Gualtiero Piccinini
2/21/2005
I argue that neural activity, strictly speaking, is not computation. This is because computation, strictly speaking, is the processing of strings of symbols, and neuroscience shows that there are no neural strings of symbols. This has two consequences. On the one hand, the following widely held consequences of computationalism must either be abandoned or supported on grounds independent of computationalism: (i) that in principle we can capture what is functionally relevant to neural processes in terms of some formalism taken from computability theory (such as Turing Machines), (ii) that it is possible to design computer programs that are functionally equivalent to neural processes in the same sense in which it is possible to design computer programs that are functionally equivalent to each other, (iii) that the study of neural (or mental) computation is independent of the study of neural implementation, (iv) that the Church-Turing thesis applies to neural activity in the sense in which it applies to digital computers. On the other hand, we need to gradually reinterpret or replace computational theories in psychology in terms of theoretical constructs that can be realized by known neural processes, such as the spike trains of neuronal ensembles.
[A]ny [functional psychological] theory that is incompatible with known facts of neurology must be, ipso facto, unacceptable. To put it slightly differently, it is sufficient to disconfirm a functional account of the behaviour of an organism to show that its nervous system is incapable of assuming states manifesting the functional characteristics that account requires (Fodor 1965, p. 176).
The brain has been compared to a digital computer because the neuron, like a switch or valve, either does or does not complete a circuit. But at that point the similarity ends. The switch in the digital computer is constant in its effect, and its effect is large in proportion to the total output of the machine. The effect produced by the neuron varies with its recovery from [the] refractory phase and with its metabolic state. The number of neurons involved in any action runs into millions so that the influence of any one is negligible. … Any cell in the system can be dispensed with. … The brain is an analogical machine, not digital. Analysis of its integrative activities will probably have to be in statistical terms.
Kark Lashley
[Quoted in Beach F. A., Hebb D. O.,
Morgan, C. T., and Nissen H. V., eds. The Neuropsychology of
In 1943, Warren McCulloch and Walter
Pitts argued that neural activity is essentially computation. I will refer to this thesis as
computationalism. According to their
computational theory of mind (CTM), mental capacities are explained in terms of
neural computations. Over the last six
decades, McCulloch and Pitts’s CTM has been the mainstream theory of thinking
and cognition. CTM—in both classicist
and connectionist incarnations—has had an enormous influence in disciplines
ranging from philosophy to psychology to neuroscience. As a consequence, today many philosophers and
scientists consider it commonsensical to say that neural activity is
computation. But computationalism and
CTM remain controversial, and there is no consensus on how the controversy may
be resolved.[2]
In this paper, I propose and implement the following
strategy for resolving the controversy.
First, we should distinguish computationalism properly so called from
theses that are weaker than or logically independent of computationalism but
are often conflated with it in the literature.
Second, we should adopt an adequate account of what it takes for a
natural process, such as neural activity, to be computation. Finally, we should look at what is known
about neural activity and see if it has what it takes to be computation. The upshot is that although there are some
superficial analogies between neural activity and computation, neural
activity—strictly speaking—is not computation.
1. Computationalism Properly So
Called
The thesis that neural activity is
computation is ambiguous between importantly different interpretations. Under some interpretations, the thesis is
relatively weak and deserves no controversy.
Under at least one interpretation, the thesis is strong and deservedly
controversial. The first step in
resolving the dispute over computationalism is to distinguish computationalism
properly so called from weaker or logically independent theses.
Thesis
one: the nervous system is an
input-output system. A first thesis
holds that neural activity generates responses by processing stimuli. Inputs come into the nervous system, they get
processed, and then outputs come out.
This thesis says nothing about the nature of the inputs, outputs, and
internal processes. In this sense, the
nervous system is analogous to any system that generates outputs in response to
inputs. If the notion of input and
output is liberal enough, any physical system can be seen as belonging to this
class. If so, then this first version of
computationalism is completely trivial.
It is equivalent to stating that the brain is a physical system. But even if the notion of input and output is
more restricted, this thesis remains very weak.
It is equivalent to stating that the brain processes inputs and outputs
of the relevant kind.
Thesis
two: the nervous system is a functional
(input-output) system. Thesis two
strengthens thesis one by adding a further condition: neural activity has the function of
generating certain responses from certain stimuli. In other words, the nervous system is
functionally organized to exhibit certain capacities and not others. Under this stronger thesis, the nervous
system belongs to the specific class of physical systems that are functionally
organized. Systems of this type include
computers as well as systems that intuitively do not perform computations, such
as engines, refrigerators, and stomachs.
This thesis is less trivial than the original one, but it remains very
weak. There is no reason to doubt it.
Thesis
three: the nervous system is a feedback
control (functional, input-output) system.
Thesis three is stronger than thesis two because it specifies the
function that is peculiar to neural activity:
the nervous system controls the behavior of an organism in response to
stimuli coming from the organism’s body and environment. The specific function of neural activity
differentiates the nervous system from other functionally organized
systems. Under thesis three, the nervous
system belongs in the class of feedback control systems, together with, for
instance, missile control mechanisms.
This thesis is far from trivial, but enough evidence supports it to make
it uncontroversial. It is intuitively
plausible and it is supported by much work in neuroscience. Its precise formulation, in terms of the
modern notion of feedback, goes back at least to Walter Cannon’s classic work
on homeostasis (Cannon 1932).[3]
Thesis
four: the nervous system is a
representational (functional, input-output) system. A fourth thesis—often called representationalism—maintains
that at least some neural states are representations, so that the relevant
neural processes are transformations of representations. The notion of representation is notoriously
vague. Depending on which notion of
representation is employed, thesis four can be made stronger or weaker. If “representation” means entity with a
compositional semantics and a syntactic structure comparable to that of a
natural language sentence, then thesis four is strong and controversial. But there are many weaker notions of representation. “Representation” can be used simply to refer
to an internal variable whose value correlates reliably with the value of some
external variable (the represented variable).
Representations in this sense are variables internal to a system that carry
information about variables external to the system. This relatively weak notion of representation
is the most commonly used in neuroscience, where the use of the notion of
information in characterizing neural activity goes back at least to the work of
Edgar Adrian (1928, cf. Garson 2003). When
formulated using this notion of representation, thesis four may be seen as a
way of specifying the means by which the nervous system performs its feedback
control. In this sense, thesis four is
almost a consequence of thesis three:
beyond a certain level of complexity, the only efficient way to perform
feedback control is to possess internal variables that correlate reliably with
relevant external variables. There is
also plenty of independent evidence for thesis four. Much contemporary neurophysiology centers on
the discovery and manipulation of neural variables that correlate reliably with
variables that are external to the nervous system. At least in this suitably weak form, thesis
four should be uncontroversial.[4]
Thesis
five: the nervous system is a computing
(functional, input-output) system. Our
fifth and final thesis is McCulloch and Pitts’s thesis that neural activity is
computation, in the sense of “computation” employed in the mathematical theory of
computation as well as computer science.
I will say more about what this means later. For now, what is important is that thesis
five draws a specific analogy between neural processes and the processes
described by computability theory and computer science. This is a strong and contentious thesis,
which does not follow from theses one through four.
Thesis five entails theses one and two, because
computing mechanisms are functionally organized systems (and functionally
organized systems are input-output systems).
