Perhaps no concept is more central to the foundations of modern cognitive science than that of computation. The ambitions of artificial intelligence rest on a computational framework, and in other areas of cognitive science, models of cognitive processes are most frequently cast in computational terms. The foundational role of computation can be expressed in two basic theses. First, underlying the belief in the possibility of artificial intelligence there is a thesis of
These theses are widely held within cognitive science, but they are quite controversial. Some have questioned the thesis of computational sufficiency, arguing that certain human abilities could never be duplicated computationally (Dreyfus 1974; Penrose 1989), or that even if a computation could duplicate human abilities, instantiating the relevant computation would not suffice for the possession of a mind (Searle 1980). Others have questioned the thesis of computational explanation, arguing that computation provides an inappropriate framework for the explanation of cognitive processes (Edelman 1989; Gibson 1979), or even that computational descriptions of a system are vacuous (Searle 1990, 1991).
Advocates of computational cognitive science have done their best to repel these negative critiques, but the positive justification for the foundational theses remains murky at best. Why should
In order for the foundation to be stable, the notion of computation itself has to be clarified. The mathematical theory of computation in the abstract is well-understood, but cognitive science and artificial intelligence ultimately deal with physical systems. A bridge between these systems and the abstract theory of computation is required. Specifically, we need a theory of
Once a theory of implementation has been provided, we can use it to answer the second key question:
The computational framework developed to answer the first question can therefore be used to justify the theses of computational sufficiency and computational explanation. In addition, I will use this framework to answer various challenges to the centrality of computation, and to clarify some difficult questions about computation and its role in cognitive science. In this way, we can see that the foundations of artificial intelligence and computational cognitive science are solid.
The short answer to question (1) is straightforward. It goes as follows:
In a little more detail, this comes to:
This is still a little vague. To spell it out fully, we must specify the class of computations in question. Computations are generally specified relative to some formalism, and there is a wide variety of formalisms: these include Turing machines, Pascal programs, cellular automata, and neural networks, among others. The story about implementation is similar for each of these; only the details differ. All of these can be subsumed under the class of
An FSA is specified by giving a set of input states
A physical system
This definition uses maximally specific physical states s rather than the grouped state-types referred to above. The state-types can be recovered, however: each corresponds to a set {
There is a lot of room to play with the details of this definition. For instance, it is generally useful to put restrictions on the way that inputs and outputs to the system map onto inputs and outputs of the FSA. We also need not map
2.1 Combinatorial-state automata
Simple finite-state automata are unsatisfactory for many purposes, due to the monadic nature of their states. The states in most computational formalisms have a combinatorial structure: a cell pattern in a cellular automaton, a combination of tape-state and head-state in a Turing machine, variables and registers in a Pascal program, and so on. All this can be accommodated within the framework of combinatorial-state automata (CSAs), which differ from FSAs only in that an internal state is specified not by a monadic label S, but by a vector [
Input and output vectors are always finite, but the internal state vectors can be either finite or infinite. The finite case is simpler, and is all that is required for any practical purposes. Even if we are dealing with Turing machines, a Turing machine with a tape limited to 10200 squares will certainly be all that is required for simulation or emulation within cognitive science and AI. The infinite case can be spelled out in an analogous fashion, however. The main complication is that restrictions have to be placed on the vectors and dependency rules, so that these do not encode an infinite amount of information. This is not too difficult, but I will not go into details here.
The conditions under which a physical system implements a CSA are analogous to those for an FSA. The main difference is that internal states of the system need to be specified as vectors, where each element of the vector corresponds to an independent element of the physical system. A natural requirement for such a “vectorization” is that each element correspond to a distinct physical region within the system, although there may be other alternatives. The same goes for the complex structure of inputs and outputs. The system implements a given CSA if there exists such a vectorization of states of the system, and a mapping from elements of those vectors onto corresponding elements of the vectors of the CSA, such that the state-transition relations are isomorphic in the obvious way. The details can be filled in straightforwardly, as follows:
Once again, further constraints might be added to this definition for various purposes, and there is much that can be said to flesh out the definition’s various parts; a detailed discussion of these technicalities must await another forum (see Chalmers 1996a for a start). This definition is not the last word in a theory of implementation, but it captures the theory’s basic form.
