{"slug": "the-computational-theory-of-mind-2015", "title": "The Computational Theory of Mind (2015)", "summary": "The Stanford Encyclopedia of Philosophy's entry on the Computational Theory of Mind (CTM), first published October 16, 2015, and substantively revised December 18, 2024, argues that the mind is a computational system, a position central to cognitive science in the 1960s and 1970s but now challenged by rival paradigms. The entry outlines key tasks for computationalists, including defining computation, defending the claim that the mind computes, and relating computational descriptions to neurophysiological and intentional descriptions, while tracing the concept's roots to Alan Turing's 1936 paper on Turing machines.", "body_md": "# The Computational Theory of Mind\n\n*First published Fri Oct 16, 2015; substantive revision Wed Dec 18, 2024*\n\nCould a machine think? Could the mind itself be a thinking machine?\nThe computer revolution transformed discussion of these questions,\noffering our best prospects yet for machines that emulate reasoning,\ndecision-making, problem solving, perception, linguistic\ncomprehension, and other mental processes. Advances in computing raise\nthe prospect that the mind itself is a computational system—a\nposition known as *the computational theory of mind* (CTM).\n*Computationalists* are researchers who endorse CTM, at least\nas applied to certain important mental processes. CTM played a central\nrole within cognitive science during the 1960s and 1970s. For many\nyears, it enjoyed orthodox status. More recently, it has come under\npressure from various rival paradigms. A key task facing\ncomputationalists is to explain what one means when one says that the\nmind “computes”. A second task is to argue that the mind\n“computes” in the relevant sense. A third task is to\nelucidate how computational description relates to other common types\nof description, especially *neurophysiological description*\n(which cites neurophysiological properties of the organism’s\nbrain or body) and *intentional description* (which cites\nrepresentational properties of mental states).\n\n[1. Turing machines](#TurMac)[2. Artificial intelligence](#ArtInt)[3. The classical computational theory of mind](#ClaComTheMin)[4. Neural networks](#NeuNet)[5. Computation and representation](#ComRep)[6. Alternative conceptions of computation](#AltConCom)[7. Arguments against computationalism](#ArgAgaCom)[Bibliography](#Bib)[Academic Tools](#Aca)[Other Internet Resources](#Oth)[Related Entries](#Rel)\n\n[1. Turing machines]\n\nThe intuitive notions of *computation* and *algorithm*\nare central to mathematics. Roughly speaking, an algorithm is an\nexplicit, step-by-step procedure for answering some question or\nsolving some problem. An algorithm provides *routine mechanical\ninstructions* dictating how to proceed at each step. Obeying the\ninstructions requires no special ingenuity or creativity. For example,\nthe familiar grade-school algorithms describe how to compute addition,\nmultiplication, and division. Until the early twentieth century,\nmathematicians relied upon informal notions of computation and\nalgorithm without attempting anything like a formal analysis.\nDevelopments in the foundations of mathematics eventually impelled\nlogicians to pursue a more systematic treatment. Alan Turing’s\nlandmark paper “On Computable Numbers, With an Application to\nthe Entscheidungsproblem” (Turing 1936) offered the analysis\nthat has proved most influential.\n\nA *Turing machine* is an abstract model of an idealized\ncomputing device with unlimited time and storage space at its\ndisposal. The device manipulates *symbols*, much as a human\ncomputing agent manipulates pencil marks on paper during arithmetical\ncomputation. Turing says very little about the nature of symbols. He\nassumes that primitive symbols are drawn from a finite alphabet. He\nalso assumes that symbols can be inscribed or erased at “memory\nlocations”. Turing’s model works as follows:\n\n- There are infinitely many memory locations, arrayed in a linear structure. Metaphorically, these memory locations are “cells” on an infinitely long “paper tape”. More literally, the memory locations might be physically realized in various media (e.g., silicon chips).\n- There is a central processor, which can access one memory location at a time. Metaphorically, the central processor is a “scanner” that moves along the paper tape one “cell” at a time.\n- The central processor can enter into finitely many\n*machine states*. - The central processor can perform four elementary operations: write a symbol at a memory location; erase a symbol from a memory location; access the next memory location in the linear array (“move to the right on the tape”); access the previous memory location in the linear array (“move to the left on the tape”).\n- Which elementary operation the central processor performs depends entirely upon two facts: which symbol is currently inscribed at the present memory location; and the scanner’s own current machine state.\n- A\n*machine table*dictates which elementary operation the central processor performs, given its current machine state and the symbol it is currently accessing. The machine table also dictates how the central processor’s machine state changes given those same factors. Thus, the machine table enshrines a finite set of routine mechanical instructions governing computation.\n\nTuring translates this informal description into a rigorous\nmathematical model. For more details, see the entry on\n[Turing machines](../turing-machine/).\n\nTuring motivates his approach by reflecting on idealized human computing agents. Citing finitary limits on our perceptual and cognitive apparatus, he argues that any symbolic algorithm executed by a human can be replicated by a suitable Turing machine. He concludes that the Turing machine formalism, despite its extreme simplicity, is powerful enough to capture all humanly executable mechanical procedures over symbolic configurations. Subsequent discussants have almost universally agreed.\n\nTuring computation is often described as *digital* rather than\n*analog*. What this means is not always so clear, but the basic\nidea is usually that computation operates over discrete\nconfigurations. By comparison, many historically important algorithms\noperate over continuously variable configurations. For example,\nEuclidean geometry assigns a large role to *ruler-and-compass\nconstructions*, which manipulate geometric shapes. For any shape,\none can find another that differs to an arbitrarily small extent.\nSymbolic configurations manipulated by a Turing machine do not differ\nto arbitrarily small extent. Turing machines operate over discrete\nstrings of elements (digits) drawn from a finite alphabet. One\nrecurring controversy concerns whether the digital paradigm is\nwell-suited to model mental activity or whether an analog paradigm\nwould instead be more fitting (MacLennan 2012; Piccinini and Bahar\n2013).[ 1]\n\nBesides introducing Turing machines, Turing (1936) proved several\nseminal mathematical results involving them. In particular, he proved\nthe existence of a *universal Turing machine* (UTM). Roughly\nspeaking, a UTM is a Turing machine that can mimic any other Turing\nmachine. One provides the UTM with a symbolic input that codes the\nmachine table for Turing machine *M*. The UTM replicates\n*M*’s behavior, executing instructions enshrined by\n*M*’s machine table. In that sense, the UTM is a\n*programmable general purpose computer*. To a first\napproximation, all personal computers are also general purpose: they\ncan mimic any Turing machine, when suitably programmed. The main\ncaveat is that physical computers have finite memory, whereas a Turing\nmachine has unlimited memory. More accurately, then, a personal\ncomputer can mimic any Turing machine *until it exhausts its\nlimited memory supply*.\n\nTuring’s discussion helped lay the foundations for *computer\nscience*, which seeks to design, build, and understand computing\nsystems. As we know, computer scientists can now build extremely\nsophisticated computing machines. All these machines implement\nsomething resembling Turing computation, although the details differ\nfrom Turing’s simplified model.\n\n[2. Artificial intelligence]\n\nRapid progress in computer science prompted many, including Turing, to\ncontemplate whether we could build a computer capable of thought.\n*Artificial intelligence* (AI) aims to construct\n“thinking machinery”. More precisely, it aims to construct\ncomputing machines that execute core mental tasks such as reasoning,\ndecision-making, problem solving, and so on. During the 1950s and\n1960s, this goal came to seem increasingly realistic (Haugeland 1985).\nA famous early success was the *Logic Theorist* computer\nprogram (Newell and Simon 1956), which proved 38 of the first 52\ntheorems from *Principia Mathematica* (Whitehead and Russell\n1925). In one case, it discovered a simpler proof than\n*Principia*’s. Initial achievements of this kind\nstimulated enormous interest inside and outside the academy. Many\nresearchers predicted that intelligent machines were only a few years\naway. When confident predictions of thinking machines proved too\noptimistic, many observers lost interest or concluded that AI was a\nfool’s errand. Nevertheless, the decades have witnessed gradual\nprogress, including some striking recent advances. A few\nmilestones:\n\n- IBM’s Deep Blue defeated chess champion Gary Kasparov in 1997 (Campbell 1999).\n- The driverless car Stanley completed a 132-mile course in the Mojave Desert, winning the 2005 Defense Advanced Research Projects Agency (DARPA) Grand Challenge (Thrun, Montemerlo, Dahlkamp, et al. 2006).\n- In 2012, AlexNet dramatically surpassed all previous computational models in a standard image classification task (Krizhevsky, Sutskever, and Hinton 2012).\n- DeepMind’s AlphaGo defeated Lee Sedol, one of the top Go players in the world, in 2016 (Silver, Schrittwieser, Simonyan, et al. 2017).\n- In 2020, OpenAI released GPT-3, which generates uncannily human-like text in response to written prompts (Brown, Mann, Ryder, et al. 2020). An improved version, ChatGPT, was released in 2022 and attracted widespread societal attention.\n\nThese and other recent advances have sparked intense renewed focus upon AI, including numerous commercial applications.\n\nSome philosophers insist that computers, no matter how sophisticated\nthey become, will at best *mimic* rather than\n*replicate* thought. A computer simulation of the weather does\nnot really rain. A computer simulation of flight does not really fly.\nEven if a computing system could simulate mental activity, why suspect\nthat it would constitute the genuine article?\n\nTuring (1950) anticipated these worries and tried to defuse them. He\nproposed a scenario, now called *the Turing Test*, where one\nevaluates whether an unseen interlocutor is a computer or a human. A\ncomputer *passes the Turing test* if one cannot determine that\nit is a computer. Turing proposed that we abandon the question\n“Could a computer think?” as hopelessly vague, replacing\nit with the question “Could a computer pass the Turing\ntest?”. Turing’s discussion has received considerable\nattention, proving especially influential within AI. Ned Block (1981)\noffers an influential critique. He argues that certain possible\nmachines pass the Turing test even though these machines do not come\nclose to genuine thought or intelligence. See the entry\n[the Turing test](../turing-test/)\nfor discussion of Block’s objection and other issues\nsurrounding the Turing Test. For discussion of the Turing test in\nrelation to ChatGPT and similar models, see (Bayne and Williams 2023;\nFloridi and Chiriatti 2020; Mahowald, Ivanova, Blank, et al.\n2024).\n\nFor more on AI, see the entry\n[logic and artificial intelligence](../logic-ai/).\nFor much more detail, see Russell and Norvig (2022).\n\n[3. The classical computational theory of mind]\n\nWarren McCulloch and Walter Pitts (1943) first suggested that\nsomething resembling the Turing machine might provide a good model for\nthe mind. In the 1960s, Turing computation became central to the\nemerging interdisciplinary initiative *cognitive science*,\nwhich studies the mind by drawing upon psychology, computer science\n(especially AI), linguistics, philosophy, economics (especially game\ntheory and behavioral economics), anthropology, and neuroscience. The\nlabel *classical computational theory of mind* (which we will\nabbreviate as CCTM) is now fairly standard. According to CCTM, the\nmind is a computational system similar in important respects to a\nTuring machine, and core mental processes (e.g., reasoning,\ndecision-making, and problem solving) are computations similar in\nimportant respects to computations executed by a Turing machine. These\nformulations are imprecise. CCTM is best seen as a family of views,\nrather than a single well-defined\nview.[ 2]\n\nIt is common to describe CCTM as embodying “the computer metaphor”. This description is doubly misleading.\n\nFirst, CCTM is better formulated by describing the mind as a\n“computing system” or a “computational system”\nrather than a “computer”. As David Chalmers (2011) notes,\ndescribing a system as a “computer” strongly suggests that\nthe system is *programmable*. As Chalmers also notes, one need\nnot claim that the mind is programmable simply because one regards it\nas a Turing-style computational system. (Most Turing machines are not\nprogrammable.) Thus, the phrase “computer metaphor”\nstrongly suggests theoretical commitments that are inessential to\nCCTM. The point here is not just terminological. Critics of CCTM often\nobject that the mind is not a programmable general purpose computer\n(Churchland, Koch, and Sejnowski 1990). Since classical\ncomputationalists need not claim (and usually do not claim) that the\nmind is a programmable general purpose computer, the objection is\nmisdirected.\n\nSecond, CCTM is not intended metaphorically. CCTM does not simply hold\nthat the mind is *like* a computing system. CCTM holds that the\nmind *literally is* a computing system. Of course, the most\nfamiliar artificial computing systems are made from silicon chips or\nsimilar materials, whereas the human body is made from flesh and\nblood. But CCTM holds that this difference disguises a more\nfundamental similarity, which we can capture through a Turing-style\ncomputational model. In offering such a model, we prescind from\nphysical details. We attain an abstract computational description that\ncould be physically implemented in diverse ways (e.g., through silicon\nchips, or neurons, or pulleys and levers). CCTM holds that a suitable\nabstract computational model offers a literally true description of\ncore mental processes.\n\nIt is common to summarize CCTM through the slogan “the mind is a Turing machine”. This slogan is also somewhat misleading, because no one regards Turing’s precise formalism as a plausible model of mental activity. The formalism seems too restrictive in several ways:\n\n- Turing machines execute pure symbolic computation. The inputs and\noutputs are symbols inscribed in memory locations. In contrast, the\nmind receives\n*sensory input*(e.g., retinal stimulations) and produces*motor output*(e.g., muscle activations). A complete theory must describe how mental computation interfaces with sensory inputs and motor outputs. - A Turing machine has infinite discrete memory capacity. Ordinary biological systems have finite memory capacity. A plausible psychological model must replace the infinite memory store with a large but finite memory store\n- Modern computers have\n*random access memory*: addressable memory locations that the central processor can directly access. Turing machine memory is not addressable. The central processor can access a location only by sequentially accessing intermediate locations. Computation without addressable memory is hopelessly inefficient. For that reason, C.R. Gallistel and Adam King (2009) argue that addressable memory gives a better model of the mind than non-addressable memory. - A Turing machine has a central processor that operates\n*serially*, executing one instruction at a time. Other computational formalisms relax this assumption, allowing multiple processing units that operate in*parallel*. Classical computationalists can allow parallel computations (Fodor and Pylyshyn 1988; Gallistel and King 2009: 174). See Gandy (1980) and Sieg (2009) for general mathematical treatments that encompass both serial and parallel computation. - Turing computation is\n*deterministic*: total computational state determines subsequent computational state. One might instead allow*stochastic*computations. In a stochastic model, current state does not dictate a unique next state. Rather, there is a certain probability that the machine will transition from one state to another.\n\nCCTM claims that mental activity is “Turing-style computation”, allowing these and other departures from Turing’s own formalism.\n\n[3.1 Machine functionalism]\n\nHilary Putnam (1967) introduced CCTM into philosophy. He contrasted\nhis position with *logical behaviorism* and *type-identity\ntheory*. Each position purports to reveal the nature of mental\nstates, including propositional attitudes (e.g., beliefs), sensations\n(e.g., pains), and emotions (e.g., fear). According to logical\nbehaviorism, mental states are behavioral dispositions. According to\ntype-identity theory, mental states are brain states. Putnam advances\nan opposing *functionalist* view, on which mental states are\nfunctional states. According to functionalism, a system has a mind\nwhen the system has a suitable *functional organization*.\nMental states are states that play appropriate roles in the\nsystem’s functional organization. Each mental state is\nindividuated by its interactions with sensory input, motor output, and\nother mental states.\n\nFunctionalism offers notable advantages over logical behaviorism and type-identity theory:\n\n- Behaviorists want to associate each mental state with a characteristic pattern of behavior—a hopeless task, because individual mental states do not usually have characteristic behavioral effects. Behavior almost always results from distinct mental states operating together (e.g., a belief and a desire). Functionalism avoids this difficulty by individuating mental states through characteristic relations not only to sensory input and behavior but also to one another.\n- Type-identity theorists want to associate each mental state with a\ncharacteristic physical or neurophysiological state. Putnam casts this\nproject into doubt by arguing that mental states are\n*multiply realizable*: the same mental state can be realized by diverse physical systems, including not only terrestrial creatures but also hypothetical creatures (e.g., a silicon-based Martian). Functionalism is tailor-made to accommodate multiple realizability. According to functionalism, what matters for mentality is a pattern of organization, which could be physically realized in many different ways. See the entry[multiple realizability](../multiple-realizability/)for further discussion of this argument.\n\nPutnam defends a brand of functionalism now called *machine\nfunctionalism*. He emphasizes *probabilistic automata*,\nwhich are similar to Turing machines except that transitions between\ncomputational states are stochastic. He proposes that mental activity\nimplements a probabilistic automaton and that particular mental states\nare machine states of the automaton’s central processor. The\nmachine table specifies an appropriate functional organization, and it\nalso specifies the role that individual mental states play within that\nfunctional organization. In this way, Putnam combines functionalism\nwith CCTM.