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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, phayes@cs.uiuc.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 pairs of trees and integers) quite congenial and not muddled or confusing. John interprets the claim that model theory can discuss relationships between symbols 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 world. 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 contain 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 architectural 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 model 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 water-muddying, 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 actions 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. Pat ---------------------------------------------------------------------------- Beckman Institute (217)244 1616 office 405 North Mathews Avenue (217)328 3947 or (415)855 9043 home Urbana, IL. 61801 (217)244 8371 fax hayes@cs.stanford.edu or Phayes@cs.uiuc.edu