One might think that CSAs are not much of an advance on FSAs. Finite CSAs, at least, are no more computationally powerful than FSAs; there is a natural correspondence that associates every finite CSA with an FSA with the same input/output behavior. Of course infinite CSAs (such as Turing machines) are more powerful, but even leaving that reason aside, there are a number of reasons why CSAs are a more suitable formalism for our purposes than FSAs.
First, the
This definition can straightforwardly be applied to yield implementation conditions for more specific computational formalisms. To develop an account of the implementation-conditions for a Turing machine, say, we need only redescribe the Turing machine as a CSA. The overall state of a Turing machine can be seen as a giant vector, consisting of (a) the internal state of the head, and (b) the state of each square of the tape, where this state in turn is an ordered pair of a symbol and a flag indicating whether the square is occupied by the head (of course only one square can be so occupied; this will be ensured by restrictions on initial state and on statetransition rules). The state-transition rules between vectors can be derived naturally from the quintuples specifying the behavior of the machine-head. As usually understood, Turing machines only take inputs at a single timestep (the start), and do not produce any output separate from the contents of the tape. These restrictions can be overridden in natural ways, for example by adding separate input and output tapes, but even with inputs and outputs limited in this way there is a natural description as a CSA. Given this translation from the Turing machine formalism to the CSA formalism, we can say that a given Turing machine is implemented whenever the corresponding CSA is implemented.
A similar story holds for computations in other formalisms. Some formalisms, such as cellular automata, are even more straightforward. Others, such as Pascal programs, are more complex, but the overall principles are the same. In each case there is some room for maneuver, and perhaps some arbitrary decisions to make (does writing a symbol and moving the head count as two state-transitions or one?) but little rests on the decisions we make. We can also give accounts of implementation for nondeterministic and probabilistic automata, by making simple changes in the definition of a CSA and the corresponding account of implementation. The theory of implementation for combinatorial-state automata provides a basis for the theory of implementation in general.
The above account may look complex, but the essential idea is very simple: the relation between an implemented computation and an implementing system is one of isomorphism between the formal structure of the former and the causal structure of the latter. In this way, we can see that as far as the theory of implementation is concerned, a computation is simply an
Does every system implement some computation? Yes. For example, every physical system will implement the simple FSA with a single internal state; most physical systems will implement the 2-state cyclic FSA, and so on. This is no problem, and certainly does not render the account vacuous. That would only be the case if every system implemented
Does every system implement any given computation? No. The conditions for implementing a given complex computation — say, a CSA whose state-vectors have 1000 elements, with 10 possibilities for each element and complex state-transition relations — will generally be sufficiently rigorous that extremely few physical systems will meet them. What is required is not just a mapping from states of the system onto states of the CSA, as Searle (1990) effectively suggests. The added requirement that the mapped states must satisfy reliable state-transition rules is what does all the work. In this case, there will effectively be at least 101000 constraints on state-transitions (one for each possible state-vector, and more if there are multiple possible inputs). Each constraint will specify one out of at least 101000 possible consequents (one for each possible resultant state-vector, and more if there are outputs). The chance that an arbitrary set of states will satisfy these constraints is something less than one in (101000)101000 (actually significantly less, because of the requirement that transitions be reliable). There is no reason to suppose that the causal structure of an arbitrary system (such as Searle’s wall) will satisfy these constraints. It is true that while we lack knowledge of the fundamental constituents of matter, it is impossible to
Can a given system implement more than one computation? Yes. Any system implementing some complex computation will simultaneously be implementing many simpler computations — not just 1-state and 2-state FSAs, but computations of some complexity. This is no flaw in the current account; it is precisely what we should expect. The system on my desk is currently implementing all kinds of computations, from EMACS to a clock program, and various sub-computations of these. In general, there is no canonical mapping from a physical object to “the” computation it is performing. We might say that within every physical system, there are numerous computational systems. To this very limited extent, the notion of implementation is “interest-relative.” Once again, however, there is no threat of vacuity. The question of whether a given system implements a given computation is still entirely objective. What counts is that a given system does not implement
If even digestion is a computation, isn’t this vacuous? This objection expresses the feeling that if every process, including such things as digestion and oxidation, implements some computation, then there seems to be nothing special about cognition any more, as computation is so pervasive. This objection rests on a misunderstanding. It is true that any given
With cognition, by contrast, the claim is that it is
What about Putnam’s argument? Putnam (1988) has suggested that on a definition like this, almost any physical system can be seen to implement every finite-state automaton. He argues for this conclusion by demonstrating that there will almost always be a mapping from physical states of a system to internal states of an FSA, such that over a given time-period (from 12:00 to 12:10 today, say) the transitions between states are just as the machine table say they should be. If the machine table requires that state