\n\nMachine functionalism faces several problems. One problem, highlighted\nby Ned Block and Jerry Fodor (1972), concerns the *productivity of\nthought*. A normal human can entertain a potential infinity of\npropositions. Machine functionalism identifies mental states with\nmachine states of a probabilistic automaton. Since there are only\nfinitely many machine states, there are not enough machine states to\npair one-one with possible mental states of a normal human. Of course,\nan actual human will only ever entertain finitely many propositions.\nHowever, Block and Fodor contend that this limitation reflects limits\non lifespan and memory, rather than (say) some psychological law that\nrestricts the class of humanly entertainable propositions. A\nprobabilistic automaton is endowed with unlimited time and memory\ncapacity yet even still has only finitely many machine states.\nApparently, then, machine functionalism mislocates the finitary limits\nupon human cognition.\n\nAnother problem for machine functionalism, also highlighted by Block\nand Fodor (1972), concerns the *systematicity of thought.* An\nability to entertain one proposition is correlated with an ability to\nthink other propositions. For example, someone who can entertain the\nthought *that John loves Mary* can also entertain the thought\n*that Mary loves John*. Thus, there seem to be systematic\nrelations between mental states. A good theory should reflect those\nsystematic relations. Yet machine functionalism identifies mental\nstates with unstructured machines states, which lack the requisite\nsystematic relations to another. For that reason, machine\nfunctionalism does not explain systematicity. In response to this\nobjection, machine functionalists might deny that they are obligated\nto explain systematicity. Nevertheless, the objection suggests that\nmachine functionalism neglects essential features of human mentality.\nA better theory would explain those features in a principled way.\n\nWhile the productivity and systematicity objections to machine functionalism are perhaps not decisive, they provide strong impetus to pursue an improved version of CCTM. See Block (1978) for additional problems facing machine functionalism and functionalism more generally.\n\n[3.2 The representational theory of mind]\n\nFodor (1975, 1981, 1987, 1990, 1994, 2008) advocates a version of CCTM\nthat accommodates systematicity and productivity much more\nsatisfactorily. He shifts attention to the *symbols*\nmanipulated during Turing-style computation.\n\nAn old view, stretching back at least to William of Ockham’s\n*Summa Logicae*, holds that thinking occurs in a *language\nof thought* (sometimes called *Mentalese*). Fodor revives\nthis view. He postulates a system of mental representations, including\nboth primitive representations and complex representations formed from\nprimitive representations. For example, the primitive Mentalese words\nJOHN, MARY, and LOVES can combine to form the Mentalese sentence JOHN\nLOVES MARY. Mentalese is *compositional*: the meaning of a\ncomplex Mentalese expression is a function of the meanings of its\nparts and the way those parts are combined. Propositional attitudes\nare relations to Mentalese symbols. Fodor calls this view *the\nrepresentational theory of mind* (*RTM*). Combining RTM\nwith CCTM, he argues that mental activity involves Turing-style\ncomputation over the language of thought. Mental computation stores\nMentalese symbols in memory locations, manipulating those symbols in\naccord with mechanical rules.\n\nA prime virtue of RTM is how readily it accommodates productivity and systematicity:\n\n*Productivity*: RTM postulates a finite set of primitive\nMentalese expressions, combinable into a potential infinity of complex\nMentalese expressions. A thinker with access to primitive Mentalese\nvocabulary and Mentalese compounding devices has the potential to\nentertain an infinity of Mentalese expressions. She therefore has the\npotential to instantiate infinitely many propositional attitudes\n(neglecting limits on time and memory).\n\n*Systematicity*: According to RTM, there are systematic\nrelations between which propositional attitudes a thinker can\nentertain. For example, suppose I can think that John loves Mary.\nAccording to RTM, my doing so involves my standing in some relation\n*R* to a Mentalese sentence JOHN LOVES MARY, composed of\nMentalese words JOHN, LOVES, and MARY combined in the right way. If I\nhave this capacity, then I also have the capacity to stand in relation\n*R* to the distinct Mentalese sentence MARY LOVES JOHN, thereby\nthinking that Mary loves John. So the capacity to think that John\nloves Mary is systematically related to the capacity to think that\nMary loves John.\n\nBy treating propositional attitudes as relations to complex mental symbols, RTM explains both productivity and systematicity.\n\nCCTM+RTM differs from machine functionalism in several other respects.\nFirst, machine functionalism is a theory of mental states *in\ngeneral*, while RTM is only a theory of propositional attitudes.\nSecond, proponents of CCTM+RTM need not say that propositional\nattitudes are individuated functionally. As Fodor (2000: 105, fn. 4)\nnotes, we must distinguish *computationalism* (mental processes\nare computational) from *functionalism* (mental states are\nfunctional states). Machine functionalism endorses both doctrines.\nCCTM+RTM endorses only the first. Unfortunately, many philosophers\nstill mistakenly assume that computationalism entails a functionalist\napproach to propositional attitudes (see Piccinini 2004 for\ndiscussion).\n\nPhilosophical discussion of RTM tends to focus mainly on\n*high-level human thought*, especially belief and desire.\nHowever, CCTM+RTM is applicable to a much wider range of mental states\nand processes. Many cognitive scientists apply it to non-human\nanimals. For example, Gallistel and King (2009) apply it to certain\ninvertebrate phenomena (e.g., honeybee navigation). Even confining\nattention to humans, one can apply CCTM+RTM to *subpersonal\nprocessing*. Fodor (1983) argues that perception involves a\nsubpersonal “module” that converts retinal input into\nMentalese symbols and then performs computations over those symbols.\nThus, talk about a language of *thought* is potentially\nmisleading, since it suggests a non-existent restriction to\nhigher-level mental activity.\n\nAlso potentially misleading is the description of Mentalese as a\n*language*, which suggests that all Mentalese symbols resemble\nexpressions in a natural language. Many philosophers, including Fodor,\nsometimes seem to endorse that position. However, there are possible\nnon-propositional formats for mental representations. Proponents of\nCCTM+RTM can adopt a pluralistic line, allowing mental computation to\noperate over items akin to images, maps, diagrams, or other\nnon-propositional representations (Johnson-Laird 2004: 187; McDermott\n2001: 69; Pinker 2005: 7; Sloman 1978: 144–176). The pluralistic\nline seems especially plausible as applied to subpersonal processes\n(such as perception) and non-human animals. Michael Rescorla (2009a,\n2009b) surveys research on *cognitive maps* (Tolman 1948;\nO’Keefe and Nadel 1978; Gallistel 1990), suggesting that some\nanimals may navigate by computing over mental representations more\nsimilar to maps than sentences. Elisabeth Camp (2009), citing research\non baboon social interaction (Cheney and Seyfarth 2007), argues that\nbaboons may encode social dominance relations through non-sentential\ntree-structured representations.\n\nCCTM+RTM is schematic. To fill in the schema, one must provide detailed computational models of specific mental processes. A complete model will:\n\n- describe the mental representations manipulated by the process;\n- isolate elementary operations that manipulate the representations\n(e.g.,\n*inscribing a symbol in a memory location*); and - delineate mechanical rules governing application of elementary operations.\n\nBy providing a detailed computational model, we decompose a complex mental process into a series of elementary operations governed by precise, routine instructions.\n\nCCTM+RTM remains neutral in the traditional debate between physicalism and substance dualism. A Turing-style model proceeds at a very abstract level, not saying whether mental computations are implemented by physical stuff or Cartesian soul-stuff (Block 1983: 522). In practice, all proponents of CCTM+RTM embrace a broadly physicalist outlook. They hold that mental computations are implemented not by soul-stuff but rather by the brain. On this view, mental representations are realized by neural states, and computational operations over mental representations are realized by neural processes. Ultimately, physicalist proponents of CCTM+RTM must produce empirically well-confirmed theories that explain how exactly neural activity implements Turing-style computation. As Gallistel and King (2009) emphasize, we do not currently have such theories—though see Zylberberg, Dehaene, Roelfsema, and Sigman (2011) and Akhlaghpour (2022) for some speculations.\n\nFodor (1975) advances CCTM+RTM as a foundation for cognitive science.\nHe discusses mental phenomena such as decision-making, perception, and\nlinguistic processing. In each case, he maintains, our best scientific\ntheories postulate Turing-style computation over mental\nrepresentations. In fact, he argues that our *only* viable\ntheories have this form. He concludes that CCTM+RTM is “the only\ngame in town”. Many cognitive scientists argue along similar\nlines. C.R. Gallistel and Adam King (2009), Philip Johnson-Laird\n(1988), Allen Newell and Herbert Simon (1976), and Zenon Pylyshyn\n(1984) all recommend Turing-style computation over mental symbols as\nthe best foundation for scientific theorizing about the mind.\n\n[4. Neural networks]\n\nIn the 1980s, connectionism emerged as a prominent rival to classical\ncomputationalism. Connectionists draw inspiration from neurophysiology\nrather than logic and computer science. They employ computational\nmodels, *neural networks*, that differ significantly from\nTuring-style models. A *neural network* is a collection of\ninterconnected nodes. Nodes fall into three categories: *input*\nnodes, *output* nodes, and *hidden* nodes (which mediate\nbetween input and output nodes). Nodes have activation values, given\nby real numbers. One node can bear a *weighted connection* to\nanother node, also given by a real number. Activations of input nodes\nare determined exogenously: these are the inputs to computation.\n*Total input activation* of a hidden or output node is a\nweighted sum of the activations of nodes feeding into it. Activation\nof a hidden or output node is a function of its total input\nactivation; the particular function varies with the network. During\nneural network computation, waves of activation propagate from input\nnodes to output nodes, as determined by weighted connections between\nnodes.\n\nIn a *feedforward network*, weighted connections flow only in\none direction. *Recurrent networks* have feedback loops, in\nwhich connections emanating from hidden units circle back to hidden\nunits. Recurrent networks are less mathematically tractable than\nfeedforward networks. However, they figure crucially in psychological\nmodeling of various phenomena, such as phenomena that involve some\nkind of memory (Elman 1990).\n\nWeights in a neural network are typically mutable, evolving in accord\nwith a *learning algorithm*. The literature offers various\nlearning algorithms, but the basic idea is usually to adjust weights\nso that *actual outputs* gradually move closer to the\n*target outputs* one would expect for the relevant inputs. The\n*backpropagation algorithm* is a widely used algorithm of this\nkind (Rumelhart, Hinton, and Williams 1986).\n\nConnectionism traces back to McCulloch and Pitts (1943), who studied\nnetworks of interconnected *logic gates* (e.g., AND-gates and\nOR-gates). One can view a network of logic gates as a neural network,\nwith activations confined to two values (0 and 1) and activation\nfunctions given by the usual truth-functions. McCulloch and Pitts\nadvanced logic gates as idealized models of individual neurons. Their\ndiscussion exerted a profound influence on computer science (von\nNeumann 1945). Modern digital computers are simply networks of logic\ngates. Within cognitive science, however, researchers usually focus\nupon networks whose elements are more “neuron-like” than\nlogic gates. In particular, modern-day connectionists typically\nemphasize analog neural networks whose nodes take continuous rather\nthan discrete activation values. Some authors even use the phrase\n“neural network” so that it exclusively denotes such\nnetworks.\n\nNeural networks received relatively scant attention from cognitive\nscientists during the 1960s and 1970s, when Turing-style models\ndominated. The 1980s witnessed a huge resurgence of interest in neural\nnetworks, especially analog neural networks, with the two-volume\n*Parallel Distributed Processing* (Rumelhart, McClelland, and\nthe PDP research group, 1986; McClelland, Rumelhart, and the PDP\nresearch group, 1987) serving as a manifesto. Researchers constructed\nconnectionist models of diverse phenomena: object recognition, speech\nperception, sentence comprehension, cognitive development, and so on.\nImpressed by connectionism, many researchers concluded that CCTM+RTM\nwas no longer “the only game in town”.\n\nIn the 2010s, a class of computational models known as *deep neural\nnetworks* became quite popular (Krizhevsky, Sutskever, and Hinton\n2012; LeCun, Bengio, and Hinton 2015). These models are neural\nnetworks with multiple layers of hidden nodes (sometimes hundreds of\nsuch layers). Deep neural networks—trained on large data sets\nthrough one or another learning algorithm (usually\nbackpropagation)—have achieved great success in many areas of\nAI, including image classification (AlexNet), strategic game-playing\n(AlphaGo), and natural language processing (ChatGPT). Deep neural\nnetworks are now widely deployed in commercial applications, and they\nare the focus of extensive ongoing investigation within both academia\nand industry. Researchers have also used them to model the mind (e.g.\nKriegeskorte 2015; Marblestone, Wayne, and Kording 2016; Storrs,\nKietzmann, Walther, et al. 2021; Zhuang, Yan, Nayebi, et al. 2021),\nalthough how much success this modeling enterprise has thus far\nachieved is a controversial question (Bowers, Malholtra,\nDujmović, et al. 2023).\n\nFor a detailed overview of neural networks, see Haykin (2008). For a user-friendly introduction, with an emphasis on psychological applications, see Marcus (2001). For a philosophically oriented introduction to deep neural networks, see Buckner (2019). For connections between deep neural networks and the history of philosophy, see Buckner (2024).\n\n[4.1 Relation between neural networks and classical computation]\n\nNeural networks have a very different “feel” than classical (i.e., Turing-style) models. Yet classical computation and neural network computation are not mutually exclusive:\n\n*One can implement a neural network in a classical model*. Indeed, every neural network ever physically constructed has been implemented on a digital computer.*One can implement a classical model in a neural network*. Modern digital computers implement Turing-style computation in networks of logic gates. Alternatively, one can implement Turing-style computation using an analog recurrent neural network whose nodes take continuous activation values (Graves, Wayne, and Danihelka 2014, Other Internet Resources; Siegelmann and Sontag 1991; Siegelmann and Sontag 1995).\n\nAlthough some researchers suggest a fundamental opposition between classical computation and neural network computation, it seems more accurate to identify two modeling traditions that overlap in certain cases but not others (cf. Boden 1991; Piccinini 2008b). In this connection, it is also worth noting that classical computationalism and connectionist computationalism have their common origin in the work of McCulloch and Pitts.\n\nPhilosophers often say that classical computation involves\n“rule-governed symbol manipulation” while neural network\ncomputation is non-symbolic. The intuitive picture is that\n“information” in neural networks is globally distributed\nacross the weights and activations, rather than concentrated in\nlocalized symbols. However, the notion of “symbol” itself\nrequires explication, so it is often unclear what theorists mean by\ndescribing computation as symbolic versus non-symbolic. As mentioned\nin\n[§1](#TurMac),\nthe Turing formalism places very few conditions on\n“symbols”. Regarding primitive symbols, Turing assumes\njust that there are finitely many of them and that they can be\ninscribed in read/write memory locations. Neural networks can also\nmanipulate symbols satisfying these two conditions: as just noted, one\ncan implement a Turing-style model in a neural network.\n\nMany discussions of the symbolic/non-symbolic dichotomy employ a more robust notion of “symbol”. On the more robust approach, a symbol is the sort of thing that represents a subject matter. Thus, something is a symbol only if it has semantic or representational properties. If we employ this more robust notion of symbol, then the symbolic/non-symbolic distinction cross-cuts the distinction between Turing-style computation and neural network computation. A Turing machine need not employ symbols in the more robust sense. As far as the Turing formalism goes, symbols manipulated during Turing computation need not have representational properties (Chalmers 2011). Conversely, a neural network can manipulate symbols with representational properties. Indeed, an analog neural network can manipulate symbols that have a combinatorial syntax and semantics (Horgan and Tienson 1996; Marcus 2001).\n\nFollowing Steven Pinker and Alan Prince (1988), we may distinguish\nbetween *eliminative connectionism* and *implementationist\nconnectionism*.\n\nEliminative connectionists advance connectionism as a rival to\nclassical computationalism. They argue that the Turing formalism is\nirrelevant to psychological explanation. Often, though not always,\nthey seek to revive the *associationist* tradition in\npsychology, a tradition that CCTM had forcefully challenged. Often,\nthough not always, they attack the mentalist, nativist linguistics\npioneered by Noam Chomsky (1965). Often, though not always, they\nmanifest overt hostility to the very notion of mental representation.\nBut the defining feature of eliminative connectionism is that it uses\nneural networks as *replacements* for Turing-style models.\nEliminative connectionists view the mind as a computing system of a\nradically different kind than the Turing machine. A few authors\nexplicitly espouse eliminative connectionism (Churchland 1989;\nRumelhart and McClelland 1986; Horgan and Tienson 1996), and many\nothers incline towards it.\n\nImplementationist connectionism is a more ecumenical position. It\nallows a potentially valuable role for both Turing-style models\n*and* neural networks, operating harmoniously at different\nlevels of description (Marcus 2001; Smolensky 1988). A Turing-style\nmodel is higher-level, whereas a neural network model is lower-level.