Changes

Expressed in abstract fashion, the injunction of a reflective capacity and the injunction of a capacity limitation are recognized to impinge on each other in a way that brings to light a number of additional issues.  Expressed in more concrete detail, the experiential instances that lead to the formation of these two points in the first place, as organizing poles of topics explicitly noticed, and that continue to surround their particular arrangements, …

Expressed in abstract fashion, the injunction of a reflective capacity and the injunction of a capacity limitation are recognized to impinge on each other in a way that brings to light a number of additional issues.  Expressed in more concrete detail, the experiential instances that lead to the formation of these two points in the first place, as organizing poles of topics explicitly noticed, and that continue to surround their particular arrangements, …

'''Point 11.'''     Computational models of intelligent agents are limited to the consideration of “finitely informed constructions and computations”, or as I more affectionately call them, “finitely informed creatures” (FICs).

'''Point 11.'''     Computational models of intelligent agents are limited to the consideration of “finitely informed constructions and computations”, or as I more affectionately call them, ''finitely informed creatures'' (FICs).

This point arises as a specialization of the point about capacity limits, where the discussion is restricted to the kinds of interpretive agents and the models of interpretive faculties that are available in a computational framework.

This point arises as a specialization of the point about capacity limits, where the discussion is restricted to the kinds of interpretive agents and the models of interpretive faculties that are available in a computational framework.

As a minimum requirement, a capacity for reflection implies an ability to generate names for the elements, processes, and principles of thought.  Assuming the tenet of pragmatism that all thought takes place in signs, this is tantamount to having signs for signs, signs for sign processes, and signs for sign relations.  Further, each higher order sign that is generated in a process of reflection is required to take its place and to find its meaning within a correspondingly higher order sign relation.

As a minimum requirement, a capacity for reflection implies an ability to generate names for the elements, processes, and principles of thought.  Assuming the tenet of pragmatism that all thought takes place in signs, this is tantamount to having signs for signs, signs for sign processes, and signs for sign relations.  Further, each higher order sign that is generated in a process of reflection is required to take its place and to find its meaning within a correspondingly higher order sign relation.

In this connection, the designation “higher order” (HO) can be used as a generic adjective to describe a sign of any object whose nature it is to involve signs as a part of its being.  The use of this adjective is subject to extension in natural ways to describe not only entire classes of signs but also the kinds of sign relations that involve them.

In this connection, the designation ''higher order'' (HO) can be used as a generic adjective to describe a sign of any object whose nature it is to involve signs as a part of its being.  The use of this adjective is subject to extension in natural ways to describe not only entire classes of signs but also the kinds of sign relations that involve them.

In order to reflect on signs themselves, it is necessary to have signs for signs, a necessary supply of which can be generated by quotation.  But reflection on sign processes requires a much larger supply of signs.  Initially, it requires a HO sign for each sign transition that actually occurs, that is, a name for each ordered pair of signs that is observed.  Eventually, it requires a HO sign for each sign sequence that actually appears in experience, that is, a name for each <math>k\!</math>-tuple of signs seen.  And reflection on sign relations requires an even larger stock of signs.  It requires, initially, a HO sign for each sign transaction of the form <math>(o, s, i)\!</math> that is observed in experience and, ultimately, a HO sign for each sign relation that is encountered in experience or contemplated in a hypothetical situation.

In order to reflect on signs themselves, it is necessary to have signs for signs, a necessary supply of which can be generated by quotation.  But reflection on sign processes requires a much larger supply of signs.  Initially, it requires a HO sign for each sign transition that actually occurs, that is, a name for each ordered pair of signs that is observed.  Eventually, it requires a HO sign for each sign sequence that actually appears in experience, that is, a name for each <math>k\!</math>-tuple of signs seen.  And reflection on sign relations requires an even larger stock of signs.  It requires, initially, a HO sign for each sign transaction of the form <math>(o, s, i)\!</math> that is observed in experience and, ultimately, a HO sign for each sign relation that is encountered in experience or contemplated in a hypothetical situation.

The combinatorial explosion engendered by reflection impinges on the capacity limitations of a FIC with such an impact that neither the standpoints of &ldquo;naive empiricism&rdquo; or &ldquo;naive intuitionism&rdquo; can continue to support viable forms of inquiry.

The combinatorial explosion engendered by reflection impinges on the capacity limitations of a FIC with such an impact that neither the standpoints of &ldquo;naive empiricism&rdquo; or &ldquo;naive intuitionism&rdquo; can continue to support viable forms of inquiry.

This is what makes the mediation of a &ldquo;higher order hypothesis&rdquo; (HOH), a hypothesis about the qualifications of a hypothesis, or a hypothesis about what can count as a hypothesis, so essential to the life of a FIC.

This is what makes the mediation of a ''higher order hypothesis'' (HOH), a hypothesis about the qualifications of a hypothesis, or a hypothesis about what can count as a hypothesis, so essential to the life of a FIC.

The process of generating signs that refer to things already signs is incited by a syntactic operation that is commonly called a &ldquo;quotation&rdquo;.  Strictly speaking, the descriptive term &ldquo;quotation&rdquo; refers to generic class of syntactic functions, each of which maps one order of signs into the next higher order of signs.  A proper form of quotation function is required to map signs in a one to one or &ldquo;injective&rdquo; fashion, and thus associates each element of its source domain with a HO sign that denotes it and it alone.  In short, a quotation produces a unique &ldquo;name&rdquo; or a distinctive &ldquo;number&rdquo; to index each piece its source material.

The process of generating signs that refer to things already signs is incited by a syntactic operation that is commonly called a &ldquo;quotation&rdquo;.  Strictly speaking, the descriptive term &ldquo;quotation&rdquo; refers to generic class of syntactic functions, each of which maps one order of signs into the next higher order of signs.  A proper form of quotation function is required to map signs in a one to one or &ldquo;injective&rdquo; fashion, and thus associates each element of its source domain with a HO sign that denotes it and it alone.  In short, a quotation produces a unique &ldquo;name&rdquo; or a distinctive &ldquo;number&rdquo; to index each piece its source material.

