The Computational Theory of Mind (Stanford Encyclopedia of Philosophy)

The intuitive notions of computation and algorithm
are central to mathematics. Roughly speaking, an algorithm is an
explicit, step-by-step procedure for answering some question or
solving some problem. An algorithm provides routine mechanical
instructions dictating how to proceed at each step. Obeying the
instructions requires no special ingenuity or creativity. For example,
the familiar grade-school algorithms describe how to compute addition,
multiplication, and division. Until the early twentieth century,
mathematicians relied upon informal notions of computation and
algorithm without attempting anything like a formal analysis.
Developments in the foundations of mathematics eventually impelled
logicians to pursue a more systematic treatment. Alan Turing’s
landmark paper “On Computable Numbers, With an Application to
the Entscheidungsproblem” (Turing 1936) offered the analysis
that has proved most influential.

A Turing machine is an abstract model of an idealized
computing device with unlimited time and storage space at its
disposal. The device manipulates symbols, much as a human
computing agent manipulates pencil marks on paper during arithmetical
computation. Turing says very little about the nature of symbols. He
assumes that primitive symbols are drawn from a finite alphabet. He
also assumes that symbols can be inscribed or erased at “memory
locations”. Turing’s model works as follows:

• 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).
• 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.
• The central processor can enter into finitely many 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”).
• 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.
• A 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.

Turing translates this informal description into a rigorous
mathematical model. For more details, see the entry on
Turing machines.

Turing 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.

Turing computation is often described as digital rather than
analog. What this means is not always so clear, but the basic
idea is usually that computation operates over discrete
configurations. By comparison, many historically important algorithms
operate over continuously variable configurations. For example,
Euclidean geometry assigns a large role to ruler-and-compass
constructions, which manipulate geometric shapes. For any shape,
one can find another that differs to an arbitrarily small extent.
Symbolic configurations manipulated by a Turing machine do not differ
to arbitrarily small extent. Turing machines operate over discrete
strings of elements (digits) drawn from a finite alphabet. One
recurring controversy concerns whether the digital paradigm is
well-suited to model mental activity or whether an analog paradigm
would instead be more fitting (MacLennan 2012; Piccinini and Bahar
2013).^[1]

Besides introducing Turing machines, Turing (1936) proved several
seminal mathematical results involving them. In particular, he proved
the existence of a universal Turing machine (UTM). Roughly
speaking, a UTM is a Turing machine that can mimic any other Turing
machine. One provides the UTM with a symbolic input that codes the
machine table for Turing machine M. The UTM replicates
M’s behavior, executing instructions enshrined by
M’s machine table. In that sense, the UTM is a
programmable general purpose computer. To a first
approximation, all personal computers are also general purpose: they
can mimic any Turing machine, when suitably programmed. The main
caveat is that physical computers have finite memory, whereas a Turing
machine has unlimited memory. More accurately, then, a personal
computer can mimic any Turing machine until it exhausts its
limited memory supply.

Turing’s discussion helped lay the foundations for computer
science, which seeks to design, build, and understand computing
systems. As we know, computer scientists can now build extremely
sophisticated computing machines. All these machines implement
something resembling Turing computation, although the details differ
from Turing’s simplified model.

Rapid progress in computer science prompted many, including Turing, to
contemplate whether we could build a computer capable of thought.
Artificial intelligence (AI) aims to construct
“thinking machinery”. More precisely, it aims to construct
computing machines that execute core mental tasks such as reasoning,
decision-making, problem solving, and so on. During the 1950s and
1960s, this goal came to seem increasingly realistic (Haugeland 1985).
A famous early success was the Logic Theorist computer
program (Newell and Simon 1956), which proved 38 of the first 52
theorems from Principia Mathematica (Whitehead and Russell
1925). In one case, it discovered a simpler proof than
Principia’s. Initial achievements of this kind
stimulated enormous interest inside and outside the academy. Many
researchers predicted that intelligent machines were only a few years
away. When confident predictions of thinking machines proved too
optimistic, many observers lost interest or concluded that AI was a
fool’s errand. Nevertheless, the decades have witnessed gradual
progress, including some striking recent advances. A few
milestones:

• IBM’s Deep Blue defeated chess champion Gary Kasparov in
  1997 (Campbell 1999).
• 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).
• In 2012, AlexNet dramatically surpassed all previous computational
  models in a standard image classification task (Krizhevsky, Sutskever,
  and Hinton 2012).
• DeepMind’s AlphaGo defeated Lee Sedol, one of the top Go
  players in the world, in 2016 (Silver, Schrittwieser, Simonyan, et al.
  2017).
• 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.

These and other recent advances have sparked intense renewed focus
upon AI, including numerous commercial applications.

Some philosophers insist that computers, no matter how sophisticated
they become, will at best mimic rather than
replicate thought. A computer simulation of the weather does
not really rain. A computer simulation of flight does not really fly.
Even if a computing system could simulate mental activity, why suspect
that it would constitute the genuine article?

Turing (1950) anticipated these worries and tried to defuse them. He
proposed a scenario, now called the Turing Test, where one
evaluates whether an unseen interlocutor is a computer or a human. A
computer passes the Turing test if one cannot determine that
it is a computer. Turing proposed that we abandon the question
“Could a computer think?” as hopelessly vague, replacing
it with the question “Could a computer pass the Turing
test?”. Turing’s discussion has received considerable
attention, proving especially influential within AI. Ned Block (1981)
offers an influential critique. He argues that certain possible
machines pass the Turing test even though these machines do not come
close to genuine thought or intelligence. See the entry
the Turing test
for discussion of Block’s objection and other issues
surrounding the Turing Test. For discussion of the Turing test in
relation to ChatGPT and similar models, see (Bayne and Williams 2023;
Floridi and Chiriatti 2020; Mahowald, Ivanova, Blank, et al.
2024).

For more on AI, see the entry
logic and artificial intelligence.
For much more detail, see Russell and Norvig (2022).

Warren McCulloch and Walter Pitts (1943) first suggested that
something resembling the Turing machine might provide a good model for
the mind. In the 1960s, Turing computation became central to the
emerging interdisciplinary initiative cognitive science,
which studies the mind by drawing upon psychology, computer science
(especially AI), linguistics, philosophy, economics (especially game
theory and behavioral economics), anthropology, and neuroscience. The
label classical computational theory of mind (which we will
abbreviate as CCTM) is now fairly standard. According to CCTM, the
mind is a computational system similar in important respects to a
Turing machine, and core mental processes (e.g., reasoning,
decision-making, and problem solving) are computations similar in
important respects to computations executed by a Turing machine. These
formulations are imprecise. CCTM is best seen as a family of views,
rather than a single well-defined
view.^[2]

It is common to describe CCTM as embodying “the computer
metaphor”. This description is doubly misleading.

First, CCTM is better formulated by describing the mind as a
“computing system” or a “computational system”
rather than a “computer”. As David Chalmers (2011) notes,
describing a system as a “computer” strongly suggests that
the system is programmable. As Chalmers also notes, one need
not claim that the mind is programmable simply because one regards it
as a Turing-style computational system. (Most Turing machines are not
programmable.) Thus, the phrase “computer metaphor”
strongly suggests theoretical commitments that are inessential to
CCTM. The point here is not just terminological. Critics of CCTM often
object that the mind is not a programmable general purpose computer
(Churchland, Koch, and Sejnowski 1990). Since classical
computationalists need not claim (and usually do not claim) that the
mind is a programmable general purpose computer, the objection is
misdirected.

Second, CCTM is not intended metaphorically. CCTM does not simply hold
that the mind is like a computing system. CCTM holds that the
mind literally is a computing system. Of course, the most
familiar artificial computing systems are made from silicon chips or
similar materials, whereas the human body is made from flesh and
blood. But CCTM holds that this difference disguises a more
fundamental similarity, which we can capture through a Turing-style
computational model. In offering such a model, we prescind from
physical details. We attain an abstract computational description that
could be physically implemented in diverse ways (e.g., through silicon
chips, or neurons, or pulleys and levers). CCTM holds that a suitable
abstract computational model offers a literally true description of
core mental processes.

It 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:

• Turing machines execute pure symbolic computation. The inputs and
  outputs are symbols inscribed in memory locations. In contrast, the
  mind receives 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
• Modern computers have 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
  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 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.

CCTM claims that mental activity is “Turing-style
computation”, allowing these and other departures from
Turing’s own formalism.

3.1 Machine functionalism

Hilary Putnam (1967) introduced CCTM into philosophy. He contrasted
his position with logical behaviorism and type-identity
theory. Each position purports to reveal the nature of mental
states, including propositional attitudes (e.g., beliefs), sensations
(e.g., pains), and emotions (e.g., fear). According to logical
behaviorism, mental states are behavioral dispositions. According to
type-identity theory, mental states are brain states. Putnam advances
an opposing functionalist view, on which mental states are
functional states. According to functionalism, a system has a mind
when the system has a suitable functional organization.
Mental states are states that play appropriate roles in the
system’s functional organization. Each mental state is
individuated by its interactions with sensory input, motor output, and
other mental states.