\nThe neural network illuminates how the brain implements the\nTuring-style model, just as a description in terms of logic gates\nilluminates how a personal computer executes a program in a high-level\nprogramming language.\n\n[4.2 Arguments for connectionism]\n\nConnectionism excites many researchers because of the analogy between neural networks and the brain. Nodes resemble neurons, while connections between nodes resemble synapses. Connectionist modeling therefore seems more “biologically plausible” than classical modeling. A connectionist model of a psychological phenomenon apparently captures (in an idealized way) how interconnected neurons might generate the phenomenon.\n\nWhen evaluating the argument from biological plausibility, one should recognize that neural networks vary widely in how closely they match actual brain activity. Many networks that figure prominently in connectionist writings are not so biologically plausible (Bechtel and Abrahamsen 2002: 341–343; Bermúdez 2010: 237–239; Clark 2014: 87–89; Harnish 2002: 359–362). A few examples:\n\n- Real neurons are much more heterogeneous than the interchangeable nodes that figure in typical connectionist networks.\n- Real neurons emit discrete spikes (action potentials) as outputs. But the nodes that figure in many prominent neural networks, including the best known deep neural networks, instead have continuous outputs.\n- The backpropagation algorithm requires that weights between nodes\ncan vary between excitatory and inhibitory, yet actual synapses cannot\nso vary (Crick and Asanuma 1986). Moreover, traditional applications\nof the algorithm assume target outputs supplied exogenously by\nmodelers\n*who know the desired answer*. In that sense, learning is*supervised*. Very little learning in actual biological systems involves anything resembling supervised training.\n\nOn the other hand, some neural networks are more biologically plausible (Buckner and Garson 2019; Illing, Gerstner, and Brea 2019). For example, there are neural networks whose nodes output discrete spikes roughly akin to those emitted by real neurons in the brain (Maass 1996; Buesing, Bill, Nessler, and Maass 2011). Furthermore, a large literature seeks to articulate biologically realistic connectionist learning algorithms, sometimes by approximating backpropagation (e.g. Lillicrap et al. 2016; Whittington and Bogacz, 2017), sometimes by replacing it with an alternative approach (e.g. Krotov and Hopfield 2019). Lillicrap et al. (2020) argue at length that backpropagation can be developed in a biologically plausible way. They note in particular that, although backpropagation was traditionally combined with supervised learning, it can instead be combined with unsupervised learning (e.g. Kingma and Welling 2019) or with reinforcement learning (e.g. Silver et al. 2016).\n\nEven when a neural network is not biologically plausible, it may still\nbe *more* biologically plausible than classical models. Neural\nnetworks certainly seem closer than Turing-style models, in both\ndetails and spirit, to neurophysiological description. Many cognitive\nscientists worry that CCTM reflects a misguided attempt at imposing\nthe architecture of digital computers onto the brain. Some doubt that\nthe brain implements anything resembling digital computation, i.e.,\ncomputation over discrete configurations of digits (Piccinini and\nBahar 2013). Others doubt that brains display clean Turing-style\nseparation between central processor and read/write memory (Dayan\n2009). Neural networks fare better on both scores: they do not require\ncomputation over discrete configurations of digits, and they do not\npostulate a clean separation between central processor and read/write\nmemory.\n\nClassical computationalists typically reply that it is premature to draw firm conclusions based upon biological plausibility, given how little we understand about the relation between neural, computational, and cognitive levels of description (Gallistel and King 2009; Marcus 2001). Using measurement techniques such as cell recordings and functional magnetic resonance imaging (fMRI), and drawing upon disciplines as diverse as physics, biology, AI, information theory, statistics, graph theory, and dynamical systems theory, neuroscientists have accumulated substantial knowledge about the brain at varying levels of granularity (Zednik 2019). We now know quite a lot about individual neurons, about how neurons interact within neural populations, about the localization of mental activity in cortical regions (e.g. the visual cortex), and about interactions among cortical regions. Yet we still have a tremendous amount to learn about how neural tissue accomplishes the tasks that it surely accomplishes: perception, reasoning, decision-making, language acquisition, and so on. Given our present state of relative ignorance, it would be rash to insist that the brain does not implement anything resembling Turing computation.\n\nConnectionists offer numerous further arguments that we should employ\nconnectionist models instead of, or in addition to, classical models.\nSee the entry\n[connectionism](../connectionism/)\nfor an overview. For purposes of this entry, we mention two\nadditional arguments.\n\nThe first argument emphasizes *learning* (Bechtel and\nAbrahamsen 2002: 51). A vast range of cognitive phenomena involve\nlearning from experience. Many connectionist models are explicitly\ndesigned to model learning, through backpropagation or some other\nalgorithm that modifies the weights between nodes. By contrast,\nconnectionists often complain that there are no good classical models\nof learning. Classical computationalists can respond by citing\nperceived defects of connectionist learning algorithms. Classical\ncomputationalists can also cite *Bayesian decision theory*, a\nmathematical model of inference and decision-making under uncertainty.\nIn the Bayesian framework, uncertainty is codified through\n*probability*. Precise rules dictate how to update\nprobabilities in light of new evidence and how to select actions in\nlight of probabilities and utilities. (See the entries\n[Bayes’s theorem](../bayes-theorem/)\nand\n[normative theories of rational choice: expected utility](../rationality-normative-utility/)\nfor details.) *Bayesian cognitive science* uses Bayesian\ndecision theory to construct mathematical models of mental activity\n(Ma 2019; Ma, Kording, and Goldreich 2023). Over the past few decades,\nBayesian cognitive science has accrued many explanatory successes.\nThis impressive track record suggests that some mental processes are\nBayesian or approximately Bayesian (Rescorla forthcoming). Moreover,\nclassical computing systems can execute or at least approximately\nexecute Bayesian updating in various realistic scenarios (Murphy 2023;\nThrun, Burgard, and Fox 2005). Arguably, then, classical computation\ncan model many important cases of learning.\n\nThe second argument emphasizes *speed of computation*. Neurons\nare much slower than silicon-based components of digital computers.\nFor this reason, neurons could not execute serial computation quickly\nenough to match rapid human performance in perception, linguistic\ncomprehension, decision-making, etc. Connectionists maintain that the\nonly viable solution is to replace serial computation with a\n“massively parallel” computational\narchitecture—precisely what neural networks provide (Feldman and\nBallard 1982; Rumelhart 1989). However, this argument is only\neffective against classical computationalists who insist upon serial\nprocessing. As noted in\n[§3](#ClaComTheMin),\nsome Turing-style models involve parallel processing. Many classical\ncomputationalists are happy to allow “massively parallel”\nmental computation, and the argument gains no traction against these\nresearchers. That being said, the argument highlights an important\nquestion that any computationalist—whether classical,\nconnectionist, or otherwise—must address: How does a brain built\nfrom relatively slow neurons execute sophisticated computations so\nquickly? Neither classical nor connectionist computationalists have\nanswered this question satisfactorily (Gallistel and King 2009: 174\nand 265).\n\n[4.3 Systematicity and productivity]\n\nFodor and Pylyshyn (1988) offer a widely discussed critique of eliminativist connectionism. They argue that systematicity and productivity fail in connectionist models, except when the connectionist model implements a classical model. Hence, connectionism does not furnish a viable alternative to CCTM. At best, it supplies a low-level description that helps bridge the gap between Turing-style computation and neuroscientific description.\n\nThis argument has elicited numerous replies and counter-replies. Some\nargue that neural networks can exhibit systematicity without\nimplementing anything like classical computational architecture\n(Horgan and Tienson 1996; Chalmers 1990; Smolensky 1991; van Gelder\n1990). Some argue that Fodor and Pylyshyn vastly exaggerate\nsystematicity (Johnson 2004) or productivity (Rumelhart and McClelland\n1986), especially for non-human animals (Dennett 1991). These issues,\nand many others raised by Fodor and Pylyshyn’s argument, have\nbeen thoroughly investigated in the literature. For further\ndiscussion, see Bechtel and Abrahamsen (2002: 156–199),\nBermúdez (2005: 244–278), Chalmers (1993), Clark (2014:\n84–86), and the encyclopedia entries on\n[the language of thought hypothesis](../language-thought/)\nand on\n[connectionism](../connectionism/).\n\nGallistel and King (2009) advance a related but distinct productivity\nargument. They emphasize *productivity of mental computation*,\nas opposed to *productivity of mental states*. Through detailed\nempirical case studies, they argue that many non-human animals can\nextract, store, and retrieve detailed records of the surrounding\nenvironment. For example, the Western scrub jay records where it\ncached food, what kind of food it cached in each location, when it\ncached the food, and whether it has depleted a given cache (Clayton,\nEmery, and Dickinson 2006). The jay can access these records and\nexploit them in diverse computations: computing whether a food item\nstored in some cache is likely to have decayed; computing a route from\none location to another; and so on. The number of possible\ncomputations a jay can execute is, for all practical purposes,\ninfinite.\n\nCCTM explains the productivity of mental computation by positing a central processor that stores and retrieves symbols in addressable read/write memory. When needed, the central processor can retrieve arbitrary, unpredicted combinations of symbols from memory. In contrast, Gallistel and King argue, connectionism has difficulty accommodating the productivity of mental computation. Although Gallistel and King do not carefully distinguish between eliminativist and implementationist connectionism, we may summarize their argument as follows:\n\n- Eliminativist connectionism cannot explain how organisms combine stored memories (e.g., cache locations) for computational purposes (e.g., computing a route from one cache to another). There are a virtual infinity of possible combinations that might be useful, with no predicting in advance which pieces of information must be combined in future computations. The only computationally tractable solution is symbol storage in readily accessible read/write memory locations—a solution that eliminativist connectionists reject.\n- Implementationist connectionists can postulate symbol storage in\nread/write memory,\n*as implemented by a neural network*. However, the mechanisms that connectionists usually propose for implementing memory are not plausible. Existing proposals are mainly variants upon a single idea: a recurrent neural network that allows reverberating activity to travel around a loop (Elman 1990). There are many reasons why the reverberatory loop model is hopeless as a theory of long-term memory. For example, noise in the nervous system ensures that signals would rapidly degrade in a few minutes. Implementationist connectionists have thus far offered no plausible model of read/write memory.[[3](notes.html#note-3)]\n\nGallistel and King conclude that CCTM is much better suited than either eliminativist or implementationist connectionism to explain a vast range of cognitive phenomena.\n\nCritics attack this new productivity argument from various angles,\nfocusing mainly on the empirical case studies adduced by Gallistel and\nKing. Peter Dayan (2009), John Donahoe (2010), and Christopher Mole\n(2014) argue that biologically plausible neural network models can\naccommodate at least some of the case studies. Dayan and Donahoe argue\nthat empirically adequate neural network models can dispense with\nanything resembling read/write memory. Mole argues that, in certain\ncases, empirically adequate neural network models can\n*implement* the read/write memory mechanisms posited by\nGallistel and King. Debate on these fundamental issues seems poised to\ncontinue well into the future.\n\n[4.4 Computational neuroscience]\n\n*Computational neuroscience* describes the nervous system\nthrough computational models (Trappenberg 2010; Miller 2018). Although\ncomputational neuroscience is grounded in mathematical modeling of\nindividual neurons, its distinctive focus is *systems* of\ninterconnected neurons. Computational neuroscientists typically model\nthese systems as neural networks. This research may be seen as a\nvariant, off-shoot, or descendant of connectionism. However, most\ncomputational neuroscientists do not self-identify as connectionists.\nThere are several differences between connectionism and computational\nneuroscience:\n\n- Neural networks employed by computational neuroscientists are much more biologically realistic than those employed by connectionists. The computational neuroscience literature is filled with talk about firing rates, action potentials, tuning curves, etc. These notions play at best a limited role in connectionist research, such as most of the research canvassed in (Rogers and McClelland 2014).\n- Computational neuroscience is driven in large measure by knowledge about the brain, and it assigns huge importance to neurophysiological data (e.g., cell recordings). Connectionists place much less emphasis upon such data. Their research is primarily driven by behavioral data (although more recent connectionist writings cite neurophysiological data with somewhat greater frequency).\n- Computational neuroscientists usually regard individual nodes in\nneural networks as idealized descriptions of actual neurons.\nConnectionists usually instead regard nodes as\n*neuron-like processing units*(Rogers and McClelland 2014) while remaining neutral about how exactly these units map onto actual neurophysiological entities.\n\nOne might say that computational neuroscience is concerned mainly with\n*neural computation* (computation by systems of neurons),\nwhereas connectionism is concerned mainly with abstract computational\nmodels *inspired* by neural computation. But the boundaries\nbetween connectionism and computational neuroscience are admittedly\nsomewhat porous. Doerig, Sommers, Seeliger, et al. (2023) propose the\nlabel *neuroconnectionism* for a research program that\nthoroughly integrates neuroscience with neural network modeling.\n\nSerious philosophical engagement with neuroscience dates back at least\nto Patricia Churchland’s *Neurophilosophy* (1986). As\ncomputational neuroscience matured, Churchland became one of its main\nphilosophical champions (Churchland, Koch, and Sejnowski 1990;\nChurchland and Sejnowski 1992). She was joined by Paul Churchland\n(1995, 2007) and others (Eliasmith 2013; Eliasmith and Anderson 2003;\nPiccinini and Bahar 2013; Piccinini and Shagrir 2014). All these\nauthors hold that theorizing about mental computation should begin\nwith the brain, not with Turing machines or other inappropriate tools\ndrawn from logic and computer science. They also hold that neural\nnetwork modeling should strive for greater biological realism than\nconnectionist models typically attain. Chris Eliasmith (2013) develops\nthis neurocomputational viewpoint through the *Neural Engineering\nFramework*, which supplements computational neuroscience with\ntools drawn from control theory (Brogan 1990). He aims to\n“reverse engineer” the brain, building large-scale,\nbiologically plausible neural network models of cognitive\nphenomena.\n\nComputational neuroscience differs in a crucial respect from CCTM and connectionism: it abandons multiple realizability. Computational neuroscientists cite specific neurophysiological properties and processes, so their models do not apply equally well to (say) a sufficiently different silicon-based creature. Thus, computational neuroscience sacrifices a key feature that originally attracted philosophers to CTM. Computational neuroscientists will respond that this sacrifice is worth the resultant insight into neurophysiological underpinnings. But many computationalists worry that, by focusing too much on neural underpinnings, we risk losing sight of the cognitive forest for the neuronal trees. Neurophysiological details are important, but don’t we also need an additional abstract level of computational description that prescinds from such details? Gallistel and King (2009) argue that a myopic fixation upon what we currently know about the brain has led computational neuroscience to shortchange core cognitive phenomena such as navigation, spatial and temporal learning, and so on. Similarly, Edelman (2014) complains that the Neural Engineering Framework substitutes a blizzard of neurophysiological details for satisfying psychological explanations.\n\nPartly in response to such worries, some researchers propose an\nintegrated *cognitive computational neuroscience* that connects\npsychological theories with neural implementation mechanisms\n(Naselaris et al. 2018; Kriegeskorte and Douglas 2018). The basic idea\nis to use neural network models to illuminate how mental processes are\ninstantiated in the brain, thereby grounding multiply realizable\ncognitive description in the neurophysiological. A good example is\nrecent work on neural implementation of Bayesian inference (Pouget et\nal. 2013; Orhan and Ma 2017; Aitchison and Lengyel 2016). Researchers\narticulate (multiply realizable) Bayesian models of various mental\nprocesses; they construct biologically plausible neural networks that\nexecute or approximately execute the posited Bayesian computations;\nand they evaluate how well these neural network models fit with\nneurophysiological data.\n\nDespite the differences between connectionism and computational\nneuroscience, these two movements raise many similar issues. In\nparticular, the dialectic from\n[§4.4](#ComNeu)\nregarding systematicity and productivity arises in similar form.\n\n[5. Computation and representation]\n\nPhilosophers and cognitive scientists use the term\n“representation” in diverse ways. Within philosophy, the\nmost dominant usage ties representation to intentionality, i.e., the\n“aboutness” of mental states. Contemporary philosophers\nusually elucidate intentionality by invoking *representational\ncontent*. A representational mental state has a content that\nrepresents the world as being a certain way, so we can ask whether the\nworld is indeed that way. Thus, representationally contentful mental\nstates are *semantically evaluable* with respect to properties\nsuch as truth, accuracy, fulfillment, and so on. To illustrate:\n\n- Beliefs are the sorts of things that can be true or false. My\nbelief\n*that Emmanuel Macron is French*is true if Emmanuel Macron is French, false if he is not. - Perceptual states are the sorts of things that can be accurate or\ninaccurate. My perceptual experience\n*as of a red sphere*is accurate only if a red sphere is before me. - Desires are the sorts of things that can fulfilled or thwarted. My\ndesire\n*to eat chocolate*is fulfilled if I eat chocolate, thwarted if I do not eat chocolate.