(biassed) summary of the argument so far.

Message-id: <199306010725.AA19857@dante.cs.uiuc.edu>
Date: Tue, 1 Jun 1993 02:28:49 +0000
To: interlingua@ISI.EDU
From: phayes@cs.uiuc.edu
X-Sender: phayes@dante.cs.uiuc.edu
Subject: (biassed) summary of the argument so far.
Cc: sowa@turing.pacss.binghamton.edu, cmenzel@kbssun1.tamu.edu, cg@cs.umn.edu,
Let me try to summarise the core of the argument. Model theory talks of 
possible interpretations of formal languages and describes them using the 
language of set theory. It seems to Pat that this allows us to interpret 
our languages as referring to physical things like trees and cats, since 
set theory is agnostic about the nature of the individuals in the sets 
which it describes. John disagrees, claiming that set theory must refer 
to abstract entities, which are the subjectmatter of pure, as opposed to 
applied, mathematics. John believes that model theory, or indeed any part
of 'pure' mathematics, can  relate formal languages only to such an abstract 
domain, which he identifies with the domains of computational or mental 
constructions (an identification which Pat disagrees with, accusing John 
of being a constructivist; but this disagreement constitutes a minor theme 
in the argument). John therefore(?) insists that any account of how this 
entire mathematical/computational system can relate to the actual, physical, 
world, must go beyond model theory (or indeed any part of pure mathematics) 
and concern itself with 'grounding', becoming involved with machine perception, 
or at any rate epistemology and metaphysics. Pat disagrees, 
claiming that it is useful to be able to simply consider interpretations of 
formal languages over domains, including physical domains, which do not need 
to be any more tightly specified than is required by the branch of mathematics 
being used: in this case, set theory. To do so does not, Pat suggests, involve 
solving any epistemological questions and need not assume any progress in 
understanding how formalisms are grounded: that is concerned with how their 
accuracy is ensured, while semantics is concerned only with what they could 
possibly mean. He rejects John's claim that 'pure' mathematics can refer only 
to abstractions, finding the idea of a set of trees, say, (or even a set of
of trees and integers) quite congenial and not muddled or confusing. John 
interprets the claim that model theory can discuss relationships between
and the real world, especially the real physical world, as amounting to a claim 
that the grounding problem has been magically solved or is trivial, and rejects 
it on these grounds: he observes repeatedly that model theory has not
solved this 
deep and complex problem. Pat repeatedly concurs, but does not find this to
be a 
criticism of model theory so much as simply an observation about what is its 
business. John is unable to countenance the combination of such talk with the 
claim that model theory can describe relations between symbols and the actual 

As an example of the mutual misundertanding, Pat has repeatedly referred 
to conventional 'tarskian' models, meaning the same by this as John does,
but since he 
(Pat) believes the universes of such things, being sets, may legitimately
physical entities; and since John finds such talk incoherent, he (John)
takes Pat 
to be referring to some mythical construction which has addressed all the 
philosophical problems of grounding, believing Pat to be guilty of intellectual 
dishonesty in making such claims (since he (Pat) couldnt, in Johns eyes, have 
been referring to ordinary models, which are made of sets, not real stuff....)

On more pragmatic issues, Pat wishes to make many distinctions that John 
wishes to deny. Since John believes that model theory can  describe only
abstract entities, which he identifies with computational ones, he sees such 
models as being computational structures, indeed as a form of representation. 
John therefore identifies 'model' in the sense of model theory (model-1) with 
'model' in the sense of vivid knowledge base or database, ie a computationally 
compact collection of ground facts (model-2). Since in a robot this would be 
the robot's 'model' (in a third, informal sense: model-3) of its world,
with its 
accuracy maintained by perceptual mechanisms, it stands between the robot's 
'formal' knowledge representations and the actual world, acting as a surrogate 
world to the former (and therefore a model-1 with a special status) and a 
representation (model-3) of the latter, but one whose semantics are given not 
using modeltheory but in some other way. John has hinted that this 
might be image-like, so that this 'model' represents by being in some sense 
similar to the world it represents, ie is an 'analogical' representation 
(model-4). Since this is also what the sensors keep uptodate, it can be thought 
of as a communication center for the robot, so it is also part of an
proposal rather reminiscent of the 'blackboard' idea.

Pats position on all this is that is seems a conflation of many (at least 5) 
different ideas, and he regrets the resulting confusion, suggesting that it 
is in any case unnecessary. More specifically, Pat urges that representations 
should be distinguished semantically, ie by what they say, and that model 
theory provides a useful and well-thought-through framework for analysing this. 
As an example, he points out that a DB is better thought of as a collection 
of ground assertions than as a model-1, and these have sharply different 
functional roles in inference. John claims that a DB can be regarded as a 
model-1 or as a model-2 because these are 'isomorphic'. It seems that John 
is more impressed than Pat with the syntactic form of a representation.

Pat also is worried about the methodological implications of insisting that
theory can only refer to 'abstract' surrogates of reality, since it seems
to imply 
that any representational project must be accompanied by a 'Principia'-like 
enterprise for the relevant domain, and this would be highly impractical as 
well as completely unneccessary. John has not addressed this concern.

John believes that Pat cannot be misunderstanding him, and is therefore overly 
concerned with terminological issues. He suggests that we use 'depiction' as a 
neutral term to refer to these things. Pat finds this useless and
since his whole problem is one of getting distinctions made carefully and not 
conflated with one another. Each is trying to be helpful, but finding the
of the other to be so unhelpful as to seem deliberately obstructive.


There are many other differences between Pat and John in ways of thinking, 
rhetorical style and opinions on various matters, but they are very similar 
in that both are determined to argue and each regularly infuriates the other 
to the point of apoplexy.


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