Functionalism offers notable advantages over logical behaviorism and
type-identity theory:

• 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.
• Type-identity theorists want to associate each mental state with a
  characteristic physical or neurophysiological state. Putnam casts this
  project into doubt by arguing that mental states are 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
  for further discussion of this argument.

Putnam defends a brand of functionalism now called machine
functionalism. He emphasizes probabilistic automata,
which are similar to Turing machines except that transitions between
computational states are stochastic. He proposes that mental activity
implements a probabilistic automaton and that particular mental states
are machine states of the automaton’s central processor. The
machine table specifies an appropriate functional organization, and it
also specifies the role that individual mental states play within that
functional organization. In this way, Putnam combines functionalism
with CCTM.

Machine functionalism faces several problems. One problem, highlighted
by Ned Block and Jerry Fodor (1972), concerns the productivity of
thought. A normal human can entertain a potential infinity of
propositions. Machine functionalism identifies mental states with
machine states of a probabilistic automaton. Since there are only
finitely many machine states, there are not enough machine states to
pair one-one with possible mental states of a normal human. Of course,
an actual human will only ever entertain finitely many propositions.
However, Block and Fodor contend that this limitation reflects limits
on lifespan and memory, rather than (say) some psychological law that
restricts the class of humanly entertainable propositions. A
probabilistic automaton is endowed with unlimited time and memory
capacity yet even still has only finitely many machine states.
Apparently, then, machine functionalism mislocates the finitary limits
upon human cognition.

Another problem for machine functionalism, also highlighted by Block
and Fodor (1972), concerns the systematicity of thought. An
ability to entertain one proposition is correlated with an ability to
think other propositions. For example, someone who can entertain the
thought that John loves Mary can also entertain the thought
that Mary loves John. Thus, there seem to be systematic
relations between mental states. A good theory should reflect those
systematic relations. Yet machine functionalism identifies mental
states with unstructured machines states, which lack the requisite
systematic relations to another. For that reason, machine
functionalism does not explain systematicity. In response to this
objection, machine functionalists might deny that they are obligated
to explain systematicity. Nevertheless, the objection suggests that
machine functionalism neglects essential features of human mentality.
A better theory would explain those features in a principled way.

While 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.

3.2 The representational theory of mind

Fodor (1975, 1981, 1987, 1990, 1994, 2008) advocates a version of CCTM
that accommodates systematicity and productivity much more
satisfactorily. He shifts attention to the symbols
manipulated during Turing-style computation.

An old view, stretching back at least to William of Ockham’s
Summa Logicae, holds that thinking occurs in a language
of thought (sometimes called Mentalese). Fodor revives
this view. He postulates a system of mental representations, including
both primitive representations and complex representations formed from
primitive representations. For example, the primitive Mentalese words
JOHN, MARY, and LOVES can combine to form the Mentalese sentence JOHN
LOVES MARY. Mentalese is compositional: the meaning of a
complex Mentalese expression is a function of the meanings of its
parts and the way those parts are combined. Propositional attitudes
are relations to Mentalese symbols. Fodor calls this view the
representational theory of mind (RTM). Combining RTM
with CCTM, he argues that mental activity involves Turing-style
computation over the language of thought. Mental computation stores
Mentalese symbols in memory locations, manipulating those symbols in
accord with mechanical rules.

A prime virtue of RTM is how readily it accommodates productivity and
systematicity:

Productivity: RTM postulates a finite set of primitive
Mentalese expressions, combinable into a potential infinity of complex
Mentalese expressions. A thinker with access to primitive Mentalese
vocabulary and Mentalese compounding devices has the potential to
entertain an infinity of Mentalese expressions. She therefore has the
potential to instantiate infinitely many propositional attitudes
(neglecting limits on time and memory).

Systematicity: According to RTM, there are systematic
relations between which propositional attitudes a thinker can
entertain. For example, suppose I can think that John loves Mary.
According to RTM, my doing so involves my standing in some relation
R to a Mentalese sentence JOHN LOVES MARY, composed of
Mentalese words JOHN, LOVES, and MARY combined in the right way. If I
have this capacity, then I also have the capacity to stand in relation
R to the distinct Mentalese sentence MARY LOVES JOHN, thereby
thinking that Mary loves John. So the capacity to think that John
loves Mary is systematically related to the capacity to think that
Mary loves John.

By treating propositional attitudes as relations to complex mental
symbols, RTM explains both productivity and systematicity.

CCTM+RTM differs from machine functionalism in several other respects.
First, machine functionalism is a theory of mental states in
general, while RTM is only a theory of propositional attitudes.
Second, proponents of CCTM+RTM need not say that propositional
attitudes are individuated functionally. As Fodor (2000: 105, fn. 4)
notes, we must distinguish computationalism (mental processes
are computational) from functionalism (mental states are
functional states). Machine functionalism endorses both doctrines.
CCTM+RTM endorses only the first. Unfortunately, many philosophers
still mistakenly assume that computationalism entails a functionalist
approach to propositional attitudes (see Piccinini 2004 for
discussion).

Philosophical discussion of RTM tends to focus mainly on
high-level human thought, especially belief and desire.
However, CCTM+RTM is applicable to a much wider range of mental states
and processes. Many cognitive scientists apply it to non-human
animals. For example, Gallistel and King (2009) apply it to certain
invertebrate phenomena (e.g., honeybee navigation). Even confining
attention to humans, one can apply CCTM+RTM to subpersonal
processing. Fodor (1983) argues that perception involves a
subpersonal “module” that converts retinal input into
Mentalese symbols and then performs computations over those symbols.
Thus, talk about a language of thought is potentially
misleading, since it suggests a non-existent restriction to
higher-level mental activity.

Also potentially misleading is the description of Mentalese as a
language, which suggests that all Mentalese symbols resemble
expressions in a natural language. Many philosophers, including Fodor,
sometimes seem to endorse that position. However, there are possible
non-propositional formats for mental representations. Proponents of
CCTM+RTM can adopt a pluralistic line, allowing mental computation to
operate over items akin to images, maps, diagrams, or other
non-propositional representations (Johnson-Laird 2004: 187; McDermott
2001: 69; Pinker 2005: 7; Sloman 1978: 144–176). The pluralistic
line seems especially plausible as applied to subpersonal processes
(such as perception) and non-human animals. Michael Rescorla (2009a,
2009b) surveys research on cognitive maps (Tolman 1948;
O’Keefe and Nadel 1978; Gallistel 1990), suggesting that some
animals may navigate by computing over mental representations more
similar to maps than sentences. Elisabeth Camp (2009), citing research
on baboon social interaction (Cheney and Seyfarth 2007), argues that
baboons may encode social dominance relations through non-sentential
tree-structured representations.

CCTM+RTM is schematic. To fill in the schema, one must provide
detailed computational models of specific mental processes. A complete
model will:

• describe the mental representations manipulated by the
  process;
• isolate elementary operations that manipulate the representations
  (e.g., inscribing a symbol in a memory location); and
• delineate mechanical rules governing application of elementary
  operations.

By providing a detailed computational model, we decompose a complex
mental process into a series of elementary operations governed by
precise, routine instructions.

CCTM+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.

Fodor (1975) advances CCTM+RTM as a foundation for cognitive science.
He discusses mental phenomena such as decision-making, perception, and
linguistic processing. In each case, he maintains, our best scientific
theories postulate Turing-style computation over mental
representations. In fact, he argues that our only viable
theories have this form. He concludes that CCTM+RTM is “the only
game in town”. Many cognitive scientists argue along similar
lines. C.R. Gallistel and Adam King (2009), Philip Johnson-Laird
(1988), Allen Newell and Herbert Simon (1976), and Zenon Pylyshyn
(1984) all recommend Turing-style computation over mental symbols as
the best foundation for scientific theorizing about the mind.

In the 1980s, connectionism emerged as a prominent rival to classical
computationalism. Connectionists draw inspiration from neurophysiology
rather than logic and computer science. They employ computational
models, neural networks, that differ significantly from
Turing-style models. A neural network is a collection of
interconnected nodes. Nodes fall into three categories: input
nodes, output nodes, and hidden nodes (which mediate
between input and output nodes). Nodes have activation values, given
by real numbers. One node can bear a weighted connection to
another node, also given by a real number. Activations of input nodes
are determined exogenously: these are the inputs to computation.
Total input activation of a hidden or output node is a
weighted sum of the activations of nodes feeding into it. Activation
of a hidden or output node is a function of its total input
activation; the particular function varies with the network. During
neural network computation, waves of activation propagate from input
nodes to output nodes, as determined by weighted connections between
nodes.