\n\nBeliefs have truth-conditions (conditions under which they are true), perceptual states have accuracy-conditions (conditions under which they are accurate), and desires have fulfillment-conditions (conditions under which they are fulfilled).\n\nIn ordinary life, we frequently predict and explain behavior by\ninvoking beliefs, desires, and other representationally contentful\nmental states. We identify these states through their representational\nproperties. When we say “Frank believes that Emmanuel Macron is\nFrench”, we specify the condition under which Frank’s\nbelief is true (namely, that Emmanuel Macron is French). When we say\n“Frank wants to eat chocolate”, we specify the condition\nunder which Frank’s desire is fulfilled (namely, that Frank eats\nchocolate). So folk psychology assigns a central role to\n*intentional descriptions*, i.e., descriptions that identify\nmental states through their representational properties. Whether\nscientific psychology should likewise employ intentional descriptions\nis a contested issue within contemporary philosophy of mind.\n\n*Intentional realism* is realism regarding representation. At a\nminimum, this position holds that representational properties are\ngenuine aspects of mentality. Usually, it is also taken to hold that\nscientific psychology should freely employ intentional descriptions\nwhen appropriate. Intentional realism is a popular position, advocated\nby Tyler Burge (2010a), Jerry Fodor (1987), Christopher Peacocke\n(1992, 1994), and many others. One prominent argument for intentional\nrealism cites *cognitive science practice*. The argument\nmaintains that intentional description figures centrally in many core\nareas of cognitive science, such as perceptual psychology and\nlinguistics. For example, perceptual psychology describes how\nperceptual activity transforms sensory inputs (e.g., retinal\nstimulations) into representations of the distal environment (e.g.,\nperceptual representations of distal shapes, sizes, and colors). The\nscience identifies perceptual states by citing representational\nproperties (e.g., representational relations to specific distal\nshapes, sizes, colors). Assuming a broadly scientific realist\nperspective, the explanatory achievements of perceptual psychology\nsupport a realist posture towards intentionality.\n\n*Eliminativism* is a strong form of anti-realism about\nintentionality. Eliminativists dismiss intentional description as\nvague, context-sensitive, interest-relative, explanatorily\nsuperficial, or otherwise problematic. They recommend that scientific\npsychology jettison representational content. An early example is W.V.\nQuine’s *Word and Object* (1960), which seeks to replace\nintentional psychology with behaviorist stimulus-response psychology.\nPaul Churchland (1981), another prominent eliminativist, wants to\nreplace intentional psychology with neuroscience.\n\nBetween intentional realism and eliminativism lie various intermediate\npositions. Daniel Dennett (1971, 1987) acknowledges that intentional\ndiscourse is predictively useful, but he questions whether mental\nstates *really* have representational properties. According to\nDennett, theorists who employ intentional descriptions are not\n*literally* asserting that mental states have representational\nproperties. They are merely adopting the “intentional\nstance”. Donald Davidson (1980) espouses a neighboring\n*interpretivist* position. He emphasizes the central role that\nintentional ascription plays within ordinary interpretive practice,\ni.e., our practice of interpreting one another’s mental states\nand speech acts. At the same time, he questions whether intentional\npsychology will find a place within mature scientific theorizing.\nDavidson and Dennett both profess realism about intentional mental\nstates. Nevertheless, both philosophers are customarily read as\nintentional anti-realists. (In particular, Dennett is frequently read\nas a kind of *instrumentalist* about intentionality.) One\nsource of this customary reading involves *indeterminacy of\ninterpretation*. Suppose that behavioral evidence allows two\nconflicting interpretations of a thinker’s mental states.\nFollowing Quine, Davidson and Dennett both say there is then “no\nfact of the matter” regarding which interpretation is correct.\nThis diagnosis indicates a less than fully realist attitude towards\nintentionality.\n\nDebates over intentionality figure prominently in philosophical discussion of CTM. Let us survey some highlights.\n\n[5.1 Computation as formal]\n\nClassical computationalists typically assume what one might call\n*the formal-syntactic conception of computation* (FSC). The\nintuitive idea is that computation manipulates symbols in virtue of\ntheir formal syntactic properties rather than their semantic\nproperties.\n\nFSC stems from innovations in mathematical logic during the late\n19th and early 20th centuries, especially\nseminal contributions by George Boole and Gottlob Frege. In his\n*Begriffsschrift* (1879/1967), Frege effected a thoroughgoing\n*formalization* of deductive reasoning. To formalize, we\nspecify a *formal language* whose component linguistic\nexpressions are individuated non-semantically (e.g., by their\ngeometric shapes). We may have some intended interpretation in mind,\nbut elements of the formal language are purely syntactic entities that\nwe can discuss without invoking semantic properties such as reference\nor truth-conditions. In particular, we can specify *inference\nrules* in formal syntactic terms. If we choose our inference rules\nwisely, then they will cohere with our intended interpretation: they\nwill carry true premises to true conclusions. Through formalization,\nFrege invested logic with unprecedented rigor. He thereby laid the\ngroundwork for numerous subsequent mathematical and philosophical\ndevelopments.\n\nFormalization plays a significant foundational role within computer science. We can program a Turing-style computer that manipulates linguistic expressions drawn from a formal language. If we program the computer wisely, then its syntactic machinations will cohere with our intended semantic interpretation. For example, we can program the computer so that it carries true premises only to true conclusions, or so that it updates probabilities as dictated by Bayesian decision theory.\n\nFSC holds that *all* computation manipulates formal syntactic\nitems, without regard to any semantic properties those items may have.\nPrecise formulations of FSC vary. Computation is said to be\n“sensitive” to syntax but not semantics, or to have\n“access” only to syntactic properties, or to operate\n“in virtue” of syntactic rather than semantic properties,\nor to be impacted by semantic properties only as\n“mediated” by syntactic properties. It is not always so\nclear what these formulations mean or whether they are equivalent to\none another. But the intuitive picture is that syntactic properties\nhave causal/explanatory primacy over semantic properties in driving\ncomputation forward.\n\nFodor’s article “Methodological Solipsism Considered as a Research Strategy in Cognitive Psychology” (1980) offers an early statement. Fodor combines FSC with CCTM+RTM. He analogizes Mentalese to formal languages studied by logicians: it contains simple and complex items individuated non-semantically, just as typical formal languages contain simple and complex expressions individuated by their shapes. Mentalese symbols have a semantic interpretation, but this interpretation does not (directly) impact mental computation. A symbol’s formal properties, rather than its semantic properties, determine how computation manipulates the symbol. In that sense, the mind is a “syntactic engine”. Virtually all classical computationalists follow Fodor in endorsing FSC.\n\nConnectionists often deny that neural networks manipulate\nsyntactically structured items. For that reason, many connectionists\nwould hesitate to accept FSC. Nevertheless, most connectionists\nendorse a *generalized formality thesis*: computation is\ninsensitive to semantic properties. The generalized formality thesis\nraises many of the same philosophical issues raised by FSC. We focus\nhere on FSC, which has received the most philosophical discussion.\n\nFodor combines CCTM+RTM+FSC with intentional realism. He holds that\nCCTM+RTM+FSC vindicates folk psychology by helping us convert common\nsense intentional discourse into rigorous science. He motivates his\nposition with a famous abductive argument for CCTM+RTM+FSC (1987:\n18–20). Strikingly, mental activity tracks semantic properties\nin a coherent way. For example, deductive inference carries premises\nto conclusions that are true if the premises are true. How can we\nexplain this crucial aspect of mental activity? Formalization shows\nthat syntactic manipulations can track semantic properties, and\ncomputer science shows how to build physical machines that execute\ndesired syntactic manipulations. If we treat the mind as a\nsyntax-driven machine, then we can explain why mental activity tracks\nsemantic properties in a coherent way. Moreover, our explanation does\nnot posit causal mechanisms radically different from those posited\nwithin the physical sciences. We thereby answer the pivotal question:\n*How is rationality mechanically possible*?\n\nStephen Stich (1983) and Hartry Field (2001) combine CCTM+FSC with eliminativism. They recommend that cognitive science model the mind in formal syntactic terms, eschewing intentionality altogether. They grant that mental states have representational properties, but they ask what explanatory value scientific psychology gains by invoking those properties. Why supplement formal syntactic description with intentional description? If the mind is a syntax-driven machine, then doesn’t representational content drop out as explanatorily irrelevant?\n\nAt one point in his career, Putnam (1983: 139–154) combined\nCCTM+FSC with a Davidson-tinged *interpretivism*. Cognitive\nscience should proceed along the lines suggested by Stich and Field,\ndelineating purely formal syntactic computational models. Formal\nsyntactic modeling co-exists with ordinary interpretive practice, in\nwhich we ascribe intentional contents to one another’s mental\nstates and speech acts. Interpretive practice is governed by holistic\nand heuristic constraints, which stymie attempts at converting\nintentional discourse into rigorous science. For Putnam, as for Field\nand Stich, the scientific action occurs at the formal syntactic level\nrather than the intentional level.\n\nCTM+FSC comes under attack from various directions. One criticism\ntargets *the causal relevance of representational content*\n(Block 1990; Figdor 2009; Kazez 1995). Intuitively speaking, the\ncontents of mental states are causally relevant to mental activity and\nbehavior. For example, my desire to drink water rather than orange\njuice causes me to walk to the sink rather than the refrigerator. The\ncontent of my desire (*that I drink water*) seems to play an\nimportant causal role in shaping my behavior. According to Fodor\n(1990: 137–159), CCTM+RTM+FSC accommodates such intuitions.\nFormal syntactic activity *implements* intentional mental\nactivity, thereby ensuring that intentional mental states causally\ninteract in accord with their contents. However, it is not so clear\nthat this analysis secures the causal relevance of content. FSC says\nthat computation is “sensitive” to syntax but not\nsemantics. Depending on how one glosses the key term\n“sensitive”, it can look like representational content is\ncausally irrelevant, with formal syntax doing all the causal work.\nHere is an analogy to illustrate the worry. When a car drives along a\nroad, there are stable patterns involving the car’s shadow.\nNevertheless, shadow position at one time does not influence shadow\nposition at a later time. Similarly, CCTM+RTM+FSC may explain how\nmental activity instantiates stable patterns described in intentional\nterms, but this is not enough to ensure the causal relevance of\ncontent. If the mind is a syntax-driven machine, then causal efficacy\nseems to reside at the syntactic rather the semantic level. Semantics\nis just “along for the ride”. Apparently, then, CTM+FSC\nencourages the conclusion that representational properties are\ncausally inert. The conclusion may not trouble eliminativists, but\nintentional realists usually want to avoid it.\n\nA second criticism dismisses the formal-syntactic picture as\nspeculation ungrounded in scientific practice. Tyler Burge (2010a,b,\n2013: 479–480) contends that formal syntactic description of\nmental activity plays no significant role within large areas of\ncognitive science, including the study of theoretical reasoning,\npractical reasoning, and perception. In each case, Burge argues, the\nscience employs intentional description *rather than* formal\nsyntactic description. For example, perceptual psychology individuates\nperceptual states not through formal syntactic properties but through\nrepresentational relations to distal shapes, sizes, colors, and so on.\nTo understand this criticism, we must distinguish *formal syntactic\ndescription* and *neurophysiological description*. Everyone\nagrees that a complete scientific psychology will assign prime\nimportance to neurophysiological description. However,\nneurophysiological description is distinct from formal syntactic\ndescription, because formal syntactic description is supposed to be\nmultiply realizable in the neurophysiological. The issue here is\nwhether scientific psychology should supplement *intentional\ndescriptions* and *neurophysiological descriptions* with\n*multiply realizable, non-intentional formal syntactic*\ndescriptions.\n\n[5.2 Externalism about mental content]\n\nPutnam’s landmark article “The Meaning of\n‘Meaning’” (1975: 215–271) introduced the\n*Twin Earth thought experiment*, which postulates a world just\nlike our own except that H2O is replaced by a qualitatively\nsimilar substance XYZ with different chemical composition. Putnam\nargues that XYZ is not water and that speakers on Twin Earth use the\nword “water” to refer to XYZ rather than to water. Burge\n(1982) extends this conclusion from *linguistic reference* to\n*mental content*. He argues that Twin Earthlings instantiate\nmental states with different contents. For example, if Oscar on Earth\nthinks *that water is thirst-quenching*, then his duplicate on\nTwin Earth thinks a thought with a different content, which we might\ngloss as *that twin-water is thirst-quenching*. Burge concludes\nthat mental content does not supervene upon internal neurophysiology.\nMental content is individuated partly by factors outside the\nthinker’s skin, including causal relations to the environment.\nThis position is *externalism about mental content*.\n\nFormal syntactic properties of mental states are widely taken to supervene upon internal neurophysiology. For example, Oscar and Twin Oscar instantiate the same formal syntactic manipulations. Assuming content externalism, it follows that there is a huge gulf between ordinary intentional description and formal syntactic description.\n\nContent externalism raises serious questions about the explanatory utility of representational content for scientific psychology:\n\n*Argument from Causation* (Fodor 1987, 1991): How can mental\ncontent exert any causal influence except as manifested within\ninternal neurophysiology? There is no “psychological action at a\ndistance”. Differences in the physical environment impact\nbehavior only by inducing differences in local brain states. So the\nonly causally relevant factors are those that supervene upon internal\nneurophysiology. Externally individuated content is *causally\nirrelevant*.\n\n*Argument from Explanation* (Stich 1983): Rigorous scientific\nexplanation should not take into account factors outside the\nsubject’s skin. Folk psychology may taxonomize mental states\nthrough relations to the external environment, but scientific\npsychology should taxonomize mental states entirely through factors\nthat supervene upon internal neurophysiology. It should treat Oscar\nand Twin Oscar as psychological\nduplicates.[ 4]\n\nSome authors pursue the two arguments in conjunction with one another. Both arguments reach the same conclusion: externally individuated mental content finds no legitimate place within causal explanations provided by scientific psychology. Stich (1983) argues along these lines to motivate his formal-syntactic eliminativism.\n\nMany philosophers respond to such worries by promoting *content\ninternalism*. Whereas content externalists favor *wide\ncontent* (content that does not supervene upon internal\nneurophysiology), content internalists favor *narrow content*\n(content that does so supervene). Narrow content is what remains of\nmental content when one factors out all external elements. At one\npoint in his career, Fodor (1981, 1987) pursued internalism as a\nstrategy for integrating intentional psychology with CCTM+RTM+FSC.\nWhile conceding that wide content should not figure in scientific\npsychology, he maintained that narrow content should play a central\nexplanatory role.\n\nRadical internalists insist that *all* content is narrow. A\ntypical analysis holds that Oscar is thinking not about water but\nabout some more general category of substance that subsumes XYZ, so\nthat Oscar and Twin Oscar entertain mental states with the same\ncontents. Tim Crane (1991) and Gabriel Segal (2000) endorse such an\nanalysis. They hold that folk psychology always individuates\npropositional attitudes narrowly. A less radical internalism\nrecommends that we recognize narrow content *in addition to*\nwide content. Folk psychology may sometimes individuate propositional\nattitudes widely, but we can also delineate a viable notion of narrow\ncontent that advances important philosophical or scientific goals.\nInternalists have proposed various candidate notions of narrow content\n(Block 1986; Chalmers 2002; Cummins 1989; Fodor 1987; Lewis 1994; Loar\n1988; Mendola 2008). See the entry\n[narrow mental content](../content-narrow/)\nfor an overview of prominent candidates.\n\nExternalists complain that existing theories of narrow content are sketchy, implausible, useless for psychological explanation, or otherwise objectionable (Burge 2007; Sawyer 2000; Stalnaker 1999). Externalists also question internalist arguments that scientific psychology requires narrow content:\n\n*Argument from Causation*: Externalists insist that wide\ncontent can be causally relevant. The details vary among externalists,\nand discussion often becomes intertwined with complex issues\nsurrounding causation, counterfactuals, and the metaphysics of mind.\nSee the entry\n[mental causation](../mental-causation/)\nfor an introductory overview, and see Burge (2007), Rescorla (2014),\nand Yablo (1997, 2003) for representative externalist discussion.\n\n*Argument from Explanation*: Externalists claim that\npsychological explanation can legitimately taxonomize mental states\nthrough factors that outstrip internal neurophysiology (Peacocke 1993;\nShea 2018). Burge observes that non-psychological sciences often\nindividuate explanatory kinds *relationally*, i.e., through\nrelations to external factors. For example, whether an entity counts\nas a heart depends (roughly) upon whether its biological function in\nits normal environment is to pump blood. So physiology individuates\norgan kinds relationally. Why can’t psychology likewise\nindividuate mental states relationally? For a notable exchange on\nthese issues, see Burge (1986, 1989, 1995) and Fodor (1987, 1991).