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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 5 (view source)
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As a result, the fundamental JOI renders the hallowed method of inquiry just another doctrine among others, equal in its manner of justification, its final appeal, and its ultimate justice to every other belief system. But this is not the criticism that finally condemns it. Being just the same as other systems of belief is not the fatal flaw. That only makes all systems of belief equal under the law, if no longer a law of inquiry but a law of compromising positions and convenient resolutions. Still, there would not necessarily have been anything wrong with this, if it were not for the self-imposed burden that inquiry brings down on itself via the dishonesty or the self-deception of promising something else.
As a result, the fundamental JOI renders the hallowed method of inquiry just another doctrine among others, equal in its manner of justification, its final appeal, and its ultimate justice to every other belief system. But this is not the criticism that finally condemns it. Being just the same as other systems of belief is not the fatal flaw. That only makes all systems of belief equal under the law, if no longer a law of inquiry but a law of compromising positions and convenient resolutions. Still, there would not necessarily have been anything wrong with this, if it were not for the self-imposed burden that inquiry brings down on itself via the dishonesty or the self-deception of promising something else.
<pre>
<br>
Could great men thunder
As Jove himself does, Jove would never be quiet,
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
For every pelting petty officer
| colspan="2" | Could great men thunder
Would use his heaven for thunder, nothing but thunder.
|-
Merciful heaven,
| colspan="2" | As Jove himself does, Jove would never be quiet,
Thou rather with thy sharp and sulphurous bolt
|-
Split'st the unwedgeable and gnarled oak
| colspan="2" | For every pelting petty officer
Than the soft myrtle. But man, proud man,
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Dressed in a little brief authority,
| colspan="2" | Would use his heaven for thunder, nothing but thunder.
Most ignorant of what he's most assured,
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His glassy essence, like an angry ape
| colspan="2" | Merciful heaven,
Plays such fantastic tricks before high heaven
|-
As makes the angels weep, who, with our spleens,
| colspan="2" | Thou rather with thy sharp and sulphurous bolt
Would all themselves laugh mortal.
|-
| colspan="2" | Split'st the unwedgeable and gnarled oak
|-
| colspan="2" | Than the soft myrtle. But man, proud man,
|-
| colspan="2" | Dressed in a little brief authority,
|-
| colspan="2" | Most ignorant of what he's most assured,
|-
| colspan="2" | His glassy essence, like an angry ape
|-
| colspan="2" | Plays such fantastic tricks before high heaven
|-
| colspan="2" | As makes the angels weep, who, with our spleens,
|-
| colspan="2" | Would all themselves laugh mortal.
|-
| width="50%" |
| ''Measure for Measure'', 2.2.113–126
|}
<br>
It is probably wise to stress this point. It is not being claimed that an authority based system of belief, simply by building itself on traditional foundations, is necessarily hypocritical or inconsistent in its own right. It can be as accurate, authentic, and honest in what it says and tries to say as any other belief system or knowledge base. In fact, a modicum of reliance on one source of authority or another is not only prudent but most likely to be found inescapable. Authority based systems, in form so analogous to axiom systems, if not in the context of their use, simply have the specific properties and the generic limitations that they can be observed to have.
It is probably wise to stress this point. It is not being claimed that an authority based system of belief, simply by building itself on traditional foundations, is necessarily hypocritical or inconsistent in its own right. It can be as accurate, authentic, and honest in what it says and tries to say as any other belief system or knowledge base. In fact, a modicum of reliance on one source of authority or another is not only prudent but most likely to be found inescapable. Authority based systems, in form so analogous to axiom systems, if not in the context of their use, simply have the specific properties and the generic limitations that they can be observed to have.
At this point, let authority based systems and axiom systems be lumped together into the same class, at least temporarily, on the basis of the forms of derivation that they allow, and without regard for the different ways that they are initially brought to light or subsequently put to use. Further, let this whole class be described as "founded systems", for the moment ignoring the distinction between informal and formal systems, or regarding all prospectively, in anticipation of their formalizations.
At this point, let authority based systems and axiom systems be lumped together into the same class, at least temporarily, on the basis of the forms of derivation that they allow, and without regard for the different ways that they are initially brought to light or subsequently put to use. Further, let this whole class be described as ''founded systems'', for the moment ignoring the distinction between informal and formal systems, or regarding all prospectively, in anticipation of their formalizations.
Every project of a founded system voluntarily risks certain limitations. But there is one limitation that appears to be a genuine defect from the standpoint of this inquiry, amounting to the chief source of worry that this inquiry has about the whole class of founded systems. This is the fact that whatever acuteness of reverence or accuracy of reference to their objects they do in fact achieve is a matter of grace or luck, and not something that can be subjected to change, criticism, or correction. This puts it outside the sphere of inquiry, as I understand it, even if its formulations are suggested by data within the sphere of experience.
Every project of a founded system voluntarily risks certain limitations. But there is one limitation that appears to be a genuine defect from the standpoint of this inquiry, amounting to the chief source of worry that this inquiry has about the whole class of founded systems. This is the fact that whatever acuteness of reverence or accuracy of reference to their objects they do in fact achieve is a matter of grace or luck, and not something that can be subjected to change, criticism, or correction. This puts it outside the sphere of inquiry, as I understand it, even if its formulations are suggested by data within the sphere of experience.