In a feedforward network, weighted connections flow only in
one direction. Recurrent networks have feedback loops, in
which connections emanating from hidden units circle back to hidden
units. Recurrent networks are less mathematically tractable than
feedforward networks. However, they figure crucially in psychological
modeling of various phenomena, such as phenomena that involve some
kind of memory (Elman 1990).

Weights in a neural network are typically mutable, evolving in accord
with a learning algorithm. The literature offers various
learning algorithms, but the basic idea is usually to adjust weights
so that actual outputs gradually move closer to the
target outputs one would expect for the relevant inputs. The
backpropagation algorithm is a widely used algorithm of this
kind (Rumelhart, Hinton, and Williams 1986).

Connectionism traces back to McCulloch and Pitts (1943), who studied
networks of interconnected logic gates (e.g., AND-gates and
OR-gates). One can view a network of logic gates as a neural network,
with activations confined to two values (0 and 1) and activation
functions given by the usual truth-functions. McCulloch and Pitts
advanced logic gates as idealized models of individual neurons. Their
discussion exerted a profound influence on computer science (von
Neumann 1945). Modern digital computers are simply networks of logic
gates. Within cognitive science, however, researchers usually focus
upon networks whose elements are more “neuron-like” than
logic gates. In particular, modern-day connectionists typically
emphasize analog neural networks whose nodes take continuous rather
than discrete activation values. Some authors even use the phrase
“neural network” so that it exclusively denotes such
networks.

Neural networks received relatively scant attention from cognitive
scientists during the 1960s and 1970s, when Turing-style models
dominated. The 1980s witnessed a huge resurgence of interest in neural
networks, especially analog neural networks, with the two-volume
Parallel Distributed Processing (Rumelhart, McClelland, and
the PDP research group, 1986; McClelland, Rumelhart, and the PDP
research group, 1987) serving as a manifesto. Researchers constructed
connectionist models of diverse phenomena: object recognition, speech
perception, sentence comprehension, cognitive development, and so on.
Impressed by connectionism, many researchers concluded that CCTM+RTM
was no longer “the only game in town”.

In the 2010s, a class of computational models known as deep neural
networks became quite popular (Krizhevsky, Sutskever, and Hinton
2012; LeCun, Bengio, and Hinton 2015). These models are neural
networks with multiple layers of hidden nodes (sometimes hundreds of
such layers). Deep neural networks—trained on large data sets
through one or another learning algorithm (usually
backpropagation)—have achieved great success in many areas of
AI, including image classification (AlexNet), strategic game-playing
(AlphaGo), and natural language processing (ChatGPT). Deep neural
networks are now widely deployed in commercial applications, and they
are the focus of extensive ongoing investigation within both academia
and industry. Researchers have also used them to model the mind (e.g.
Kriegeskorte 2015; Marblestone, Wayne, and Kording 2016; Storrs,
Kietzmann, Walther, et al. 2021; Zhuang, Yan, Nayebi, et al. 2021),
although how much success this modeling enterprise has thus far
achieved is a controversial question (Bowers, Malholtra,
Dujmović, et al. 2023).

For 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).

4.1 Relation between neural networks and classical computation

Neural networks have a very different “feel” than
classical (i.e., Turing-style) models. Yet classical computation and
neural network computation are not mutually exclusive:

• 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).

Although 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.

Philosophers often say that classical computation involves
“rule-governed symbol manipulation” while neural network
computation is non-symbolic. The intuitive picture is that
“information” in neural networks is globally distributed
across the weights and activations, rather than concentrated in
localized symbols. However, the notion of “symbol” itself
requires explication, so it is often unclear what theorists mean by
describing computation as symbolic versus non-symbolic. As mentioned
in
§1,
the Turing formalism places very few conditions on
“symbols”. Regarding primitive symbols, Turing assumes
just that there are finitely many of them and that they can be
inscribed in read/write memory locations. Neural networks can also
manipulate symbols satisfying these two conditions: as just noted, one
can implement a Turing-style model in a neural network.

Many 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).

Following Steven Pinker and Alan Prince (1988), we may distinguish
between eliminative connectionism and implementationist
connectionism.

Eliminative connectionists advance connectionism as a rival to
classical computationalism. They argue that the Turing formalism is
irrelevant to psychological explanation. Often, though not always,
they seek to revive the associationist tradition in
psychology, a tradition that CCTM had forcefully challenged. Often,
though not always, they attack the mentalist, nativist linguistics
pioneered by Noam Chomsky (1965). Often, though not always, they
manifest overt hostility to the very notion of mental representation.
But the defining feature of eliminative connectionism is that it uses
neural networks as replacements for Turing-style models.
Eliminative connectionists view the mind as a computing system of a
radically different kind than the Turing machine. A few authors
explicitly espouse eliminative connectionism (Churchland 1989;
Rumelhart and McClelland 1986; Horgan and Tienson 1996), and many
others incline towards it.

Implementationist connectionism is a more ecumenical position. It
allows a potentially valuable role for both Turing-style models
and neural networks, operating harmoniously at different
levels of description (Marcus 2001; Smolensky 1988). A Turing-style
model is higher-level, whereas a neural network model is lower-level.
The neural network illuminates how the brain implements the
Turing-style model, just as a description in terms of logic gates
illuminates how a personal computer executes a program in a high-level
programming language.

4.2 Arguments for connectionism

Connectionism 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.

When 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:

• Real neurons are much more heterogeneous than the interchangeable
  nodes that figure in typical connectionist networks.
• 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.
• The backpropagation algorithm requires that weights between nodes
  can vary between excitatory and inhibitory, yet actual synapses cannot
  so vary (Crick and Asanuma 1986). Moreover, traditional applications
  of the algorithm assume target outputs supplied exogenously by
  modelers who know the desired answer. In that sense, learning
  is supervised. Very little learning in actual biological
  systems involves anything resembling supervised training.

On 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).

Even when a neural network is not biologically plausible, it may still
be more biologically plausible than classical models. Neural
networks certainly seem closer than Turing-style models, in both
details and spirit, to neurophysiological description. Many cognitive
scientists worry that CCTM reflects a misguided attempt at imposing
the architecture of digital computers onto the brain. Some doubt that
the brain implements anything resembling digital computation, i.e.,
computation over discrete configurations of digits (Piccinini and
Bahar 2013). Others doubt that brains display clean Turing-style
separation between central processor and read/write memory (Dayan
2009). Neural networks fare better on both scores: they do not require
computation over discrete configurations of digits, and they do not
postulate a clean separation between central processor and read/write
memory.

Classical 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.

Connectionists offer numerous further arguments that we should employ
connectionist models instead of, or in addition to, classical models.
See the entry
connectionism
for an overview. For purposes of this entry, we mention two
additional arguments.

The first argument emphasizes learning (Bechtel and
Abrahamsen 2002: 51). A vast range of cognitive phenomena involve
learning from experience. Many connectionist models are explicitly
designed to model learning, through backpropagation or some other
algorithm that modifies the weights between nodes. By contrast,
connectionists often complain that there are no good classical models
of learning. Classical computationalists can respond by citing
perceived defects of connectionist learning algorithms. Classical
computationalists can also cite Bayesian decision theory, a
mathematical model of inference and decision-making under uncertainty.
In the Bayesian framework, uncertainty is codified through
probability. Precise rules dictate how to update
probabilities in light of new evidence and how to select actions in
light of probabilities and utilities. (See the entries
Bayes’s theorem
and
normative theories of rational choice: expected utility
for details.) Bayesian cognitive science uses Bayesian
decision theory to construct mathematical models of mental activity
(Ma 2019; Ma, Kording, and Goldreich 2023). Over the past few decades,
Bayesian cognitive science has accrued many explanatory successes.
This impressive track record suggests that some mental processes are
Bayesian or approximately Bayesian (Rescorla forthcoming). Moreover,
classical computing systems can execute or at least approximately
execute Bayesian updating in various realistic scenarios (Murphy 2023;
Thrun, Burgard, and Fox 2005). Arguably, then, classical computation
can model many important cases of learning.

The second argument emphasizes speed of computation. Neurons
are much slower than silicon-based components of digital computers.
For this reason, neurons could not execute serial computation quickly
enough to match rapid human performance in perception, linguistic
comprehension, decision-making, etc. Connectionists maintain that the
only viable solution is to replace serial computation with a
“massively parallel” computational
architecture—precisely what neural networks provide (Feldman and
Ballard 1982; Rumelhart 1989). However, this argument is only
effective against classical computationalists who insist upon serial
processing. As noted in
§3,
some Turing-style models involve parallel processing. Many classical
computationalists are happy to allow “massively parallel”
mental computation, and the argument gains no traction against these
researchers. That being said, the argument highlights an important
question that any computationalist—whether classical,
connectionist, or otherwise—must address: How does a brain built
from relatively slow neurons execute sophisticated computations so
quickly? Neither classical nor connectionist computationalists have
answered this question satisfactorily (Gallistel and King 2009: 174
and 265).

