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On the way to integrating dynamic and symbolic approaches to systems there is one important watershed that has to be crossed and recrossed, time and time again.  This is a form of continental divide that decides between two alternative and exclusive ''modes of description'' (MODs) or ''categories of representation'' (CORs), and marks a writer's moment to moment selection of ''extensional representation'' (ER), on the one side, or ''intensional representation'' (IR), on the other.  To apply the theme, in this section I address the task of building conceptual bridges between two different ways of describing or representing sign relations:  (1) the ER that describes a sign relation in terms of its instances, and (2) the IR that describes a sign relation in terms of its properties.

On the way to integrating dynamic and symbolic approaches to systems there is one important watershed that has to be crossed and recrossed, time and time again.  This is a form of continental divide that decides between two alternative and exclusive ''modes of description'' (MODs) or ''categories of representation'' (CORs), and marks a writer's moment to moment selection of ''extensional representation'' (ER), on the one side, or ''intensional representation'' (IR), on the other.  To apply the theme, in this section I address the task of building conceptual bridges between two different ways of describing or representing sign relations:  (1) the ER that describes a sign relation in terms of its instances, and (2) the IR that describes a sign relation in terms of its properties.

It is best to begin the work of bridge-building on informal grounds, using concrete examples of ERs and IRs and taking advantage of basic ideas about their relationship that are readily available to every reader.  After the overall scheme of construction is roughed out in this fashion, I plan to revisit the concept of representation in a more formal style, examining the balance of its in- and ex- “tensions” with a sharper eye to the relevant details and a greater chance of compassing the depths of form that arise between the two points of view.

It is best to begin the work of bridge building on informal grounds, using concrete examples of ERs and IRs and taking advantage of basic ideas about their relationship that are readily available to every reader.  After the overall scheme of construction is roughed out in this fashion, I plan to revisit the concept of representation in a more formal style, examining the balance of its in and ex "tensions" with a sharper eye to the relevant details and a greater chance of compassing the depths of form that arise between the two points of view.

The task of building this bridge is not trivial.  In places, the basic elements of construction are yet to be forged from the available stocks, in others, the needed materials still lie in their ores, awaiting a suitable process to extract them, refine them, and bring them to a usable state.  Due to the difficulties of this task and the length of time it will take to carry it out, I think it is advisable to establish two points of reference before setting to work.

The task of building this bridge is not trivial.  In places, the basic elements of construction are yet to be forged from the available stocks, in others, the needed materials still lie in their ores, awaiting a suitable process to extract them, refine them, and bring them to a usable state.  Due to the difficulties of this task and the length of time it will take to carry it out, I think it is advisable to establish two points of reference before setting to work.

1. As a way of providing sufficient motivation for the effort, I will indicate the importance of this bridge with respect to the aims of inquiry in general.

# As a way of providing sufficient motivation for the effort, I will indicate the importance of this bridge with respect to the aims of inquiry in general.

 

# As a guard against a host of precipitous shortcuts that have been tried in the past, I will point out as clearly as possible a few of the obstacles that need to be surmounted.  Once their structures are rightly understood, the obstructions that lie in the path of this bridge can be chalked up to experience with the reality of its construction, turned to use as stepping stones in the advance of its ultimate course, and given a fitting place in the progress of instruction.

2. As a guard against a host of precipitous shortcuts that have been tried in the past, I will point out as clearly as possible a few of the obstacles that need to be surmounted.  Once their structures are rightly understood, the obstructions that lie in the path of this bridge can be chalked up to experience with the reality of its construction, turned to use as stepping stones in the advance of its ultimate course, and given a fitting place in the progress of instruction.

Terms referring to properties of sign relations make it possible to formulate propositions about sign relations, either as occasioned by a clear and present example or in abstraction from any concrete instance.  In turn, this makes it possible to carry on chains of reasoning about the properties of sign relations in detachment from the presence of actual cases that may or may not come to mind in the immediate present.  This mode of abstraction, invoking the kind of IR that is involved in mediating every form of propositional reasoning, gives logic its wings and can lead to theories of great conceptual power, but it incurs the risk of leading reasoning astray into realms of irreferent pretension, eventually degenerating into spurious sounds that signify nothing.

Terms referring to properties of sign relations make it possible to formulate propositions about sign relations, either as occasioned by a clear and present example or in abstraction from any concrete instance.  In turn, this makes it possible to carry on chains of reasoning about the properties of sign relations in detachment from the presence of actual cases that may or may not come to mind in the immediate present.  This mode of abstraction, invoking the kind of IR that is involved in mediating every form of propositional reasoning, gives logic its wings and can lead to theories of great conceptual power, but it incurs the risk of leading reasoning astray into realms of irreferent pretension, eventually degenerating into spurious sounds that signify nothing.

It is only by means of an IR that logical reasoning, properly speaking, is able to begin.  The stringency of this precept, if it is taken too strictly as a starting condition and applied solely in absolute terms, would be correctly perceived as demanding a provision that is jarring to every brand of good sense.  But it was never meant to be taken this severely.  In practice, the starkness of this tentative stipulation is moderated by the degree of fuzziness that still continues to reside in the interpretive distinction between ERs and IRs.

