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 1.3.4.15 (Application of OF: Motive Level)
|
| http://members.door.net/arisbe/menu/library/aboutcsp/awbrey/inquiry.htm
1.3.4.15 Application of OF: Motive Level
Now that an adequate variety of formal tools have been set in order and
the virtual workspace afforded by an objective framework has been rendered
reasonably clear, the structural theory of sign relations can now be pursued
with greater precision. In support of this aim, the concept of an objective
genre and the particular example provided by OG(Prop, Inst) have served to
rough out the basic shapes of the more refined analytic instruments to be
developed in this Subsection.
The notion of an "objective motive" or an "objective motif" (OM) is intended
to personalize and to specialize the application of objective genres to take
particular interpreters into account. For example, staying with the pattern
of OG(Prop, Inst), a prospective OM of this genre does not merely tell about
the properties and instances that objects can have in general, it recognizes
a particular arrangement of objects and supplies them with its own ontology,
giving "a local habitation and a name" to the bunch. What matters to an OM
is a particular collection of objects (of thought) and a personal selection
of links that go from each object (of thought) to higher and lower objects
(of thought), all things being relative to a subjective ontology or a live
"hierarchy of thought" (HOT), one that is currently acknowledged by and
actively pursued by the designated interpreter of these very thoughts.
The cautionary details interspersed at critical points in the preceding
paragraph are intended to keep this inquiry vigilant against a constant
danger of using ontological language, namely, the illusion that one can
analyze the being of any real object merely by articulating the grammar
of one's own thoughts, that is to say, simply parsing signs in the mind.
As always, it is best to regard OG's and OM's as "filters" and "reticles",
as transparent templates that are used to view a space, constituting the
structures of objects only in one respect at a time, but never with any
assurance of totality.
With these refinements at the ready, the use of 2-adic projections to
investigate sign relations can be combined with the vantage points of
objective motives to "factor the facets" or "decompose the components"
of sign relations in a more systematic fashion. Given a homogeneous
sign relation H of iconic or indexical type, the 2-adic projections
H_OS and H_OI can be analyzed as compound relations over the basis
supplied by the G_j in G. As an application that is sufficiently
important in its own right, the investigation of icons and indices
continues to provide a useful testing ground for breaking in likely
proposals of concepts and notation.
To pursue the analysis of icons and indices at the next stage of
formalization, fix the OG of this discussion to be of the type
generated by {-<- , ->-}, and let each sign relation under
discussion be articulated in terms of an objective motif
that tells what objects and signs, plus what mediating
linkages through properties and instances, are assumed
to be recognized by its interpreter.
Let X collect the objects of thought that fall within a particular OM,
and let X include the whole world W = O |_| S |_| I of a sign relation
plus everything needed to support and contain it. Thus, X collects all
the types of things that go into a sign relation, O |_| S |_| I = W c X,
plus whatever else in the way of distinct object qualities (OQ's) and
object exemplars (OE's) is discovered or established to be generated
out of this basis by the relations of the OM.
In order to keep this X simple enough to contemplate on a single pass,
but still make it deep enough to cover the issues of interest at present,
I restrict X to having just three disjoint layers of things to worry about:
| The middle layer X_0 is the initial collection of objects and signs:
|
| X_0 = W = O |_| S |_| I
|
| The top layer Q is the relevant set of object qualities:
|
| Q = (X_0 -<-) = (W -<-)
|
| The bottom layer E is a suitable set of object exemplars:
|
| E = (X_0 ->-) = (W ->-)
Recall the reading of the staging relations:
| "h : x -<- m" = "h regards x as an instance of m"
|
| "h : m ->- y" = "h regards m as a property of y"
|
| "h : x ->- n" = "h regards x as a property of n"
|
| "h : n -<- y" = "h regards n as an instance of y"
Express the analysis of icons and indices as follows:
| For Icons: M_OS : x -<-->- x's sign
|
| For Indices: N_OS : x ->--<- x's sign
Let j and k be hypothetical interpreters that do the jobs of M and N,
respectively. In this case we have the following series of equations:
| For Icons: x's sign = x · M_OS = x-<j<-->j>-
|
| For Indices: x's sign = x · N_OS = x->k>--<k<-
Factor out the names of the interpreters j and k to act as
identifiers of objective motifs, and we have the following:
| For Icons: j : x -<-->- x's sign
|
| For Indices: k : x ->--<- x's sign
Finally, the constant motif names j and k can be collected to one
side of a composition or else distributed to its individual links:
| j : x -<-->- y <=> j : x -<- m and j : m ->- y, for some m in Q.
|
| k : x ->--<- y <=> k : x ->- n and k : n -<- y, for some n in E.
These statements can be read to say:
1. j thinks x an icon of y if and only if there is an m such that
j thinks x an instance of m and j thinks m a property of y.
2. k thinks x an index of y if and only if there is an n such that
k thinks x a property of n and k thinks n an instance of y.
Readers who object to the anthropomorphism or the approximation of
these statements can replace every occurrence of the verb "thinks"
with the phrase "interprets ... as", or even less committally with
the circumlocution "acts in every formally significant way as if",
changing what must be changed elsewhere. For the moment, I am not
concerned with the exact order of reflective sensitivity that goes
into these interpretive linkages, but only with a rough outline of
the pragmatic equivalence classes implied by the potential conduct
of their interpretive agents.
In the discussion of the dialogue between A and B, it was allowed that
the same signs "A" and "B" could reference, with a systematic ambiguity
a deliberate duality, the different categories of things that they name.
Used informally as parts of the peripheral discussion, they indicate the
entirety of the sign relations themselves. Used formally within the focal
dialogue that is being examined, they denote the objects of two particular
sign relations. In just this way, or what amounts to an elaboration of it,
the signs "j" and "k" can have their meanings extended to encompass both the
objective motifs (OM's) that inform and regulate experience and also the object
experiences (OE's) that fill out and substantiate the forms of these same motifs.
Jon Awbrey
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