However, to suppose that this system implements the FSA in question is to misconstrue the state-transition conditionals in the definition of implementation. What is required is not simply that state
(Two notes. First, Putnam responds briefly to the charge that his system fails to support counterfactuals, but considers a different class of counterfactuals — those of the form “if the system had not been in state
What about semantics? It will be noted that nothing in my account of computation and implementation invokes any semantic considerations, such as the representational content of internal states. This is precisely as it should be: computations are specified syntactically, not semantically. Although it may very well be the case that any implementations of a given computation share some kind of semantic content, this should be a
The original account of Turing machines by Turing (1936) certainly had no semantic constraints built in. A Turing machine is defined purely in terms of the mechanisms involved, that is, in terms of syntactic patterns and the way they are transformed. To implement a Turing machine, we need only ensure that this formal structure is reflected in the causal structure of the implementation. Some Turing machines will certainly support a systematic semantic interpretation, in which case their implementations will also, but this plays no part in the definition of what it is to be or to implement a Turing machine. This is made particularly clear if we note that there are some Turing machines, such as machines defined by random sets of statetransition quintuples, that support no non-trivial semantic interpretation. We need an account of what it is to implement these machines, and such an account will then generalize to machines that support a semantic interpretation. Certainly, when computer designers ensure that their machines implement the programs that they are supposed to, they do this by ensuring that the mechanisms have the right causal organization; they are not concerned with semantic content. In the words of Haugeland (1985), if you take care of the syntax, the semantics will take care of itself.
I have said that the notion of computation should not be dependent on that of semantic content; neither do I think that the latter notion should be dependent on the former. Rather, both computation and content should be dependent on the common notion of
What about computers? Although Searle (1990) talks about what it takes for something to be a “digital computer,” I have talked only about computations and eschewed reference to computers. This is deliberate, as it seems to me that computation is the more fundamental notion, and certainly the one that is important for AI and cognitive science. AI and cognitive science certainly do not require that cognitive systems be computers, unless we stipulate that all it takes to be a computer is to implement some computation, in which case the definition is vacuous.
What does it take for something to be a computer? Presumably, a computer cannot merely implement a single computation. It must be capable of implementing many computations - that is, it must be
Is the brain a computer in this sense? Arguably. For a start, the brain can be “programmed” to implement various computations by the laborious means of conscious serial rule-following; but this is a fairly incidental ability. On a different level, it might be argued that learning provides a certain kind of programmability and parameter-setting, but this is a sufficiently indirect kind of parameter-setting that it might be argued that it does not qualify. In any case, the question is quite unimportant for our purposes. What counts is that the brain implements various complex computations, not that it is a computer.
1I take it that something like this is the “standard” definition of implementation of a finite-state automaton; see, for example, the definition of the description of a system by a probabilistic automaton in Putnam (1967). It is surprising, however, how little space has been devoted to accounts of implementation in the literature in theoretical computer science, philosophy of psychology, and cognitive science, considering how central the notion of computation is to these fields. It is remarkable that there could be a controversy about what it takes for a physical system to implement a computation (e.g. Searle 1990, 1991) at this late date. 2See Pylyshyn 1984, p. 71, for a related point.
The above is only half the story. We now need to exploit the above account of computation and implementation to outline the relation between computation and cognition, and to justify the foundational role of computation in AI and cognitive science.
Justification of the thesis of computational sufficiency has usually been tenuous. Perhaps the most common move has been an appeal to the Turing test, noting that every implementation of a given computation will have a certain kind of behavior, and claiming that the right kind of behavior is sufficient for mentality. The Turing test is a weak foundation, however, and one to which AI need not appeal. It may be that any behavioral description can be implemented by systems lacking mentality altogether (such as the giant lookup tables of Block 1981). Even if behavior suffices for
Instead, the central property of computation on which I will focus is one that we have already noted: the fact that a computation provides an abstract specification of the causal organization of a system. Causal organization is the nexus between computation and cognition. If cognitive systems have their mental properties in virtue of their causal organization, and if that causal organization can be specified computationally, then the thesis of computational sufficiency is established. Similarly, if it is the causal organization of a system that is primarily relevant in the explanation of behavior, then the thesis of computational explanation will be established. By the account above, we will always be able to provide a computational specification of the relevant causal organization, and therefore of the properties on which cognition rests.
