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There is a thought that forms the theme of the present inquiry, indeed, as a chorus to a lyric are its evocations to the text that records this inquiry, and I find myself returning to its expressions on a constantly recurring basis, however much I strive to introduce variations for the sake of developing its implications and reflecting on its meanings from a fresh angle. So let me give the current rendition:

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The present inquiry, <math>y_0,\!</math> portraying itself as an inquiry into inquiry, <math>y \cdot y,\!</math> proceeds on the premiss that a generic inquiry, <math>y,\!</math> can generally inquire into a generic inquiry, <math>y,\!</math> thereby achieving a settled result, one that awaits a mere determination to be signified by the name <math>{}^{\backprime\backprime} y \cdot y {}^{\prime\prime}.</math> Thus the present inquiry, acting on the pretext of a ''formal posability'', that is, a poetic license, a verbal permission, or a written suggestion, being motivated and justified by no more authority than these connote, is led to define itself in terms that appose its own term to its own term, and so it is led to take on a recursive, a reflective, or a reflexive cast.

+

The present inquiry, <math>y_0,\!</math> portraying itself as an inquiry into inquiry, <math>y \cdot y,\!</math> proceeds on the premiss that a generic inquiry, <math>y,\!</math> can generally inquire into a generic inquiry, <math>y,\!</math> thereby achieving a settled result, one that awaits a mere determination to be signified by the name <math>{}^{\backprime\backprime} y \cdot y {}^{\prime\prime}.\!</math> Thus the present inquiry, acting on the pretext of a ''formal posability'', that is, a poetic license, a verbal permission, or a written suggestion, being motivated and justified by no more authority than these connote, is led to define itself in terms that appose its own term to its own term, and so it is led to take on a recursive, a reflective, or a reflexive cast.

The terms of this description need to be inquired into, and their implications pursued in greater detail.

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The present inquiry, <math>y_0,\!</math> portraying itself as an inquiry into inquiry, <math>y \cdot y,\!</math> proceeds on the premiss that a generic inquiry, <math>y,\!</math> can generally inquire into a generic inquiry, <math>y,\!</math> and thereby achieve a settled result, and that this result awaits nothing other than its determination by the present inquirer to confer an objective significance on the name <math>{}^{\backprime\backprime} y \cdot y {}^{\prime\prime}.</math> All of this is summed up in the formula: <math>{}^{\backprime\backprime} y_0 = y \cdot y {}^{\prime\prime}.</math>

+

The present inquiry, <math>y_0,\!</math> portraying itself as an inquiry into inquiry, <math>y \cdot y,\!</math> proceeds on the premiss that a generic inquiry, <math>y,\!</math> can generally inquire into a generic inquiry, <math>y,\!</math> and thereby achieve a settled result, and that this result awaits nothing other than its determination by the present inquirer to confer an objective significance on the name <math>{}^{\backprime\backprime} y \cdot y {}^{\prime\prime}.\!</math> All of this is summed up in the formula: <math>{}^{\backprime\backprime} y_0 = y \cdot y {}^{\prime\prime}.\!</math>

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Thus the present inquiry, acting on the pretext of a ''formal posability'', namely, the circumstance that the rules of a prospective formal grammar allow one to write the expression <math>{}^{\backprime\backprime} y \cdot y {}^{\prime\prime}</math> and to inquire after its meaning, is led to define itself in terms that apply to its own case as argument, since the present inquiry, <math>y_0,\!</math> must be an example of whatever genus, <math>Y,\!</math>, that a generic inquiry, <math>y,\!</math> is selected to represent. As a consequence, the present inquiry is forced to pursue the development of its own case in terms that appose its own actions to its own motives, and so is led to take on a recursive, a reflective, or a reflexive cast.

+

Thus the present inquiry, acting on the pretext of a ''formal posability'', namely, the circumstance that the rules of a prospective formal grammar allow one to write the expression <math>{}^{\backprime\backprime} y \cdot y {}^{\prime\prime}\!</math> and to inquire after its meaning, is led to define itself in terms that apply to its own case as argument, since the present inquiry, <math>y_0,\!</math> must be an example of whatever genus, <math>Y,\!</math>, that a generic inquiry, <math>y,\!</math> is selected to represent. As a consequence, the present inquiry is forced to pursue the development of its own case in terms that appose its own actions to its own motives, and so is led to take on a recursive, a reflective, or a reflexive cast.

=====5.1.2.2. The Symbolic Object=====

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To paraphrase, the present inquiry acts on the pretense that an inquiry can inquire into other inquiries, perhaps even those that are presently ongoing, and even inquire into itself, in sum, being entitled to inquire into the full genus of inquiry, <math>Y,\!</math> a class that includes <math>y_0\!</math> as a member. But these representations, under cross examination, lead to a number of unanswered questions, like: Just what is a “generic inquiry”, anyway? Even more critically, their close and repeated examination leads to a host of “unquestioned answers”, answers already accepted as adequate, but whose appearances as answers need to be questioned again.

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The ''formal posability'' of a self application, for example, as expressed by the term <math>{}^{\backprime\backprime} y \cdot y {}^{\prime\prime},</math> especially when the formal calculus that is called on to make sense of these applications is still merely prospective and still highly speculative, ought to arouse a lot of suspicion from the purely formal point of view. Indeed, I cannot justify this way of proceeding, beginning in the middle of things and without stopping to establish a well defined formal system ahead of time, except to say that something very like it is unavoidable in a large number of natural circumstances, and so one ought to find a way of getting used to it. A way of getting used to the natural situation of inquiry is one of the things that the present inquiry hopes to find.

+

The ''formal posability'' of a self application, for example, as expressed by the term <math>{}^{\backprime\backprime} y \cdot y {}^{\prime\prime},\!</math> especially when the formal calculus that is called on to make sense of these applications is still merely prospective and still highly speculative, ought to arouse a lot of suspicion from the purely formal point of view. Indeed, I cannot justify this way of proceeding, beginning in the middle of things and without stopping to establish a well defined formal system ahead of time, except to say that something very like it is unavoidable in a large number of natural circumstances, and so one ought to find a way of getting used to it. A way of getting used to the natural situation of inquiry is one of the things that the present inquiry hopes to find.

If it appears that this allows the present inquiry an unlimited scope or an excessive freedom, it has to be remembered that a ''formal posability'' is barely enough of a formal subsistence to begin an inquiry, but rarely enough to finish it. It can be invaluable as the provisional ''grubstake'' for a prospecting expedition, supplying the initial overhead it takes to ''prime the pump'' of subsequent exploration, but it is not sufficient to continue very far with an investigation. In essence, it is nothing more substantial than a grammatical allowance or a syntactic hypothesis, in effect, a poetic license, a verbal permission, or a written suggestion. Taking all of these cautions into account, it leaves the present inquiry motivated and justified by no more authority than their titles connote, and it obliges the precocity of what is written to be atoned for with all the critical benevolence of afterthought that can be mustered after the fact, to wit, through the diligent application of that turn of mind that allows one to write first and only later to think on the meaning.

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|}

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The present inquiry acts on the purely formal suggestion that a generic inquiry can inquire into other inquiries, perhaps even those that remain ongoing, moreover, that a particular inquiry can even inquire into itself. Interpolating the appropriate symbols, the present inquiry, referring to itself as <math>{}^{\backprime\backprime} y_0 {}^{\prime\prime},</math> acts on the instance of a purely formal possibility, one that it expresses as a premiss in the formula <math>{}^{\backprime\backprime} y_0 = y \cdot y {}^{\prime\prime},</math> intending this to be interpreted to the effect that an inquiry can inquire into a class of inquiries that includes itself as a member, and this is a hypothesis that is based on little more authority than the fact of its expression a prospective formal language, in other words, one whose interpretation is still a largely prospective matter.

+

The present inquiry acts on the purely formal suggestion that a generic inquiry can inquire into other inquiries, perhaps even those that remain ongoing, moreover, that a particular inquiry can even inquire into itself. Interpolating the appropriate symbols, the present inquiry, referring to itself as <math>{}^{\backprime\backprime} y_0 {}^{\prime\prime},\!</math> acts on the instance of a purely formal possibility, one that it expresses as a premiss in the formula <math>{}^{\backprime\backprime} y_0 = y \cdot y {}^{\prime\prime},\!</math> intending this to be interpreted to the effect that an inquiry can inquire into a class of inquiries that includes itself as a member, and this is a hypothesis that is based on little more authority than the fact of its expression a prospective formal language, in other words, one whose interpretation is still a largely prospective matter.

Stepping back and reflecting on the situation, one needs to ask how in general and how in particular does one fall so blithely into these forms and into these manners of representation. Once that process is better understood then it becomes possible to evaluate in a fairer way whether this direction of fall is tantamount to a happy accident of the natural intuition or whether it constellates a disastrous catastrophe that needs to be remedied through the application of a severer style of reasoning. Generally speaking, the point at which intellectual developments like these begin to take on an automatic character is when the intention is formed of devising a formal calculus, in the present case, a prospective calculus of ''applications'' or ''appositions'' of the form <math>f \cdot g,\!</math> the terms of which are intended to be capable of referring to processes potentially as complex as inquiries. The project of an ''appositional calculus'' (AC) is what formalizes the intuitive possibility of an inquiry into inquiry and continues to suggest the formal possibility that any inquiry can be applied to itself, at least, any inquiry that can be symbolized in this calculus.

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The present situation, as far as it goes, is a suitable subject for being investigated along the lines of the pragmatic theory of sign relations.

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Since <math>{}^{\backprime\backprime} x {}^{\prime\prime}</math> is a sign, it has the potential to denote an object <math>x,\!</math> if and when there is determined to be a signified object, and one with a power to impress itself on the mind of the operative interpreter of that sign. Likewise, since <math>{}^{\backprime\backprime} y_0 = y \cdot y {}^{\prime\prime}</math> is a sign, it has the potential to denote an object, one that syntactic compunctions stop me from saying is <math>y_0 = y \cdot y,</math> that is, if I want to avoid a definite risk of failing to be understood. But what is this object, if it exists? At any rate, what sort of object is the receiver of the sign thereby entitled to expect it to be, whether or not the object that it foreshadows ever does come to be actualized?

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Since <math>{}^{\backprime\backprime} x {}^{\prime\prime}\!</math> is a sign, it has the potential to denote an object <math>x,\!</math> if and when there is determined to be a signified object, and one with a power to impress itself on the mind of the operative interpreter of that sign. Likewise, since <math>{}^{\backprime\backprime} y_0 = y \cdot y {}^{\prime\prime}\!</math> is a sign, it has the potential to denote an object, one that syntactic compunctions stop me from saying is <math>y_0 = y \cdot y,\!</math> that is, if I want to avoid a definite risk of failing to be understood. But what is this object, if it exists? At any rate, what sort of object is the receiver of the sign thereby entitled to expect it to be, whether or not the object that it foreshadows ever does come to be actualized?

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In order to have a variety of more convenient names for referring to the object potentially denoted by the sign <math>{}^{\backprime\backprime} y_0 = y \cdot y {}^{\prime\prime},</math> I refer to the expression <math>{}^{\backprime\backprime} y_0 = y \cdot y {}^{\prime\prime}</math> as ''“The Initial Equation”'', or as ''“TIE”'', for short. Although it is not strictly necessary for such a small piece of text as <math>{}^{\backprime\backprime} y_0 = y \cdot y {}^{\prime\prime},</math> I here obey the rule that the titles of texts are italicized. Furthermore, the object, situation, or state that satisfies ''TIE'', to the effect that <math>y_0 = y \cdot y,\!</math> and is therefore potentially denoted by ''TIE'', can also be referred to as “the intended state”, or as “TIS”, for short.

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In order to have a variety of more convenient names for referring to the object potentially denoted by the sign <math>{}^{\backprime\backprime} y_0 = y \cdot y {}^{\prime\prime},\!</math> I refer to the expression <math>{}^{\backprime\backprime} y_0 = y \cdot y {}^{\prime\prime}\!</math> as ''“The Initial Equation”'', or as ''“TIE”'', for short. Although it is not strictly necessary for such a small piece of text as <math>{}^{\backprime\backprime} y_0 = y \cdot y {}^{\prime\prime},\!</math> I here obey the rule that the titles of texts are italicized. Furthermore, the object, situation, or state that satisfies ''TIE'', to the effect that <math>y_0 = y \cdot y,\!</math> and is therefore potentially denoted by ''TIE'', can also be referred to as “the intended state”, or as “TIS”, for short.

{| align="center" border="0" cellpadding="0" cellspacing="0" width="90%"

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Are virtues the species and teachings the genus, or perhaps vice versa? Or do virtues and teachings form domains that are essentially distinct? Whether one is a species of the other or whether the two are essentially different, what are the features that apparently distinguish the one from the other?

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Let me begin by assuming a situation that is plausibly general enough, that some virtues can be taught, symbolized as <math>V \land T</math>, and that some cannot, symbolized as <math>V \land \lnot T</math>. I am not trying to say yet whether both kinds of cases actually occur, but merely wish to consider what follows from the likely alternatives. Then the question as to what distinguishes virtues from teachings has two senses:

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Let me begin by assuming a situation that is plausibly general enough, that some virtues can be taught, symbolized as <math>V \land T\!</math>, and that some cannot, symbolized as <math>V \land \lnot T\!</math>. I am not trying to say yet whether both kinds of cases actually occur, but merely wish to consider what follows from the likely alternatives. Then the question as to what distinguishes virtues from teachings has two senses:

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# Among virtues that are special cases of teachings, <math>V \land T</math>, the features that distinguish virtues from teachings are known as ''specific differences''. These qualities serve to mark out virtues for special consideration from amidst the common herd of teachings and tend to distinguish the more exemplary species of virtues from the more inclusive genus of teachings.

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# Among virtues that are special cases of teachings, <math>V \land T\!</math>, the features that distinguish virtues from teachings are known as ''specific differences''. These qualities serve to mark out virtues for special consideration from amidst the common herd of teachings and tend to distinguish the more exemplary species of virtues from the more inclusive genus of teachings.

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# Among virtues that transcend the realm of teachings, <math>V \land \lnot T</math>, the features that distinguish virtues from teachings are aptly called ''exclusionary exemptions''. These properties place the reach of virtues beyond the grasp of what is attainable through any order of teachings and serve to remove the orbit of virtues a discrete pace from the general run of teachings.

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# Among virtues that transcend the realm of teachings, <math>V \land \lnot T\!</math>, the features that distinguish virtues from teachings are aptly called ''exclusionary exemptions''. These properties place the reach of virtues beyond the grasp of what is attainable through any order of teachings and serve to remove the orbit of virtues a discrete pace from the general run of teachings.

In either case it can always be said, though without contributing anything of substance to the understanding of the problem, that it is their very property of ''virtuosity'' or their very quality of ''excellence'' that distinguishes the virtues from the teachings, whether this character appears to do nothing but add specificity to what can be actualized through learning alone, or solely through teaching, or whether it requires a nature that transcends the level of what can be achieved through any learning or teaching at all. But this sort of answer only begs the question. The real question is whether this mark is apparent or real, and how it ought to be analyzed and construed.

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<li>Did Socrates assert or believe that virtue can be taught, or not? In symbols, did he assert or believe that <math>V \Rightarrow T</math>, or not?</li>

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<li>Did Socrates assert or believe that virtue can be taught, or not? In symbols, did he assert or believe that <math>V \Rightarrow T\!</math>, or not?</li>

<li>Did he think that:</li>

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<li>knowledge is virtue, in the sense that <math>U \Rightarrow V</math>?</li>

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<li>knowledge is virtue, in the sense that <math>U \Rightarrow V\!</math>?</li>

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<li>virtue is knowledge, in the sense that <math>U \Leftarrow V</math>?</li>

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<li>virtue is knowledge, in the sense that <math>U \Leftarrow V\!</math>?</li>

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<li>knowledge is virtue, in the sense that <math>U \Leftrightarrow V</math>?</li></ol>

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<li>knowledge is virtue, in the sense that <math>U \Leftrightarrow V\!</math>?</li></ol>

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<li>Did he teach or try to teach that knowledge can be taught? In symbols, did he teach or try to teach that <math>U \Rightarrow T</math>?</li></ol>

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<li>Did he teach or try to teach that knowledge can be taught? In symbols, did he teach or try to teach that <math>U \Rightarrow T\!</math>?</li></ol>

My current understanding of the record that is given to us in Plato's Socratic Dialogues can be summarized as follows:

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At one point Socrates seems to assume the rule that knowledge can be taught, <math>U \Rightarrow T</math>, but simply in order to pursue the case that virtue is knowledge, <math>V \Rightarrow U</math>, toward the provisional conclusion that virtue can be taught, <math>V \Rightarrow T</math>. This seems straightforward enough, if it were not for the good chance that all of this reasoning is taking place under the logical aegis of an indirect argument, a reduction to absurdity, designed to show just the opposite of what it has assumed for the sake of initiating the argument. The issue is further clouded by the circumstance that the full context of the argument most likely extends over several Dialogues, not all of which survive, and the intended order of which remains in question.

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At one point Socrates seems to assume the rule that knowledge can be taught, <math>U \Rightarrow T\!</math>, but simply in order to pursue the case that virtue is knowledge, <math>V \Rightarrow U\!</math>, toward the provisional conclusion that virtue can be taught, <math>V \Rightarrow T\!</math>. This seems straightforward enough, if it were not for the good chance that all of this reasoning is taking place under the logical aegis of an indirect argument, a reduction to absurdity, designed to show just the opposite of what it has assumed for the sake of initiating the argument. The issue is further clouded by the circumstance that the full context of the argument most likely extends over several Dialogues, not all of which survive, and the intended order of which remains in question.

At other points Socrates appears to claim that knowledge and virtue are neither learned nor taught, in the strictest senses of these words, but can only be ''divined'', ''recollected'', or ''remembered'', that is, recalled, recognized, or reconstituted from the original acquaintance that a soul, being immortal, already has with the real idea or the essential form of each thing in itself. Still, this leaves open the possibility that one person can help another to guess a truth or to recall what both of them already share in knowing, as if locked away in one or another partially obscured or temporarily forgotten part of their inmost being. And it is just this freer interpretation of ''learning'' and ''teaching'', whereby one agent catalyzes not catechizes another, that a liberal imagination would yet come to call ''education''. Therefore, the real issue at stake, both with regard to the aim and as it comes down to the end of this inquiry, is not so much whether knowledge and virtue can be learned and taught as what kind of education is apt to achieve their actualization in the individual and is fit to maintain their realization in the community.

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|}

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Of course, there is much that is open to interpretation about the maxim "knowledge is virtue". In particular, does the copula "is" represent a necessary implication (<math>\Rightarrow</math>), a sufficient reduction ("is only", <math>\Leftarrow</math>), or a necessary and sufficient identification (<math>\Leftrightarrow</math>)?

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Of course, there is much that is open to interpretation about the maxim "knowledge is virtue". In particular, does the copula "is" represent a necessary implication (<math>\Rightarrow\!</math>), a sufficient reduction ("is only", <math>\Leftarrow\!</math>), or a necessary and sufficient identification (<math>\Leftrightarrow\!</math>)?