But theses one and two do not entail thesis five: there are plenty of systems—including
functionally organized systems—that do not perform computations in the sense of
computability and computer science. (Computer
science is the study of computers and other computing mechanisms; it says
little if anything of interest about engines, refrigerators, or stomachs.) Furthermore, thesis five is logically
independent of theses three and four. In
one direction, there are feedback control mechanisms as well as
representational systems that do not perform computations in the relevant
sense. Examples of such feedback control
systems include Watt governors; examples of such representational systems
include videotapes. In the other
direction, there are computing mechanisms that either perform no feedback
control function, or possess no representations, or both.
By
asserting that neural activity is computation, many authors appear to be saying
little or nothing more than some subset of what is expressed by theses one
through four. (Different authors may
include different subsets). Much of
their belief in computationalism is due to the plausibility of these
theses. But much of what opponents of
computationalism oppose is what they find implausible in thesis five. The problem is that in the literature on
computationalism, these five theses are often not kept separate. When philosophers or scientists state that
neural activity is computation, they often appear to hold views that conflate
various combinations of these theses.
This is true even outside neuroscience and psychology. For instance, consider the use of the terms
“computer” and “information processor.”
Since the early cybernetics literature from the 1940s, these terms have
been generally used as interchangeable.
But although computers can be information processors, they need not be,
and although information processors can be computers, they need not be. Information, in the technical sense, is a
measure of the reliable correlation between two (concrete) variables. The more information about something, the
more we can predict about it. The
processing of information is, presumably, the processing of variables that
carry information. But these variables
need not be processed by performing computations, and the variables processed
by computing mechanisms need not carry any information in the technical
sense. They can be about abstract
objects (such as numbers), non-existent objects (such as unicorns), or they can
be uninterpreted symbols, lacking any semantic content.[5]
The debate over computationalism has been less focused
and productive than it could be.
Opponents attack computationalism because of what they find implausible
in thesis five, while supporters resist the objections because of what they
find plausible in theses one through four.[6] The resulting stalemate is only
apparent: participants are not fully
addressing the substantive issue, and often they talk past each other. In what follows, I will leave aside theses
one through four. They are true and
important but irrelevant to computationalism properly so called.
If we focus on thesis five alone, we can begin to make
progress on the question of whether neural activity is computation in an
interesting sense. What would it take
for neural processes to be computations?
To be such that the
mathematics of computability theory can be used to capture what is functionally
relevant. Can the essence of neural
processes be captured in this way? The
rest of this paper is an exploration of what constraints would need to apply to
neural processes for them to fit computational descriptions. Although this exercise is valuable in its own
right, I will argue that it yields a univocal verdict: neural activity is not computation. Computationalism and CTM are false, and
neuroscience can prove it.
My goal is not to criticize those who say, loosely speaking, that neural mechanisms perform computations. Rather, my goal is to get clear on what may or may not be inferred from it. Saying that neural mechanisms perform computations is a harmless statement, provided that we avoid inferring from it certain conclusions that supporters of CTM (beginning with McCulloch) have often inferred. These conclusions include: (i) that in principle we possess an explanation of (all or most) mental phenomena in terms of neural computations, (ii) that it is possible to program computers so that they have minds, (iii) that we can capture what is functionally relevant to neural activity in terms of the mathematics of computability theory (e.g., Turing Machines), (iv) that there can be computer programs functionally equivalent to neural processes in the sense in which computer programs can be computationally equivalent to each other, (v) that the study of neural (or mental) computation is independent of the study of neural implementation, (vi) that the Church-Turing thesis applies to neural activity in the sense in which it applies to digital computers. Although these conclusions do follow from a strict construal of CTM (which is false according to the present argument), they do not follow from the claim that neural mechanisms perform computations in a loose sense. This is not to say that the listed conclusions are all false, either, although I believe most of them are. My point is that if any of them is true, this cannot be established by appealing to a generic notion of neural computation, a notion looser than the notion of computation that is employed in computability theory and computer science.
If we
abandon CTM, what happens to McCulloch’s project of explaining mental phenomena
in terms of neural mechanisms? There are
very effective mathematical concepts and techniques for studying neural spikes,
sets of spikes, and networks of neurons (Dayan and Abbott 2001). These concepts and techniques are the main
ground for my argument against computationalism, because they have little to do
with those of computability theory and computer design, and they are relevantly
different, in important respects, from the kinds of “neural” networks (such as
McCulloch and Pitts’s nets) that can be said to compute in the relevant
sense. The concepts and techniques
currently employed in theoretical neuroscience deserve to be developed and
applied. They hold great promise for
explaining the activity of neural mechanisms and ultimately, for explaining
many mental phenomena.
2. Computation Properly So
Called
The notion of computation that is relevant to CTM is the mathematical one developed by Alan Turing (1936-7) and other logicians beginning in the 1930s. This notion is the relevant one for several reasons: it’s the one that was initially employed in formulating CTM by McCulloch and Pitts (1943), it’s the one that was employed by subsequent influential formulations of CTM (Wiener 1948, von Neumann 1956, Fodor 1975, Newell and Simon 1976, etc.), and it’s the one that is employed by those who study the computational properties of certain artificial “neural” networks (Minsky and Papert 1969, Siegelmann 1999, etc.). I will proceed under the assumption that the notion of computation relevant to CTM is the classical mathematical notion of computation used in computability theory and computer science.
There has been some dispute concerning the individuation of computational states. The received view is that they ought to be individuated (primarily) by their semantic properties. This is perhaps the main source of the conflation, discussed above, between computationalism and representationalism. Indeed, CTM was initially formulated in semantic terms, namely as a theory of semantically interpreted states and processes, and this was part of the motivation for the view that CTM would explain intentionality (Piccinini 2004a, 2004b). Nevertheless, the view that computational states are semantically individuated faces an insuperable obstacle: it neglects that the assignment of semantic properties to strings of symbols presupposes the independent individuation of the strings of symbols. As I have argued elsewhere, in computability theory and computer science, strings of symbols and the computations defined over them are individuated by their functional properties, not by their semantic properties (Piccinini 2003). From now on, I will proceed under the assumption that this is the appropriate way of individuating computations.
Formally (or mathematically), strings of symbols are
concatenations of letters from a finite alphabet. The concrete realizations of abstract symbols
are entities or states that are discrete in the sense that each symbol belongs
to one of a finite number of types. The
symbol types are individuated by the fact that the mechanism that manipulates
the symbol tokens can distinguish unambiguously between tokens of different
types, in the sense that the mechanism can perform different operations on
symbols of different types. More
precisely, ceteris paribus, substituting a symbol of type T2
for a symbol of type T1 in a string may result in a different
computation, which may generate a different output string, if and only if T2
¹ T1.
A concrete realization of a string is a sequence of permutable symbols identified by the symbols’ types, their number, and their order within the string. Every finite string has a first and a last symbol member and each symbol member (except for the last member) has a unique successor. The ordering is determined by the way the mechanism processes the string. A symbol within a string can be substituted by another symbol without affecting the other symbols’ type, number, or position within the string. In particular, when an input string is processed by a mechanism, ceteris paribus, the symbols’ types, their number, and their order within the string make a difference to what output string is generated.
For present purposes, two points about strings of symbols are especially important: (i) whether a token symbol belongs to a type is unambiguous relative to the behavior of the system; (ii) the output of a computation depends (either deterministically or probabilistically) only on the internal state of the system and on the number of input symbols, their types, and the way they are concatenated within the string during a given time interval.