In effect, there is no amplification of intelligence, no leverage of reason, in short, no instrumental gain or "mechanical advantage" to be acquired from the use of a founded system. It can transmit the force of reason, in a conservative way at best, from premisses to conclusions, but the effective output of the system achieves no greater level of certainty as it bears on any question than the level of authority it can grant itself on input or justly claim for itself at the outset. If I can continue to use the image of a lever, while delaying the examination of its exactness until a later point of this work, it is as if the lack of leverage in a founded system can be traced back to one of several defects:
In effect, there is no amplification of intelligence, no leverage of reason, in short, no instrumental gain or “mechanical advantage” to be acquired from the use of a founded system. It can transmit the force of reason, in a conservative way at best, from premisses to conclusions, but the effective output of the system achieves no greater level of certainty as it bears on any question than the level of authority it can grant itself on input or justly claim for itself at the outset. If I can continue to use the image of a lever, while delaying the examination of its exactness until a later point of this work, it is as if the lack of leverage in a founded system can be traced back to one of several defects:
# The ''fulcrum'' of a founded system, the fixed point of its critique, is the ''examen'' of its critical powers, the tongue of its balance, and this has to be placed so evenly between the objective domain, whereof its ignorance is writ so large, and the fund of applied information, wherein its share of accumulated knowledge resides, that no gain in the effective intelligence of the actions thus founded can be derived.
# A founded system is forced to be a ''grounded system'', that is, one that requires a moderately strong emplacement on grounds already settled and a preponderance of certainty on the side of the applied intelligence.
# In effect, a ''founded or grounded'' (FOG) system requires absolute certainty with respect to some of its points, the points on which it is said to rest. It is as if these fixed points put it in contact with an infinite source of knowledge or connect it to an infinite sink for uncertainties. Of course, a FOG system that casts itself as a beacon of enlightenment and sells itself under the label of “science” can never admit to seeing itself in this image, since the very act of making the claim explicit already puts its grant in jeopardy. But that is what it amounts to, nevertheless.
Another way to see the over-constrained nature of these FOG conditions, for the certainty of foundations, is by expressing them in terms of the ''boundary conditions'' that a given system of belief is assumed to have. In this regard, it helps to make the following definition. An ''open'' system of belief is one that has each of its points ''mediated'' by the system itself, in other words, surrounded by, apprehended within, and evidentially or argumentatively justified by a neighborhood of similar points that falls entirely within the system in question.
When it is considered in the light of this definition of ''openness'', a FOG system is clearly seen to constitute a ''non-open'' system of belief. In short, not all of its axioms, points, or tenets are mediated within the system itself, but have their motives, reasons, and supports lying in points ulterior to it. In hopes of serving both the understanding and the memory, let me try to express this situation in a couple of striking, if slightly ludicrous, metaphors, a pair of judicial, if not entirely judicious, figures of speech:
# The ''corpus delicti'', the body of material evidence and substantial fact that is necessary to justify the institution of the system and the initiation of its every process, is always found to lie in such a disposition that it rests partially beyond the system in question.
# The ''habeas corpus'', the body of probable causes and sufficient reasons that is tendered to justify the holding of certain points, is always deposed in such a demeanor that its true warrant either stays unwrit or is writ largely outside the system in question.
Whether it is verifiably jurisprudent or merely a fantastic simile, whether it is really a conspiracy of their natural bents or purely a coincidence of their accustomed distortions, the parody of a judicial process that one constantly sees being carried on in the name of this or that FOG system, and always apparently up to the limits of their several FOG boundaries, makes a mockery of the spirit of inquiry, and of all its pretensions to a critical reflection, since it places not only the first apprehension but the final justice of such a system beyond all question of executive examination, judicial review, and constitutional amendment. The whole matter is even more deceptive that it appears at first sight, precisely because a FOG system, as lit within, or according to its own lights, often takes on all the appearance of being open. But this is only because the boundaries of its viability and the outlines of the external obstacles that represent a threat to the illusions of its omni pervasiveness are actively being obscured by the limitations inherent in its unreflective nature.
Whether it is verifiably jurisprudent or merely a fantastic simile, whether it is really a conspiracy of their natural bents or purely a coincidence of their accustomed distortions, the parody of a judicial process that one constantly sees being carried on in the name of this or that FOG system, and always apparently up to the limits of their several FOG boundaries, makes a mockery of the spirit of inquiry, and of all its pretensions to a critical reflection, since it places not only the first apprehension but the final justice of such a system beyond all question of executive examination, judicial review, and constitutional amendment. The whole matter is even more deceptive that it appears at first sight, precisely because a FOG system, as lit within, or according to its own lights, often takes on all the appearance of being open. But this is only because the boundaries of its viability and the outlines of the external obstacles that represent a threat to the illusions of its omni pervasiveness are actively being obscured by the limitations inherent in its unreflective nature.
This is just the kind of situation that one would expect in the purely deductive or demonstrative sections of science, for instance, in logics and mathematics of the "purer" and less "applied" sorts. In these more abstract traces and more refined extracts of a fully scientific method, the authority of the conclusions, or the level of certainty achieved on output, is no greater than the authority of the premisses, or the level of certainty possessed on input. Thus, the work of reasoning in such a case is purely "expliative", that is, wholly expository or explicational.
This is just the kind of situation that one would expect in the purely deductive or demonstrative sections of science, for instance, in logics and mathematics of the “purer” and less “applied” sorts. In these more abstract traces and more refined extracts of a fully scientific method, the authority of the conclusions, or the level of certainty achieved on output, is no greater than the authority of the premisses, or the level of certainty possessed on input. Thus, the work of reasoning in such a case is purely ''expliative'', that is, wholly expository or explicational.
But a truly synthetic or "ampliative" analysis should be able to reduce a complex induction to simple inductions, meanwhile gaining a measure of certainty in the process, and all without losing the power to reconstruct the complex from the simple. The perceived gain of practical certainty that develops in this analysis can be explained in the following manner. A complex induction, prior to analysis, is likely to be a very uncertain induction, but is likely to have its certainty shored up if the analysis to simple inductions is successful.
But a truly synthetic or ''ampliative'' analysis should be able to reduce a complex induction to simple inductions, meanwhile gaining a measure of certainty in the process, and all without losing the power to reconstruct the complex from the simple. The perceived gain of practical certainty that develops in this analysis can be explained in the following manner. A complex induction, prior to analysis, is likely to be a very uncertain induction, but is likely to have its certainty shored up if the analysis to simple inductions is successful.