But a level of genuine reflection on sign processes and sign relations exceeds the generative capacity of mere quotation.

But a level of genuine reflection on sign processes and sign relations exceeds the generative capacity of mere quotation.

'''Point 13.''' &nbsp;&nbsp;&nbsp; A &ldquo;finitely informed creature&rdquo; (FIC), if it is reflective up to the point that it reflects on its own nature as such, crosses a singular threshold of reflection, whereupon it not only obeys its own capacity limitations, as it instinctively and necessarily must, but also observes and reflects on their character.

'''Point 13.''' &nbsp;&nbsp;&nbsp; A ''finitely informed creature'' (FIC), if it is reflective up to the point that it reflects on its own nature as such, crosses a singular threshold of reflection, whereupon it not only obeys its own capacity limitations, as it instinctively and necessarily must, but also observes and reflects on their character.

'''Point 14.''' &nbsp;&nbsp;&nbsp; Higher order sign relations tax the pragmatic resources of an interpretive agent to such a severe extent that they impinge on the practical limits of its representational capacity and computational ability.

'''Point 14.''' &nbsp;&nbsp;&nbsp; Higher order sign relations tax the pragmatic resources of an interpretive agent to such a severe extent that they impinge on the practical limits of its representational capacity and computational ability.

The acuteness of this point, if taken in its full generality, brings the discussion to an appreciation of the next point.

The acuteness of this point, if taken in its full generality, brings the discussion to an appreciation of the next point.

'''Point 15.''' &nbsp;&nbsp;&nbsp; Pragmatic incapacities have practical consequences.

Point 15. Pragmatic incapacities have practical consequences.

A limitation of an agent's capacity along a pragmatic dimension  

A limitation of an agent's capacity along a pragmatic dimension &hellip;

Point 16. Reflection involves a sense of context, and this involves a notion of community.

'''Point 16.''' &nbsp;&nbsp;&nbsp; Reflection involves a sense of context, and this involves a notion of community.

The capacity for reflection involves an ability to view one's own conduct in a context of other conceivable actions, and this implies viewing one's choices not just in a context of other possible actions for oneself, but also in a context of other conceivable actors, ones that are comparable to but characteristically distinct from oneself.

The capacity for reflection involves an ability to view one's own conduct in a context of other conceivable actions, and this implies viewing one's choices not just in a context of other possible actions for oneself, but also in a context of other conceivable actors, ones that are comparable to but characteristically distinct from oneself.

Remarkably, the capacities for criticism and creativity that are needed for reflection spring from a common source, namely, from the sense of possibility that can regard every process as occurring within a context of alternative actions.  An inquiry, to be intelligent and innovative, critical and creative, has to be reflective, with the capacity to regard itself as one inquiry among others.  In this "regard" is implied the ability of an interpretive agent to reference and to evaluate its own progress in inquiry, to observe it more dispassionately in subsequent reflections as the conduct of one inquirer among a host of many others, choosing one way of doing inquiry from the array of others conceivable.  Accordingly, solely out of these reflections is developed the notion of a virtual or a potential community, quite independently of the empirical matter of how any actual or present community is constituted or realized at the moment.

Remarkably, the capacities for criticism and creativity that are needed for reflection spring from a common source, namely, from the sense of possibility that can regard every process as occurring within a context of alternative actions.  An inquiry, to be intelligent and innovative, critical and creative, has to be reflective, with the capacity to regard itself as one inquiry among others.  In this &ldquo;regard&rdquo; is implied the ability of an interpretive agent to reference and to evaluate its own progress in inquiry, to observe it more dispassionately in subsequent reflections as the conduct of one inquirer among a host of many others, choosing one way of doing inquiry from the array of others conceivable.  Accordingly, solely out of these reflections is developed the notion of a virtual or a potential community, quite independently of the empirical matter of how any actual or present community is constituted or realized at the moment.

Point 17. Recalling the proposed application "y.y" once again, it needs to be pointed out that an action cannot really act on an action, but only on its signs.

'''Point 17.''' &nbsp;&nbsp;&nbsp; Recalling the proposed application <math>{}^{\backprime\backprime}y \cdot y{}^{\prime\prime}\!</math> once again, it needs to be pointed out that an action cannot really act on an action, but only on its signs.

In technical terms, an action can only act on certain signs that exist in association with another or the same action, signs that are often called the "images" of the action to be affected.

In technical terms, an action can act only on certain signs that exist in association with another or the same action, signs that are often called the &ldquo;images&rdquo; of the action to be affected.

Point 18. The images, depictions, or descriptions of conduct generated by reflection, as records of experience, can be accumulated into theories and compiled into models of the corresponding conduct.

'''Point 18.''' &nbsp;&nbsp;&nbsp; The images, depictions, or descriptions of conduct generated by reflection, as records of experience, can be accumulated into theories and compiled into models of the corresponding conduct.

The collected images of conduct serve as "codes", in both the senses of a descriptive datum or a prescriptive emblem.  Both types of code fall subject to being tested in future experience, for their trustworthiness as bodies of observation or recommendation, respectively, with regard to their objects or intentions, as the case may be.  Reviving an old term with just this spectrum of meanings, an encyclopedic corpus of received code can be called a "pandect".

The collected images of conduct serve as &ldquo;codes&rdquo;, in both the senses of a descriptive datum and a prescriptive emblem.  Both types of code fall subject to being tested in future experience, for their trustworthiness as bodies of observation or recommendation, respectively, with regard to their objects or intentions, as the case may be.  Reviving an old term with just this spectrum of meanings, an encyclopedic corpus of received code can be called a &ldquo;pandect&rdquo;.

Point 19. The power of reflection involves a risk of distortion.

'''Point 19.''' &nbsp;&nbsp;&nbsp; The power of reflection involves a risk of distortion.

