[2] Sentiments such as these run quite deeply throughout much of cognitive science, and those advocating studying qualitative experience in an information processing paradigm are generally viewed with suspicion. In an effort to give these sentiments a principled foundation, Tim Maudlin (1989) argues that the impossibility of any computationalist theory of consciousness follows more or less directly from three very simple principles of computationalism. If correct, this would indeed be a significant result, for then the issue of how to understand consciousness within an information processing framework would be laid to rest. However, I believe that Maudlin errs in his argument. I find the error instructive because understanding it helps to clarify an important distinction in computational theory.

[3] Maudlin argues that a computational theory of consciousness is in principle impossible. In response, I suggest that Maudlin misunderstands the difference between an algorithm for computing some function and the actual computations themselves. This distinction is important because it helps clarify the significance of supervenience in theories of the mind.

[5] Generally, computationalists adhere to a stricter form of
supervenience, a version restricted by the additional dimension of
time. Mental events or episodes supervene on *concurrent*
brain events or processes. Any computational theory of consciousness
then must hold that two identical physical systems engaged in
precisely the same activity over time would support the same
phenomenal experiences through that time. A materialist would hold
that the occurance or emergence of a conscious state must depend
completely upon the physical changes in the system that instantiates
those states at the time of the experience. Thus, only the motion of
the system at that time can be relevant to the conscious state. This
more restricted principle tells us that if we introduce a causally and
physically inert object into the system, the same physical changes
would still support the same conscious state.

[6] Maudlin's second fundamental principle of computationalism concerns matters we have already hinted at above, that the important level of organization for understanding cognition is the level which does our information processing. We can understand this level in terms of a machine table for a Turing machine which describes all possible connections among the internal states of a machine and their various input and output mechanisms. The advantage of this description is that it is very precise. We can determine by straightforward analysis exactly what a machine table looks like once we have been given the internal states and the proper operating parameters. We gain this predictive precision, of course, at the expense of a machine table's descriptive paucity. As already alluded to above, this sort of computational description specifies no underlying physical mechanisms. A computational description of consciousness would therefore assume that phenomenal experiences require only that the correct program is executed by an appropriate machine, for consciousness would occur whenever that program is being run.

[7] Maudlin holds that these two principles, plus the third condition that consciousness requires a nontrivial computation, are mutually inconsistent, and he concludes that a computational theory of consciousness would not be possible. He illustrates his point using a very simple device made out of pipes, tanks, water, and a hose. A computation is simulated in this machine when a hose squirting water is attached to an apparatus and run by a series of tanks. This hose apparatus can either (1) fill empty tanks with squirting water, (2) empty full ones by knocking out their stoppers which protrude from the bottom, or (3) do nothing to tanks that lack a protruding stopper and are surrounded by a shield which blocks the incoming stream of water. In this sort of machine, a computation then amounts to any attempt by the armature to change the level of the water in some tank. The question before us is whether this simple device could instantiate consciousness, despite the fact that it could instantiate any computation we choose.

[8] Maudlin maintains that even though this machine could compute any
input-output pair, the hose apparatus alone could not instantiate any
actual *program* since what it does is completely unresponsive
to any of the "data" stored at the tank addresses.{1} If we had to define some algorithm that it
is executing, we would have to say that it is "computing" a constant
function since it gives the same "output" (squirting water),
regardless of "input" (a stoppered, unstoppered, or shielded tank).
Now such a simple algorithm or program could not support a conscious
state, for otherwise it would go against the third principle, that
only a nontrivial program can simulate consciousness.

[9] What would we have to do to our device such that we would conclude
that it no longer computes a trivial function? We would have to
arrange matters so that the machine could give a different output were
it to receive a different input. That is, we need to arrange matters
so that the machine would not always give the same output for any
input set; it would just give the same output for the
*particular* input set that it happens to have received in the
case just sketched. In other words, we need to redesign our machine
so that it could support counterfactual conditions. So let us add to
our original machine additional tanks with floats, and chains
connecting the stoppers, and other similar gizmos and gadgets, so that
we could say the hose apparatus would counterfactually behave
differently, given different initial conditions (even though it
actually never does).

[10] Notice that now we should conclude that it is actually calculating a more complex function, even though we could not make this inference just using the input-ouput pairs it actually produces.