This is a pretty sorry picture, especially in view of all the bright promises of enlightenment through inquiry that inquiry makes, to be a veritable system of belief for constituting systems of veritable belief. But the promise of inquiry to be better than all that, to be an advance over other systems of belief, not just another dogma in the management of uncertainty but a unique way of life, holds out hopes that are still tempting and that deserve to be pursued further. So it is time to ask: If not by means of these foundations, then what form of constitution can provide the sought for JOI?
This is a pretty sorry picture, especially in view of all the bright promises of enlightenment through inquiry that inquiry makes, to be a veritable system of belief for constituting systems of veritable belief. But the promise of inquiry to be better than all that, to be an advance over other systems of belief, not just another dogma in the management of uncertainty but a unique way of life, holds out hopes that are still tempting and that deserve to be pursued further. So it is time to ask: If not by means of these foundations, then what form of constitution can provide the sought for JOI?
Fortunately, there is another JOI, arising from the pragmatic critique of even the most enlightened fundamentalism. If the fundamental approach is viewed as a project to conjoin three positive features — "founding", "beginning", and "certain" — in single point of conceptual architecture, then the pragmatic critique of this plan can be understood as objecting that this point is overloaded. There are ways to preserve this triarchic association, but not without protracting other angles of approach to the juncture and not without compassing other senses of the terms than the meanings originally intended. It is perhaps easier just to abrogate one of the terms, either rescinding its constraint or trading it in for its logical negation.
Fortunately, there is another JOI, arising from the pragmatic critique of even the most enlightened fundamentalism. If the fundamental approach is viewed as a project to conjoin three positive features — ''founding'', ''beginning'', and ''certain'' — in a single point of conceptual architecture, then the pragmatic critique of this plan can be understood as objecting that this point is overloaded. There are ways to preserve this triarchic association, but not without protracting other angles of approach to the juncture and not without compassing other senses of the terms than the meanings originally intended. It is perhaps easier just to abrogate one of the terms, either rescinding its constraint or trading it in for its logical negation.
The pragmatic approach to the foundations of inquiry, more precisely, its approach to the hoped for JOI, whether or not this leaves room in the end for a notion of secure foundations, suggests that reason does begin with unreason, but only in the sense that inquiry starts from a state of uncertainty. If one objects that this doubt is not radical, because many things in the meantime are never in fact doubted at all, then this is correct, but only in the sense that these things are not doubted because they are never even consciously questioned. If that sort of lack of doubt is the type one plans to found their reason on, then I think it is a very fond notion indeed.
The pragmatic approach to the foundations of inquiry, more precisely, its approach to the hoped for JOI, whether or not this leaves room in the end for a notion of secure foundations, suggests that reason does begin with unreason, but only in the sense that inquiry starts from a state of uncertainty. If one objects that this doubt is not radical, because many things in the meantime are never in fact doubted at all, then this is correct, but only in the sense that these things are not doubted because they are never even consciously questioned. If that sort of lack of doubt is the type one plans to found their reason on, then I think it is a very fond notion indeed.
There's a double meaning in that.
<br>
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
| colspan="2" | There's a double meaning in that.
|-
| width="50%" |
| ''Much Ado About Nothing'', 2.3.246
|}
<br>
(Yes, there is a subtext. (There is always a subtext.) A reader who has access to the subtext, who can read it in the face of the pretext, and who remains both sensitive to and sensible about its connotations, is already beginning to suspect that what I intend to argue in the end is exactly that the chief justification of inquiry is nothing less and nothing more than the pure joy of it. But the moment that I depend on this subtext to carry the logical argument, to go beyond supporting the intuition and encouraging the effort of reasoning, is the moment that I utterly fail in my intention. This bears on the matter of a harmonious balance between rhetoric and logic, where the former appreciates and is bound to consider the affective and the impressionable nature of the interpreter, and takes into account the need for reason's ponderous beacon to be buoyed over the deep by incidental glosses and light exhortations.)
(Yes, there is a subtext. (There is always a subtext.) A reader who has access to the subtext, who can read it in the face of the pretext, and who remains both sensitive to and sensible about its connotations, is already beginning to suspect that what I intend to argue in the end is exactly that the chief justification of inquiry is nothing less and nothing more than the pure joy of it. But the moment that I depend on this subtext to carry the logical argument, to go beyond supporting the intuition and encouraging the effort of reasoning, is the moment that I utterly fail in my intention. This bears on the matter of a harmonious balance between rhetoric and logic, where the former appreciates and is bound to consider the affective and the impressionable nature of the interpreter, and takes into account the need for reason's ponderous beacon to be buoyed over the deep by incidental glosses and light exhortations.)
Self-awareness is our capacity to stand apart from ourselves and examine our thinking, our motives, our history, our scripts, our actions, and our habits and tendencies. It enables us to take off our "glasses" and look at them as well as through them. It makes it possible for us to become aware of the social and psychic history of the programs that are in us and to enlarge the separation between stimulus and response.
{| align="center" cellpadding="0" cellspacing="0" width="90%"
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<p>Self-awareness is our capacity to stand apart from ourselves and examine our thinking, our motives, our history, our scripts, our actions, and our habits and tendencies. It enables us to take off our “glasses” and look at them as well as through them. It makes it possible for us to become aware of the social and psychic history of the programs that are in us and to enlarge the separation between stimulus and response.</p>
|-
| align="right" | Covey, Merrill, and Merrill, ''First Things First'', [CMM, 59]
|}
How is it possible for one to use an organization of thought in order to think about that same organization of thought, or indeed, about others? How is it possible to draw distinctions, even the most basic distinctions necessary to thought, in such a way that they can be redrawn and even withdrawn when necessary? In other words, what are the conditions for having a "critical reflection of inquiry" (CROI), a system of assumptions and methods that acts continuously and self-correctively to constitute a critically reflective belief system? This would be tantamount to a POV where no assumption is forced to be taken for granted, even if at any given moment many assumptions are contingently being acted on just as if they were true. For instance, if a distinction between dynamic and symbolic systems, or aspects of systems, is a part of one's present POV, to what extent can one reflect on that fact, and thus be able to think about alternative POV's or to think about changing one's current POV?