4.3 Systematicity and productivity

Fodor 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.

This argument has elicited numerous replies and counter-replies. Some
argue that neural networks can exhibit systematicity without
implementing anything like classical computational architecture
(Horgan and Tienson 1996; Chalmers 1990; Smolensky 1991; van Gelder
1990). Some argue that Fodor and Pylyshyn vastly exaggerate
systematicity (Johnson 2004) or productivity (Rumelhart and McClelland
1986), especially for non-human animals (Dennett 1991). These issues,
and many others raised by Fodor and Pylyshyn’s argument, have
been thoroughly investigated in the literature. For further
discussion, see Bechtel and Abrahamsen (2002: 156–199),
Bermúdez (2005: 244–278), Chalmers (1993), Clark (2014:
84–86), and the encyclopedia entries on
the language of thought hypothesis
and on
connectionism.

Gallistel and King (2009) advance a related but distinct productivity
argument. They emphasize productivity of mental computation,
as opposed to productivity of mental states. Through detailed
empirical case studies, they argue that many non-human animals can
extract, store, and retrieve detailed records of the surrounding
environment. For example, the Western scrub jay records where it
cached food, what kind of food it cached in each location, when it
cached the food, and whether it has depleted a given cache (Clayton,
Emery, and Dickinson 2006). The jay can access these records and
exploit them in diverse computations: computing whether a food item
stored in some cache is likely to have decayed; computing a route from
one location to another; and so on. The number of possible
computations a jay can execute is, for all practical purposes,
infinite.

CCTM 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:

• 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.
• Implementationist connectionists can postulate symbol storage in
  read/write memory, 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]

Gallistel and King conclude that CCTM is much better suited than
either eliminativist or implementationist connectionism to explain a
vast range of cognitive phenomena.

Critics attack this new productivity argument from various angles,
focusing mainly on the empirical case studies adduced by Gallistel and
King. Peter Dayan (2009), John Donahoe (2010), and Christopher Mole
(2014) argue that biologically plausible neural network models can
accommodate at least some of the case studies. Dayan and Donahoe argue
that empirically adequate neural network models can dispense with
anything resembling read/write memory. Mole argues that, in certain
cases, empirically adequate neural network models can
implement the read/write memory mechanisms posited by
Gallistel and King. Debate on these fundamental issues seems poised to
continue well into the future.

4.4 Computational neuroscience

Computational neuroscience describes the nervous system
through computational models (Trappenberg 2010; Miller 2018). Although
computational neuroscience is grounded in mathematical modeling of
individual neurons, its distinctive focus is systems of
interconnected neurons. Computational neuroscientists typically model
these systems as neural networks. This research may be seen as a
variant, off-shoot, or descendant of connectionism. However, most
computational neuroscientists do not self-identify as connectionists.
There are several differences between connectionism and computational
neuroscience:

• 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).
• 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).
• Computational neuroscientists usually regard individual nodes in
  neural networks as idealized descriptions of actual neurons.
  Connectionists usually instead regard nodes as neuron-like
  processing units (Rogers and McClelland 2014) while remaining
  neutral about how exactly these units map onto actual
  neurophysiological entities.

One might say that computational neuroscience is concerned mainly with
neural computation (computation by systems of neurons),
whereas connectionism is concerned mainly with abstract computational
models inspired by neural computation. But the boundaries
between connectionism and computational neuroscience are admittedly
somewhat porous. Doerig, Sommers, Seeliger, et al. (2023) propose the
label neuroconnectionism for a research program that
thoroughly integrates neuroscience with neural network modeling.

Serious philosophical engagement with neuroscience dates back at least
to Patricia Churchland’s Neurophilosophy (1986). As
computational neuroscience matured, Churchland became one of its main
philosophical champions (Churchland, Koch, and Sejnowski 1990;
Churchland and Sejnowski 1992). She was joined by Paul Churchland
(1995, 2007) and others (Eliasmith 2013; Eliasmith and Anderson 2003;
Piccinini and Bahar 2013; Piccinini and Shagrir 2014). All these
authors hold that theorizing about mental computation should begin
with the brain, not with Turing machines or other inappropriate tools
drawn from logic and computer science. They also hold that neural
network modeling should strive for greater biological realism than
connectionist models typically attain. Chris Eliasmith (2013) develops
this neurocomputational viewpoint through the Neural Engineering
Framework, which supplements computational neuroscience with
tools drawn from control theory (Brogan 1990). He aims to
“reverse engineer” the brain, building large-scale,
biologically plausible neural network models of cognitive
phenomena.

Computational 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.

Partly in response to such worries, some researchers propose an
integrated cognitive computational neuroscience that connects
psychological theories with neural implementation mechanisms
(Naselaris et al. 2018; Kriegeskorte and Douglas 2018). The basic idea
is to use neural network models to illuminate how mental processes are
instantiated in the brain, thereby grounding multiply realizable
cognitive description in the neurophysiological. A good example is
recent work on neural implementation of Bayesian inference (Pouget et
al. 2013; Orhan and Ma 2017; Aitchison and Lengyel 2016). Researchers
articulate (multiply realizable) Bayesian models of various mental
processes; they construct biologically plausible neural networks that
execute or approximately execute the posited Bayesian computations;
and they evaluate how well these neural network models fit with
neurophysiological data.

Despite the differences between connectionism and computational
neuroscience, these two movements raise many similar issues. In
particular, the dialectic from
§4.4
regarding systematicity and productivity arises in similar form.

Philosophers and cognitive scientists use the term
“representation” in diverse ways. Within philosophy, the
most dominant usage ties representation to intentionality, i.e., the
“aboutness” of mental states. Contemporary philosophers
usually elucidate intentionality by invoking representational
content. A representational mental state has a content that
represents the world as being a certain way, so we can ask whether the
world is indeed that way. Thus, representationally contentful mental
states are semantically evaluable with respect to properties
such as truth, accuracy, fulfillment, and so on. To illustrate:

• Beliefs are the sorts of things that can be true or false. My
  belief 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
  inaccurate. My perceptual experience 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
  desire to eat chocolate is fulfilled if I eat chocolate,
  thwarted if I do not eat chocolate.

Beliefs 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).

In ordinary life, we frequently predict and explain behavior by
invoking beliefs, desires, and other representationally contentful
mental states. We identify these states through their representational
properties. When we say “Frank believes that Emmanuel Macron is
French”, we specify the condition under which Frank’s
belief is true (namely, that Emmanuel Macron is French). When we say
“Frank wants to eat chocolate”, we specify the condition
under which Frank’s desire is fulfilled (namely, that Frank eats
chocolate). So folk psychology assigns a central role to
intentional descriptions, i.e., descriptions that identify
mental states through their representational properties. Whether
scientific psychology should likewise employ intentional descriptions
is a contested issue within contemporary philosophy of mind.

Intentional realism is realism regarding representation. At a
minimum, this position holds that representational properties are
genuine aspects of mentality. Usually, it is also taken to hold that
scientific psychology should freely employ intentional descriptions
when appropriate. Intentional realism is a popular position, advocated
by Tyler Burge (2010a), Jerry Fodor (1987), Christopher Peacocke
(1992, 1994), and many others. One prominent argument for intentional
realism cites cognitive science practice. The argument
maintains that intentional description figures centrally in many core
areas of cognitive science, such as perceptual psychology and
linguistics. For example, perceptual psychology describes how
perceptual activity transforms sensory inputs (e.g., retinal
stimulations) into representations of the distal environment (e.g.,
perceptual representations of distal shapes, sizes, and colors). The
science identifies perceptual states by citing representational
properties (e.g., representational relations to specific distal
shapes, sizes, colors). Assuming a broadly scientific realist
perspective, the explanatory achievements of perceptual psychology
support a realist posture towards intentionality.

Eliminativism is a strong form of anti-realism about
intentionality. Eliminativists dismiss intentional description as
vague, context-sensitive, interest-relative, explanatorily
superficial, or otherwise problematic. They recommend that scientific
psychology jettison representational content. An early example is W.V.
Quine’s Word and Object (1960), which seeks to replace
intentional psychology with behaviorist stimulus-response psychology.
Paul Churchland (1981), another prominent eliminativist, wants to
replace intentional psychology with neuroscience.