====5.2.9. Principle of Rational Action====

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|}

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How does this ancient issue, concerning the relation of reason, to action, to the good that is overall desired or intended, transform itself through the medium of intellectual history onto the modern scene? In particular, what bearing does it have on the subjects of artificial intelligence and systems theory, and on the object of the present inquiry? As it turns out, in classical cybernetics and in systems theory, and especially in the parts of AI and cognitive science that have to do with heuristic reasoning, the transformations of the problem have tarried so long in the vicinity of a singular triviality that the original form of the question is nearly unmistakable in every modern version. The transposition of the theme <math>(\text{Reason}, \text{Action}, \text{Good})</math> into the mode of <math>(\text{Intelligence}, \text{Operation}, \text{Goal})</math> can make for an interesting variation, but it does not alter the given state of accord or discord among its elements and does nothing to turn the lock into its key.

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How does this ancient issue, concerning the relation of reason, to action, to the good that is overall desired or intended, transform itself through the medium of intellectual history onto the modern scene? In particular, what bearing does it have on the subjects of artificial intelligence and systems theory, and on the object of the present inquiry? As it turns out, in classical cybernetics and in systems theory, and especially in the parts of AI and cognitive science that have to do with heuristic reasoning, the transformations of the problem have tarried so long in the vicinity of a singular triviality that the original form of the question is nearly unmistakable in every modern version. The transposition of the theme <math>(\text{Reason}, \text{Action}, \text{Good})\!</math> into the mode of <math>(\text{Intelligence}, \text{Operation}, \text{Goal})\!</math> can make for an interesting variation, but it does not alter the given state of accord or discord among its elements and does nothing to turn the lock into its key.

How do these questions bear on the present inquiry? Suppose that one is trying to understand something like an agency of life, a capacity for inquiry, a faculty of intelligence, or a power of learning and reasoning. For starters, ''something like'' is a little vague, so let me suggest calling the target class of agencies, capacities, faculties, or powers that most hold my interest here by the name of ''virtues'', thereby invoking as an offstage direction the classical concepts of ''anima'' and ''arete'' that seem to prompt them all. What all of these virtues have in common is their appearance, whether it strikes one on first impression or only develops in one's appreciation through a continuing acquaintance over time, of transcending or rising infinitely far beyond all of one's attempts to construct them from or reduce them to the sorts of instrumentalities that are much more basic, familiar, mundane, ordinary, simpler, in short, the kinds of abilities that one already understands well enough and is granted to have well under one's command or control. For convenience, I dub this class of abilities, that a particular agent has a thorough understanding of and a complete competency in, as the ''resources'' of that agent.

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====5.2.11. Reflective Interpretive Frameworks====

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<~~pre~~>

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~~Tell me, good Brutus, can you see your face?~~

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No, Cassius, for the eye sees not itself

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{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"

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But by reflection, by some other things.

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| colspan="2" | Tell me, good Brutus, can you see your face?

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|-

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| colspan="2" |  

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|-

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| colspan="2" | No, Cassius, for the eye sees not itself

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|-

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| colspan="2" | But by reflection, by some other things.

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|-

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| colspan="2" |  

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|-

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| colspan="2" | 'Tis just;

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|-

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| colspan="2" | And it is very much lamented, Brutus,

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|-

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| colspan="2" | That you have no such mirrors as will turn

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|-

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| colspan="2" | Your hidden worthiness into your eye,

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|-

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| colspan="2" | That you might see your shadow. …

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|-

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| colspan="2" |  

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|-

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| colspan="2" | Into what dangers would you lead me, Cassius,

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|-

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| colspan="2" | That you would have me seek into myself

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|-

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| colspan="2" | For that which is not in me?

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|-

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| colspan="2" |  

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|-

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| colspan="2" | Therefor, good Brutus, be prepared to hear.

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|-

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| colspan="2" | And since you know you cannot see yourself

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|-

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| colspan="2" | So well as by reflection, I, your glass,

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|-

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| colspan="2" | Will modestly discover to yourself

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|-

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| colspan="2" | That of yourself which you yet know not of.

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|-

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| width="50%" |  

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| ''Julius Caesar'', 1.2.53–72

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|}

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~~'Tis just;~~

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~~And it is very much lamented, Brutus,~~

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~~That you have no such mirrors as will turn~~

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~~Your hidden worthiness into your eye,~~

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~~That you might see your shadow. ...~~

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~~Into what dangers would you lead me, Cassius,~~

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~~That you would have me seek into myself~~

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~~For that which is not in me?~~

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~~Therefor, good Brutus, be prepared to hear.~~

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~~And since you know you cannot see yourself~~

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~~So well as by reflection, I, your glass,~~

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~~Will modestly discover to yourself~~

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~~That of yourself which you yet know not of.~~

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~~Julius Caesar: 1.2.53-72~~

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<~~/pre~~>

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The rest of this Section ???, continuing the discussion of formalization in terms of concrete examples and extending over the next 50 ??? Subsections ???, details the construction of a ''reflective interpretive framework'' (RIF). This is a special type of sign theoretic setting, illustrated in the present case as based on the sign relations A and B, but intended more generally to constitute a fully developed environment of objective and interpretive resources, in the likes of which an ''inquiry into inquiry'' can reasonably be expected to find its home.

+

The rest of this Section (?), continuing the discussion of formalization in terms of concrete examples and extending over the next 50 (?) Subsections (?), details the construction of a ''reflective interpretive framework'' (RIF). This is a special type of sign theoretic setting, illustrated in the present case as based on the sign relations A and B, but intended more generally to constitute a fully developed environment of objective and interpretive resources, in the likes of which an ''inquiry into inquiry'' can reasonably be expected to find its home.

An inquiry into inquiry necessarily involves itself in various forms of self application and self reference. Even when the ''inquiree'' and the ''inquirer'', the operand inquiry and the operant inquiry, are conceived to be separately instituted and disjointly embodied in material activity, they still must share a common form and enjoy a collection of definitive characteristics, or else the use of a common term for both sides of the application is equivocal and hardly justified. But this depiction of an inquiry into inquiry, if it is imagined to be valid, raises a couple of difficult issues, of how a form of activity like inquiry can be said to apply and to refer to itself, and of how a general form of activity can be materialized in concretely different processes, that is, represented in the parametrically diverse instantiations of its own generic principles. Before these problems can be clarified to any degree it is necessary to develop a suitable framework of discussion, along with a requisite array of conceptual tools. This is where the construction of a RIF comes in.

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In accord with this analysis of inquiry as a process of clarification, and of clarification in turn as a process that operates on sign relations, the next few paragraphs consider various interpretations of the clarification task, initiating the process of comparing and contrasting their elements, and ultimately seeking to classify their variety. This discussion notices one general feature that all types of clarification process appear to have in common and it discerns another general feature that splits the genus of clarification processes into a couple of broad moieties or species.

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Inquiry, considered as a process of clarification, is the chief way that a sign relation can grow and develop in service to the life of its agent. If not assured as the principal way, at least, while the jurisdictions of automatic adaptation, oblique evolution, and random ramification are yet uncharted and unassessed, it is probably still the most principled way that sign relations have of adapting and evolving to meet the objectives of interpretive agents in their given environments of needs and objects. By way of a general comparison, then, all reasonable interpretations of the clarification task involve the augmentation of sign relations by the addition of ''elementary sign relations'', that is, ordered triples of the form <math>(o, s, i).</math>

+

Inquiry, considered as a process of clarification, is the chief way that a sign relation can grow and develop in service to the life of its agent. If not assured as the principal way, at least, while the jurisdictions of automatic adaptation, oblique evolution, and random ramification are yet uncharted and unassessed, it is probably still the most principled way that sign relations have of adapting and evolving to meet the objectives of interpretive agents in their given environments of needs and objects. By way of a general comparison, then, all reasonable interpretations of the clarification task involve the augmentation of sign relations by the addition of ''elementary sign relations'', that is, ordered triples of the form <math>(o, s, i).\!</math>

−

Treating the process of clarification as one that affects the growth and development of a sign relation, even if constrained to the medium of its syntactic domain, there is, of course, an overwhelming diversity of ways that one can imagine an arbitrary sign relation as growing through time. No matter whether it restrains its labors to the monotonic annexation of ever more triples <math>(o, s, i)</math> to the masses of data already accumulated or whether it liberates the full deliberations of a discursive process, thus invoking the ebb and flow of corrective, editorial, reflective, remedial, and reversible processes, not every mode of growth or development that can occur in a sign relation has a bearing on reducing the uncertainty of an agent about an object or has the effect of promoting the clarity of the given signs.

+

Treating the process of clarification as one that affects the growth and development of a sign relation, even if constrained to the medium of its syntactic domain, there is, of course, an overwhelming diversity of ways that one can imagine an arbitrary sign relation as growing through time. No matter whether it restrains its labors to the monotonic annexation of ever more triples <math>(o, s, i)\!</math> to the masses of data already accumulated or whether it liberates the full deliberations of a discursive process, thus invoking the ebb and flow of corrective, editorial, reflective, remedial, and reversible processes, not every mode of growth or development that can occur in a sign relation has a bearing on reducing the uncertainty of an agent about an object or has the effect of promoting the clarity of the given signs.

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With regard to inquiry as clarification, and clarification in turn as the evolution of a sign relation, it does not matter whether one views it as a process of exploration and discovery, taking place in a preconceived cartesian space <math>O \times S \times I</math> and seeking to find clearer signs for each known object, or whether one views it as a process of creation and invention, staking out the syntactic parts of elementary sign relations <math>(o, s, i),</math> following the directions of transient clarity to the signs of maximal achievable clarity, making and testing novel combinations with an eye toward present objects, and picking out the clearest indications for inclusion in one's current sign relation.

+

With regard to inquiry as clarification, and clarification in turn as the evolution of a sign relation, it does not matter whether one views it as a process of exploration and discovery, taking place in a preconceived cartesian space <math>O \times S \times I\!</math> and seeking to find clearer signs for each known object, or whether one views it as a process of creation and invention, staking out the syntactic parts of elementary sign relations <math>(o, s, i),\!</math> following the directions of transient clarity to the signs of maximal achievable clarity, making and testing novel combinations with an eye toward present objects, and picking out the clearest indications for inclusion in one's current sign relation.

To review: Inquiry depends on clarification, and clarification depends on the augmentation or the evolution of sign relations in various ways. In order to stay within the realms of possibility that are accessible to computational processes and covered by computational models, it is best to look for varieties of clarification process that are tantamount to recursive forms of development in sign relations, those that one can contemplate being carried out by a recursively defined growth process. Even working under these constraints, there is still an amazingly large variety of different ways that the ''eking out'' of initial sign relations and the ''imping out'' of fledgling sign relations can proceed.

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=====5.2.11.5. Of Signs and the Mind=====

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~~<pre>~~

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In the process of trying to clarify my initial description of inquiry, I worked my way back through several modern animadversions, credulous and critical at turns, to an original classical source for many of the ideas that are involved in it. In the process of attempting to understand this text, encountered as a foundation stone in the discussion of sign relations, I found myself invoking, almost reflexively, a number of distinctions, for instance, that between ''figure'' and ''letter'', as they are used to mark a manner of interpretation, and that between ''form'' and ''matter'', as they concern the content of an indication, and each distinction in its turn seemed to be necessary just in order to outline a sufficient indication of what I sense to be a proper reading of this text.

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In the process of trying to clarify my ID of inquiry, I worked my way back through several modern animadversions, credulous and critical at turns, to an original classical source for many of the ideas that are involved in it. In the process of attempting to understand this text, encountered as a foundation stone in the discussion of sign relations, I found myself invoking, almost reflexively, a number of distinctions, for instance, that between "figure" and "letter", as they are used to mark a manner of interpretation, and that between "form" and "matter", as they concern the content of an indication, and each distinction in its turn seemed to be necessary just in order to outline a sufficient indication of what I sense to be a proper reading of this text.

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But the mere formation and the occasional invocation of these words, no matter how familiar the sound of them, is of little benefit to my reader if I cannot explain the sense of them, whether long established meanings or any new gleanings that I intend, and the instrumentality intended for these distinctions can be of little use to anyone unless I can say, with regard to each conceivable distinction, how it is made or how I make it. In accordance with this reflection on the making of distinctions, I am thus led to ask: Who makes these distinctions, and how are they made? Are they made before us, by us, or after us?

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But the mere formation and the occasional invocation of these words, no matter how familiar the sound of them, is of little benefit to my reader if I cannot explain the sense of them, whether long established meanings or any new gleanings that I intend, and the instrumentality intended for these distinctions can be of little use to anyone unless I can say, with regard to each conceivable distinction, how it is made or how I make it. In accordance with this reflection on the making of distinctions, I am thus led to ask: “Who makes these distinctions, and how are they made? Are they made before us, by us, or after us?”

I think I began innocently enough, with no predominating desire either to dispatch or else to vindicate any particular line of thought, but simply to trace the effects of certain ideas, and this means tracking them down to their sources, in whatever places they are to be found, whether ancient or modern, as well as trying to deduce or to foresee their consequences in theory or in action, whether for good or for ill. And now this form of investigation, more like a process of divestiture, brings me to an array of questions that I have only the slightest clues how to answer.

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For instance, consider the distinction between form and matter.

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No matter what distinction forms the interest of the moment, there is that which discerns, draws, finds, follows, grasps, makes, sees, or seizes the distinction in question, an experimental agency that might as well be called an "interpreter", a "maker", or an "observer" of that distinction. With regard to any form of distinction, the agency of a "distinguisher" or a "former" is a role that seems to suit what the Greeks fairly often described, but just barely hinted at, under the name of an "entelechy". In general, this is a somewhat mysterious designation, stemming from a complex of terms whose various connotations are commonly translated as "actuality" or "reality", and often as "actualization" or "realization", seeming to suggest "actualizer" or "realizer" for the duty of this agent. Sticking more literally to its etymology, the function of an "entelechy" can be taken to mean "that which has or is its end in itself", and thus "that which exists for its own sake" or "that which is complete as it is". Whether the interpreter actively creates the distinction as it is drawn or passively discovers the distinction as it is traced is not yet the issue of interest, and I leave this matter to a future distinction.

+

No matter what distinction forms the interest of the moment, there is that which discerns, draws, finds, follows, grasps, makes, sees, or seizes the distinction in question, an experimental agency that might as well be called an ''interpreter'', a ''maker'', or an ''observer'' of that distinction. With regard to any form of distinction, the agency of a ''distinguisher'' or a ''former'' is a role that seems to suit what the Greeks fairly often described, but just barely hinted at, under the name of an ''entelechy''. In general, this is a somewhat mysterious designation, stemming from a complex of terms whose various connotations are commonly translated as ''actuality'' or ''reality'', and often as ''actualization'' or ''realization'', seeming to suggest ''actualizer'' or ''realizer'' for the duty of this agent. Sticking more literally to its etymology, the function of an entelechy can be taken to mean “that which has or is its end in itself”, and thus “that which exists for its own sake” or “that which is complete as it is”. Whether the interpreter actively creates the distinction as it is drawn or passively discovers the distinction as it is traced is not yet the issue of interest, and I leave this matter to a future distinction.

The relevance of the distinction between form and matter can be traced, not solely by way of illustration, to another passage from Aristotle:

−

~~...~~

+

: (Aristotle)

−

One should not let the phrases "tertium quid" or "third something" lead one astray, going so far as to think that an additional essence, a new kind of material, or a novel substance is implied, when it might be only a third way of being, mode of existence, degree of freedom, dimension of motion, or an extra role in a relation that is actually required.

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One should not let the phrases ''tertium quid'' or ''third something'' lead one astray, going so far as to think that an additional essence, a new kind of material, or a novel substance is implied, when it might be only a third way of being, mode of existence, degree of freedom, dimension of motion, or an extra role in a relation that is actually required.

To this seminal account of interpretation the pragmatic theory of signs adds an array of general and specific elaborations, equipping it with a fully developed corpus of formal, instrumental, and material features. Since the pragmatic line of development is in some sense an alternative track to what is usually called the modern line, the naive enlightenment, or the cartesian tradition, and yet shares many aims and basic methods with this still current mode of inquiry, it is necessary to distinguish these different trends, to detect their different impacts on the present scene, and to discern their different imports for the future of inquiry. The accidental, intentional, and specific differences that the pragmatic theory of sign relations, in its currently developing form, is able to deploy over and above the ancient account, along with the differential circumstances that exist in the context of its present day applications, are taken up next, starting with the most salient augmentations and the most significant extensions of its overall lines of growth.

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Some of the most important general features that mark out the pragmatic theory of sign relations from its original material are instrumental in character and arise largely due to changes in the "technological base", formally speaking, between the ancient and the present times, that is, by innovations in the formal languages and the technical methods that are made available for carrying out the discussion. Three of these general instrumental features are taken up next.

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Some of the most important general features that mark out the pragmatic theory of sign relations from its original material are instrumental in character and arise largely due to changes in the technological base, formally speaking, between the ancient and the present times, that is, by innovations in the formal languages and the technical methods that are made available for carrying out the discussion. Three of these general instrumental features are taken up next.

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1. In conformity with the modern facility for thinking of relations in general in extensional terms, as collections of ordered n tuples of domain components that belong to the relation in question, current versions of the theory of signs render it easiest to think of each given sign relation as a particular collection of ordered triples. Elements of a sign relation are called "elementary sign relations" (~~ESR's~~), and the data of each given element of the sign relation can be represented as an ordered triple, of the form <o, s, i>, that names its object, sign, and interpretant, respectively.

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# In conformity with the modern facility for thinking of relations in general in extensional terms, as collections of ordered n tuples of domain components that belong to the relation in question, current versions of the theory of signs render it easiest to think of each given sign relation as a particular collection of ordered triples. Elements of a sign relation are called ''elementary sign relations'' (ESRs), and the data of each given element of the sign relation can be represented as an ordered triple, of the form <math>(o, s, i),\!</math> that names its object, sign, and interpretant, respectively.

−

+

# Among the other props on the modern stage, the pragmatic theory of sign relations can make especially good use of the bounteous ''logics'' of relations and ''algebras'' of relative terms that are currently available, as expressed in any one of several symbolic calculi with approximately the power of predicate logic. Indeed, many of these algebras, calculi, and logics of relations received their first “modern&redquo; formulations in the work of C.S. Peirce, and in the very process of trying to deal with the problems presented by the classical theory of signs. As it happens, this coincidence of origins and this parallelism of derivations may help to account for the appearance of a quality of pre-established harmony that is presently manifested between the general subject of relations and the special subject of sign relations.

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2. Among the other props on the modern stage, the pragmatic theory of sign relations can make especially good use of the bounteous "logics" of relations and "algebras" of relative terms that are currently available, as expressed in any one of several symbolic calculi with approximately the power of predicate logic. Indeed, many of these algebras, calculi, and logics of relations received their first "modern" formulations in the work of C.S. Peirce, and in the very process of trying to deal with the problems presented by the classical theory of signs. As it happens, this coincidence of origins and this parallelism of derivations may help to account for the appearance of a quality of "pre established harmony" that is presently manifested between the general subject of relations and the special subject of sign relations.