The quality that separates reflection from introspection is its admission of fallibility.  Although it is often troublesome to undo its distortions, the very fact that it can be in error, can miss its mark, or is by nature defeasible and falsifiable is exactly what makes a reflective image useful as a hypothesis, as an approximation to an infinitely subtler reality and as a simplification of an infinitely more complex and detailed truth, and yet one that retains a sufficient measure of realistic truth to be useful in the meaner times of a mortal existence.

The quality that separates reflection from introspection is its admission of fallibility.  Although it is often troublesome to undo its distortions, the very fact that it can be in error, can miss its mark, or is by nature defeasible and falsifiable is exactly what makes a reflective image useful as a hypothesis, as an approximation to an infinitely subtler reality and as a simplification of an infinitely more complex and detailed truth, and yet one that retains a sufficient measure of realistic truth to be useful in the meaner times of a mortal existence.

The capacity of reflection to create an image in description of an action incurs a liability toward corruption in the image, both before and after its initial form is cast.  The way that an image produced by reflection is designed to act as a sign of the action or permitted to behave as a code of the conduct is bound to be an imperfect device, due in large part to limitations of the media and affected in unaccounted measures by flaws in the mechanisms of reflection.  How these distortions can be undone with repeated reflections, and how this clarification can be achieved without waylaying the conduct that reflection is meant to describe and control, is one of the main technical problems for empirical inquiry.

The capacity of reflection to create an image in description of an action incurs a liability toward corruption in the image, both before and after its initial form is cast.  The way that an image produced by reflection is designed to act as a sign of the action or permitted to behave as a code of the conduct is bound to be an imperfect device, due in large part to limitations of the media and affected in unaccounted measures by flaws in the mechanisms of reflection.  How these distortions can be undone with repeated reflections, and how this clarification can be achieved without waylaying the conduct that reflection is meant to describe and control, is one of the main technical problems for empirical inquiry.

The power of reflection involves a capacity to project false images and thereby to generate distorting perspectives.  The possibilities include: (1) views in which small things seem large and large things seem small, (2) value systems in which the apparent imports of things are reversed in relation to their actual imports, (3) forms of representation in which the places of contents interior and exterior to the surfaces of reflection are exchanged, reversed, or transposed.

The power of reflection involves a capacity to project false images and thereby to generate distorting perspectives.  The possibilities include the following:

 

# Views in which small things seem large and large things seem small,

# Value systems in which the apparent imports of things are reversed in relation to their actual imports,

# Forms of representation in which the places of contents interior and exterior to the surfaces of reflection are exchanged, reversed, or transposed.

There is a positive spin on the fallibility of the reflective imagination.  In terms of its practical bearings on continued experience, the fallibility of reflection involves an ability, not only to make its errors over again in the form of their consequences for experience, but eventually to find its faults recognized as such in a finite order of subsequent reflections.

There is a positive spin on the fallibility of the reflective imagination.  In terms of its practical bearings on continued experience, the fallibility of reflection involves an ability, not only to make its errors over again in the form of their consequences for experience, but eventually to find its faults recognized as such in a finite order of subsequent reflections.

In sum, the feature of reflection that seems to render it most defective, its fallibility, which involves its ability to be recognized as false in the future of reflection, is the main trait that allows it to play a part in the staging of empirical inquiry.

In sum, the feature of reflection that seems to render it most defective, its fallibility, which involves its ability to be recognized as false in the future of reflection, is the main trait that allows it to play a part in the staging of empirical inquiry.

Point 20. The capacity for reflection involves an ability to question one's working assumptions, especially when there is occasion to suspect that they are no longer working as well as they once did.

'''Point 20.''' &nbsp;&nbsp;&nbsp; The capacity for reflection involves an ability to question one's working assumptions, especially when there is occasion to suspect that they are no longer working as well as they once did.

Whenever one operates on a particular assumption, whether knowingly or otherwise, one tends to see certain patterns of features in perception and to miss others, but until one reflects on the operative assumption, makes it explicit, considers its alternatives, and thereby is empowered to put it in question, then one lacks a fundamental insight into how these figures are generated in perception, failing to see how one's own sensitivities and dispositions are biased toward allowing them to arise.

Whenever one operates on a particular assumption, whether knowingly or otherwise, one tends to see certain patterns of features in perception and to miss others, but until one reflects on the operative assumption, makes it explicit, considers its alternatives, and thereby is empowered to put it in question, then one lacks a fundamental insight into how these figures are generated in perception, failing to see how one's own sensitivities and dispositions are biased toward allowing them to arise.

To act on the basis of a certain assumption, as though the assumption were already certain, is to act in abstraction of the total situation.  When a feature or a pattern of features is abstracted from a situation, there is always something left behind, the grounds from which a feature or pattern originally rises and against which it subsequently becomes a figure of importance to the moment.  There needs to be a name for this actively recessed background, suggesting the potential complement of alternative features and elliptic patterns that it contains within its share of the total configuration.  But it is important to remember that this is not just the ground that comes to complement a figure in the present situation but the ground that is dynamically pushed into the past so that the current configuration can come to be formed as it is.

To act on the basis of a certain assumption, as though the assumption were already certain, is to act in abstraction of the total situation.  When a feature or a pattern of features is abstracted from a situation, there is always something left behind, the grounds from which a feature or pattern originally rises and against which it subsequently becomes a figure of importance to the moment.  There needs to be a name for this actively recessed background, suggesting the potential complement of alternative features and elliptic patterns that it contains within its share of the total configuration.  But it is important to remember that this is not just the ground that comes to complement a figure in the present situation but the ground that is dynamically pushed into the past so that the current configuration can come to be formed as it is.

Exactly what it is that abstraction leaves out is something that seems currently to escape description, failing to be pinned down by any name I can think of in common or in technical use.  The abstraction itself, as the process whose result is signaled by its " ionized" designation, acts toward the end of constellating a figure that is relevant to the moment.  But the concurrent and complementary process that results in a residual plurality is one that lacks a common denomination.  For the sake of a harmonious balance between the syntactic expressions of these actions, it would be good if the process that recesses the background were also to be assigned an "-ionized" term.

