Friday, December 09, 2005
(new thread on Emergency Medical Ontology Project planning à [home] )
find Leonid Perlovsky
Note
in response to Arun
Majumdar à [285]
Arun,
I have read and re-read
several of your papers with John Sowa.
We share an interest in
formalization of analogy, but feel that analogy cannot be fully formalized –
because the formalization process itself must use induction to create a set of
axioms. So the relationship to the
algebra of toposes (for those
that are familiar with it) and axiomatic theories is one where induction is
critical. The work on similarity
measure by Douglas Hofstadter has strongly influenced my thinking on the notion
of analogy. It was certain not his
position that similarity was something that one could render computationally.
I am sure that John Sowa
would want me to agree with him about the definition of induction. However, I must say that induction is not
something on which there is a lot of agreement. John should agree with this, as this is the position of
Whitehead, Russell and others. My take
is that natural induction is part of the process involved in the formation of
any mental event. So “interpretation”
and “induction” have certain strong relationships.
This “take” upsets many
people, who want induction to be something formalizable. I once had a long eforum debate with Joe
Firestone, founder of KMCI (a knowledge management organization in Washington
DC) where he wanted the statement that induction could be reduced to mere
deduction to be true. This type of
desire is common. I realize that I am
not mainstream. But being not
mainstream is not the same as being un-informed and incorrect.
I know that John has
specific thoughts about deduction, induction and abduction. But his belief system is really different in
fundamental ways from mine and from those I have studied and known.
This is ok, except that my
group takes the position that the mainstream (of which your work with John
really is in the center of) is incorrect in certain specific ways, and is
approaching the formalization of human knowledge in a way that will not be
successful (ever) in our opinion.
I have said all this before,
so I need not say it again.
Quasi Axiomatic Theory
approached this entire subject in a way that is similar to but with
considerable differences to the work developed by Alexander Grothendiech, and
later extended in your own work and to work on toposes and Chu spaces.
But these approaches are
still acting as if formalism can solve more of the problem that formalism has
been shown to solve.
Chu spaces and toposes
pushes knowledge technology further out into a esoteric discipline that only a
few can understand. I often say that
the complications of many things – particularly computer science – is due to an
inability of the mainstream to recognize the limits of formalism and the key
role that complexity plays in everyday everything. The complexity is most evident when there is the emergence of
something, like when there is an interpretation of experience by an
individual.
Category theory is also
developed by Robert Rosen and his mentor N. Rashensky. Rashensky is one of the fathers of
mathematical biology, theoretical biology.
This type of category
theory, Rosen’s, is present in a large percentage of the Grossberg type
biologically feasible models of neural architecture. The category theory of Rosen focuses on anticipatory
mechanisms (one of his books was titled
“Anticipatory Systems”). The point is
that this literature and discipline is quite different from the Chu Space and
toposes constructions.
The foundations to the
notion of representational basis for knowledge representation can be traced to
C S Peirce, but not in the way that Sowa interprets Peirce. John knows Peirce as well as anyone, but the
interpretation is different form that developed by the Russians.
I have developed an appreciation
for the way that the Soviet school headed by Pospelov and Finn interpreted
Peirce. I met both Pospelov and Finn
several times, including during by visit to Moscow in 1997, where I gave a
lecture on quasi axiomatic theory.