Rescuing Computationalism with Platonism

In my last post I discussed some issues with identifying objectively which computations a physical system could legitimately be interpreted as instantiating. Computationalism is usually taken to be the view that all it takes to create a conscious mind is to implement the right computation, so the idea that we can't tell objectively when a computation is implemented implies either that there is no objective fact of the matter regarding when minds exist, that all minds exist (everywhere) or that no minds exist. None of these conclusions is particularly appealing!

I find the arguments discussed on the last post to be somewhat persuasive. Indeed, I had had similar concerns before becoming aware of these. What's more, I think the problem may be worse than even Putnam, Searle and Bishop have suggested.

I'm going to use variations on Searle's Chinese Room thought experiment to illustrate some of these related problems just because the image of a man manually performing a computation is one we can all picture relatively clearly.

Firstly, let's acknowledge Searle's usual conclusion, that if he is the system and he doesn't understand Chinese, then the system doesn't understand Chinese. The most promising computationalist response is that Searle's brain is actually creating two minds operating at different levels. This implies that there are at least two interpretations of Searle's brain as implementing a mind and they describe very different minds. So far so good, I suppose, but it does at least demonstrate the point that there may be many different ways to interpret a physical system as a mind and so it's wrong to assume that a physical system is identical to a mind or even that it has a one-to-one relationship with a mind. Whatever a mind is, then, it isn't quite a physical thing. Minds are not brains, in other words. If we are very strict physicalists and if we think our minds and our consciousnesses really objectively exist (as opposed to being interpreted to exist, a pattern we project onto the world like particular genes or institutions or whatever), this may be a problem.

Next, consider what happens when Searle stops executing his program and goes home to sleep for the night, mid-execution. While Searle is sleeping, does the Chinese Room mind still exist? The Chinese Room program isn't in any meaningful sense executing. It isn't really instantiated anywhere.

You could regard it as paused, a mind held in suspense. The state of the algorithm will at least be recorded physically somewhere. But what is the difference, I wonder, between such a mind and that of a potentially conscious algorithm written on paper but never executed at all? Perhaps all written algorithms are essentially computations in suspense? If that is so, then simply writing an algorithm out on paper must be enough to bring a suspended mind into existence. Whatever about whether we can tell whether a given system implements a given algorithm, it seems clear that there can be no fact of the matter about whether a physical system represents the code of an algorithm (because it is not hard to invent an encoding by which any physical artifact could represent any text), so even if the rocks around us don't host active "pixies" (see the last post if you don't get what I mean by "pixies"), they might at least host pixies in suspended animation! For reasons such as these, I don't think it is plausible to regard a paused computation as having a continuous physical existence.

So perhaps the mind doesn't exist while the computation is paused. But it doesn't seem to me that there is much of a difference between Searle pausing for the night and the necessary momentary pause between each step of Searle's calculation. Does a mind therefore flicker in and out of existence as he works? Is each new instance a new mind or the same mind revived? How could we even pin down to specific points of time when the mind exists and when it does not, when all we have to go on are steps in a computation? At any given point of time, it doesn't seem to me we can really say whether Searle is actively computing right now or whether he is in between computing steps. I don't think there is a fact of the matter about whether pausing to pick up a pen so as to make a note is actually part of the computation or not. For this reason, I don't think we can really say precisely when computing steps begin or end, because the physical actions corresponding to computational steps are not terribly well defined. If the steps of a computation don't really exist for well-defined time spans, it's hard to say how the mind can either.

So even though we may some day have an objective way of telling whether a given computation is being instantiated, we still have the problem of identifying when it is instantiated. It seems to me there is no fact of the matter in this case either.

There's another set of issues when we consider the same computation being performed in different places or at different times. Let's say Searle has a partner who performs every calculation with him to check for any error that might occur. If we regard his partner as part of the same system, then one mind is brought into existence. If we regard his partner as a parallel system, then a two minds are brought into existence. In general, it seems to me that in many cases we are free to divide up a computational system in a number of ways so that the number of copies of a mind in existence is whatever we want it to be. For instance, the electrons flowing through a computer could perhaps be divided into a thousand distinct sets, each of which parallels the computation of interest.

We might be tempted to simply adopt the rule that these are all simply part of the same computation and so the same mind. It seems most parsimonious. But what if we offset the duplication in time a little? Say Searle's partner takes the night shift and duplicates Searle's efforts from earlier in the day. Or say he is working a thousand years after Searle has already ceased his efforts. Wouldn't it seem a little weird now to regard them as part of the same computation, that one mind could be physically and temporally so widely distributed? But, again, it's perhaps not so easy to define an objective cut-off point so that we could really satisfyingly distinguish two parts of the same computation creating one mind from two distinct identical computations creating two identical minds.

So, to add to the concerns of whether and when a given mind is instantiated, we have to grapple with the question of how many times a mind is instantiated in the case of  computations we could interpret either as being duplicated or as singletons.