Exactly what it is that abstraction leaves out is something that seems currently to escape description, failing to be pinned down by any name I can think of in common or in technical use.  The abstraction itself, as the process whose result is signaled by its &ldquo;-ionized&rdquo; designation, acts toward the end of constellating a figure that is relevant to the moment.  But the concurrent and complementary process that results in a residual plurality is one that lacks a common denomination.  For the sake of a harmonious balance between the syntactic expressions of these actions, it would be good if the process that recesses the background were also to be assigned an &ldquo;-ionized&rdquo; term.

Point 21. There appears to be a large variety of ways that the process of reflection can go wrong.

'''Point 21.''' &nbsp;&nbsp;&nbsp; There appears to be a large variety of ways that the process of reflection can go wrong.

One of the jobs of an inquiry into inquiry is to classify this variety, compassing the diversity of incidental errors and systematic distortions that are likely to occur in reflection.

One of the jobs of an inquiry into inquiry is to classify this variety, compassing the diversity of incidental errors and systematic distortions that are likely to occur in reflection.

One dimension of variation that runs through this variety of pathologies characterizes the degree of fixity or persistence that is invested in the images of conduct.  The range of variation conceivable can be suggested by marking the prototypical figures that fall at its two extremes.

One dimension of variation that runs through this variety of pathologies characterizes the degree of fixity or persistence that is invested in the images of conduct.  The range of variation conceivable can be suggested by marking the prototypical figures that fall at its two extremes.

1. At one extreme there is the character of a stolid fixity that can be adumbrated in terms of a mythological or a psychological archetype, appearing to be ruled by the image of Narcissus.  This identifies the kind of regressive and fixed ideation that leads one to seize on a single image of one's characteristic conduct, to fix it in mind as a static ideal, and to resist at all costs letting go of its hold on the imagination.

# At one extreme there is the character of a stolid fixity that can be adumbrated in terms of a mythological or a psychological archetype, appearing to be ruled by the image of Narcissus.  This identifies the kind of regressive and fixed ideation that leads one to seize on a single image of one's characteristic conduct, to fix it in mind as a static ideal, and to resist at all costs letting go of its hold on the imagination.

# At the other extreme there is the character of an insipid volatility that corresponds to the complementary archetype, answering a bit dully to the name of Echo.  This identifies the kind of digressive and fluid skepticism that leaves one in a permanently fugitive state.  Paradoxically enough, it is typically pursuant to a precocious but transient condition of dedication, one that marks its earliest forms of conscious recognition.  If it follows the usual course, it can start from being too soon fixed on the initial object of attention or the original ideal of conduct, but it eventually falls into a compensatory, defensive, and reactionary pattern.  Soon it withers away into little more than the afterimage of a reflexive reaction, an account due to the ensuing trauma of disappointment, and a record commemorating a final disillusionment with its distant illusions.  Whatever the initial case, the issue is such that it makes one reluctant to commit to any future image of behavior or ideal of conduct, at least, readily enough to try its utility in action or steadily enough to test it out in practice.  Instead, it disposes one merely to keep repeating in an automatic, derivative, imitative, involuntary, reflexive, stereotypical, and tautologous manner any impression of the outside world that seems to inform the moment.

2. At the other extreme there is the character of an insipid volatility that corresponds to the complementary archetype, answering a bit dully to the name of Echo.  This identifies the kind of digressive and fluid skepticism that leaves one in a permanently fugitive state.  Paradoxically enough, it is typically pursuant to a precocious but transient condition of dedication, one that marks its earliest forms of conscious recognition.  If it follows the usual course, it can start from being too soon fixed on the initial object of attention or the original ideal of conduct, but it eventually falls into a compensatory, defensive, and reactionary pattern.  Soon it withers away into little more than the afterimage of a reflexive reaction, an account due to the ensuing trauma of disappointment, and a record commemorating a final disillusionment with its distant illusions.  Whatever the initial case, the issue is such that it makes one reluctant to commit to any future image of behavior or ideal of conduct, at least, readily enough to try its utility in action or steadily enough to test it out in practice.  Instead, it disposes one merely to keep repeating in an automatic, derivative, imitative, involuntary, reflexive, stereotypical, and tautologous manner any impression of the outside world that seems to inform the moment.

'''Point 22.''' &nbsp;&nbsp;&nbsp; Intelligent inquiry involves inquiry into inquiry.

Point 22. Intelligent inquiry involves inquiry into inquiry.

In view of the previous points, it appears that intelligent inquiry is necessarily reflective inquiry, seeing itself as one inquiry among others and evaluating its own progress in a setting of comparable alternatives.  This means that intelligent inquiry into any subject whatever is forced to embody a component of self-study, of inquiry into inquiry. Thus, the general capacity for successfully conducting inquiry both relies on and bears on a specialized kernel of talent for doing inquiry into inquiry.

In view of the previous points, it appears that intelligent inquiry is necessarily reflective inquiry, seeing itself as one inquiry among others and evaluating its own progress in a setting of comparable alternatives. This means that intelligent inquiry into any subject whatever is forced to embody a component of self study, of inquiry into inquiry.  Thus, the general capacity for successfully conducting inquiry both relies on and bears on a specialized kernel of talent for doing inquiry into inquiry.

'''Point 23.''' &nbsp;&nbsp;&nbsp; Inquiry into inquiry involves integrating independent inquiries.

Point 23.

One way of gathering data that is relevant to the task of self-study is to conduct a multiplicity of independent studies, each of which tries to track what the others are most likely to miss.  This requires a monitor, a moderator, or a non-parallel but mutually concurred upon medium of comparison for overseeing and reconciling the mosaic of disparate and scattered results that can derive from a multitude of isolated studies.