\n\nExternalists doubt that we have any good reason to replace or supplement wide content with narrow content. They dismiss the search for narrow content as a wild goose chase.\n\nBurge (2007, 2010a) defends externalism by analyzing current cognitive science. He argues that many branches of scientific psychology (especially perceptual psychology) individuate mental content through causal relations to the external environment. He concludes that scientific practice embodies an externalist perspective. By contrast, he maintains, narrow content is a philosophical fantasy ungrounded in current science.\n\nSuppose we abandon the search for narrow content. What are the\nprospects for combining CTM+FSC with externalist intentional\npsychology? The most promising option emphasizes *levels of\nexplanation*. We can say that intentional psychology occupies one\nlevel of explanation, while formal-syntactic computational psychology\noccupies a different level. Fodor advocates this approach in his later\nwork (1994, 2008). He comes to reject narrow content as otiose. He\nsuggests that formal syntactic mechanisms implement externalist\npsychological laws. Mental computation manipulates Mentalese\nexpressions in accord with their formal syntactic properties, and\nthese formal syntactic manipulations ensure that mental activity\ninstantiates appropriate law-like patterns defined over wide\ncontents.\n\nIn light of the internalism/externalism distinction, let us revisit\nthe eliminativist challenge raised in\n[§5.1](#ComFor):\nwhat explanatory value does intentional description add to\nformal-syntactic description? Internalists can respond that suitable\nformal syntactic manipulations determine and maybe even constitute\nnarrow contents, so that internalist intentional description is\nalready implicit in suitable formal syntactic description (cf. Field\n2001: 75). Perhaps this response vindicates intentional realism,\nperhaps not. Crucially, though, no such response is available to\ncontent externalists. Externalist intentional description is not\nimplicit in formal syntactic description, because one can hold formal\nsyntax fixed while varying wide content. Thus, content externalists\nwho espouse CTM+FSC must say what we gain by supplementing\nformal-syntactic explanations with intentional explanations. Once we\naccept that mental computation is sensitive to syntax but not\nsemantics, it is far from clear that any useful explanatory work\nremains for wide content. Fodor addresses this challenge at various\npoints, offering his most systematic treatment in *The Elm and the\nExpert* (1994). See Arjo (1996), Aydede (1998), Aydede and Robbins\n(2001), Wakefield (2002); Perry (1998), and Wakefield (2002) for\ncriticism. See Rupert (2008) and Schneider (2005) for positions close\nto Fodor’s. Dretske (1993) and Shea (2018, pp. 197–226)\npursue alternative strategies for vindicating the explanatory\nrelevance of wide content.\n\n[5.3 Content-involving computation]\n\nThe perceived gulf between computational description and intentional\ndescription animates many writings on CTM. A few philosophers try to\nbridge the gulf using computational descriptions that individuate\ncomputational states in representational terms. These descriptions are\n*content-involving*, to use Christopher Peacocke’s (1994)\nterminology. On the content-involving approach, there is no rigid\ndemarcation between computational and intentional description. In\nparticular, certain scientifically valuable descriptions of mental\nactivity are both computational and intentional. Call this position\n*content-involving computationalism*.\n\nContent-involving computationalists need not say that all\ncomputational description is intentional. To illustrate, suppose we\ndescribe a simple Turing machine that manipulates symbols individuated\nby their geometric shapes. Then the resulting computational\ndescription is not plausibly content-involving. Accordingly,\ncontent-involving computationalists do not usually advance\ncontent-involving computation as a general theory of computation. They\nclaim only that *some* important computational descriptions are\ncontent-involving.\n\nOne can develop content-involving computationalism in an internalist\nor externalist direction. *Internalist content-involving\ncomputationalists* hold that some computational descriptions\nidentify mental states partly through their *narrow* contents.\nMurat Aydede (2005) recommends a position along these lines.\n*Externalist content-involving computationalism* holds that\ncertain computational descriptions identify mental states partly\nthrough their *wide* contents. Tyler Burge (2010a:\n95–101), Christopher Peacocke (1994, 1999), and Mark Sprevak\n(2010) espouse this position. Oron Shagrir (2001, 2020, 2022)\nadvocates a content-involving computationalism that is neutral between\ninternalism and externalism.\n\nExternalist content-involving computationalists typically cite cognitive science practice as a motivating factor. For example, perceptual psychology describes the perceptual system as computing an estimate of some object’s size from retinal stimulations and from an estimate of the object’s depth. Perceptual “estimates” are identified representationally, as representations of specific distal sizes and depths. Quite plausibly, representational relations to specific distal sizes and depths do not supervene on internal neurophysiology. Quite plausibly, then, perceptual psychology type-identifies perceptual computations through wide contents. So externalist content-involving computationalism seems to harmonize well with current cognitive science.\n\nA major challenge facing content-involving computationalism concerns the interface with standard computationalism formalisms, such as the Turing machine. How exactly do content-involving descriptions relate to the computational models found in logic and computer science? Philosophers usually assume that these models offer non-intentional descriptions. If so, that would be a major and perhaps decisive blow to content-involving computationalism.\n\nArguably, though, many familiar computational formalisms allow a\ncontent-involving rather than formal syntactic construal. To\nillustrate, consider the Turing machine. One *can* individuate\nthe “symbols” comprising the Turing machine alphabet\nnon-semantically, through factors akin to geometric shape. But does\nTuring’s formalism *require* a non-semantic individuative\nscheme? Arguably, the formalism allows us to individuate symbols\npartly through their contents. Of course, the machine table for a\nTuring machine does not explicitly cite semantic properties of symbols\n(e.g., denotations or truth-conditions). Nevertheless, the machine\ntable can encode mechanical rules that describe how to manipulate\nsymbols, where those symbols are type-identified in content-involving\nterms. In this way, the machine table dictates transitions among\ncontent-involving states without explicitly mentioning semantic\nproperties. Aydede (2005) suggests an internalist version of this\nview, with symbols type-identified through their narrow\ncontents.[ 5]\nRescorla (2017a) develops the view in an externalist direction, with\nsymbols type-identified through their wide contents. He argues that\nsome Turing-style models describe computational operations over\nexternalistically individuated Mentalese\nsymbols.\n\n[\n\n[6](notes.html#note-6)]\nIn principle, one might embrace both externalist content-involving\ncomputational description *and* formal syntactic description.\nOne might say that these two kinds of description occupy distinct\nlevels of explanation. Peacocke suggests such a view. Other\ncontent-involving computationalists regard formal syntactic\ndescriptions of the mind more skeptically. For example, Burge\nquestions what explanatory value formal syntactic description\ncontributes to certain areas of scientific psychology (such as\nperceptual psychology). From this viewpoint, the eliminativist\nchallenge posed in\n[§5.1](#ComFor)\nhas matters backwards. We should not assume that formal syntactic\ndescriptions are explanatorily valuable and then ask what value\nintentional descriptions contribute. We should instead embrace the\nexternalist intentional descriptions offered by current cognitive\nscience and then ask what value formal syntactic description\ncontributes.\n\nProponents of formal syntactic description often respond by citing\n*implementation mechanisms*. Externalist description of mental\nactivity presupposes that suitable causal-historical relations between\nthe mind and the external physical environment are in place. But\nsurely we want a “local” description that ignores external\ncausal-historical relations, a description that reveals underlying\ncausal mechanisms. Fodor (1987, 1994) argues in this way to motivate\nthe formal syntactic picture. For possible externalist responses to\nthe argument from implementation mechanisms, see Burge (2010b),\nRescorla (2017b), Shea (2013), and Sprevak (2010). For an argument\nthat current cognitive science practice does indeed assign an\nimportant explanatory role to formal syntax, see Calzavarini and\nPaternoster (2022). Debate over the explanatory value of formal\nsyntax, and more generally over the relation between computation and\nrepresentation, seems likely to continue into the indefinite\nfuture.\n\n[6. Alternative conceptions of computation]\n\nThe literature offers several alternative conceptions, usually advanced as foundations for CTM. In many cases, these conceptions overlap with one another or with the conceptions considered above.\n\n[6.1 Information-processing]\n\nIt is common for cognitive scientists to describe computation as “information-processing”. It is less common for proponents to clarify what they mean by “information” or “processing”. Lacking clarification, the description is little more than an empty slogan.\n\nClaude Shannon introduced a scientifically important notion of\n“information” in his 1948 article “A Mathematical\nTheory of Communication”. The intuitive idea is that information\nmeasures *reduction in uncertainty*, where reduced uncertainty\nmanifests as an altered probability distribution over possible states.\nShannon codified this idea within a rigorous mathematical framework,\nlaying the foundation for *information theory* (Cover and\nThomas 2006). Shannon information is fundamental to modern\nengineering. It finds fruitful application within cognitive science,\nespecially cognitive neuroscience. Does it support a convincing\nanalysis of computation as “information-processing”?\nConsider an old-fashioned tape machine that records messages received\nover a wireless radio. Using Shannon’s framework, one can\nmeasure how much information is carried by some recorded message.\nThere is a sense in which the tape machine “processes”\nShannon information whenever we replay a recorded message. Still, the\nmachine does not seem to implement a non-trivial computational\nmodel.[ 7]\nCertainly, neither the Turing machine formalism nor the neural\nnetwork formalism offers much insight into the machine’s\noperations. Arguably, then, a system can process Shannon information\nwithout executing computations in any interesting sense.\n\nConfronted with such examples, one might try to isolate a more\ndemanding notion of “processing”, so that the tape machine\ndoes not “process” Shannon information. Alternatively, one\nmight insist that the tape machine executes non-trivial computations.\nPiccinini and Scarantino (2010) advance a highly general notion of\ncomputation—which they dub *generic\ncomputation*—with that consequence.\n\nA second prominent notion of information derives from Paul\nGrice’s (1989) influential discussion of *natural\nmeaning*. Natural meaning involves reliable,\ncounterfactual-supporting correlations. For example, tree rings\ncorrelate with the age of the tree, and pox correlate with chickenpox.\nWe colloquially describe tree rings as carrying information about tree\nage, pox as carrying information about chickenpox, and so on. Such\ndescriptions suggest a conception that ties information to reliable,\ncounterfactual-supporting correlations. Fred Dretske (1981) develops\nthis conception into a systematic theory, as do various subsequent\nphilosophers. Does Dretske-style information subserve a plausible\nanalysis of computation as “information-processing”?\nConsider an old-fashioned *bimetallic strip thermostat*. Two\nmetals are joined together into a strip. Differential expansion of the\nmetals causes the strip to bend, thereby activating or deactivating a\nheating unit. Strip state reliably correlates with current ambient\ntemperature, and the thermostat “processes” this\ninformation-bearing state when activating or deactivating the heater.\nYet the thermostat does not seem to implement any non-trivial\ncomputational model. One would not ordinarily regard the thermostat as\ncomputing. Arguably, then, a system can process Dretske-style\ninformation without executing computations in any interesting sense.\nOf course, one might try to handle such examples through maneuvers\nparallel to those from the previous paragraph.\n\nA third prominent notion of information is *semantic\ninformation*, i.e., representational\ncontent.[ 8]\nSome philosophers hold that a physical system computes only if the\nsystem’s states have representational properties (Dietrich 1989;\nFodor 1998: 10; Ladyman 2009; Shagrir 2006; Sprevak 2010). In that\nsense, information-processing is\n\n*necessary*for computation. As Fodor memorably puts it, “no computation without representation” (1975: 34). However, this position is debatable. Chalmers (2011) and Piccinini (2008a) contend that a Turing machine might execute computations even though symbols manipulated by the machine have no semantic interpretation. The machine’s computations are purely syntactic in nature, lacking anything like semantic properties. On this view, representational content is not necessary for a physical system to count as computational.\n\nIt remains unclear whether the slogan “computation is information-processing” provides much insight. Nevertheless, the slogan seems unlikely to disappear from the literature anytime soon. For further discussion of possible connections between computation and information, see Gallistel and King (2009: 1–26), Lizier, Flecker, and Williams (2013), Miłkowski (2013), Piccinini and Scarantino (2010), and Sprevak (2020).\n\n[6.2 Function evaluation]\n\nIn a widely cited passage, the perceptual psychologist David Marr (1982) distinguishes three levels at which one can describe an “information-processing device”:\n\nComputational theory: “[t]he device is characterized as a mapping from one kind of information to another, the abstract properties of this mapping are defined precisely, and its appropriateness and adequacy for the task at hand are demonstrated” (p. 24).\n\nRepresentation and algorithm: “the choice of representation for the input and output and the algorithm to be used to transform one into the other” (pp. 24–25).\n\nHardware implementation: “the details of how the algorithm and representation are realized physically” (p. 25).\n\nMarr’s three levels have attracted intense philosophical scrutiny. For our purposes, the key point is that Marr’s “computational level” describes a mapping from inputs to outputs, without describing intermediate steps. Marr illustrates his approach by providing “computational level” theories of various perceptual processes, such as edge detection.\n\nMarr’s discussion suggests a *functional conception of\ncomputation*, on which computation is a matter of transforming\ninputs into appropriate outputs. Frances Egan elaborates the\nfunctional conception over a series of articles (1991, 1992, 1999,\n2003, 2010, 2014, 2019, 2020). Like Marr, she treats computational\ndescription as description of input-output relations. She also claims\nthat computational models characterize a purely *mathematical*\nfunction: that is, a mapping from mathematical inputs to mathematical\noutputs. She illustrates by considering a visual mechanism (called\n“Visua”) that computes an object’s depth from\nretinal disparity. She imagines a neurophysiological duplicate\n(“Twin Visua”) embedded so differently in the physical\nenvironment that it does not represent depth. Visua and Twin Visua\ninstantiate perceptual states with different representational\nproperties. Nevertheless, Egan says, vision science treats Visua and\nTwin Visua as *computational duplicates*. Visua and Twin Visua\ncompute the same mathematical function, even though the computations\nhave different representational import in the two cases. Egan\nconcludes that computational modeling of the mind yields an\n“abstract mathematical description” consistent with many\nalternative possible representational descriptions. Intentional\nattribution is just a heuristic gloss upon underlying computational\ndescription.\n\nChalmers (2012) argues that the functional conception neglects important features of computation. As he notes, computational models usually describe more than just input-output relations. They describe intermediate steps through which inputs are transformed into outputs. These intermediate steps, which Marr consigns to the “algorithmic” level, figure prominently in computational models offered by logicians and computer scientists. Restricting the term “computation” to input-output description does not capture standard computational practice.\n\nAn additional worry faces functional theories, such as Egan’s,\nthat exclusively emphasize *mathematical* inputs and outputs.\nCritics complain that Egan mistakenly elevates mathematical functions,\nat the expense of intentional explanations routinely offered by\ncognitive science (Burge 2005; Rescorla 2015; Silverberg 2006; Sprevak\n2010). To illustrate, suppose perceptual psychology describes the\nperceptual system as estimating that some object’s depth is 5\nmeters. The perceptual depth-estimate has a representational content:\nit is accurate only if the object’s depth is 5 meters. We cite\nthe number 5 to identify the depth-estimate. But our choice of this\nnumber depends upon our arbitrary choice of measurement units. Critics\ncontend that the content of the depth-estimate, not the arbitrarily\nchosen number through which we theorists specify that content, is what\nmatters for psychological explanation. Egan’s theory places the\nnumber rather than the content at explanatory center stage. According\nto Egan, computational explanation should describe the visual system\nas computing a *particular mathematical function* that carries\n*particular mathematical inputs* into *particular\nmathematical outputs*. Those particular mathematical inputs and\noutputs depend upon our arbitrary choice of measurement units, so they\narguably lack the explanatory significance that Egan assigns to\nthem.