+

# Developments in other fields in the intervening times have caused the prevailing paradigms to shift a number of times. For starters, the lately recognized inescapability of participatory observation, and the multitude of constraints on knowledgeable action that the necessity of this contingency implies, that ought to have always been clear in marking the horizons of anthropology, economics, politics, psychology, and sociology, and the phenomenological consequences of this unavoidability that have recently forced themselves to the status of physical principles and tardily made their appearance in the symbolic rites of the attendant formalities, against all the fields of reluctance that physics can generate, and in spite of the full recalcitrance that its occasional ancillary, mathematics, can bring to heel. These cautions leave even the casual observer nowadays much more suspicious about declaring the self evident independence of diverse aspects and axes of experience, whether assuming the disentanglement of different features of experiential quality or presuming on the orthogonality of their coordinate dimensions of formal quantity, for instance, as represented by the aspects of particles versus waves, or the axes of space versus time. Features and dimensions of experience that appear as relevant or arise into salience at one level of action, exchange, or observation can disappear from the scene of relevant regard at other stages of participation and weigh imponderably on other scales of transaction. In relation to one another, aspects and axes of experience that appear unrelated just so long as they are considered at one level of interaction and perception may not preserve their appearance of indifference and independence if the scales of participation under consideration are radically shifted, whether up or down in their order of magnitude. As a result, the sort of consideration that makes a line of experience conspicuous as it falls on one plane of existence is seldom enough to draw it through every plane of being. In a related fashion, the brand of consideration whose bearing on an intermediate scale of treatment causes one to regard two features or dimensions of experience as ''moderately independent'' or as ''relatively orthogonal'' is rarely ever relevant to all levels of regard and is almost never enough to justify one's calling these aspects ''absolutely independent'' or to support one's calling these axes "perfectly orthogonal".

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3. Developments in other fields in the intervening times have caused the prevailing paradigms to shift a number of times. For starters, the lately recognized inescapability of "participatory observation", and the multitude of constraints on knowledgeable action that the necessity of this contingency implies, that ought to have always been clear in marking the horizons of anthropology, economics, politics, psychology, and sociology, and the phenomenological consequences of this unavoidability that have recently forced themselves to the status of physical principles and tardily made their appearance in the symbolic rites of the attendant formalities, against all the fields of reluctance that physics can generate, and in spite of the full recalcitrance that its occasional ancillary, mathematics, can bring to heel. These cautions leave even the casual observer nowadays much more suspicious about declaring the self evident independence of diverse aspects and axes of experience, whether assuming the disentanglement of different features of experiential quality or presuming on the orthogonality of their coordinate dimensions of formal quantity, for instance, as represented by the aspects of particles versus waves, or the axes of space versus time. Features and dimensions of experience that appear as relevant or arise into salience at one level of action, exchange, or observation can disappear from the scene of relevant regard at other stages of participation and weigh imponderably on other scales of transaction. In relation to one another, aspects and axes of experience that appear unrelated just so long as they are considered at one level of interaction and perception may not preserve their appearance of indifference and independence if the scales of participation under consideration are radically shifted, whether up or down in their order of magnitude. As a result, the sort of consideration that makes a line of experience conspicuous as it falls on one plane of existence is seldom enough to draw it through every plane of being. In a related fashion, the brand of consideration whose bearing on an intermediate scale of treatment causes one to regard two features or dimensions of experience as "moderately independent" or as "relatively orthogonal" is rarely ever relevant to all levels of regard and is almost never enough to justify one's calling these aspects "absolutely independent" or to support one's calling these axes "perfectly orthogonal".

Next, I examine the more specific features of the pragmatic theory of sign relations, focusing on attributes that are augmented in the degrees of their development and that acquire a distinctive emphasis along with the extension and growth of this theory. These features happen to be material in character, that is, they concern the contents of individual sign relations, affecting the aspects of relational structure and the orders of relational complexity that become especially conspicuous from the pragmatic point of view. Two of these specific material features are taken up next.

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1. Direct relation between objects and signs.

+

# Direct relation between objects and signs.

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# Irreducibly triadic sign relations.

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~~2. Irreducibly triadic~~ sign relations.

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A few more things can now be said about the conditions that are usually taken for granted in the theoretical use of sign relations. Although it is often the case that the structure of the object domain is marked for reconstruction, part for part, in the partition of the syntactic domain, as one says, in the ''divisions'' of its ''quotient structure'', or equally, in the structure of its ''semantic equivalence classes'' (SECs), which are also called its ''semantic orbits'', it is advisable not to imagine, except in the most abstractly artificial and purely formal cases, that an object is “nothing but” an orbit of signs. In every situation of concrete or practical interest, the object domain is something that has a real existence, one that is independent of the syntactic domain to some degree, and to a degree of qualified independence that can be specified, for example, as ''absolutely'', ''moderately'', or ''relatively''. That is, an object exists in a manner that is more or less independent of both the signs and the interpretants that are used to talk and to think about it, as one sooner or later discovers in any real case where one is tempted to ignore the implications of this fact.

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~~A few more things can now be said about~~ the ~~conditions that are usually taken~~ for ~~granted in~~ the ~~theoretical use of sign relations.~~ ~~Although it~~ is ~~often~~ the ~~case that~~ the ~~structure~~ of ~~the object domain is marked for reconstruction~~, ~~part for part, in~~ the ~~partition~~ of ~~the syntactic domain, as~~ one ~~says, in the "divisions" of its "quotient structure", or equally, in the structure of its "semantic equivalence classes" (SEC~~'s~~), which are also called its "semantic orbits" (SO's), it is advisable not to imagine, except~~ in the ~~most abstractly artifical~~ and ~~the most purely formal cases~~, that ~~an object is "nothing but" an orbit of signs. In every situation~~ of ~~concrete or practical interest,~~ the ~~object domain is something~~ that ~~has a real existence,~~ one ~~that is "independent of" the syntactic domain~~ to ~~some degree~~, ~~and to a degree of qualified independence that can be specified, for example, as "absolutely", "moderately, or "relatively". That~~ is, an ~~object exists in a manner~~ that ~~is more or less "independent~~ of~~" both the signs~~ and ~~the interpretants that are used to talk and to think about it~~, as ~~one sooner or later discovers~~ in ~~any real case where one is tempted~~ to ~~ignore~~ the ~~implications~~ of ~~this fact~~.

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But this explanation of the status intended for objects only serves to elevate into prominence the subordinate question: What is meant by the relation ''independent of''? Outside the realm of mathematics, where the necessity has long been recognized of declaring one's independence in the form of an explicit and public definition, one that makes clear the sense of the term that one plans to uphold, this is an issue that still manages to incite an uproarious confusion of obvious claims and often just as obvious counter claims, each of which is just as insistent in what it attributes to the terms of its relation as the actual basis for what it considers evident is kept implicit.

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~~But this explanation of~~ the ~~status intended for objects only serves to elevate into prominence the subordinate question~~: ~~What~~ is ~~meant by~~ the relation "independent of"? ~~Outside the realm~~ of ~~mathematics~~, ~~where~~ the ~~necessity has long been recognized~~ of ~~declaring one~~'~~s "independence"~~ in the ~~form~~ of ~~an explicit and public definition~~, ~~one that makes clear~~ the ~~sense of the term~~ that one ~~plans~~ to ~~uphold~~, ~~this is an issue that still manages to incite an uproarious confusion of "obvious" claims~~ and ~~often just as "obvious" counter claims~~, ~~each~~ of which is ~~just as insistent in what it attributes to~~ the ~~terms~~ of ~~its~~ relation ~~as the actual basis for what it considers "evident" is kept implicit~~.

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One thing does appear certain, at least, once the issue is addressed: Whatever it means, and however it is qualified, the relation of being ''independent of'' does not mean a relation of being ''not in relation to''. After all, did I not just call this, with all due justice, a relation? Indeed, independently of all questions of independence, the very notion of there being a relation ''not in relation to'' is a self cancelling nullity. Perhaps the closest that one can approach to conceiving of relations like ''not related to'' or ''not a relative of'', in short, perhaps the simplest analogues or approximations to such a relation that one can devise are: ''considered as not in relation to'' or ''treated as not in relation to'', prompting the questions: ''considered by whom?'' and ''treated by whom?'', all of which goes to make it manifest that a triadic relation is the minimal support needed for any such brand of speculative relation.

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~~One thing does appear~~ certain, ~~at least, once~~ the ~~issue~~ is ~~addressed: Whatever it means,~~ and ~~however it is qualified~~, ~~the relation~~ of ~~being "independent of" does not mean~~ a relation of ~~being "not in relation to". After all~~, ~~did I not just call this, with all due justice~~, a ~~relation?~~ ~~Indeed~~, ~~independently of all questions of independence~~, the ~~very notion~~ of ~~there being~~ a ~~relation "not in~~ relation to~~" is a self cancelling nullity~~. ~~Perhaps~~ the ~~closest~~ that ~~one can approach~~ to ~~conceiving~~ of relations ~~like "not related to" or "not a relative~~ of", ~~in short~~, ~~perhaps~~ the ~~simplest analogues or approximations to such a relation~~ that ~~one~~ can ~~devise are: "considered as not in relation~~ to~~" or "treated as not in~~ relation ~~to"~~, ~~prompting~~ the ~~questions:~~ ~~"considered by who?" and "treated by who?"~~, ~~all of which goes to make it manifest that a triadic relation~~ is the ~~minimal support needed~~ for ~~any such brand of speculative~~ relation.

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In trying to reach a form of relation that is minimal in a certain regard, the analysis comes to a point where it is forced to reverse its direction and to synthesize a complex relation, one that possesses a higher arity than might be expected of a structure intended as a primitive rudiment. What is ultimately suggested is a triadic relation that formulates the idea of a ''consideration'', a ''regard'', or a ''treatment''. This involves an agent that acts as the overseer of the consideration, the regard, or the treatment in question along with a couple of other entities that fall in a dyadic relation to each other under this consideration, this regard, or this treatment. The way to treat this triadic relation as sparingly as possible, in regard to the level of consideration that is assigned to it, is to let the agency of this oversight ignore as much as it possibly can about all the relations that conceivably exist between the overseen pair, the couple of agents, entities, or objects that fall within its purview. Thus, the least that the overseer can manage to do is to mark a relation between the other two parties, without codifying, conveying, recording, or retaining any information about the particular kind of relation it is. At any rate, this is the best interpretation that I find myself able to contrive at present for “<math>X\!</math> regards <math>Y\!</math> as not in relation to <math>Z\!</math>”.

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~~In trying~~ to ~~reach~~ a ~~form of relation that is minimal in a certain regard~~, the ~~analysis comes~~ to a ~~point where it~~ is ~~forced~~ to ~~reverse its direction and to synthesize a complex relation~~, ~~one~~ that ~~possesses a higher arity than might be expected~~ of ~~a structure intended as a primitive rudiment~~. ~~What is ultimately suggested is a triadic relation~~ that ~~formulates~~ the ~~idea~~ of ~~a "consideration", a "regard", or a "treatment"~~. ~~This involves an agent~~ that ~~acts as the overseer~~ of ~~the consideration~~, ~~the regard~~, ~~or the treatment in question along with a couple~~ of ~~other entities that fall~~ in ~~a dyadic relation~~ to ~~each other under this consideration, this regard, or this treatment~~. The ~~way~~ to ~~treat~~ this ~~triadic relation as sparingly as possible, in~~ regard to the ~~level of consideration~~ that ~~is assigned to it, is to let the agency of this oversight ignore as much as it possibly~~ can ~~about all the relations that conceivably exist between the overseen pair, the couple~~ of ~~agents~~, ~~entities, or objects that fall within its purview. Thus~~, the ~~least~~ that ~~the overseer can manage~~ to ~~do is to mark a relation between~~ the ~~other two parties, without codifying, conveying~~, ~~recording, or retaining any information about the particular kind of relation~~ it is~~. At any rate, this is the best interpretation~~ that ~~I find myself able~~ to ~~contrive at present for "X regards Y as not in relation to Z"~~.

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The preceding analysis may appear to lead up to a trivial point, but the argument just recounted is formally identical to a demonstration that is basic to pragmatic thinking, namely, that “we have no conception of the absolutely incognizable” (Peirce, CP 5.265). Whether or not one wishes to say that there are such things as the “absolutely incognizable”, we have no conception of them. Any concept that we do have cannot truly be a concept ''of'' them, that is, it cannot be held to be ''true'' of them, since this all by itself would amount in fact to making them cognizable. The idea that a successful conception is intended by its very nature to result in a true concept is critical and crucial in this regard. If one merely wants to point out the triviality that we can have false concepts of anything we please, for example, the false concepts that are attached to the verbal formula “absolutely incognizable”, then it is easy enough to stipulate that we are likely to have false conceits and misleading concepts about very many things indeed.

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The preceding analysis may appear to lead up to a trivial point, but the argument just recounted is formally identical to a demonstration that is basic to pragmatic thinking, namely, that "we have no conception of the absolutely incognizable" (Peirce, CP 5.265). Whether or not one wishes to say that there are such things as the "absolutely incognizable", we have no conception of them. Any concept that we do have cannot truly be a concept "of" them, that is, it cannot be held to be "true" of them, since this all by itself would amount in fact to making them cognizable. The idea that a successful conception is intended by its very nature to result in a true concept is critical and crucial in this regard. If one merely wants to point out the triviality that we can have false concepts of anything we please, for example, the false concepts that are attached to the verbal formula "absolutely incognizable", then it is easy enough to stipulate that we are likely to have false conceits and misleading concepts about very many things indeed.

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Since the pragmatic theory of sign relations welcomes partial symbols and verbal formulas of every species of description as well as mental impressions, concepts, and ideas of every genus and level of generation into the same broad class of entities that it takes as signs, the idea of an object that is not the object of a sign imparts a formal impression within its material that is identical, or at least indistinguishable in the structure of the relations that it suggests, to the idea of a relation that fits the verbal formula or the specious specification ''not in relation to''. A rigorous critique of these very ideas is required in order to prevent their specious impressions from flowering into malign oppressions that obsess both the mind and the spirit. The pragmatic critique of prior philosophy and the pragmatic theory of signs are intended, in part, precisely to address this task of weeding out delusive ideas.

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Since the pragmatic theory of sign relations welcomes partial symbols and verbal formulas of every species of description as well as mental impressions, concepts, and ideas of every genus and level of generation into the same broad class of entities that it takes as "signs", the idea of an object that is not the object of a sign imparts a formal impression within its material that is identical, or at least indistinguishable in the structure of the relations that it suggests, to the idea of a relation that fits the verbal formula or the specious specification "not in relation to". A rigorous critique of these very ideas is required in order to prevent their specious impressions from flowering into malign oppressions that obsess both the mind and the spirit. The pragmatic critique of prior philosophy and the pragmatic theory of signs are intended, in part, precisely to address this task of "weeding out" delusive ideas.

−

~~</pre>~~

=====5.2.11.6. Questions of Justification=====

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~~<pre>~~

+

There is a singular misunderstanding of this pragmatic perspective that needs to have its equally singular but bad effects blunted at this point. There is a definition of good conduct that is implicit in the pragmatic ordering of the normative sciences, but it is a characterization whose true import is frequently misinterpreted by seizing too quickly on one partial formulation or another of its full intention. If the pragmatic definition of good conduct is properly considered, in light of the full circumstances of its intended application, it does not lead to the bad end often associated with the fallacy of “the ends justifying the means”. In fact, the bad effects accountable to even so facile a formulation of the pragmatic desideratum, can be seen to result, in actual practice, from a faulty application of its own stated principle, going even so far as to ignore the expressly indicated pluralities of “ends” and “means”. But that is merely a verbal scruple. In the end, it does not matter whether one speaks of “ends” or the “end”. What really matters is that the term not be interpreted in too singular a way, but only with regard to the whole conceivable effect of each contemplated form of conduct.

−

There is a singular misunderstanding of this pragmatic perspective that needs to have its equally singular but bad effects blunted at this point. There is a definition of good conduct that is implicit in the pragmatic ordering of the normative sciences, but it is a characterization whose true import is frequently misinterpreted by seizing too quickly on one partial formulation or another of its full intention. If the pragmatic definition of good conduct is properly considered, in light of the full circumstances of its intended application, it does not lead to the bad end often associated with the fallacy of "the ends justifying the means". In fact, the bad effects accountable to even so facile a formulation of the pragmatic ~~desideration~~, can be seen to result, in actual practice, from a faulty application of its own stated principle, going even so far as to ignore the expressly indicated pluralities of "ends" and "means". But that is merely a verbal scruple. In the end, it does not matter whether one speaks of "ends" or the "end". What really matters is that the term not be interpreted in too singular a way, but only with regard to the whole conceivable effect of each contemplated form of conduct.

Accordingly, in order to counteract the brands of bad faith that arise from ignoring this holistic sense, one needs to remember that an action has many consequences. Since an action has a multitude of results, a plurality of which conceivably contribute in significant ways to a truly balanced judgment of its goodness, an action is good only in so far as all of these results are good. If an action, intended primarily for the purpose of achieving a particular good, however successful it is toward that end, nevertheless has collateral consequences that are not so good, then the action is to that degree not so good as it otherwise might be. These are moral trivialities, of course, but just as easily trifled with, and apparently as likely to slip into oblivion for all concerned as they are likely to be slighted by some. But this is the nature of singularity.

−

From this pragmatic point of view, it is possible to deal with many questions of justification by invoking the contexts of amenities that surround the reasoning process, outside of which it cannot be pursued and without which it makes no sense. In this frame, one can say that "reason" is justified by its alternative, that is to say, by "unreason", but only in the peculiar sense that reason is justified by considering the properties of unreason, by contemplating the ethical consequences of acting according to its dictates, and by recognizing the aesthetic fact that one does not like these consequences. Of course, this strategy of argument does not amount to a justification of "reason" in any positive sense of the word "justification". In logical force it is tantamount to the aesthetic tautology of simply insisting that one likes what one likes, but I see nothing unreasonable about this "form of justification" (FOJ), at least, as it is employed in this case. The whole point of noticing the placement of logic within the concentric spheres of ethics and aesthetics is that logical arguments depend on prior considerations of ethical and aesthetic casts, so a logical argument that merely recovers and iterates this context is acting in conformity with the only objective it knows.