Finally, this project of self study demands a comprehensive method for integrating the divergent and fragmentary imports of individual studies into a unified form, constituting the resultant bearing that they are meant to have on the main inquiry.  Toward this end, it is a frequent stratagem of intelligent inquiry to maintain a form of &ldquo;outrigger&rdquo;, an attached but esthetically distant study that serves to steady the main course of study by embodying a full program of peripheral perspectives and exploratory investigations.  In this way, the global aims of even a specialized inquiry can be achieved more robustly by keeping a studied eye out for its own systematic alternatives, often involving precisely those &ldquo;outliers&rdquo; that are ignored by the more focal styles of inquiry.

 

Finally, this project of self study demands a comprehensive method for integrating the divergent and fragmentary imports of individual studies into a unified form, constituting the resultant bearing that they are meant to have on the main inquiry.  Toward this end, it is a frequent stratagem of intelligent inquiry to maintain a form of "outrigger", an attached but esthetically distant study that serves to steady the main course of study by embodying a full program of peripheral perspectives and exploratory investigations.  In this way, the global aims of even a specialized inquiry can be achieved more robustly by keeping a studied eye out for its own systematic alternatives, often involving precisely those "outliers" that are ignored by the more focal styles of inquiry.

In times of shifting paradigms the outrigger of an established inquiry can take on a signal purpose as the forerunner of a new investigation, and can with added reinforcements even take over the role of the main.  With nothing more than a few spare kernels of aptitude for reflective inquiry, that is, with a minimal but germinal talent for inquiry into inquiry to serve as a catalyst, the outriding projections and their deponent objections, testifying all along in what seems like a purely negative fashion to the mounting accumulations of anomalous evidence, can find themselves converted, refitted, and positively reconditioned.  Transformed in this way, the original outrigger, with its outrageous hypotheses and its crew of motley anomalies, are ready to become the new hull, the mainstays, and the supporting constituency of a renewed constitution for inquiry, one that can sustain its overall course but more significantly its overriding cause through another day.

In times of shifting paradigms the outrigger of an established inquiry can take on a signal purpose as the forerunner of a new investigation, and can with added reinforcements even take over the role of the main.  With nothing more than a few spare kernels of aptitude for reflective inquiry, that is, with a minimal but germinal talent for inquiry into inquiry to serve as a catalyst, the outriding projections and their deponent objections, testifying all along in what seems like a purely negative fashion to the mounting accumulations of anomalous evidence, can find themselves converted, refitted, and positively reconditioned.  Transformed in this way, the original outrigger, with its outrageous hypotheses and its crew of motley anomalies, are ready to become the new hull, the mainstays, and the supporting constituency of a renewed constitution for inquiry, one that can sustain its overall course but more significantly its overriding cause through another day.

Point 24.

'''Point 24.''' &nbsp;&nbsp;&nbsp; Reflective projects being partial, their refractory parts are likely to remain partial to their outward projections.

An "unreflective framework" (UF), if it does not devolve into a condition of total confusion, and thus deserves to be called a framework at all, ordinarily maintains a clear separation between the objective and the interpretive parts of its organization.  This pragmatic division of labor coincides with a substantive distinction that is ordained to exist between the object system that is subject to observation or interpretation and the agent system that observes or interprets it.

An ''unreflective framework'' (UF), if it does not devolve into a condition of total confusion, and thus deserves to be called a framework at all, ordinarily maintains a clear separation between the objective and the interpretive parts of its organization.  This pragmatic division of labor coincides with a substantive distinction that is ordained to exist between the object system that is subject to observation or interpretation and the agent system that observes or interprets it.

But the goal of reflection is to make one's own conduct an object among other objects, something that can be critically evaluated as one choice among many and subsequently amended if found wanting.  In this aim a realistic project of reflection never sees more than partial success.  There is always a refractory residue of ongoing conduct that resists analysis and remains unreflected in any clear form of representation.  Thus, the actual effect of a reflective project is to represent only a part of one's interpretive conduct as a part of one's objective regard, in other words, to reconfigure a part of one's IF as a part of one's OF.

But the goal of reflection is to make one's own conduct an object among other objects, something that can be critically evaluated as one choice among many and subsequently amended if found wanting.  In this aim a realistic project of reflection never sees more than partial success.  There is always a refractory residue of ongoing conduct that resists analysis and remains unreflected in any clear form of representation.  Thus, the actual effect of a reflective project is to represent only a part of one's interpretive conduct as a part of one's objective regard, in other words, to reconfigure a part of one's IF as a part of one's OF.

Point 25.

'''Point 25.'''

The purpose of constructing a RIF is to demonstrate how it might be possible for interpretive agents to reflect on their own processes of interpretation, to critically evaluate the interpretive choices they make, and to choose from alternate interpretations based on the results of this reflection and evaluation.  These are the abilities that interpreters need to carry out inquiry, and especially to pursue an inquiry into inquiry.

The purpose of constructing a RIF is to demonstrate how it might be possible for interpretive agents to reflect on their own processes of interpretation, to critically evaluate the interpretive choices they make, and to choose from alternate interpretations based on the results of this reflection and evaluation.  These are the abilities that interpreters need to carry out inquiry, and especially to pursue an inquiry into inquiry.

It seems that human beings do have the ability to reflect on their own interpretive processes, at least, to the extent that they can observe the obvious aspects of the interpretive experience and control the overt features of the interpretive activity, and insofar as these aspects and features of the experimental activity are manifested at the phenomenal surfaces of its underlying processes.  Moreover, it seems that people do know how to interrogate their own judgments, turning again and again to investigate the traces of their past reflections and pausing in anticipation to examine the balance of their next evaluation.

It seems that human beings do have the ability to reflect on their own interpretive processes, at least, to the extent that they can observe the obvious aspects of the interpretive experience and control the overt features of the interpretive activity, and insofar as these aspects and features of the experimental activity are manifested at the phenomenal surfaces of its underlying processes.  Moreover, it seems that people do know how to interrogate their own judgments, turning again and again to investigate the traces of their past reflections and pausing in anticipation to examine the balance of their next evaluation.

