Changes

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 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.

1. 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.

2. 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.

a. 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.

:* 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.

b. 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.

To express the nature of this integration task in logical terms, it combines elements of both proof theory and model theory, interweaving:  (1) A phase that develops theories about the symbolic competence or ''knowledge'' of intelligent agents, using abstract formal systems to represent the theories and phenomenological data to constrain them;  (2) A phase that seeks concrete models of these theories, looking to the kinds of mathematical structure that have a dynamic or system-theoretic interpretation, and compiling the constraints that a recursive conceptual analysis imposes on the ultimate elements of their construction.

To express the nature of this integration task in logical terms, it combines elements of both proof theory and model theory, interweaving:  (1) A phase that develops theories about the symbolic competence or ''knowledge'' of intelligent agents, using abstract formal systems to represent the theories and phenomenological data to constrain them;  (2) A phase that seeks concrete models of these theories, looking to the kinds of mathematical structure that have a dynamic or system-theoretic interpretation, and compiling the constraints that a recursive conceptual analysis imposes on the ultimate elements of their construction.

The set of sign relations {''A'', ''B''} is an example of an extremely simple formal system, encapsulating aspects of the symbolic competence and the pragmatic performance that might be exhibited by potentially intelligent interpretive agents, however abstractly and partially given at this stage of description.  The symbols of a formal system like {''A'', ''B''} can be held subject to abstract constraints, having their meanings in relation to each other determined by definitions and axioms (for example, the laws defining an equivalence relation), making it possible to manipulate the resulting information by means of the inference rules in a proof system.  This illustrates the ''proof-theoretic'' aspect of a symbol system.

The set of sign relations {A, B} is an example of an extremely simple formal system, encapsulating aspects of the symbolic competence and the pragmatic performance that might be exhibited by potentially intelligent interpretive agents, however abstractly and partially given at this stage of description.  The symbols of a formal system like {A, B} can be held subject to abstract constraints, having their meanings in relation to each other determined by definitions and axioms (for example, the laws defining an equivalence relation), making it possible to manipulate the resulting information by means of the inference rules in a proof system.  This illustrates the ''proof-theoretic'' aspect of a symbol system.

Suppose that a formal system like {''A'', ''B''} is initially approached from a theoretical direction, in other words, by listing the abstract properties one thinks it ought to have.  Then the existence of an extensional model that satisfies these constraints, as exhibited by the sign relation tables, demonstrates that one's theoretical description is logically consistent, even if the models that first come to mind are still a bit too abstractly symbolic and do not have all the dynamic concreteness that is demanded of system-theoretic interpretations.  This amounts to the other side of the ledger, the ''model-theoretic'' aspect of a symbol system, at least insofar as the present account has dealt with it.

Suppose that a formal system like {A, B} is initially approached from a theoretical direction, in other words, by listing the abstract properties one thinks it ought to have.  Then the existence of an extensional model that satisfies these constraints, as exhibited by the sign relation tables, demonstrates that one's theoretical description is logically consistent, even if the models that first come to mind are still a bit too abstractly symbolic and do not have all the dynamic concreteness that is demanded of system-theoretic interpretations.  This amounts to the other side of the ledger, the ''model-theoretic'' aspect of a symbol system, at least insofar as the present account has dealt with it.

More is required of the modeler, however, in order to find the desired kinds of system-theoretic models (for example, state transition systems), and this brings the search for realizations of formal systems down to the toughest part of the exercise.  Some of the problems that emerge were highlighted in the example of ''A'' and ''B''.  Although it is ordinarily possible to construct state transition systems in which the states of interpreters correspond relatively directly to the acceptations of the primitive signs given, the conflict of interpretations that develops between different interpreters from these prima facie implementations is a sign that there is something superficial about this approach.

The integration of model-theoretic and proof-theoretic aspects of ''physical symbol systems'', besides being closely analogous to the integration of denotative and connotative aspects of sign relations, is also relevant to the job of integrating dynamic and symbolic frameworks for intelligent systems.  This is so because the search for dynamic realizations of symbol systems is only a more pointed exercise in model theory, where the mathematical materials made available for modeling are further constrained by system-theoretic principles, like being able to say what the states are and how the transitions are determined.

The integration of model-theoretic and proof-theoretic aspects of ''physical symbol systems'', besides being closely analogous to the integration of denotative and connotative aspects of sign relations, is also relevant to the job of integrating dynamic and symbolic frameworks for intelligent systems.  This is so because the search for dynamic realizations of symbol systems is only a more pointed exercise in model theory, where the mathematical materials made available for modeling are further constrained by system-theoretic principles, like being able to say what the states are and how the transitions are determined.