[sci.math.symbolic] The symbol grounding problem

berleant@ut-sally.UUCP (Dan Berleant) (06/22/87)

In article <847@mind.UUCP> harnad@mind.UUCP (Stevan Harnad) writes:
(Concerning the derivability of intrinsic meaning via the model thoery of

>I am not a model theorist, so the following reply may be inadequate, but it
>seems to me that the semantic model for an uninterpreted formal system
>in formal model-theoretic semantics is always yet another formal
>object, only its symbols are of a different type from the symbols of the
>system that is being interpreted. That seems true of *formal* models.
>Of course, there are informal models, in which the intended interpretation
>of a formal system corresponds to conceptual or even physical objects. We
>can say that the intended interpretation of the primitive symbol tokens
>and the axioms of formal number theory are "numbers," by which we mean
>either our intuitive concept of numbers or whatever invariant physical
>property quantities of objects share. But such informal interpretations 
>are not what formal model theory trades in. As far as I can tell,
>formal models are not intrinsically grounded, but depend on our
>concepts and our linking them to real objects. And of course the
>intrinsic grounding of our concepts and our references to objects is
>what we are attempting to capture in confronting the symbol grounding

What I have in mind is this: The more statements you have (that you wish
to be deemed correct), the more the possible meanings of the terms will
be constrained.  To illustrate, consider the statement FISH SWIM.  Think
of the terms FISH and SWIM as variables with no predetermined meaning --
so that FISH SWIM is just another way of writing A B.  What variable
bindings satisfy this?  Well, many do. We could assign to the variable
FISH, the meaning we normally assign to the word "fish", and to the
variable SWIM the meaning we normally think of for the word "swim".  We
could also assign the English meaning of the word "mountains" to the
variable FISH, and the English meaning of "erode" to the variable SWIM.
Obviously, many assignments to the variables FISH and SWIM would work.

Now consider the statement FISH LIVE, where FISH and LIVE are variables.
Now there are two statements to be satisfied. The assignment to the
variable LIVE restricts the possible assignments to the variable SWIM,
since e.g. if LIVE is assigned the English meaning of "live", then SWIM
can no longer have the meaning of the English "erode". 

Of course, we have many many statements in our minds that must be
simultaneously satisfied, so the possible meanings that each word name
can be assigned is correspondingly restricted. Could the restrictions be
sufficient to require such a small amount of ambiguity that the word
names could be said to have intrinsic meaning?

footnote: This leaves unanswered the question of how the meanings
themselves are grounded. Non-symbolically, seems to be the gist of the
discussion, in which case logic would be useless for that task even in
an 'in principle' capacity since the stuff of logic is symbols.

>I hope model theorists will correct me if I'm wrong. But even if the
>model-theoretic interpretation of some formal symbol systems can truly
>be regarded as the "objects" to which it refers, it is not clear that
>this can be generalized to natural language or to the "language of
>thought," which must, after all, have Total-Turing-Test scope, rather
>than the scope of the circumscribed artificial languages of logic and
>mathematics. Is there any indication that all that can be formalized

An interesting question regarding this is, just how much can model
theory do to provide intrinsic meaning to (say) language? Nothing? Only
in principle? Could it be practically useful?

I'm taking the liberty of cross posting this followup to
sci.math.symbolic and sci.philosophy.meta (in hopes of increased

Dan Berleant
UUCP: {gatech,ucbvax,ihnp4,seismo...& etc.}!ut-sally!berleant
ARPA: ai.berleant@r20.utexas.edu