+

From this pragmatic point of view, it is possible to deal with many questions of justification by invoking the contexts of amenities that surround the reasoning process, outside of which it cannot be pursued and without which it makes no sense. In this frame, one can say that reason is justified by its alternative, that is to say, by unreason, but only in the peculiar sense that reason is justified by considering the properties of unreason, by contemplating the ethical consequences of acting according to its dictates, and by recognizing the aesthetic fact that one does not like these consequences. Of course, this strategy of argument does not amount to a justification of reason in any positive sense of the word ''justification''. In logical force it is tantamount to the aesthetic tautology of simply insisting that one likes what one likes, but I see nothing unreasonable about this ''form of justification'' (FOJ), at least, as it is employed in this case. The whole point of noticing the placement of logic within the concentric spheres of ethics and aesthetics is that logical arguments depend on prior considerations of ethical and aesthetic casts, so a logical argument that merely recovers and iterates this context is acting in conformity with the only objective it knows.

−

By way of concrete examples, ~~FOJ's~~ of a negative character frequently arise in situations that are affected by a genuine dilemma, where it is necessary to choose just one action from a set of two or more actions, where it is impossible to do nothing and impossible to do everything, and where each action excludes all the others. At such a juncture the structure of that very situation, or a reference to it as described, is itself a sufficiently valid FOJ for choosing some action, even if not yet a full justification for any one specific choice. If an agent challenged: "Why did you do that?", responds: "It was necessary to do something!", then that is "just" as far as it goes, to a general not a specific extent. In summary, one finds that there are ~~FOJ's~~ of a negative character, that proceed by the rejection of an alternative, but that are perfectly valid in their doing so. These ~~FOJ's~~ of a negative character exist in contrast to the more familiar ~~FOJ's~~, at least, the more often expressed ~~FOJ's~~, all of which are positive and transitive in character, identical or analogous to the various forms of logical implication and logical consequence.

+

By way of concrete examples, FOJs of a negative character frequently arise in situations that are affected by a genuine dilemma, where it is necessary to choose just one action from a set of two or more actions, where it is impossible to do nothing and impossible to do everything, and where each action excludes all the others. At such a juncture the structure of that very situation, or a reference to it as described, is itself a sufficiently valid FOJ for choosing some action, even if not yet a full justification for any one specific choice. If an agent challenged: “Why did you do that?”, responds: “It was necessary to do something!”, then that is “just” as far as it goes, to a general not a specific extent. In summary, one finds that there are FOJs of a negative character, that proceed by the rejection of an alternative, but that are perfectly valid in their doing so. These FOJs of a negative character exist in contrast to the more familiar FOJs, at least, the more often expressed FOJs, all of which are positive and transitive in character, identical or analogous to the various forms of logical implication and logical consequence.

−

The dictum to the effect that "there is no argument in matters of taste", for what it is worth, enjoins an "argument to", not an "argument from". An aesthetic principle or judgment, that I prefer to live, for example, can have definite logical consequences, even if every justification I can expect to find for it is ultimately circular, tautologous, or logically speaking, trivial in form: "Why do I like it?~~" — "~~Just because I do!" To me, this cannot help but seem, if challenged in a case of this kind, to be a perfectly adequate and a reasonably sufficient answer. But to maintain this reason means to preserve this life, and that in its turn has decidedly logical consequences. It is likely that artisans and engineers have an easier time understanding this pragmatic principle, what it means in active practice and the wisdom it holds in general, than many varieties of logicians, mathematicians, philosophers, and scientists, although if I say that I pick my axioms with an eye to the beauty of what they can shape, in other words, that I select my logical and mathematical principles for what are essentially aesthetic reasons, then there are evidently some in these guilded ilks who already know what I mean.

+

The dictum to the effect that ''there is no argument in matters of taste'', for what it is worth, enjoins an ''argument to'', not an ''argument from''. An aesthetic principle or judgment, that I prefer to live, for example, can have definite logical consequences, even if every justification I can expect to find for it is ultimately circular, tautologous, or logically speaking, trivial in form: “Why do I like it?” — “Just because I do!” To me, this cannot help but seem, if challenged in a case of this kind, to be a perfectly adequate and a reasonably sufficient answer. But to maintain this reason means to preserve this life, and that in its turn has decidedly logical consequences. It is likely that artisans and engineers have an easier time understanding this pragmatic principle, what it means in active practice and the wisdom it holds in general, than many varieties of logicians, mathematicians, philosophers, and scientists, although if I say that I pick my axioms with an eye to the beauty of what they can shape, in other words, that I select my logical and mathematical principles for what are essentially aesthetic reasons, then there are evidently some in these guilded ilks who already know what I mean.

−

Socrates not only used irony but was so dedicated to irony that he himself succumbed to it.

+

{| align="center" cellpadding="0" cellspacing="0" width="90%"

−

Kierkegaard, The Concept of Irony, [Kier, 5]

+

|

+

Socrates not only used irony but was so dedicated to irony that he himself succumbed to it.

+

|-

+

| align="right" | Kierkegaard, ''The Concept of Irony'', [Kier, 5]

+

|}

A person who drinks an extract of hemlock for what he says is a reason of logic either suffers from a confusion of priorities or acts according to a higher aesthetic than that of saving his own small portion of life. But a person who drains the tendered glass for lack of lighting quickly enough on a reason why not is a person who has let his extract of logic turn to a poison in its own right.

−

~~</pre>~~

=====5.2.11.7. The Experience of Satisfaction=====

−

~~<pre>~~

+

{| align="center" border="0" cellpadding="0" cellspacing="0" width="90%"

−

Die unbegreiflich hohen Werke

+

| Die unbegreiflich hohen Werke

−

Sind herrlich wie am ersten Tag.

+

|-

+

| Sind herrlich wie am ersten Tag.

+

|-

+

|  

+

|-

+

| The world's unwithered countenance

+

|-

+

| Is bright as on the earliest day.

+

|-

+

| width="60%" |   || Goethe, ''Faust'', …,

+

|-

+

| width="60%" |   || quoted in Weyl, ''The Open World'', [Weyl, 29].

+

|}

−

~~The world's unwithered countenance~~

+

With these considerations freshly in mind, it is possible to return to the more immediate questions:

−

~~Is bright as on the earliest day.~~

−

~~Goethe, Faust, ...,~~

−

~~quoted~~ in ~~Weyl~~, ~~The Open World, [Weyl, 29].~~

−

~~With these considerations freshly in mind, it is possible to return to the more immediate questions~~: Why is it useful to keep a store of memory? How does a record of past experiences serve an agent in meeting its present goals and thereby in achieving future satisfactions?

+

: Why is it useful to keep a store of memory?

+

: How does a record of past experiences serve an agent in meeting its present goals and thereby in achieving future satisfactions?

Assuming that an agent, however accidentally, elliptically, obliquely, occasionally, partially, or transiently it may happen, ever experiences a state of satisfaction, as reflects its achievement of one of its objects or as marks its identity with one of its goals, then it is likely to be useful for that agent to try to keep track of all the incidental experiences that accompany or surround this "experience of satisfaction" (EOS). Because the questions of causal order and even of purely temporal simultaneity are difficult in general to resolve in real time, in medias res, it is advisable for the agent not to focus too fixedly on trying to sort out the precedents from the consequents, at least, at first. But why is it likely to be useful? And what does it mean to be useful? Responding to these questions requires another apparent departure, as follows.

Line 2,285: Line 2,317:

If there is any consistency to experience, in other words, any form of lawful relationship between one sample of experience and other samples of experience, then it follows that almost any kind of memory structure, any facility for attention and retention that an agent can contrive to organize the interaction between transient experience and the orders of its more persistent signs, any faculty that allows an agent to note the sundry aspects of a satisfying experience or the circumstantial details of a satisfying situation, any organization of processes that permits an agent to fashion periodic or persistent notes of the tangent experiences that surround an EOS, whether these stores are internal to its initially given body of resources or external to its innate endowment, is likely to be of service in achieving future satisfactions. Properly organized for quick access, the whole index of past experience can serve as a catalyst for future achievements, in other words, it can act on the whole as the sort of sign that is conducive to actualizing its object.

−

One may well ask: Is there any form of lawful relationship between one sample of experience and other samples of experience? To say "yes" too quickly is practically vacuous, that is, it is empty of anything beyond the vaguest hopes of an implication for action, until one is willing to risk the assumption of a specific form of lawful relationship. For the sake of proposing a non trivial stake, what one needs and desires is an "informative" form of lawful relationship. I am not making any form of fixed assumption here, but merely contemplating the forms of hypotheses that I am able to consider as possible. I admit to occasionally having experiences that cause me to question all the more frequently exploited answers to this question, that tempt me to say "no" even to this modest quantum of presumption, but then I note that it is particular varieties of experience that lead me to say this and specific brands of laws that I am led to question. Then I notice that all the forms of contrariety, disagreement, discord, discrepancy, disharmony, disparity, dispersion, dissension, distribution, diversification, incongruity, and opposition that I encounter at these junctures are themselves distinctions with a difference, and each in its way renders a generic form of distinction, "which, taken at the flood, leads on to fortune", to wit, a wealth of unsuspected approaches to the problems that positive experience poses. Without being tempted to classify or to enumerate the full diversity of logical forms by which differing samples of experience come to grate on and to grind against each other, it is possible at this point to notice their essentially differential, negative, and oppositional characters.

+

One may well ask: Is there any form of lawful relationship between one sample of experience and other samples of experience? To say ''yes'' too quickly is practically vacuous, that is, it is empty of anything beyond the vaguest hopes of an implication for action, until one is willing to risk the assumption of a specific form of lawful relationship. For the sake of proposing a non trivial stake, what one needs and desires is an ''informative'' form of lawful relationship. I am not making any form of fixed assumption here, but merely contemplating the forms of hypotheses that I am able to consider as possible. I admit to occasionally having experiences that cause me to question all the more frequently exploited answers to this question, that tempt me to say ''no'' even to this modest quantum of presumption, but then I note that it is particular varieties of experience that lead me to say this and specific brands of laws that I am led to question. Then I notice that all the forms of contrariety, disagreement, discord, discrepancy, disharmony, disparity, dispersion, dissension, distribution, diversification, incongruity, and opposition that I encounter at these junctures are themselves distinctions with a difference, and each in its way renders a generic form of distinction, “which, taken at the flood, leads on to fortune”, to wit, a wealth of unsuspected approaches to the problems that positive experience poses. Without being tempted to classify or to enumerate the full diversity of logical forms by which differing samples of experience come to grate on and to grind against each other, it is possible at this point to notice their essentially differential, negative, and oppositional characters.

−

In this way, I arrive at the conclusion that "forms of negation" (~~FON's~~), or fundamentally negative logical relations, are unavoidable necessities, needed to anchor any adequate basis for stating the forms of interaction among different samples of experience. One finds, instead of a positive foundation, that irreducibly negative operations are inescapable notions, needed to support any satisfactory system of notations for detailing the collisions and the collusions that particles of experience impart to one another. In spite of the aura of negativity that chances to shade their logical aspects, to color their evidential impacts, and to weigh against their positive receptions, the counter exemplary characters and conducts of these bearings of experience on experience do, at a minimum, contrive to convey "informative forms of lawful relationship between one sample of experience and other samples of experience".

+

In this way, I arrive at the conclusion that ''forms of negation'' (FONs), or fundamentally negative logical relations, are unavoidable necessities, needed to anchor any adequate basis for stating the forms of interaction among different samples of experience. One finds, instead of a positive foundation, that irreducibly negative operations are inescapable notions, needed to support any satisfactory system of notations for detailing the collisions and the collusions that particles of experience impart to one another. In spite of the aura of negativity that chances to shade their logical aspects, to color their evidential impacts, and to weigh against their positive receptions, the counter exemplary characters and conducts of these bearings of experience on experience do, at a minimum, contrive to convey “informative forms of lawful relationship between one sample of experience and other samples of experience”.

−

The circumstance that absence, necessity, and privation are the mothers of invention, possibility, and plenitude is a difficult fact of logic to accustom oneself to, apparently because of the mind's innate blind spots in regard to its own nature and partly due to the mind's acquired bias in favor of positive relationships. Against these blocks and in accord with this bias, the aspects of nullity and vacuity that arise in respect of logical ~~FON's~~ are frequently responsible for leading the mind astray, for instance, into supposing that these ~~FON's~~ are: ~~(1) purely~~ derivative abstractions from wholly positive contents and structures of experience, ~~(2) partially~~ selective extractions from primary materials of experience and primitive elements of reasoning, ~~(3) secondary~~, tertiary, and higher order constructions that are based on and built from basically positive forms of empirical and rational connection, and ~~(4) wholly~~ dependent for their practical utility and their rational justification on contents of positive experience to fill out their sparingly minimal forms.

+

The circumstance that absence, necessity, and privation are the mothers of invention, possibility, and plenitude is a difficult fact of logic to accustom oneself to, apparently because of the mind's innate blind spots in regard to its own nature and partly due to the mind's acquired bias in favor of positive relationships. Against these blocks and in accord with this bias, the aspects of nullity and vacuity that arise in respect of logical FONs are frequently responsible for leading the mind astray, for instance, into supposing that these FONs are:

+

# Purely derivative abstractions from wholly positive contents and structures of experience,

+

# Partially selective extractions from primary materials of experience and primitive elements of reasoning,

+

# Secondary, tertiary, and higher order constructions that are based on and built from basically positive forms of empirical and rational connection, and

+

# Wholly dependent for their practical utility and their rational justification on contents of positive experience to fill out their sparingly minimal forms.

By way of contrast, it is possible to identify a couple of dimensions along which the variety of clarification tasks can be classified into coherent associations among themselves and coordinated with each other.

−

1. One interpretation of the clarification task fixes the object and the class of signs that figure in as implied arguments of the operation, and thus it understands the task as a process of refining the quality of significance that stems from the individual signs, that is, developing a clearer interpretant for each sign given in the input class. I refer to this brand of clarification as a "~~modeling~~" ~~process, for several reasons:~~

+

−

~~a. Speaking~~ of ~~"signs" in~~ the ~~generic sense, this mode of~~ clarification ~~process involves~~ the ~~finding or~~ the ~~making~~ of ~~"model"~~ signs ~~to serve~~ as ~~their clarified interpretants. In other words~~, it ~~takes in signs~~ of ~~an arbitrary~~ quality of ~~clarity and replaces them with their "canonical"~~, ~~"normal"~~, ~~or "standard" equivalents, ones that have an improved or optimal level of clarity~~.

+

<li>One interpretation of the clarification task fixes the object and the class of signs that figure in as implied arguments of the operation, and thus it understands the task as a process of refining the quality of significance that stems from the individual signs, that is, developing a clearer interpretant for each sign given in the input class. I refer to this brand of clarification as a ''modeling'' process, for several reasons:</li>

−

~~b. Speaking of signs in the sense of logical expressions, this mode of clarification process involves the detection, enumeration, and organization of their logical~~ "~~models~~"~~, that is, their logically satisfying interpretations.~~

+

−

~~Overall~~, this ~~brand~~ of clarification ~~can be viewed a purely cognitive~~, ~~intellectual~~, ~~syntactic~~, or ~~rational process~~, ~~one~~ that ~~goes on in the absence of any interaction with the object domain beyond the initial sample~~ of ~~signs~~.

+

<li>Speaking of signs in the generic sense, this mode of clarification process involves the finding or the making of model signs to serve as their clarified interpretants. In other words, it takes in signs of an arbitrary quality of clarity and replaces them with their ''canonical'', ''normal'', or ''standard'' equivalents, ones that have an improved or optimal level of clarity.</li>

−

~~2. Another interpretation~~ of the ~~clarification task allows the object, or the information that the object avails~~ of ~~itself~~, ~~to change over time. It is not that agents always have a lot~~ of ~~choice in~~ the ~~matter of whether changes occur or what changes take place~~, ~~but only that they do have the option to envision the possibility of changes in the objects or the data~~, and ~~accordingly to contrive systematic ways~~ of ~~tracking these changes and accounting for the developments of objects and signs through time. This rendition of the general requirement to~~ "~~increase the clarity of the signs that the agent possesses about the object~~" ~~comprehends the task of clarification as a matter of increasing the quantity of the agent's possessions in~~ that ~~regard~~, ~~and it leads to a class of strategies in which agents proceed by gathering each new sign that they find of the object into the class of signs that forms~~ their ~~sample~~.

+

<li>Speaking of signs in the sense of logical expressions, this mode of clarification process involves the detection, enumeration, and organization of their logical "models", that is, their logically satisfying interpretations.</li>

−

</~~pre~~>

−

~~=====5.2.11.8. An Organizational Difficulty=====~~

+

</ol>

−

<~~pre~~>

+

Overall, this brand of clarification can be viewed a purely cognitive, intellectual, syntactic, or rational process, one that goes on in the absence of any interaction with the object domain beyond the initial sample of signs.

−

~~Moreover~~, ~~I did not wish to begin to reject completely any~~ of the ~~opinions which might have slipped earlier into my mind without having been introduced by reason, until I had first given myself enough time to make a plan~~ of the ~~work I was undertaking, and to seek~~ the ~~true method~~ of ~~arriving at knowledge of everything my mind was capable of grasping~~.

−

~~Rene Descartes, Discourse on Method, [Des1, 39-40]~~

−

~~At this point in my text I run into what I think~~ of ~~as an "organizational difficulty" (OD)~~. I have ~~already written sixty plus pages~~ of ~~this text~~ and~~, if~~ the ~~stacks~~ of ~~notes~~ and ~~previous drafts~~ that ~~I find around me are any evidence~~, ~~I am likely~~ to ~~write many pages more. ..~~.

+

<li>Another interpretation of the clarification task allows the object, or the information that the object avails of itself, to change over time. It is not that agents always have a lot of choice in the matter of whether changes occur or what changes take place, but only that they do have the option to envision the possibility of changes in the objects or the data, and accordingly to contrive systematic ways of tracking these changes and accounting for the developments of objects and signs through time. This rendition of the general requirement to “increase the clarity of the signs that the agent possesses about the object” comprehends the task of clarification as a matter of increasing the quantity of the agent's possessions in that regard, and it leads to a class of strategies in which agents proceed by gathering each new sign that they find of the object into the class of signs that forms their sample.</li>

−

~~...~~

+

</ol>

−

</~~pre~~>

−

=====5.2.11.9. Pragmatic Certainties=====

+

=====5.2.11.8. An Organizational Difficulty=====

−

+

−

~~<pre>~~

+

{| align="center" cellpadding="0" cellspacing="0" width="90%"

−

This brings me to the point of asking: What does "certainty" mean in practice, that is, what meanings can be revealed for the concept if one attempts to translate the intentions behind it into operational terms? Once one bothers to ask this eminently practical question, it becomes reasonably clear almost immediately that no brand of absolute certainty is ever in required practice. For practical purposes, only a moderate amount of certainty is demanded, just enough for a particular agent to settle on a particular course of action. A question about the kind of certainty expected or the level of certainty needed in order to make a decision is itself an interpretive issue. In other words, no matter whether its instances remain to be decided on a case by case basis, or whether a general rule can be formed to cover them, their resolution occurs in a manner that retains an irreducible degree of arbitrariness about it, since it must relate to the degrees of freedom possessed by the agents who arbitrate the matter in question. In the final analysis, this is an issue that devolves upon the nature and the constitution of the very form of agency that finds itself concerned with the question and exerts itself according to its interest in the action. Namely and solely, this form of agency can be comprised of nothing other than the particular agents and the communities of agents who are compelled or inspired to act at the moment in question.