Obviously, I have raised a large number of questions, perhaps too many to be discussed all in one go. Many of these questions may have plausible answers. My feeling, however, is that these issues can never be satisfyingly dealt with. To me, the whole idea of objectively telling whether or when or how many times a given computation is executing is hopeless, and if this is the case then we cannot say that minds exist because of physical implementations of computations. Searle really is right that computation is observer relative, that no objective fact about the physical world can depend on whether a computation is instantiated.

So where does that leave computationalism?

Platonism to the rescue!

I think Platonism resolves these and many other problems. On Platonism, a running computer program is just an instantiation of an algorithm, and an algorithm is a mathematical object which exists necessarily and timelessly even if it is never instantiated. If we allow ourselves to adopt the mental toolkit of Platonism, then it becomes possible to attribute consciousness not to a physical implementation of an algorithm but to the algorithm itself (or at least to an abstract run of an algorithm on particular input). In this view, it's not such a problem that there is no fact of the matter regarding whether physical systems instantiate a computation or not. No metaphysical fact depends on how we answer that question.

At first, this appears to be absurd. Am I really saying that it doesn't matter if a mind is physically instantiated, it exists regardless?

Yes, that is my view, but there's a lot of explaining to do about how this actually works and how it differs from belief in souls and the like. Much of the rest of this post is therefore dedicated to discussion what it means for a mind to exist Platonically, considering issues such as death, brain damage, identity and so on.

When I say that a given mind exists, if we want to think of that mind as having conscious experience, then we need to think about it processing information of some kind. So we need to define its inputs, its environment and so on. Different inputs yield different "biographies" for the mind. In each different environment, it has a different life story, will think different thoughts, will develop differently and so on. For our purposes, we should consider each life story to be a different mathematical object. So when we ask how a mind (say my mind) can exist without being instantiated, we are really asking how my mind and its environment can exist without being instantiated. For instance, if life on earth had been wiped out billions of years ago, how is it that I and all my fellow humans could still exist?

Well, even if this had happened, there would still be a mathematical object isomorphic to the status quo we observe. A mathematician of infinite patience and capacity could in principle explore this mathematical object (e.g. by simulating it) and learn what transpires within. That mathematical object defines every event within our world, every word that we utter, every thought that we think. If our conscious experience is made up of every thought that we think, then we would still be conscious even if we only existed within this mathematical object.

But, since I'm saying it is the algorithm itself that realises consciousness and not any particular implementation, it doesn't matter if the mathematician never simulates it. We would regard ourselves as conscious beings and the environment around us as physical regardless. The intriguing possibility arises that this is in fact the case -- that this is not a physical world but a world which only exists as a mathematical object. Furthermore, this may be the case for all worlds. There may be no physical world and indeed the very concept of an objectively physical world may be meaningless. This, of course, is just the Mathematical Universe Hypothesis I have discussed previously.

On this view, simulating an algorithm does not bring anything new (not conscious entities anyway) into existence. Rather it provides a window onto another world. So if you accidentally pull the plug on your simulation of a virtual world populated by conscious beings, don't worry, you have not committed genocide!

But what if you shoot a person in the head? Have you not committed murder? I would say you have, not necessarily because you cause that person to cease to exist but because you have removed him or her from causal contact with his or her loved ones. You have become the cause of grief and suffering and so your act is morally impermissable for this reason (on most conceptions of morality at least).

Whether you have actually caused the person to cease to exist is an interesting question. If the world were completely deterministic, then arguably you have terminated that mind. If we define the mind of the victim as the life story of that mind in this world, then it necessarily has to end at this point. It exists at no time after this event within the mathematical object of our world. The input to that mind after this point is undefined, and so the further life story of that mind is undefined, and so we should say it does not exist at times after the shooting. Of course, the proximate cause of this can be attributed to your action, so you bear responsibility for the death (on compatibilist accounts of free-will and responsibility at least).

But of course one cannot destroy a mathematical object, so how could one destroy a mind if a mind is a mathematical object? From a mathematical Platonist view, actually you haven't really destroyed the mind even if you have terminated its life story. Its life story, including every moment of experience, every thought it ever entertained and so on continues to exist just as a biography on the shelf does. In this view, the shooting constitutes a terminus to the story rather than a destruction of the story itself. There is no way to destroy a person utterly just as there is no way to destroy a mathematical object because there is no way to prevent a person from having existed in the first place.

Now, if the world is not completely deterministic (as appears to be the case), then at each point there are many possible futures. If there exist possible futures where the person was not killed, then there is another sense in which the shooting does not cause them to cease to exist. Though it may cause them to cease to exist in your world from that moment on -- they continue to live on in another possible future, effectively a parallel universe. Even if the world is deterministic after all, as long as there is some mathematical object which corresponds to that person continuing to live (e.g. in an alternative world that was identical from their limited perspective but subtly different in just the right way to prevent the shooting from happening), then in effect they can be regarded as continuing to live in that world.

Moving on, what of the relationship between the mind and brain? Changes to the brain clearly affect the mind, so how can I say the mind is independent of the brain?

