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 1.3.4.14 (Application of OF: Generic Level)
|
| http://members.door.net/arisbe/menu/library/aboutcsp/awbrey/inquiry.htm
1.3.4.14 Application of OF: Generic Level (cont.)
Turning to the language of objective concerns, what can now be said
about the compositional structures of the iconic sign relation M and
the indexical sign relation N? In preparation for this topic, a few
additional steps must be taken to continue formalizing the concept of
an objective genre and to begin developing a calculus for composing
objective motifs.
I recall the OG of "properties and instances" and introduce the
symbols "-<-" and "->-" for the converse pair of 2-adic relations
that generate it. Reverting to the convention I employ in formal
discussions of applying relational operators on the right, I will
express the relative terms "property of x" and "instance of x" by
means of a case inflection on x, that is, as "x's property" and
as "x's instance", respectively. Described in this fashion,
OG(Prop, Inst) is generated by the set {-<- , ->-}, where:
| "x -<-" = "x's property" = "property of x" = "object above x"
|
| "x ->-" = "x's instance" = "instance of x" = "object below x"
A symbol like "x -<-" or "x ->-", by itself or linked together in chains,
with extra spaces or raised dots being optional, is called a "catenation",
where "x" is the "catenand" and "-<-" or "->-" is the "catenator". Due to
the fact that "-<-" and "->-" designate 2-adic relations, the significance
of these so-called "unsaturated" catenations can be rationalized as follows:
| "x -<-" = "x is the instance of what?" = "x's property"
|
| "x ->-" = "x is the property of what?" = "x's instance"
Working in this manner, the definitions of icons and indices
can be reformulated in terms of the following two equations:
| x's icon = x's property's instance = x -<-->-
|
| x's index = x's instance's property = x ->--<-
According to the earlier definitions of the
homogeneous iconic sign relation M and the
homogeneous indexical sign relation N,
we have the following equations:
| x's icon = x · M_OS
|
| x's index = x · N_OS
Equating the results of the corresponding pairs of equations
yields an analysis of M and N as forms of composition within
the genre of properties and instances:
| x's icon = x · M_OS = x · -<-->-
|
| x's index = x · N_OS = x · ->--<-
On the assumption (to be examined more closely later) that any object x
can be taken as a sign, the converse relations appear to be manifestly
identical to the obverse relations:
| For Icons: x's object = x · M_SO = x · -<-->-
|
| For Indices: x's object = x · N_SO = x · ->--<-
Abstracting from the applications to an otiose x delivers the results:
| For Icons: M_OS = M_SO = -<-->-
|
| For Indices: N_OS = N_SO = ->--<-
This appears to suggest that icons and their objects are icons of each other,
and that indices and their objects are indices of each other. Are the results
of these symbolic manipulations really to be trusted? Given that there is no
mention of the interpretive agent to whom these sign relations are supposed
to appear, one might well suspect that these results can only amount to
approximate truths or potential verities.
Jon Awbrey
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