Alternative conceptions of symbol systems

[Peter Cariani]

Comments on Harnad's definition of symbol system:
   We all owe to Steve Harnad the initiation of this important discussion.
I believe that Harnad has taken the discourse of the symbol grounding problem
in the right direction, toward the grounding of symbols in their interactions
with the world at large. I think, however, that we could go further in
this direction, and in the process continue to re-examine some of the
fundamental assumptions that are still in force.
   The perspective presented here is elaborated much more fully and
systematically in a doctoral dissertation that I completed in May of this year:

Cariani, Peter (1989) On the Design of Devices With Emergent Semantic Functions
   Ph.D. Dissertation, Department of Systems Science, SUNY-Binghamton,
   University Microfilms, Ann Arbor Michigan.

   My work is primarily based on that of theoretical biologists Howard Pattee
and Robert Rosen.  Pattee has been elaborating on the evolutionary origins
of symbols in biological systems while Rosen has concentrated on the
modelling relations that biological organisms implement. The Hungarian
theoretical biologist George Kampis has also recently published work along
these lines. I would like to apologise for the length of this response, but I
come out of a field which is very small and virtually unknown by those
outside of it, so many of the basic concepts must be covered to avoid
misunderstandings.

   Here are some suggestions for clarifying this murky discourse about symbol
systems:

1) Define the tokens in terms of observable properties.
   The means of recognizing the tokens or states of the system must be given
explicitly, such that all members of a community of observer-participants can
reliably agree on what "state" the physical system is in. Without this
specification the definition is gratuitous hand-waving. I stress this because
there are a number of papers in the literature which discuss "computations"
in the physical world (e.g. "the universe is a gigantic computation in
progress") without the slightest indication of what the symbol tokens are
that being manipulated, what the relevant states of such systems might be, or
how we would go about determining, in concrete terms, whether a given
physical system is to be classified as a physical symbol system.
  One has to be careful when one says "practically everything can be
interpreted as rule-governed." Of course we can easily wave our hands and say,
yes, those leaves fluttering in the breeze over there are rule-governed,
without having any idea what the specific rules are or for that matter, what
the states are), but to demonstrate that a phenomenon is rule-governed,
we should show how we would come to see it as such: we should
concretely show what measurements need to be made, we should make them, and
then articulate the rules which describe/govern the behavior.
   If we say "a computer is a physical symbol system" we mean that if we look
at the computer through the appropriate observational frame, measuring the
appropriate voltages at the logic gates, then we can use this device to
consistently and reliably implement a deterministic input-output function.
For each initial distinguishable state of affairs, by operating the device
we always arrive at one and only one end state within some humanly-relevant
amount of time. This is a functionally-based physically-implemented concept
of a formal system, one which is related to Hilbert's idea of reliable
physical operations on concrete symbols leading to consistent results.
   Note that this definition is distinct from logicist/platonist definitions
which include nonconcrete objects (e.g. sets of sets) or physically
unrealizable objects (e.g. potential and actual infinities, indefinitely
extendible tapes).

2) Abandon the explicit-implicit rule distinction.
   First, I'm not sure if Wittgenstein's distinction between "explicit" and
"implicit" rule-following is appropriate here, since we are taking the role
of external observers rather than participants in a language-game. If the
purpose of the definition is to give us criteria to decide whether we are
participating in a formal system, then we must know the rules to follow them.
   If the purpose is to identify "physical symbol systems" in nature and in
human artefacts, then this distinction is irrelevant. What does it mean for
a computer to explicitly or implicitly carry out a logical operation? If it
made a difference, then the device would cease to be wholly syntactic. If it
doesn't make a difference then we don't need it in our definition. Does
the brain implement a physical symbol system, and if so, does it follow rules
explicitly or implicitly? How would we decide?

