what the is a symbol?

What the \0.70, 1.17, 0.99, 1.07[ is a Symbol?

Istvan S. N. Berkeley

Received: 21 November 2006 / Accepted: 6 December 2007 / Published online: 28 December 2007

� Springer Science+Business Media B.V. 2007

Abstract The notion of a ‘symbol’ plays an important role in the disciplines of

Philosophy, Psychology, Computer Science, and Cognitive Science. However, there

is comparatively little agreement on how this notion is to be understood, either

between disciplines, or even within particular disciplines. This paper does not

attempt to defend some putatively ‘correct’ version of the concept of a ‘symbol.’

Rather, some terminological conventions are suggested, some constraints are pro-

posed and a taxonomy of the kinds of issue that give rise to disagreement is

articulated. The goal here is to provide something like a ‘geography’ of the various

notions of ‘symbol’ that have appeared in the various literatures, so as to highlight

the key issues and to permit the focusing of attention upon the important dimen-

sions. In particular, the relationship between ‘tokens’ and ‘symbols’ is addressed.

The issue of designation is discussed in some detail. The distinction between simple

and complex symbols is clarified and an apparently necessary condition for a system

to be potentially symbol, or token bearing, is introduced.

Keywords Symbols � Tokens � Subsymbols � Interpretation � Complexity

Introduction: The Problem

There are a number of related notions that frequently feature prominently in

discussion within Cognitive Science, the Philosophy of Mind, and related

disciplines. These notions include the concepts of ‘Symbol,’ ‘Token,’ ‘Represen-

tation,’ ‘Subsymbol,’ and even occasionally ‘Symboloid’ (see Fodor 1975; Newell

and Simon 1976; Haugeland 1985; Smolensky 1988; Cummins 1989; Clark 1992;

I. S. N. Berkeley (&)

The Institute of Cognitive Science, The University of Louisiana at Lafayette,

P.O. Box 43770, Lafayette, LA 70504, USA

e-mail: [email protected]

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Minds & Machines (2008) 18:93–105

DOI 10.1007/s11023-007-9086-y

Berkeley 2000; Marcus 2001; Bechtel and Abrahamsen 2002; Dawson 2004; Port

and Leary 2005; Berkeley 2006) for illustrative examples). In this paper, the focus

will be primarily on the notions of ‘Symbol’ and ‘Token,’ which will be closely

related to one another. The reason for choosing this focus is that the notion of

symbolhood has played an especially important and controversial, role in cognitive

theorizing.

The importance of symbols is illustrated nicely by Newell and Simon’s (1976)

Physical Symbol Hypothesis (PSSH). This is the hypothesis that,

A physical symbol system has the necessary and sufficient means for general

intelligent action.

However, until such times as the notion of symbolhood is clearly understood, the

possibilities of putting this hypothesis to a test will be severely limited. This is

unfortunate, as the PSSH is one of the few clearly articulated, in principle

empirically testable, hypotheses to emerge from early computational research on

intelligence. Thus, difficulties with the concept of something being a symbol creates

a significant impediment to progress in computer science.

The difficulties with the notion do not end here, however. Eventually, even

Newell and Simon appear to have disagreed over the members of the class of

symbol systems. In the paper ‘‘Physical Symbol Systems,’’ Newell (1980, p. 171)

contrasts ‘‘neural nets’’ with physical symbol systems, implying that the networks

fall outside the class. By contrast, Vera and Simon (1994) argue that ALVINN, the

neural network component of an autonomous land vehicle (see Pomerleau 1993),

counts as a physical symbol system. When questioned about this apparent

discrepancy, Simon (personal communication, 1997) noted that this was not a

topic that he and Newell discussed much and that their views appeared to have

diverged.

The confusion on the topic of symbols is not restricted to computer science.

Indeed, the notion becomes even more problematic when the term is used across

disciplines. For instance, Hayes et al. (1997, p. 391) observe that,

Computers contain and manipulate symbols. To a philosopher this is one of

the most controversial claims and to a computer scientist one of the most

obvious. This contrast needs to be accounted for.

