Changes

=====1.3.4.1.  Formal Models : A Sketch=====

=====1.3.4.1.  Formal Models : A Sketch=====

To sketch the features of the modeling activity that are relevant to the immediate purpose:  The modeler begins with a "phenomenon of interest" or a "process of interest" (POI) and relates it to a formal "model of interest" (MOI), the whole while working within a particular "interpretive framework" (IF) and relating the results from one "system of interpretation" (SOI) to another, or to a subsequent development of the same SOI.

To sketch the features of the modeling activity that are relevant to the immediate purpose:  The modeler begins with a ''phenomenon of interest'' or a ''process of interest'' (POI) and relates it to a formal ''model of interest'' (MOI), the whole while working within a particular ''interpretive framework'' (IF) and relating the results from one ''system of interpretation'' (SOI) to another, or to a subsequent development of the same SOI.

The POI's that define the intents and the purposes of this project are the closely related processes of inquiry and interpretation, so the MOI's that must be formulated are models of inquiry and interpretation, species of formal systems that are even more intimately bound up than usual with the IF's employed and the SOI's deployed in their ongoing development as models.

The POI's that define the intents and the purposes of this project are the closely related processes of inquiry and interpretation, so the MOI's that must be formulated are models of inquiry and interpretation, species of formal systems that are even more intimately bound up than usual with the IF's employed and the SOI's deployed in their ongoing development as models.

Since all of the interpretive systems and all of the process models that are being mentioned here come from the same broad family of mathematical objects, the different roles that they play in this investigation are mainly distinguished by variations in their manner and degree of formalization:

Since all of the interpretive systems and all of the process models that are being mentioned here come from the same broad family of mathematical objects, the different roles that they play in this investigation are mainly distinguished by variations in their manner and degree of formalization:

1. The typical POI comes from natural sources and casual conduct.  It is not formalized in itself but only in the form of its image or model, and just to the extent that aspects of its structure and function are captured by a formal MOI.  But the richness of any natural phenomenon or realistic process seldom falls within the metes and bounds of any final or finite formula.

# The typical POI comes from natural sources and casual conduct.  It is not formalized in itself but only in the form of its image or model, and just to the extent that aspects of its structure and function are captured by a formal MOI.  But the richness of any natural phenomenon or realistic process seldom falls within the metes and bounds of any final or finite formula.

 

# Beyond the initial stages of investigation, the MOI is postulated as a completely formalized object, or is quickly on its way to becoming one.  As such, it serves as a pivotal fulcrum and a point of application poised between the undefined reaches of ''phenomena'' and ''noumena'', respectively, terms that serve more as directions of pointing than as denotations of entities.  What enables the MOI to grasp these directions is the quite felicitous mathematical circumsatnce that there can be well-defined and finite relations between entities that are infinite and even indefinite in themselves.  Indeed, exploiting this handle on infinity is the main trick of all computational models and effective procedures.  It is how a ''finitely informed creature'' (FIC) can "make infinite use of finite means".  Thus, my reason for calling the MOI cardinal or pivotal is that it forms a model in two senses, loosely analogical and more strictly logical, integrating twin roles of the model concept in a single focus.

2. Beyond the initial stages of investigation, the MOI is postulated as a completely formalized object, or is quickly on its way to becoming one.  As such, it serves as a pivotal fulcrum and a point of application poised between the undefined reaches of "phenomena" and "noumena", respectively, terms that serve more as directions of pointing than as denotations of entities.  What enables the MOI to grasp these directions is the quite felicitous mathematical circumsatnce that there can be well-defined and finite relations between entities that are infinite and even indefinite in themselves.  Indeed, exploiting this handle on infinity is the main trick of all computational models and effective procedures.  It is how a "finitely informed creature" (FIC) can "make infinite use of finite means".  Thus, my reason for calling the MOI cardinal or pivotal is that it forms a model in two senses, loosely analogical and more strictly logical, integrating twin roles of the model concept in a single focus.

# Finally, the IF's and the SOI's always remain partly out of sight, caught up in various stages of explicit notice between casual informality and partial formalization, with no guarantee or even much likelihood of a completely articulate formulation being forthcoming or even possible.  Still, it is usually worth the effort to try lifting one edge or another of these frameworks and backdrops into the light, at least for a time.

 

3. Finally, the IF's and the SOI's always remain partly out of sight, caught up in various stages of explicit notice between casual informality and partial formalization, with no guarantee or even much likelihood of a completely articulate formulation being forthcoming or even possible.  Still, it is usually worth the effort to try lifting one edge or another of these frameworks and backdrops into the light, at least for a time.

=====1.3.4.2.  Sign Relations : A Primer=====

=====1.3.4.2.  Sign Relations : A Primer=====