How is it possible for one to use an organization of thought in order to think about that same organization of thought, or indeed, about others? How is it possible to draw distinctions, even the most basic distinctions necessary to thought, in such a way that they can be redrawn and even withdrawn when necessary? In other words, what are the conditions for having a ''critical reflection of inquiry'' (CROI), a system of assumptions and methods that acts continuously and self-correctively to constitute a critically reflective belief system? This would be tantamount to a POV where no assumption is forced to be taken for granted, even if at any given moment many assumptions are contingently being acted on just as if they were true. For instance, if a distinction between dynamic and symbolic systems, or aspects of systems, is a part of one's present POV, to what extent can one reflect on that fact, and thus be able to think about alternative POVs or to think about changing one's current POV?
This ends my preview of the kinds of issues that the pragmatic theory of sign relations and their reflective extensions is intended to comprehend.
This ends my preview of the kinds of issues that the pragmatic theory of sign relations and their reflective extensions is intended to comprehend.
In the sequel I propose a particular way of approaching these problems. I introduce a simplified model of the general situation to be addressed, but one with sufficient structure to embody analogous versions of many of the problems and phenomena of ultimate interest. By exploring the issues that develop in this miniature model, and by looking for ways of resolving them that work on this scale, I hope to gain insight into ways of dealing with the corresponding issues in the larger study of inquiry.
In the sequel I propose a particular way of approaching these problems. I introduce a simplified model of the general situation to be addressed, but one with sufficient structure to embody analogous versions of many of the problems and phenomena of ultimate interest. By exploring the issues that develop in this miniature model, and by looking for ways of resolving them that work on this scale, I hope to gain insight into ways of dealing with the corresponding issues in the larger study of inquiry.
To be specific, I restrict my discussion at first to "propositional" or "sentential" models of POV's, and I examine a particular type of logical strategy that allows agents operating within this framework to describe the constitutions of a broad class of POV's. If this strategy turns out to be flexible enough, it can permit agents to reflect on the bases and the biases of their POV's and those of others, at least, to some degree.
To be specific, I restrict my discussion at first to ''propositional'' or ''sentential'' models of POVs, and I examine a particular type of logical strategy that allows agents operating within this framework to describe the constitutions of a broad class of POVs. If this strategy turns out to be flexible enough, it can permit agents to reflect on the bases and the biases of their POVs and those of others, at least, to some degree.
This circumscription of expressions with a double meaning properly constitutes the hermeneutic field.
{| align="center" cellpadding="0" cellspacing="0" width="90%"
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<p>This circumscription of expressions with a double meaning properly constitutes the hermeneutic field.</p>
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| align="right" | Paul Ricoeur, ''The Conflict of Interpretations'', [Ric, 13]
|}
Even with its meaning duly circumscribed, "reflection" retains the dual senses of an " ionized" word, referring to both a process and a result. As such, it is already on its way to becoming a highly charged term in this investigation. Even though a complete analysis of inquiry, from the top to the bottom of its putative hierarchy, is yet to be made available, the tendency to invoke "reflection" at every step and stage of inquiry is already apparent. This is clear from the fragmentary and scattered, but steadily mounting evidence of the word's textual circumstances that is currently piling up at the level of inquiry's most primitive details.
Even with its meaning duly circumscribed, “reflection” retains the dual senses of an “-ionized” word, referring to both a process and a result. As such, it is already on its way to becoming a highly charged term in this investigation. Even though a complete analysis of inquiry, from the top to the bottom of its putative hierarchy, is yet to be made available, the tendency to invoke “reflection” at every step and stage of inquiry is already apparent. This is clear from the fragmentary and scattered, but steadily mounting evidence of the word's textual circumstances that is currently piling up at the level of inquiry's most primitive details.
In other words, the constant invocation of "reflection" as an auxiliary to inquiry is apparent from the elementary syntactic fact that the charge of "reflection" is found in the mission statements of so many processes that are already noted to be involved in inquiry. In this connection, any time one senses the need to add the adjective "reflective" to the title of an agent, process, or faculty, then it speaks to the suspicion that the simple carrying out of actions and the perfunctory execution of procedures is not enough for the sake of composing intelligent conduct, but that there is an obligation to adjoin a component of reflection to whatever else is going on.
In other words, the constant invocation of “reflection” as an auxiliary to inquiry is apparent from the elementary syntactic fact that the charge of “reflection” is found in the mission statements of so many processes that are already noted to be involved in inquiry. In this connection, any time one senses the need to add the adjective “reflective” to the title of an agent, process, or faculty, then it speaks to the suspicion that the simple carrying out of actions and the perfunctory execution of procedures is not enough for the sake of composing intelligent conduct, but that there is an obligation to adjoin a component of reflection to whatever else is going on.
The elliptic nature of the discussion in this subsection, touching on topics that must be left in the forms of questions, raising issues that cannot be answered or even fully addressed until later sections of this project, lighting on a range of promontories in a field of problematic icebergs, and glancing up against problems that stay largely submerged and keep barely connected only through a medium of chance associations constantly in flux — all of this makes it advisable for the writer to come up with a device for continually warning the reader of the text's approaching discontinuities.
The elliptic nature of the discussion in this subsection, touching on topics that must be left in the forms of questions, raising issues that cannot be answered or even fully addressed until later sections of this project, lighting on a range of promontories in a field of problematic icebergs, and glancing up against problems that stay largely submerged and keep barely connected only through a medium of chance associations constantly in flux — all of this makes it advisable for the writer to come up with a device for continually warning the reader of the text's approaching discontinuities.