[11] Nevertheless, we still would have a problem. The supervenience
thesis tells us that any phenomenal experience must supervene on the
physical motion that instantiates the computation. Hence, in
Maudlin's example of a consciousness machine, the phenomenal
experiences must supervene just on the activity of the hose apparatus,
and possibly the water, since that is all the activity that there is.
The tanks and whatnot added to make the program nontrivial are
irrelevant for supervenience, since nothing *actually* happens
to or with them. However, without them we are prevented from saying
that the hose is performing some nontrivial calculation and from
saying that consciousness (the alleged product or by- product of a
series of computation) supervenes on its activity alone. In sum, a
computationalist is committed to saying that the system with the hose
moving and squirting water, but without the extra stuff being hooked
up, *cannot* be conscious, yet the system with the hose moving
and with the extra tanks *could* be conscious. The actual
physical movements in the two systems are the same, regardless of
whether the extra tanks are there, so the two claims contradict the
principle of supervenience. That is, the physical motion is the same
in the two machines (even though the parts of the machines that do not
move differ) and only that physical motion is important for
supervenience. However, only one of the machines is conscious and
ipso facto has phenomenal states, so whatever consciousness is cannot
be captured just in the physical computations of the system. As
Maudlin writes, "the supervenience space of [the system's] ...
computational description, indeed whether [it] is computing at all,
depends vitally on the counterfactuals that the idle machinery
supports. Hence, [its] conscious phenomenal states cannot derive from
[its] computational structure" (423). Therefore, he concludes, a
computational theory of consciousness is not possible.

[13] In order to maintain that the system is actually running the multiplication program, and not some other algorithm which looks something like multiplication under certain circumstances, we have to ensure that the program supports counterfactuals such that, given any two positive numbers as input, the machine would in fact multiply them together. Now, we could arrange the input sets such that all this program actually got to multiply together were zero and some positive integer, so that it looked as though the program were actually calculating a constant function. It would appear that, regardless of the input, the machine would always spit out zero as output, though counterfactually it does behave quite differently.

[14] This multiplication program could be instantiated on any number
of physical systems, just like a consciousness program could. We
could instantiate it, like Maudlin's example, in a system of water,
tanks, stoppers, and a hose. If we assume the level of water in each
tank represents a natural number (and an empty tank denotes zero),
then given the input set mentioned above, all our hose apparatus would
do is knock out stoppers. For in order for our machine to multiply
*these particular* numbers together, all we would need to do is
to arrange matters so that the system gives the same output,
regardless of the input chosen from our input set.

[15] Now, were we to stumble upon such a machine exhibiting such an input-output set, we might be tempted to say that this system is calculating a constant function, for all that is actually occurring in this instance is that a series of tanks -- each filled to a different level with water -- have their protruding stoppers knocked out by a hose apparatus. Moreover, we could claim that the apparent "constant function" supervenes on the physical activity of the machine alone.

[16] However, if we want to maintain that the system is actually
running the multiplication *program*, and not just some
constant function, then we would have to attach different sorts of
tanks with floats and such to our machine in order to guarantee that,
regardless of the inputs the system might receive, it could still
multiply the water levels together. Now, by hypothesis, our input set
is arranged such that the machine will in fact only multiply natural
numbers by zero. Hence, these additional constructions are causally
and physically inert. Nevertheless, they are required in order for us
to say that the machine truly instantiates a program that could
multiply any two natural numbers together. Notice that since the
extra apparatus is inert in this instantiation -- just as in Maudlin's
case -- we are prevented from saying that the actual multiplication
processing supervenes over the additional stuff.

[17] We seem now to be in the same situation as in Maudlin's
consciousness program. The additional tanks are irrelevant for
supervenience, since nothing happens to or with them, but without
them, we are prevented from saying that the hose is performing some
nontrivial calculation and from saying that multiplicative states
supervene on its activity alone. According to this Maudlin-style
argument, then, a computationalist is committed to saying that the
system with the hose moving, but without the extra tanks being hooked
up, *cannot* be performing multiplication, and the system with
the hose moving and with the extra tanks attached *could*
perform multiplication. As before, the physical activity is still the
same, regardless of whether the extra tanks are there, so the two
claims must contradict the principle of supervenience.

[18] Do we now want to conclude that a computational program (or theory) of multiplication is not possible? I would scarcely think so.{2}

[19] What has gone wrong with Maudlin's example and discussion then?
I believe that what Maudlin glosses over is that the actual set of
input-output pairs used, which is what supervenes over the physical
activity, is not the same thing as the algorithm or program of which
the input-output set comprises one instance. The *actual*
computation space, which makes up one relata of the supervenience
relation, is not equivalent to the *theoretical* computational
domain a program operates over.

