Скачать 144.94 Kb.

Chapter Nine Computationalism Gualtiero Piccinini This is a preprint of an article whose final and definitive form will be published in the Oxford Handbook of Philosophy and Cognitive Science. Please refer to the published version. Computationalism is the view that cognitive capacities have a computational explanation or, somewhat more strongly, that cognition is (a kind of) computation. For simplicity, I will use these two formulations interchangeably. Most cognitive scientists endorse some version of computationalism and pursue computational explanations as their research program. Thus, when cognitive scientists propose an explanation of a cognitive capacity, the explanation typically involves computations that result in the cognitive capacity. Computationalism is controversial but resilient to criticism. To understand why mainstream cognitive scientists endorse computationalism and what, if any, alternatives there might be, we need to understand what computationalism says. That, in turn, requires an account of computation. 1. A Substantive Empirical Hypothesis Computationalism is usually introduced as an empirical hypothesis that can be disconfirmed. Whether computationalism has empirical bite depends on how we construe the notion of computation: the more inclusive a notion of computation, the weaker the version of computationalism formulated in its terms. At one end of the continuum, some notions of computation are so loose that they encompass virtually everything. For instance, if computation is construed as the production of outputs from inputs and if any state of a system qualifies as an input (or output), then every process is a computation. Sometimes, computation is construed as information processing, which is somewhat more stringent, yet the resulting version of computationalism is quite weak. There is little doubt that organisms gather and process information about their environment (more on this below). Processing information is surely an important aspect of cognition. Thus, if computation is information processing, then cognition involves computation. But this doesn’t tell us much about how cognition works. In addition, the notions of information and computation in their most important uses are conceptually distinct, have different histories, are associated with different mathematical theories, and have different roles to play in a theory of cognition. It’s best to keep them separate (Piccinini and Scarantino 2010). Computationalism becomes most interesting when it has explanatory power. The most relevant and explanatory notion of computation is that associated with digital computers. Computers perform impressive feats: they solve mathematical problems, play difficult games, prove logical theorems, etc. Perhaps cognitive systems work like computers. To a first approximation, this analogy between computers and cognitive systems is the original motivation behind computationalism. The resulting form of computationalism is a strong hypothesis—one that should be open to empirical testing. To understand it further, it will help to briefly outline three research traditions associated with computationalism and how they originated. 2. Three Research Traditions: Classicism, Connectionism, and Computational Neuroscience The view that thinking has something to do with computation may be found in the works of some modern materialists, such as Thomas Hobbes (Boden 2006, p. 79). But computationalism properly socalled could not begin in earnest until a number of logicians (most notably Alonzo Church, Kurt Gödel, Stephen Kleene, Emil Post, and especially Alan Turing) laid the foundations for the mathematical theory of computation. Turing (19367) analyzed computation in terms of what are now called Turing machines—a kind of simple processor operating on an unbounded tape. The tape is divided into squares, which the processor can read and write on. The processor moves along the tape reading and writing on one square at a time depending on what is already on the square as well as on the rules that govern the processor’s behavior. The rules state what to write on the tape and where to move next depending on what is on the tape as well as which of finitely many states the processor is in. Turing argued convincingly that any function that can be computed by following an algorithm (i.e., an unambiguous list of instructions operating on discrete symbols) can be computed by a Turing machine. Church (1936) offered a similar proposal in terms of general recursive functions, and it turns out that a function is general recursive if and only if it can be computed by a Turing machine. Given this extensional equivalence between Turing machines and general recursive functions, the thesis that any algorithmically computable function is computable by some Turing machine (or equivalently, is general recursive) is now known as the ChurchTuring thesis (Kleene, 1952, §62, §67). Turing made two other relevant contributions. First, he showed how to construct universal Turing machines. These are Turing machines that can mimic any other Turing machine by encoding the rules that govern the other machine as instructions, storing the instructions on a portion of their tape, and then using the encoded instructions to determine their behavior on the input data. Notice that ordinary digital computers, although they have more complex components than universal Turing machines, are universal in the same sense (up to their memory limitations). That is, digital computers can compute any function computable by a Turing machine until they run out of memory. Second, Turing showed that the vast majority of functions whose domain is denumerable (e.g., functions of strings of symbols or of natural numbers) are actually not computable by Turing machines. These ideas can be put together as follows: assuming the ChurchTuring thesis, a universal digital computer can compute any function computable by algorithm, although the sum total of these Turingcomputable functions is a tiny subset of all the functions whose domain is denumerable. Modern computationalism began when Warren McCulloch and Walter Pitts (1943) connected three things: Turing’s work on computation, the explanation of cognitive capacities, and the mathematical study of neural networks. Neural networks are sets of connected signalprocessing elements (“neurons”). Typically, they have elements that receive inputs from the environment (input elements), elements that yield outputs to the environment (output elements), and elements that communicate only with other elements in the system (hidden elements). Each element receives input signals and delivers output signals as a function of its input and current state. As a result of their elements’ activities and organization, neural networks turn the input received by their input elements into the output produced by their output elements. A neural network may be either a concrete physical system or an abstract mathematical system. An abstract neural network may be used to model another system (such as a network of actual neurons) to some degree of approximation. The mathematical study of neural networks using biophysical techniques began around the 1930s (Rashevsky, 1938, 1940; Householder and Landahl, 1945). But before McCulloch and Pitts, no one had suggested that neural networks have something to do with computation. McCulloch and Pitts defined networks that operate on sequences of discrete inputs in discrete time, argued that they are a useful idealization of what is found in the nervous system, and concluded that the activity of their networks explains cognitive phenomena. McCulloch and Pitts also pointed out that their networks can perform computations like those of Turing machines. More precisely, McCullochPitts networks are computationally equivalent to Turing machines without tape or finite state automata (Kleene 1956). Notice that modern digital computers are a kind of McCullochPitts neural network (von Neumann, 1945). Digital computers are sets of logic gates—digital signalprocessing elements equivalent to McCullochPitts neurons—connected to form a specific architecture. McCulloch and Pitts’s account of cognition contains three important aspects: an analogy between neural processes and digital computations, the use of mathematically defined neural networks as models, and an appeal to neurophysiological evidence to support their way of defining neural networks. After McCulloch and Pitts, many others linked computation and cognition, though they often abandoned one or more aspects of McCulloch and Pitts’s theory. Computationalism evolved into three main traditions, each emphasizing a different aspect of McCulloch and Pitts’s account. One tradition, sometimes called classicism, emphasizes the analogy between cognitive systems and digital computers while downplaying the relevance of neuroscience to the theory of cognition (Miller, Galanter, and Pribram, 1960; Fodor, 1975; Newell and Simon, 1976; Pylyshyn, 1984; Newell, 1990; Pinker, 1997; Gallistel and King, 2009). When researchers in this tradition offer computational models of a cognitive capacity, the models take the form of computer programs for producing the capacity in question. One strength of the classicist tradition lies in programming computers to exhibit higher cognitive capacities such as problem solving, language processing, and languagebased inference. A second tradition, most closely associated with the term connectionism (although this label can be misleading, see Section 7 below), downplays the analogy between cognitive systems and digital computers in favor of computational explanations of cognition that are “neurally inspired” (Rosenblatt, 1958; Feldman and Ballard, 1982; Rumelhart and McClelland, 1986; Bechtel and Abrahamsen, 2002). When researchers in this tradition offer computational models of a cognitive capacity, the models take the form of neural networks for producing the capacity in question. Such models are primarily constrained by psychological data, as opposed to neurophysiological data. In fact, each “neuron” in a connectionist network need not even represent a real neuron; it may represent an entire brain area. One strength of the connectionist tradition lies in designing artificial neural networks that exhibit cognitive capacities such as perception, motor control, learning, and implicit memory. A third tradition is most closely associated with the term computational neuroscience, which in turn is one aspect of theoretical neuroscience. Computational neuroscience downplays the analogy between cognitive systems and digital computers even more than the connectionist tradition. In fact, neurocomputational models exhibit more continuity with the neural network models that preceded McCulloch and Pitts (Rashevsky, 1938, 1940; Householder and Landahl, 1945) than to McCullochPitts networks. This is because neurocomputational models aim to describe actual neural systems such as (parts of) the hippocampus, cerebellum, or cortex, and are constrained by neurophysiological data in addition to psychological data (Schwartz, 1990; Churchland and Sejnowski, 1992; O’Reilly and Munakata, 2000; Dayan and Abbott, 2001; Eliasmith and Anderson, 2003). It turns out that McCullochPitts networks and many of their connectionist descendents are quite unfaithful to the details of neural activity, whereas other types of neural networks are more biologically realistic. Computational neuroscience offers models of how real neural systems may exhibit cognitive capacities, especially perception, motor control, learning, and implicit memory. Although the three traditions just outlined are in competition with one another to some extent (more on this in Section 7), there is also some fuzziness at their borders. Some cognitive scientists propose hybrid theories, which combine explanatory resources drawn from both the classicist and the connectionist traditions (e.g., Anderson, 2007). In addition, biological realism comes in degrees, so there is no sharp divide between connectionist and neurocomputational models. 