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Date: Sun, 13 Feb 94 12:01:20 EST From: sowa <sowa@turing.pacss.binghamton.edu> Message-id: <9402131701.AA11959@turing.pacss.binghamton.edu> To: cg@cs.umn.edu, fritz@rodin.wustl.edu, interlingua@ISI.EDU Subject: Re: Intension/Sinn Cc: phayes@cs.uiuc.edu, wille@mathematik.th-darmstadt.de

Fritz and Pat, This discussion is another case where metalevel reasoning becomes important. Frege's Sinn corresponds to Peirce's Interpretant in his triad of sign-object-interpretant. Peirce's most important contribution was in the recognition that the interpretant itself can be a sign about which further reasoning can be done. Peirce's interpretants correspond to percepts (when the sign is a sensory stimulus), to concepts (when the sign is a word), or to propositions (when the sign is a sentence). But Peirce allowed for arbitrary iteration of the meaning triangles to generate as many metalevels as necessary -- you can, if you like, talk about triangles as sensory percepts, as the mathematical abstraction or concept Triangle, at the metalevel as the concept of Triangularity (which would include the associated axioms and theorems that one could prove about triangles), and at the metametalevel as a theory of how geometric shapes are defined by axiomatizations. I certainly grant that concepts, when represented somehow in the brain, are not publicly inspectable. But when we are trying to develop KR theories, we must be able to discuss each of the many metalevels in a way that is relatively independent of the nuts and bolts of the computer implementation. That goal of an implementation-independent way of talking about propositions and concepts was my motivation for defining a proposition as an "equivalence class of intertranslatable sentences in a family of languages." If your family has only one language, and your translation rule is identity, then the terms sentence and proposition are in exact one-for-one correspondence. But if we are concerned about knowledge sharing in multiple languages and implementations, the notion of propositions independent of any particular representation becomes essential. I will not claim that the interpretation of proposition as an equivalence class is the only possible one. But it does allow me to use extensional language to talk about intensions. For people who disapprove of intensions on philosophical grounds, this interpretation makes dialog possible. John Sowa