This analysis of computation establishes the first premise of the argument: in the sense relevant to CTM, computation is the manipulation of strings of symbols in accordance with a general rule that applies to all symbols and depends on the inputs (and perhaps internal states) for its application. Systems that qualify as performing computations in this sense include standard computability theory formalisms such as Turing Machines and finite state automata, ordinary computers and calculators, and any connectionist system that is characterized in terms of the processing of strings of discrete inputs and outputs. The latter category includes McCulloch-Pitts nets (McCulloch and Pitts 1943), perceptrons (Minsky and Papert 1969), Hopfield nets (Hopfield 1982), standard PDP networks (Rumelhart and McClelland 1986), and many other connectionist systems.
In later sections, I’ll argue that the evidence we have from neuroscience suggests that networks of real neurons do not perform computations in this sense. The full argument will be as follows:
(1) Computation is the manipulation of strings of symbols (in accordance with a general rule that applies to all symbols and depends on the inputs and internal states for its application);
(2) Neural spikes are not symbols, and even if they were symbols, spike sets would not be strings;
(3) Therefore, the manipulation of spike sets is not computation;
(4) There is no reason to believe that other aspects of in neural activity are computations;
(5) Therefore, there is no reason to believe that neural activity is computation.
Although I will discuss mainly properties of neurons and individual spike trains, rather than neuronal populations, the argument does not depend on what the fundamental neural processing unit is, or even whether there is a fundamental processing unit. My argument rules out not only any form of classical CTM, but also any form of connectionism according to which neural activity is computation, regardless of the level (neural populations, neurons, dendrites) at which neural activity is alleged to be computation.
I must stress that the present argument is not formulated in terms of the notion of representation. It rests on the notion of symbols as discrete entities that can be concatenated to form strings—entities over which computations, in the sense of computability theory and computer science, can be defined. The symbols discussed in this paper may be vehicles for many types of representations, including so called “sub-symbolic” ones. My argument does not depend on which notion of representation is adopted. Specifically, it is indifferent to the distinctions between localized vs. distributed representation, and “symbolic” vs. “sub-symbolic” representation (cf. Rumelhart and McClelland 1986, Smolensky 1989). In fact, my argument is consistent both with representationalism and with intentional eliminativism—the view that mental states are not representations (Stich 1983). The truth value of representationalism is simply not affected by my argument.
Before proceeding, we need to see why computationalism (properly so called) is not already refuted by existing objections.
3. Old Reasons Against CTM
Ever since its formulation, CTM has been controversial, but it has also proven very resilient to objections. In this section, I will briefly review the main objections that have been raised against computationalism and CTM. There are two classes of objections: those that object to CTM based on alleged differences between computations and mental processes, and those that object directly to computationalism based on alleged differences between computations and neural processes.
3.1 Computations vs. Mental
Processes
There is a long tradition of attempts to show that computation is insufficient for some special capacity P that minds allegedly have. These are by far the most popular and widely discussed objections to CTM. Candidates for P include but are not limited to mathematical insight (Lucas 1961, Penrose 1994), consciousness (Nagel 1974), and intentionality (Searle 1980). There is no room here to review the complex issues associated with all candidate P’s. For present purposes, a few simple considerations will suffice. First, whether or not computation is sufficient for any of the proposed P’s remains controversial. Second, and more importantly, even if computation is insufficient for some mental capacity P, CTM can be retained in a weakened form. In its strongest formulation, CTM says that all mental capacities are explained by neural computations. But CTM may be weakened to the claim that computation is a proper part of the explanation for all mental capacities. Thus weakened, CTM survives the current class of objections. CTM may be weakened even further and still serve its ordinary function within the sciences of mind and brain. In the sciences or mind and brain, CTM is especially popular and effective in explaining capacities that pertain to the control of motor outputs on the basis of the processing of sensory input and internal states. Even if there is some mental capacity P in whose explanation computation plays no part at all, this is compatible with the possibility that some, or even most, mental capacities are explained, in whole or in part, by neural computations.
3.2 Computations vs. Neural
Processes
There are many objections to computationalism based on alleged differences between neural processes and computations. The following is a representative sample.
3.2.1 Non-electrical Processes
Neural processes are not (only) electrical, like those of electronic computers, but also chemical; hence, neural processes are not computations (e.g., Perkel 1990). More specifically, there are at least two classes of neural events that have no analogue in electronic computers: the release and uptake of neurotransmitters at synaptic junctions, and the release and effects of hormones. This objection is easy to dismiss. Computations are realizable by an indefinite number of physical substrates, so computing mechanisms can be built out of an indefinite number of technologies. Today’s computing technology is electronic, but computers used to be built out of mechanical or electromechanical components, and there is active research on the possibilities of optical, DNA, and quantum computing. There is no principled reason why computations cannot be realized by chemical processes.
Even if the chemical processes in question were essentially noncomputational, pointing out that they occur in the brain would not be enough to show that neural processes are not computations. Here, different considerations apply to neurotransmitters and hormones.
With respect to hormones, hormones are released and absorbed at the periphery of the nervous system. So, the release and uptake of hormones might be simply treated as part of the input-output interface of the neural computing mechanisms, in the way sensory and motor processes are.
With respect to neurotransmitters, we need to remember that computational explanations apply at some levels of description but not others. For example, at one level of description, the activities of ordinary electronic computers are explained by appealing to the programs they execute; at another level, they are explained by electrical circuit theory; at yet another level, by quantum mechanics. So, those who appeal to chemical processes need to show not only that those chemical processes are noncomputational (which they have not shown) but also that they are relevant to the level of description at which neural systems are purported to perform computations.
3.2.2 Temporal Constraints
Neural processes are temporally constrained, whereas computations are not; hence, neural processes are not computations (e.g., Globus 1992, van Gelder 1998). This objection trades on an ambiguity between mathematical representation of time and real time. Computations are temporally unconstrained in the sense that they can be defined and individuated in terms of computational steps, independently of how much time it takes to complete a step. But this is not due to the fact that the process being defined is computational. The same is true of any mathematically described process, whether computational or not. Differential equations contain time variables, but these do not correspond to real time any more than the time steps of a Turing Machine correspond to any particular real time interval. In order for the time variables of differential equations to correspond to real time, a temporal scale must be specified (e.g., whether time is being measured in seconds, nanoseconds, years, or whathaveyou). By the same token, the time steps of a digital computing mechanism can be made to correspond to real time by specifying an appropriate time scale. When this is done, computations are no less temporally constrained than any other dynamical process. In fact, supporters of CTM have always been concerned with temporal constraints on the computations that explain mental capacities under their theory (e.g., Pylyshyn 1984, Newell 1990).
3.2.3 Embeddedness
Neural processes are embedded within a body and an environment whereas computations are not; therefore, neural processes are not computations (e.g., van Gelder 1998). The reply is that neither premise of this objection is generally true. On the one hand, neural systems can perform many of their activities without being embedded, as the success of in vitro neurophysiology attests. On the other hand, there is no reason why computations cannot be embedded within a body and an environment. Many useful computations are performed by mechanisms that are embedded within robots or directly within environments (e.g., your car’s computer).
The problem with the above three objections is that the properties being canvassed are irrelevant to whether a process is computational. It is easy to show why they miss their target. The following are objections that are more promising, because they are based on properties that are relevant to whether neural processes are computations.