It is only by means of an IR that logical reasoning, properly speaking, is able to begin.  The stringency of this precept, if it is taken too strictly as a starting condition and applied solely in absolute terms, would be correctly perceived as demanding a provision that is jarring to every brand of good sense.  But it was never meant to be taken this severely.  In practice, the starkness of this tentative stipulation is moderated by the degree of fuzziness that still continues to reside in the interpretive distinction between ERs and IRs.

The alleged distinction between ERs and IRs, when it is projected to have a global application, remains arbitrary so long as it is taken at that level of abstraction, and it comes to take on the semblance of a definition only in relation to the interpretive conduct of a particular arbiter.  No representation in actual practice is purely of one sort or the other, nor fails to have the characters of both types as a part of its mix.  In other words, extensions and intensions are only abstractions from a profounder "tension" that is logically prior but functionally intermediate to them both, and every representation of any use will have its aspect of extensional particularity permeated by its aspect of intensional generality.

The alleged distinction between ERs and IRs, when it is projected to have a global application, remains arbitrary so long as it is taken at that level of abstraction, and it comes to take on the semblance of a definition only in relation to the interpretive conduct of a particular arbiter.  No representation in actual practice is purely of one sort or the other, nor fails to have the characters of both types as a part of its mix.  In other words, extensions and intensions are only abstractions from a profounder “tension” that is logically prior but functionally intermediate to them both, and every representation of any use will have its aspect of extensional particularity permeated by its aspect of intensional generality.

Toward the end of this construction I hope it will become clear that this bridge is a project intermediate in scale between the elementary linkage of signs to interpretants that is built into every sign relation and all the courses of conduct that go to span the gulf and build communication between vastly different systems of interpretation.  In the meantime, there are strong analogies that make the architecture of this bridge parallel in form to the structures existing at both ends of the scale, shaping it in congruence with patterns of action that reside at both the micro and the macro levels.  Observing these similarities and their lines of potential use as they arise will serve to guide the current work.

Toward the end of this construction I hope it will become clear that this bridge is a project intermediate in scale between the elementary linkage of signs to interpretants that is built into every sign relation and all the courses of conduct that go to span the gulf and build communication between vastly different systems of interpretation.  In the meantime, there are strong analogies that make the architecture of this bridge parallel in form to the structures existing at both ends of the scale, shaping it in congruence with patterns of action that reside at both the micro and the macro levels.  Observing these similarities and their lines of potential use as they arise will serve to guide the current work.

A sign relation is a complex object and its representations, insofar as they faithfully preserve its structure, are complex signs.  Accordingly, the problems of translating between ERs and IRs of sign relations, of detecting when representations alleged to be of sign relations do indeed represent objects of the specified character, and of recognizing whether different representations do or do not represent the same sign relation as their common object — these are the familiar questions that would be asked of the signs and interpretants in a simple sign relation, but this time asked at a higher level, in regard to the complex signs and complex interpretants that are posed by the different stripes of representation.  At the same time, it should be obvious that these are also the natural questions to be faced in building a bridge between representations.

A sign relation is a complex object and its representations, insofar as they faithfully preserve its structure, are complex signs.  Accordingly, the problems of translating between ERs and IRs of sign relations, of detecting when representations alleged to be of sign relations do indeed represent objects of the specified character, and of recognizing whether different representations do or do not represent the same sign relation as their common object — these are the familiar questions that would be asked of the signs and interpretants in a simple sign relation, but this time asked at a higher level, in regard to the complex signs and complex interpretants that are posed by the different stripes of representation.  At the same time, it should be obvious that these are also the natural questions to be faced in building a bridge between representations.

How many different sorts of entities are conceivably involved in translating between ERs and IRs of sign relations?  To address this question it helps to introduce a system of type notations that can be used to keep track of the various sorts of things, or the varieties of objects of thought, that are generated in the process of answering it.  Table 47.1 summarizes the basic types of things that are needed in this pursuit, while the rest can be derived by constructions of the form "X of Y", notated "X(Y)" or just "XY", for any basic types X and Y.  The constructed types of things involved in the ERs and IRs of sign relations are listed in Tables 47.2 and 47.3, respectively.

How many different sorts of entities are conceivably involved in translating between ERs and IRs of sign relations?  To address this question it helps to introduce a system of type notations that can be used to keep track of the various sorts of things, or the varieties of objects of thought, that are generated in the process of answering it.  Table 47.1 summarizes the basic types of things that are needed in this pursuit, while the rest can be derived by constructions of the form "X of Y", notated "X(Y)" or just "XY", for any basic types X and Y.  The constructed types of things involved in the ERs and IRs of sign relations are listed in Tables 47.2 and 47.3, respectively.

Table 47.1  Basic Types for ERs & IRs of Sign Relations

Table 47.1  Basic Types for ERs & IRs of Sign Relations