3. Three Accounts of Computation: Causal, Semantic, and Mechanistic To fully understand computationalism—the view that cognition is computation—and begin to sort out the disagreements between different computational theories of cognition on one hand and anticomputationalist theories on the other, we need to understand what concrete computation is. Philosophers have offered three main (families of) accounts. (For a more complete survey, see Section 2 of Piccinini, 2010a.) 3.1 The Causal Account According to the causal account, a physical system S performs computation C just in case (i) there is a mapping from the states ascribed to S by a physical description to the states defined by computational description C, such that (ii) the state transitions between the physical states mirror the state transitions between the computational states. Clause (ii) requires that for any computational state transition of the form s_{1} → s_{2} (specified by the computational description C), if the system is in the physical state that maps onto s_{1}, its physical state causes it to go into the physical state that maps onto s_{2} (Chrisley, 1995; Chalmers, 1994, 1996; Scheutz, 1999, 2001; see also Klein, 2008 for a similar account built on the notion of disposition rather than cause). To this causal constraint on acceptable mappings, David Chalmers (1994, 1996) adds a further restriction: a genuine physical implementation of a computational system must divide into separate physical components, each of which maps onto the components specified by the computational formalism. As GodfreySmith (2009, p. 293) notes, this combination of a causal and a localizational constraint goes in the direction of mechanistic explanation (Machamer, Darden, and Craver, 2000). An account of computation that is explicitly based on mechanistic explanation will be discussed below. For now, the causal account simpliciter requires only that the mappings between computational and physical descriptions be such that the causal relations between the physical states are isomorphic to the relations between state transitions specified by the computational description. Thus, according to the causal account, computation is the causal structure of a physical process. It is important to note that under the causal account, there are mappings between any physical system and at least some computational descriptions. Thus, according to the causal account, everything performs at least some computations (Chalmers, 1996, p. 331; Scheutz, 1999. p. 191). This (limited) pancomputationalism strikes some as overly inclusive.^{i} By entailing pancomputationalism, the causal account trivializes the claim that a system is computational. For according to pancomputationalism, digital computers perform computations in the same sense in which rocks, hurricanes, and planetary systems do. This does an injustice to computer science—in computer science, only relatively few systems count as performing computations and it takes a lot of difficult technical work to design and build systems that perform computations reliably. Or consider computationalism, which was introduced to shed new and explanatory light on cognition. If every physical process is a computation, computationalism seems to lose much of its explanatory force (Piccinini, 2007a). Another objection to pancomputationalism begins with the observation that any moderately complex system satisfies indefinitely many objective computational descriptions (Piccinini, 2010b). This may be seen by considering computational modeling. A computational model of a system may be pitched at different levels of granularity. For example, consider cellular automata models of the dynamics of a galaxy or a brain. The dynamics of a galaxy or a brain may be described using an indefinite number of cellular automata—using different state transition rules, different time steps, or cells that represent spatial regions of different sizes. Furthermore, an indefinite number of formalisms different from cellular automata, such as Turing machines, can be used to compute the same functions computed by cellular automata. It appears that pancomputationalists are committed to the galaxy or the brain performing all these computations at once. But that does not appear to be the sense in which computers (or brains) perform computations. In the face of these objections, supporters of the causal account of computation are likely to maintain that the explanatory force of computational explanations does not come merely from the claim that a system is computational. Rather, explanatory force comes from the specific computations that a system is said to perform. Thus, a rock and a digital computer perform computations in the same sense. But they perform radically different computations, and it is the difference between their computations that explains the difference between the rock and the digital computer. As to the objection that there are still too many computations performed by each system, pancomputationalists have two main options: either to bite the bullet and accept that every system implements indefinitely many computations, or to find a way to single out, among the many computational descriptions satisfied by each system, the one that is ontologically privileged—the one that captures the computation performed by the system. As to those who are unsatisfied by these replies and wish to avoid pancomputationalism, they may look for accounts of computation that are less inclusive than the causal account. Such accounts may be found by adding restrictions to the causal account. 