3.2.4 Analog vs. Digital
Neural processes are analog whereas computations are digital; hence, neural processes are not computations (e.g., Dreyfus 1972, Perkel 1990). This is probably the oldest and most often repeated objection to computationalism. Unfortunately, it is formulated using an ambiguous terminology that brings with it notorious conceptual traps.
A common but superficial reply to this objection is that computations may be analog as well as digital. If neural processes are analog, they might be analog computations, and if so, then computationalism remains in place in an analog version. In fact, the original proponents of the analog-vs.-digital objection did not offer it as a refutation of all forms of computationalism, but only of McCulloch and Pitts’s specific (digital) version of computationalism (Gerard 1951). This reply is superficial, however, because it employs the same ambiguous terminology. Depending on what is meant by “analog” and “computation,” an analog process may or may not be an analog computation.
In a loose sense, “analog” refers to the processes of any system that at some level of description can be characterized as the temporal evolution of real (i.e., continuous, or analog) variables. Some authors who argue that the neural processes are not computations because they are analog seem to employ some variant of this broad notion (e.g., Churchland and Sejnowski 1992, van Gelder 1998). It is easy to see that neural processes fall in this class, but this does not help to either refute or establish computationalism. On one hand, most processes that are analog in this sense, such as the weather, planetary motion, and digestion, are paradigmatic examples of processes that are not computations in any interesting sense. So, neural processes could fall into this class without being computations. On the other hand, it is also easy to see that most or perhaps all systems, including computing mechanisms such as computers and connectionist computing mechanisms, fall within this class. Continuous variables have more expressive power than discrete ones, so they can be used to express the same information and more. But more importantly, most of our physics and engineering of midsize objects, including digital computers, is carried out in terms of differential equations, which employ continuous variables.[7] So, the trivial fact that neural mechanisms are analog in this loose sense does nothing to either refute computationalism or establish an analog version of it.
In a more restricted sense, “analog” refers to analog computers. Analog computers are a class of machines that used to be employed for solving certain classes of equations (Pour-El 1974). Analog computers are either explicitly or implicitly invoked by many of those who formulate the analog-vs.-digital objection. Claiming that neural mechanisms are analog in the sense that they are analog computers is a strong empirical hypothesis. Notice that since this hypothesis claims that neural mechanisms are analog computing mechanisms, it is still a form of computationalism. Nevertheless, this form of computationalism is incompatible with the mainstream form of computationalism, which is the one under discussion in this paper. But in spite of some valiant attempts to argue for this analog version of computationalism (Rubel 1985), neural mechanisms and analog computers (in the present strict sense) have little in common. The principal difference is that the vehicles of analog computation are “real variables,” namely variables that vary continuously over time, whereas the main vehicles of neural processes appear to be neuronal spikes, which are all-or-none events. (To say more about the differences between neural processes and analog computations would be an interesting exercise but it would take up a lot of space, so I will leave it for another occasion.)
3.2.5 Spontaneous Activity
Neural processes are not the effect of inputs alone because they also include a large amount of spontaneous activity; hence, neural processes are not computations (e.g., Perkel 1990). The obvious problem with this objection is that computations need not be the effect of inputs alone either. Computations may be the effect of inputs together with internal states.
To date, these last two objections have been formulated too vaguely to be effective. But the method they follow is sound: they compare relevant functional properties of neural and computing mechanisms. In order to improve on past debates over CTM, we need to identify some general features of computations and compare them with relevant functional properties of neural mechanisms. To get started, let us look at the properties that neural and computing mechanisms have in common.
4. How Spikes Could Be
Symbols
The mathematical modeling of neural
processes can be traced back to the mathematical biophysics pioneered by
Nicolas Rashevsky and his associates (Rashevsky 1938, Householder and Landahl
1945). They hypothesized neural
processes that might explain neural and psychological phenomena and employed integral
and differential equations to describe and analyze those processes. In their explanations, they employed neither
the notion of computation nor the mathematical tools of computability theory
and computer science. Those tools were
introduced into theoretical neuroscience by the youngest member of Rashevsky’s
group, Walter Pitts, in collaboration with neurophysiologist and psychiatrist
Warren McCulloch.
Like Rashevsky’s mathematical biophysicists, McCulloch
and Pitts (1943) attempted to explain mental phenomena in terms of putative
neural processes. But unlike Rashevsky’s
mathematical biophysicists, McCulloch and Pitts’s theory employs concepts and
techniques from logic and computability theory to model what is functionally
relevant to the activity of neurons and neural nets, in such a way that (in
modern terminology) a neural spike can be treated mathematically as a symbol,
and a set of spikes can be treated as a string of symbols.
McCulloch and Pitts’s empirical justification for
their theory was the similarity between symbols and spikes—spikes appear
to be discrete or digital, i.e., to a first approximation, their occurrence is
an unambiguous event relative to the functioning of the system. This was the main motivation behind
McCulloch’s identification between spikes and atomic mental events, which was
the main motivation behind his formulation of CTM (Piccinini 2004a). I will leave aside the question of the
plausibility of McCulloch’s assumption that spikes correspond to atomic mental
events; I will limit my discussion to the question of whether spikes are
symbols and whether sets of spikes are strings of symbols. The latter two assumptions can be discussed
independently of the first.
Since the
presence and absence of spikes are discrete events, prima facie it should be
possible to identify a relation of concatenation between them, so that strings
of neural events can be identified. In
the case of spike trains from a single neuron, the temporal ordering of spikes
and their absence may be taken to be a natural candidate for a concatenation
relation between them. In the case of
sets of synchronous spikes from different neurons, a concatenation relation
might be defined by first identifying a relevant set of neurons, and then
taking all synchronous spikes from that set as belonging to the same
string. The set of neurons might be
defined purely anatomically or by a combination of anatomical and functional
criteria. The ordering of the spikes
within a string thus defined might be identified by functional criteria or
perhaps, for some purposes, it might be taken to be arbitrary.
The suggestive analogy between spikes and symbols—based on the all-or-none character of spikes—is far from sufficient to treat a spike as a symbol, and even less sufficient to treat a set of spikes as a string of symbols. In order to build their theory, according to which neural activity is computation (in the strict sense discussed here), McCulloch and Pitts made numerous other assumptions. I will briefly discuss the two most crucial ones.
McCulloch
and Pitts assumed that a fixed number of neural stimuli are always necessary
and sufficient to generate a neuron’s pulse.
They knew this was a false assumption:
they explicitly mentioned that the “excitability” of a neuron does vary
over time, due to, among other things, refractory periods and “learning”
(McCulloch and Pitts 1943, p. 20-21). In
fact, neurons exhibit both absolute and relative refractory periods as well as
varying degrees of plasticity ranging from short to long term potentiation and
depression. To this, it should be added
that spiking is not deterministic but probabilistic.
Another crucial assumption was that all neurons within a network are synchronized so that all relevant events in the network—conduction of the impulses along nerve fibers, refractory periods, and synaptic delays—occur within temporal intervals of fixed and uniform length, which are equal to the time of synaptic delay. In addition, according to McCulloch and Pitts, all events within one temporal interval only affect the relevant events within the following temporal interval. This assumption makes the dynamics of the net discrete: it allows the use of logical functions of discrete inputs or states to fully describe the transition between neural events.
Together, these two assumptions allowed McCulloch and Pitts to employ the mathematics of the logicians and computability theorists to describe neural events and their transitions. But as McCulloch and Pitts pointed out, these assumptions are not based on empirical evidence. The reason for these assumptions was, presumably, that they allowed the mathematics of computation to describe what they presumed to be functionally relevant to neural activity.