[20] Supervenience marks a relationship between a *current* and
*particular* calculation (or whatever) and *concurrent*
and *particular* physical activity. However, *running a
program* is an event which extends over not only current and
particular calculations and concurrent and particular physical
activity, but also has information-theoretic ties with possible
calculations and unrealized physical activity. As suggested above,
these ties are needed to eliminate alternative interpretations of the
ongoing calculations.

[21] What Maudlin does notice is that even if the objects in the computational space are already specified, unless we have a complete machine table -- that is, unless we know all the counterfactual alternatives -- the machine's actual behavior is ambiguous. For the only way to eliminate the constant function interpretation in the examples above is by understanding how the machine would behave given a different input set. (Of course, we have to specify the program prior to pinpointing any particular computation just because the program is what properly individuates the computational space for us. As Maudlin remarks, "A particular physical state only becomes interpretable as a machine state of a system ... in virtue of standing in the right counterfactual or subjunctive relations to ... to the whole constellation of other states in the machine table" (419).) What Maudlin's examples show is that there is a double indeterminacy in any computational theory. Once we somehow overcome the general problem of semantic interpretation of the objects in the computational domain, we are still left with the difficulty of specifying the actual function computed. To solve this second problem, we must know more than the actual behavior of the system -- we have to understand how the system would behave were it to receive different inputs.

[22] However, these facts do not mean that for the instances we
discussed these sets of actual input-output pairs so defined could not
be a subset of the input-output pairs for more than one program nor
that these sets do not supervene over the actual physical activity.
These examples pull apart the domain entailed by the supervenience
relation from the domain needed to specify a computational theory and
show that the relata of supervenience form a subset of the
computational universe. Multiplying a set of numbers together does
supervene on the physical activity which underwrites those particular
computations, but running a multiplication program is a different
beast entirely, and it extends over more than what actually changes in
the world. Thus, it is entirely consistent to say that while the act
of multiplying supervenes on some physical activity, running the
multiplication program does *not* supervene on the same
activity.

[23] Any computational theory of consciousness would work in the same
way. To have a particular conscious state at a particular time does
supervene on concurrent brain activity, for exhibiting any particular
phenomenal state just is exhibiting the appropriate input-output pair
(just as multiplying two particular numbers together just is
exhibiting the appropriate input-output pair) -- even though that
input-output pair is perfectly consistant with any number of different
algorithms. For a materialist, this just means that to have any
particular conscious state in any particular brain just is to have the
appropriate neurons firing in the correct order (or whatever).
However, to say something is a conscious *system* (or is
running a consciousness program) requires more than a set of
input-output pairs. It require more than the particular neurons
firing (or whatever). It requires the possibility for other sorts of
states of consciousness than those that actually obtain, given
different inputs.

[24] A computational theory of consciousness remains possible. (At least, Maudlin's arguments against one do not work.)

[26] This conclusion should be intuitively plausible for materialists (at least as intuitively plausible as any claim about what consciousness amounts to). For example, assume that for a moment the wind blew the leaves in my backyard into the right configuration such that they (for a moment) mimicked my brain state upon awaking this morning. Surely, we would have to maintain that the leaves, for a moment, instantiated a phenomenal state, just because my brain state this morning had a phenomenal quality. And these phenomenal states supervene on both my brain state and the leaves' state. But we would not want to maintain that the leaves blowing about in my backyard are conscious, just because under different conditions (e.g., a moment later) they do not instantiate anyone's brain state.

[27] To summarize: prior acceptance of materialism entails that mental
states supervene on brain states such that no (relevant) change in our
brain states could occur without also altering the corresponding
mental state. This supervenience shows itself when we study
particular mental or brain phenomenon. However, in detailing a
functional *program* designed to explain consciousness, we
should not expect the entire set of possible input-output pairs to
supervene over past and future physical states since the function or
functions our cognitive systems compute must include counterfactual
events that the system may never instantiate.

[28] Thus, any computational theory will always extend beyond any evidence we could gather concerning particular phenomenal states, and the referents of the predicates in the theories will be determined by more than any particular set of observational data. But these underdeterminacy conditions are no different than those for any other computational/functional theory.{3}

{2} I am assuming here (fairly uncontroversially, I believe) that (i) computational theories are in principle possible, and that (ii) mathematics, if anything, is computational, and so should be implementable on an appropriate computational machine. Return

{3} I would like to thank Bruce Glymour and an anonymous referee for their comments on earlier drafts of this paper. Return

ISSN 1071-5800

Copyright 1993