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From: kp@uts.amdahl.com (Ken Presting)
Newsgroups: comp.ai
Subject: Re: Emergence and Static Vs. Dynamic properties (was: Re: Another letter to the New York Review)
Summary: Homomorphism of logical structure occurs between descriptions
Keywords: homomorphism, logical structure, music, implementation
Message-ID: <2cSD02rC93BD01@amdahl.uts.amdahl.com>
Date: 17 Mar 90 21:02:57 GMT
References: <12143@venera.isi.edu> <b1UF028Q90Pd01@amdahl.uts.amdahl.com> <14431@phoenix.Princeton.EDU>
Reply-To: kp@amdahl.uts.amdahl.com (Ken Presting)
Organization: Amdahl Corporation, Sunnyvale CA
Lines: 86

In article <14431@phoenix.Princeton.EDU> eliot@phoenix.Princeton.EDU (Eliot Handelman) writes:
>In article <b1UF028Q90Pd01@amdahl.uts.amdahl.com> kp@amdahl.uts.amdahl.com (Ken Presting) writes:
>;. . .  Susanne Langer, ... from "Feeling and Form" (1952)
>;
>;     "The tonal structures we call "music" bear a close logical
>;   similarity to the forms of human feeling ... forms of growth
>;   and of attenuation ... speed, arrest ... the greatness and
>;   brevity and eternal passing of everything vitally felt.  Such is
>;   the pattern, or logical form, of sentience; and the pattern of
>;   music is that same form worked out in pure, measured sound and
>;   silence.  Music is a tonal analogue of emotive life.
>;      Such formal analogy, or congruence of logical structures, is
>;   the prime requisite for the relation between a symbol and whatever
>;   it is to mean.  The symbol and the object symbolized must have
>;   some common logical form."
>; . . .
>;Returning to the topic of abstraction and computation, I want to use the
>;second paragraph of the quote from Langer. . . .
>
>;Consider a formal theory of arithemetic, such as Peano's.  . . .
>;. . .   there is a homomorphism under deduction between
>;arithmetic and set theory.  Michael Resnick applies a similar idea to
>;the philosophy of mathematics, Langer applies it to symbolism in art,
>
>I don' really understand what you're trying to get at, maybe you could 
>clarify? 
>--eliot handelman

(Eliot expanded on this question via E-mail:)
>. . . The idea that music, sed Langer, is the "logical form" of emotions
>would mean, in your terms, that there is a homomorphism between music and
>emotions. I'm curious to see if this is what you're saying, and why you
>think this might be.

It's important (at least for logical purity) to distinguish between
the claim that music is the logical form of emotions (which neither
Langer nor I believe) and the claim that music and emotions have the
same logical form (which is closer to the position I have adopted from
her work).

The first problem is that no actual object or event literally has a
logical structure.  Only a set of assertions has a logical structure.
Even a set of assertions may have a vague or ambiguous logical
structure, if the assertions are informal, etc.

It makes some sense to talk about the logical structure of music or
emotions by extension - a true description of a musical performance
has (literally) a logical structure, which may then be attributed
to the performance.  Likewise, a phenomenological description of an
experience, emotional or otherwise, has a logical structure.

So the homomorphism of logical structure exists between the descriptions,
rather than between the phenomena.  The analogous relation which obtains
between the phenomena is *resemblance*.  The concepts of logical
structure and homomorphism serve to analyze resemblance.  (Homomorphism
is a suggestive analog for resemblance, but does not literally apply
outside the context of formal algebraic structures.)

The role of descriptions in this analysis introduces a number of serious
problems.  Langer does *not* take this approach, and avoids most of the
problems.  I am primarily interested in philosophy of science and
metaphysics, so I prefer to highlight the problems of descriptive
abstractions.  This makes my analysis more cumbersome in application
to the experience of music - the selection of a descriptive abstraction
becomes a central theoretical issue, rather than a practical matter to
be decided according to the interests of a composer, reviewer, or
listener.  (Btw, Langer seems to be more influenced by Clive Bell's
concept of "Significant Form" than by Wagner directly)

On the other hand, selection (or invention!) of a descriptive framework
is naturally a central issue for physical sciences, AI, and psychology
of perception.  So I think the concept of logical structure and
homomorphism organizes the problems in a useful way.  In particular,
phenomenology and physics each purport (or at least strive) to offer a
general descriptive abstraction, adequate for the expression of any
insight or hypothesis in their respective domains.  The theory of
computation makes a similar claim within its own domain.

I propose that AI is the attempt to find an "alignment" (or, better,
*implementation*) between these three domains, such that the truth of
each claim is simultaneously shown to be true.  I regard it as a very
happy accident (but not a very surprising one) that Langer, whose thought
is motivated largely by the aesthetics of music, provides the concept
that just might do the trick.

Ken Presting