The similarity between symbols and spikes can hardly be doubted. But to the best of my knowledge, after McCulloch and Pitts’s brief discussion, no one has discussed in detail the differences between spikes and symbols, and between spike sets—either spike trains from the same neuron or sets of more or less synchronous spikes from different neurons—and strings of symbols. In 1943, relatively little was empirically known about the functional properties of neural spikes and spike trains. Since then, neurophysiology has made great progress, and it is past time to bring what is currently known about neural processes to bear on the question of whether they are computations.
Although McCulloch and Pitts’s theory became
fundamental to computer science and computability theory (Piccinini 2004a), as
a theory of neural activity it was soon abandoned in favor of more
sophisticated and neurally plausible mathematical models. From a mathematical point of view, the models
employed by theoretical neuroscientists after McCulloch and Pitts are closer to
those of Rashevsky’s original mathematical biophysics, in that they do not
employ concepts and techniques from computability theory. I take it as a fact that in the models
currently employed by theoretical neuroscientists, spikes are not treated as
symbols, and spike sets are not treated as strings of symbols. The rest of this paper is devoted to
identifying principled reasons, based on empirical evidence, for why this is
so.
The point of the exercise is not to beat a long dead horse—McCulloch and Pitts’s theory. The point is that if we reject McCulloch and Pitts’s assumptions, which were the original motivation for calling neural activity computation, it remains to be seen whether there is any way to replace McCulloch and Pitts’s assumptions with assumptions that are both empirically plausible and allow us to retain the view that neural activity is computation in the relevant sense. If no such assumptions are forthcoming, computationalism properly so called needs to be abandoned. The level of neural activity on which we should primarily focus is the level that motivated McCulloch and Pitts’s theory—the level of neurons and neuronal spike sets.
5. Why Spikes Are Not Symbols
and Spike Sets Are Not Strings
For a class of event tokens to constitute symbols within a computing mechanism, it must be possible to type them in an appropriate way. The difficulties in doing so for spikes are discussed in the next subsection. For a set of symbols to constitute a string, it must be possible to determine, at the very least, which symbols belong to which strings. The difficulties in doing so for sets of spikes are discussed in the subsequent subsection.
5.1 Typing Spikes as Symbols
Strings are composed of atomic symbols. Atomic symbols belong to finitely many types, which must be unambiguously distinguishable by the system that manipulates them. (Otherwise, it would be indeterminate whether the system performs the relevant computational operations, which are defined as manipulations of symbols.) So for spikes and their absence to be atomic symbols, it must be possible to type them into finitely many types that are unambiguously distinguishable by neural mechanisms.
To be sure, the presence or absence of spikes has unambiguous physiological significance. Spikes are all-or-none events; either they occur or not. And they certainly affect neural systems in a way that their absence does not. So there might be two types of atomic symbols: the presence and the absence of a spike at a time. This was McCulloch and Pitts’s proposal. For this proposal to be adequate, more needs to be said about the time during which the presence or absence of spikes is to be counted.
Notice that the relevant time cannot be instantaneous. Otherwise, there would be uncountably many symbols in any finite amount of time, which is incompatible with the notion of symbol, and besides that, spikes do take some time (about 1 msec) to occur. So the relevant time must be a finite time interval. This is consistent with the structure of the mathematics of computation: every computational formalism, including connectionist computing formalisms assumes, either explicitly or implicitly, that there are finite time intervals during which it can be determined what counts as a system’s inputs and outputs. (This is true whether or not those inputs and outputs are interpreted as corresponding to individual spikes or absences of spikes.)
McCulloch and Pitts’s proposal was to divide time into intervals whose length was equal to synaptic delay. Their proposal has no motivation independent of the need to find a suitable time interval for counting atomic symbols, and it suffers from a number of shortcomings. I will list the most obvious ones. First, McCulloch and Pitts’s proposal assumes that synaptic delay is constant from spike to spike and from neuron to neuron.[8] Second, it assumes that any time interval that separates two spikes within any neuron will be equal to an exact multiple of the master time interval.[9] Third, in order to count the presence or absence of spikes from different neurons as belonging to the same computation, it assumes that neurons are perfectly synchronized, in the sense that the time intervals that are relevant to identifying the presence and absence of spikes in different neurons begin and end in unison. The third assumption is also relevant to the concatenation of symbols into strings, so I will discuss it in subsequent subsections. In what follows, I will focus on the first two assumptions.
The lack of evidence for the first two assumptions could be remedied by choosing a fixed time interval of unambiguous physiological significance. Unfortunately, there is no reason to believe that any fixed time interval is appropriate, for there is no evidence that there are precise, finite time intervals that are relevant to counting spikes in the relevant sense. There seems to be no discrete time interval of fixed duration during which the presence of absence of a spike has unambiguous physiological significance. One reason for this is that spiking is affected in varying degrees by events (such as input spikes) that occur at different times in the past history of the neuron, and there is no known principled way of typing both relevant causes and the time intervals during which they occur into finitely many types. Another reason has to do with the way in which spikes are believed to be probabilistic events.
Spikes are not deterministic but probabilistic events. By itself, this need not undermine the analogy between spikes and symbols. For as is well-known, computations may be probabilistic as well as deterministic (e.g., Davis et al. 1994, section 9.2). In a probabilistic computation, given an input or internal state, there are a finite number of possible outcomes, each of which has a certain probability of occurring. In other words, the sample space of a probabilistic computation is finite. This seems superficially analogous to the spiking of a neuron, which occurs with a certain probability at a time (given a certain input).
But there is a crucial disanalogy. The relation of these probabilistic events to time is relevantly different, because whereas events within (probabilistic) computing mechanisms are temporally discrete, spike times are continuous variables. In the case of a probabilistic computation, events occur within fixed functionally significant time intervals; this makes it possible to specify the probabilities of the finitely many outcomes effectively, outcome by outcome, so that each can be treated as a symbol. By contrast, there appear to be no functionally significant time intervals during which spikes are to be counted, and as a result, spikes must be counted over real time. Because of this, the probability that a spike occurs at any instant of real time is zero. In other words, the sample space for spiking events during a time interval is uncountably infinite. Spike probabilities need to be given by probability densities, which specify the probability that a spike occurs within a time interval as the time interval goes to zero (Dayan and Abbott 2001, p. 24).
In summary, probabilistic computation and neural processes are both nondeterministic, but in two different ways. In the first case, there is a finite probability that any of a finite number of possible events occurs during a time interval of fixed (finite) duration. In the other case, there is a finite probability that any of a finite number of possible events occurs during a time interval of any (finite) duration. The mathematics that is employed in the two cases is very different. Since there can only be finitely many symbol types but there are an uncountable number of possible spiking events, spiking events cannot count as symbols.
There is another, independent and perhaps deeper reason for denying that the presence or absence of a spike can constitute a primitive symbol. Until now, the discussion has been based on the implicit assumption that the physiological significance of the presence or absence of individual spikes is functionally relevant to the processing of neural signals. But this assumption is unwarranted. Although the presence or absence of spikes does affect neural systems differentially, no individual spike (or absence of a spike, if we could make sense of that notion) seems to have unambiguous functional significance for the processing of neural signals. Here, at least two considerations are in order.