Consequently, it must be possible to explain these apparent abilities in just one of two ways:  either to account for the faculties of reflection and selection by presenting a logical model of the processes involved, or else to dispell the illusion of each performance by showing what goes on in its place.  In either case, an inquiry into the virtues of critically reflective phenomena is called on to provide a plausible model for what is happening beneath the semblances of reflective and critical thought.  Whether the resulting resolution of a particular phenomenon preserves or dissolves its appearances is a matter that depends on the details of the case, and perhaps to a degree on personal taste.

Consequently, it must be possible to explain these apparent abilities in just one of two ways:  either to account for the faculties of reflection and selection by presenting a logical model of the processes involved, or else to dispel the illusion of each performance by showing what goes on in its place.  In either case, an inquiry into the virtues of critically reflective phenomena is called on to provide a plausible model for what is happening beneath the semblances of reflective and critical thought.  Whether the resulting resolution of a particular phenomenon preserves or dissolves its appearances is a matter that depends on the details of the case, and perhaps to a degree on personal taste.

Point 26. This marks a branch point.  I tentatively assume that the apparent power of reflection is really more or less as it appears to be, at least, in the same spirit as it appears to be, and not some radically insidious self deception arising on the part of its apparent agents.

'''Point 26.''' &nbsp;&nbsp;&nbsp; This marks a branch point.  I tentatively assume that the apparent power of reflection is really more or less as it appears to be, at least, in the same spirit as it appears to be, and not some radically insidious self-deception arising on the part of its apparent agents.

Setting out initially on the positive track, I begin with the assumption that a RIF is a real possibility.  In order to conceive of a RIF being possible it is necessary to set aside a host of set theoretic difficulties that might be imagined to afflict any invocation of self referent themes.  No matter whether interpretation is presented in terms of a framework, a faculty, a process, a trajectory, or a hypostatic agent that is assumed to carry out its procedures, there is a problem about how anything so fleeting and so sweeping as an ongoing interpretation can refer to itself as a situated form of activity, in other words, as an objective system of interpretation that rests within a context of alternative interpretations.

Setting out initially on the positive track, I begin with the assumption that a RIF is a real possibility.  In order to conceive of a RIF being possible it is necessary to set aside a host of set theoretic difficulties that might be imagined to afflict any invocation of self referent themes.  No matter whether interpretation is presented in terms of a framework, a faculty, a process, a trajectory, or a hypostatic agent that is assumed to carry out its procedures, there is a problem about how anything so fleeting and so sweeping as an ongoing interpretation can refer to itself as a situated form of activity, in other words, as an objective system of interpretation that rests within a context of alternative interpretations.

There is a piece of terminology that is often useful in this connection.  In set theoretic contexts, I use either one of the phrases "X collects Y" or "X encases Y" to mean that Y C X.  These formulations can be taken as abbreviated ways of saying that "X enumerates Y among its cases".  Thus, they express the converse of the membership relation but manage to avoid the ambiguity of the phrase "X contains Y", a form that would otherwise have to be qualified on each occasion of its use by specifying whether one means "contains as an element" or "contains as a subset", as the case may be.

There is a piece of terminology that is often useful in this connection.  In set-theoretic contexts, either one of the phrases ''X collects Y'' or ''X encases Y'' can be used to mean the same thing as ''Y'' &isin; ''X''.  These formulations can be taken as abbreviated ways of saying that ''X'' enumerates ''Y'' among its cases.  Thus, they express the converse of the membership relation but manage to avoid the ambiguity of the phrase ''X contains Y'', a form that would otherwise have to be qualified on each occasion of its use by specifying whether one means ''contains as an element'' or ''contains as a subset'', as the case may be.

To wrap up the development of this reflective project in a single line:  When the mind's original effort to catch itself at work seizes on the inventions of set theory to encapsulate its speculations, the ensuing breed of self reification that comes from mingling an unbridled capacity for self referent expressions with an unchecked propensity for creating abstract objects gives rise to the generation of set theoretic paradoxes.  As a result, it is incumbent on me to show how the concretely limited kinds of constructions that I have in mind can avoid a similar excess and steer clear of the corresponding difficulties.

To wrap up the development of this reflective project in a single line:  When the mind's original effort to catch itself at work seizes on the inventions of set theory to encapsulate its speculations, the ensuing breed of self reification that comes from mingling an unbridled capacity for self referent expressions with an unchecked propensity for creating abstract objects gives rise to the generation of set theoretic paradoxes.  As a result, it is incumbent on me to show how the concretely limited kinds of constructions that I have in mind can avoid a similar excess and steer clear of the corresponding difficulties.

If formalized, a RIF would be an IF that can properly, if only partially, refer to itself as an OF.  Thus, as formalized, a RIF amounts to both a reflexive and a recursive SOI, one that can refer to itself as an object, to the extent that any formal system can.  As a reflexive SOI, a RIF has a sign that refers to itself.  As a recursive SOI, a RIF has a character that can be determined by invoking the record of signs that it uses to refer to simpler versions and earlier developments of itself.

If formalized, a RIF would be an IF that can properly, if only partially, refer to itself as an OF.  Thus, as formalized, a RIF amounts to both a reflexive and a recursive SOI, one that can refer to itself as an object, to the extent that any formal system can.  As a reflexive SOI, a RIF has a sign that refers to itself.  As a recursive SOI, a RIF has a character that can be determined by invoking the record of signs that it uses to refer to simpler versions and earlier developments of itself.

But more than all this, in order to be genuinely reflective a RIF's consideration of itself as a situated form of activity must extend to the consideration of alternative selves.  This means that a RIF must have references to other SOI's, not only those that are continuous with the space of its own potential conduct and correlated to the course of its own form of activity, but also those that are discontinuous from and independent of its own way of being.