+

|

+

Moreover, I did not wish to begin to reject completely any of the opinions which might have slipped earlier into my mind without having been introduced by reason, until I had first given myself enough time to make a plan of the work I was undertaking, and to seek the true method of arriving at knowledge of everything my mind was capable of grasping.

+

|-

+

| align="right" | Rene Descartes, ''Discourse on Method'', [Des1, 39-40]

+

|}

+

At this point in my text I run into what I think of as an ''organizational difficulty'' (OD). I have already written sixty plus pages of this text and, if the stacks of notes and previous drafts that I find around me are any evidence, I am likely to write many pages more. …

+

=====5.2.11.9. Pragmatic Certainties=====

+

This brings me to the point of asking: What does ''certainty'' mean in practice, that is, what meanings can be revealed for the concept if one attempts to translate the intentions behind it into operational terms? Once one bothers to ask this eminently practical question, it becomes reasonably clear almost immediately that no brand of absolute certainty is ever in required practice. For practical purposes, only a moderate amount of certainty is demanded, just enough for a particular agent to settle on a particular course of action. A question about the kind of certainty expected or the level of certainty needed in order to make a decision is itself an interpretive issue. In other words, no matter whether its instances remain to be decided on a case by case basis, or whether a general rule can be formed to cover them, their resolution occurs in a manner that retains an irreducible degree of arbitrariness about it, since it must relate to the degrees of freedom possessed by the agents who arbitrate the matter in question. In the final analysis, this is an issue that devolves upon the nature and the constitution of the very form of agency that finds itself concerned with the question and exerts itself according to its interest in the action. Namely and solely, this form of agency can be comprised of nothing other than the particular agents and the communities of agents who are compelled or inspired to act at the moment in question.

The idea that certainty is needed to begin, whether to start thinking or to get moving in any direction of conduct, is one of the most paralyzing traps that the mind can let itself fall into. This is why the pragmatic theory of inquiry emphasizes uncertainty as the literal start of inquiry, since there is certainly no difficulty about the mind finding itself in a state of uncertainty. Thus, there is no scarcity of events to throw the mind into confusion, no trouble at all getting into trouble, and so this renders the whole fabric of one's experience rife with moments of doubt. But what is the mind to make of this dubious resource, and what is the ultimate good of noticing this abundance of ambivalence in the mind?

−

There is much that is curious in the picture of uncertainty that I just presented. The paradoxical phrase "certainly no difficulty", that seemed to pop up from nowhere in my description of the situation, is evidently an artifact of reflection, that is, due to the reflective character of the description but not an element of the situation described. Specifically, it focuses on what appears at first to be a purely incidental triviality: How easy it is to find oneself in a state of uncertainty. More carefully, since to "find oneself" may be still too much to expect at such an early stage of the game, it may be said: How easy it is to be for the moment or to end up momentarily in a state of uncertainty. And yet, with yet another reflection, one is forced to ask: To what exactly, whether an aspect of the original situation, a newly introduced amendment to it, or a newly generated outlook on the situation, do all these attributions of certainty, ease, freedom from trouble, and lack of difficulty apply? Since it seems a contradiction to attribute these predicates to the problematic state of uncertainty itself, that is to say, they are not what's the matter in the original situation, they must belong either to the attitude of approach that is capable of reflection, to the ensuing state that is entered on reflection, or to the manner of viewing the whole situation.

+

There is much that is curious in the picture of uncertainty that I just presented. The paradoxical phrase “certainly no difficulty”, that seemed to pop up from nowhere in my description of the situation, is evidently an artifact of reflection, that is, due to the reflective character of the description but not an element of the situation described. Specifically, it focuses on what appears at first to be a purely incidental triviality: How easy it is to find oneself in a state of uncertainty. More carefully, since to "find oneself" may be still too much to expect at such an early stage of the game, it may be said: How easy it is to be for the moment or to end up momentarily in a state of uncertainty. And yet, with yet another reflection, one is forced to ask: To what exactly, whether an aspect of the original situation, a newly introduced amendment to it, or a newly generated outlook on the situation, do all these attributions of certainty, ease, freedom from trouble, and lack of difficulty apply? Since it seems a contradiction to attribute these predicates to the problematic state of uncertainty itself, that is to say, they are not what's the matter in the original situation, they must belong either to the attitude of approach that is capable of reflection, to the ensuing state that is entered on reflection, or to the manner of viewing the whole situation.

+

Thus, it is possible to distinguish between two collections of properties, or, if one prefers, between two different applications of the same set of predicates:

−

~~Thus, it is possible to distinguish between two collections of properties, or, if one prefers, between two different applications of the same set of predicates: (1) those~~ that affect the state of inquiry, its matter, and ~~(2) those~~ that affect the attitude toward it, the manner of regarding it, whether of absorption and irreflection or reflection and understanding~~. In order to keep track of this distinction, I introduce the designations of "lower order" (LO) and "higher order" (HO) properties, attitudes, or applications of predicates~~.

+

# Those that affect the state of inquiry, its matter, and

+

# Those that affect the attitude toward it, the manner of regarding it, whether of absorption and irreflection or reflection and understanding.

−

~~"Aha!" you might say, here is the hidden certainty that is needed~~ to ~~begin the inquiry, the initial knowledge~~ of ~~its true motive force that makes the whole process of inquiry feasible, the unshakable faith in its prime mover that is required to rest before the rest can get started~~, ~~or the ultimate security that is necessary to sustain~~ the ~~entire endeavor. But it is not that, not yet. The particular brand~~ of HO ~~certainty that arises in this situation is actually of very little use in resolving the original uncertainty. Although it can provide a modicum of security, a small peace of mind~~, ~~and serve as a "sop to Cerberus" at critical times~~, the invitations to this escape can be as distracting as the delights of its certainties are in fact seductive, and the exercise of this method to the exclusion of risking the perils of real experience can just as easily become the main obstruction to the further progress of ~~inquiry~~.

+

In order to keep track of this distinction, I introduce the designations of ''lower order'' (LO) and ''higher order'' (HO) properties, attitudes, or applications of predicates.

−

~~This business of "being certain that one~~ is ~~uncertain",~~ the ~~enterprises of reasoning~~ that ~~vie~~ to ~~capitalize on its purely derivative securities,~~ the ~~foundations of thought that try to indemnify themselves against all risk and against all hope through the guarantees of its instruments~~, the ~~certificates~~ of its ~~stocks, and~~ the ~~surety~~ of ~~its bonds~~, the ~~companies of philosophers, incorporated and limited, who leave their precious earnings so heavily invested~~ in the ~~specious lightness of its bearing~~, ~~and all~~ the ~~subsidiary entertainments~~ that ~~are produced in pursuit of this spectacle, that grow in the absence of more penetrating lights~~ to ~~delight~~ the ~~hosts of spectators~~, ~~to enrich the parasites~~ of ~~apparent productivity,~~ that ~~accrue~~ in ~~lieu~~ of ~~more genuine profits to all~~ the ~~participants and their silent partners who count themselves party to this form~~ of ~~gamble~~, ~~and that provide nothing more than~~ a ~~nominal incentive~~, ~~both for those who stake their personal fortunes on the receipts of the intervening days~~ and ~~those who bet their pari mutuel interests on the outcome of running along this track — this entire business, that strives~~ to ~~busy itself~~ at ~~any cost whatsoever~~, to ~~protect its investment for its own sake, and to insure its continuance by means of any excuse it~~ can ~~arrange for itself, eventually leads to~~ the ~~following strategy: to institute a discipline whose rationale is precisely that~~ of ~~issuing warrants for unnamed and probably unnameable apprehensions, of handing down sealed indictments whose principals on principle remain as impeccable as they~~ are ~~obscure~~, and of ~~rendering forms~~ of ~~certification for forms~~ of ~~belief that have already surrendered their original contents — this tiresome business~~ can easily become ~~so all consuming and global in its sphere of influence, while curiously remaining so provincial and local in its motives, that it totally derails~~ the ~~original train~~ of ~~thought~~.

+

“Aha!” you might say, here is the hidden certainty that is needed to begin the inquiry, the initial knowledge of its true motive force that makes the whole process of inquiry feasible, the unshakable faith in its prime mover that is required to rest before the rest can get started, or the ultimate security that is necessary to sustain the entire endeavor. But it is not that, not yet. The particular brand of HO certainty that arises in this situation is actually of very little use in resolving the original uncertainty. Although it can provide a modicum of security, a small peace of mind, and serve as a sop to Cerberus at critical times, the invitations to this escape can be as distracting as the delights of its certainties are in fact seductive, and the exercise of this method to the exclusion of risking the perils of real experience can just as easily become the main obstruction to the further progress of inquiry.

−

What accounts for the fact that one way to certainty, the ostensibly "higher" order, so often gets favored to the exclusion of the other? Perhaps it is something in the nature of the one track mind that only one brand of certainty can be pursued at a time. Perhaps it is partly due to the implicit judgments of "lower" and "higher" and partially on account of the adventitious implications that cannot help but slip into their making. Although these terms originally attach themselves to the discussion as convenient labels, intended solely to mark the sides of a purely formal distinction, and in spite of all the arbitrary characters that go into their nominal conventions, the nature of the associative mind is such that these tokens are almost bound to mount up in time to the point where they come to represent judgments of value, to symbolize in intuitively suggestive or in strictly illicit manners something beyond their original intentions, and thus to connote guilt or gilt by means of their informal associations. Absurd, I know, almost as if the even more innocuous words "left" and "right" could come to represent significant value judgments. Still, it happens.

+

This business of ''being certain that one is uncertain'', the enterprises of reasoning that vie to capitalize on its purely derivative securities, the foundations of thought that try to indemnify themselves against all risk and against all hope through the guarantees of its instruments, the certificates of its stocks, and the surety of its bonds, the companies of philosophers, incorporated and limited, who leave their precious earnings so heavily invested in the specious lightness of its bearing, and all the subsidiary entertainments that are produced in pursuit of this spectacle, that grow in the absence of more penetrating lights to delight the hosts of spectators, to enrich the parasites of apparent productivity, that accrue in lieu of more genuine profits to all the participants and their silent partners who count themselves party to this form of gamble, and that provide nothing more than a nominal incentive, both for those who stake their personal fortunes on the receipts of the intervening days and those who bet their pari mutuel interests on the outcome of running along this track — this entire business, that strives to busy itself at any cost whatsoever, to protect its investment for its own sake, and to insure its continuance by means of any excuse it can arrange for itself, eventually leads to the following strategy: to institute a discipline whose rationale is precisely that of issuing warrants for unnamed and probably unnameable apprehensions, of handing down sealed indictments whose principals on principle remain as impeccable as they are obscure, and of rendering forms of certification for forms of belief that have already surrendered their original contents — this tiresome business can easily become so all consuming and global in its sphere of influence, while curiously remaining so provincial and local in its motives, that it totally derails the original train of thought.

+

What accounts for the fact that one way to certainty, the ostensibly “higher” order, so often gets favored to the exclusion of the other? Perhaps it is something in the nature of the one track mind that only one brand of certainty can be pursued at a time. Perhaps it is partly due to the implicit judgments of “lower” and “higher” and partially on account of the adventitious implications that cannot help but slip into their making. Although these terms originally attach themselves to the discussion as convenient labels, intended solely to mark the sides of a purely formal distinction, and in spite of all the arbitrary characters that go into their nominal conventions, the nature of the associative mind is such that these tokens are almost bound to mount up in time to the point where they come to represent judgments of value, to symbolize in intuitively suggestive or in strictly illicit manners something beyond their original intentions, and thus to connote guilt or gilt by means of their informal associations. Absurd, I know, almost as if the even more innocuous words ''left'' and ''right'' could come to represent significant value judgments. Still, it happens.

As a guard against the deleterious effects that frequently emerge from the drawing of a distinction between LO and HO attitudes of certainty, no matter whether the division concerns the attributions of properties or the applications of predicates, and that commonly arise from making the various lines of LO and HO tracks express enough to carry between them a significant import but not equal enough for both to carry their share of the moment, I must take care that the tracks laid down in the building of a RIF, and all the actions conducted on their basis, are always adequate to facilitating both levels of inquiry in parallel.

Line 2,336: Line 2,384:

Triadic relations are a staple element of architecture that can serve the purpose of coordinating LO and HO inquiries, since a triadic relation can incorporate the dyadic relation that describes the transition from one state of inquiry to a subsequent state of inquiry, while still keeping track of its relationship to developments occurring on the other track. This allows the orders of developments taking place within each inquiry, and the sequences of states extracted from their processes, to proceed uninterrupted, but not uninterpreted, by each other's concerns, and to exhibit a partial independence, but an adequate correlation, with each other's progress.

−

In order to carry this discussion of certainty through with a maximum of ease, I need to find a battery of descriptive terms for the situation of uncertainty that is neutral with respect to two interpretations, that covers with equal facility the two kinds of uncertainty that one usually faces in a situation: (1) uncertainty about what is true in a situation, and (2) uncertainty about what to do in a situation. Along these lines, I describe the typical situation of uncertainty, encompassing both kinds of doubt that are fraught with peril for an agent, as "junctures".

+

In order to carry this discussion of certainty through with a maximum of ease, I need to find a battery of descriptive terms for the situation of uncertainty that is neutral with respect to two interpretations, that covers with equal facility the two kinds of uncertainty that one usually faces in a situation: (1) uncertainty about what is true in a situation, and (2) uncertainty about what to do in a situation. Along these lines, I describe the typical situation of uncertainty, encompassing both kinds of doubt that are fraught with peril for an agent, as ''junctures''.

−

For the sake of a convenient classification, I label the juncture that presents a problematic phenomenon, a surprising or unexpected state of affairs, with the generic name of a "surprise", and I label the juncture that presents a phenomenal problem, a demanding or unintended state of affairs, with the generic name of a "problem". Junctures do not always sort themselves out into cases that are clearly one or the other type, but when they do it simplifies the manners of addressing, approaching, and ultimately resolving the difficulties they present for the agent.

+

For the sake of a convenient classification, I label the juncture that presents a problematic phenomenon, a surprising or unexpected state of affairs, with the generic name of a ''surprise'', and I label the juncture that presents a phenomenal problem, a demanding or unintended state of affairs, with the generic name of a ''problem''. Junctures do not always sort themselves out into cases that are clearly one or the other type, but when they do it simplifies the manners of addressing, approaching, and ultimately resolving the difficulties they present for the agent.

−

1. If it is the aspect of a "surprise" that is dominant at a juncture, or the role of a spectator that is prominent for an agent, then the juncture is resolved, in its theoretical aspects, by finding an "explanation", a statement expressing a way of looking at the juncture that renders it less of a surprise.

+

# If it is the aspect of a ''surprise'' that is dominant at a juncture, or the role of a spectator that is prominent for an agent, then the juncture is resolved, in its theoretical aspects, by finding an ''explanation'', a statement expressing a way of looking at the juncture that renders it less of a surprise.

−

+

# If it is the aspect of a ''problem'' that is dominant at a juncture, or the role of an actor that is prominent for an agent, then the juncture is resolved, in its theoretical aspects, by finding a ''plan of action'', a statement expressing a way of moving from the juncture that renders it less of a problem. Of course, it remains for the plan or theoretical resolution to be carried out in practice before the problem itself can disappear.

−

2. If it is the aspect of a "problem" that is dominant at a juncture, or the role of an actor that is prominent for an agent, then the juncture is resolved, in its theoretical aspects, by finding a "plan of action", a statement expressing a way of moving from the juncture that renders it less of a problem. Of course, it remains for the plan or theoretical resolution to be carried out in practice before the problem itself can disappear.

If the uncertainty that one experiences in facing a juncture reflects the complexity of the juncture that faces one there, and if these are related to the difficulty that one is likely to have in resolving the juncture, then the appropriate analysis of these complexities, difficulties, and uncertainties into several parts can serve to advance the process of their resolution.

−

With this picture of an agent at a juncture, appraising the uncertainties that affect the agent in that situation, indicating the complexities and the difficulties that the situation presents for the agent to resolve, sketching the forms of analysis that are called for in the process of resolution, and suggesting the relationships that obtain among these diverse ingredients of the situation, it is feasible to return to the problem of the "cartesian step", the one that moves from ~~"ego~~ dubito" to "ergo sum", and that simultaneously, as if perforce its very passing, creates the distinction between the LO and the HO attitudes of certainty. Can the cartesian step be viewed in this light, that is, can it be placed in a suitable way within this picture of junctures and resolutions, to be specific, posing a form of analysis that advances the cause of certainty? And if so, how does it appear when regarded in this light, that is, how well does it perform with respect to its conjectural role in reducing a fundamental uncertainty of the agent concerned?

+

With this picture of an agent at a juncture, appraising the uncertainties that affect the agent in that situation, indicating the complexities and the difficulties that the situation presents for the agent to resolve, sketching the forms of analysis that are called for in the process of resolution, and suggesting the relationships that obtain among these diverse ingredients of the situation, it is feasible to return to the problem of the ''cartesian step'', the one that moves from ''dubito'' to ''ergo sum'', and that simultaneously, as if perforce its very passing, creates the distinction between the LO and the HO attitudes of certainty. Can the cartesian step be viewed in this light, that is, can it be placed in a suitable way within this picture of junctures and resolutions, to be specific, posing a form of analysis that advances the cause of certainty? And if so, how does it appear when regarded in this light, that is, how well does it perform with respect to its conjectural role in reducing a fundamental uncertainty of the agent concerned?

−

In a sense, the cartesian step splits the agent's initial juncture into a couple of parts, or "subjunctures". In this attempt at resolution, there is a part identical to the initial juncture, and thus with an uncertainty of the original severity, plus a part that the agent is sure of, and thus with an uncertainty of zero. But this sort of analysis only works if it brings to light subjunctures of the initial juncture, or subsituations of the initial situation, that are actual ingredients, proper components, or non trivial constituents of it. When the HO certainty does not have an effective bearing on resolving the LO uncertainty, then the pretense of analysis is only a distraction, not a step toward a genuine resolution.

+

In a sense, the cartesian step splits the agent's initial juncture into a couple of parts, or ''subjunctures''. In this attempt at resolution, there is a part identical to the initial juncture, and thus with an uncertainty of the original severity, plus a part that the agent is sure of, and thus with an uncertainty of zero. But this sort of analysis only works if it brings to light subjunctures of the initial juncture, or subsituations of the initial situation, that are actual ingredients, proper components, or non trivial constituents of it. When the HO certainty does not have an effective bearing on resolving the LO uncertainty, then the pretense of analysis is only a distraction, not a step toward a genuine resolution.