First, neurons exhibit spontaneous activity, that is, activity that is not obviously related to sensory or motor activity. According to our most recent and accurate estimates, spontaneous neural activity accounts for about 75% of the brain’s energy consumption, and in that sense it constitutes most of neural activity (Raichle 2004). Spontaneous activity need not be noise, i.e. functionally irrelevant activity. There are hypotheses about the function of spontaneous activity; for instance, some have suggested that neural signals consist in relatively small deviations from a background level of activity, which is required for the signaling to be functionally significant. Be that as it may, we saw above that spontaneous activity per se is not an objection to computationalism. For computations can depend on both inputs and internal states. In principle, spontaneous activity could be analogous to (an aspect of) the internal state of a computing mechanism. But the internal states of computing mechanisms are such that their contribution to a computation can be described as symbols (discrete states) and specified independently of the contribution given by the input. By contrast, spontaneous neural activity has all the characteristics already noted, which prevent it from being represented as symbols, and more importantly, there is no known way to sharply separate its contribution to the neural output from the contribution of the neural input. What seems to matter for a properly functioning neural mechanism is not the presence or absence of any particular spike, but rather the presence of a certain average level of spontaneous activity.
Second, regardless of whether a spike is caused by spontaneous activity or by the processing of a sensory input, what appears to have functional significance is not any individual spike, but rather the firing rate of a neuron. Any individual spike may be removed from a spike train without appreciably altering the functional significance of the spike train. For that matter, many individual spikes may be added to or removed from a spike train without appreciably altering its functional significance (Dayan and Abbott 2001, chap. 1). In fact, neuroscientists assess the functional significance of neural activity by computing average firing rates, namely by averaging the firing rates exhibited by a neuron over many identical trials. The variability across trials is well known to be large (ibid.). So, although the presence of a spike is a temporally discrete phenomenon, the presence or absence of individual spikes is not a sufficient basis for understanding the processing of neural signals. What matters are not individual spikes but average firing rates. The same point applies to sets of more or less synchronous spikes from different neurons.
Thus, there are principled reasons to doubt that spikes and their absence can be treated mathematically as primitive symbols, to be concatenated into strings. But individual spikes are not the only candidates to the role of primitive symbols. Before abandoning the issue of primitive symbols, we should briefly look at two other proposals.
One possibility is that primitive symbols are to be found in precise patterns of several spikes. In recent years, there have been serious attempts to demonstrate that some repeating triplets or quadruplets of precisely timed (»1 msec) spikes from single neurons have functional significance. If this could be established, it may constitute a first step towards finding atomic symbols in neural activity. However, rigorous statistical analysis indicates that both the number and types of precisely timed spike patterns are those that should be expected by chance (Oram et al. 1999). In fact, there is evidence that signals coming from individual neurons are too noisy to constitute the minimal units of neural processing; according to some estimates, the minimal signaling units in the brain are of the order of 50-100 neurons (Shadlen and Newsome 1998).
Another possibility is that spike frequencies themselves should be taken to be primitive symbols of sorts. This was von Neumann’s proposal (von Neumann 1958). Unlike the previous proposal, this one is based on variables that are functionally significant for the processing of neural signals. But this proposal raises more problems than it solves. Again, there is the problem of finding a significant time interval. Spike frequencies vary continuously over time in response to continuous variations of the stimuli, so there seems to be no non-arbitrary way to parse them into time intervals so as to count the resulting units as primitive symbols. Also, it’s unclear how spike trains from individual neurons, understood as primitive symbols, could be concatenated with other spike trains from other neurons to form strings. Perhaps most importantly, spike frequencies cannot be symbols in the standard sense, because they cannot be typed into finitely many types of unambiguous physiological significance. As von Neumann noted, there is a limit to the precision of spike frequencies, so if we attempt to treat them as symbols, there will be a significant margin of error as to which type any putative symbol belongs to. As a consequence, computability theory as normally formulated does not apply to these entities—a different mathematical theory is needed. Von Neumann pointed out that he didn’t know how to do logic or arithmetic over such entities as spike frequencies, and hence he didn’t know how the brain could perform logic or arithmetic using such a system. As far as I know, no one after von Neumann has addressed this problem. And without a solution to this problem, von Neumann’s proposal remains an empty shell.
5.2 Fitting
Spikes into Strings
In the previous section, we saw that there is no reason to believe that spikes, or sets thereof, can be treated as the atomic symbols of a computation. But even if they could, it wouldn’t follow that neural mechanisms perform computations in any useful sense. For although some trivial computations are defined over single atomic symbols or pairs of them (i.e., those performed by ordinary logic gates), nontrivial computations are defined over strings of symbols. Strings of symbols are entities with finitely many atomic symbols concatenated together, in which there is no ambiguity as to which atomic symbols belong to a string. If sets of spikes were to count as strings of symbols, there should be a way to unambiguously determine which spikes belong to which string. But there is no reason to believe that this can be done. The two natural candidates for strings are sets of spikes from synchronous neurons and spike trains from individual neurons. I will discuss them in turn.
5.2.1 Strings and Synchronous
Spikes
In the case of sets of synchronous spikes, the concatenation relation might be given by spatial and temporal contiguity within a structure defined by some combination of anatomical and functional properties. For instance, synchronous spikes from a cortical column may be seen as belonging to the same string. Implicitly, this is how inputs and outputs of connectionist computing mechanisms are defined.
A first difficulty with this proposal is the looseness of the boundaries between neural structures. It doesn’t appear that neural structures, such as cortical columns, are defined precisely enough that one can determine, neuron-by-neuron, whether each neuron belongs to one structure or another. The boundaries are fuzzy, so that neurons can be recruited to perform different functions as they are needed, and the functional organization of neural structures is reshaped as a result (Recanzone, Merzenich, and Schreiner 1992, Elbert and Rockstroh 2004). This leaves the question of which synchronous spikes belong to a string unanswered, which makes the notion of a string of synchronous spikes undefined. This first problem may not be fatal, however. Perhaps the boundaries between neural structures are fuzzy, and yet at any time, there is a way to assign each spike to one and only one string of spikes synchronous to it.
But this proposal does face a fatal problem: synchrony between spikes is a matter of degree. If synchronous spikes are to count as belonging to the same string, there must be an unambiguous and functionally significant way to determine which spikes are synchronous and which are not. But there is no reason to believe that this is possible. The existing evidence indicates that synchrony between neurons is not an absolute matter but rather comes in indefinitely many degrees. Just as there is no meaningful way to divide the activity of a neuron into discrete functionally significant time intervals (see section 5.1), there is no meaningful way to divide the activity of neural ensembles into discrete functionally significant time intervals to determine in an absolute manner whether their spikes are synchronous. Synchrony between spikes is an interesting feature, which has attracted significant attention. But the interesting question about neural synchrony is not whether, in an absolute sense, there is synchrony in a neural process; rather, the interesting question is how much synchrony there is at a given temporal scale, how many neurons it involves, and whether it is functionally relevant.
As a result, even if neural spikes could be treated as atomic symbols (which they can’t), sets of synchronous spikes could not be treated as strings of symbols.
5.2.2 Strings and Spike Trains
In a spike train from a single neuron, the concatenation relation may be straightforwardly identified with the temporal order of the spikes. Nevertheless, in order to treat a spike train as a string, its beginning (first spike) and end (end spike) must be identified unambiguously, so that the output coming from a neuron can be divided into discrete subsets of finitely many spikes. Each subset must be such as to have functional significance on its own, independent of the other subsets, so that computational operations can be defined over it. But again, two independent problems undermine this proposal.
