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

particular formal system or collection of systems. In other words,
since mental operations are held to be the operations of formal
systems, mental operations are held to be computations. So to have a
mind, claims the computationalist, just is to be engaged in certain
computational processes.
Computationalism is clearly a species of functionalism. The func-
tionalist holds that states are mental solely by virtue of their charac-
teristic functions in mediating relations between inputs, outputs and
other mental states. Computationalism is simply a way of fleshing out
these mediating relations – the relations in question are held to be
computations.
Computationalism is not the view that the operations of formal
systems per se are mental operations. That is, it is not the view that
instantiating any formal system at all is su
fficient for having a mind.
This clearly overcommits the computationalist as it would require
them to attribute mentality to all manner of artefacts – thermostats,
tra
ffic lights, handheld electronic games – in a patently ludicrous
fashion.
So in fairness to the computationalists, let’s be clear that they are
committed only to the view that instantiating a particular formal
system – let’s call it [MIND] – is su
fficient for having a mind.
This is rather a strong formulation of computationalism. A compu-
tationalist might hold that there is no single overarching formal system
to be identified but, rather, that mentality is a function of some number
of distinct algorithms. I want to advance a particular understanding of
mentality – which I take to be fairly intuitive – which assumes a single
overarching formal system, so I shall continue to work with this strong
thesis until further notice. Do be aware though that the version of the
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theory I am describing is not the only story available to a computa-
tionalist. If, however, a strong version of the theory turns out to be
defensible then, a fortiori, any weaker version is defensible.
The computationalist, then, is not committed to the view that the
operations of your personal computer are mental operations. Nor is
she committed to the view that very powerful computational devices,
such as supercomputers, have minds. She is committed only to
holding that should some substrate run the program [MIND] then
that substrate thereby has a mind.
I have referred to [MIND] in three di
fferent ways now – as a formal
system, as an algorithm and as a register machine program. Recall
from Chapter 9 that by the Church/Turing thesis, these three are
equivalent ways of speaking. If [MIND] is an algorithm, it can be
implemented by a register machine program (which just is a deter-
ministic formal system).
Let’s clear up another possible misconception of the theory. The
computationalist claim di
ffers in another important way from the
view that personal computers can or do have minds. Modern digital
computers, as we saw in the last chapter, are instantiated universal
machines. The computationalist is not claiming that to have a mind is
to instantiate a universal machine. She is claiming that to have a mind
is to instantiate a particular register machine – namely [MIND].
We need to be careful on a couple of points here. Firstly, we need
to appreciate that, while digital computers, as we know them, are
instantiated universal machines, they are imperfectly instantiated.
Universal machines are theoretical devices whose resources, while
finite by stipulation, are otherwise unlimited. Instantiated universal
machines are physical devices which are bound by physical con-
straints. So while universal machines can in principle run any program
(a fortiori can run [MIND]), instantiated universal machines are
limited in practice by their physical constraints and, as such, may not
have su
fficient computational resources at the hardware level to run
certain programs, such as [MIND].
So there is a sense in which it is not quite correct to say that modern
digital computers are instantiated universal machines, as there may
be programs beyond their computational resources. Digital comput-
ers, as we know them, are approximations to universal machines.
Successive generations of computational hardware provide closer and
closer approximations as they provide greater and greater computa-
tional resources.
Even perfectly instantiating a universal machine in a substrate
would not in itself be su
fficient for that substrate to have a mind. The
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substrate must then run the right program, since having a mind, says
the computationalist, is having the program [MIND] in operation.
We can give a fair measure of practical computational power along
two parameters – storage space and processing speed. A given
program’s requirements can be said to exceed the practical compu-
tational power of a given device if its requirements exceed either the
storage capacity or the speed of computation of the device (or
both).
So while the computationalist is committed to holding that any
universal machine (without constraints) can run [MIND] – and
would thereby have a mind – she is not ipso facto committed to
holding that any existent digital computer could have a mind. A com-
putationalist might hold that the requirements of [MIND] exceed the
practical computational power of (some or all) currently available
(non-biological) computational devices.
Consequently a computationalist need not hold that your personal
computer could have a mind. In all likelihood they will hold that it
could not by virtue of its physical limitations. A computationalist will
hold to the view that the human brain provides the biological com-
putational hardware for implementing [MIND] in humans. Given
what we know of the extraordinary storage capacity and speed of
operation of the human brain, the computationalist is likely to argue
that any non-biological computational device powerful enough to run
[MIND] must have (at least approximately) the storage capacity and
speed of operation of human brains. Digital computers, as powerful
as they are becoming, are still not even close.
There is one final point of possible confusion to clear up before we
move on. Recall from section 7.1 that for a procedure to be e
ffective,
it must, in principle, be able to be carried out, given su
fficient time, by
a human using only piles of stones (or paper and pencil) and bring-
ing no understanding to the task. The operations of universal
machines are entirely e
ffective, so one of the things a human mind can
do is approximate a universal machine (albeit with considerable con-
straints) by actively working stepwise through the operations of any
given register machine program. Consequently, one of the things that
a device running [MIND] must be able to do is approximate a uni-
versal machine (in at least the same fairly weak fashion in which
humans can).
This does not, however, mean that approximating a universal
machine is su
fficient for having a mind. Quite the opposite. It means
that irrespective of the status of computationalism, having a mind is
su
fficient for (very weakly) approximating a universal machine.
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Let’s recap the points of possible confusion we have covered so far.
Firstly, a computationalist is not committed to the view that any
computation is a mental operation. They are committed to the view
that particular computations – those which are the operations of
[MIND] – are mental operations.
Secondly, a computationalist is not committed to the view that
instantiating a universal machine is su
fficient for having a mind. They
are committed to the view that a perfectly instantiated (unconstrained)
universal machine has the capacity to have a mind. Since one of the
things a mind can do is approximate a universal machine, the compu-
tationalist is also committed to the ability of any computational device
running [MIND] to weakly approximate a universal machine.
Finally, a computationalist is not committed to the view that any
given computational device could instantiate [MIND], as the program
may have requirements which exceed the practical computational
resources of the given device. Consequently, a computationalist can
happily deny that a device such as your personal computer – an
approximation to a universal machine – could ever have a mind. The
computationalist is committed, however, to holding that any physical
device with su
fficient practical computational power to run [MIND]
does have the capacity to have a mind. Precisely what computational
resources are required by [MIND] is a matter for empirical discovery.
Now that we have carefully identified several possible misconcep-
tions of computationalism, we can see that certain arguments against
the theory which trade on these misconceptions are unsound.
For instance, the following argument should clearly not be licensed:
P1
Computationalism says that all mental operations are
computations.
P2
My personal computer performs computations.