Unless the HO answer that is revealed by dint of the cartesian step has an application to the LO question that instigated the original inquiry, one that reduces the LO uncertainty that initially justified the effort, then it does not have a genuine bearing on the LO juncture that led to putting this inquiry in gear and setting its proceedings into motion, and it cannot bring to bear on the ensuing activity or the ongoing process the modicum of traction that is needed to put a brake on its continuing. But a partition of a level of uncertainty into the very same amount plus a quantity of zero is hardly a sum, however much it seems on the level, that inspires much confidence in either the practical sincerity or the ergo nomic utility of the putative sum.

−

When Descartes set about the reconstruction of philosophy, his first step was to (theoretically) permit scepticism and to discard the practice of the schoolmen of looking to authority as the ultimate source of truth. That done, he sought a more natural fountain of true principles, and thought he found it in the human mind; ~~...~~

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{| align="center" cellpadding="0" cellspacing="0" width="90%"

+

|

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When Descartes set about the reconstruction of philosophy, his first step was to (theoretically) permit scepticism and to discard the practice of the schoolmen of looking to authority as the ultimate source of truth. That done, he sought a more natural fountain of true principles, and thought he found it in the human mind; …

−

Self-consciousness was to furnish us with our fundamental truths, and to decide what was agreeable to reason. But since, evidently, not all ideas are true, he was led to note, as the first condition of infallibility, that they must be clear. The distinction between an idea seeming clear and really being so, never occurred to him.

+

Self-consciousness was to furnish us with our fundamental truths, and to decide what was agreeable to reason. But since, evidently, not all ideas are true, he was led to note, as the first condition of infallibility, that they must be clear. The distinction between an idea seeming clear and really being so, never occurred to him.

−

(Peirce, CP 5.391).

+

|-

−

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| align="right" | (Peirce, CP 5.391).

−

In the discussion that follows, I am going to use the letters "C", "L", and "M" to stand for three generic features or classes of properties, yet to be fully analyzed or completely specified, that are commonly appreciated, desired, or valued as virtues of signs and expressions. For now, a list of adjectives appropriate to each class can give a sufficient indication of their intended characters, even though it is easily possible and eventually necessary to find important distinctions that exist among the items in each given list of exemplary properties.

+

|}

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~~1. The class "C" is suggested by the adjectives: "certain", "cogent", "compelling", or "convincing", and, in some of their senses, by: "apparent", "evident", "obvious", or "patent".~~

−

~~2. The class "~~L~~" is suggested by the adjectives: "clear"~~, ~~"lucid"~~, ~~"perspicuous"~~, ~~"plain"~~, ~~"relevant"~~, or ~~"vivid"~~. ~~To the geometric imagination~~, ~~these terms suggest~~ a ~~"bluntness" (~~of ~~surfaces) or~~ a ~~"sharpness" (~~of ~~edges)~~.

+

In the discussion that follows, I am going to use the letters <math>C, L, M\!</math> to stand for three generic features or classes of properties, yet to be fully analyzed or completely specified, that are commonly appreciated, desired, or valued as virtues of signs and expressions. For now, a list of adjectives appropriate to each class can give a sufficient indication of their intended characters, even though it is easily possible and eventually necessary to find important distinctions that exist among the items in each given list of exemplary properties.

−

3. The class "M" is suggested by the adjectives~~: "~~distinct", "decided", "defined", "definite", "determinate", "different", "differentiated", or "discrete", and, within a stretch of the imagination, by~~: "~~acute", "conspicuous", "eminent", "manifest", "poignant", "salient", or "striking". To the geometric imagination, these terms suggest a "pointedness".

+

# The class <math>C\!</math> is suggested by the adjectives ''certain'', ''cogent'', ''compelling'', or ''convincing'', and, in some of their senses, by ''apparent'', ''evident'', ''obvious'', or ''patent''.

+

# The class <math>L\!</math> is suggested by the adjectives ''clear'', ''lucid'', ''perspicuous'', ''plain'', ''relevant'', or ''vivid''. To the geometric imagination, these terms suggest a ''bluntness'' (of surfaces) or a ''sharpness'' (of edges).

+

# The class <math>M\!</math> is suggested by the adjectives ''distinct'', ''decided'', ''defined'', ''definite'', ''determinate'', ''different'', ''differentiated'', or ''discrete'', and, within a stretch of the imagination, by ''acute'', ''conspicuous'', ''eminent'', ''manifest'', ''poignant'', ''salient'', or ''striking''. To the geometric imagination, these terms suggest a ''pointedness''.

−

In this frame of thought, it needs to be understood that the intended sense of these last two classes excludes the common usage of words like "clear", "clearly", and so on, or "distinct", "distinctly", and so on, as elliptic figures of speech that are intended to be taken in a more literal way to mean "clearly true", and so on, or "distinctly true", and so on.

+

In this frame of thought, it needs to be understood that the intended sense of these last two classes excludes the common usage of words like ''clear'', ''clearly'', and so on, or ''distinct'', ''distinctly'', and so on, as elliptic figures of speech that are intended to be taken in a more literal way to mean ''clearly true'', and so on, or ''distinctly true'', and so on.

−

In this connection, when I mention one of these properties it is only meant as a representative of its class. Also, as they are used in this context, these terms are intended only in what is diversely called their "impressionistic", "nominal", "subjective", "superficial", or "topical" sense, implying the sorts of qualities that one can judge "by inspection" of the expression and its immediate situation, and without the need of a prolonged investigation. Thus, none of their intentions is damaged for this purpose by prefacing their proposal with an attitude of "seeming". For all one cares in these concerns, "seems X" = "X", for X = C, L, M. This makes the judgment of these qualities a matter of "seeming syntax" and "seeming semantics", involving only the sorts of decision that are commonly and easily made without carrying out complex computations or without delving into the abstruse equivalence classes of expressions.

+

In this connection, when I mention one of these properties it is only meant as a representative of its class. Also, as they are used in this context, these terms are intended only in what is diversely called their ''impressionistic'', ''nominal'', ''subjective'', ''superficial'', or ''topical'' sense, implying the sorts of qualities that one can judge “by inspection” of the expression and its immediate situation, and without the need of a prolonged investigation. Thus, none of their intentions is damaged for this purpose by prefacing their proposal with an attitude of ''seeming''. For all one cares in these concerns, <math>{}^{\backprime\backprime} \operatorname{seems}~X {}^{\prime\prime} = {}^{\backprime\backprime} X {}^{\prime\prime},\!</math> for <math>X = C, L, M.\!</math> This makes the judgment of these qualities a matter of ''seeming syntax'' and ''seeming semantics'', involving only the sorts of decision that are commonly and easily made without carrying out complex computations or without delving into the abstruse equivalence classes of expressions.

−

People frequently use the adverbs "immediately" or "intuitively" to get this sense across, and even though these terms have technical meanings that prevent me from using them in this way in anything but a casual setting, they can do for the moment. Still, when I use "immediately" in this sense it is meant in contrast only to "ultimately", and more or less synonymous to "mediately", suggesting that which holds in the meantime. In a pinch, a determination of seeming certainty or seeming clarity is enough to put an inquiry on hold for a time being, but the distinction between "seeming so to me, for now" and "seeming so to all, forever" still holds, with only the latter deserving the title of "being so".

+

People frequently use the adverbs ''immediately'' or ''intuitively'' to get this sense across, and even though these terms have technical meanings that prevent me from using them in this way in anything but a casual setting, they can do for the moment. Still, when I use ''immediately'' in this sense it is meant in contrast only to ''ultimately'', and more or less synonymous to ''mediately'', suggesting that which holds in the meantime. In a pinch, a determination of seeming certainty or seeming clarity is enough to put an inquiry on hold for a time being, but the distinction between ''seeming so to me, for now'' and ''seeming so to all, forever'' still holds, with only the latter deserving the title of ''being so''.

−

These observations on im/mediate, intuitive, or meantime determinations of certainty, clarity, and distinctness have a bearing on the styles of mathematical formulation and the modes of computational implementation that are candidates for mediating a natural style of inquiry, in other words, the sort of inquiry that a human being can relate to. Because a decision that a sign or expression has one of the virtues C, L, M, even to a mediate, a moderate, or a modest degree, is often enough to end an inquiry on a temporary basis, it becomes necessary to recognize a form of recursive foundation that also rests on a temporal basis. And yet, because these modes of judgment are all the while fallible and subject to change, it is possible that deeper foundations remain to be found.

+

These observations on im/mediate, intuitive, or meantime determinations of certainty, clarity, and distinctness have a bearing on the styles of mathematical formulation and the modes of computational implementation that are candidates for mediating a natural style of inquiry, in other words, the sort of inquiry that a human being can relate to. Because a decision that a sign or expression has one of the virtues <math>C, L, M,\!</math> even to a mediate, a moderate, or a modest degree, is often enough to end an inquiry on a temporary basis, it becomes necessary to recognize a form of recursive foundation that also rests on a temporal basis. And yet, because these modes of judgment are all the while fallible and subject to change, it is possible that deeper foundations remain to be found.

What does this mean for the topic of reflection? Well, reflection is precisely that mode of thinking that is capable of beginning with the axioms and working backward, that is, of searching out the more basic forms that conceivably underlie one's received formulations.

−

I thereby concluded that I was a substance, of which the whole essence or nature consists in thinking, and which, in order to exist, needs no place and depends on no material thing; so that this "I", that is to say, the mind, by which I am what I am, is entirely distinct from the body, and even that it is easier to know than the body, and moreover, that even if the body were not, it would not cease to be all that it is.

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{| align="center" cellpadding="0" cellspacing="0" width="90%"

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Rene Descartes, Discourse on Method, [Des1, 54]

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|

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I thereby concluded that I was a substance, of which the whole essence or nature consists in thinking, and which, in order to exist, needs no place and depends on no material thing; so that this “I”, that is to say, the mind, by which I am what I am, is entirely distinct from the body, and even that it is easier to know than the body, and moreover, that even if the body were not, it would not cease to be all that it is.

+

|-

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| align="right" | Rene Descartes, ''Discourse on Method'', [Des1, 54]

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|}

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And voila, I have, finally, spontaneously returned to there where I wanted to be. For because it now be known to me that bodies themselves are properly perceived not by the senses or by the faculty of imagining, but rather by the intellect alone, and that bodies are perceived not from thence that they would be touched or seen, but rather from thence only that they were to be understood, I cognize overtly that nothing can be perceived by me more easily or more evidently than my mind.

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{| align="center" cellpadding="0" cellspacing="0" width="90%"

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Rene Descartes, Meditations on First Philosophy, [Des2, 117]

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|

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And voila, I have, finally, spontaneously returned to there where I wanted to be. For because it now be known to me that bodies themselves are properly perceived not by the senses or by the faculty of imagining, but rather by the intellect alone, and that bodies are perceived not from thence that they would be touched or seen, but rather from thence only that they were to be understood, I cognize overtly that nothing can be perceived by me more easily or more evidently than my mind.

+

|-

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| align="right" | Rene Descartes, ''Meditations on First Philosophy'', [Des2, 117]

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|}

−

On reflection, the observation that appeared just before these last questions arose can be seen to make a very broad claim about a certain class of properties affecting expressions, namely, all those properties that can be analogous to the ordered measures of expressive quality. For future reference, let me call this the "monotone assumption" (MA). This generatrix of so many future and specious assumptions takes for granted a sweeping claim about the ways that an order of analysis of expressions translates into an order of comparison of their measures under one of these properties. But this entire and previously unstated assumption is itself just another manner of working hypothesis for the mental procedure or the process of inquiry that makes use of it, and its proper understanding is perhaps better served if it is rephrased as a question: Can the X of a claim or a concept be greater than the X of the subordinate claims and concepts that it calls on, where "X" stands for "certainty", "clarity", or any one of the corresponding class of measures, orders, properties, qualities, or virtues?

+

On reflection, the observation that appeared just before these last questions arose can be seen to make a very broad claim about a certain class of properties affecting expressions, namely, all those properties that can be analogous to the ordered measures of expressive quality. For future reference, let me call this the ''monotone assumption'' (MA). This generatrix of so many future and specious assumptions takes for granted a sweeping claim about the ways that an order of analysis of expressions translates into an order of comparison of their measures under one of these properties. But this entire and previously unstated assumption is itself just another manner of working hypothesis for the mental procedure or the process of inquiry that makes use of it, and its proper understanding is perhaps better served if it is rephrased as a question: Can the <math>X\!</math> of a claim or a concept be greater than the <math>X\!</math> of the subordinate claims and concepts that it calls on, where <math>{}^{\backprime\backprime} X {}^{\prime\prime}\!</math> stands for ''certainty'', ''clarity'', or any one of the corresponding class of measures, orders, properties, qualities, or virtues?

−

Rather than taking this claim for granted, suppose I go looking for any properties, that might be similar to certainty or clarity, for which the measure of a whole expression is capable of exceeding the measure of its parts. Is there an order property that is dependent on the constitution of the whole expression and a function of its analytic constituents but not necessarily tied down to ~~monotonely~~ conservative relationships like the sum, the average, or the lowest common denominator of the measures affecting its syntactic elements? Once I take the trouble to formulate the question in explicit terms, any number of familiar examples are free to come to mind as fitting its requirements. Indeed, since the notions of dependency and independence that accompany the use of mathematical functions and mathematical forms of decomposition do not by themselves implicate the more constrained types of dependency and the more radical types of independence that arise in relation and in reaction to the MA, it is rather easy to think of many that will do.

+

Rather than taking this claim for granted, suppose I go looking for any properties, that might be similar to certainty or clarity, for which the measure of a whole expression is capable of exceeding the measure of its parts. Is there an order property that is dependent on the constitution of the whole expression and a function of its analytic constituents but not necessarily tied down to monotonically conservative relationships like the sum, the average, or the lowest common denominator of the measures affecting its syntactic elements? Once I take the trouble to formulate the question in explicit terms, any number of familiar examples are free to come to mind as fitting its requirements. Indeed, since the notions of dependency and independence that accompany the use of mathematical functions and mathematical forms of decomposition do not by themselves implicate the more constrained types of dependency and the more radical types of independence that arise in relation and in reaction to the MA, it is rather easy to think of many that will do.

−

~~</pre>~~

=====5.2.11.10. Problems and Methods=====

−

~~<pre>~~

+

The relationship between a “problem” and a “method” needs to be given another look, in view of the discussion that has transpired since the initial steps of this proposal. …

−

The relationship between a "problem" and a "method" needs to be given another look, in view of the discussion that has transpired since the initial steps of this proposal. ~~...~~

−

To approach the distinction between problem and method in the present setting, in the light of the discussion that has transpired since I naively assumed a distinction between them, ~~...~~

+

To approach the distinction between problem and method in the present setting, in the light of the discussion that has transpired since I naively assumed a distinction between them, …

−

What is the nature of the relationship between a problem and a method? What is the distinction between them, and what sort of difference is it? These questions are made especially acute in view of the fact that the present inquiry nominates "inquiry" to both of these roles, proposing to take "inquiry" as naming both a problem and a method. If it makes any sense to do this, and if there is anything to the distinction between a problem and a method, then it must be a distinction of relational roles rather than a distinction of absolute essences. Trying to make sense of this requires me to ask: What manner of common, generic, indifferent, or shared existence do a problem and a method both possess, logically prior to taking on their distinctive roles in relation to each other?

+

What is the nature of the relationship between a problem and a method? What is the distinction between them, and what sort of difference is it? These questions are made especially acute in view of the fact that the present inquiry nominates “inquiry” to both of these roles, proposing to take “inquiry” as naming both a problem and a method. If it makes any sense to do this, and if there is anything to the distinction between a problem and a method, then it must be a distinction of relational roles rather than a distinction of absolute essences. Trying to make sense of this requires me to ask: What manner of common, generic, indifferent, or shared existence do a problem and a method both possess, logically prior to taking on their distinctive roles in relation to each other?

In approaching the distinction between a problem and a method, I use a piece of advice that is helpful in approaching any important distinction, especially a distinction that is naively taken as given or a distinction that has been taken for granted for too long a spell of time, like the distinction between the problem and the method, the work and the tool, or the object and the sign. This recommends that one stand back from a full involvement in the drawing of the distinction under review, to partially withdraw one's commitment to having it drawn the way it is, and to contemplate how it came to be drawn that way in the first place, in other words, to consider the process that initially draws it and that keeps on drawing it in just the way that it presently appears.

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If this is done, then one realizes that the problem and the method are both constituted in part by the way their distinction is drawn, by the sort of distinction that one takes it to be, whether a sign of the roles that entities take up in relation to each other or a mark of the natures that entities have in and of themselves, and by the items that one takes as instances on either side of the distinction. In this way, every form of distinction, with respect to the contents of its counterposed sides, plays the role of a mediator in their mutual constitution of each other.

−

Standing back from the picture a little further, one can see that the distinction between a problem and a method is itself a tool of method, and one that is not ordinarily considered to be a problem. To see this, notice that "distinction" is an " ionized" term, and thus denotes both a process and a result, the process being the drawing of the distinction and the product being the distinction drawn, so any form of distinction is available for consideration in the light of its instrumental meaning. In this regard, the distinction between a problem and a method is itself an instrumentality of reasoning, a procedural means to an end, in short, a method or a tool. This particular distinction, between a problem and a method, falls among those of a very basic order, the kind that one takes as given without hesitation or reflection, uses to construe almost every situation that one finds oneself in, and does not usually question the utility of, until, as presently, some special attention is drawn to it. In summary, the distinction that is drawn between the problem seen and the method used, the conventional form of designation that says what is the work and what is the tool, is itself an artifice, a construct, an invention of the mind, or an intervention of the thinking process whose correspondence with anything else in reality and whose constitution as an enduring reality in itself is something that demands to be tested.

+

Standing back from the picture a little further, one can see that the distinction between a problem and a method is itself a tool of method, and one that is not ordinarily considered to be a problem. To see this, notice that ''distinction'' is an ''-ionized'' term, and thus denotes both a process and a result, the process being the drawing of the distinction and the product being the distinction drawn, so any form of distinction is available for consideration in the light of its instrumental meaning. In this regard, the distinction between a problem and a method is itself an instrumentality of reasoning, a procedural means to an end, in short, a method or a tool. This particular distinction, between a problem and a method, falls among those of a very basic order, the kind that one takes as given without hesitation or reflection, uses to construe almost every situation that one finds oneself in, and does not usually question the utility of, until, as presently, some special attention is drawn to it. In summary, the distinction that is drawn between the problem seen and the method used, the conventional form of designation that says what is the work and what is the tool, is itself an artifice, a construct, an invention of the mind, or an intervention of the thinking process whose correspondence with anything else in reality and whose constitution as an enduring reality in itself is something that demands to be tested.

−

If the terms "problem" and "method" refer to phenomena and activities that take place in the world, then that is one mode of existence they have in common. If the "world" is further circumscribed to the kinds of phenomena that have effective descriptions, that is, computational models, and the kinds of activities that have effective prescriptions, that is, computational implementations, then the mode of existence one commonly denotes by means of programs, codes, effective procedures, or other practical recipes is another domain that is capable of providing instances that fill both the roles of a problem or a method. Taking a clue from this interpretation, I can shift my approach to the question and consider the medium of signs that is used to address the things in comparison. By starting with the syntactic side of the issue I avail myself of ready made handles on the question, even if the mechanism of these conventional modes quickly becomes a difficulty in its own right, blocking further progress and demanding to be tackled in terms of the influential biases and the instrumental characters it brings to bear.