Indeed, when Newell and Simon’s (1976) paper was reprinted in Haugeland’s

(1997) Mind Design II collection, Haugeland (1997, p. 86) felt compelled to add an

editor’s note clarifying the differences between Newell and Simon’s use of the term

‘symbol’ and the kinds of use that the same term found in linguistics and

philosophy. This is a symptom of the equivocal use of the term ‘symbol,’ across

disciplines. Even in the strictly philosophical domain, the term ‘symbol’ is

problematic. For instance, Searle (1992, p. 15), notes that, ‘‘...even very technical

sounding notions are poorly defined—notions such as... ‘symbol,’ for example.’’

This terminology is also important in psychology (see Pylyshyn 1984; Dawson

1998, 2004; Pezzulo and Castelfranchi 2007). For these reasons then, it is important

to try and clarify the issues at hand. This will be the primary goal of this paper. The

strategy will not be to attempt to defend some putatively ‘correct’ version of the

94 I. S. N. Berkeley

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concept of a ‘symbol.’ Rather, some terminological conventions will be suggested,

some constraints will be proposed and a taxonomy of the kinds of issue that give rise

to disagreement will be articulated. The goal here is to provide something like a

‘geography’ of the various notions of ‘symbol’ that have appeared in the various

literatures, so as to focus attention on the key issues and to permit the focusing of

attention upon the key dimensions about which disagreement can arise.

Designation and Constraints

Before proceeding further, it is worth noting that the type of symbol under

discussion here is the kind that is found in philosophical and scientific discussions

concerning minds, computers and similar entities. What are explicitly not under

discussion are the broader notions of symbolism that are found in art. For instance,

although it has been claimed that in pictures of a certain era a skull symbolizes

death, or mortality, this is not the notion of symbol under consideration here.

One of the primary functions of symbols is to ‘stand for,’ ‘represent,’ or ‘denote’

something else. The processes involved here can be usefully divided into two

distinct stages. First, there is the selection of the entities that potentially may play a

symbolic role. Second, there is the designation, or provision of an interpretation for

those entities. The reason these two stages are worth distinguishing is because there

will be cases where potentially symbolic entities have been selected, but not applied

an interpretation. For instance, it is common when describing formal languages to

designate certain letters as standing for individual constants and variables, prior to

actually ascribing values for these letters (see for example, Mates 1972, pp. 44–45).

For purposes of clarity, potentially symbolic entities, prior to receiving their

interpretations, will be termed ‘tokens,’ in order to distinguish them from entities

that have had interpretations supplied. This terminology broadly follows that

adopted by Haugeland (1985). Only once entities have an interpretation will they

correctly fall into the scope of the term ‘symbol,’ as it will be used here. The topic

of how to determine whether something is a ‘token’ will be returned to presently.

The business of designation or interpretation is far from straightforward, so some

discussion is in order. In the simplest case, a token may go through something like a

‘baptismal’ process in order to become a symbol. Once again, the case of formal

languages provides a clear example of this kind of situation (see Mates 1972, pp.

58–59, for example). An analogous case can arise in Common LISP with a

command string such as ‘‘(setq my_name ‘*****’)’’. In this case, the token

‘my_name’ is assigned the value ‘‘*****’’ and thereby becomes a symbol.

This ‘baptismal’ style of assigning designation or interpretation is not the only

manner in which this process occurs, of course. Indeed, there are a variety of

mechanisms that have been discussed in the literature and that are manifest in actual

practice (see Fodor 1980; Pylyshyn 1984, pp. 40–48; Haugeland 1985, pp. 93–112),

for classic discussions of these issues, Cummins (1989), offers a more comprehen-

sive overview, whilst Egan (1995) and Dawson (1998), offer some slightly more

recent reflections). As these are contentious and controversial matters, further

explicit discussion will be avoided here, so as to prevent being taken too far a field

What the \0.70, 1.17, 0.99, 1.07[ is a Symbol? 95

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from the main topic under consideration. However, this does not preclude a few

further remarks being made about designation or interpretation, with respect to

issues that are, for the most part, independent of these matters.

One important point about designation, or interpretation, concerns the level of

detail at which it is applied. It is crucial that any interpretation apply at a single

level. This point can be clarified by an example. Consider the case of the vector

\0.70, 1.17, 0.99, 1.07[ in the title of this paper. It could just be specified that the

entire vector \0.70, 1.17, 0.99, 1.07[ stands for the term ‘heck.’ In this case, the

title of this paper would become ‘‘What the heck is a symbol?.’’ Alternatively, a set

of designation relations could be specified at a lower level. Consider the scheme

below:

‘\’ and ‘[’ are boundary markers and do not designate anything

‘,’ is a mere place separator and does not designate anything.

