ONT Re: Inquiry Driven Systems
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
| 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
The three levels of objective detail to be discussed are referred to as
the objective "framework", "genre", and "motive" that one finds actively
involved in organizing, guiding, and regulating a particular inquiry.
1. An "objective framework" (OF) consists of one or several
"objective genres" (OG's), each of which may also be known
as a "form of analysis" (FOA), a "form of synthesis" (FOS),
or an "ontological hierarchy (OH). Typically, these span
a diverse spectrum of formal characteristics and intended
interpretations.
2. An OG is made up of one or more "objective motives"
or "objective motifs" (OM's), each of which may also
be regarded as a particular "instance of analysis" (IOA)
or a particular "instance of synthesis" (IOS). All of the
OM's that are governed by a particular OG exhibit a kinship
of structures and intentions, and each OM roughly fits the
pattern or "follows in the footsteps" of its guiding OG.
3. An OM can be identified with a certain moment of interpretation,
one in which a particular 2-adic relation appears to govern all of
the objects in its purview. Initially presented as an abstraction,
an individual OM is commonly fleshed out by identifying it with its
interpretive agent. As this practice amounts to a very loose form
of personification, it is subject to all of the dangers of its type
and is bound eventually to engender a multitude of misunderstandings.
In contexts where more precision is needed it is best to acknowledge
that the application of an OM is restricted to special instants and
to limited intervals of time. This means that an individual OM must
look to the "interpretive moment" (IM) of its immediate activity to
find the materials available for both its concrete instantiation and
its real implementation. Finally, having come round to the picture
of an objective motive that is realized in an interpretive moment,
this discussion has achieved a discrete advance toward the desired
forms of dynamically realistic models, providing itself with what
begins to look like the elemental states and dispositions that
are needed to build fully actualized systems of interpretation.
A major theoretical task that remains outstanding for this project is to
discover a minimally adequate basis for defining the state of uncertainty
that an interpretive system has with respect to the questions it is able to
formulate about the state of an object system. Achieving this would permit
a measure of definiteness to be brought to the question of inquiry's nature,
since it can already be grasped intuitively that the gist of inquiry is to
reduce an agent's level of uncertainty about its object, its objective,
or its objectivity through appropriate changes of state.
Accordingly, one of the roles intended for this OF is to provide
a set of standard formulations for describing the moment to moment
uncertainty of interpretive systems. The formally definable concepts
of the MOI (the objective case of a SOI) and the IM (the momentary state
of a SOI) are intended to formalize the intuitive notions of a generic
mental constitution and a specific mental disposition that usually
serve in discussing states and directions of mind.
The structures present at each objective level are formulated by means
of converse pairs of "staging relations", prototypically symbolized by
the signs "-<-" and "->-". At the more generic levels of OF's and OG's
the "staging operations" associated with the generators "-<-" and "->-"
involve the application of 2-adic relations analogous to those of class
membership "element of" and its converse, but the increasing amounts of
parametric information that are needed to determine specific motives and
detailed motifs give OM's the full power of triadic relations. Using the
same pair of symbols to denote staging relations at all objective levels
helps to prevent an excessive proliferation of symbols, but it means that
the meaning of these symbols is always heavily dependent on the context.
In particular, even fundamental properties like the effective "arity"
or "valence" of the relations signified can vary from level to level.
The staging relations divide into two orientations, "-<-" versus "->-",
indicating opposing senses of direction with respect to the distinction
between analytic and synthetic projects:
1. The "standing relations", indicated by "-<-", are analogous to
the "element of", "belongs to", or the membership relation "in".
Another interpretation of "-<-" is the "instance of" relation.
At least with respect to the more generic levels of analysis,
any distinction between these readings is largely immaterial
to the formal interests and the structural objectives of
this discussion.
2. The "propping relations", indicated by "->-", are analogous to
the "class of" relation or converse of the membership relation.
An alternative meaning for "->-" is the "property of" relation.
Although it is possible to maintain a distinction in this regard,
the present discussion is mainly concerned with a level of purely
formal structure to which this difference is largely irrelevant.
Although it is strictly speaking logically redundant to do so,
it turns out to be extremely useful in practice to introduce
efficient symbolic devices for both directions of the staging
relations, "-<-" and "->-", and to maintain a formal calculus
that treats analogous pairs of relations on an equal footing.
Extra measures of convenience come into play if the relations
are used as assignment operations or as "field promotions",
that is, to create titles, to define terms, and to establish
the offices of objects in active contexts of given relations.
Accordingly, I regard these dual relationships as symmetric
primitives and employ them as the "generating relations"
of all three objective levels.
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