To spell out this story in more detail, I will introduce the notion of the
Call a property
Most properties are not organizational invariants. The property of flying is not, for instance: we can move an airplane to the ground while preserving its causal topology, and it will no longer be flying. Digestion is not: if we gradually replace the parts involved in digestion with pieces of metal, while preserving causal patterns, after a while it will no longer be an instance of digestion: no food groups will be broken down, no energy will be extracted, and so on. The property of being tube of toothpaste is not an organizational invariant: if we deform the tube into a sphere, or replace the toothpaste by peanut butter while preserving causal topology, we no longer have a tube of toothpaste.
In general, most properties depend essentially on certain features that are not features of causal topology. Flying depends on height, digestion depends on a particular physiochemical makeup, tubes of toothpaste depend on shape and physiochemical makeup, and so on. Change the features in question enough and the property in question will change, even though causal topology might be preserved throughout.
3.2 The organizational invariance of mental properties
The central claim of this section is that most mental properties are organizational invariants. It does not matter how we stretch, move about, or replace small parts of a cognitive system: as long as we preserve its causal topology, we will preserve its mental properties.
An exception has to be made for properties that are partly supervenient on states of the environment. Such properties include knowledge (if we move a system that knows that
The central claim can be justified by dividing mental properties into two varieties: psychological properties — those that are characterized by their causal role, such as belief, learning, and perception — and phenomenal properties, or those that are characterized by way in which they are consciously experienced. Psychological properties are concerned with the sort of thing the mind does, and phenomenal properties are concerned with the way it
Psychological properties, as has been argued by Armstrong (1968) and Lewis (1972) among others, are effectively defined by their role within an overall causal system: it is the pattern of interaction between different states that is definitive of a system’s psychological properties. Systems with the same causal topology will share these patterns of causal interactions among states, and therefore, by the analysis of Lewis (1972), will share their psychological properties (as long as their relation to the environment is appropriate).
Phenomenal properties are more problematic. It seems unlikely that these can be
Nevertheless, I believe that they can be seen to be organizational invariants, as I have argued elsewhere. The argument for this, very briefly, is a
The key step in the thought-experiment is to take the relevant neural circuit in
But given the assumptions, there is no way for the system to
If all this works, it establishes that most mental properties are organizational invariants: any two systems that share their fine-grained causal topology will share their mental properties, modulo the contribution of the environment.
To establish the thesis of computational sufficiency, all we need to do now is establish that organizational invariants are fixed by some computational structure. This is quite straightforward.
An organizationally invariant property depends only on some pattern of causal interaction between parts of the system. Given such a pattern, we can straightforwardly abstract it into a CSA description: the parts of the system will correspond to elements of the CSA state-vector, and the patterns of interaction will be expressed in the state-transition rules. This will work straightforwardly as long as each part has only a finite number of states that are relevant to the causal dependencies between parts, which is likely to be the case in any biological system whose functions cannot realistically depend on infinite precision. (I discuss the issue of analog quantities in more detail below.) Any system that implements this CSA will share the causal topology of the original system. In fact, it turns out that the CSA formalism provides a perfect formalization of the notion of causal topology. A CSA description specifies a division of a system into parts, a space of states for each part, and a pattern of interaction between these states. This is precisely what is constitutive of causal topology.
If what has gone before is correct, this establishes the thesis of computational sufficiency, and therefore the the view that Searle has called “strong artificial intelligence”: that there exists some computation such that any implementation of the computation possesses mentality. The fine-grained causal topology of a brain can be specified as a CSA. Any implementation of that CSA will share that causal topology, and therefore will share organizationally invariant mental properties that arise from the brain.
The thesis of computational explanation can be justified in a similar way. As mental properties are organizational invariants, the physical properties on which they depend are properties of causal organization. Insofar as mental properties are to be explained in terms of the physical at all, they can be explained in terms of the causal organization of the system.4 We can invoke further properties (implementational details) if we like, but there is a clear sense in which they are not vital to the explanation. The neural or electronic composition of an element is irrelevant for many purposes; to be more precise, composition is relevant only insofar as it determines the element’s causal role within the system. An element with different physical composition but the same causal role would do just as well. This is not to make the implausible claim that neural properties, say, are entirely irrelevant to explanation. Often the best way to investigate a system’s causal organization is to investigate its neural properties. The claim is simply that insofar as neural properties are explanatorily relevant, it is in virtue of the role they play in determining a systems causal organization.