‘0.70’ designates ‘h’

‘1.17’ designates ‘e’

‘0.99’ designates ‘c’

‘1.07’ designates ‘k’

If this scheme was followed, then the title to the paper would again come out as

‘‘What the heck is a Symbol?,’’ as in the previous case. The point here is that despite

the fact that these two interpretations result in the same outcome, they are applied at

different levels. Clearly, attempting to mix these levels would necessarily

complicate matters and would likely give rise to equivocal, or problematic results.

This point can also be illustrated with an example concerning Morse code. In

Morse code, the letter ‘E’ is represented by a single dot (i.e., ‘.’), whilst the letter ‘T’

is represented by a single dash (i.e., ‘-’). However, the letter ‘A’ is represented by a

dot-dash (i.e., ‘.-’,). It is only by the correct spacing of the dots and dashes that ‘ET’

(i.e., ‘. -’) can be distinguished from ‘A.’ Analogously, the letter ‘N’ is signaled by

dash-dot (i.e., ‘-.’). However, the letter ‘P’ is represented by dot-dash-dash-dot (i.e.,

‘.- -.’). So, only due to careful signaling on the part of the transmitting party is it

possible to distinguish between ‘AN’ and ‘P.’ Of course, Morse code operators have

conventions to avoid these difficulties. Ideally, each dash (or ‘dah’) should last three

times the length or each dot (or ‘di’). Parts of letters should be separated by the

length of a single dot, individual letters should be separated by a space equivalent to

three dots and words should be separated by a space equivalent to seven dots.

However, this is an ideal that is hard for people to live up to in practice. Morse code

operators use the term ‘a bad fist’ for operators whose code is hard to understand.

Having a ‘bad fist’ can present real difficulties to communication, (see Anonymous

2006). The point behind this example is to illustrate how determining an appropriate

level of aggregation can present real difficulties in practical contexts.

A more problematic constraint upon interpretations is that an interpretation must

be, in Haugeland’s (1996, p. 18) phrase, ‘‘...consistently reasonable and sensible,

given the situation.’’ Haugeland (1985, pp. 93–112) provides a fuller discussion of

these issues. The main point is that interpretations should not be too arbitrary, or

capricious. Whilst this is not necessarily crucial for the current discussion, it is

included here for the sake of completeness. If a proposed interpretation for a set of


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symbols were too odd, or counter-intuitive, then it might prove difficult (or

computationally expensive) for the symbols to play a useful role in getting some

task done.

A final constraint upon interpretation concerns what may be termed the

‘representational power’ of a symbol, or set of symbols. It is crucial that any set of

symbols have the necessary flexibility to make manifest all the things that it needs to

for the task at hand. This point is perhaps best illustrated with an example. Consider

the case of a symbolic system for representing the natural numbers. For many years,

prior to the adopting of the Arabic numerals that are commonly used today, numbers

were routinely represented using the Roman system of numerals. One of the

significant differences between Roman numerals and Arabic numerals is that the

latter has a symbol for ‘zero,’ whilst the former does not. Another important

difference between the two systems is that Arabic numerals are positional, whereas

Roman numerals are not. In fact, Kaplan (1999) has suggested that a positional

system of writing numbers was crucial to the development of ‘zero.’ However,

whether or not a system of numerals had a representational convention for zero

could make a crucial difference to the kinds of uses that the system could be used

for. For instance, a discussion of dividing numbers by zero would be a non-starter, if

one was limited to the basic set of Roman numerals. This is because the Roman

numerals, as a set of symbols, lack the representational power to express zero.

Simplicity and Complexity

Many discussions of tokens and symbols rely upon an important distinction between

simple tokens and complex tokens (see for example Haugeland 1985; Fodor and

Pylyshyn 1988). It appears to be widely assumed that this distinction is, in some

important sense, a principled one. However, this assumption is the source of

significant confusion.

Simplicity

At first glance, the idea of a ‘simple’ token appears to be reasonably straightforward,

at least in certain paradigm cases. For instance, the individual constants in formal

languages, or even individual words in a natural language, appear to be plausible

cases of simple tokens or symbols. Even this is not entirely unproblematic though.