Between intentional realism and eliminativism lie various intermediate
positions. Daniel Dennett (1971, 1987) acknowledges that intentional
discourse is predictively useful, but he questions whether mental
states really have representational properties. According to
Dennett, theorists who employ intentional descriptions are not
literally asserting that mental states have representational
properties. They are merely adopting the “intentional
stance”. Donald Davidson (1980) espouses a neighboring
interpretivist position. He emphasizes the central role that
intentional ascription plays within ordinary interpretive practice,
i.e., our practice of interpreting one another’s mental states
and speech acts. At the same time, he questions whether intentional
psychology will find a place within mature scientific theorizing.
Davidson and Dennett both profess realism about intentional mental
states. Nevertheless, both philosophers are customarily read as
intentional anti-realists. (In particular, Dennett is frequently read
as a kind of instrumentalist about intentionality.) One
source of this customary reading involves indeterminacy of
interpretation. Suppose that behavioral evidence allows two
conflicting interpretations of a thinker’s mental states.
Following Quine, Davidson and Dennett both say there is then “no
fact of the matter” regarding which interpretation is correct.
This diagnosis indicates a less than fully realist attitude towards
intentionality.

Debates over intentionality figure prominently in philosophical
discussion of CTM. Let us survey some highlights.

5.1 Computation as formal

Classical computationalists typically assume what one might call
the formal-syntactic conception of computation (FSC). The
intuitive idea is that computation manipulates symbols in virtue of
their formal syntactic properties rather than their semantic
properties.

FSC stems from innovations in mathematical logic during the late
19^th and early 20^th centuries, especially
seminal contributions by George Boole and Gottlob Frege. In his
Begriffsschrift (1879/1967), Frege effected a thoroughgoing
formalization of deductive reasoning. To formalize, we
specify a formal language whose component linguistic
expressions are individuated non-semantically (e.g., by their
geometric shapes). We may have some intended interpretation in mind,
but elements of the formal language are purely syntactic entities that
we can discuss without invoking semantic properties such as reference
or truth-conditions. In particular, we can specify inference
rules in formal syntactic terms. If we choose our inference rules
wisely, then they will cohere with our intended interpretation: they
will carry true premises to true conclusions. Through formalization,
Frege invested logic with unprecedented rigor. He thereby laid the
groundwork for numerous subsequent mathematical and philosophical
developments.

Formalization 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.

FSC holds that all computation manipulates formal syntactic
items, without regard to any semantic properties those items may have.
Precise formulations of FSC vary. Computation is said to be
“sensitive” to syntax but not semantics, or to have
“access” only to syntactic properties, or to operate
“in virtue” of syntactic rather than semantic properties,
or to be impacted by semantic properties only as
“mediated” by syntactic properties. It is not always so
clear what these formulations mean or whether they are equivalent to
one another. But the intuitive picture is that syntactic properties
have causal/explanatory primacy over semantic properties in driving
computation forward.

Fodor’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.

Connectionists often deny that neural networks manipulate
syntactically structured items. For that reason, many connectionists
would hesitate to accept FSC. Nevertheless, most connectionists
endorse a generalized formality thesis: computation is
insensitive to semantic properties. The generalized formality thesis
raises many of the same philosophical issues raised by FSC. We focus
here on FSC, which has received the most philosophical discussion.

Fodor combines CCTM+RTM+FSC with intentional realism. He holds that
CCTM+RTM+FSC vindicates folk psychology by helping us convert common
sense intentional discourse into rigorous science. He motivates his
position with a famous abductive argument for CCTM+RTM+FSC (1987:
18–20). Strikingly, mental activity tracks semantic properties
in a coherent way. For example, deductive inference carries premises
to conclusions that are true if the premises are true. How can we
explain this crucial aspect of mental activity? Formalization shows
that syntactic manipulations can track semantic properties, and
computer science shows how to build physical machines that execute
desired syntactic manipulations. If we treat the mind as a
syntax-driven machine, then we can explain why mental activity tracks
semantic properties in a coherent way. Moreover, our explanation does
not posit causal mechanisms radically different from those posited
within the physical sciences. We thereby answer the pivotal question:
How is rationality mechanically possible?

Stephen 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?

At one point in his career, Putnam (1983: 139–154) combined
CCTM+FSC with a Davidson-tinged interpretivism. Cognitive
science should proceed along the lines suggested by Stich and Field,
delineating purely formal syntactic computational models. Formal
syntactic modeling co-exists with ordinary interpretive practice, in
which we ascribe intentional contents to one another’s mental
states and speech acts. Interpretive practice is governed by holistic
and heuristic constraints, which stymie attempts at converting
intentional discourse into rigorous science. For Putnam, as for Field
and Stich, the scientific action occurs at the formal syntactic level
rather than the intentional level.

CTM+FSC comes under attack from various directions. One criticism
targets the causal relevance of representational content
(Block 1990; Figdor 2009; Kazez 1995). Intuitively speaking, the
contents of mental states are causally relevant to mental activity and
behavior. For example, my desire to drink water rather than orange
juice causes me to walk to the sink rather than the refrigerator. The
content of my desire (that I drink water) seems to play an
important causal role in shaping my behavior. According to Fodor
(1990: 137–159), CCTM+RTM+FSC accommodates such intuitions.
Formal syntactic activity implements intentional mental
activity, thereby ensuring that intentional mental states causally
interact in accord with their contents. However, it is not so clear
that this analysis secures the causal relevance of content. FSC says
that computation is “sensitive” to syntax but not
semantics. Depending on how one glosses the key term
“sensitive”, it can look like representational content is
causally irrelevant, with formal syntax doing all the causal work.
Here is an analogy to illustrate the worry. When a car drives along a
road, there are stable patterns involving the car’s shadow.
Nevertheless, shadow position at one time does not influence shadow
position at a later time. Similarly, CCTM+RTM+FSC may explain how
mental activity instantiates stable patterns described in intentional
terms, but this is not enough to ensure the causal relevance of
content. If the mind is a syntax-driven machine, then causal efficacy
seems to reside at the syntactic rather the semantic level. Semantics
is just “along for the ride”. Apparently, then, CTM+FSC
encourages the conclusion that representational properties are
causally inert. The conclusion may not trouble eliminativists, but
intentional realists usually want to avoid it.

A second criticism dismisses the formal-syntactic picture as
speculation ungrounded in scientific practice. Tyler Burge (2010a,b,
2013: 479–480) contends that formal syntactic description of
mental activity plays no significant role within large areas of
cognitive science, including the study of theoretical reasoning,
practical reasoning, and perception. In each case, Burge argues, the
science employs intentional description rather than formal
syntactic description. For example, perceptual psychology individuates
perceptual states not through formal syntactic properties but through
representational relations to distal shapes, sizes, colors, and so on.
To understand this criticism, we must distinguish formal syntactic
description and neurophysiological description. Everyone
agrees that a complete scientific psychology will assign prime
importance to neurophysiological description. However,
neurophysiological description is distinct from formal syntactic
description, because formal syntactic description is supposed to be
multiply realizable in the neurophysiological. The issue here is
whether scientific psychology should supplement intentional
descriptions and neurophysiological descriptions with
multiply realizable, non-intentional formal syntactic
descriptions.

5.2 Externalism about mental content

Putnam’s landmark article “The Meaning of
‘Meaning’” (1975: 215–271) introduced the
Twin Earth thought experiment, which postulates a world just
like our own except that H₂O is replaced by a qualitatively
similar substance XYZ with different chemical composition. Putnam
argues that XYZ is not water and that speakers on Twin Earth use the
word “water” to refer to XYZ rather than to water. Burge
(1982) extends this conclusion from linguistic reference to
mental content. He argues that Twin Earthlings instantiate
mental states with different contents. For example, if Oscar on Earth
thinks that water is thirst-quenching, then his duplicate on
Twin Earth thinks a thought with a different content, which we might
gloss as that twin-water is thirst-quenching. Burge concludes
that mental content does not supervene upon internal neurophysiology.
Mental content is individuated partly by factors outside the
thinker’s skin, including causal relations to the environment.
This position is externalism about mental content.

Formal 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.

Content externalism raises serious questions about the explanatory
utility of representational content for scientific psychology:

Argument from Causation (Fodor 1987, 1991): How can mental
content exert any causal influence except as manifested within
internal neurophysiology? There is no “psychological action at a
distance”. Differences in the physical environment impact
behavior only by inducing differences in local brain states. So the
only causally relevant factors are those that supervene upon internal
neurophysiology. Externally individuated content is causally
irrelevant.

Argument from Explanation (Stich 1983): Rigorous scientific
explanation should not take into account factors outside the
subject’s skin. Folk psychology may taxonomize mental states
through relations to the external environment, but scientific
psychology should taxonomize mental states entirely through factors
that supervene upon internal neurophysiology. It should treat Oscar
and Twin Oscar as psychological
duplicates.^[4]

Some 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.

Many philosophers respond to such worries by promoting content
internalism. Whereas content externalists favor wide
content (content that does not supervene upon internal
neurophysiology), content internalists favor narrow content
(content that does so supervene). Narrow content is what remains of
mental content when one factors out all external elements. At one
point in his career, Fodor (1981, 1987) pursued internalism as a
strategy for integrating intentional psychology with CCTM+RTM+FSC.
While conceding that wide content should not figure in scientific
psychology, he maintained that narrow content should play a central
explanatory role.