In the explanation of behavior, too, causal organization takes center stage. A system’s behavior is determined by its underlying causal organization, and we have seen that the computational framework provides an ideal language in which this organization can be specified. Given a pattern of causal interaction between substates of a system, for instance, there will be a CSA description that captures that pattern. Computational descriptions of this kind provide a general framework for the explanation of behavior.
For some explanatory purposes, we will invoke properties that are not organizational invariants. If we are interested in the biological basis of cognition, we will invoke neural properties. To explain situated cognition, we may invoke properties of the environment. This is fine; the thesis of computational explanation is not an
A computational basis for cognition can be challenged in two ways. The first sort of challenge argues that computation cannot
But a computational model is just a simulation! According to this objection, due to Searle (1980), Harnad (1989), and many others, we do not expect a computer model of a hurricane to be a real hurricane, so why should a computer model of mind be a real mind? But this is to miss the important point about organizational invariance. A computational simulation is not a mere formal abstraction, but has rich internal dynamics of its own. If appropriately designed it will share the causal topology of the system that is being modeled, so that the system’s organizationally invariant properties will be not merely simulated but
The question about whether a computational model simulates or replicates a given property comes down to the question of whether or not the property is an organizational invariant. The property of being a hurricane is obviously not an organizational invariant, for instance, as it is essential to the very notion of hurricanehood that wind and air be involved. The same goes for properties such as digestion and temperature, for which specific physical elements play a defining role. There is no such obvious objection to the organizational invariance of cognition, so the cases are disanalogous, and indeed, I have argued above that for mental properties, organizational invariance actually holds. It follows that a model that is computationally equivalent to a mind will itself be a mind.
Syntax and semantics. Searle (1984) has argued along the following lines: (1) A computer program is syntactic; (2) Syntax is not sufficient for semantics; (3) Minds have semantics; therefore (4) Implementing a computer program is insufficient for a mind. Leaving aside worries about the second premise, we can note that this argument equivocates between programs and implementations of those programs. While programs themselves are syntactic objects, implementations are not: they are real physical systems with complex causal organization, with real physical causation going on inside. In an electronic computer, for instance, circuits and voltages push each other around in a manner analogous to that in which neurons and activations push each other around. It is precisely in virtue of this causation that implementations may have cognitive and therefore semantic properties.
It is the notion of implementation that does all the work here. A program and its physical implementation should not be regarded as equivalent — they lie on entirely different levels, and have entirely different properties. It is the program that is syntactic; it is the implementation that has semantic content. Of course, there is still a substantial question about how an implementation comes to possess semantic content, just as there is a substantial question about how a
The Chinese room. There is not room here to deal with Searle’s famous Chinese room argument in detail. I note, however, that the account I have given supports the “Systems reply”, according to which the entire system understands Chinese even if the homunculus doing the simulating does not. Say the overall system is simulating a brain, neuron-by-neuron. Then like any implementation, it will share important causal organization with the brain. In particular, if there is a symbol for every neuron, then the patterns of interaction between slips of paper bearing those symbols will mirror patterns of interaction between neurons in the brain, and so on. This organization is implemented in a baroque way, but we should not let the baroqueness blind us to the fact that the causal organization —
It is precisely in virtue of this causal organization that the system possesses its mental properties. We can rerun a version of the “dancing qualia” argument to see this. In principle, we can move from the brain to the Chinese room simulation in small steps, replacing neurons at each step by little demons doing the same causal work, and then gradually cutting down labor by replacing two neighboring demons by one who does the same work. Eventually we arrive at a system where a single demon is responsible for maintaining the causal organization, without requiring any real neurons at all. This organization might be maintained between marks on paper, or it might even be present inside the demon’s own head, if the calculations are memorized. The arguments about organizational invariance all hold here — for the same reasons as before, it is implausible to suppose that the system’s experiences will change or disappear.