For instance, linguists currently believe the morpheme to be the smallest unit of

meaning in natural languages (O’Grady et al. 2005, p. 113). The points made

previously concerning the importance of a consistent choice of a level of

aggregation are also relevant in this context. More precisely, we may say that the

paradigm case of something that is simple is akin to the situation with a singleton

set, that is to say, a set with a single member. An entity of this type would be

unequivocally simple, in the manner needed here. Haugeland (1985, p. 72) describes

this type of simplicity as ‘‘having no part; not put together out of several

components.’’ What Haugeland (1985) has in mind here is the case of the atom, in

chemical theory, as contrasted with molecules.


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If it is granted that this kind of idea provides the basis for a reasonable

understanding of the notion of a simple token, or symbol, the problem presented by

the notion of complexity remains. It turns out that the notion of complexity can be

construed in a number of ways. These different understandings of complexity are

the cause of many of the more important confusions that arise with respect to

symbols and tokens. For the purposes of the current discussion, three distinct

notions of complexity will be illustrated. This list is not supposed to be exhaustive,

however. These examples are offered to demonstrate the different ways the simple/

complex distinction can be construed.

Complexity I

The first kind of complexity, which for convenience, I will call ‘complexity I,’

includes cases where the contrast is analogous to that between the simple singleton

set, as compared to a set with multiple members. Haugeland (1985, p. 72) describes

complexity in this sense as being ‘‘composed or put together out of several

components; having more than one part.’’ Here he has in mind again the contrast

between the atom and the molecule in chemical theory. It is this notion of

complexity that Haugeland (1985) believes himself to be using in his discussion. It

is worth noting that level of aggregation is important here. After all, if we stopped

looking at atoms, as contrasted with molecules and instead started considering

matters like the number of electrons, then this notion of complexity would unravel.

On the face of it, the distinction between simple and complex I symbols or tokens

is remarkably straightforward. The conditions under which the contrast can be

detected are about as simple as it is possible to be. Indeed, if this was the only notion

of complexity that appeared in the literature, then much of the confusion would

simply not arise. Unfortunately, there are other notions of complexity that appear in

the literature and it is the confusions between these various notions that can give rise

to the difficulties.

Complexity II

Although Haugeland’s (1985) analogy of the simple/complex distinction as being

similar to the distinction between atoms and molecules is suggestive, it is also

overly simplistic and is thus problematic. Consider the case of the molecule C4H10,

otherwise known as butane. There are in fact two kinds of butane, so-called n-

butane (or ‘normal butane’) and isobutane. Despite each molecule having a common

composition, in terms of their constituent atoms, they differ from one another in

terms of the arrangement of those atoms. The two kinds of butane have distinct

properties. For instance, n-butane boils at -0.5�C, whereas isobutane boils at -

11.6�C. Indeed, this is not an isolated case either. For instance, Pentane (C5H12)

occurs as three distinct molecules, n-pentane, isopentane, and neopentane (Silber-

berg 2007, pp. 465–466). These facts suggests that there is another notion of

complexity that can be usefully distinguished. This I will term ‘complexity II.’


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Whereas the distinction between simple and complex I symbols or tokens may be

thought as being a bit like the difference between a single marble, as compared to a

bag of marbles, something more is required by complexity II. The additional feature

in the case of complexity II is some kind of structure, or ordering of the elements of

complex II symbols, or tokens. This notion of complexity would be sufficient to

distinguish between the two cases of butane mentioned above. This is because,

although each type of butane shares a common number of component atoms, the

arrangement of the atoms is different in each case. Simple verses complex II is more

like the difference between a singleton set and an ordered (partially, or otherwise)

set, with multiple members.

This type of complexity seems to naturally be applicable to entities such as

vectors. If vectors are considered to exhibit complexity II, then the contrasting case

of a simple might be something like a scalar value. In the case of a vector, order

matters. Consider the issues that can arise with pairs of values of latitude and

longitude. By convention, latitude and longitude are expressed as two place vectors,

with latitude first, followed by longitude. Assuming that degrees are expressed in

decimal notation, there is a significant difference between the location at\51.4833,

0.0000[, which is approximately the location of London, England and the location

at\0.0000, 51.4833[, which is in the Indian Ocean, off the coast of Somalia, not far

from Mogadishu. Thus, latitude and longitude and indeed vectors in general, exhibit

complexity II.