Radical internalists insist that all content is narrow. A
typical analysis holds that Oscar is thinking not about water but
about some more general category of substance that subsumes XYZ, so
that Oscar and Twin Oscar entertain mental states with the same
contents. Tim Crane (1991) and Gabriel Segal (2000) endorse such an
analysis. They hold that folk psychology always individuates
propositional attitudes narrowly. A less radical internalism
recommends that we recognize narrow content in addition to
wide content. Folk psychology may sometimes individuate propositional
attitudes widely, but we can also delineate a viable notion of narrow
content that advances important philosophical or scientific goals.
Internalists have proposed various candidate notions of narrow content
(Block 1986; Chalmers 2002; Cummins 1989; Fodor 1987; Lewis 1994; Loar
1988; Mendola 2008). See the entry
narrow mental content
for an overview of prominent candidates.

Externalists 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:

Argument from Causation: Externalists insist that wide
content can be causally relevant. The details vary among externalists,
and discussion often becomes intertwined with complex issues
surrounding causation, counterfactuals, and the metaphysics of mind.
See the entry
mental causation
for an introductory overview, and see Burge (2007), Rescorla (2014),
and Yablo (1997, 2003) for representative externalist discussion.

Argument from Explanation: Externalists claim that
psychological explanation can legitimately taxonomize mental states
through factors that outstrip internal neurophysiology (Peacocke 1993;
Shea 2018). Burge observes that non-psychological sciences often
individuate explanatory kinds relationally, i.e., through
relations to external factors. For example, whether an entity counts
as a heart depends (roughly) upon whether its biological function in
its normal environment is to pump blood. So physiology individuates
organ kinds relationally. Why can’t psychology likewise
individuate mental states relationally? For a notable exchange on
these issues, see Burge (1986, 1989, 1995) and Fodor (1987, 1991).

Externalists 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.

Burge (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.

Suppose we abandon the search for narrow content. What are the
prospects for combining CTM+FSC with externalist intentional
psychology? The most promising option emphasizes levels of
explanation. We can say that intentional psychology occupies one
level of explanation, while formal-syntactic computational psychology
occupies a different level. Fodor advocates this approach in his later
work (1994, 2008). He comes to reject narrow content as otiose. He
suggests that formal syntactic mechanisms implement externalist
psychological laws. Mental computation manipulates Mentalese
expressions in accord with their formal syntactic properties, and
these formal syntactic manipulations ensure that mental activity
instantiates appropriate law-like patterns defined over wide
contents.

In light of the internalism/externalism distinction, let us revisit
the eliminativist challenge raised in
§5.1:
what explanatory value does intentional description add to
formal-syntactic description? Internalists can respond that suitable
formal syntactic manipulations determine and maybe even constitute
narrow contents, so that internalist intentional description is
already implicit in suitable formal syntactic description (cf. Field
2001: 75). Perhaps this response vindicates intentional realism,
perhaps not. Crucially, though, no such response is available to
content externalists. Externalist intentional description is not
implicit in formal syntactic description, because one can hold formal
syntax fixed while varying wide content. Thus, content externalists
who espouse CTM+FSC must say what we gain by supplementing
formal-syntactic explanations with intentional explanations. Once we
accept that mental computation is sensitive to syntax but not
semantics, it is far from clear that any useful explanatory work
remains for wide content. Fodor addresses this challenge at various
points, offering his most systematic treatment in The Elm and the
Expert (1994). See Arjo (1996), Aydede (1998), Aydede and Robbins
(2001), Wakefield (2002); Perry (1998), and Wakefield (2002) for
criticism. See Rupert (2008) and Schneider (2005) for positions close
to Fodor’s. Dretske (1993) and Shea (2018, pp. 197–226)
pursue alternative strategies for vindicating the explanatory
relevance of wide content.

5.3 Content-involving computation

The perceived gulf between computational description and intentional
description animates many writings on CTM. A few philosophers try to
bridge the gulf using computational descriptions that individuate
computational states in representational terms. These descriptions are
content-involving, to use Christopher Peacocke’s (1994)
terminology. On the content-involving approach, there is no rigid
demarcation between computational and intentional description. In
particular, certain scientifically valuable descriptions of mental
activity are both computational and intentional. Call this position
content-involving computationalism.

Content-involving computationalists need not say that all
computational description is intentional. To illustrate, suppose we
describe a simple Turing machine that manipulates symbols individuated
by their geometric shapes. Then the resulting computational
description is not plausibly content-involving. Accordingly,
content-involving computationalists do not usually advance
content-involving computation as a general theory of computation. They
claim only that some important computational descriptions are
content-involving.

One can develop content-involving computationalism in an internalist
or externalist direction. Internalist content-involving
computationalists hold that some computational descriptions
identify mental states partly through their narrow contents.
Murat Aydede (2005) recommends a position along these lines.
Externalist content-involving computationalism holds that
certain computational descriptions identify mental states partly
through their wide contents. Tyler Burge (2010a:
95–101), Christopher Peacocke (1994, 1999), and Mark Sprevak
(2010) espouse this position. Oron Shagrir (2001, 2020, 2022)
advocates a content-involving computationalism that is neutral between
internalism and externalism.

Externalist 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.

A 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.

Arguably, though, many familiar computational formalisms allow a
content-involving rather than formal syntactic construal. To
illustrate, consider the Turing machine. One can individuate
the “symbols” comprising the Turing machine alphabet
non-semantically, through factors akin to geometric shape. But does
Turing’s formalism require a non-semantic individuative
scheme? Arguably, the formalism allows us to individuate symbols
partly through their contents. Of course, the machine table for a
Turing machine does not explicitly cite semantic properties of symbols
(e.g., denotations or truth-conditions). Nevertheless, the machine
table can encode mechanical rules that describe how to manipulate
symbols, where those symbols are type-identified in content-involving
terms. In this way, the machine table dictates transitions among
content-involving states without explicitly mentioning semantic
properties. Aydede (2005) suggests an internalist version of this
view, with symbols type-identified through their narrow
contents.^[5]
Rescorla (2017a) develops the view in an externalist direction, with
symbols type-identified through their wide contents. He argues that
some Turing-style models describe computational operations over
externalistically individuated Mentalese
symbols.^[6]

In principle, one might embrace both externalist content-involving
computational description and formal syntactic description.
One might say that these two kinds of description occupy distinct
levels of explanation. Peacocke suggests such a view. Other
content-involving computationalists regard formal syntactic
descriptions of the mind more skeptically. For example, Burge
questions what explanatory value formal syntactic description
contributes to certain areas of scientific psychology (such as
perceptual psychology). From this viewpoint, the eliminativist
challenge posed in
§5.1
has matters backwards. We should not assume that formal syntactic
descriptions are explanatorily valuable and then ask what value
intentional descriptions contribute. We should instead embrace the
externalist intentional descriptions offered by current cognitive
science and then ask what value formal syntactic description
contributes.

Proponents of formal syntactic description often respond by citing
implementation mechanisms. Externalist description of mental
activity presupposes that suitable causal-historical relations between
the mind and the external physical environment are in place. But
surely we want a “local” description that ignores external
causal-historical relations, a description that reveals underlying
causal mechanisms. Fodor (1987, 1994) argues in this way to motivate
the formal syntactic picture. For possible externalist responses to
the argument from implementation mechanisms, see Burge (2010b),
Rescorla (2017b), Shea (2013), and Sprevak (2010). For an argument
that current cognitive science practice does indeed assign an
important explanatory role to formal syntax, see Calzavarini and
Paternoster (2022). Debate over the explanatory value of formal
syntax, and more generally over the relation between computation and
representation, seems likely to continue into the indefinite
future.

The 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.

6.1 Information-processing

It 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.

Claude Shannon introduced a scientifically important notion of
“information” in his 1948 article “A Mathematical
Theory of Communication”. The intuitive idea is that information
measures reduction in uncertainty, where reduced uncertainty
manifests as an altered probability distribution over possible states.
Shannon codified this idea within a rigorous mathematical framework,
laying the foundation for information theory (Cover and
Thomas 2006). Shannon information is fundamental to modern
engineering. It finds fruitful application within cognitive science,
especially cognitive neuroscience. Does it support a convincing
analysis of computation as “information-processing”?
Consider an old-fashioned tape machine that records messages received
over a wireless radio. Using Shannon’s framework, one can
measure how much information is carried by some recorded message.
There is a sense in which the tape machine “processes”
Shannon information whenever we replay a recorded message. Still, the
machine does not seem to implement a non-trivial computational
model.^[7]
Certainly, neither the Turing machine formalism nor the neural
network formalism offers much insight into the machine’s
operations. Arguably, then, a system can process Shannon information
without executing computations in any interesting sense.

Confronted with such examples, one might try to isolate a more
demanding notion of “processing”, so that the tape machine
does not “process” Shannon information. Alternatively, one
might insist that the tape machine executes non-trivial computations.
Piccinini and Scarantino (2010) advance a highly general notion of
computation—which they dub generic
computation—with that consequence.