Performing the thought-experiment this way makes it clear that we should not expect the experiences to be had by the
What about the environment? Some mental properties, such as knowledge and even belief, depend on the environment being a certain way. Computational organization, as I have outlined it, cannot determine the environmental contribution, and therefore cannot fully guarantee this sort of mental property. But this is no problem. All we need computational organization to give us is the
This is to some extent an empirical issue, but the relevant evidence is solidly on the side of computability. We have every reason to believe that the low-level laws of physics are computable. If so, then low-level neurophysiological processes can be computationally simulated; it follows that the function of the whole brain is computable too, as the brain consists in a network of neurophysiological parts. Some have disputed the premise: for example, Penrose (1989) has speculated that the effects of quantum gravity are noncomputable, and that these effects may play a role in cognitive functioning. He offers no arguments to back up this speculation, however, and there is no evidence of such noncomputability in current physical theory (see Pour-El and Richards (1989) for a discussion). Failing such a radical development as the discovery that the fundamental laws of nature are uncomput able, we have every reason to believe that human cognition can be computationally modeled.
What about Gödel’s theorem? Gödel’s theorem states that for any consistent formal system, there are statements of arithmetic that are unprovable within the system. This has led some (Lucas 1963; Penrose 1989) to conclude that humans have abilities that cannot be duplicated by any computational system. For example, our ability to “see” the truth of the Gödel sentence of a formal system is argued to be non-algorithmic. I will not deal with this objection in detail here, as the answer to it is not a direct application of the current framework. I will simply note that the assumption that we can see the truth of arbitrary Gödel sentences requires that we have the ability to determine the consistency or inconsistency of any given formal system, and there is no reason to believe that we have this ability in general (For more on this point, see Putnam 1960, Bowie 1982 and the commentaries on Penrose 1990).
Discreteness and continuity. An important objection notes that the CSA formalism only captures
A number of responses to this are possible. The first is to note that the current framework can fairly easily be extended to deal with computation over continuous quantities such as real numbers. All that is required is that the various substates of a CSA be represented by a real parameter rather than a discrete parameter, where appropriate restrictions are placed on allowable state-transitions (for instance, we can require that parameters are transformed polynomially, where the requisite transformation can be conditional on sign). See Blum, Shub and Smale (1989) for a careful working-out of some of the relevant theory of computability. A theory of implementation can be given along in a fashion similar to the account I have given above, where continuous quantities in the formalism are required to correspond to continuous physical parameters with an appropriate correspondence in state-transitions.
This formalism is still discrete in time: evolution of the continuous states proceeds in discrete temporal steps. It might be argued that cognitive organization is in fact continuous in time, and that a relevant formalism should capture this. In this case, the specification of discrete state-transitions between states can be replaced by differential equations specifying how continuous quantities change in continuous time, giving a thoroughly continuous
We need not go this far, however. There are good reasons to suppose that whether or not cognition in the brain is continuous, a discrete framework can capture everything important that is going on. To see this, we can note that a discrete abstraction can describe and simulate a continuous process to any required degree of accuracy. It might be objected that chaotic processes can amplify microscopic differences to significant levels. Even so, it is implausible that the correct functioning of mental processes
Indeed, the presence of noise in physical systems suggests that any given continuous computation of the above kinds can never be reliably implemented in practice, but only approximately implemented. For the purposes of artificial intelligence we will do just as well with discrete systems, which can also give us approximate implementations of continuous computations.
It follows that these considerations do not count against the theses of computational sufficiency or of computational explanation. To see the first, note that a discrete simulation can replicate everything
This is not to exclude continuous formalisms from cognitive explanation. The thesis of computational explanation is not an exclusive thesis. It may be that continuous formalisms will provide a simpler and more natural framework for the explanation of many dynamic processes, as we find in the theory of neural networks. Perhaps the most reasonable version of the computationalist view accepts the thesis of (discrete) computational sufficiency, but supplements the thesis of computational explanation with the proviso that continuous computation may sometimes provide a more natural explanatory framework (a discrete explanation could do the same job, but more clumsily). In any case, continuous computation does not give us anything fundamentally new.
