Changes

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 POIs that define the intents and the purposes of this project are the closely related processes of inquiry and interpretation, so the MOIs 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 IFs employed and the SOIs 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:

# 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.

# 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'' 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.

# Finally, the IFs and the SOIs 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=====

A large number of the problems arising in this work have to do with the integration of different interpretive frameworks over a common objective basis, or the prospective bases provided by shared objectives.  The main concern of this project continues to be the integration of dynamic and symbolic frameworks for understanding intelligent systems, concentrating on the kinds of interpretive agents that are capable of being involved in inquiry.

A large number of the problems arising in this work have to do with the integration of different interpretive frameworks over a common objective basis, or the prospective bases provided by shared objectives.  The main concern of this project continues to be the integration of dynamic and symbolic frameworks for understanding intelligent systems, concentrating on the kinds of interpretive agents that are capable of being involved in inquiry.

Integrating divergent IF's and reconciling their objectifications is, generally speaking, a very difficult maneuver to carry out successfully.  Two factors that contribute to the near intractability of this task can be described and addressed as follows.

Integrating divergent IFs and reconciling their objectifications is, generally speaking, a very difficult maneuver to carry out successfully.  Two factors that contribute to the near intractability of this task can be described and addressed as follows.

# The trouble is partly due to the ossified taxonomies and obligatory tactics that come through time and training to inhabit the conceptual landscapes of agents, especially if they have spent the majority of their time operating according to a single IF.  The IF informs their activity in ways they no longer have to think about, and thus rarely find a reason to modify.  But it also inhibits their interpretive and practical conduct to the customary ways of seeing and doing things that are granted by that framework, and it restricts them to the ''forms of intuition'' that are suggested and sanctioned by the operative IF.  Without critical reflection, or a mechanism to make amendments to its own constitution, an IF tends to operate behind the scenes of observation in such a way as to obliterate any inkling of flexibility in thought or practice and to obstruct every hint or threat (so perceived) of conceptual revision.

# The trouble is partly due to the ossified taxonomies and obligatory tactics that come through time and training to inhabit the conceptual landscapes of agents, especially if they have spent the majority of their time operating according to a single IF.  The IF informs their activity in ways they no longer have to think about, and thus rarely find a reason to modify.  But it also inhibits their interpretive and practical conduct to the customary ways of seeing and doing things that are granted by that framework, and it restricts them to the ''forms of intuition'' that are suggested and sanctioned by the operative IF.  Without critical reflection, or a mechanism to make amendments to its own constitution, an IF tends to operate behind the scenes of observation in such a way as to obliterate any inkling of flexibility in thought or practice and to obstruct every hint or threat (so perceived) of conceptual revision.

# Apparently it is so much easier to devise techniques for taking things apart than it is to find ways of putting them back together that there seem to be only a few heuristic strategies of general application that are available to guide the work of integration.  A few of the tools and materials needed for these constructions have been illustrated in concrete form throughout the presentation of examples in this section.  An overall survey of their principles can be summed up as follows.

# Apparently it is so much easier to devise techniques for taking things apart than it is to find ways of putting them back together that there seem to be only a few heuristic strategies of general application that are available to guide the work of integration.  A few of the tools and materials needed for these constructions have been illustrated in concrete form throughout the presentation of examples in this section.  An overall survey of their principles can be summed up as follows.

:* One integration heuristic is the ''lattice'' metaphor, also called the ''partial order'' or ''common denominator'' paradigm.  When IF's can be objectified as OF's that are organized according to the principles of suitable orderings, then it is often possible to ''lift'' or extend these order properties to the space of frameworks themselves, and thereby to enable construction of the desired kinds of integrative frameworks as upper and lower bounds in the appropriate ordering.

:* One integration heuristic is the ''lattice'' metaphor, also called the ''partial order'' or ''common denominator'' paradigm.  When IFs can be objectified as OFs that are organized according to the principles of suitable orderings, then it is often possible to ''lift'' or extend these order properties to the space of frameworks themselves, and thereby to enable construction of the desired kinds of integrative frameworks as upper and lower bounds in the appropriate ordering.

:* Another integration heuristic is the ''mosaic'' metaphor, also called the ''stereoscopic'' or ''inverse projection'' paradigm.  This technique has been illustrated especially well by the methods used throughout this section to analyze the three-dimensional structures of sign relations.  In fact, the picture of any sign relation offers a paradigm in microcosm for the macroscopic work of integration, showing how reductive aspects of structure can be projected from a shared but irreducible reality.  The extent to which the ''full-bodied'' structure of a triadic sign relation can be reconstructed from its dyadic projections, although a limited extent in general, presents a near perfect epitome of the larger task in this situation, namely, to find an integrated framework that embodies the diverse facets of reality severally observed from inside the individual frameworks.  Acting as gnomonic recipes for the higher order processes they limn and delimit, sign relations keep before the mind the ways in which a higher dimensional structure determines its fragmentary aspects but is not in general determined by them.

:* Another integration heuristic is the ''mosaic'' metaphor, also called the ''stereoscopic'' or ''inverse projection'' paradigm.  This technique has been illustrated especially well by the methods used throughout this section to analyze the three-dimensional structures of sign relations.  In fact, the picture of any sign relation offers a paradigm in microcosm for the macroscopic work of integration, showing how reductive aspects of structure can be projected from a shared but irreducible reality.  The extent to which the ''full-bodied'' structure of a triadic sign relation can be reconstructed from its dyadic projections, although a limited extent in general, presents a near perfect epitome of the larger task in this situation, namely, to find an integrated framework that embodies the diverse facets of reality severally observed from inside the individual frameworks.  Acting as gnomonic recipes for the higher order processes they limn and delimit, sign relations keep before the mind the ways in which a higher dimensional structure determines its fragmentary aspects but is not in general determined by them.