3) Abandon semantic interpretability.
   I'm not sure if I understand fully the motivation behind this criterion of
semantic interpretability. An external observer can assign whatever meanings
s/he chooses to the tokens of the formal device. This criterion makes the
definition very subjective, because it depends upon an arbitrary assignment
of meaning. I don't even see how this is restrictive, since the observer
can always come up with purely whimsical mappings, or to simply let the tokens
stand for themselves. 
   Note that "semantic interpretability" does not confer upon the physical
symbol system its own semantics. The relations of the symbols manipulated in
computer programs to the world at large are completely parasitical on human
interpreters, unless the computer is part of a robot (i.e. possesses its own
sensors and effectors).  Merely being semantically interpretable doesn't
ground the semantics in a definite way; when we say "X in my program
represents the number of speeding violations on the Mass Pike" we stabilize
the relation of the symbol X in the computer relative to ourselves (assuming
that we can be completely consistent in our interpretation of the program).
But each of us has a different tacit interpretation of what "the number of
speeding violations on the Mass Pike" means. (Does a violator have to be
caught for it to be a violation? Are speeding police cars violations? How is
speed measured?) In order for this tacit interpretation to be made explicit
we would need to calibrate our perceptions and their classifications along
with our use of language to communicate them so that we as a community
could reach agreement on our interpretations.
   The wrong turn that Carnap and many others made in the 1930's was to assume
that these interpretations could be completely formalized, that a "logical
semantics" was possible in which one could unambiguously determine the "meaning
of an expression" within the context of other expressions. The only way to do
this is to formalize completely the context, but in doing so you transform a
semantic relation into a syntactic one. The semantic relation of the symbol to
the nonsymbolic world at large gets reduced to a syntactic rule-governed
relation of the symbol to other symbols. (Contingent truths become reduced to
necessary truths.) What Carnap tried to say was that as long as a proposition
referred to an observation statement (which refers to an act of observation),
then that proposition has a semantic content. This has led us astray to the
point that many people no longer believe that they need to materially
connect the symbols to the world through perception and action, that merely
referring to a potential connection is enough. This is perhaps the most
serious failing of symbolic AI, the failure to ground the symbols used
by their programs in materially implemented connections to the external world.

4) Abandon semantic theories based on reference
   A much better alternative to logical semantics involves replacing these
syntactic theories of reference with a pragmatist semiotic when we go to
analyze the roles of symbols in various kinds of devices. Pragmatist
semiotics (as developed within Charles Morris' framework) avoid the
formal reductionism and realist assumptions of referential theories of
meaning by replacing correspondences between "objective" referents with
physically implemented semantic operations (e.g. measurement, perception,
control, action). These ideas are developed more fully in my dissertation.
What one must do to semantically ground the symbols is to connect them to
the world via sensors and effectors. If they are to be useful to the device
or organism, they must be materially linked to the world in a nonarbitrary way,
rather than referentially connected in someone's mind or postulated as 
unspecified logical ("causal") connections (as in "possible world" semantics).

4) Abandon Newell and Pylyshyn's Symbol Level.
   Upon close examination of both of their rationales for a separate symbol
level, one finds that it rests precariously upon a distinction, between the
Turing machine's internal states and the state of affairs on the tape
(Pylyshyn, 1984, pp.68-74). Now the essential nature of this distinction is
maintained because one is potentially infinite and the other is finite (else
one could simply make a big finite-state-automaton and the distinction would
be an abitrary labelling of the global machine states), but physically
realizable devices cannot be potentially infinite, so the essential,
nonarbitrary character of the distinction vanishes (Cariani, 1989, Appendix 2).

5) Purge the definition of nonphysical, platonic entities (or at least
recognize them as such and be aware of them).
   For example, the definition of physical symbol systems is intimately tied
up with Turing's definition of computation, but, as von Neumann noted, this
is not a physical definition; it is a formal one. Now, physically realizable
automata cannot have indefinitely extendible tapes, so the relevance of
potentially-infinite computations to real world computations is dubious.
Everything we can physically compute can be described in terms of finite-state
automata (finite tape Turing machines). We run out of memory space and
processing time long before we ever encounter computability limitations.
Computational complexity matters, computability doesn't. I'd be especially
interested in thoughtful counter-arguments to this point.

6) Alternative I: Adopt a physical theory of symbolic action.
   Howard Pattee has been developing a physical theory of symbolic function for
20 years--symbolic processes are those which can be described in terms of
nonholonomic constraints (in terms of the equations of motion and basins of 
attraction (in terms of trajectories)(see refs: Pattee; Cariani, Minch, Rosen).
   (Next summer there will be a workshop entitled "Symbols and Dynamics" at
   the ISSS meeting in Portland, Ore., July 8-13, 1990. Contact: Gail
   Fleischaker, 76 Porter St., Somerville, MA 02143 for more info.)
The only disadvantage of these approaches lie in their classical/
realist assumption of complete knowledge of the state space within which
the symbolic activity occurs. These premises are deeply embedded in the
very terms of the disourse, but nevertheless, this descriptive physical
language is exceedingly useful as long as the limitations of these
assumptions are constantly kept in mind.
   To translate from the semiotic to the physical, syntactic relations are
those processes for which a nonholonomic rate-independent equation of
constraint can completely replace the rate-dependent laws of motion. For an
electronic computer, we can replace all of the microscopic electromagnetic
equations of motion describing the trajectories of electrons with macroscopic
state-transition rules describing gate voltages in terms of binary states.
These state transition rules are not rate-dependent, since they depend upon
successions of states rather than time; consequently time need not enter
explicitly when describing the behavior of a computer in terms of binary
states of gate voltages.
   Semantic relations are those processes which can be described in terms of
rate-independent terms coupled to rate-dependent terms: one side of the
constraint equation is symbolic and rate-independent, the other half is
nonsymbolic and rate-dependent. Processes of measurement are semantic in
character: a rate-dependent, nonsymbolic interaction gives rise to a
rate-independent symbolic output.
   Here pragmatic relations are those processes which change the structure of
the organism or device, which appear in the formalism as changes in the
nonholonomic constraints over time.