A second prominent notion of information derives from Paul
Grice’s (1989) influential discussion of natural
meaning. Natural meaning involves reliable,
counterfactual-supporting correlations. For example, tree rings
correlate with the age of the tree, and pox correlate with chickenpox.
We colloquially describe tree rings as carrying information about tree
age, pox as carrying information about chickenpox, and so on. Such
descriptions suggest a conception that ties information to reliable,
counterfactual-supporting correlations. Fred Dretske (1981) develops
this conception into a systematic theory, as do various subsequent
philosophers. Does Dretske-style information subserve a plausible
analysis of computation as “information-processing”?
Consider an old-fashioned bimetallic strip thermostat. Two
metals are joined together into a strip. Differential expansion of the
metals causes the strip to bend, thereby activating or deactivating a
heating unit. Strip state reliably correlates with current ambient
temperature, and the thermostat “processes” this
information-bearing state when activating or deactivating the heater.
Yet the thermostat does not seem to implement any non-trivial
computational model. One would not ordinarily regard the thermostat as
computing. Arguably, then, a system can process Dretske-style
information without executing computations in any interesting sense.
Of course, one might try to handle such examples through maneuvers
parallel to those from the previous paragraph.

A third prominent notion of information is semantic
information, i.e., representational
content.^[8]
Some philosophers hold that a physical system computes only if the
system’s states have representational properties (Dietrich 1989;
Fodor 1998: 10; Ladyman 2009; Shagrir 2006; Sprevak 2010). In that
sense, information-processing is 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.

It 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).

6.2 Function evaluation

In a widely cited passage, the perceptual psychologist David Marr
(1982) distinguishes three levels at which one can describe an
“information-processing device”:

Computational 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).

Representation 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).

Hardware implementation: “the details of how the
algorithm and representation are realized physically” (p.
25).

Marr’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.

Marr’s discussion suggests a functional conception of
computation, on which computation is a matter of transforming
inputs into appropriate outputs. Frances Egan elaborates the
functional conception over a series of articles (1991, 1992, 1999,
2003, 2010, 2014, 2019, 2020). Like Marr, she treats computational
description as description of input-output relations. She also claims
that computational models characterize a purely mathematical
function: that is, a mapping from mathematical inputs to mathematical
outputs. She illustrates by considering a visual mechanism (called
“Visua”) that computes an object’s depth from
retinal disparity. She imagines a neurophysiological duplicate
(“Twin Visua”) embedded so differently in the physical
environment that it does not represent depth. Visua and Twin Visua
instantiate perceptual states with different representational
properties. Nevertheless, Egan says, vision science treats Visua and
Twin Visua as computational duplicates. Visua and Twin Visua
compute the same mathematical function, even though the computations
have different representational import in the two cases. Egan
concludes that computational modeling of the mind yields an
“abstract mathematical description” consistent with many
alternative possible representational descriptions. Intentional
attribution is just a heuristic gloss upon underlying computational
description.

Chalmers (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.

An additional worry faces functional theories, such as Egan’s,
that exclusively emphasize mathematical inputs and outputs.
Critics complain that Egan mistakenly elevates mathematical functions,
at the expense of intentional explanations routinely offered by
cognitive science (Burge 2005; Rescorla 2015; Silverberg 2006; Sprevak
2010). To illustrate, suppose perceptual psychology describes the
perceptual system as estimating that some object’s depth is 5
meters. The perceptual depth-estimate has a representational content:
it is accurate only if the object’s depth is 5 meters. We cite
the number 5 to identify the depth-estimate. But our choice of this
number depends upon our arbitrary choice of measurement units. Critics
contend that the content of the depth-estimate, not the arbitrarily
chosen number through which we theorists specify that content, is what
matters for psychological explanation. Egan’s theory places the
number rather than the content at explanatory center stage. According
to Egan, computational explanation should describe the visual system
as computing a particular mathematical function that carries
particular mathematical inputs into particular
mathematical outputs. Those particular mathematical inputs and
outputs depend upon our arbitrary choice of measurement units, so they
arguably lack the explanatory significance that Egan assigns to
them.

We should distinguish the functional approach, as pursued by Marr and
Egan, from the functional programming paradigm in computer
science. The functional programming paradigm models evaluation of a
complex function as successive evaluation of simpler functions. To
take a simple example, one might evaluate \(f(x,y) = (x^💬+y)\) by
first evaluating the squaring function and then evaluating the
addition function. Functional programming differs from the
“computational level” descriptions emphasized by Marr,
because it specifies intermediate computational stages. The functional
programming paradigm stretches back to Alonzo Church’s (1936)
lambda calculus, continuing with programming languages such
as PCF and LISP. It plays an important role in AI and theoretical
computer science. Some authors suggest that it offers special insight
into mental computation (Klein 2012; Piantadosi, Tenenbaum, and
Goodman 2012). However, many computational formalisms do not conform
to the functional paradigm: Turing machines; imperative programming
languages, such as C; logic programming languages, such as Prolog; and
so on. Even though the functional paradigm describes numerous
important computations (possibly including mental computations), it
does not plausibly capture computation in general.

6.3 Structuralism

Many philosophical discussions embody a structuralist conception
of computation: a computational model describes an abstract
causal structure, without taking into account particular physical
states that instantiate the structure. This conception traces back at
least to Putnam’s original treatment (1967). Chalmers (1995,
1996a, 2011, 2012) develops it in detail. He introduces the
combinatorial-state automaton (CSA) formalism, which subsumes
most familiar models of computation (including Turing machines and
neural networks). A CSA provides an abstract description of a physical
system’s causal topology: the pattern of causal
interaction among the system’s parts, independent of the nature
of those parts or the causal mechanisms through which they interact.
Computational description specifies a causal topology.

Chalmers deploys structuralism to delineate a very general version of
CTM. He assumes the functionalist view that psychological states are
individuated by their roles in a pattern of causal organization.
Psychological description specifies causal roles, abstracted away from
physical states that realize those roles. So psychological properties
are organizationally invariant, in that they supervene upon
causal topology. Since computational description characterizes a
causal topology, satisfying a suitable computational description
suffices for instantiating appropriate mental properties. It also
follows that psychological description is a species of computational
description, so that computational description should play a central
role within psychological explanation. Thus, structuralist computation
provides a solid foundation for cognitive science. Mentality is
grounded in causal patterns, which are precisely what computational
models articulate.

Structuralism comes packaged with an attractive account of the
implementation relation between abstract computational models
and physical systems. Under what conditions does a physical system
implement a computational model? Structuralists say that a physical
system implements a model just in case the model’s causal
structure is “isomorphic” to the model’s formal
structure. A computational model describes a physical system by
articulating a formal structure that mirrors some relevant causal
topology. Chalmers elaborates this intuitive idea, providing detailed
necessary and sufficient conditions for physical realization of CSAs.
Few if any alternative conceptions of computation can provide so
substantive an account of the implementation relation.

We may instructively compare structuralist computationalism with some
other theories discussed above:

Machine functionalism. Structuralist computationalism
embraces the core idea behind machine functionalism: mental states are
functional states describable through a suitable computational
formalism. Putnam advances CTM as an empirical hypothesis, and he
defends functionalism on that basis. In contrast, Chalmers follows
David Lewis (1972) by grounding functionalism in the conceptual
analysis of mentalistic discourse. Whereas Putnam defends
functionalism by defending computationalism, Chalmers defends
computationalism by assuming functionalism.

Classical computationalism, connectionism, and computational
neuroscience. Structuralist computationalism emphasizes
organizationally invariant descriptions, which are multiply
realizable. In that respect, it diverges from computational
neuroscience. Structuralism is compatible with both classical and
connectionist computationalism, but it differs in spirit from those
views. Classicists and connectionists present their rival positions as
bold, substantive hypotheses. Chalmers advances structuralist
computationalism as a relatively minimalist position unlikely to be
disconfirmed.

Intentional realism and eliminativism. Structuralist
computationalism is compatible with both positions. CSA description
does not explicitly mention semantic properties such as reference,
truth-conditions, representational content, and so on. Structuralist
computationalists need not assign representational content any
important role within scientific psychology. On the other hand,
structuralist computationalism does not preclude an important role for
representational content.

The formal-syntactic conception of computation. Wide content
depends on causal-historical relations to the external environment,
relations that outstrip causal topology. Thus, CSA description leaves
wide content underdetermined. Narrow content presumably supervenes
upon causal topology, but CSA description does not explicitly mention
narrow contents. Overall, then, structuralist computationalism
prioritizes a level of formal, non-semantic computational description.
In that respect, it resembles FSC. On the other hand, structuralist
computationalists need not say that computation is
“insensitive” to semantic properties, so they need not
endorse all aspects of FSC.