3In analyzing a related thought-experiment, Searle (1991) suggests that a subject who has undergone silicon replacement might react as follows: “You want to cry out, `I can’t see anything. I’m going totally blind’. But you hear your voice saying in a way that is completely out of your control, `I see a red object in front of me’” (pp. 66-67). But given that the system’s causal topology remains constant, it is very unclear where there is room for such “wanting” to take place, if it is not in some Cartesian realm. Searle suggests some other things that might happen, such as a reduction to total paralysis, but these suggestions require a change in causal topology and are therefore not relevant to the issue of organizational invariance. 4I am skeptical about whether phenomenal properties can be explained in wholly physical terms. As I argue in Chalmers 1996b, given any account of the physical or computational processes underlying mentality, the question of why these processes should give rise to conscious experience does not seem to be explainable within physical or computational theory alone. Nevertheless, it remains the case that phenomenal properties depend on physical properties, and if what I have said earlier is correct, the physical properties that they depend on are organizational properties. Further, the explanatory gap with respect to conscious experience is compatible with the computational explanation of cognitive processes and of behavior, which is what the thesis of computational explanation requires. 5Of course there is a sense in which it can be said that connectionist models perform “computation over representation”, in that connectionist processing involves the transformation of representations, but this sense is to weak to cut the distinction between symbolic and subsymbolic computation at its joints. Perhaps the most interesting foundational distinction between symbolic and connectionist systems is that in the former but not in the latter, the computational (syntactic) primitives are also the representational (semantic) primitives.
4. Other kinds of computationalism
Artificial intelligence and computational cognitive science are committed to a kind of computationalism about the mind, a computationalism defined by the theses of computational sufficiency and computational explanation. In this paper I have tried to justify this computationalism, by spelling out the role of computation as a tool for describing and duplicating causal organization. I think that this kind of computationalism is all that artificial intelligence and computational cognitive science are committed to, and indeed is all that they need. This sort of computationalism provides a
The fields have often been taken to be committed to stronger claims, sometimes by proponents and more often by opponents. For example, Edelman (1989) criticizes the computational approach to the study of the mind on the grounds that:
But artificial intelligence and computational cognitive science are not committed to the claim that the brain is literally a Turing machine with a moving head and a tape, and even less to the claim that that tape is the environment. The claim is simply that some computational framework can
In a similar way, a computationalist need not claim that the brain is a von Neumann machine, or has some other specific architecture. Like Turing machines, von Neumann machines are just one kind of architecture, particularly well-suited to programmability, but the claim that the brain implements such an architecture is far ahead of any empirical evidence and is most likely false. The commitments of computationalism are more general.
Computationalism is occasionally associated with the view that cognition is rule-following, but again this is a strong empirical hypothesis that is inessential to the foundations of the fields. It is entirely possible that the only “rules” found in a computational description of thought will be at a very low level, specifying the causal dynamics of neurons, for instance, or perhaps the dynamics of some level between the neural and the cognitive. Even if there are no rules to be found at the cognitive level, a computational approach to the mind can still succeed. Another claim to which a computationalist need not be committed are “the brain is a computer”; as we have seen, it is not computers that are central but computations).
The most ubiquitous “strong” form of computationalism has been what we may call
Symbolic computationalism has been a popular and fruitful approach to the mind, but it does not exhaust the resources of computation. Not all computations are symbolic computations. We have seen that there are some Turing machines that lack semantic content altogether, for instance. Perhaps systems that carry semantic content are more plausible models of cognition, but even in these systems there is no reason why the content must be carried by the systems’ computational primitives. In connectionist systems, for example, the basic bearers of semantic content are
Note that the distinction between symbolic and subsymbolic computation does not coincide with the distinction between different computational formalisms, such as Turing machines and neural networks. Rather, the distinction divides the class of computations within each of these formalisms. Some Turing machines perform symbolic computation, and some perform subsymbolic computation; the same goes for neural networks. (Of course it is sometimes said that all Turing machines perform “symbol manipulation”, but this holds only if the ambiguous term “symbol” is used in a purely syntactic sense, rather than in the semantic sense I am using here.)