In view of these requirements, the text proceeds by highlighting a number of thematic points that find themselves to be reinforced in prior stages of its own construction, not all of which stages survive erasure enough to be explicitly marked in the text, and all in all continuing to develop as if by a pattern of constructive and destructive interference. It is hoped that this can reveal significant aspects, however partial and confounded, of its subject, its medium, and the forms that shape them.
In view of these requirements, the text proceeds by highlighting a number of thematic points that find themselves to be reinforced in prior stages of its own construction, not all of which stages survive erasure enough to be explicitly marked in the text, and all in all continuing to develop as if by a pattern of constructive and destructive interference. It is hoped that this can reveal significant aspects, however partial and confounded, of its subject, its medium, and the forms that shape them.
A few words need to be spent in advance on the status of these points. Most of them are no longer controversial from my current POV, indeed, they partially constitute that POV. However, I recognize that some of them are likely to be controversial from the perspective of other POV's. Thus, these points are not intended to be taken as self-evident axioms, the kinds of logistical supports on the basis of which one customarily and confidently marches forward to the conquest of ever more powerful theorems. It is true that one of the best ways of testing these points is to take them up as premisses and to reason forward from them as far as one can. But the main reason for pointing them out in an explicit form of expression is so that their meanings, their logical implications, and their practical consequences can be examined in a circumspect light.
A few words need to be spent in advance on the status of these points. Most of them are no longer controversial from my current POV, indeed, they partially constitute that POV. However, I recognize that some of them are likely to be controversial from the perspective of other POVs. Thus, these points are not intended to be taken as self-evident axioms, the kinds of logistical supports on the basis of which one customarily and confidently marches forward to the conquest of ever more powerful theorems. It is true that one of the best ways of testing these points is to take them up as premisses and to reason forward from them as far as one can. But the main reason for pointing them out in an explicit form of expression is so that their meanings, their logical implications, and their practical consequences can be examined in a circumspect light.
In short, none of the points to be staked out here is taken as evident or proven, and nothing of final certainty can be proved from them, but a demonstration can be made from them in the sense of an illustration, showing and testing their strength, trustworthiness, and utility for organizing an otherwise overwhelming complexity and depth of material. This process of examination and clarification, just as often as it has to reason forward, in the direction of the contingent theorems, also has to reason backward, to interrogate the mediately obvious principals and to ask whether more basic points can be discerned, as if lurking within the points already noted and secretly required to shore them up.
In short, none of the points to be staked out here is taken as evident or proven, and nothing of final certainty can be proved from them, but a demonstration can be made from them in the sense of an illustration, showing and testing their strength, trustworthiness, and utility for organizing an otherwise overwhelming complexity and depth of material. This process of examination and clarification, just as often as it has to reason forward, in the direction of the contingent theorems, also has to reason backward, to interrogate the mediately obvious principals and to ask whether more basic points can be discerned, as if lurking within the points already noted and secretly required to shore them up.
Out of this material I need to develop a method of inquiry, one that is extensible to its self-application. As an adjunct, or in adjutant fashion, I need to develop a justification of this method that can lend support to the justification of inquiry in general, and in its turn help to justify the application of inquiry to itself. Accordingly, the prospective aim to be sighted through the series of points ahead, and the line of survey to be projected through the elliptic text that charts it, are directed toward an effective theory of sign relations, one that is capable of resolving some of the subtleties it discerns in discourse, on occasions when a resolution is what is called for.
Out of this material I need to develop a method of inquiry, one that is extensible to its self-application. As an adjunct, or in adjutant fashion, I need to develop a justification of this method that can lend support to the justification of inquiry in general, and in its turn help to justify the application of inquiry to itself. Accordingly, the prospective aim to be sighted through the series of points ahead, and the line of survey to be projected through the elliptic text that charts it, are directed toward an effective theory of sign relations, one that is capable of resolving some of the subtleties it discerns in discourse, on occasions when a resolution is what is called for.
====5.3.4. Points Forward====
====5.3.4. Points Forward====
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'''Point 1.''' Thought takes place in signs.
Point 1. Thought takes place in signs.
This makes a sign relation the setting of thought, where thought occurs. In particular, the connotative plane of a sign relation is the medium of thought proper, and the denotative plane of a sign relation embodies the lines of thought's orientation toward its objects.
This makes a sign relation the setting of thought, where thought occurs. In particular, the connotative plane of a sign relation is the medium of thought proper, and the denotative plane of a sign relation embodies the lines of thought's orientation toward its objects.
This point is one that may be thought controversial, until it is realized that the meaning of the term "sign" is being extended to cover anything that might conceivably occur in thought. Far from intending to restrict thought to a circumscribed domain of signs, it expands the definition of "sign" to encompass anything that might enter into thought, so long as this entrance into thought is understood not in the sense of being its object but as something that lends a place to it. Properly taken, this point is tantamount to an empirical definition of the term "sign", more like an indication of where in experience a ready supply of examples can be found. It says that if you seek signs then look to your thoughts.
This point is one that may be thought controversial, until it is realized that the meaning of the term “sign” is being extended to cover anything that might conceivably occur in thought. Far from intending to restrict thought to a circumscribed domain of signs, it expands the definition of “sign” to encompass anything that might enter into thought, so long as this entrance into thought is understood not in the sense of being its object but as something that lends a place to it. Properly taken, this point is tantamount to an empirical definition of the term “sign”, more like an indication of where in experience a ready supply of examples can be found. It says that if you seek signs then look to your thoughts.
Point 2. Thinking is a form of conduct.
'''Point 2.''' Thinking is a form of conduct.
Conduct is action with a purpose. Synonymous with the term "purpose", as used in this statement, is "aim", "end", "goal", or "object". The object domain of a sign relation is the place where these objects are envisioned to be, and thinking is the action that is carried out with a view to these ends.
