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From: fateman@renoir.Berkeley.EDU (Richard Fateman)
Newsgroups: comp.ai
Subject: Re: What is a Symbol System?
Keywords: computation, symbol manipulation, syntax, formality
Message-ID: <32690@ucbvax.BERKELEY.EDU>
Date: 20 Nov 89 17:19:49 GMT
References: <11640@phoenix.Princeton.EDU>
Sender: usenet@ucbvax.BERKELEY.EDU
Reply-To: fateman@renoir.Berkeley.EDU.UUCP (Richard Fateman)
Organization: University of California, Berkeley
Lines: 33

In article <11640@phoenix.Princeton.EDU> harnad@phoenix.Princeton.EDU (S. R. Harnad) writes:
>
>
>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
......>
[manipulated based on a rule system that is]
>i.e., it is purely SYNTACTIC, ....

If you believe the syntactic rules (a^b)^c <--> a^(b*c) and a*b <--> b*a  then
-1 = (-1)^1 = (-1)^(2* (1/2)) = ((-1)^2)^1/2) = 1^(1/2) = 1.
from which anything else can be proven.
So if you want to do mathematics correctly, this approach 
or representation is wrong.
....
>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.

In other words, with respect to symbolic mathematical symbol
manipulation systems, Harnad is making an observation that pertains
to those "syntactic" ones which (perhaps inevitably incorrectly) manipulate
uninterpreted trees. His observation is merely that anything else
should not be called a "symbol system".  Since usage contradicts
Harnad's contention, what's the point? Should we change the name
of our newsgroup? :)


Richard Fateman
 fateman@renoir.berkeley.edu