Although 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.

6.4 Mechanistic theories

The mechanistic nature of computation is a recurring theme in logic,
philosophy, and cognitive science. Several authors develop this theme
into a mechanistic conception of computing systems (Coelho Mollo,
2017; Dewhurst 2016; Fresco 2014, 2017; Miłkowski 2013; Piccinini
2007, 2012, 2015). On Gualtiero Piccinini’s (2015) influential
development, a functional mechanism is a system of
interconnected components, where each component performs some function
within the overall system. Mechanistic explanation proceeds
by decomposing the system into parts, describing how the parts are
organized into the larger system, and isolating the function performed
by each part. A computing system is a functional mechanism of a
particular kind: it is a mechanism whose components are functionally
organized to process vehicles in accord with rules. Echoing
Putnam’s discussion of multiple realizability, Piccinini demands
that the rules be medium-independent, in that they abstract
away from the specific physical implementations of the vehicles.
Computational explanation decomposes the system into parts and
describes how each part helps the system process the relevant
vehicles. If the system processes discretely structured vehicles, then
the computation is digital. If the system processes continuous
vehicles, then the computation is analog. Marcin
Miłkowski’s (2013) version of the mechanistic approach is
similar. He differs from Piccinini by pursuing an
“information-processing” gloss, so that computational
mechanisms operate over information-bearing states. Miłkowski and
Piccinini deploy their respective mechanistic theories to defend
computationalism. Piccinini (2020) focuses especially upon
neural computation, drawing extensive connections with
cognitive neuroscience.

Mechanistic computationalists typically individuate computational
states non-semantically. They therefore encounter worries about the
explanatory role of representational content, similar to worries
encountered by FSC and structuralism. Critics protest that mechanistic
computationalism does not accommodate cognitive science explanations
that are simultaneously computational and representational (Rescorla
2016; Shagrir 2014; Shagrir 2022). The perceived force of this
criticism will depend upon one’s sympathy for content-involving
computationalism. To defuse the criticism, Miłkowski (2017)
retorts that mechanistic computationalists can assign a central
theoretical role to representational content by attributing
representational functions to certain computing
mechanisms.

6.5 Pluralism

We have surveyed various contrasting and sometimes overlapping
conceptions of computation: classical computation, connectionist
computation, neural computation, formal-syntactic computation,
content-involving computation, information-processing computation,
functional computation, structuralist computation, and mechanistic
computation. Each conception yields a different form of
computationalism. Each conception has its own strengths and
weaknesses. One might adopt a pluralistic stance that
recognizes distinct legitimate conceptions. Rather than elevate one
conception above the others, pluralists happily employ whichever
conception seems useful in a given explanatory context. Edelman (2008)
takes a pluralistic line, as does Chalmers (2012) in his most recent
discussion.

The 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.

CTM has attracted numerous objections. In many cases, the objections
apply only to specific versions of CTM (such as classical
computationalism or connectionist computationalism). Here are a few
prominent objections. See also the entry on
the Chinese room argument
for a widely discussed objection to classical computationalism
advanced by John Searle (1980).

7.1 Triviality arguments

A recurring worry is that CTM is trivial, because we can
describe almost any physical system as executing computations. Searle
(1990) claims that a wall implements any computer program,
since we can discern some pattern of molecular movements in the wall
that is isomorphic to the formal structure of the program. Putnam
(1988: 121–125) defends a less extreme but still very strong
triviality thesis along the same lines. Triviality arguments play a
large role in the philosophical literature. Anti-computationalists
deploy triviality arguments against computationalism, while
computationalists seek to avoid triviality.

Computationalists 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.

Pancomputationalism holds that every physical system
implements a computational model. This thesis is plausible, since any
physical system arguably implements a sufficiently trivial
computational model (e.g., a one-state finite state automaton). As
Chalmers (2011) notes, pancomputationalism does not seem worrisome for
computationalism. What would be worrisome is the much stronger
triviality thesis that almost every physical system implements almost
every computational model.

For further discussion of triviality arguments and computational
implementation, see Sprevak (2019) and the entry
computation in physical systems.

7.2 Gödel’s incompleteness theorem

According to some authors, Gödel’s incompleteness theorems
show that human mathematical capacities outstrip the capacities of any
Turing machine (Nagel and Newman 1958). J.R. Lucas (1961) develops
this position into a famous critique of CCTM. Roger Penrose pursues
the critique in The Emperor’s New Mind (1989) and
subsequent writings. Various philosophers and logicians have answered
the critique, arguing that existing formulations suffer from
fallacies, question-begging assumptions, and even outright
mathematical errors (Bowie 1982; Chalmers 1996b; Feferman 1996; Lewis
1969, 1979; Putnam 1975: 365–366, 1994; Shapiro 2003). There is
a wide consensus that this criticism of CCTM lacks any force. It may
turn out that certain human mental capacities outstrip
Turing-computability, but Gödel’s incompleteness theorems
provide no reason to anticipate that outcome.

7.3 Limits of computational modeling

Could a computer compose the Eroica symphony? Or discover
general relativity? Or even replicate a child’s effortless
ability to perceive the environment, tie her shoelaces, and discern
the emotions of others? Intuitive, creative, or skillful human
activity may seem to resist formalization by a computer program
(Dreyfus 1972, 1992). More generally, one might worry that crucial
aspects of human cognition elude computational modeling, especially
classical computational modeling.

Ironically, Fodor promulgates a forceful version of this critique.
Even in his earliest statements of CCTM, Fodor (1975: 197–205)
expresses considerable skepticism that CCTM can handle all important
cognitive phenomena. The pessimism becomes more pronounced in his
later writings (1983, 2000), which focus especially on abductive
reasoning as a mental phenomenon that potentially eludes
computational modeling. His core argument may be summarized as
follows:

(1)

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.

(2)

Many mental processes, paradigmatically abduction, are sensitive
to “nonlocal” properties such as relevance, simplicity,
and conservatism.

(3)

Hence, we may have to abandon Turing-style modeling of the
relevant processes.

(4)

Unfortunately, we have currently have no idea what alternative
theory might serve as a suitable replacement.

Some 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.

The scope and limits of computational modeling remain controversial.
We may expect this topic to remain an active focus of inquiry, pursued
jointly with AI.

7.4 Temporal arguments

Mental activity unfolds in time. Moreover, the mind accomplishes
sophisticated tasks (e.g., perceptual estimation) very quickly. Many
critics worry that computationalism, especially classical
computationalism, does not adequately accommodate temporal aspects of
cognition. A Turing-style model makes no explicit mention of the time
scale over which computation occurs. One could physically implement
the same abstract Turing machine with a silicon-based device, or a
slower vacuum-tube device, or an even slower pulley-and-lever device.
Critics recommend that we reject CCTM in favor of some alternative
framework that more directly incorporates temporal considerations. van
Gelder and Port (1995) use this argument to promote a
non-computational dynamical systems framework for modeling
mental activity. Eliasmith (2003, 2013: 12–13) uses it to
support his Neural Engineering Framework.

Computationalists respond that we can supplement an abstract
computational model with temporal considerations (Piccinini 2010;
Weiskopf 2004). For example, a Turing machine model presupposes
discrete “stages of computation”, without describing how
the stages relate to physical time. But we can supplement our model by
describing how long each stage lasts, thereby converting our
non-temporal Turing machine model into a theory that yields detailed
temporal predictions. Many advocates of CTM employ supplementation
along these lines to study temporal properties of cognition (Newell
1990). Similar supplementation figures prominently in computer
science, whose practitioners are quite concerned to build machines
with appropriate temporal properties. Computationalists conclude that
a suitably supplemented version of CTM can adequately capture how
cognition unfolds in time.

A second temporal objection highlights the contrast between
discrete and continuous temporal evolution (van
Gelder and Port 1995). Computation by a Turing machine unfolds in
discrete stages, while mental activity unfolds in a continuous time.
Thus, there is a fundamental mismatch between the temporal properties
of Turing-style computation and those of actual mental activity. We
need a psychological theory that describes continuous temporal
evolution.

Computationalists respond that this objection assumes what is to be
shown: that cognitive activity does not fall into explanatory
significant discrete stages (Weiskopf 2004). Assuming that physical
time is continuous, it follows that mental activity unfolds in
continuous time. It does not follow that cognitive models
must have continuous temporal structure. A personal computer operates
in continuous time, and its physical state evolves continuously. A
complete physical theory will reflect all those physical changes. But
our computational model does not reflect every physical
change to the computer. Our computational model has discrete temporal
structure. Why assume that a good cognitive-level model of the mind
must reflect every physical change to the brain? Even if there is a
continuum of evolving physical states, why assume a continuum
of evolving cognitive states? The mere fact of continuous
temporal evolution does not militate against computational models with
discrete temporal structure.

For 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).

7.5 Embodied cognition

Embodied 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.

Computationalists 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.