\n\nWe should distinguish the functional approach, as pursued by Marr and\nEgan, from the *functional programming paradigm* in computer\nscience. The functional programming paradigm models evaluation of a\ncomplex function as successive evaluation of simpler functions. To\ntake a simple example, one might evaluate \\(f(x,y) = (x^{2}+y)\\) by\nfirst evaluating the squaring function and then evaluating the\naddition function. Functional programming differs from the\n“computational level” descriptions emphasized by Marr,\nbecause it specifies intermediate computational stages. The functional\nprogramming paradigm stretches back to Alonzo Church’s (1936)\n*lambda calculus*, continuing with programming languages such\nas PCF and LISP. It plays an important role in AI and theoretical\ncomputer science. Some authors suggest that it offers special insight\ninto mental computation (Klein 2012; Piantadosi, Tenenbaum, and\nGoodman 2012). However, many computational formalisms do not conform\nto the functional paradigm: Turing machines; imperative programming\nlanguages, such as C; logic programming languages, such as Prolog; and\nso on. Even though the functional paradigm describes numerous\nimportant computations (possibly including mental computations), it\ndoes not plausibly capture computation *in general*.\n\n[6.3 Structuralism]\n\nMany philosophical discussions embody a *structuralist conception\nof computation*: a computational model describes an abstract\ncausal structure, without taking into account particular physical\nstates that instantiate the structure. This conception traces back at\nleast to Putnam’s original treatment (1967). Chalmers (1995,\n1996a, 2011, 2012) develops it in detail. He introduces the\n*combinatorial-state automaton* (CSA) formalism, which subsumes\nmost familiar models of computation (including Turing machines and\nneural networks). A CSA provides an abstract description of a physical\nsystem’s *causal topology*: the pattern of causal\ninteraction among the system’s parts, independent of the nature\nof those parts or the causal mechanisms through which they interact.\nComputational description specifies a causal topology.\n\nChalmers deploys structuralism to delineate a very general version of\nCTM. He assumes the functionalist view that psychological states are\nindividuated by their roles in a pattern of causal organization.\nPsychological description specifies causal roles, abstracted away from\nphysical states that realize those roles. So psychological properties\nare *organizationally invariant*, in that they supervene upon\ncausal topology. Since computational description characterizes a\ncausal topology, satisfying a suitable computational description\nsuffices for instantiating appropriate mental properties. It also\nfollows that psychological description is a species of computational\ndescription, so that computational description should play a central\nrole within psychological explanation. Thus, structuralist computation\nprovides a solid foundation for cognitive science. Mentality is\ngrounded in causal patterns, which are precisely what computational\nmodels articulate.\n\nStructuralism comes packaged with an attractive account of the\n*implementation relation* between abstract computational models\nand physical systems. Under what conditions does a physical system\nimplement a computational model? Structuralists say that a physical\nsystem implements a model just in case the model’s causal\nstructure is “isomorphic” to the model’s formal\nstructure. A computational model describes a physical system by\narticulating a formal structure that mirrors some relevant causal\ntopology. Chalmers elaborates this intuitive idea, providing detailed\nnecessary and sufficient conditions for physical realization of CSAs.\nFew if any alternative conceptions of computation can provide so\nsubstantive an account of the implementation relation.\n\nWe may instructively compare structuralist computationalism with some other theories discussed above:\n\n*Machine functionalism*. Structuralist computationalism\nembraces the core idea behind machine functionalism: mental states are\nfunctional states describable through a suitable computational\nformalism. Putnam advances CTM as an empirical hypothesis, and he\ndefends functionalism on that basis. In contrast, Chalmers follows\nDavid Lewis (1972) by grounding functionalism in the conceptual\nanalysis of mentalistic discourse. Whereas Putnam defends\nfunctionalism by defending computationalism, Chalmers defends\ncomputationalism by assuming functionalism.\n\n*Classical computationalism, connectionism, and computational\nneuroscience*. Structuralist computationalism emphasizes\norganizationally invariant descriptions, which are multiply\nrealizable. In that respect, it diverges from computational\nneuroscience. Structuralism is compatible with both classical and\nconnectionist computationalism, but it differs in spirit from those\nviews. Classicists and connectionists present their rival positions as\nbold, substantive hypotheses. Chalmers advances structuralist\ncomputationalism as a relatively minimalist position unlikely to be\ndisconfirmed.\n\n*Intentional realism and eliminativism*. Structuralist\ncomputationalism is compatible with both positions. CSA description\ndoes not explicitly mention semantic properties such as reference,\ntruth-conditions, representational content, and so on. Structuralist\ncomputationalists need not assign representational content any\nimportant role within scientific psychology. On the other hand,\nstructuralist computationalism does not preclude an important role for\nrepresentational content.\n\n*The formal-syntactic conception of computation*. Wide content\ndepends on causal-historical relations to the external environment,\nrelations that outstrip causal topology. Thus, CSA description leaves\nwide content underdetermined. Narrow content presumably supervenes\nupon causal topology, but CSA description does not explicitly mention\nnarrow contents. Overall, then, structuralist computationalism\nprioritizes a level of formal, non-semantic computational description.\nIn that respect, it resembles FSC. On the other hand, structuralist\ncomputationalists need not say that computation is\n“insensitive” to semantic properties, so they need not\nendorse all aspects of FSC.\n\nAlthough structuralist computationalism is distinct from CTM+FSC, it raises some similar issues. For example, Rescorla (2012) denies that causal topology plays the central explanatory role within cognitive science that structuralist computationalism dictates. He suggests that externalist intentional description rather than organizationally invariant description enjoys explanatory primacy. Coming from a different direction, computational neuroscientists will recommend that we forego organizationally invariant descriptions and instead employ more neurally specific computational models. In response to such objections, Chalmers (2012) argues that organizationally invariant computational description yields explanatory benefits that neither intentional description nor neurophysiological description replicate: it reveals the underlying mechanisms of cognition (unlike intentional description); and it abstracts away from neural implementation details that are irrelevant for many explanatory purposes.\n\n[6.4 Mechanistic theories]\n\nThe mechanistic nature of computation is a recurring theme in logic,\nphilosophy, and cognitive science. Several authors develop this theme\ninto a mechanistic conception of computing systems (Coelho Mollo,\n2017; Dewhurst 2016; Fresco 2014, 2017; Miłkowski 2013; Piccinini\n2007, 2012, 2015). On Gualtiero Piccinini’s (2015) influential\ndevelopment, a *functional mechanism* is a system of\ninterconnected components, where each component performs some function\nwithin the overall system. *Mechanistic explanation* proceeds\nby decomposing the system into parts, describing how the parts are\norganized into the larger system, and isolating the function performed\nby each part. A computing system is a functional mechanism of a\nparticular kind: it is a mechanism whose components are functionally\norganized to process vehicles in accord with rules. Echoing\nPutnam’s discussion of multiple realizability, Piccinini demands\nthat the rules be *medium-independent*, in that they abstract\naway from the specific physical implementations of the vehicles.\nComputational explanation decomposes the system into parts and\ndescribes how each part helps the system process the relevant\nvehicles. If the system processes discretely structured vehicles, then\nthe computation is digital. If the system processes continuous\nvehicles, then the computation is analog. Marcin\nMiłkowski’s (2013) version of the mechanistic approach is\nsimilar. He differs from Piccinini by pursuing an\n“information-processing” gloss, so that computational\nmechanisms operate over information-bearing states. Miłkowski and\nPiccinini deploy their respective mechanistic theories to defend\ncomputationalism. Piccinini (2020) focuses especially upon\n*neural* computation, drawing extensive connections with\ncognitive neuroscience.\n\nMechanistic computationalists typically individuate computational\nstates non-semantically. They therefore encounter worries about the\nexplanatory role of representational content, similar to worries\nencountered by FSC and structuralism. Critics protest that mechanistic\ncomputationalism does not accommodate cognitive science explanations\nthat are simultaneously computational and representational (Rescorla\n2016; Shagrir 2014; Shagrir 2022). The perceived force of this\ncriticism will depend upon one’s sympathy for content-involving\ncomputationalism. To defuse the criticism, Miłkowski (2017)\nretorts that mechanistic computationalists can assign a central\ntheoretical role to representational content by attributing\nrepresentational *functions* to certain computing\nmechanisms.\n\n[6.5 Pluralism]\n\nWe have surveyed various contrasting and sometimes overlapping\nconceptions of computation: classical computation, connectionist\ncomputation, neural computation, formal-syntactic computation,\ncontent-involving computation, information-processing computation,\nfunctional computation, structuralist computation, and mechanistic\ncomputation. Each conception yields a different form of\ncomputationalism. Each conception has its own strengths and\nweaknesses. One might adopt a *pluralistic* stance that\nrecognizes distinct legitimate conceptions. Rather than elevate one\nconception above the others, pluralists happily employ whichever\nconception seems useful in a given explanatory context. Edelman (2008)\ntakes a pluralistic line, as does Chalmers (2012) in his most recent\ndiscussion.\n\nThe pluralistic line raises some natural questions. Can we provide a general analysis that encompasses all or most types of computation? Do all computations share certain characteristic marks with one another? Are they perhaps instead united by something like family resemblance? Deeper understanding of computation requires us to grapple with these questions.\n\n[7. Arguments against computationalism]\n\nCTM has attracted numerous objections. In many cases, the objections\napply only to specific versions of CTM (such as classical\ncomputationalism or connectionist computationalism). Here are a few\nprominent objections. See also the entry on\n[the Chinese room argument](../chinese-room/)\nfor a widely discussed objection to classical computationalism\nadvanced by John Searle (1980).\n\n[7.1 Triviality arguments]\n\nA recurring worry is that CTM is *trivial*, because we can\ndescribe almost any physical system as executing computations. Searle\n(1990) claims that a wall implements *any* computer program,\nsince we can discern some pattern of molecular movements in the wall\nthat is isomorphic to the formal structure of the program. Putnam\n(1988: 121–125) defends a less extreme but still very strong\ntriviality thesis along the same lines. Triviality arguments play a\nlarge role in the philosophical literature. Anti-computationalists\ndeploy triviality arguments against computationalism, while\ncomputationalists seek to avoid triviality.\n\nComputationalists usually rebut triviality arguments by insisting that the arguments overlook constraints upon computational implementation, constraints that bar trivializing implementations. The constraints may be counterfactual, causal, semantic, or otherwise, depending on one’s favored theory of computation. For example, David Chalmers (1995, 1996a) and B. Jack Copeland (1996) hold that Putnam’s triviality argument ignores counterfactual conditionals that a physical system must satisfy in order to implement a computational model. Other philosophers say that a physical system must have representational properties to implement a computational model (Fodor 1998: 11–12; Ladyman 2009; Sprevak 2010) or at least to implement a content-involving computational model (Rescorla 2013). The details here vary considerably, and computationalists debate amongst themselves exactly which types of computation can avoid which triviality arguments. But most computationalists agree that we can avoid any devastating triviality worries through a sufficiently robust theory of the implementation relation between computational models and physical systems.\n\n*Pancomputationalism* holds that every physical system\nimplements a computational model. This thesis is plausible, since any\nphysical system arguably implements a sufficiently trivial\ncomputational model (e.g., a one-state finite state automaton). As\nChalmers (2011) notes, pancomputationalism does not seem worrisome for\ncomputationalism. What would be worrisome is the much stronger\ntriviality thesis that almost every physical system implements almost\nevery computational model.\n\nFor further discussion of triviality arguments and computational\nimplementation, see Sprevak (2019) and the entry\n[computation in physical systems](../computation-physicalsystems/).\n\n[7.2 Gödel’s incompleteness theorem]\n\nAccording to some authors, Gödel’s incompleteness theorems\nshow that human mathematical capacities outstrip the capacities of any\nTuring machine (Nagel and Newman 1958). J.R. Lucas (1961) develops\nthis position into a famous critique of CCTM. Roger Penrose pursues\nthe critique in *The Emperor’s New Mind* (1989) and\nsubsequent writings. Various philosophers and logicians have answered\nthe critique, arguing that existing formulations suffer from\nfallacies, question-begging assumptions, and even outright\nmathematical errors (Bowie 1982; Chalmers 1996b; Feferman 1996; Lewis\n1969, 1979; Putnam 1975: 365–366, 1994; Shapiro 2003). There is\na wide consensus that this criticism of CCTM lacks any force. It may\nturn out that certain human mental capacities outstrip\nTuring-computability, but Gödel’s incompleteness theorems\nprovide no reason to anticipate that outcome.\n\n[7.3 Limits of computational modeling]\n\nCould a computer compose the *Eroica* symphony? Or discover\ngeneral relativity? Or even replicate a child’s effortless\nability to perceive the environment, tie her shoelaces, and discern\nthe emotions of others? Intuitive, creative, or skillful human\nactivity may seem to resist formalization by a computer program\n(Dreyfus 1972, 1992). More generally, one might worry that crucial\naspects of human cognition elude computational modeling, especially\nclassical computational modeling.\n\nIronically, Fodor promulgates a forceful version of this critique.\nEven in his earliest statements of CCTM, Fodor (1975: 197–205)\nexpresses considerable skepticism that CCTM can handle all important\ncognitive phenomena. The pessimism becomes more pronounced in his\nlater writings (1983, 2000), which focus especially on *abductive\nreasoning* as a mental phenomenon that potentially eludes\ncomputational modeling. His core argument may be summarized as\nfollows:\n\n- (1)\n- Turing-style computation is sensitive only to “local” properties of a mental representation, which are exhausted by the identity and arrangement of the representation’s constituents.\n- (2)\n- Many mental processes, paradigmatically abduction, are sensitive to “nonlocal” properties such as relevance, simplicity, and conservatism.\n- (3)\n- Hence, we may have to abandon Turing-style modeling of the relevant processes.\n- (4)\n- Unfortunately, we have currently have no idea what alternative theory might serve as a suitable replacement.\n\nSome critics deny (1), arguing that suitable Turing-style computations can be sensitive to “nonlocal” properties (Schneider 2011; Wilson 2005). Some challenge (2), arguing that typical abductive inferences are sensitive only to “local” properties (Carruthers 2003; Ludwig and Schneider 2008; Sperber 2002). Some concede step (3) but dispute step (4), insisting that we have promising non-Turing-style models of the relevant mental processes (Pinker 2005). Partly spurred by such criticisms, Fodor elaborates his argument in considerable detail. To defend (2), he critiques theories that model abduction by deploying “local” heuristic algorithms (2005: 41–46; 2008: 115–126) or by positing a profusion of domain-specific cognitive modules (2005: 56–100). To defend (4), he critiques various theories that handle abduction through non-Turing-style models (2000: 46–53; 2008), such as connectionist networks.\n\nThe scope and limits of computational modeling remain controversial. We may expect this topic to remain an active focus of inquiry, pursued jointly with AI.\n\n[7.4 Temporal arguments]\n\nMental activity unfolds in time. Moreover, the mind accomplishes\nsophisticated tasks (e.g., perceptual estimation) very quickly. Many\ncritics worry that computationalism, especially classical\ncomputationalism, does not adequately accommodate temporal aspects of\ncognition. A Turing-style model makes no explicit mention of the time\nscale over which computation occurs. One could physically implement\nthe same abstract Turing machine with a silicon-based device, or a\nslower vacuum-tube device, or an even slower pulley-and-lever device.\nCritics recommend that we reject CCTM in favor of some alternative\nframework that more directly incorporates temporal considerations. van\nGelder and Port (1995) use this argument to promote a\nnon-computational *dynamical systems framework* for modeling\nmental activity. Eliasmith (2003, 2013: 12–13) uses it to\nsupport his Neural Engineering Framework.\n\nComputationalists respond that we can *supplement* an abstract\ncomputational model with temporal considerations (Piccinini 2010;\nWeiskopf 2004). For example, a Turing machine model presupposes\ndiscrete “stages of computation”, without describing how\nthe stages relate to physical time. But we can supplement our model by\ndescribing how long each stage lasts, thereby converting our\nnon-temporal Turing machine model into a theory that yields detailed\ntemporal predictions. Many advocates of CTM employ supplementation\nalong these lines to study temporal properties of cognition (Newell\n1990). Similar supplementation figures prominently in computer\nscience, whose practitioners are quite concerned to build machines\nwith appropriate temporal properties. Computationalists conclude that\na suitably supplemented version of CTM can adequately capture how\ncognition unfolds in time.\n\nA second temporal objection highlights the contrast between\n*discrete* and *continuous* temporal evolution (van\nGelder and Port 1995). Computation by a Turing machine unfolds in\ndiscrete stages, while mental activity unfolds in a continuous time.\nThus, there is a fundamental mismatch between the temporal properties\nof Turing-style computation and those of actual mental activity. We\nneed a psychological theory that describes continuous temporal\nevolution.