ONT Re: Inquiry Driven Systems
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| Document History
|
| Subject: Inquiry Driven Systems: An Inquiry Into Inquiry
| Contact: Jon Awbrey <jawbrey@oakland.edu>
| Version: Draft 8.70
| Created: 23 Jun 1996
| Revised: 06 Jan 2002
| Advisor: M.A. Zohdy
| Setting: Oakland University, Rochester, Michigan, USA
| Excerpt: Section 1.3.4 (Discussion of Formalization: Concrete Examples)
| Excerpt: Subsection 1.3.4.13 (Formalization of OF: Objective Levels)
|
| http://members.door.net/arisbe/menu/library/aboutcsp/awbrey/inquiry.htm
1.3.4.13 Formalization of OF: Objective Levels (cont.)
Next, I present several different ways of formalizing OG's and OM's.
The reason for employing multiple descriptions is just to capture
the diversity of ways that these patterns of organization appear
in actual practice.
One way to approach the formalization of an objective genre G
is through an indexed collection of 2-adic relations:
G = {G_j} = {G_j : j in J}, with G_j c P_j x Q_j for all j in J.
Here, J is a set of actual (not formal) parameters used to index the OG,
while P_j and Q_j are domains of objects (initially in the informal sense)
that enter into the 2-adic relation G_j.
Aside from their indices, many of the G_j in G can be abstractly identical
to each other. This would earn G the designation of a "multi-family" or
a "multi-set" according to some customs of usage, but I prefer to treat
the index j as a concrete part of the indexed relation G_j, and in this
way distinguishing G_j from all other members of the indexed family G.
Ordinarily, it is desirable to avoid making individual mention
of the separately indexed domains, P_j and Q_j for all j in J.
Common strategies for getting around this nuisance involve the
introduction of additional domains, designed to encompass all
of the objects that may happen to be needed in given contexts.
Toward this end, an adequate supply of intermediate domains,
called the "rudiments of universal mediation" (RUM's), can be
defined as follows:
X_j = P_j |_| Q_j, where P = |_|^j P_j and Q = |_|^j Q_j.
Ultimately, all of these "totalitarian" strategies end the same way,
at first, by envisioning a domain X that is big enough to encompass
all of the objects of thought that might demand entry into a given
discussion, and then, by invoking one of the following conventions:
| Rubric of Universal Inclusion (RUI): X = |_|^j (P_j |_| Q_j).
|
| Rubric of Universal Equality (RUE): X = P_j = Q_j for all j in J.
Working under the aegis of either one of these rubrics,
G can be provided with a simpler style of presentation:
G = {G_j} = {G_j : j in J}, with G_j c X x X for all j in J.
However, it serves a purpose of this project to preserve the
individual indexing of relational domains for while longer,
or at least to keep this usage available as an alternative
formulation. Generally speaking, it is always possible in
principle to form the union required by the RUI, or without
loss of generality to assume the equality imposed by the RUE.
The problem is that the unions and equalities invoked by these
rubrics may not be effectively definable, or perhaps not testable
in a computational context. Further, even when these sets or tests
can be constructed or certified by some computational agent or other,
the ultimately pertinent question at any interpretive moment is whether
each collection or constraint is actively being apprehended or warranted
by the particular interpreter that is charged with responsibility for it
by the indicated assignment of domains.
But an overall purpose of this formalism is to represent the objects and
the constituencies that are "known to" specific interpreters at definite
moments of their interpretive proceedings, in other words, to depict the
information about objective existence and constituent structure that is
actually possessed, recognized, responded to, acted on, and followed up
by concrete agents as they move through their own immediate contexts of
activity. Therefore, keeping individual tabs on the relational domains
P_j and Q_j, though it does not solve this array of problems, does serve
to mark the pressing concern with particularity and to keep before one's
mind the issues of individual attention and personal responsibility that
are appropriate to interpretive agents. In short, whether or not domains
appear with explicit subscripts, one should always be ready to answer the
challenge that is gaged by the question "Who subscribes to these domains?"
It is important to emphasize that the index set J and the particular
attachments of indices to 2-adic relations are part and parcel to G,
befitting the concrete character intended for the concept of an OG,
which is expected, in some semblance of a realistic way, to embody
in the character of each G_j both "a local habitation and a name".
For this reason, among others, the G_j can safely be described
as "individual dyadic relations" (IDR's). Since the classical
notion of an "individual" as a "perfectly determinate entity"
has no application in finite information contexts, it appears
safe enough for our sake to recycle the term to distinguish
the "terminally informative particulars" (TIP's) that the
concrete index j adds to its thematic object G_j, whether
it is read parenthetically or taken purely paraphytically.
Depending on the prevailing direction of interest in the genre G,
"-<-" or "->-", the same symbol is used equivocally for all the
relations G_j. The G_j can be regarded as formalizing the OM's
that make up the genre G, provided it is understood that the
information corresponding to the parameter j constitutes
an integral part of the "motive" or the "motif" of G_j.
In this formulation, G constitutes an "ontological hierarchy" (OH)
of an extremely plenary and potentiating type, one that determines
the complete array of objects and relationships that are conceivably
available and describably "effable" within the discussion in question.
Operating with reference to the global field of possibilities that is
afforded by G, each G_j corresponds to the specialized competence of
a particular agent, selecting out the objects and the links of the
general purpose hierarchy that are known to, owing to, or owned by
the given interpreter j.
Jon Awbrey
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