Re: Intension/Sinnsowa <email@example.com>
Date: Sun, 13 Feb 94 12:01:20 EST
From: sowa <firstname.lastname@example.org>
To: email@example.com, firstname.lastname@example.org, interlingua@ISI.EDU
Subject: Re: Intension/Sinn
Cc: email@example.com, firstname.lastname@example.org
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.