\n\nComputationalists respond that this objection assumes what is to be\nshown: that cognitive activity does not fall into explanatory\nsignificant discrete stages (Weiskopf 2004). Assuming that physical\ntime is continuous, it follows that mental activity unfolds in\ncontinuous time. It does *not* follow that cognitive models\nmust have continuous temporal structure. A personal computer operates\nin continuous time, and its physical state evolves continuously. A\ncomplete physical theory will reflect all those physical changes. But\nour *computational* model does not reflect every physical\nchange to the computer. Our computational model has discrete temporal\nstructure. Why assume that a good cognitive-level model of the mind\nmust reflect every physical change to the brain? Even if there is a\ncontinuum of evolving *physical* states, why assume a continuum\nof evolving *cognitive* states? The mere fact of continuous\ntemporal evolution does not militate against computational models with\ndiscrete temporal structure.\n\nFor discussion of how to reconcile CTM with a dynamical systems perspective, see (Beer and Williams 2015; Phattanasri, Chiel, and Beer 2007; Weinberger and Allen 2022).\n\n[7.5 Embodied cognition]\n\nEmbodied cognition is a research program that draws inspiration from the continental philosopher Maurice Merleau-Ponty, the perceptual psychologist J.J. Gibson, and other assorted influences. It is a fairly heterogeneous movement, but the basic strategy is to emphasize links between cognition, bodily action, and the surrounding environment. See Varela, Thompson, and Rosch (1991) for an influential early statement. In many cases, proponents deploy tools of dynamical systems theory. Proponents typically present their approach as a radical alternative to computationalism (Chemero 2009; Kelso 1995; Thelen and Smith 1994). CTM, they complain, treats mental activity as static symbol manipulation detached from the embedding environment. It neglects myriad complex ways that the environment causally or constitutively shapes mental activity. We should replace CTM with a new picture that emphasizes continuous links between mind, body, and environment. Agent-environment dynamics, not internal mental computation, holds the key to understanding cognition. Often, a broadly eliminativist attitude towards intentionality propels this critique.\n\nComputationalists respond that CTM allows due recognition of cognition’s embodiment. Computational models can take into account how mind, body, and environment continuously interact. After all, computational models can incorporate sensory inputs and motor outputs. There is no obvious reason why an emphasis upon agent-environment dynamics precludes a dual emphasis upon internal mental computation (Clark 2014: 140–165; Rupert 2009). Computationalists maintain that CTM can incorporate any legitimate insights offered by the embodied cognition movement. They also insist that CTM remains our best overall framework for explaining numerous core psychological phenomena.\n\n[Bibliography]\n\n- Akhlaghpour, H., 2022, “An RNA-Based Theory of Natural\nUniversal Computation”,\n*Journal of Theoretical Biology*, 537: 110984. - Aitchison, L. and Lengyel, M., 2016, “The Hamiltonian Brain:\nEfficient Probabilistic Inference with Excitatory-Inhibitory Neural\nCircuit Dynamics”,\n*PloS Computational Biology*, 12: e1005186. - Arjo, D., 1996, “Sticking Up for Oedipus: Fodor on\nIntentional Generalizations and Broad Content”,\n*Mind and Language*, 11: 231–245. - Aydede, M., 1998, “Fodor on Concepts and Frege\nPuzzles”,\n*Pacific Philosophical Quarterly*, 79: 289–294. - –––, 2005, “Computationalism and\nFunctionalism: Syntactic Theory of Mind Revisited”, in\n*Turkish Studies in the History and Philosophy of Science*, G. Irzik and G. Güzeldere (eds), Dordrecht: Springer. - Aydede, M. and P. Robbins, 2001, “Are Frege Cases Exceptions\nto Intentional Generalizations?”,\n*Canadian Journal of Philosophy*, 31: 1–22. - Bayne, T., and I. Williams, 2023, “The Turing Test is not a\nGood Benchmark for Thought in LLMs”,\n*Nature Human Behavior*, 7: 1806–1807. - Bechtel, W. and A. Abrahamsen, 2002,\n*Connectionism and the Mind*, Malden: Blackwell. - Beer, R., and P. Williams, 2015, “Information Processing an\nDynamics in Minimally Cognitive Agents”,\n*Cognitive Science*, 39: 1–38. - Bermúdez, J.L., 2005,\n*Philosophy of Psychology: A Contemporary Introduction*, New York: Routledge. - –––, 2010,\n*Cognitive Science: An Introduction to the Science of the Mind*, Cambridge: Cambridge University Press. - Block, N., 1978, “Troubles With Functionalism”,\n*Minnesota Studies in the Philosophy of Science*, 9: 261–325. - –––, 1981, “Psychologism and\nBehaviorism”,\n*Philosophical Review*, 90: 5–43. - –––, 1983, “Mental Pictures and Cognitive\nScience”,\n*Philosophical Review*, 92: 499–539. - –––, 1986, “Advertisement for a Semantics\nfor Psychology”,\n*Midwest Studies in Philosophy*, 10: 615–678. - –––, 1990, “Can the Mind Change the\nWorld?”, in\n*Meaning and Method: Essays in Honor of Hilary Putnam*, G. Boolos (ed.), Cambridge: Cambridge University Press. - –––, 1995,\n*The Mind as the Software of the Brain*, in*Invitation to Cognitive Science, vol. 3: Thinking*, E. Smith and B. Osherson (eds), Cambridge, MA: MIT Press. - Block, N. and J. Fodor, 1972, “What Psychological States Are\nNot”,\n*The Philosophical Review*, 81: 159–181. - Boden, M., 1991, “Horses of a Different Color?”, in Ramsey et al. 1991: 3–19.\n- Bontly, T., 1998, “Individualism and the Nature of Syntactic\nStates”,\n*The British Journal for the Philosophy of Science*, 49: 557–574. - Bowers, J., G. Malhotra, M. Dujmović, M. Llera Montero, C.\nTsvetkov, V. Biscione, G. Puebla, F. Adolfi, J. Hummel, R. Heaton, B.\nEvans, J. Mitchell, and R. Blything, 2023, “Deep Problems with\nNeural Network Models of Human Vision”,\n*Behavioral and Brain Sciences*, 46: e386. - Bowie, G.L., 1982, “Lucas’s Number is Finally\nUp”,\n*Journal of Philosophical Logic*, 11: 79–285. - Brogan, W., 1990,\n*Modern Control Theory*, 3rd edition. Englewood Cliffs: Prentice Hall. - Brown, T., B. Mann, N. Ryder, M. Subbiah, J. Kaplan, P. Dhariwal,\nA. Neelakantan, P. Shyam, G. Sastry, A. Askell, S. Agarwal, A.\nHerbert-Voss, G. Krueger, T. Henighan, R. Child, A. Ramesh, D.\nZiegler, J. Wu, C. Winter, C. Hesse, M. Chen, E. Sigler, M. Litwin, S.\nGray, B. Chess, J. Clark, C. Berner, S. McCandlish, A. Radford, I.\nSutskever, and D. Amodei, 2020, “Language Models Are Few-Shot\nLearners”,\n*Advances in Neural Information Processing Systems*, 33: 1877–1901. - Buckner, C., 2019, “Deep Learning: A Philosophical\nIntroduction”,\n*Philosophy Compass*, 14: e12625. - –––, 2024,\n*From Deep Learning to Rational Machines: What the History of Philosophy Can Teach Us about the Future of Artificial Intelligence*, Oxford: Oxford University Press. - Buckner, C., and J. Garson, 2019, “Connectionism and Post-Connectionist Models”, in Sprevak and Colombo 2019: 175–191.\n- Buesing, L., J. Bill, B. Nessler, and W. Maass, W., 2011,\n“Neural Dynamics of Sampling: A Model for Stochastic Computation\nin Recurring Networks of Spiking Neurons”,\n*PLOS Computational Biology*, 7: e1002211. - Burge, T., 1982, “Other Bodies”, in\n*Thought and Object*, A. Woodfield (ed.), Oxford: Oxford University Press. Reprinted in Burge 2007: 82–99. - –––, 1986, “Individualism and\nPsychology”,\n*The Philosophical Review*, 95: 3–45. Reprinted in Burge 2007: 221–253. - –––, 1989, “Individuation and Causation in\nPsychology”,\n*Pacific Philosophical Quarterly*, 70: 303–322. Reprinted in Burge 2007: 316–333. - –––, 1995, “Intentional Properties and\nCausation”, in\n*Philosophy of Psychology*, C. MacDonald and G. MacDonald (eds), Oxford: Blackwell. Reprinted in Burge 2007: 334–343. - –––, 2005, “Disjunctivism and Perceptual\nPsychology”,\n*Philosophical Topics*, 33: 1–78. - –––, 2007,\n*Foundations of Mind*, Oxford: Oxford University Press. - –––, 2010a,\n*Origins of Objectivity*, Oxford: Oxford University Press. - –––, 2010b, “Origins of Perception”,\n*Disputatio*, 4: 1–38. - –––, 2010c, “Steps Towards Origins of\nPropositional Thought”,\n*Disputatio*, 4: 39–67. - –––, 2013,\n*Cognition through Understanding*, Oxford: Oxford University Press. - Calzavarini, F., and A. Paternoster, 2022, “The Semantic\nView of Computation and the Argument from the Cognitive Science\nPractice”,\n*Synthese*, 200: 77. doi:10.1007/s11229-022-03542-z - Camp, E., 2009, “A Language of Baboon Thought?”, in\n*The Philosophy of Animal Minds*, R. Lurz (ed.), Cambridge: Cambridge University Press. - Campbell, M., 1999, “Knowledge Discovery in Deep\nBlue”,\n*Communications of the ACM*, 42: 65–67. - Carruthers, P., 2003, “On Fodor’s Problem”,\n*Mind and Language*, 18: 508–523. - Chalmers, D., 1990, “Syntactic Transformations on\nDistributed Representations”,\n*Connection Science*, 2: 53–62. - –––, 1993, “Why Fodor and Pylyshyn Were\nWrong: The Simplest Refutation”,\n*Philosophical Psychology*, 63: 305–319. - –––, 1995, “On Implementing a\nComputation”,\n*Minds and Machines*, 4: 391–402. - –––, 1996a, “Does a Rock Implement Every\nFinite State Automaton?”,\n*Synthese*, 108: 309–333. - –––, 1996b, “Minds, Machines, and\nMathematics”,\n*Psyche*, 2: 11–20. - –––, 2002, “The Components of\nContent”, in\n*Philosophy of Mind: Classical and Contemporary Readings*, D. Chalmers (ed.), Oxford: Oxford University Press. - –––, 2011, “A Computational Foundation for\nthe Study of Cognition”,\n*The Journal of Cognitive Science*, 12: 323–357. - –––, 2012, “The Varieties of Computation:\nA Reply”,\n*The Journal of Cognitive Science*, 13: 213–248. - Chemero, A., 2009,\n*Radical Embodied Cognitive Science*, Cambridge, MA: MIT Press. - Cheney, D. and R. Seyfarth, 2007,\n*Baboon Metaphysics: The Evolution of a Social Mind*, Chicago: University of Chicago Press. - Chomsky, N., 1965,\n*Aspects of the Theory of Syntax*, Cambridge, MA: MIT Press. - Church, A., 1936, “An Unsolvable Problem of Elementary\nNumber Theory”,\n*American Journal of Mathematics*, 58: 345–363. - Churchland, P.M., 1981, “Eliminative Materialism and the\nPropositional Attitudes”,\n*Journal of Philosophy*, 78: 67–90. - –––, 1989,\n*A Neurocomputational Perspective: The Nature of Mind and the Structure of Science*, Cambridge, MA: MIT Press. - –––, 1995,\n*The Engine of Reason, the Seat of the Soul*, Cambridge, MA: MIT Press. - –––, 2007,\n*Neurophilosophy At Work*, Cambridge: Cambridge University Press. - Churchland, P.S., 1986,\n*Neurophilosophy*, Cambridge, MA: MIT Press. - Churchland, P.S., C. Koch, and T. Sejnowski, 1990, “What Is\nComputational Neuroscience?”, in\n*Computational Neuroscience*, E. Schwartz (ed.), Cambridge, MA: MIT Press. - Churchland, P.S. and T. Sejnowski, 1992,\n*The Computational Brain*, Cambridge, MA: MIT Press. - Clark, A., 2014,\n*Mindware: An Introduction to the Philosophy of Cognitive Science*, Oxford: Oxford University Press. - Clayton, N., N. Emery, and A. Dickinson, 2006, “The\nRationality of Animal Memory: Complex Caching Strategies of Western\nScrub Jays”, in\n*Rational Animals?*, M. Nudds and S. Hurley (eds), Oxford: Oxford University Press. - Coelho Mollo, D., 2018, “Functional Individuation,\nMechanistic Implementation: The Proper Way of Seeing the Mechanistic\nView of Concrete Computation”,\n*Synthese*, 195: 3477–3497. - Copeland, J., 1996, “What is Computation?”,\n*Synthese*, 108: 335–359. - Cover, T. and J. Thomas, 2006,\n*Elements of Information Theory*, Hoboken: Wiley. - Crane, T., 1991, “All the Difference in the World”,\n*Philosophical Quarterly*, 41: 1–25. - Crick, F. and C. Asanuma, 1986, “Certain Aspects of the Anatomy and Physiology of the Cerebral Cortex”, in McClelland et al. 1987: 333–371.\n- Cummins, R., 1989,\n*Meaning and Mental Representation*, Cambridge, MA: MIT Press. - Davidson, D., 1980,\n*Essays on Actions and Events*, Oxford: Clarendon Press. - Dayan, P., 2009, “A Neurocomputational Jeremiad”,\n*Nature Neuroscience*, 12: 1207. - Dennett, D., 1971, “Intentional Systems”,\n*Journal of Philosophy*, 68: 87–106. - –––, 1987,\n*The Intentional Stance*, Cambridge, MA: MIT Press. - –––, 1991, “Mother Nature versus the Walking Encyclopedia”, in Ramsey, et al. 1991: 21–30.\n- Dewhurst, J., 2018, “Computing Mechanisms Without Proper\nFunctions”,\n*Minds and Machines*, 28: 569–588. - Dietrich, E., 1989, “Semantics and the Computational\nParadigm in Cognitive Psychology”,\n*Synthese*, 79: 119–141. - Donahoe, J., 2010, “Man as Machine: A Review of\n*Memory and Computational Brain*, by C.R. Gallistel and A.P. King”,*Behavior and Philosophy*, 38: 83–101. - Doerig, A., R. Sommers, K. Seeliger, B. Richards, J. Ismael, G.\nLindsay, K. Kording, T. Konkle, M. van Gerven, N. Kriegeskorte, and T.\nKietzmann, 2023, “The Neuroconnectionist Research\nProgramme”,\n*Nature Reviews Neuroscience*, 24: 431–450. - Dreyfus, H., 1972,\n*What Computers Can’t Do*, Cambridge, MA: MIT Press. - –––, 1992,\n*What Computers Still Can’t Do*, Cambridge, MA: MIT Press. - Dretske, F., 1981,\n*Knowledge and the Flow of Information*, Oxford: Blackwell. - –––, 1993, “Mental Events as Structuring\nCauses of Behavior”, in\n*Mental Causation*, J. Heil and A. Mele (eds), Oxford: Clarendon Press. - Edelman, S., 2008,\n*Computing the Mind*, Oxford: Oxford University Press. - –––, 2014, “How to Write a ‘How a\nBuild a Brain’ Book”,\n*Trends in Cognitive Science*, 18: 118–119. - Egan, F., 1991, “Must Psychology be Individualistic?”,\n*Philosophical Review*, 100: 179–203. - –––, 1992, “Individualism, Computation,\nand Perceptual Content”,\n*Mind*, 101: 443–459. - –––, 1999, “In Defense of Narrow\nMindedness”,\n*Mind and Language*, 14: 177–194. - –––, 2003, “Naturalistic Inquiry: Where\nDoes Mental Representation Fit In?”, in\n*Chomsky and His Critics*, L. Antony and N. Hornstein (eds), Malden: Blackwell. - –––, 2010, “A Modest Role for\nContent”,\n*Studies in History and Philosophy of Science*, 41: 253–259. - –––, 2014, “How to Think About Mental\nContent”,\n*Philosophical Studies*, 170: 115–135. - –––, 2019, “The Nature and Function of Content in Computational Models”, in Sprevak and Colombo 2019: 247–258.\n- –––, 2020, “A Deflationary Account of\nMental Representation”, in\n*What Are Mental Representations?*, J. Smortchkova, K. Dołęga, and T. Schlicht (eds), Oxford: Oxford University Press. - Eliasmith, C., 2003, “Moving Beyond Metaphors: Understanding\nthe Mind for What It Is”,\n*Journal of Philosophy*, 100: 493–520. - –––, 2013,\n*How to Build a Brain*, Oxford: Oxford: University Press. - Eliasmith, C. and C.H. Anderson, 2003,\n*Neural Engineering: Computation, Representation and Dynamics in Neurobiological Systems*, Cambridge, MA: MIT Press. - Elman, J., 1990, “Finding Structure in Time”,\n*Cognitive Science*, 14: 179–211. - Feferman, S., 1996, “Penrose’s Gödelian\nArgument”,\n*Psyche*, 2: 21–32. - Feldman, J. and D. Ballard, 1982, “Connectionist Models and\ntheir Properties”,\n*Cognitive Science*, 6: 205–254. - Field, H., 2001,\n*Truth and the Absence of Fact*, Oxford: Clarendon Press. - Figdor, C., 2009, “Semantic Externalism and the Mechanics of\nThought”,\n*Minds and Machines*, 19: 1–24. - Floridi, L., and M. Chiriatti, 2020, “GPT-3: Its Nature,\nScope, Limits, and Consequences”,\n*Minds and Machines*, 30: 681–694. - Fodor, J., 1975,\n*The Language of Thought*, New York: Thomas Y. Crowell. - –––, 1980, “Methodological Solipsism\nConsidered as a Research Strategy in Cognitive Psychology”,\n*Behavioral and Brain Science*, 3: 63–73. Reprinted in Fodor 1981: 225–253. - –––, 1981,\n*Representations*, Cambridge: MIT Press. - –––, 1983,\n*The Modularity of Mind*, Cambridge, MA: MIT Press. - –––, 1987,\n*Psychosemantics*, Cambridge: MIT Press. - –––, 1990,\n*A Theory of Content and Other Essays*, Cambridge, MA: MIT Press. - –––, 1991, “A Modal Argument for Narrow\nContent”,\n*Journal of Philosophy*, 88: 5–26. - –––, 1994,\n*The Elm and the Expert*, Cambridge, MA: MIT Press. - –––, 1998,\n*Concepts*, Oxford: Clarendon Press. - –––, 2000,\n*The Mind Doesn’t Work That Way*, Cambridge, MA: MIT Press. - –––, 2005, “Reply to Steven Pinker\n‘So How Does the Mind Work?’”,\n*Mind and Language*, 20: 25–32. - –––, 2008,\n*LOT2*, Oxford: Clarendon Press. - Fodor, J. and Z. Pylyshyn, 1988, “Connectionism and\nCognitive Architecture: A Critical Analysis”,\n*Cognition*, 28: 3–71. - Frege, G., 1879/1967,\n*Begriffsschrift, eine der Arithmetischen Nachgebildete Formelsprache des Reinen Denkens*. Reprinted as*Concept Script, a Formal Language of Pure Thought Modeled upon that of Arithmetic*, in*From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931*, J. van Heijenoort (ed.), S. Bauer-Mengelberg (trans.), Cambridge: Harvard University Press. - Fresco, N. 2014,\n*Physical Computation and Cognitive Science*, Berlin: Springer. - –––, 2021, “Long-Arm Functional\nIndividuation of Computation”,\n*Synthese*, 199: 13993–14016. - Gallistel, C.R., 1990,\n*The Organization of Learning*, Cambridge, MA: MIT Press. - Gallistel, C.R. and King, A., 2009,\n*Memory and the Computational Brain*, Malden: Wiley-Blackwell. - Gandy, R., 1980, “Church’s Thesis and Principles for\nMechanism”, in\n*The Kleene Symposium*, J. Barwise, H. Keisler, and K. Kunen (eds). Amsterdam: North Holland. - Gödel, K., 1936/65. “On Formally Undecidable\nPropositions of Principia Mathematica and Related Systems”,\nReprinted with a new Postscript in\n*The Undecidable*, M. Davis (ed.), New York: Raven Press Books. - Grice, P., 1989,\n*Studies in the Ways of Words*, Cambridge: Harvard University Press. - Hadley, R., 2000, “Cognition and the Computational Power of\nConnectionist Networks”,\n*Connection Science*, 12: 95–110. - Harnish, R., 2002,\n*Minds, Brains, Computers*, Malden: Blackwell. - Haykin, S., 2008,\n*Neural Networks: A Comprehensive Foundation*, New York: Prentice Hall. - Haugeland, J., 1985,\n*Artificial Intelligence: The Very Idea*, Cambridge, MA: MIT Press. - Horgan, T. and J. Tienson, 1996,\n*Connectionism and the Philosophy of Psychology*, Cambridge, MA: MIT Press. - Horowitz, A., 2007, “Computation, External Factors, and\nCognitive Explanations”,\n*Philosophical Psychology*, 20: 65–80. - Illing, B., W. Gerstner, and J. Brea, 2019, “Biologically\nPlausible Deep Learning—But How Far Can We Go with Shallow\nNetworks”,\n*Neural Networks*, 118: 90–101. - Johnson, K., 2004, “On the Systematicity of Language and\nThought”,\n*Journal of Philosophy*, 101: 111–139. - Johnson-Laird, P., 1988,\n*The Computer and the Mind*, Cambridge: Harvard University Press. - –––, 2004, “The History of Mental\nModels”, in\n*Psychology of Reasoning: Theoretical and Historical Perspectives*, K. Manktelow and M.C. Chung (eds), New York: Psychology Press. - Kazez, J., 1995, “Computationalism and the Causal Role of\nContent”,\n*Philosophical Studies*, 75: 231–260. - Kelso, J., 1995,\n*Dynamic Patterns*, Cambridge, MA: MIT Press. - Kingma, D. and M. Welling, 2019, “An Introduction to\nVariational Autoencoders”,\n*Foundations and Trends in Machine Learning*, 12: 307–392. - Klein, C., 2012, “Two Paradigms for Individuating\nImplementations”,\n*Journal of Cognitive Science*, 13: 167–179. - Kriegeskorte, K., 2015, “Deep Neural Networks: A New\nFramework for Modeling Biological Vision and Brain Information\nProcessing”,\n*Annual Review of Vision Science*, 1: 417–446. - Kriegeskorte, K. and P. Douglas, 2018, “Cognitive\nComputational Neuroscience”,\n*Nature Neuroscience*, 21: 1148–1160. - Krishevsky, A., I. Sutskever, and G. Hinton, 2012, “ImageNet\nClassification with Deep Convolutional Neural Networks”,\n*Advances in Neural Information Processing Systems*, 25: 1097–1105. - Krotov, D., and J. Hopfield, 2019, “Unsupervised Learning by\nCompeting Hidden Units”,\n*Proceedings of the National Academy of Sciences*, 116: 7723–7731. - Ladyman, J., 2009, “What Does it Mean to Say that a Physical\nSystem Implements a Computation?”,\n*Theoretical Computer Science*, 410: 376–383. - LeCun, Y., Y. Bengio, and G. Hinton, 2015, “Deep\nLearning”,\n*Nature*, 521: 436–444. - Lewis, D., 1969, “Lucas against Mechanism”,\n*Philosophy*, 44: 231–3. - –––, 1971, “Analog and Digital”,\n*Noûs*, 5: 321–327. - –––, 1972, “Psychophysical and Theoretical\nIdentifications”,\n*Australasian Journal of Philosophy*, 50: 249–58. - –––, 1979, “Lucas Against Mechanism\nII”,\n*Canadian Journal of Philosophy*, 9: 373–376. - –––, 1994, “Reduction of Mind”, in\n*A Companion to the Philosophy of Mind*, S. Guttenplan (ed.), Oxford: Blackwell. - Lillicrap, T., D. Cownden, D. Tweed, and C. Akerman, 2016,\n“Random Synaptic Feedback Weights Support Error Backpropagation\nfor Deep Learning”,\n*Nature Communications*, 7: 13276–346. - Lillicrap, T., A. Sontoro, L. Marris, C. Akerman, and G. Hinton,\n2020, “Backpropagation and the Brain”,\n*Nature Reviews Neuroscience*, 21: 335–346. - Lizier, J., B. Flecker, and P. Williams, 2013, “Towards a\nSynergy-based Account of Measuring Information Modification”,\n*Proceedings of the 2013 IEEE Symposium on Artificial Life (ALIFE)*, Singapore: 43–51. - Ludwig, K. and S. Schneider, 2008, “Fodor’s Critique\nof the Classical Computational Theory of Mind”,\n*Mind and Language*, 23: 123–143. - Lucas, J.R., 1961, “Minds, Machines, and Gödel”,\n*Philosophy*, 36: 112–137. - Ma, W. J., 2019, “Bayesian Decision Models: A Primer”,\n*Neuron*, 104: 164–175. - Ma, W. J., K. Kording, and D. Goldreich, 2023,\n*Bayesian Models of Perception and Action: An Introduction*, Cambridge, MA: MIT Press. - Maass, W., 1997, “Networks of Spiking Neurons: The Next\nGeneration of Neural Network Models”,\n*Neural Networks*, 10: 1659–1671. - MacLennan, B., 2012, “Analog Computation”,\n*Computational Complexity*, R. Meyers (ed.), New York: Springer. - Mahowald, K., A. Ivanova, I. Blank, N. Kanwisher, J. Tenenbaum,\nand E. Fedorenko, 2024, “Dissociating Language and Thought in\nLarge Language Models”,\n*Trends in Cognitive Sciences*, 28: 517–540. - Maley, C., 2011, “Analog and Digital, Continuous and\nDiscrete”,\n*Philosophical Studies*, 155: 117–131. - –––, 2023, “Analogue Computation and\nRepresentation”,\n*The British Journal for the Philosophy of Science*, 739: 249–769. - Marblestone, A., G. Wayne, and K. Kording, 2016, “Toward an\nIntegration of Deep Learning and Neuroscience”,\n*Frontiers in Computational Neuroscience*, 10: 1–41. - Marcus, G., 2001,\n*The Algebraic Mind*, Cambridge, MA: MIT Press. - Marr, D., 1982,\n*Vision*, San Francisco: W.H. Freeman. - McClelland, J., D. Rumelhart, and G. Hinton, 1986, “The Appeal of Parallel Distributed Processing”, in Rumelhart et al. 1986: 3–44.