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Friday, December 09, 2005

 

 The BCNGroup Beadgames

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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.