The first problem is that in the case of spike trains, the question of which spikes belong to a string (i.e., which spike is first and which is last in any given subset of a spike train) appears to be ill defined. Generally, spike trains are the combined effect of spontaneous activity of a neuron plus that neuron’s response to its inputs. As to spontaneous activity, there doesn’t seem to be any functionally significant way to divide it into discrete units of independent functional significance. As to neural responses to inputs, they last as long as inputs last. There doesn’t seem to be any useful way to divide the input-driven outputs from a neuron into subsets with unambiguous beginnings and ends, each of which has independent functional significance. The same point applies to the two components taken together.
The second problem is that given the amount of noisiness in neural activity, individual spike trains are not useful units of functional analysis. What has functional significance is not a specific train of spikes, each of which occurs during a particular time interval, but something held in common by many different spike trains that are generated by the same neuron in response to the same stimulus. The only known way to find useful units of functional analysis is to average spike trains from single neurons over many trials and use average spike trains as units of functional analysis.
For these reasons, even if neural spikes could be treated as atomic symbols (which they can’t), spike trains could not be meaningfully treated as strings of symbols.
6. What About the Neural Code?
A final relevant issue is the relationship between neural codes and computational codes. In both cases, the same term is used, which suggests an analogy between the two. Is there such an analogy?
The expression “neural code” usually refers to the functional relationship between properties of neural activity and variables external to the nervous system (e.g., see Dayan and Abbott 2001). Roughly speaking, the functional dependence of some property of a neural response on some property of an environmental stimulus is called neural encoding, whereas the inference from some property of a neural response to some property of the stimulus is called neural decoding. Neural encoding is a measure of how accurately a neural response reflects a stimulus, and neural decoding is a measure of how accurately a neural mechanism can respond to a stimulus on the grounds of some neural response.
By contrast, in the theory of computation, “coding” refers to one-one mappings between classes of strings of symbols (e.g., see Rogers 1967, pp. 27-29). Given each member of a (countably infinite) class of strings over some alphabet, any algorithm that produces a corresponding member of a different class of strings (possibly over a different alphabet) is called an encoding. This kind of encoding is always fully reversible: by definition, for any encoding algorithm there is a decoding algorithm, which recovers the inputs of the encoding algorithm from its outputs.
Neural coding is only loosely analogous to computational coding. Both are relationships between two classes of entities, and both give procedures for retrieving one class of entities from the other. But the disanalogies are profound. Whereas neural encoding is only approximate and approximately reversible, computational coding is exact and exactly reversible. Whereas neural encoding is asymmetric (neural responses encode stimuli but not vice versa), computational coding is symmetric (if a encodes b, then b encodes a). Most importantly, whereas neural encoding relates physical quantities in the environment to neural responses, neither one of which is likely to be accurately described as a class of symbolic strings, computational coding is a relationship between classes of symbolic strings. For these reasons, neural coding should not be confused with computational coding. The existence of a neural code has no consequences on whether neural mechanisms are computational.
7. Conclusion
Given current evidence, the most significant units of functional analysis for the purpose of understanding the processing of neural signals are neural spikes. I have argued that neither spike trains from a single neuron nor sets of synchronous spikes from several neurons are viable candidates for strings of symbols. If we take spike trains from ensembles of neurons, none of the features that make them unviable as strings is eliminated; therefore, spike trains from neuronal ensembles are not viable candidates for strings.
If we could identify strings of symbols in neural mechanisms, then we could look for operations defined over them, that is, we could specify (either deterministically or probabilistically) the output strings that ought to be expected given any input strings (plus eventual internal states). Those operations would constitute the fundamental computational operations performed by neural mechanisms, and by looking at sequences of such operations, we could discover the computations performed by neural mechanisms. But we have seen that there is little hope of identifying strings of symbols in neural spike sets. And without identifying strings, we can’t identify operations defined over strings. And without operations defined over strings, we can’t have computations (in the strict sense of the term).
I believe that similar points to those made about spikes—to the effect that they are not strings of symbols—could be made for any other relevant variable pertaining to neural activity. But I do not believe it is necessary to repeat the present exercise for all other variables, such as synaptic activity or molecular events within neurons (in spite of some suggestions that those are the relevant levels at which computations occur, e.g., by Koch 1999). For one thing, even if something that occurs below the level of spikes can be usefully understood as a computation, this does not overcome the conclusion that spikes trains and sets are not strings of symbols, and hence that the processing of neural signals—which is constituted by the processing of spikes—is not computation. I have focused on neurons because that is the level at which a serious computational theory was once proposed. Anything below the level of neurons is irrelevant, and any neural process above the level of neurons is going to run into the same problem unless it is shown that what is functionally relevant at the higher level is such as to be captured by a computational description—something that no one has done.
The discrete nature of spikes was the main empirical motivation for CTM. Once the original assumptions about spikes that supported CTM are rejected, the burden is on supporters of CTM to find evidence that some neural variables are suited to being treated as strings of symbols, and that this has something to do with explaining mental phenomena. In principle, this could be done in the future—my argument is based on our current neurophysiology, which might in the future be replaced by a neurophysiology more congenial to computationalism. In practice, however, the evidence accumulated over the last six decades has gone in the opposite direction, and there is no reason to believe that the trend is going to be reversed.
Given the present state of the art, a defense of CTM is not only implausible—it is unmotivated. For unlike in 1943, when CTM was initially proposed, today we have an advanced science of neural mechanisms and processes, based on sophisticated mathematical concepts and techniques. I’m referring to what is often called theoretical or computational neuroscience. Theoretical neuroscientists build mathematical models of neural mechanisms and processes, and use them to explain neural and mental phenomena. Philosophers and psychologists have unduly neglected the development of this discipline. Specifically, they have rarely noticed that in realistic mathematical models of neural processes, the explanatory role of computability theory and computer design is nil.
In light of this, why do so many neuroscientists profess to believe that neural activity is computation? I think one important reason is that computationalism properly so called is not kept distinct from other theses that are weaker than or logically independent of it. At least two issues are relevant here.
The first issue has to do with the relationship between computationalism and representationalism. Computationalism and representationalism have been bound together in the literature. Many authors believe that the mind (or brain) has content, and from this they conclude that the mind (or brain) computes: “It is useful … to class certain functions in the brain as computational because nervous systems represent and they respond on the basis of representations” (Churchland, Koch, and Sejnowski 1990, 48; emphasis original). If the argument of this paper is sound, the inference from representationalism to computationalism is unsound. Whether something is a computation is a separate question from whether it has content. Many spike trains are representations, at least in the sense that they reliably correlate with variables external to the nervous system. Much theoretical neuroscience is devoted to studying how these correlations originate and how neural representations are processed. It simply doesn’t follow that the processing of neural representations is computation in the relevant sense.
The second issue has to do with the relationship between computationalism and mechanistic, or functional, explanation. Computationalism and mechanism have been run together in the literature. For example, David Marr dubbed the mathematical analysis of the functions of neural mechanisms “computational theory,” by which he meant theory of neural computations (Marr 1982). From this, it follows that neural processes are computations. But thus understood, computationalism ceases to be an empirical hypothesis about the specific functional nature of neural processes, to become a trivial consequence of the definition of mechanistic explanation. Suppose, instead, that we begin our investigation with a rich notion of mechanistic explanation (see Craver 2001, unpublished). Under such a notion, computation is one kind of mechanistic process among others. Then, we may ask—with McCulloch and Pitts and many other computationalists—whether neural processes are computations in the sense of computability theory and computer science, and, as I argued, we can find a negative answer in the empirical evidence from neuroscience.