But more than all this, in order to be genuinely reflective a RIF's consideration of itself as a situated form of activity must extend to the consideration of alternative selves.  This means that a RIF must have references to other SOIs, not only those that are continuous with the space of its own potential conduct and correlated to the course of its own form of activity, but also those that are discontinuous from and independent of its own way of being.

In keeping with the spirit of a discussion based on concrete examples, the RIF to be improvised here is restrained to the scale of a minimal IF that can reflect on the scene of A and B, in this case, synthesizing a portion of the OF's and IF's suggested by the sign relations A and B into an integrated SOI.  While I do not plan to specify the additional constraints that would be needed to determine this RIF uniquely, even to say whether it is finite or infinite, it forms a convenient reference point for the rest of this section to designate the purported ideal as "the RIF generated by A and B" and to notate it as "RIF (A, B)".

In keeping with the spirit of a discussion based on concrete examples, the RIF to be improvised here is restrained to the scale of a minimal IF that can reflect on the scene of A and B, in this case, synthesizing a portion of the OFs and IFs suggested by the sign relations <math>A\!</math> and <math>B\!</math> into an integrated SOI.  While I do not plan to specify the additional constraints that would be needed to determine this RIF uniquely, even to say whether it is finite or infinite, it forms a convenient reference point for the rest of this section to designate the purported ideal as ''the RIF generated by <math>A\!</math> and <math>B\!</math>'' and to notate it as <math>\operatorname{RIF}(A, B).\!</math>

In accord with the customary figure of speech, a RIF can be personified in the agency of a "reflective interpreter" that possesses the faculties to carry out its actions, and this agent is in turn characterized as the localized representative of a suitably reflective and situated process of interpretation.

In accord with the customary figure of speech, a RIF can be personified in the agency of a &ldquo;reflective interpreter&rdquo; that possesses the faculties to carry out its actions, and this agent is in turn characterized as the localized representative of a suitably reflective and situated process of interpretation.

A reflective interpreter needs a capacity for referring to its own role in the process of interpretation, for conceptualizing each transition from sign to interpretant sign as occurring within a context of alternatives, and for noticing that each option has a potentially distinctive value with respect to a prevailing object or objective.  "Capacity", as used in this connection, is a word with both structural and functional connotations.  It implies the structural capacity that is required to articulate, record, and maintain data about observable forms of interpretive conduct, and it involves the functional capacity that is demanded to create and exploit this data, in effect, constituting a higher order of interpretive activity.

A reflective interpreter needs a capacity for referring to its own role in the process of interpretation, for conceptualizing each transition from sign to interpretant sign as occurring within a context of alternatives, and for noticing that each option has a potentially distinctive value with respect to a prevailing object or objective.  ''Capacity'', as used in this connection, is a word with both structural and functional connotations.  It implies the structural capacity that is required to articulate, record, and maintain data about observable forms of interpretive conduct, and it involves the functional capacity that is demanded to create and exploit this data, in effect, constituting a higher order of interpretive activity.

If one tries to understand the conduct of a reflective interpreter as a process of interpretation there are a number of questions that arise.  How can anything so ongoing as a process of interpretation refer to an object, and how can anything so fleeting as a process of interpretation be referred to as an object?

If one tries to understand the conduct of a reflective interpreter as a process of interpretation there are a number of questions that arise.  How can anything so ongoing as a process of interpretation refer to an object, and how can anything so fleeting as a process of interpretation be referred to as an object?

A process that refers to itself is not like a set that collects itself, or a collection that would enroll itself among its own elements, even if some attempts to process the reference and to lay it out in a literal account do try to dissect and explain it as such.  A sign that is elemental to a universe, perhaps by means of which one seeks to explain the universe, does not in fact collect, dominate, or encase the entire universe simply by referring to it, even if some interpretive interloper, at the risk of vitiating the whole account, is tempted to explain the elementary part in terms of the complex totality.

A process that refers to itself is not like a set that collects itself, or a collection that would enroll itself among its own elements, even if some attempts to process the reference and to lay it out in a literal account do try to dissect and explain it as such.  A sign that is elemental to a universe, perhaps by means of which one seeks to explain the universe, does not in fact collect, dominate, or encase the entire universe simply by referring to it, even if some interpretive interloper, at the risk of vitiating the whole account, is tempted to explain the elementary part in terms of the complex totality.

One reason for introducing the distinction between OF's and IF's into the present discussion is to keep track of the complex relationships between object domains and sign domains, between the constitutions of objects and the constitutions of signs.  It is a frequent practice in mathematics to blur this distinction, often saying that an object is constituted as a set of further objects when one really means that the sign or information one has about the object is constituted as a set of further signs or further informations about the object, all of which can refer to further objects, but not always the sorts of objects that are literally intended as elementary constituents of the original object.  Furthermore, each use of the directive "further" in this description marks a place where a suitably reflective interpreter ought to ask whether "further" implies "simpler" or merely "other", and in turn whether "other" means essentially other or only otherwise appearing.

One reason for introducing the distinction between OFs and IFs into the present discussion is to keep track of the complex relationships between object domains and sign domains, between the constitutions of objects and the constitutions of signs.  It is a frequent practice in mathematics to blur this distinction, often saying that an object is constituted as a set of further objects when one really means that the sign or information one has about the object is constituted as a set of further signs or further informations about the object, all of which can refer to further objects, but not always the sorts of objects that are literally intended as elementary constituents of the original object.  Furthermore, each use of the directive ''further'' in this description marks a place where a suitably reflective interpreter ought to ask whether ''further'' implies ''simpler'' or merely ''other'', and in turn whether ''other'' means essentially other or only otherwise appearing.

But the distinction between object and sign, however important, is still a pragmatic distinction, involving a thing's use in a particular role, and not an essential distinction, fixing a thing's prior and eternal nature.  Of course, it can turn out that some objects will never serve as signs and that some signs will never be observed as objects, but these types of eventuality involve empirical questions and contingent facts, and their actualization depends on the kinds of circumstances that have to be discovered after the fact rather than dictated a priori.