+

If the terms ''problem'' and ''method'' refer to phenomena and activities that take place in the world, then that is one mode of existence they have in common. If the “world” is further circumscribed to the kinds of phenomena that have effective descriptions, that is, computational models, and the kinds of activities that have effective prescriptions, that is, computational implementations, then the mode of existence one commonly denotes by means of programs, codes, effective procedures, or other practical recipes is another domain that is capable of providing instances that fill both the roles of a problem or a method. Taking a clue from this interpretation, I can shift my approach to the question and consider the medium of signs that is used to address the things in comparison. By starting with the syntactic side of the issue I avail myself of ready made handles on the question, even if the mechanism of these conventional modes quickly becomes a difficulty in its own right, blocking further progress and demanding to be tackled in terms of the influential biases and the instrumental characters it brings to bear.

−

~~</pre>~~

===5.3. Reflection on Reflection===

−

====Looking Back====

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====5.3.1. Looking Back====

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~~<pre>~~

+

Let me review the developments that bring me to this point. I began by describing my present inquiry, <math>y_0,\!</math> as an inquiry into inquiry, <math>y \cdot y.\!</math> Then I focused on the activities of discussion, <math>d,\!</math> and formalization, <math>f,\!</math> as two components of the faculty or the process of inquiry, <math>y >\!\!= \{ d , f \}.\!</math> This led me to the present discussion of formalization, <math>f \cdot d.\!</math> Considered as classes of activities, the collective instances of formalization, <math>F,\!</math> appeared to be encompassed by the collective instances of discussion, <math>D,\!</math> thereby yielding the relationship <math>F \subseteq D.\!</math>

−

Let me review the developments that bring me to this point. I began by describing my present inquiry, y0, as an inquiry into inquiry, y.y. Then I ~~focussed~~ on the activities of discussion, d, and formalization, f, as two components of the faculty or the process of inquiry, y >= {d,f}. This led me to the present discussion of formalization, f.d. Considered as classes of activities, the collective instances of formalization, F, appeared to be encompassed by the collective instances of discussion, D, thereby yielding the relationship F c D.

−

I initially characterized discussion and formalization, in regard to each other, as being an "actively instrumental" versus a "passively objective" aspect, component, or "face" of the inquiry y >= {d,f}. In casting them this way I clearly traded on the ambiguity of " ionized" terms to force the issue a bit. In other words, I used the flexibility that is freely available within their " ionic" construals, as processes or as products, to cast discussion and formalization into sundry molds, drawing out the patent energies that are manifested by the active process of discussion and placing them in contrast with the latent inertias that are immanent in the dormant product of formalization. In this partially arbitrary way, I decided on the one hand to treat discussion in respect of its ongoing process, the only thing that it has any assurance of accomplishing, but I decided on the other hand to treat formalization in respect of its end product, the abstract image or the formal model that constitutes its chief qualification and thus becomes the mark of what it is.

+

I initially characterized discussion and formalization, in regard to each other, as being an “actively instrumental” versus a “passively objective” aspect, component, or “face” of the inquiry <math>y >\!\!= \{ d , f \}.\!</math> In casting them this way I clearly traded on the ambiguity of “-ionized” terms to force the issue a bit. In other words, I used the flexibility that is freely available within their “-ionic” construals, as processes or as products, to cast discussion and formalization into sundry molds, drawing out the patent energies that are manifested by the active process of discussion and placing them in contrast with the latent inertias that are immanent in the dormant product of formalization. In this partially arbitrary way, I decided on the one hand to treat discussion in respect of its ongoing process, the only thing that it has any assurance of accomplishing, but I decided on the other hand to treat formalization in respect of its end product, the abstract image or the formal model that constitutes its chief qualification and thus becomes the mark of what it is.

−

By casting inquiry into the form y >= {d,f}, I made it more likely that my development of its self application, y.y >= {d,f}{d,f}, would first take up the application of discussion to formalization, f.d, and only later get around to the application of formalization to discussion, d.f, that brings the active side of the formalization process into a greater prominence. But the bias that I exploited in these readings does not seem at present to be a property of the incipient algebra that would determine the sense of the applications and the decompositions envisioned here. Thus, if I initially saw a difference between the two presentations {d,f} and {f,d}, then it must have been a purely interpretive and not a substantial one, and the task of giving explicit notice to these interpretive distinctions and working out their algebra or calculus yet remains to be carried out in any sort of convincing fashion.

+

By casting inquiry into the form <math>y >\!\!= \{ d , f \},\!</math> I made it more likely that my development of its self application <math>y \cdot y >\!\!= \{ d , f \}\{ d , f \}\!</math> would first take up the application of discussion to formalization, <math>f \cdot d,\!</math> and only later get around to the application of formalization to discussion, <math>d \cdot f,\!</math> that brings the active side of the formalization process into a greater prominence. But the bias that I exploited in these readings does not seem at present to be a property of the incipient algebra that would determine the sense of the applications and the decompositions envisioned here. Thus, if I initially saw a difference between the two presentations <math>\{ d , f \}\!</math> and <math>\{ f , d \},\!</math> then it must have been a purely interpretive and not a substantial one, and the task of giving explicit notice to these interpretive distinctions and working out their algebra or calculus yet remains to be carried out in any sort of convincing fashion.

−

Still, the casting of discussion and formalization as active and inert, respectively, was not entirely out of character with their distinctive natures, since a process that has an end is more naturally suited to be represented by its result than a process that conceivably never ends. And whereas a "discussion" was allowed to be a form of discourse that does not need to have an end, with the possible exception of itself, a "formalization" was sensed to be a form of discourse that has, needs, seeks, or wants a distinct end, not just any end but a form of product that is preferred to satisfy a general description, and one that most likely resides outside the form of a vacuous vanity that simply refers, in a reflexive but hollow echo, to the entirety of its own proceedings.

+

Still, the casting of discussion and formalization as active and inert, respectively, was not entirely out of character with their distinctive natures, since a process that has an end is more naturally suited to be represented by its result than a process that conceivably never ends. And whereas a ''discussion'' was allowed to be a form of discourse that does not need to have an end, with the possible exception of itself, a ''formalization'' was sensed to be a form of discourse that has, needs, seeks, or wants a distinct end, not just any end but a form of product that is preferred to satisfy a general description, and one that most likely resides outside the form of a vacuous vanity that simply refers, in a reflexive but hollow echo, to the entirety of its own proceedings.

In this merely penultimate analysis, and to the extent that the question of ends has been analyzed up to the present, it needs to be noted that more than a bit of ambiguity yet remains. When one speaks of a form of discourse each of whose instances necessarily has an end, does one mean that the definition of the form requires each instance to have an end, and does one then mean that each valid instance actually achieves its end, or does one only mean that each instance of some empirically given class of discourses actually reaches some end or another?

−

The word "reflection" first entered this discussion in what seemed like a purely incidental and instrumental way, as a part of the definition of a "meditation" as "a discourse intended to express its author's reflections or to guide others in contemplation" (Webster's). I converted this term to my own use as a name for a particular class of activities, describing the class of "meditations", M, as a brand of "measured" and "motivated" discussions that can serve to mediate formalizations within the realm of discussions at large. Thus, I borrowed the term for no better reason than that of interposing a middle term between formalized discussions and discussions in general, thereby yielding the relationship F c M c D.

+

The word “reflection” first entered this discussion in what seemed like a purely incidental and instrumental way, as a part of the definition of a “meditation” as “a discourse intended to express its author's reflections or to guide others in contemplation” (Webster's). I converted this term to my own use as a name for a particular class of activities, describing the class of ''meditations'', <math>M,\!</math> as a brand of ''measured'' and ''motivated'' discussions that can serve to mediate formalizations within the realm of discussions at large. Thus, I borrowed the term for no better reason than that of interposing a middle term between formalized discussions and discussions in general, thereby yielding the relationship <math>F \subseteq M \subseteq D.\!</math>

In this respect, it seems to be instructive that the issue of reflection first arrived on the present scene, quietly enough, under the aegis of a borrowed term, imported without deliberate design among the components and the connotations of its associated sample of discourse, and involved in a process that seeks to negotiate the conflicting claims that arise between formal and casual discourse. In the simplest sense of the word, an activity of reflection implies only that an agent thinks quietly and calmly about a matter, the etymology of the word suggesting the actions of bending, bounding, casting, folding, giving, turning, throwing, or yielding back again, and hence a pause, a return, or a review. In this regard, the word "reflection" barely alludes to the idea that what the agent turns back to is something that involves itself, its own patterns of activity, and thus the word only hints as yet at the complicities of self reference and self application that are involved in an agent turning back to view its past, its present, or its ongoing forms of conduct.

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When one crosses a critical threshold or a threshold of decision, ...

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A notion of reflection, in a more authentically "reflexive" sense, was implicitly involved in the application of inquiry to itself, y0 = y.y, and was eventually encountered on a recurring basis in the application of each newly recognized component of inquiry to itself: y.y >= d.d, f.f. In a more substantial role, the option of a capacity for reflection was already noticed as a significant parameter in the constitution of an IF.

+

A notion of reflection, in a more authentically reflexive sense, was implicitly involved in the application of inquiry to itself, <math>y_0 = y \cdot y,\!</math> and was eventually encountered on a recurring basis in the application of each newly recognized component of inquiry to itself: <math>y \cdot y >\!\!= d \cdot d, f \cdot f.\!</math> In a more substantial role, the option of a capacity for reflection was already noticed as a significant parameter in the constitution of an IF.

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Often, an IF is founded and persists in operation long before any participant is able to reflect on its structure or to post a note of its character to the constituting members of the framework. (SS 1.3.3.5, page 14).

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{| align="center" cellpadding="0" cellspacing="0" width="90%"

+

|

+

Often, an IF is founded and persists in operation long before any participant is able to reflect on its structure or to post a note of its character to the constituting members of the framework.

+

|-

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| align="right" | (§ 1.3.3.5, page 14)

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|}

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More substantially, a notion of reflection was invoked as something necessary ~~...~~

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More substantially, a notion of reflection was invoked as something necessary …

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In other contexts, something called "reflection" was seen as necessary to avoid certain types of unfortunate outcomes,

+

In other contexts, something called “reflection” was seen as necessary to avoid certain types of unfortunate outcomes, …

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To avoid the types of cul de sac (cultist act) encountered above, I am taking some pains to ensure a reflective capacity for the interpretive frameworks I develop in this project. (SS 1.3.3.5, page 15).

+

{| align="center" cellpadding="0" cellspacing="0" width="90%"

−

+

|

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A radical form of analysis ... requires interpreters ... to reflect on their own motives and motifs for construing and employing objects in the ways they do, and to deconstruct how their own aims and biases enter into the form and use of objects. (SS 1.3.4.12, page 36).

+

To avoid the types of cul de sac (cultist act) encountered above, I am taking some pains to ensure a reflective capacity for the interpretive frameworks I develop in this project.

+

|-

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| align="right" | (§ 1.3.3.5, page 15)

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|}

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Thus, the radical project in all of these directions demands forms of interpretation, analysis, synthesis that can reflect a measure of light on the initially unstated assumptions of their prospective agents. (SS 1.3.4.12, page 36).

+

{| align="center" cellpadding="0" cellspacing="0" width="90%"

+

|

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A radical form of analysis &hellip requires interpreters … to reflect on their own motives and motifs for construing and employing objects in the ways they do, and to deconstruct how their own aims and biases enter into the form and use of objects.

+

|-

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| align="right" | (§ 1.3.4.12, page 36)

+

|}

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{| align="center" cellpadding="0" cellspacing="0" width="90%"

+

|

+

Thus, the radical project in all of these directions demands forms of interpretation, analysis, synthesis that can reflect a measure of light on the initially unstated assumptions of their prospective agents.

+

|-

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| align="right" | (§ 1.3.4.12, page 36)

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|}

The relationships among the activities and faculties of discussion, contemplation, formalization, meditation, and reflection need to be explored in more detail. In particular, the relationship between formalization and reflection is especially relevant to the task of constructing a RIF.

−

Unlike a discussion of discussion, d.d, which is easy to start and hard to put an end to once it gets going, it is difficult for a reflection on reflection, r.r, to get itself going with nothing to reflect on but itself. I have just illustrated one way of doing this, namely, by leading a text to reflect on itself, as long as you understand this figure of speech to mean that it leads its interpreters, its writer and reader, without whose agency there would be no reflection at all, to reflect on how it reflects on itself. But I obviously need other ways than this to demonstrate the functions and properties of reflection in anything like their full variety.

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Unlike a discussion of discussion, <math>d \cdot d,\!</math> which is easy to start and hard to put an end to once it gets going, it is difficult for a reflection on reflection, <math>r \cdot r,\!</math> to get itself going with nothing to reflect on but itself. I have just illustrated one way of doing this, namely, by leading a text to reflect on itself, as long as you understand this figure of speech to mean that it leads its interpreters, its writer and reader, without whose agency there would be no reflection at all, to reflect on how it reflects on itself. But I obviously need other ways than this to demonstrate the functions and properties of reflection in anything like their full variety.

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Toward this end, it can also help to illustrate the action of reflection if I find it some material besides itself to reflect off of, in other words, if I supply it with an independently generated and concretely finished text as an argument to exercise its powers of reflection on. Accordingly, in the next part of this discussion I will interleave my text with ~~...~~

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Toward this end, it can also help to illustrate the action of reflection if I find it some material besides itself to reflect off of, in other words, if I supply it with an independently generated and concretely finished text as an argument to exercise its powers of reflection on. Accordingly, in the next part of this discussion I will interleave my text with …

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The preview that follows takes up the first stirrings of many subjects that cannot be meaningfully engaged, much less fully formalized, until much later in the investigation. In many cases the ongoing discussion can afford to pause only long enough to toss a provisional name in the direction of a prospective topic, both the name and the place of which promise an eventual return and revision, if not a recurring visitation. If I were forced to give a formal title to my sketch in reconnaissance of this area, I would call it the "phenomenology of inquiry", but this fine label is already too heavy an emblem for my effort to bear at this point.

+

The preview that follows takes up the first stirrings of many subjects that cannot be meaningfully engaged, much less fully formalized, until much later in the investigation. In many cases the ongoing discussion can afford to pause only long enough to toss a provisional name in the direction of a prospective topic, both the name and the place of which promise an eventual return and revision, if not a recurring visitation. If I were forced to give a formal title to my sketch in reconnaissance of this area, I would call it the “phenomenology of inquiry”, but this fine label is already too heavy an emblem for my effort to bear at this point.

This subsection presents a broad overview of the questions raised and the conceptual needs occasioned by the prospects of constructing a RIF. It makes no attempt to completely cover the topics it identifies and does not try to answer the questions it raises or to fill the needs it notices, but it merely points out a selective sample of the most salient concerns that need to be addressed.

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The long route which I propose also aspires to carry reflection to the level of an ontology, but it will do so by degrees, following successive investigations into semantics and reflection.

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{| align="center" cellpadding="0" cellspacing="0" width="90%"

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Paul Ricoeur, The Conflict of Interpretations, [Ric, 6]

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|

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The long route which I propose also aspires to carry reflection to the level of an ontology, but it will do so by degrees, following successive investigations into semantics and reflection.

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|-

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| align="right" | Paul Ricoeur, ''The Conflict of Interpretations'', [Ric, 6]

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|}

The subject of reflection is first approached in a topical, paraphrastic, or even periphrastic manner. The notion of a capacity for reflection is submitted to a tentative analysis, as treated in a variety of different modes of conception, by listing the duties that are typically demanded of a reflective agent, by compiling and reconciling the properties that are commonly ascribed to the process of reflection, and by contemplating the responsibilities and the results that the faculty of reflection is supposed to have in the many contexts where it is expected to serve.

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"Reflection" is a word that is used with a wide variety of meanings in both ordinary language and technical contexts. Some of these uses have little to do with the sorts of inquiry being pursued here. Other uses, though related to inquiry, refer to processes that are fully as complex as inquiry itself. Neither of these extremes of meaning falls within the present focus of discussion.

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“Reflection” is a word that is used with a wide variety of meanings in both ordinary language and technical contexts. Some of these uses have little to do with the sorts of inquiry being pursued here. Other uses, though related to inquiry, refer to processes that are fully as complex as inquiry itself. Neither of these extremes of meaning falls within the present focus of discussion.

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The task for this project is to identify a coherent set of operations: (1) that fall within the scope of conceptual analysis and computational modeling, (2) that bear a recognizable and illuminating relationship to what is commonly called "reflection", ~~and~~ (3) that make an operational contribution to inquiry, ~~while~~ (4) ~~constituting~~ simpler components of it.

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The task for this project is to identify a coherent set of operations: (1) that fall within the scope of conceptual analysis and computational modeling, (2) that bear a recognizable and illuminating relationship to what is commonly called “reflection”, (3) that make an operational contribution to inquiry, and (4) that constitute simpler components of the operation of inquiry.

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I define "symbol" as any structure of signification in which a direct, primary, literal meaning designates, in addition, another meaning which is indirect, secondary, and figurative and which can be apprehended only through the first.

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{| align="center" cellpadding="0" cellspacing="0" width="90%"

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Paul Ricoeur, The Conflict of Interpretations, [Ric, 12]

+

|

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I define “symbol” as any structure of signification in which a direct, primary, literal meaning designates, in addition, another meaning which is indirect, secondary, and figurative and which can be apprehended only through the first.

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|-

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| align="right" | Paul Ricoeur, ''The Conflict of Interpretations'', [Ric, 12]

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|}

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~~This~~ types of reflective operations of interest in this work are best approached and analyzed within a sign theoretic setting. ~~...~~

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The types of reflective operations of interest in this work are best approached and analyzed within a sign theoretic setting. …

Presented in the guise of an allegorical figure, reflection appears as the bailiff or the sergeant at arms who escorts an agent, faculty, or process from the office of power to the dockets of observation, examination, and potential revision. But still, putting all allegory aside, this mode of transport goes nowhere at all, nor travels through any space, but turns on a mere change of views for all that it ushers in. One is perfectly capable of using a power of inquiry of which no account is yet given. But reflection is a part of the inquiry into conduct that gives the conduct in question a description.

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He paused and nibbled absentmindedly on his branch for a while, as if gathering his thoughts.

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{| align="center" cellpadding="0" cellspacing="0" width="90%"

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Daniel Quinn, Ishmael, [DQ, 11]

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|

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He paused and nibbled absentmindedly on his branch for a while, as if gathering his thoughts.

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|-

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| align="right" | Daniel Quinn, ''Ishmael'', [DQ, 11]

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|}

If inquiry is viewed as a process of reasoning, then it takes place in thought, and so in the signs that are the public expression of thought. This means that an inquiry into inquiry has the duty to concern itself with thoughts, signs, and the relationship between them. To do this in an appropriate setting, it has to consider thoughts and signs as things taken apart from, but placed in relation to, their own particular objects. Indeed, the task that distinguishes an inquiry into inquiry, the specific difference that sets it apart, both from all of its object inquiries and again from inquiry in general, is the question of how thought is to be conducted if the goals of inquiry are to be met.