There are (at least) two ways to view this. If you define the mind in conjunction with its environment as one object, then altering the state of the brain (e.g. with an injury or an electric probe) is in effect just another kind of input and so the mathematical object already incorporates the change. If you want to draw a border around the mind and treat it as a mathematical object in its own right, treating only sensory data as input, then a brain injury corresponds to instantiating an alternative mathematical object in its place. Rather than providing input to an algorithm you are replacing it with an alternative as we do when we rewrite and recompile a computer program. Either way of looking at this is fine with me.

On this view, the brain doesn't really create the mind, rather it taps into it and exploits it in order to navigate the world. In the same way, bees didn't really invent the hexagonal tiling of the plane. This is a solution which exists timelessly and Platonically. But bees did, through a process of evolution by natural selection, stumble into this tiling and exploit it because it is efficient. The mind is just a vastly more complex pattern that our ancestors stumbled into. Rather than causing the mind to exist, the brain should be regarded as a medium for the algorithm of the mind to interact with its environment, just as a computer is a medium that allows a computer program to take input and output but (on Platonism at least) does not cause the algorithm itself to exist. Destroying the brain therefore removes that mind from causal contact with its environment (the world), making a material difference to the world but not really to the mind/algorithm itself.

Getting back to the pixies

Recall Mark Bishop's argument that if to be conscious is to instantiate a certain class of computation, and that if there are ways to interpret any object as instantiating any computation, then all objects must be instantiating all kinds of conscious experience. There are an infinite number of "pixies" living in every rock (and so computationalism is absurd and can be rejected).

How does my view of Platonic computationalism help us?

Unfortunately, it seems we are stuck with the pixies -- if all mathematical objects exist, and if algorithms are mathematical objects, and if all it takes to be conscious is to be a certain algorithm, then each of Bishop's pixies must exist. Perhaps we're back where we started.

Actually, I don't think so. What I find absurd about the DwP argument is not so much that the pixies exist but that they exist in every rock, and so that we should be attributing consciousness to the rocks themselves. But, on Platonic computationalism, the rocks are not conscious and the pixies are not located in the rocks. Indeed, they are not located anywhere within our coordinate system. If they are located anywhere, it is only within a coordinate system local to their own environment, which is part of the mathematical object or algorithm in which they find themselves embedded. From our perspective they are abstract, just as from their perspective we are abstract. Destroying the rock has no impact on the pixies because they were never inside it in the first place.

I don't find it absurd that the pixies exist because I am already committed to the Mathematical Universe Hypothesis, which predicts the existence of all possible minds somewhere within the mathematical multiverse. Bishop's pixies correspond therefore to observers in other universes causally disconnected from our own. Since they are not in our universe, we don't need to concern ourselves with them. For all practical purposes, they do not exist from our perspective.

I say they are in other universes rather than in our own (despite the possibility of finding a Putnam-style mapping to show them reflected in our universe) because they are causally disconnected from us. Nothing we can do can affect them or they us, until that is we build a system of input/output which would allow us to interact with them. At that point, we can consider them and their world to be embedded in our own universe, but to do so we would have to build a very complex machine, effectively a supercomputer. Now, it hardly contradicts computationalism to suppose that a mind can be brought into our universe by a supercomputer, so this conclusion meshes well with the computationalist viewpoint.

Furthermore, on the DwP argument, it would seem that there are distinct identical copies of each pixie in every rock. On Platonism, these identical copies are just instances of the same mathematical object, of which there is only one. This also strikes me as less absurd.

Bishop has suggested to me that the MUH is a kind of panpsychism, but I disagree. To me, panpsychism is the view that consciousness is all around us, pervading the universe, so that even elementary particles can be considered to be conscious in some way. But my view is rather that matter is never conscious, that consciousness is rather a property of abstract structures. Consciousness is not all around us -- frankly, it doesn't physically exist anywhere in our universe. We are conscious but we (or at least our minds) are not physical things, we are instead the algorithms our brains are most usefully interpreted to be computing as they take sensory input, process it and output motor commands. To me, this is anything but panpsychism. It might be called a kind of dualism, but as I have argued before, dualism need not be a dirty word, and in any case, I'm really a monist because I think that even the so-called "physical" world is actually an abstract mathematical structure.

Conclusion

For reasons I have discussed before, I think computationalism has to be correct. That is, if we were to build an AI that was just as capable as we are, and particularly if it were modelled after the processes going on in human brains, we would be obliged to think of it as conscious in the same way that we are. But this does not mean that we have to attribute consciousness to the physical object of the computer. Neither do we need to attribute consciousness to the physical brain. The assumption from many computationalists that consciousness is a physical phenomenon, that there is a fact of the matter regarding when and where consciousness is instantiated, is in my view untenable. Rather we need to see consciousness as a property of certain abstract structures. It is useful and practical to regard the brain and the computer as instantiating such structures, but there need not be a fact of the matter because these structures exist Platonically regardless of whether they are instantiated or not.