Conduct is action with a purpose. Synonymous with the term “purpose”, as used in this statement, are “aim”, “end”, “goal”, or “object”. The object domain of a sign relation is the place where these objects are envisioned to be, and thinking is the action that is carried out with a view to these ends.
Rightly taken, this point, too, is purely definitional. It classifies thinking as a species of action that has, or is meant to have, a purpose. In particular, thinking is the kind of action that passes from sign to interpretant sign in relation to an object. If one wishes to object that not all that passes for thinking has any assignable purpose, and if one desires to maintain an alternative POV that recognizes forms of aimless thinking, then it is nothing more than a technical problem to translate between the two ways of thinking, reclassifing unconducive thinking as a "degenerate form" from the standpoint of the pragmatic POV.
Rightly taken, this point, too, is purely definitional. It classifies thinking as a species of action that has, or is meant to have, a purpose. In particular, thinking is the kind of action that passes from sign to interpretant sign in relation to an object. If one wishes to object that not all that passes for thinking has any assignable purpose, and if one desires to maintain an alternative POV that recognizes forms of aimless thinking, then it is nothing more than a technical problem to translate between the two ways of thinking, reclassifying unconducive thinking as a “degenerate form” from the standpoint of the pragmatic POV.
Point 3. Reflection on thinking is reflection on conduct.
'''Point 3.''' Reflection on thinking is reflection on conduct.
Even though it can appear too evident, too immediate, and too obvious to bear pointing out, there are several good reasons to make a point of noticing this simple corollary of the previous point, namely, that if thinking is a special case of conduct then reflection on thinking is a special case of reflection on conduct.
Even though it can appear too evident, too immediate, and too obvious to bear pointing out, there are several good reasons to make a point of noticing this simple corollary of the previous point, namely, that if thinking is a special case of conduct then reflection on thinking is a special case of reflection on conduct.
First of all, it means that reflection on thinking and relection on conduct have a reciprocal bearing on each other, the way that special cases and general types always do. Reflection on thinking can tell us something about reflection on conduct in general. This is because the special case informs the general type and can be used inductively to discover its possible properties. Reflection on conduct in general can tell us something about reflection on thinking. This is because the general type constrains the special case and can be used deductively to derive its necessary properties.
First of all, it means that reflection on thinking and reflection on conduct have a reciprocal bearing on each other, the way that special cases and general types always do. Reflection on thinking can tell us something about reflection on conduct in general. This is because the special case informs the general type and can be used inductively to discover its possible properties. Reflection on conduct in general can tell us something about reflection on thinking. This is because the general type constrains the special case and can be used deductively to derive its necessary properties.
(Bearing on the order of the normative sciences : logic < ethics < aesthetics?)
logic < ethics < aesthetics
There is more to this point than first meets the eye, especially when it is considered in the light of its abstract form. Aside from its present application to the matters of reflection, thinking, and conduct, one can see in this instance the form of a distributive law, that distributes an operation ("reflection") across a relation ("implication" or "inclusion"), and where this order of dyadic relation is the very one that constitutes the ordering of special cases under general forms. The point of this is that the general intention of this dyadic relation, in its full extension, must be to capture the relation of a special application of any principle (say, a distributive law) to its own general formulation. For instance, therefore, reflection on a special kind of distribution is a special kind of reflection on distribution in general.
There is more to this point than first meets the eye, especially when it is considered in the light of its abstract form. Aside from its present application to the matters of reflection, thinking, and conduct, one can see in this instance the form of a distributive law, that distributes an operation (“reflection”) across a relation (“implication” or “inclusion”), and where this order of dyadic relation is the very one that constitutes the ordering of special cases under general forms. The point of this is that the general intention of this dyadic relation, in its full extension, must be to capture the relation of a special application of any principle (say, a distributive law) to its own general formulation. For instance, therefore, reflection on a special kind of distribution is a special kind of reflection on distribution in general.
In light of these relations between the specialization of thinking and the general capacity for conduct, I can now turn to a logical analysis of the concept of conduct for the light it reflects on the nature of thought.
In light of these relations between the specialization of thinking and the general capacity for conduct, I can now turn to a logical analysis of the concept of conduct for the light it reflects on the nature of thought.
Point 4.
'''Point 4.''' Conduct = (Act, End) = (State<sub>1</sub>, State<sub>2</sub>, State<sub>3</sub>).
One can say that a conduct is a pair comprised of an act and an end. In this formula, the act can be anything from a complex activity to an extended action and the end can be anywhere among a vast diversity of destinations that are found to be encompassed by a general description. If it is recognized that the data needed to specify a minimum of action, a mere transition, is an ordered pair of states, and if it is remembered that the data appropriate to specifying a singular end is a single state, then an element of conduct, at its minimum, can be conceived to consist of an ordered triple of states.
One can say that a conduct is a pair comprised of an act and an end. In this formula, the act can be anything from a complex activity to an extended action and the end can be anywhere among a vast diversity of destinations that are found to be encompassed by a general description. If it is recognized that the data needed to specify a minimum of action, a mere transition, is an ordered pair of states, and if it is remembered that the data appropriate to specifying a singular end is a single state, then an element of conduct, at its minimum, can be conceived to consist of an ordered triple of states.
Point 5. Reflection, joined to conduct, generates an image of it.
'''Point 5.''' Reflection, joined to conduct, generates an image of it.
Reflection on conduct produces an image of that conduct. In relation to the active nature of the conduct the image is just what its etymology says it is, an inactive sign or an inert icon of the action. The image of a conduct presents itself as a hypothesis about it, a tentative decription that may or may be accurate out of the starting blocks and may or may not continue to be useful in the long run.
Reflection on conduct produces an image of that conduct. In relation to the active nature of the conduct the image is just what its etymology says it is, an inactive sign or an inert icon of the action. The image of a conduct presents itself as a hypothesis about it, a tentative description that may or may not be accurate out of the starting blocks and may or may not continue to be useful in the long run.