Before moving on, there are two further points about complexity II that need to

be highlighted. The first is the fact that symbols or tokens that exhibit complexity II

will also exhibit complexity I. This may perhaps explain why the two notions have

been conflated (or at least, not properly distinguished) in the literature. The second

point is that this notion of complexity is somewhat vague. This is to a degree

deliberate. This is because this kind of complexity may well need to be subject to

further subdivision at some point in the future. The role it is supposed to play here is

to provide a contrast to the cases of complexity I and complexity III, which each

have the role of being limit cases.

Complexity III

Complexity III is the most rigorously specified type of complexity. In addition to the

requirement that tokens or symbols that exhibit this kind of complexity have some kind

of structure, the structure must be such that it is governed by precisely specified (or

specifiable) set of rules, which are entirely formal in nature. In the ideal case, things

which exhibit complexity III should also be strongly systematic and compositional

(C.f. Fodor and Pylyshyn 1988; Hadley 1994, 1997). A paradigm case of a system of

symbols or tokens that exhibits complexity III would be first-order predicate calculus.

Many computer languages appear to exhibit this kind of complexity also.

This type of complexity is arguably the most familiar kind, at least to

philosophers. It is interesting to note that Haugeland (1985) seems to be talking

about this kind of complexity, for the most part in the main body of his text. This is

despite the fact that, when he explicitly mentions the simple/complex distinction, he


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claims to understand the distinction as being similar to that between simple and

complexity I. This kind of confusion is one of the main things that motivates

drawing attention to these different notions of complexity here.

There is a further interesting ‘wrinkle’ that arises with complexity III. It turns out

that sets of tokens or symbols may exhibit this kind of complexity in a variety of

ways, that give rise to systems which have different capacities (see Bever et al.

1968; Hopcroft and Ullman 1979) for more detailed explorations of these issues). In

the current context however, as the notion of complexity III is supposed to play the

role of a limiting concept, the most powerful interpretation of systems involving

these features, will be assumed. Whether weaker versions should count as

constituting sub-categories of complexity III, or should instead count as falling

into complexity II, is a debate for another time. As was the case with the other kinds

of complexity, if a system exhibits complexity III, then that system will also exhibit

complexity I and II. As suggested before, this fact may explain some of the

confusions that arise with respect to these different kinds of complexity.

These three distinct notions of complexity all appear from time to time in the

literature that discusses symbols, tokens and related entities. However, as these

distinct notions are not explicitly distinguished from one another, this provides an

excellent situation in which misunderstandings and confusions can arise. This is a

particular danger when authors from different disciplines are debating with one

another. However, as will be illustrated in a later section, having this more subtle

specification of the various ways that the simple/complex distinction can be

construed, in conjunction with the other considerations under discussion here, can

be very helpful in understanding apparent disagreements and confusions that

occasionally arise. However, before considering the usefulness of the issues raised

thus far, one further matter needs to be dealt with. This concerns attempting to

develop a clearer notion of what it is for something to be a token.

What is a Token?

The paradigm case of a symbolic system is the Turing Machine (Turing 1936).

Given the terminological convention adopted here, it follows that Turing Machines

will provide a paradigm instance of a system that contains tokens. It is for this

reason that considering the case of the Turing Machine is a reasonable place to

begin when trying to figure out what a token is.

Although there are many discussions of Turing machines, arguably the most

rigorous and technically sophisticated discussion of this class of systems arises in

the broader context of technical computational theory. It is for this reason that this

discussion of tokens and Turing machines will begin with the account found in

Hopcroft and Ullman (1979, pp. 146–176). They (1979, p. 148) characterize a

Turing machine as follows,

Formally, a Turing machine (TM) is denoted

M ¼ (Q, R, C, d, q0, B, F),

where, Q is the finite set of states, C is the finite set of allowable tape symbols, B, a

symbol of C is the blank, R a subset of C not including B, is the set of input symbols,


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d is the next move function, a mapping from Q x C to, Q x C x {L, R} (d may,

however be undefined for some arguments), q0 in Q is the start state, F 7 Q is the

set of final states.

This formal specification can be adapted, for instance, by replacing their term

‘symbol’ with the term ‘token,’ as used here, to provide a rigorous answer to the

question ‘What is a token in a Turing machine?.’ The answer to this question thus

becomes,

A token for some Turing machine M is just a member ai of a finite input

alphabet C for which there is some operation d(ai, Q) defined in the machine

table of M, where Q is the finite set of possible states of M.