But the distinction between object and sign, however important, is still a pragmatic distinction, involving a thing's use in a particular role, and not an essential distinction, fixing a thing's prior and eternal nature.  Of course, it can turn out that some objects will never serve as signs and that some signs will never be observed as objects, but these types of eventuality involve empirical questions and contingent facts, and their actualization depends on the kinds of circumstances that have to be discovered after the fact rather than dictated ''a priori''.

The construction of a RIF forces the discussion to a point where the OF's and IF's and the relationships between them suddenly become much more complex, and where confusion can arise precisely from the fact that the purpose of a RIF is to convert an IF into the sort of thing that can be referred to and reflected on as an object.  Developments like these make it all the more necessary to understand the exact character of the distinction between OF's and IF's.  In a complex IF signs do participate in constitutional relationships, with complex signs being constructed out of simpler signs.  But the relations involved in denotation and connotation are not limited to constitutional linkages of this sort, and thus they cannot be expected to generate by themselves the necessary sorts of analytic and synthetic hierarchies.

The construction of a RIF forces the discussion to a point where the OFs and IFs and the relationships between them suddenly become much more complex, and where confusion can arise precisely from the fact that the purpose of a RIF is to convert an IF into the sort of thing that can be referred to and reflected on as an object.  Developments like these make it all the more necessary to understand the exact character of the distinction between OFs and IFs.  In a complex IF signs do participate in constitutional relationships, with complex signs being constructed out of simpler signs.  But the relations involved in denotation and connotation are not limited to constitutional linkages of this sort, and thus they cannot be expected to generate by themselves the necessary sorts of analytic and synthetic hierarchies.

All in all, a RIF involves the close coordination of an OF and an IF, plus mechanisms for carrying out the so called "reflective operations" (RO's) that go to negotiate between the objective and the interpretive realms.  The work of ROing permits processes of interpretation, initially taking place largely in the IF and impinging on the OF only at isolated points, to be formalized and objectified, thereby becoming segments of the OF.  Taken over time the cumulative effect of this ROing motion gradually turns more and more of the IF into new sectors and layers of the OF.

All in all, a RIF involves the close coordination of an OF and an IF, plus mechanisms for carrying out the so called ''reflective operations'' (ROs) that go to negotiate between the objective and the interpretive realms.  The work of ROing permits processes of interpretation, initially taking place largely in the IF and impinging on the OF only at isolated points, to be formalized and objectified, thereby becoming segments of the OF.  Taken over time the cumulative effect of this ROing motion gradually turns more and more of the IF into new sectors and layers of the OF.

Point 27.

'''Point 27.'''

There is a portion of reasoning that consists in drawing distinctions, signifying the features thereby distinguished by means of logical terms, recognizing constraints on the conjoint occurrences of these features, expressing these constraints in the form of logical premisses, and then drawing the implications of these premisses as the occasion warrants.  This part of logic, in its formalizable aspects, is generally referred to as "propositional calculus" (PropC), "sentential logic" (SL), or sometimes as "zeroth order logic" (ZOL).

There is a portion of reasoning that consists in drawing distinctions, signifying the features thereby distinguished by means of logical terms, recognizing constraints on the conjoint occurrences of these features, expressing these constraints in the form of logical premisses, and then drawing the implications of these premisses as the occasion warrants.  This part of logic, in its formalizable aspects, is generally referred to as ''propositional calculus'' (PropC), ''sentential logic'' (SL), or sometimes as ''zeroth order logic'' (ZOL).

With any system of logic, at least, that does not propose a purely syntactic rationale for itself, it is necessary to draw a distinction between the logical object that is denoted, expressed, or represented in thinking and the logical sign that denotes, expresses, or represents it.  Often one uses the contrast between "proposition" and "expression" or the shade of difference between "statement" and "sentence" to convey the distinction between the logical object signified and the syntactic assemblage that signifies it.  Another option is to let the division lie between a "position" and a "proposition", with the suggestion being that the function of a symbolic proposition is to indicate indifferently a plurality of logical positions.  In accord with my personal preference, I use the term "proposition" ambiguously, expecting context to resolve the question, and resorting to the term "expression" when it does not.

With any system of logic, at least, that does not propose a purely syntactic rationale for itself, it is necessary to draw a distinction between the logical object that is denoted, expressed, or represented in thinking and the logical sign that denotes, expresses, or represents it.  Often one uses the contrast between ''proposition'' and ''expression'' or the shade of difference between ''statement'' and ''sentence'' to convey the distinction between the logical object signified and the syntactic assemblage that signifies it.  Another option is to let the division lie between a ''position'' and a ''proposition'', with the suggestion being that the function of a symbolic proposition is to indicate indifferently a plurality of logical positions.  In accord with my personal preference, I use the term ''proposition'' ambiguously, expecting context to resolve the question, and resorting to the term ''expression'' when it does not.

Point 28. Adequate reasoning about the propositional constitution or the sentential representatation of POV's and POD's requires a logical system that can work with "higher order propositions" (HOP's).

'''Point 28.''' &nbsp;&nbsp;&nbsp; Adequate reasoning about the propositional constitution or the sentential representation of POVs and PODs requires a logical system that can work with ''higher order propositions'' (HOPs).

Point 29.

'''Point 29.'''

Finally, interlaced with the structures of the OF and the IF, there is a need for a structure that I call a "dynamic evaluative framework" (DEF).  This is intended to isolate the twin aspects of process and purpose that are observable on either side of the objective interpretive divide and to assist in formalizing the graded notions of directed change that are able to be actualized in the medium of a RIF.

Finally, interlaced with the structures of the OF and the IF, there is a need for a structure that I call a ''dynamic evaluative framework'' (DEF).  This is intended to isolate the twin aspects of process and purpose that are observable on either side of the objective interpretive divide and to assist in formalizing the graded notions of directed change that are able to be actualized in the medium of a RIF.

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[[Category:Artificial Intelligence]]

[[Category:Artificial Intelligence]]