Point 6. There is a type of reflection that only reproduces the images produced by previous reflections.
'''Point 6.''' There is a type of reflection that only reproduces the images produced by previous reflections.
The images produced by this kind of reflection, affected by an imitative or nearly identical character, can be referred to as "reproductions", "stereotypes", or "simple copies". A reproductive reflection has the option of attaching additional marks to distinguish the reproduced copy from the original image. If it does add a distinguishing mark or a distinctive notation to identify the source, then one has the type of reproduction that can safely be regarded as a reflective "quotation".
The images produced by this kind of reflection, affected by an imitative or nearly identical character, can be referred to as “reproductions”, “stereotypes”, or “simple copies”. A reproductive reflection has the option of attaching additional marks to distinguish the reproduced copy from the original image. If it does add a distinguishing mark or a distinctive notation to identify the source, then one has the type of reproduction that can safely be regarded as a reflective “quotation”.
Point 7. There is a type of reflection that captures an extended sequence of events in a single image.
'''Point 7.''' There is a type of reflection that captures an extended sequence of events in a single image.
The images produced by this kind of reflection, affected by a creative, critical, reductive, selective, or truly imaginative character, using manners of plastic representation that can condense, edit, summarize, and transform, all at the risk of serious distortions that go beyond simple errors in the transmission, can be referred to as "adaptations", "redactions", "renditions", "versions", or "transformed interpretations".
The images produced by this kind of reflection, affected by a creative, critical, reductive, selective, or truly imaginative character, using manners of plastic representation that can condense, edit, summarize, and transform, all at the risk of serious distortions that go beyond simple errors in the transmission, can be referred to as “adaptations”, “redactions”, “renditions”, “versions”, or “transformed interpretations”.
These effect of reflection, when it is efficient, is to do just this, to produce a single image that captures a poignant, salient, or relevant aspect of an entire dramatic sequence.
These effect of reflection, when it is efficient, is to do just this, to produce a single image that captures a poignant, salient, or relevant aspect of an entire dramatic sequence.
Point 8. Inquiry, if deliberate and critical, involves reflection.
'''Point 8.''' Inquiry, if deliberate and critical, involves reflection.
The capacity for reflection is necessary to carry out the deliberately conducted and critically controlled varieties of inquiry that make up the principal interest of this work, and especially to entertain any form of inquiry into inquiry.
The capacity for reflection is necessary to carry out the deliberately conducted and critically controlled varieties of inquiry that make up the principal interest of this work, and especially to entertain any form of inquiry into inquiry.
The pragmatic theory of signs sets the stage for a broad definition of inquiry. It includes under "inquiry" all the fortuitous and instinctive processes that agents exploit to escape from states of uncertainty, to soothe the "irritation of doubt", in Peirce's phrase, along with all the deliberate and intelligent procedures that enable communities of agents to deal in systematic ways with the surprises and the problems that they encounter in their several and common experiences. At one end of this spectrum, the more incidental, instinctive, and casually intuitive forms of inquiry can be carried on without the interruptions of critical reflection. But an intelligent inquiry is necessarily a reflective inquiry.
The pragmatic theory of signs sets the stage for a broad definition of inquiry. It includes under “inquiry” all the fortuitous and instinctive processes that agents exploit to escape from states of uncertainty, to soothe the “irritation of doubt”, in Peirce's phrase, along with all the deliberate and intelligent procedures that enable communities of agents to deal in systematic ways with the surprises and the problems that they encounter in their several and common experiences. At one end of this spectrum, the more incidental, instinctive, and casually intuitive forms of inquiry can be carried on without the interruptions of critical reflection. But an intelligent inquiry is necessarily a reflective inquiry.
Point 9. The need for a capacity of reflection is the reflection of a certain incapacity to see certain things without it.
'''Point 9.''' The need for a capacity of reflection is the reflection of a certain incapacity to see certain things without it.
This point has a bearing on the capacity that one has to recognize one's own character as an objective form of being and to realize it within an active pattern of conduct.
This point has a bearing on the capacity that one has to recognize one's own character as an objective form of being and to realize it within an active pattern of conduct.
Point 10. At this point, the circumstances bearing on the previous few points interact in such a way as to produce a series of further points.
'''Point 10.''' At this point, the circumstances bearing on the previous few points interact in such a way as to produce a series of further points.
Expressed in an 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" (FIC's).
'''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.
Something is a FIC to the extent that it falls into any of the following sorts: (1) anything that exists in the form of a finite number of bits, (2) anything whose objective being can be described in terms of a finite number of bits, or (3) anything whose moment to moment activity can be specified by means of a finite number of bits.
Something is a FIC to the extent that it falls into any of the following sorts:
# Anything that exists in the form of a finite number of bits,
# Anything whose objective being can be described in terms of a finite number of bits,
# Anything whose moment to moment activity can be specified by means of a finite number of bits.
Notice that this depiction makes being a FIC a term of description, and thus of possible approximation, not of necessity an exact definition of the thing's essential substance. An objective being or a real activity, even one that escapes all bounds of finite description, can be usefully represented "as" or "by means of" a FIC precisely to the extent that a particular description of it in this form succeeds in helping the agent concerned to orient toward its underlying reality and to deal with its ultimate consequences.
Notice that this depiction makes being a FIC a term of description, and thus of possible approximation, not of necessity an exact definition of the thing's essential substance. An objective being or a real activity, even one that escapes all bounds of finite description, can be usefully represented “as” or “by means of” a FIC precisely to the extent that a particular description of it in this form succeeds in helping the agent concerned to orient toward its underlying reality and to deal with its ultimate consequences.
Point 12. Reflection involves higher orders of sign relations.
'''Point 12.''' Reflection involves higher orders of sign relations.
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 k 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 <o, s, i> 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.
If reflection is to constitute more than a transient form of observation, then provision needs to be made for permanently recording its HO signs. Under these conditions the capacity for instituting and maintaining an order of reflection is just a capacity for creating and storing HO signs.