Of course, Turing machines are not the only class of entities that utilize tokens

and symbols. However, this specification provides a concrete and rigorous starting

point upon which a more general version of this specification can be based.

Naturally, a more general formulation will have to remove any references to

Turing machine specific features, such as the machine table. For the most part, this

can be done in a relatively straightforward manner. However, the key issue of the

more general specification will require a more general substitute for the ‘finite

alphabet C’ term. This needs to be handled with some care.

In the case of the Turing machine, there is a crucial interaction between the states

of the device Q, the set of allowable symbols (or tokens) C, and the function d, that

specifies the mapping between Q and C. ‘C’ is problematic in the more general case

in two ways. First off, by making symbolhood (or tokenhood) dependent upon a

relation to a set of symbols, there appears to be a danger of vicious circularity.

Second, as the set of entities in ‘C’ is finite, this would appear to rule out the

possibility of genuine symbols (or tokens) ever being such that they could have

continuous values. However, both these problems can be overcome by removing the

reliance on ‘C,’ whilst retaining the mapping between operations and states. By

making this change, and the others that are necessary to abstract away from the

particulars of the Turing machine, a more general answer to the question ‘What is a

token?’ can be formulated as follows.

A token is any entity ai for which there is some operation d(ai, Q), which is

defined for some device M, that has a set of states Q.

Provided that the notion of ‘a device M,’ is construed fairly broadly, this

specification of what it is for something to be a token should suffice in most cases.

There are a number of further refinements that can be made to this formulation

however, in order to deal with potential objections. For instance, some may object

that this specification of the conditions for something to be a token is too narrow, as

on the face of it, biological entities do not appear to be ‘devices’ in the relevant

sense. However, this objection could be easily be handled by either explicitly

including biological entities in M, or by replacing this part of the answer offered

above with the phrase ‘some entity M.’ A related objection may be raised over the

requirement that there be a ‘definition’ of the operation d(ai, Q). After all, it is at

least counter-intuitive to construe biological entities as being composed at least in


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part, of ‘definitions.’ Embracing these considerations, a final answer to the question

‘What is a token?’ would go as follows,

A token is any entity ai for which there is some operation d(ai, Q), which is

instantiated by some entity M, that has a set of states Q.

Although on the face of it, this specification of tokenhood appears to avoid

certain objections, it may appear to be too broad. This difficulty can be handled

though. Crucial to the determination of whether or not a particular entity of system

is token bearing will be the determination of whether or not there are ‘operations.’

In this formulation, this condition does most of the work. This being the case, some

constraints upon what is to be considered an ‘operation’ in the relevant sense might

appear to be in order.

In most cases, whether or not there are ‘operations’ in the relevant sense will be

quite straightforward to determine. However, this will not always be the case. So,

what is to be done in these problematic cases? After all, these are the kind of cases

in which the previously mentioned constraints seem to be most important. This

impression can be misleading though. After all, it will not be possible to anticipate

all the issues that might be relevant to future potentially token bearing systems.

Instead, a pragmatic determination of whether or not a particular system, or entity

has operations in the relevant sense seems most appropriate. Although this may not

appear too satisfying, it is a solution that has precedent. For example, Hardcastle

(1996) argues that a pragmatic approach is the best strategy when it comes

determining what is to count as a computation (see also the discussion in Hayes

et al. (1997)). Of course, adopting this approach put the burden of justification on

any theorist who wishes to advocate that a particular system, class of systems, or

entities have operations in the sense required here. So, the plausibility of the claims

can be determined at the time that the claim is advanced.

Although this kind of answer to the question of ‘what is a token?’ may not be

ideal, it does provide a set of guidelines that token bearing systems will have to

satisfy. No doubt there will remain problematic cases. As the intent here is not to

once and for all develop a veridical answer to all questions pertaining to tokenhood,

this will nonetheless be good enough for most cases and is thus sufficient for current

purposes.

One final point is worth emphasizing here, the answer to the question ‘what is a

token?’ given above constitutes a necessary condition on something being a token

(and thus a potential symbol), not a sufficient condition. This is because, for

example, some theorist may wish to argue that a system must support complexity

III, to be truly token-bearing. In fact, just this kind of opinion appears to have been

held by Newell (1980).

