instantia-
tions of [MIND] will vary greatly in terms of the values which are cur-
rently assigned to variables of the system.
It seems, at least prima facie, that beliefs and desires play the same
functional role in all minds. That is not to say that my belief that
(whatever) performs exactly the same functional role in my mental life
as does your belief of the same content in your mental life. Rather, it
is to say that beliefs, qua beliefs, have a functional role in deliberation,
planning, motivation to action and so on.
Because beliefs and desires interact in a highly complex fashion in
these mental functions, we should not expect that my belief that
(whatever) will result in the same action as your belief of the same
content. We should expect, however, that, qua belief, both of our
beliefs function in deliberation, planning, etc.
Now, a computationalist is likely to argue that the content of
beliefs, desires and the like – that which they are about – is to be under-
stood in terms of the assigning of values to variables. In the system
[ADD], the content of R
2
(whatever it might be) always functions
in the same way – it is the value which is decremented while we
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increment R
1
. Similarly, says the computationalist, the content of a
‘belief-box’ in [MIND] will always function in the same way, even
though its content (what the belief is about) might be markedly
di
fferent in different instantiations of the system or at different stages
in the operation of the same system.
Consequently, a computationalist can hold that minds are isomor-
phisms (functional equivalents) of [MIND], yet still happily concede
that all minds will vary, in small measure or large, in terms of the con-
tents of beliefs, desires and the like. They can also readily explain vari-
ation among isomorphisms of [MIND] in terms of the particular
actions which are partially determined by beliefs, desires, etc. with