3.2 The Semantic Account In our everyday life, we usually employ computations to process meaningful symbols, in order to extract information from them. The semantic account of computation turns this practice into a metaphysical doctrine: computation is the processing of representations—or at least, the processing of appropriate representations in appropriate ways (Fodor, 1975; Cummins, 1983; Pylyshyn, 1984; Churchland and Sejnowski, 1992; Shagrir, 2006; Sprevak, 2010). Opinions as to which representational manipulations constitute computations vary. What all versions of the semantic account have in common is that according to them, there is “no computation without representation” (Fodor, 1981, p. 180). The semantic account may be formulated (and is usually understood) as a restricted causal account. In addition to the causal account’s requirement that a computational description mirror the causal structure of a physical system, the semantic account adds a semantic requirement. Only physical states that qualify as representations may be mapped onto computational descriptions, thereby qualifying as computational states. If a state is not representational, it is not computational either. The semantic account of computation is closely related to the common view that computation is information processing. This idea is less clear than it may seem, because there are several notions of information. The connection between information processing and computation is different depending on which notion of information is at stake. What follows is a brief disambiguation of the view that computation is information processing based on four important notions of information. 1. Information in the sense of thermodynamics is closely related to thermodynamic entropy. Entropy is a property of every physical system. Thermodynamic entropy is, roughly, a measure of an observer’s uncertainty about the microscopic state of a system after she considers the observable macroscopic properties of the system. The study of the thermodynamics of computation is a lively field with many implications in the foundations of physics (Leff and Rex, 2003). In this thermodynamic sense of ‘information,’ any difference between two distinguishable states of a system may be said to carry information. Computation may well be said to be information processing in this sense, but this has little to do with semantics properly socalled. 2. Information in the sense of communication theory is a measure of the average likelihood that a given message is transmitted between a source and a receiver (Shannon and Weaver, 1949). This has little to do with semantics too. 3. Information in one semantic sense is approximately the same as “natural meaning” (Grice, 1957). A signal carries information in this sense just in case it reliably correlates with a source (Dretske, 1981). The view that computation is information processing in this sense is prima facie implausible, because many computations—such as arithmetical calculations carried out on digital computers—do not seem to carry any natural meaning. Nevertheless, this notion of semantic information is relevant here because it has been used by some theorists to ground an account of representation (Dretske, 1981; Fodor, 2008). 4. Information in another semantic sense is just ordinary semantic content or “nonnatural meaning” (Grice, 1957). The view that computation is information processing in this sense is similar to a generic semantic account of computation. The semantic account is popular in the philosophy of mind and in cognitive science because it appears to fit its specific needs better than a purely causal account. Since minds and computers are generally assumed to manipulate (the right kind of) representations, they turn out to compute. Since most other systems are generally assumed not to manipulate (the relevant kind of) representations, they do not compute. Thus, the semantic account appears to avoid pancomputationalism and to accommodate some common intuitions about what does and does not count as a computing system. It keeps minds and computers in while leaving most everything else out, thereby vindicating computationalism as a strong and nontrivial theory. The semantic account faces its share of problems too. For starters, representation does not seem to be presupposed by the notion of computation employed in at least some areas of cognitive science as well as computability theory and computer science—the very sciences that gave rise to the notion of computation at the origin of the computational theory of cognition (Piccinini, 2008a). If this is correct, the semantic account may not even be adequate to the needs of philosophers of mind—at least those philosophers of mind who wish to make sense of the analogy between minds and the systems designed and studied by computer scientists and computability theorists. Another criticism of the semantic account is that specifying the kind of representation and representational manipulation that is relevant to computation seems to require a nonsemantic way of individuating computations (Piccinini, 2004). These concerns motivate efforts to account for concrete computation in nonsemantic terms. 