7) Alternative II: Adopt a phenomenally grounded systems-theoretic definition.
   Part of my work has been to ground the definition of symbol in terms of the
observed behavior of a system. This is the only way we will arrive at an
unambiguous definition. We select a set of measuring devices which implement
distinctions on the world which become our observable "states." We observe the
behavior of the physical system through this observational framework. This
strategy is similar to the way W. Ross Ashby grounded his theory of systems.
   Either the state-transitions are deterministic--state A is always followed
by state B which is always followed by state G--or they are nondeterministic--
state D is sometimes followed by state F and sometimes followed by state J.
Here the relation between states A,B, and G appears to be symbolic, because
the behavior can be completely captured in terms of rules, where the relation
between the states D, F, and J appears nonsymbolic, because the behavior
depends upon aspects of the world which are not captured by this observational
frame. Syntactic, rule-governed, symbol manipulations appear to an external
observer as deterministic state transitions (in Ashby's terms, "a
state-determined system"). Semantic processes appear to the observer as
nondeterministic, contingent state transitions leading to states which appear
as symbolic. Pragmatic relations appear as changes in the structure of the
observed state-transitions.

8) Alternative III: Adopt a physical, mechanism-based definition of symbol
systems.
   Symbolic and nonsymbolic can also be viewed in terms of "digital" and
"analog" in the sense of differentiated (discrete) and nondifferentiated
(continuous). Sensors implement semantic A-to-D operations. Logical operations
("computations") implement syntactic, determinate D-to-D transformations.
Controls implement semantic D-to-A operations. One has to be careful here,
because there are many confusing uses of these words (e.g. "analog
computation"), and what appears to be "analog" or "digital" is a function
of how you look at the device. Given a particular observational framework
and a common usage of terms, however, these distinctions can be made reliable.
I would argue that von Neumann's major philosophical works (General & Logical
Theory of Automata, Self-Reproducing Automata, The Computer and the Brain)
all take this approach.

9) Alternative IV: Adopt a semiotic-functionalist definition of symbol systems.
   It can be argued that the basic functionalities needed in the modelling
relation are the ability to convert nonsymbolic interactions with the world
into symbols (measurement), the ability to manipulate symbols in a definite,
rule-governed way (computations), and the ability to use a symbol to direct
action on the nonsymbolic world (controls). I have argued that these
functionalities are irreducible; One cannot achieve measurements by doing
computations simply because measurement involves a contingent state-transition
where two or more possible observed outcomes are reduced to one observed
outcome, whereas computation involves a necessary state-transition, where
each state has but one observed outcome. These assertions are similar to the
epistemological positions adopted by Bohr, von Neumann, Aristotle and many
others.
   In such a definition, a physical symbol system is defined in terms of its
use to us as observer-participants. Are we trying to gain information about
the external world by reducing the possible observed states of a sensor to
one (by performing a measurement)? Are we trying to manipulate symbols in a
consistent, reliable way so that we always arrive at the same outcome given
the same input strings and rules. If so, we are performing computations.
Are we trying to use symbols to change the nonsymbolic world by acting on it.
If so, we are employing symbolically-directed control operations.

   In summary, there are many worthwile alternatives to the basic assumptions
that have been handed down to us through logical positivism, model-theoretic
semantics, artificial intelligence and cognitive psychology. Steve Harnad has
done us a great service in making many of these assumptions visible to us
and clarifying them in the process.  There are other conceptual frameworks
which can be of great assistance to us as we engage in this process:
theoretical biology, semiotics/pragmatist philosophy, cybernetics and systems
theory. It is difficult to entertain ideas which challenge cherished modes of
thought, but such critical questioning and debate are indispensible if we
are to deepen our understanding of the world around us.

References:
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