harnad@phoenix.Princeton.EDU (S. R. Harnad) (11/20/89)
What is a symbol system? From Newell (1980) Pylyshyn (1984), Fodor
(1987) and the classical work of Von Neumann, Turing, Goedel, Church,
etc.(see Kleene 1969) on the foundations of computation, we can
reconstruct the following definition:
A symbol system is:
(1) a set of arbitrary PHYSICAL TOKENS (scratches on paper, holes on
a tape, events in a digital computer, etc.) that are
(2) manipulated on the basis of EXPLICIT RULES that are
(3) likewise physical tokens and STRINGS of tokens. The rule-governed
symbol-token manipulation is based
(4) purely on the SHAPE of the symbol tokens (not their "meaning"),
i.e., it is purely SYNTACTIC, and consists of
(5) RULEFULLY COMBINING and recombining symbol tokens. There are
(6) primitive ATOMIC symbol tokens and
(7) COMPOSITE symbol-token strings. The entire system and all its parts
-- the atomic tokens, the composite tokens, the syntactic manipulations
(both actual and possible) and the rules -- are all
(8) SEMANTICALLY INTERPRETABLE: The syntax can be SYSTEMATICALLY
assigned a meaning (e.g., as standing for objects, as describing states
of affairs).
According to proponents of the symbolic model of mind such as Fodor
(1980) and Pylyshyn (1980, 1984), symbol-strings of this sort capture
what mental phenomena such as thoughts and beliefs are. Symbolists
emphasize that the symbolic level (for them, the mental level) is a
natural functional level of its own, with ruleful regularities that are
independent of their specific physical realizations. For symbolists,
this implementation-independence is the critical difference between
cognitive phenomena and ordinary physical phenomena and their
respective explanations. This concept of an autonomous symbolic level
also conforms to general foundational principles in the theory of
computation and applies to all the work being done in symbolic AI, the
branch of science that has so far been the most successful in
generating (hence explaining) intelligent behavior.
All eight of the properties listed above seem to be critical to this
definition of symbolic. Many phenomena have some of the properties, but
that does not entail that they are symbolic in this explicit, technical
sense. It is not enough, for example, for a phenomenon to be
INTERPRETABLE as rule-governed, for just about anything can be
interpreted as rule-governed. A thermostat may be interpreted as
following the rule: Turn on the furnace if the temperature goes below
70 degrees and turn it off if it goes above 70 degrees, yet nowhere in
the thermostat is that rule explicitly represented.
Wittgenstein (1953) emphasized the difference between EXPLICIT and
IMPLICIT rules: It is not the same thing to "follow" a rule
(explicitly) and merely to behave "in accordance with" a rule
(implicitly). The critical difference is in the compositeness (7) and
systematicity (8) criteria. The explicitly represented symbolic rule is
part of a formal system, it is decomposable (unless primitive), its
application and manipulation is purely formal (syntactic,
shape-dependent), and the entire system must be semantically
interpretable, not just the chunk in question. An isolated ("modular")
chunk cannot be symbolic; being symbolic is a combinatory, systematic
property.
So the mere fact that a behavior is "interpretable" as ruleful does not
mean that it is really governed by a symbolic rule. Semantic
interpretability must be coupled with explicit representation (2),
syntactic manipulability (4), and systematicity (8) in order to be
symbolic. None of these criteria is arbitrary, and, as far as I can
tell, if you weaken them, you lose the grip on what looks like a
natural category and you sever the links with the formal theory of
computation, leaving a sense of "symbolic" that is merely unexplicated
metaphor (and probably differs from speaker to speaker).
Any rival definitions, counterexamples or amplifications?
Excerpted from:
Harnad, S. (1990) The Symbol Grounding Problem. Physica D (in press)
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References:
Fodor, J. A. (1975) The language of thought. New York: Thomas Y. Crowell
Fodor, J. A. (1987) Psychosemantics. Cambridge MA: MIT/Bradford.
Fodor, J. A. & Pylyshyn, Z. W. (1988) Connectionism and cognitive
architecture: A critical appraisal. Cognition 28: 3 - 71.
Harnad, S. (1989) Minds, Machines and Searle. Journal of Theoretical
and Experimental Artificial Intelligence 1: 5-25.
Kleene, S. C. (1969) Formalized recursive functionals and formalized
realizability. Providence, R.I.: American Mathematical Society.
Newell, A. (1980) Physical Symbol Systems. Cognitive Science 4: 135-83.
Pylyshyn, Z. W. (1980) Computation and cognition: Issues in the
foundations of cognitive science. Behavioral and Brain Sciences
3: 111-169.
Pylyshyn, Z. W. (1984) Computation and cognition. Cambridge MA:
MIT/Bradford
Turing, A. M. (1964) Computing machinery and intelligence. In: Minds
and machines, A.R. Anderson (ed.), Engelwood Cliffs NJ: Prentice Hall.
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