The term “neural computation” is well entrenched in the literature and is unlikely to be abandoned. People will go on saying that neural activity is computation. There is no harm in doing so, provided that we are clear about what we mean by that. Computationalism is often used to derive various consequences, which do not follow from the thesis that neural activity is computation in a looser sense.
If neural activity is computation, it is sometimes alleged that we gain (at least part of) an explanation of various mental capacities, such as intentionality and consciousness, and it should be possible to program computers so that they have minds (e.g., Kurzweil 1999). How much of this is true depends on how much of the mind is explained by neural processes. I will not venture here into the minefield of consciousness. With respect to intentionality, it is often maintained that as least some aspect of it is explained by some notion of neural representation. Plausible as this may be, it is irrelevant to computationalism. As I pointed out, representationalism is logically independent of computationalism.
There are a number of more plausible consequences of computationalism: (i) that in principle we can capture what is functionally relevant to neural processes in terms of some formalism taken from computability theory (such as Turing Machines), (ii) that it is possible to design computer programs that are functionally equivalent to neural processes in the sense in which computer programs can be computationally equivalent to each other, (iii) that the study of neural (or mental) computation is independent of the study of neural implementation, (iv) that the Church-Turing thesis applies to neural activity in the sense in which it applies to digital computers.
None of these consequences follow from the view that neural activity is computation in a loose sense. For if neural activity is not the processing of strings of symbols, as I have argued, then there is no reason to suppose that formalisms that manipulate strings of symbols can capture what is functionally relevant to neural processes. They might be used to build computational models of neural processes, but the functional explanation of neural processes will be given by the constructs of theoretical neuroscience, not computability theory. The relationship between computer programs that model neural processes and the processes they simulate is significantly different from the relationship between computer programs that simulate each other. When a computer program simulates another program, (some aspect of) the computations of the simulating program encode (in the sense of computer science) the computations of the simulated program. By contrast, when a computer program implements a mathematical model of a neural process, the computations of the simulating program are a means for generating approximate representations of the states that the mathematical model attributes to the neural process. This kind of model attempts to capture something essential to a neural process based on what is known about the process by employing suitable abstractions and idealizations. There is no sense in which such modeling work can proceed independently of the empirical study of neural processes. There is no room here for an in-depth treatment of the methodology of mathematical modeling. It is a complex issue in the philosophy of science, which deserves to be studied in detail.[10] For present purpose, what matters is that mathematical modeling is a different game, with different rules, from the simulation of one computer program by another program.
Finally, the Church-Turing thesis is a very complex issue, and there is no room here to do it justice. For present purposes, the following brief remark will suffice. To a first approximation, the Church-Turing thesis states that any function that is computable in an intuitive sense is computable by some Turing Machine. Many authors have argued that the Church-Turing thesis proves computationalism to be true. But as Jack Copeland has pointed out, this argument commits the fallacy of conflating mechanism and a form of computationalism restricted to the computations that fall under the Church-Turing thesis (Copeland 2000). When mechanism and computationalism are kept separate, two separate questions about neural computation arise. One question—the most discussed in the literature—is whether neural computations are computable by Turing Machines. If McCulloch and Pitts’s theory of the brain (or a similar theory) were correct, then the answer would be positive. Otherwise, as some have suggested, neural computations might be more powerful than those of Turing Machines—neural mechanisms might be hypercomputers (Copeland 2000, Bringjord 1998). The more fundamental question, however, is whether neural activity is computation in the first place. If, as I have argued here, neural activity is not computation (in the relevant sense), then the question of whether neural computation is computable by Turing Machines doesn’t even arise. Of course, there remains the question of whether computing humans can do more than Turing Machines. People can certainly perform computations, as anyone who has learned basic arithmetic can attest. And presumably, there are neural processes that explain human computing. But at this level, there is no evidence that humans are more powerful than Turing Machines. No human has ever been able to compute functions, such as the halting function, that are not computable by Turing Machines. In this limited sense, the Church-Turing thesis appears to be true.
If neural activity is not computation, what happens to computational theories in psychology? Frames, production rules, and mental models are only a few examples of the many computational constructs employed by psychologists to explain cognitive phenomena. For over sixty years, various forms of computationalism—either classical or connectionist—have provided the background assumption against which computational constructs in psychology have been interpreted and justified. Computational psychological theories are legitimate, the assumption goes, because the computations they postulate can be realized by neural computations. But if there are no neural computations, what should we do with computational psychological theories? Some have been tempted to eliminate them, but I think that would be premature. Computational theories in psychology are our current best way of capturing and explaining a wide range of psychological phenomena; eliminating them without remainder would be a great loss. What needs to be done, instead, is to gradually reinterpret or replace computational constructs in psychology in terms of theoretical constructs that can be realized by known neural processes, such as the spike trains of neuronal ensembles. The shift that psychology is currently undergoing, from classical cognitive psychology to cognitive neuroscience, may be seen as a step in this direction. Much groundbreaking work in theoretical psychology over the past two decades, from Stephen Kosslyn’s work on mental imagery (Kosslyn 1994) to Larry Barsalou’s work on concepts (Barsalou 1999) to Todd Braver’s work on cognitive control (***), may be seen as contributing to this project. We are on our way to explaining more and more neural and mental phenomena in terms of neural mechanisms and processes. There is no longer any reason why we should restrict our rich discipline of theoretical neuroscience and psychology to the narrow framework of CTM.
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[1] Thanks to Ken Aizawa, Carl Craver, and Sam Scott for helpful comments on a previous draft.
[2] Influential defenses of CTM include McCulloch and Pitts 1943, Wiener 1948, von Neumann 1958, Marr 1982, Churchland and Sejnowski 1992; a similar thesis, without explicit reference to the nervous system, is defended by Fodor 1975, Newell and Simon 1976, Pylyshyn 1984, and others; influential attacks on CTM include Lucas 1961, Dreyfus 1979, Searle 1980, Penrose 1994, van Gelder 1998.
[3] Of course, there are many different kinds of feedback control mechanisms, some of which are more sophisticated than others. Therefore, there is plenty of room for disagreement over which control mechanisms are present or absent within the nervous system. For a recent discussion of some options, see Grush 2003.
[4] Representationalism comes in many varieties, which deserve to be explored and discussed in detail. I will not address debates pertaining to representationalism, because as I shall point out, representationalism is logically independent of computationalism properly so called.
[5] For more evidence and details on some of these conflations, see Piccinini 2004b and 2004c.
[6] Due to the common conflation between theses four and five, some opponents of computationalism have objected to what they see as implausible in strong forms of representationalism (e.g., van Gelder 1998), or to the claim that computationalism can explain intentionality (Searle 1980). When theses four and five are properly distinguished and seen to be logically independent, these purported attacks on computationalism can be seen to be irrelevant. See below for more discussion of objections to computationalism.
[7] It has been argued that at the fundamental physical level, everything is discrete (e.g., Toffoli 1984). This remains a very speculative hypothesis for which there is no direct evidence. Moreover, it would still be true that midsize objects, including digital computers, can be characterized as the temporal evolution of continuous variables.
[8] Is there any relevant evidence one way or the other?
[9] Is there any relevant evidence one way or the other?
[10] For a start, see REFF.