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From: mcdermott-drew@CS.YALE.EDU (Drew McDermott)
Newsgroups: comp.ai
Subject: Re: What is a Symbol System?
Summary: Symbol systems don't have to have a semantics
Keywords: symbol manipulation, syntax, formality, semantics
Message-ID: <6170@cs.yale.edu>
Date: 20 Nov 89 18:44:01 GMT
References: <11640@phoenix.Princeton.EDU>
Sender: news@cs.yale.edu
Reply-To: mcdermott-drew@CS.YALE.EDU (Drew McDermott)
Organization: Yale University Computer Science Dept, New Haven CT  06520-2158
Lines: 74

In article <11640@phoenix.Princeton.EDU> harnad@phoenix.Princeton.EDU (S. R. Harnad) writes:
   > 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.
   >  [...]   
   >Any rival definitions, counterexamples or amplifications?
   >
   >-- Stevan Harnad INTERNET: harnad@confidence.princeton.edu
   >harnad@princeton.edu

I have two quibbles with this list:

(a) Items 2&3: I agree that the rules have to be explicit, but they are
usually written in a different notation from the one they manipulate.
Example: A theorem prover written in Lisp.  Another example: The
weights in a neural net.

(b) Item 8: Why is it necessary that a symbol system have a semantics
in order to be a symbol system?  I mean, you can define it any way
you like, but then most AI programs wouldn't be symbol systems in 
your sense.  I and others have spent some time arguing that symbol
systems *ought* to have a semantics, and it's odd to be told that I
was arguing in favor of a tautology.  (Or that, now that I've changed
my mind, I believe a contradiction.)

Perhaps you have in mind that a system couldn't really think, or
couldn't really refer to the outside world without all of its symbols
being part of some seamless Tarskian framework.  (Of course, *you*
don't think this, but you feel that charity demands you impute this
belief to your opponents.)  I think you have to buy several extra
premises about the potency of knowledge representation to believe that
formal semantics is that crucial. 
      
                                              -- Drew McDermott