[Inquiry] Re: Prospects for Inquiry Driven Systems

[Jon Awbrey]

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PRO.  Note 36

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1.2.2.3.  Pragmatic Theory of Signs (concl.)

It is helpful to view the definition of individual sign relations on analogy
with another important class of three-place relations of broad significance
in mathematics and far-reaching application in physics, namely, the binary
operations or ternary relations that fall under the definition of abstract
groups.  Viewed as a definition of individual groups, the axioms defining
a group are what logicians would call highly "non-categorical", that is,
not every two models are isomorphic (Wilder, p. 36).  But viewing the
category of groups as a whole, if indeed such a category can be said
to form a whole (MacLane, 1971), the definition allows a vast number
of non-isomorphic objects, namely, the individual groups.

In mathematical inquiry the closure property of abstract groups mitigates most of
the difficulties that might otherwise attach to the precision of their individual
definition.  In physics, however, the application of mathematical structures to
the unknown nature of the enveloping world is always very tentative.  Starting
from the most elemental levels of instrumental trial and error, this kind of
application is fraught with intellectual difficulty, indeed, with the risk
of physical pain.  The act of abstracting a particular structure from a
concrete situation is no longer merely abstract.  It becomes, in effect,
a hypothesis, a guess, a bet on what is thought to be the most relevant
aspect of a current, potentially dangerous, and always ever-insistently
pressing reality.  And this hypothesis is not just a paper belief but
determines action in accord with its character.  Consequently, due to
the abyss of ignorance that always remains to our kind and the chaos
that can result from acting on what little is actually known, risk
and pain always accompany our extraction of particular structures,
our attempts to isolate particular forms, and our best guesses
at the most viable factorizations of phenomena.

Likewise in semiotics, it is hard to find any examples of autonomous
sign relations and to isolate them from their ulterior entanglements.
This kind of extraction is frequently all the more painful because of
the circumstance that the full analysis of each element in a particular
sign relation may involve references to other object-systems, sign-systems,
and interpretant-systems outside of its ostensible, initially secure bounds.
As a result, it is even more difficult with sign systems than with the simpler
physical systems to find coherent subassemblies that can be studied in isolation
from the rest of the universe, discursive or otherwise, that appears to envelop it.

These remarks should be enough to convey the plan of this work.
Progress can be made toward new resettlements of ancient regions
where only turmoil has reigned to date.  Existing structures can
be rehabilitated by continuing to unify the terms licensing AI
representations with the terms leasing free space over dynamic
manifolds.  A large section of habitable space for dynamically
intelligent systems could be extended in the following fashion:
The agents of change and the images of state that are customary
in symbolic AI could be related to the elements and the operators
that form familiar planks in the tangent spaces of dynamic systems.
The higher order concepts that fill out AI could be connected with the
more complex constructions that are accessible from the moving platforms
of these tangent spaces, inhabited as incidental universes of discourse.

Jon Awbrey

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