Both proponents and opponents of a computational approach have often implicitly identified computation with symbolic computation. A critique called
On the other side of the fence, Fodor (1992) uses the name “Computational Theory of Mind” for a version of symbolic computationalism, and suggests that Turing’s main contribution to cognitive science is the idea that syntactic state-transitions between symbols can be made to respect their semantic content. This strikes me as false. Turing was concerned very little with the semantic content of internal states, and the concentration on symbolic computation came later. Rather, Turing’s key contribution was the formalization of the notion of
Indeed, a focus on symbolic computation sacrifices the universality that is at the heart of Turing’s contribution. Universality applies to entire classes of automata, such as Turing machines, where these classes are defined syntactically. The requirement that an automaton performs computation over representation is a strong further constraint, a semantic constraint that plays no part in the basic theory of computation. There is no reason to suppose that the much narrower class of Turing machines that perform symbolic computation is universal. If we wish to appeal to universality in a defense of computationalism, we must cast the net more widely than this.7
The various strong forms of computationalism outlined here are bold empirical hypotheses with varying degrees of plausibility. I suspect that they are all false, but in any case their truth and falsity is not the issue here. Because they are such strong empirical hypotheses, they are in no position to serve as a
6[Note added 2011.] In order to make them compatible with the views of consciousness in Chalmers 1996b, the thesis of computational sufficiency and the claim that mental properties are organizational invariants must be understood in terms of nomological rather metaphysical necessity: the right kind of computation suffices with nomological necessity for possession of a mind, mental properties supervene nomologically on causal topology. These claims are compatible with the metaphysical possibility of systems with the same organization and no consciousness. As for the thesis of computational explanation: if one construes cognitive processes to include arbitrary intentional or representational states, then I think these cannot be explained wholly in terms of computation, as I think that phenomenal properties and environmental properties play a role here. One might qualify the thesis by understanding “cognitive processes” and “behavior” in functional and nonintentional terms, or by saying that computational explanation can undergird intentional explanation when appropriately supplemented, perhaps by phenomenal and environmental elements. Alternatively, the version of the thesis most directly supported by the argument in the text is that computation provides a general framework for the mechanistic explanation of cognitive processes and behavior. That is, insofar as cognitive processes and behavior are explainable mechanistically, they are explainable computationally. 7It is common for proponents of symbolic computationalism to hold, usually as an unargued premise, that what makes a computation a computation is the fact that it involves representations with semantic content. The books by Fodor (1975) and Pylyshyn (1984), for instance, are both premised on the assumption that there is no computation without representation. Of course this is to some extent a terminological issue, but as I have stressed in 2.2 and here, this assumption has no basis in computational theory and unduly restricts the role that computation plays in the foundations of cognitive science. 8Some other claims with which computationalism is sometimes associated include “the brain is a computer”, “the mind is to the brain as software is to hardware”, and “cognition is computation”. The first of these is not required, for the reasons given in 2.2: it is not computers that are central to cognitive theory but computations. The second claim is an imperfect expression of the computationalist position for similar reasons: certainly the mind does not seem to be something separable that the brain can load and run, as a computer’s hardware can load and run software. Even the third does not seem to me to be central to computationalism: perhaps there is a sense in which it is true, but what is more important is that computation suffices for and explains cognition. See Dietrich (1990) for some related distinctions between computationalism, “computerism”, and “cognitivism”.
5. Conclusion: Toward a minimal computationalism
The view that I have advocated can be called
Unlike the stronger forms of computationalism, minimal computationalism is not a bold empirical hypothesis. To be sure, there are some ways that empirical science might prove it to be false: if it turns out that the fundamental laws of physics are noncomputable and if this noncomputability reflects itself in cognitive functioning, for instance, or if it turns out that our cognitive capacities depend essentially on infinite precision in certain analog quantities, or indeed if it turns out that cognition is mediated by some non-physical substance whose workings are not computable. But these developments seem unlikely; and failing developments like these, computation provides a general framework in which we can express the causal organization of cognition, whatever that organization turns out to be.
Minimal computationalism is compatible with such diverse programs as connectionism, logicism, and approaches focusing on dynamic systems, evolution, and artificial life. It is occasionally said that programs such as connectionism are “noncomputational”, but it seems more reasonable to say that the success of such programs would vindicate Turing’s dream of a computational intelligence, rather than destroying it.
Computation is such a valuable tool precisely because almost any theory of cognitive mechanisms can be expressed in computational terms, even though the relevant computational formalisms may vary. All such theories are theories of causal organization, and computation is sufficiently flexible that it can capture almost any kind of organization, whether the causal relations hold between high-level representations or among low-level neural processes. Even such programs as the Gibsonian theory of perception are ultimately compatible with minimal computationalism. If perception turns out to work as the Gibsonians imagine, it will still be mediated by causal mechanisms, and the mechanisms will be expressible in an appropriate computational form. That expression may look very unlike a traditional computational theory of perception, but it will be computational nevertheless.
In this light, we see that artificial intelligence and computational cognitive science do not rest on shaky empirical hypotheses. Instead, they are consequences of some very plausible principles about the causal basis of cognition, and they are compatible with an extremely wide range of empirical discoveries about the functioning of the mind. It is precisely because of this flexibility that computation serves as a