If reflection is to constitute more than a transient form of observation, then provision needs to be made for permanently recording its HO signs. Under these conditions the capacity for instituting and maintaining an order of reflection is just a capacity for creating and storing HO signs.
This gives a brief glimpse of the issues involved in the effort toward reflection and the roughest possible estimate of the kinds of growth rates in the population of HO signs that are engendered by the need to provide a durable and stable medium for reflection. Further discussion of these topics can be put off to a later point. At this point it only needs to be clear that the injunction of a reflective capacity and the injunction of capacity limitations have an acute bearing on each other.
This gives a brief glimpse of the issues involved in the effort toward reflection and the roughest possible estimate of the kinds of growth rates in the population of HO signs that are engendered by the need to provide a durable and stable medium for reflection. Further discussion of these topics can be put off to a later point. At this point it only needs to be clear that the injunction of a reflective capacity and the injunction of capacity limitations have an acute bearing on each other.
The combinatorial explosion engendered by reflection impinges on the capacity limitations of a FIC with such an impact that neither the standpoints of "naive empiricism" or "naive intuitionism" 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 “naive empiricism” or “naive intuitionism” can continue to support viable forms of inquiry.
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.
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 "quotation". Strictly speaking, the descriptive term "quotation" 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 "injective" 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 "name" or a distinctive "number" 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 “quotation”. Strictly speaking, the descriptive term “quotation” 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 “injective” 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 “name” or a distinctive “number” to index each piece its source material.
Some sort of quotation operation has to be made available as a standard mechanism to support almost any level of theoretical discussion about syntax. In computational settings, various types of quotation operation need to be implemented as computable functions and provided among the basic resources for almost any adequate system of symbolic computation. Conceived as a stock device of computation, and supplied with domains of arguments already well established as signs, quotation is relatively easy to implement.
Some sort of quotation operation has to be made available as a standard mechanism to support almost any level of theoretical discussion about syntax. In computational settings, various types of quotation operation need to be implemented as computable functions and provided among the basic resources for almost any adequate system of symbolic computation. Conceived as a stock device of computation, and supplied with domains of arguments already well established as signs, quotation is relatively easy to implement.
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. 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 13.''' 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. 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.''' 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.
When it is necessary to be precise, I use the term "matriculation" to refer to the first permanent recording of a sign by an agent, the one that marks in a relatively indelible fashion the initial recognition, original declaration, or principal registration of a sign by an agent, on which every subsequent use of that sign by that agent depends, and to which every later usage of that sign by that agent implicitly or explicitly refers.
When it is necessary to be precise, I use the term “matriculation” to refer to the first permanent recording of a sign by an agent, the one that marks in a relatively indelible fashion the initial recognition, original declaration, or principal registration of a sign by an agent, on which every subsequent use of that sign by that agent depends, and to which every later usage of that sign by that agent implicitly or explicitly refers.
The feature of matriculation that is important to the present argument is that it uses up memory capacity in a monotonic way. It is an economical strategy of memory usage to matriculate only the first token of each sign type observed and to let the observation of each subsequent token generate only a derivative reference to the primary registration. However, the present argument does not depend on the hypothesis of such a model actually being used, since this standard is only proposed to establish a lower bound on memory usage.
The feature of matriculation that is important to the present argument is that it uses up memory capacity in a monotonic way. It is an economical strategy of memory usage to matriculate only the first token of each sign type observed and to let the observation of each subsequent token generate only a derivative reference to the primary registration. However, the present argument does not depend on the hypothesis of such a model actually being used, since this standard is only proposed to establish a lower bound on memory usage.
In order to reflect on sign relations, it is necessary to have signs for sign relations. Failing this, the laws or principles that sign processes follow, even if fleetingly half intuited, remain forever semi conscious, and thus they continue to rule in a subcritical state of representation.
In order to reflect on sign relations, it is necessary to have signs for sign relations. Failing this, the laws or principles that sign processes follow, even if fleetingly half intuited, remain forever semi conscious, and thus they continue to rule in a subcritical state of representation.
At this point it becomes clear that the ideals of a naive empiricism must be left behind. The combinatorial explosion set off by the need to contemplate HO sign relations ...
At this point it becomes clear that the ideals of a naive empiricism must be left behind. The combinatorial explosion set off by the need to contemplate HO sign relations …
If it becomes necessary to entertain hypotheses about sign transitions, then the space of HO signs that has to be matriculated is potentially as large as the space of all ordered pairs of signs from the initial domain. If it becomes necessary to hypothesize about sign processes in general, then the space of HO signs that has to be matriculated grows like the union of the spaces of k tuples of signs from the initial domain, where k = 1, 2, 3, ..., and possibly increases with no limit in principal.
If it becomes necessary to entertain hypotheses about sign transitions, then the space of HO signs that has to be matriculated is potentially as large as the space of all ordered pairs of signs from the initial domain. If it becomes necessary to hypothesize about sign processes in general, then the space of HO signs that has to be matriculated grows like the union of the spaces of <math>k\!</math>-tuples of signs from the initial domain, where <math>k = 1, 2, 3, \ldots,\!</math> and possibly increases with no limit in principal.
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. 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 …
Point 16. Reflection involves a sense of context, and this involves a notion of community.
'''Point 16.''' 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 “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.
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.''' 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 “images” 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.''' 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 “codes”, 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 “pandect”.
Point 19. The power of reflection involves a risk of distortion.
'''Point 19.''' 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.''' 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 “-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.
Point 21. There appears to be a large variety of ways that the process of reflection can go wrong.
'''Point 21.''' 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.
# 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.
Point 22. 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.
'''Point 23.''' Inquiry into inquiry involves integrating independent inquiries.
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.
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 "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.
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.''' 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.''' 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'' ∈ ''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 “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.
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.''' 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]]