Computationalism says that the operations of my personal
computer are mental operations.
P3
But my personal computer clearly does not have a mind.


Computationalism is false.
The premises P1 – P3 are not in dispute. P2 and P3 are clearly true
and computationalism does make the claim attributed to it in P1.
The argument goes wrong in the transition from P1 and P2 to the
interim conclusion. The inference is not truth-preserving; the interim
conclusion is, in fact, false.
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We can prove that the inference is not truth-preserving by giving
counter-examples to the form of inference employed, since truth-
preservation is a matter of logical form (more on this in Chapter 15).
The inference is of the logical form: C claims that everything which is
A is B; x is B; therefore C claims x is A. Instantiate A as ‘in Melbourne’
and B as ‘in Australia’ (and anything you like for C and x) and we have
a clear counter-example to the validity of this argument form – a
demonstration that the truth of the premises does not guarantee the
truth of the conclusion.
We can clearly see though how a misinterpretation of P1 could lead
us to infer the interim conclusion, given P2. Computationalism does
claim that all mental operations are computations but the converse,
as we have seen, does not hold. Consequently, the fact that something
performs computations does not guarantee that it performs mental
operations. Were we to mistakenly read P1 as its converse (that only
mental operations are computations – which is to say that all compu-
tations are mental operations), we would be led, erroneously, to
believe that the above argument instances a valid form.