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Reply-To: cg@cs.umn.edu Date: Fri, 4 Jun 93 05:35:26 EDT From: sowa <sowa@turing.pacss.binghamton.edu> Message-id: <9306040935.AA24073@turing.pacss.binghamton.edu> To: interlingua@ISI.EDU, phayes@cs.uiuc.edu, sowa@turing.pacss.binghamton.edu Subject: Re: (biassed) summary of the argument so far. Cc: cg@cs.umn.edu, cmenzel@kbssun1.tamu.edu

Pat, Your "biassed" summary was fairly accurate, and I deleted the points that I was willing to accept without too much reservation. > I see why, given your views on the difference between pure and > applied mathematics, you would object to my saying that model > theory can refer to relations between symbols and the world. But > I do not share those views, as I have now explained carefully > twice. So please don't go through them again like a patient teacher. OK. I hadn't realized that we had a disagreement about the difference between pure & applied math. You quoted that remark by Bertrand Russell, which I had intended to quote to you before you grabbed it first. I interpreted that to mean that pure mathematics isn't about anything until you make a decision to apply it to something. To me, this distinction between pure & applied mathematics seems so fundamental and so elegant that I can't see why anyone would object to it. Please excuse me for bringing it up again, but you made the comment that tensor calculus was "applied mathematics". But I said that it is just as pure as set theory. Originally, the subject was developed for the purpose of applying it to stresses and strains in solid objects (whence the name "tensor"). But then the same mathematical structure was applied to relativity. If you make the distinction, tensor calculus is pure and it has two very different major applications. But if you don't make the distinction, it becomes very difficult to talk separately about the mathematical operations and the domain of application. > ... I find your insistence that > lexical representations must refer only via a computational > 'simalcrum' of something real, which itself is only related > vaguely to the actual world, to be alarmingly confusing on > precisely this issue.... Fine, we seem to agree about the distinction between lexical and nonlexical items. In an earlier note, I believe that you were also willing to accept the meaning triangle, which puts concepts in the middle between words and things. Is that correct? If you don't accept the meaning triangle, then I can understand your objecting to my computational surrogates. But if you do accept the meaning triangle as a reasonable hypothesis about intervening mental states in human use of language, I cannot understand why you would object to an intervening level of surrogates in a computational system that is used to relate a language (natural or artificial) to the world. And I am not sure about your use of the word "vaguely" in your comment above. Did you mean that in a deprecating sense as some sort of criticism of my point? I don't recall actually using the word "vaguely" in my previous notes about the relationship between surrogates and the world, but it's fairly close to what I intended. The notion of surrogate gives me a very clear way of distinguishing the perceived reality (either in my head or in a computer simulation) >From the actual reality, which may in fact be quite different. To me, it seems to be a very natural way of talking about things. I really don't understand why you object to it so strenuously. Are you objecting because you want to distinguish some abstract theory of meaning from some computational implementation? Perhaps the reason for your objection is that you have a Platonic view of mathematics where you really believe that integers and uncountable sets of points exist in the same sense that dogs, houses, and people exist. When I see the phrase "there exists" in a mathematical textbook, I interpret it in a metaphorical sense, similar to the way I would interpret a novel or a myth. Then the data structures in my computer are a finite realization or simulation of that abstract mathematical realm (or portion thereof, if it happens to be infinite). In that sense, they are similar to a movie that depicts the scenes in a novel. John