\n- McClelland, J., D. Rumelhart, and the PDP Research Group, 1987,\n*Parallel Distributed Processing*, vol. 2. Cambridge, MA: MIT Press. - McCulloch, W. and W. Pitts, 1943, “A Logical Calculus of the\nIdeas Immanent in Nervous Activity”,\n*Bulletin of Mathematical Biophysics*, 7: 115–133. - McDermott, D., 2001,\n*Mind and Mechanism*, Cambridge, MA: MIT Press. - Mendola, J., 2008,\n*Anti-Externalism*, Oxford: Oxford University Press. - Miłkowski, M., 2013,\n*Explaining the Computational Mind*, Cambridge, MA: MIT Press. - –––, 2017, “The False Dichotomy between\nCausal Realization and Semantic Computation”,\n*Hybris. Internetowy Magazyn Filozoficzny*, 38: 1–21. - Miller, P., 2018,\n*An Introductory Course in Computational Neuroscience*, Cambridge, MA: MIT Press. - Mole, C., 2014, “Dead Reckoning in the Desert Ant: A Defense\nof Connectionist Models”,\n*Review of Philosophy and Psychology*, 5: 277–290. - Murphy, K., 2023,\n*Probabilistic Machine Learning: Advanced Topics*, Cambridge, MA: MIT Press. - Naselaris, T., Bassett, D., Fletcher, A., Körding, K.,\nKriegeskorte, N., Nienborg, H., Poldrack, R., Shohamy, D., and Kay,\nK., 2018, “Cognitive Computational Neuroscience: A New\nConference for an Emerging Discipline”,\n*Trends in Cognitive Science*, 22: 365–367. - Nagel, E. and J.R. Newman, 1958,\n*Gödel’s Proof*, New York: New York University Press. - Newell, A., 1990,\n*Unified Theories of Cognition*, Cambridge: Harvard University Press. - Newell, A. and H. Simon, 1956, “The Logic Theory Machine: A\nComplex Information Processing System”,\n*IRE Transactions on Information Theory, IT-2*, 3: 61–79. - –––, 1976, “Computer Science as Empirical\nInquiry: Symbols and Search”,\n*Communications of the ACM*, 19: 113–126. - O’Keefe, J. and L. Nadel, 1978,\n*The Hippocampus as a Cognitive Map*, Oxford: Clarendon University Press. - Ockham, W., 1957,\n*Summa Logicae*, in his*Philosophical Writings, A Selection*, P. Boehner (ed. and trans.), London: Nelson. - Orhan, A. E. and Ma, W. J., 2017, “Efficient Probabilistic\nInference in Generic Neural Networks Trained with Non-probabilistic\nFeedback ”,\n*Nature Communications*, 8: 1–14. - Peacocke, C., 1992,\n*A Study of Concepts*, Cambridge, MA: MIT Press. - –––, 1993, “Externalist\nExplanation”,\n*Proceedings of the Aristotelian Society*, 67: 203–230. - –––, 1994, “Content, Computation, and\nExternalism”,\n*Mind and Language*, 9: 303–335. - –––, 1999, “Computation as Involving\nContent: A Response to Egan”,\n*Mind and Language*, 14: 195–202. - Penrose, R., 1989,\n*The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics*, Oxford: Oxford University Press. - Perry, J., 1998, “Broadening the Mind”,\n*Philosophy and Phenomenological Research*, 58: 223–231. - Phattanasri, P., H. Chiel, and R. Beer, 2007, “The Dynamics\nof Associative Learning in Evolved Model Circuits”,\n*Adaptive Behavior*, 15: 377–396. - Piantadosi, S., J. Tenenbaum, and N. Goodman, 2012,\n“Bootstrapping in a Language of Thought”,\n*Cognition*, 123: 199–217. - Piccinini, G., 2004, “Functionalism, Computationalism, and\nMental States”,\n*Studies in History and Philosophy of Science*, 35: 811–833. - –––, 2007, “Computing Mechanisms”,\n*Philosophy of Science*, 74: 501–526. - –––, 2008a, “Computation Without\nRepresentation”,\n*Philosophical Studies*, 137: 205–241. - –––, 2008b, “Some Neural Networks Compute,\nOthers Don’t”,\n*Neural Networks*, 21: 311–321. - –––, 2010, “The Resilience of\nComputationalism”,\n*Philosophy of Science*, 77: 852–861. - –––, 2012, “Computationalism”, in\n*The Oxford Handbook of Philosophy and Cognitive Science*, E. Margolis, R. Samuels, and S. Stich (eds), Oxford: Oxford University Press. - –––, 2015,\n*Physical Computation: A Mechanistic Account*, Oxford: Oxford University Press. - –––, 2020,\n*Neurocognitive Mechanisms: Explaining Biological Cognition*, Oxford: Oxford University Press. - Piccinini, G. and A. Scarantino, 2010, “Computation vs.\nInformation processing: Why their Difference Matters to Cognitive\nScience”,\n*Studies in History and Philosophy of Science*, 41: 237–246. - Piccinini, G. and S. Bahar, 2013, “Neural Computation and\nthe Computational Theory of Cognition”,\n*Cognitive Science*, 37: 453–488. - Piccinini, G. and O. Shagrir, 2014, “Foundations of\nComputational Neuroscience”,\n*Current Opinion in Neurobiology*, 25: 25–30. - Pinker, S., 2005, “So How Does the Mind Work?”,\n*Mind and Language*, 20: 1–24. - Pinker, S. and A. Prince, 1988, “On Language and\nConnectionism”,\n*Cognition*, 28: 73–193. - Pouget, A., Beck, J., Ma., W. J., and Latham, P., 2013,\n“Probabilistic Brains: Knowns and Unknowns”,\n*Nature Neuroscience*, 16: 1170–1178. - Putnam, H., 1967, “Psychophysical Predicates”, in\n*Art, Mind, and Religion*, W. Capitan and D. Merrill (eds), Pittsburgh: University of Pittsburgh Press. Reprinted in Putnam 1975 as “The Nature of Mental States”: 429–440. - –––, 1975,\n*Mind, Language, and Reality: Philosophical Papers, vol. 2*, Cambridge: Cambridge University Press. - –––, 1983,\n*Realism and Reason: Philosophical Papers*, vol. 3. Cambridge: Cambridge University Press. - –––, 1988,\n*Representation and Reality*, Cambridge, MA: MIT Press. - –––, 1994, “The Best of All Possible\nBrains?”,\n*The New York Times*, November 20, 1994: 7. - Pylyshyn, Z., 1984,\n*Computation and Cognition*, Cambridge, MA: MIT Press. - Quine, W.V.O., 1960,\n*Word and Object*, Cambridge, MA: MIT Press. - Ramsey, W., S. Stich, and D. Rumelhart (eds), 1991,\n*Philosophy and Connectionist Theory*, Hillsdale: Lawrence Erlbaum Associates. - Rescorla, M., 2009a, “Chrysippus’s Dog as a Case Study\nin Non-Linguistic Cognition”, in\n*The Philosophy of Animal Minds*, R. Lurz (ed.), Cambridge: Cambridge University Press. - –––, 2009b, “Cognitive Maps and the\nLanguage of Thought”,\n*The British Journal for the Philosophy of Science*, 60: 377–407. - –––, 2012, “How to Integrate\nRepresentation into Computational Modeling, and Why We Should”,\n*Journal of Cognitive Science*, 13: 1–38. - –––, 2013, “Against Structuralist Theories\nof Computational Implementation”,\n*British Journal for the Philosophy of Science*, 64: 681–707. - –––, 2014, “The Causal Relevance of\nContent to Computation”,\n*Philosophy and Phenomenological Research*, 88: 173–208. - –––, 2015, “Bayesian Perceptual\nPsychology”, in\n*The Oxford Handbook of the Philosophy of Perception*, M. Matthen (ed.), Oxford: Oxford University Press. - –––, 2016, “Review of Gualtiero\nPiccinini’s\n*Physical Computation*”,*British Journal for the Philosophy of Science Review of Books*. [[Rescorla 2016 available online](https://www.thebsps.org/reviewofbooks/gualtiero-piccinini-physical-computation/)] - –––, 2017a, “From Ockham to\nTuring—and Back Again”, in\n*Turing 100: Philosophical Explorations of the Legacy of Alan Turing*, (*Boston Studies in the Philosophy and History*), A. Bokulich and J. Floyd (eds), Springer. - –––, 2017b, “Levels of Computational\nExplanation”, in\n*Philosophy and Computing: Essays in Epistemology, Philosophy of Mind, Logic, and Ethics*, T. Powers (ed.), Cham: Springer. - –––, forthcoming,\n*Bayesian Models of the Mind*, Cambridge: Cambridge University Press. - Rogers, T. and J. McClelland, 2014, “Parallel Distributed\nProcessing at 25: Further Explorations of the Microstructure of\nCognition”,\n*Cognitive Science*, 38: 1024–1077. - Rumelhart, D., 1989, “The Architecture of Mind: A\nConnectionist Approach”, in\n*Foundations of Cognitive Science*, M. Posner (ed.), Cambridge, MA: MIT Press. - Rumelhart, D., G. Hinton, and R. Williams, 1986, “Learning\nRepresentations by Back-propagating Errors”,\n*Nature*, 323: 533–536. - Rumelhart, D. and J. McClelland, 1986, “PDP Models and General Issues in Cognitive Science”, in Rumelhart et al. 1986: 110–146.\n- Rumelhart, D., J. McClelland, and the PDP Research Group, 1986,\n*Parallel Distributed Processing*, vol. 1. Cambridge: MIT Press. - Rupert, R., 2008, “Frege’s Puzzle and Frege Cases:\nDefending a Quasi-Syntactic Solution”,\n*Cognitive Systems Research*, 9: 76–91. - –––, 2009,\n*Cognitive Systems and the Extended Mind*, Oxford: Oxford University Press. - Russell, S. and P. Norvig, 2022,\n*Artificial Intelligence: A Modern Approach*, 4thed., Global ed. Harlow: Pearson. - Sawyer, S., 2000, “There Is No Viable Notion of Narrow\nContent”, in\n*Contemporary Debates in Philosophy of Mind*, B. McLaughlin and J. Cohen (eds), Malden: Blackwell. - Schneider, S., 2005, “Direct Reference, Psychological\nExplanation, and Frege Cases”,\n*Mind and Language*, 20: 423–447. - –––, 2011,\n*The Language of Thought: A New Philosophical Direction*, Cambridge, MA: MIT Press. - Searle, J., 1980, “Minds, Brains, and Programs”,\n*Behavioral and Brain Sciences*, 3: 417–457. - –––, 1990, “Is the Brain a Digital\nComputer?”,\n*Proceedings and Addresses of the American Philosophical Association*, 64: 21–37. - Segal, G., 2000,\n*A Slim Book About Narrow Content*, Cambridge, MA: MIT Press. - Shagrir, O., 2001, “Content, Computation, and\nExternalism”,\n*Mind*, 110: 369–400. - –––, 2006, “Why We View the Brain as a\nComputer”,\n*Synthese*, 153: 393–416. - –––, 2014, “Review of\n*Explaining the Computational Theory of Mind*, by Marcin Miłkowski”,*Notre Dame Review of Philosophy*, January 2014. - –––, 2020, “In Defense of the Semantic\nView of Computation”,\n*Synthese*, 197: 4083–4108 - –––, 2022,\n*The Nature of Physical Computation*, Oxford: Oxford University Press. - Shannon, C., 1948, “A Mathematical Theory of\nCommunication”,\n*Bell System Technical Journal*27: 379–423, 623–656. - Shapiro, S., 2003, “Truth, Mechanism, and Penrose’s\nNew Argument”,\n*Journal of Philosophical Logic*, 32: 19–42. - Shea, N., 2013, “Naturalizing Representational\nContent”,\n*Philosophy Compass*, 8: 496–509. - –––, 2018,\n*Representation in Cognitive Science*, Oxford: Oxford University Press. - Sieg, W., 2009, “On Computability”, in\n*Philosophy of Mathematics*, A. Irvine (ed.), Burlington: Elsevier. - Siegelmann, H. and E. Sontag, 1991, “Turing Computability\nwith Neural Nets”,\n*Applied Mathematics Letters*, 4: 77–80. - Siegelmann, H. and E. Sontag, 1995, “On the Computational\nPower of Neural Nets”,\n*Journal of Computer and Science Systems*, 50: 132–150. - Silver, D., J. Schrittwieser, K. Simonyan, I. Antonoglou, A.\nHuang, A. Guez, T. Hubert, L. Baker, M. Lai, A. Bolton, Y. Chen, T.\nLillicrap, F. Hui, L. Sifre, G. van den Driessche, T. Graepel, and D.\nHassabis, 2016, “Mastering the Game of Go with Deep Neural\nNetworks and Tree Search”,\n*Nature*, 529: 484–489. - Silverberg, A., 2006, “Chomsky and Egan on Computational\nTheories of Vision”,\n*Minds and Machines*, 16: 495–524. - Sloman, A., 1978,\n*The Computer Revolution in Philosophy*, Hassocks: The Harvester Press. - Smolensky, P., 1988, “On the Proper Treatment of\nConnectionism”,\n*Behavioral and Brain Sciences*, 11: 1–74. - –––, 1991, “Connectionism, Constituency,\nand the Language of Thought”, in\n*Meaning in Mind: Fodor and His Critics*, B. Loewer and G. Rey (eds), Cambridge: Blackwell. - Sperber, D., 2002, “In Defense of Massive Modularity”,\nin\n*Language, Brain, and Cognitive Development: Essays in Honor of Jacques Mehler*, E. Dupoux (ed.), Cambridge, MA: MIT Press. - Sprevak, M., 2010, “Computation, Individuation, and the\nReceived View on Representation”,\n*Studies in History and Philosophy of Science*, 41: 260–270. - –––, 2019, “Triviality Arguments About Computational Implementation”, in Sprevak and Colombo 2019: 175–191.\n- –––, 2020, “Two Kinds of Information\nProcessing in Cognition”,\n*Review of Philosophy and Psychology*, 11: 591–611. - Sprevak, M. and M. Colombo, 2019,\n*The Routledge Handbook of the Computational Mind*, New York: Routledge. - Stalnaker, R., 1999,\n*Context and Content*, Oxford: Oxford University Press. - Stich, S., 1983,\n*From Folk Psychology to Cognitive Science*, Cambridge, MA: MIT Press. - Storrs, K., T. Kietzmann, A. Walther, J. Mehrer, and N.\nKriegeskorte, 2021, “Diverse Deep Neural Networks All Predict\nHuman Inferior Temporal Cortex Well, After Training and\nFitting”,\n*Journal of Cognitive Neuroscience*, 33: 2044–2064. - Thelen, E. and L. Smith, 1994,\n*A Dynamical Systems Approach to the Development of Cognition and Action*, Cambridge, MA: MIT Press. - Thrun, S., W. Burgard, and D. Fox, 2005,\n*Probabilistic Robotics*, Cambridge, MA: MIT Press. - Thrun, S., M. Montemerlo, and H. Dahlkamp, et al., 2006,\n“Stanley: The Robot That Won the DARPA Grand Challenge”,\n*Journal of Field Robotics*, 23: 661–692. - Tolman, E., 1948, “Cognitive Maps in Rats and Men”,\n*Psychological Review*, 55: 189–208. - Trappenberg, T., 2010,\n*Fundamentals of Computational Neuroscience*, Oxford: Oxford University Press. - Turing, A., 1936, “On Computable Numbers, with an\nApplication to the Entscheidungsproblem”,\n*Proceedings of the London Mathematical Society*, 42: 230–265. - –––, 1950, “Computing Machinery and\nIntelligence”,\n*Mind*, 49: 433–460. - Ulmann, B., 2023,\n*Analog Computation*, 2nd edition, Boston: de Gruyter. - van Gelder, T., 1990, “Compositionality: A Connectionist\nVariation on a Classical Theme”,\n*Cognitive Science*, 14: 355–384. - van Gelder, T. and R. Port, 1995, “It’s About Time: An\nOverview of the Dynamical Approach to Cognition”, in\n*Mind as Motion: Explorations in the Dynamics of Cognition*, R. Port and T. van Gelder (eds), Cambridge, MA: MIT Press. - Varela, F., Thompson, E. and Rosch, E., 1991,\n*The Embodied Mind: Cognitive Science and Human Experience*, Cambridge, MA: MIT Press. - von Neumann, J., 1945, “First Draft of a Report on the EDVAC”, Moore School of Electrical Engineering, University of Pennsylvania. Philadelphia, PA.\n- Wakefield, J., 2002, “Broad versus Narrow Content in the\nExplanation of Action: Fodor on Frege Cases”,\n*Philosophical Psychology*, 15: 119–133. - Weinberg, N., and C. Allen, 2022, “Static-Dynamic Hybridity\nin Dynamical Models of Cognition”,\n*Philosophy of Science*, 89: 1–20. - Weiskopf, D., 2004, “The Place of Time in Cognition”,\n*British Journal for the Philosophy of Science*, 55: 87–105. - Whitehead, A.N. and B. Russell, 1925,\n*Principia Mathematica*, vol. 1, 2nded., Cambridge: Cambridge University Press. - Wilson, R., 2005, “What Computers (Still, Still) Can’t\nDo”, in\n*New Essays in Philosophy of Language and Mind*, R. Stainton, M. Ezcurdia, and C.D. Viger (eds).*Canadian Journal of Philosophy*, supplementary issue 30: 407–425. - –––, 2003, “Causal Relevance”,\n*Philosophical Issues*, 13: 316–327. - Whittington, J., and R. Bogacz, 2017, “An Approximation of\nthe Error Backpropagation Algorithm in a Predictive Coding Network\nwith Local Hebbian Synaptic Plasticity”,\n*Neural Computation*, 29: 1229–1262. - Zednik, C., 2019, “Computational Cognitive Neuroscience”, in Sprevak and Colombo 2019: 357–369.\n- Zhuang, C., S. Yan, A. Nayebi, M. Schrimpf, M. Frank, J. DiCarlo,\nand D. Yamins, 2021, “Unsupervised Neural Network Models of the\nVentral Visual Stream”,\n*Proceedings of the National Academy of Sciences*, 118: e2014196118. - Zylberberg, A., S. Dehaene, P. Roelfsema, and M. Sigman, 2011,\n“The Human Turing Machine”,\n*Trends in Cognitive Science*, 15: 293–300.\n\n## Academic Tools\n\n[How to cite this entry].[Preview the PDF version of this entry]at the[Friends of the SEP Society].[Look up topics and thinkers related to this entry]at the Internet Philosophy Ontology Project (InPhO).[Enhanced bibliography for this entry]at[PhilPapers], with links to its database.\n\n[Other Internet Resources]\n\n- Graves, A., G. Wayne, and I. Danihelko, 2014,\n“\n[Neural Turing Machines](https://arxiv.org/abs/1410.5401)”, manuscript at arXiv.org. - Horst, Steven, “The Computational Theory of Mind”,\n*Stanford Encyclopedia of Philosophy*(Summer 2015 Edition), Edward N. Zalta (ed.), URL = <[https://plato.stanford.edu/archives/sum2015/entries/computational-mind/](https://plato.stanford.edu/archives/sum2015/entries/computational-mind/)>. [This is the previous entry on the Computational Theory of Mind in the*Stanford Encyclopedia of Philosophy*— see the[version history](https://plato.stanford.edu/cgi-bin/encyclopedia/archinfo.cgi?entry=computational-mind).] - Marcin Miłkowski,\n“\n[The Computational Theory of Mind](http://www.iep.utm.edu/compmind/),” in the*Internet Encyclopedia of Philosophy*. [Bibliography on philosophy of artificial intelligence](http://philpapers.org/browse/philosophy-of-artificial-intelligence), in Philpapers.org.", "url": "https://wpnews.pro/news/the-computational-theory-of-mind-2015", "canonical_source": "https://plato.stanford.edu/entries/computational-mind/", "published_at": "2026-08-02 22:35:35+00:00", "updated_at": "2026-08-02 22:52:31.766395+00:00", "lang": "en", "topics": ["artificial-intelligence", "machine-learning", "ai-research"], "entities": ["Stanford Encyclopedia of Philosophy", "Alan Turing", "Turing machine"], "alternates": {"html": "https://wpnews.pro/news/the-computational-theory-of-mind-2015", "markdown": "https://wpnews.pro/news/the-computational-theory-of-mind-2015.md", "text": "https://wpnews.pro/news/the-computational-theory-of-mind-2015.txt", "jsonld": "https://wpnews.pro/news/the-computational-theory-of-mind-2015.jsonld"}}