3.3 The Mechanistic Account Some implicit appeal to mechanisms or aspects of mechanisms may be found in many accounts of computation, usually in combination with an appeal to causal or semantic properties (Chalmers, 1996; Cummins, 1983; Egan, 1995; Fodor, 1980; Glymour, 1991; Horst, 1999; Newell, 1980; Pylyshyn, 1984; Shagrir, 2001; and Stich, 1983). Nevertheless, the received view is that computational explanations and mechanistic explanations are distinct and belong at different “levels” (Marr 1982, Rusanen and Lappi 2007). By contrast, this section introduces an explicitly mechanistic account of computation, which does not rely on semantics (or syntax) (Piccinini, 2007b; Piccinini and Scarantino, 2010, Section 3). According to this account, computational explanation is a species of mechanistic explanation; concrete computing systems are functionally organized mechanisms of a special kind—mechanisms that perform concrete computations. Like the semantic account, the mechanistic account may be understood as a restricted causal account. In addition to the causal account’s requirement that a computational description mirror the causal structure of a physical system, the mechanistic account adds a requirement about the functional organization of the system. Only physical states that have a specific functional significance within a specific type of mechanism may be mapped onto computational descriptions, thereby qualifying as computational states. If a state lacks the appropriate functional significance, it is not a computational state. A functional mechanism is a system of organized components, each of which has functions to perform (cf. Craver, 2007; Wimsatt, 2002). When appropriate components and their functions are appropriately organized and functioning properly, their combined activities constitute the capacities of the mechanism. Conversely, when we look for an explanation of the capacities of a mechanism, we decompose the mechanism into its components and look for their functions and organization. The result is a mechanistic explanation of the mechanism’s capacities. This notion of mechanism is familiar to biologists and engineers. For example, biologists explain physiological capacities (digestion, respiration, etc.) in terms of the functions performed by systems of organized components (the digestive system, the respiratory system, etc.). A computation in the generic sense is the processing of vehicles according to rules that are sensitive to certain vehicle properties, and specifically, to differences between different portions of the vehicles. The processing is performed by a functional mechanism, that is, a mechanism whose components are functionally organized to perform the computation. Thus, if the mechanism malfunctions, a miscomputation occurs. When we define concrete computations and the vehicles that they manipulate, we need not consider all of their specific physical properties. We may consider only the properties that are relevant to the computation, according to the rules that define the computation. A physical system can be described at different levels of abstraction. Since concrete computations and their vehicles are described sufficiently abstractly as to be defined independently of the physical media that implement them, they may be called mediumindependent. In other words, a vehicle is mediumindependent just in case the rules (i.e., the inputoutput maps) that define a computation are sensitive only to differences between portions of the vehicles along specific dimensions of variation—they are insensitive to any more concrete physical properties of the vehicles. Put yet another way, the rules are functions of state variables associated with a set of functionally relevant degrees of freedom, which can be implemented differently in different physical media. Thus, a given computation can be implemented in multiple physical media (e.g., mechanical, electromechanical, electronic, magnetic, etc.), provided that the media possess a sufficient number of dimensions of variation (or degrees of freedom) that can be appropriately accessed and manipulated and that the components of the mechanism are functionally organized in the appropriate way. Notice that the mechanistic account avoids pancomputationalism. First, physical systems that are not functional mechanisms are ruled out. Functional mechanisms are complex systems of components that are organized to perform functions. Any system whose components are not organized to perform functions is not a computing system because it is not a functional mechanism. Second, mechanisms that lack the function of manipulating mediumindependent vehicles are ruled out. Finally, mediumindependent vehicle manipulators whose manipulations fail to accord with appropriate rules are ruled out. The second and third constraints appeal to special functional properties—manipulating mediumindependent vehicles, doing so in accordance with rules defined over the vehicles—that are possessed only by relatively few concrete mechanisms. According to the mechanistic account, those few mechanisms are the genuine computing systems. Another feature of the mechanistic account is that it makes sense of miscomputation—a notion difficult to make sense of under the causal and semantic accounts. Consider an ordinary computer programmed to compute function f on input i. Suppose that the computer malfunctions and produces an output different from f(i). According to the causal (semantic) account, the computer just underwent a causal process (a manipulation of representations), which may be given a computational description and hence counts as computing some function g(i), where g≠f. By contrast, according to the mechanistic account, the computer simply failed to compute, or at least failed to complete its computation. Given the importance of avoiding miscomputations in the design and use of computers, the ability of the mechanistic account to make sense of miscomputation gives it a further advantage over rival accounts. The most important advantage of the mechanistic account over other accounts is that it distinguishes and characterizes precisely many different kinds of computing systems based on their specific mechanistic properties. Given its advantages, from now on I will presuppose the mechanistic account. I will now describe some important kinds of computation. 