Applications

The main goal here is to provide some insight into the kinds of issues that are

relevant to discussions of tokens and symbols. These considerations can throw some

light upon apparent disagreements that can arise in the relevant literatures.


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Consider the case of apparent disagreement of the scope of symbol systems that

arose between Newell and Simon, that was discussed earlier. It would appear that

this apparent disagreement can now be understood. It is clear from his discussion

that Newell (1980) believed that a system had to exhibit complexity III in order to

be a proper symbol system. By contrast, Vera and Simon (1994) seem to think that

complexity II is sufficient. Thus the framework outlined here is useful in

understanding disagreements such as this. In another example, it appears that

Smolensky’s (1988) talk about ‘subsymbols’ does not necessarily amount to a

serious deviation from the views of other theorists, other than the fact that he wishes

the designation of the interpretation to occur at a level that is in some sense ‘lower’

than is usually the case. This may explain in part, why some commentators (see

Berkeley 2000, 2006) have suggested that there are instances when subsymbols

appear to be highly symbolic in nature.

A disagreement that has arisen between Berkeley (2000, 2006) and Dawson and

Piercey (2001) over whether or not a particular network, known as L10, should

count as being symbolic. The L10 network was trained on a logic problem,

originally described in the 1991 first edition of Bechtel and Abrahamsen (2002). A

detailed description of the network, along with a complete analysis can be found in

Berkeley et al. (1995). The network is clearly token bearing, in the required sense

here. Recently, Berkeley (2006) argued that there was a serious methodological

problem with a study of this network described by Dawson and Piercey’s (2001).

However, there were some unresolved issues about the symbolic status of L10, due

to the problems associated with the notion of symbolhood. Given the discussion

offered here though, provided that it is acceptable to only require complexity II, for

a system to count as symbolic, then the L10 system should be classified as a case of

a symbolic system, once and for all. Interestingly, Dawson (personal communica-

tion, 2007) is now neutral on this topic.

The versatility of the proposed framework can be illustrated by considering its

application to a set of proposals concerning symbols, that generally speaking, falls

largely outside the computational domain. For example, Deacon (1997) argues for a

position on the origins of language, that is essentially predicated upon the notion of

a ‘symbolic threshold.’ As Lumsden (2002) notes, Deacon’s account of language

turns crucially on his notion of what is to count as a symbol. However, it is clear that

Deacon’s ideas about symbols clearly presuppose something like complexity III, as

described above. This is because Deacon (1997, p. 32) identifies the special nature

of human communication systems (as contrasted with animal communication

systems) as being based upon the combinatorial power of the system. He (1997, p.

100) also maintains that syntactic structure is a crucial feature. While Deacon’s

(1997) conclusions are not without their critics (see Lumsden 2002), they do serve

to show the utility of the analysis of the various notions of symbolhood offered here.

Unfortunately, not all examples are entirely clear cut and straightforward.

Consider, for example, the position argued for in Clark (2006). Clark (2006) argues

that ‘material symbols’ seem to play some ‘hybrid’ role in cognition. The argument

here appears to crucially trade upon the idea that there can be symbols with radically

different properties. Clark (2006) contrasts his position with two ‘translation’ views

on symbols, one of which he attributes to Fodor (1998) and his allies, the other


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which he attributes to Churchland (1989). The problem that arises in the current

context is that Fodor’s position appears to be predicated upon the idea of type III

complexity being necessary for something to count as being symbolic, while

Churchland’s position appears to take type II complexity as being sufficient. The

problem here is that Clark does not describe sufficient details of his own hybrid

proposal to know where exactly he would stand on this matter. So, it is difficult to

know where in the geography of symbolic proposals, his position should be located.

However, the fact that the discussion above can be used to clearly identify the issues

that may arise with this proposal, once again illustrates the usefulness of the

proposed framework.

Conclusion

In conclusion, it is to be hoped that the considerations discussed here will help to

bring some clarity to the various discussions of symbols, tokens and related entities

that appear in the literatures where these entities are important. While the analysis

may ultimately require some extensions, it provides a framework within which

discussions on symbols can be compared. Hopefully, this analysis will serve to

reduce the degree the confusion in the various literatures in which the term ‘symbol’

appears.

Acknowledgment Thanks to the late James Patrick Dugal for the Morse Code example that appears in

Section ‘‘Designation and Constraints.’’

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