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In such places (he went on at last), where animals are simply penned up, they are almost always more thoughtful than their cousins in the wild.

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{| align="center" cellpadding="0" cellspacing="0" width="90%"

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Daniel Quinn, Ishmael, [DQ, 11]

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|

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In such places (he went on at last), where animals are simply penned up, they are almost always more thoughtful than their cousins in the wild.

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|-

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| align="right" | Daniel Quinn, ''Ishmael'', [DQ, 11]

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|}

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If one considers the formula that characterizes an inquiry into inquiry, ~~"y0~~ = y.y", and examines the term y.y that factors y0 along the lines of an ostensible self application, it is evident that any power invoked on the right is instantly echoed on the left and so required to survive the application or else be revoked. If the use of a given power of inquiry, working from the right and serving in the role of an operator, leads to a prospective description of inquiry, worked on the left from the role of an operand to the role of a result, and if the ~~proferred~~ characterization of inquiry is found to be out of accord with significant instances of its actual practice, then either the depiction of inquiry, as it is mediately improvised in progress, or the performance of inquiry, as it is actually conducted in practice, can turn out to be at fault.

+

If one considers the formula that characterizes an inquiry into inquiry, <math>y_0 = y \cdot y,\!</math> and examines the term <math>y \cdot y\!</math> that factors <math>y_0\!</math> along the lines of an ostensible self-application, it is evident that any power invoked on the right is instantly echoed on the left and so required to survive the application or else be revoked. If the use of a given power of inquiry, working from the right and serving in the role of an operator, leads to a prospective description of inquiry, worked on the left from the role of an operand to the role of a result, and if the proffered characterization of inquiry is found to be out of accord with significant instances of its actual practice, then either the depiction of inquiry, as it is mediately improvised in progress, or the performance of inquiry, as it is actually conducted in practice, can turn out to be at fault.

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This is because even the dimmest of them cannot help but sense that something is very wrong with this style of living.

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{| align="center" cellpadding="0" cellspacing="0" width="90%"

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Daniel Quinn, Ishmael, [DQ, 11]

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|

+

This is because even the dimmest of them cannot help but sense that something is very wrong with this style of living.

+

|-

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| align="right" | Daniel Quinn, ''Ishmael'', [DQ, 11]

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|}

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The philosophical point of view called "pragmatism" takes a particular position on the relation of thoughts to signs, and this determines a particular method of approach to the nature of thinking. To preview here what is presented in detail later, the pragmatic point of view involves: (1) an assertion that thoughts are a special case of signs, (2) a theoretical definition of signs in terms of sign relations, and (3) a corresponding approach to the nature of thought as "praxis", in other words, of thinking as a process, or inquiry as a form of conduct.

+

The philosophical point of view called “pragmatism” takes a particular position on the relation of thoughts to signs, and this determines a particular method of approach to the nature of thinking. To preview here what is presented in detail later, the pragmatic point of view involves: (1) an assertion that thoughts are a special case of signs, (2) a theoretical definition of signs in terms of sign relations, and (3) a corresponding approach to the nature of thought as “praxis”, in other words, of thinking as a process, or inquiry as a form of conduct.

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When I say that they are more thoughtful, I don't mean to imply that they acquire powers of ratiocination.

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{| align="center" cellpadding="0" cellspacing="0" width="90%"

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Daniel Quinn, Ishmael, [DQ, 11]

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|

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+

When I say that they are more thoughtful, I don't mean to imply that they acquire powers of ratiocination.

−

The way that reflection turns action into depiction and description, how it gives a sign to the act and provides a code for its future conduct, is the chief mystery of the whole process of reflection. Expressed in the substantive fashion that the " ionized" character of "reflection" permits, this riddle arises from wondering how a reflection on the action can be transubstantiated as a sign of the action and resurrect itself in a code of the conduct. In other words, how does a signification calling for an interpretation arise from the very interruption of its full transmission, the comical section of its secular extension, the transient abdication of its permanent tradition, ..., or the discrete truncation of a continuous conduction?

+

|-

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| align="right" | Daniel Quinn, ''Ishmael'', [DQ, 11]

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|}

−

But the tiger you see madly pacing its cage is nevertheless preoccupied with something that a human would certainly recognize as a thought.

+

The way that reflection turns action into depiction and description, how it gives a sign to the act and provides a code for its future conduct, is the chief mystery of the whole process of reflection. Expressed in the substantive fashion that the “-ionized” character of “reflection” permits, this riddle arises from wondering how a reflection on the action can be transubstantiated as a sign of the action and resurrect itself in a code of the conduct. In other words, how does a signification calling for an interpretation arise from the very interruption of its full transmission, the comical section of its secular extension, the transient abdication of its permanent tradition, …, or the discrete truncation of a continuous conduction?

−

Daniel Quinn, Ishmael, [DQ, 11]

+

{| align="center" cellpadding="0" cellspacing="0" width="90%"

+

|

+

But the tiger you see madly pacing its cage is nevertheless preoccupied with something that a human would certainly recognize as a thought.

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|-

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| align="right" | Daniel Quinn, ''Ishmael'', [DQ, 11]

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|}

The way that inquiry obstructs itself, or that each inquiry interferes with every other, is a phenomenon that constitutes a principal target of this investigation. At times it seems as if the present construction is always the main obstruction to the intentions that are embodied in it, forestalling every chance of change, every hope of growth, and every possibility of progress into the future. How do the very processes of analysis, inquiry, and reflection come to have their aims so distorted, their airs so polluted, and their purposes so perverted that the very bodies of their own past effects become the blocks to their moving on?

−

And this thought is a question: Why?

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{| align="center" cellpadding="0" cellspacing="0" width="90%"

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Daniel Quinn, Ishmael, [DQ, 11]

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|

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And this thought is a question: ''Why?''

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|-

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| align="right" | Daniel Quinn, ''Ishmael'', [DQ, 11]

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|}

An inquiry into inquiry can start out so close to the start of its subject that it finds its subject inquiry in a state of inchoate incipience, one where no hint of reflection is yet to be discerned. But once the action of reflection is suspected to lie beneath the manifest activity of the subject inquiry, from the effects of reflection that are discovered to issue from the inquiry in question, the analysis of this reflection can take its charge to such outrageous extremes, breaking down the actual process of reflection to its most inert levels of miniscule details, breaking up the living continuity that is appropriate to a realistic depiction, incrementally revealing the fragments of reflection that are revealed by this analysis, omitting every sense of connection and surgically excising every ligament of extenuating context, or that are incrementally and inspecting revealed by this analysis with such a myopic scope, that no trace of the overriding imagination appears among the pieces that remain, the original aspect of reflection is lost among the residual debris.

−

When it comes to understanding a living activity, like reflection, or inquiry, or analysis itself for that matter, there are forms of analysis that go too far in their favored or particular directions while failing to take into account the workings of significant "ligaments", or connective factors, that help to constitute and coordinate both their subjects and themselves, and on which the integrity of both depends. In particular, the purely syntactic analysis of a reflective narrative is liable to be carried to the bounds of such extremities that no trace of reflection is evident within the functional structures of the parts that are obtained or appears beneath the few points of light that the analysis yet throws. At this point, the instrument of reflection is broken so utterly, into so many pieces, and of such a small size that neither a close nor a distant inspection of any fraction of their number reveals any longer the aspect of reflection for which their matter was originally prized and pried into. When this state of analysis is reached, the medium of reflection, though it is still reflective in a certain sense, scatters the ambient light of nature that remains to it and disperses its sense through an evanescent void that presents nothing more illuminating to the imagination than the shimmering opacity of an opalescent haze.

+

When it comes to understanding a living activity, like reflection, or inquiry, or analysis itself for that matter, there are forms of analysis that go too far in their favored or particular directions while failing to take into account the workings of significant “ligaments”, or connective factors, that help to constitute and coordinate both their subjects and themselves, and on which the integrity of both depends. In particular, the purely syntactic analysis of a reflective narrative is liable to be carried to the bounds of such extremities that no trace of reflection is evident within the functional structures of the parts that are obtained or appears beneath the few points of light that the analysis yet throws. At this point, the instrument of reflection is broken so utterly, into so many pieces, and of such a small size that neither a close nor a distant inspection of any fraction of their number reveals any longer the aspect of reflection for which their matter was originally prized and pried into. When this state of analysis is reached, the medium of reflection, though it is still reflective in a certain sense, scatters the ambient light of nature that remains to it and disperses its sense through an evanescent void that presents nothing more illuminating to the imagination than the shimmering opacity of an opalescent haze.

−

The way that reflection, in adjunction to conduct, leads that conduct to a description of itself, not only in the sense of begetting an image but also in the sense of encountering a design, needs itself to have a name. I dub this turn of reflection, through which it converts the conduct of experience into an experience of conduct, by the name "metamorphism". The way that a reflection of the action is a sign of the action needs to be investigated further, and is pursued through the rest of this work. An apology is due for continuing to harp on this point, but it remains a crucial point for the whole method of reflection, if it is to be a method.

+

The way that reflection, in adjunction to conduct, leads that conduct to a description of itself, not only in the sense of begetting an image but also in the sense of encountering a design, needs itself to have a name. I dub this turn of reflection, through which it converts the conduct of experience into an experience of conduct, by the name “metamorphism”. The way that a reflection of the action is a sign of the action needs to be investigated further, and is pursued through the rest of this work. An apology is due for continuing to harp on this point, but it remains a crucial point for the whole method of reflection, if it is to be a method.

−

"Why, why, why, why, why, why?" the tiger asks itself hour after hour, day after day, year after year, as it treads its endless path behind the bars of its cage.

+

{| align="center" cellpadding="0" cellspacing="0" width="90%"

−

Daniel Quinn, Ishmael, [DQ, 11]

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|

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“Why, why, why, why, why, why?” the tiger asks itself hour after hour, day after day, year after year, as it treads its endless path behind the bars of its cage.

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|-

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| align="right" | Daniel Quinn, ''Ishmael'', [DQ, 11]

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|}

−

Returning to the formula of an inquiry into inquiry, y0 = y.y, it is possible to derive a few of its consequences for the character of the operation that is to be called "reflection". In general, a formula like f = g.h constitutes a movement of conceptual reorganization, one whose resultant syntactic structure may or may not reflect an objective form of being, that is, an aspect of structure in the being that constitutes its object. If there is a similarity of structure to be found between the formula and the object, then one has what is called an "iconic formula", but this is not always the case, and even this special situation requires the proper interpretation to tell in exactly what respect the form of the sign and the form of the object are alike. Whatever the case, the role of the formula as a sign should not be confused with the role of the object in reality, no matter how similar their forms may be.

+

Returning to the formula of an inquiry into inquiry, <math>y_0 = y \cdot y,\!</math> it is possible to derive a few of its consequences for the character of the operation that is to be called “reflection”. In general, a formula like <math>f = g \cdot h\!</math> constitutes a movement of conceptual reorganization, one whose resultant syntactic structure may or may not reflect an objective form of being, that is, an aspect of structure in the being that constitutes its object. If there is a similarity of structure to be found between the formula and the object, then one has what is called an ''iconic formula'', but this is not always the case, and even this special situation requires the proper interpretation to tell in exactly what respect the form of the sign and the form of the object are alike. Whatever the case, the role of the formula as a sign should not be confused with the role of the object in reality, no matter how similar their forms may be.

−

It cannot analyze the question or elaborate on it.

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{| align="center" cellpadding="0" cellspacing="0" width="90%"

−

Daniel Quinn, Ishmael, [DQ, 11]

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|

+

It cannot analyze the question or elaborate on it.

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|-

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| align="right" | Daniel Quinn, ''Ishmael'', [DQ, 11]

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|}

−

If one reads the form "y.y" according to the convention adopted, where a latently but actively instrumentalized inquiry on the right applies to a patently but patiently objectified inquiry on the left, almost as if they were two distinct agencies, faculties, or processes, then it is clear that an inquiry into inquiry can begin with little more than a nominal object, taking the name of "inquiry" in its sights to yield a clue in name only, while it can reserve all the power of an established capacity for inquiry to conduct its review, of which no account, no prescribed code, nor any catalog of procedure has to be given at the outset of its investigation.

+

If one reads the form <math>y \cdot y\!</math> according to the convention adopted, where a latently but actively instrumentalized inquiry on the right applies to a patently but patiently objectified inquiry on the left, almost as if they were two distinct agencies, faculties, or processes, then it is clear that an inquiry into inquiry can begin with little more than a nominal object, taking the name of “inquiry” in its sights to yield a clue in name only, while it can reserve all the power of an established capacity for inquiry to conduct its review, of which no account, no prescribed code, nor any catalog of procedure has to be given at the outset of its investigation.

−

If you were somehow able to ask the creature, "Why what?" it would be unable to answer you.

+

{| align="center" cellpadding="0" cellspacing="0" width="90%"

−

Daniel Quinn, Ishmael, [DQ, 11]

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|

+

If you were somehow able to ask the creature, “Why ''what''?” it would be unable to answer you.

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|-

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| align="right" | Daniel Quinn, ''Ishmael'', [DQ, 11]

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|}

−

But it is important to remember that the full intention of this factious formulation is more analogous to an interpretive doubling of vision, an amplification of resolving power and a coordination of perspectives, than it is to an objective division of being, a substantial disconnection of essentials or a disintegration of being. Even when the factions of the term "y.y" are conceived in practice to be implemented by substantially different parts of the same agency, constitutionally they embody but a single power.

+

But it is important to remember that the full intention of this factious formulation is more analogous to an interpretive doubling of vision, an amplification of resolving power and a coordination of perspectives, than it is to an objective division of being, a substantial disconnection of essentials or a disintegration of being. Even when the factions of the term <math>y \cdot y\!</math> are conceived in practice to be implemented by substantially different parts of the same agency, constitutionally they embody but a single power.

−

Before long I too began to ask myself why.

+

{| align="center" cellpadding="0" cellspacing="0" width="90%"

−

Daniel Quinn, Ishmael, [DQ, 11]

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|

+

Before long I too began to ask myself ''why''.

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|-

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| align="right" | Daniel Quinn, ''Ishmael'', [DQ, 11]

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|}

−

The form of inquiry into inquiry, y.y, requires that any power assumed on the part of the right is open to be indicted on the part of the left. This entails that any power arrogated for the ends of inquiry has to be given a name, not only under which it is invoked as an executive power, but also by which it is entered on the agenda of issues to inquire into, and finally through which it is indicted for submission to all the powers of inquiry that be. This combination of "appellation" and "supplication", or "nomination for" and "submission to" the jurisdiction of a reflexive application, makes up a large part of what is usually called "reflection".

+

The form of inquiry into inquiry, <math>y \cdot y,\!</math> requires that any power assumed on the part of the right is open to be indicted on the part of the left. This entails that any power arrogated for the ends of inquiry has to be given a name, not only under which it is invoked as an executive power, but also by which it is entered on the agenda of issues to inquire into, and finally through which it is indicted for submission to all the powers of inquiry that be. This combination of ''appellation'' and ''supplication'', or ''nomination for'' and ''submission to'' the jurisdiction of a reflexive application, makes up a large part of what is usually called ''reflection''.

−

Being neurologically far in advance of the tiger, I was able to examine what I meant by the question, at least in a rudimentary way.

+

{| align="center" cellpadding="0" cellspacing="0" width="90%"

−

Daniel Quinn, Ishmael, [DQ, 11]

+

|

+

Being neurologically far in advance of the tiger, I was able to examine what I meant by the question, at least in a rudimentary way.

+

|-

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| align="right" | Daniel Quinn, ''Ishmael'', [DQ, 11]

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|}

−

Many times, otherwise unrelated uses of the word "reflection" in the physical sciences can be suggestive. For example, reflection is one of the ways that a continuous appearing phenomenon can be brought into a form of interaction with itself and thereby to exhibit its nature as a pattern of activity with definite features and discrete characteristics. But metaphors like these can be kept from spinning out misleading clues only if the keys to understanding them as analogies can be found.

+

Many times, otherwise unrelated uses of the word ''reflection'' in the physical sciences can be suggestive. For example, reflection is one of the ways that a continuous appearing phenomenon can be brought into a form of interaction with itself and thereby to exhibit its nature as a pattern of activity with definite features and discrete characteristics. But metaphors like these can be kept from spinning out misleading clues only if the keys to understanding them as analogies can be found.

−

+

−

I remembered a different sort of life, which was, for those who lived it, interesting and pleasant.

+

{| align="center" cellpadding="0" cellspacing="0" width="90%"

−

Daniel Quinn, Ishmael, [DQ, 11-12]

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|

+

I remembered a different sort of life, which was, for those who lived it, interesting and pleasant.

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|-

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| align="right" | Daniel Quinn, ''Ishmael'', [DQ, 11–12]

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|}

With respect to the present project, that peers into its own appearances for the sake of seeing what logic lies in the rawness of experience, the analogous question is: How can the continuation of experience be conducted in such a way as to reveal within experience itself the conditions that connect its unconducted to its conducted course?

−

By contrast, this life was agonizingly boring and never pleasant.

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{| align="center" cellpadding="0" cellspacing="0" width="90%"

−

Daniel Quinn, Ishmael, [DQ, 12]

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By contrast, this life was agonizingly boring and never pleasant.

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|-

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| align="right" | Daniel Quinn, ''Ishmael'', [DQ, 12]

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|}

−

This motion, the kind of movement just put in question or the form of development just wondered about, occurs throughout the whole field of inquiry, making it convenient to find a name for it. Because it steps across a boundary in a state space while keeping its eye on both sides of the displayed distinction, it can be called a "circumspect transition" or, more dramatically, a "peripeteic strophe". At times it appears in lights that earn it the titles of the "yoke of knowing existence" (YOKE), the "conduct of subjectivity" (COS), or just the "junctive element" (JE). It is pertinent in this connection that I am treating the condition of subjectivity as a special case of pragmatic objectivity, as it appears in this instance, one that involves an element of reflection.

+

This motion, the kind of movement just put in question or the form of development just wondered about, occurs throughout the whole field of inquiry, making it convenient to find a name for it. Because it steps across a boundary in a state space while keeping its eye on both sides of the displayed distinction, it can be called a ''circumspect transition'' or, more dramatically, a ''peripeteic strophe''. At times it appears in lights that earn it the titles of the ''yoke of knowing existence'' (YOKE), the ''conduct of subjectivity'' (COS), or just the ''junctive element'' (JE). It is pertinent in this connection that I am treating the condition of subjectivity as a special case of pragmatic objectivity, as it appears in this instance, one that involves an element of reflection.

−

Thus, in asking why, I was trying to puzzle out why life should be divided in this way, half of it interesting and pleasant and half of it boring and unpleasant.

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{| align="center" cellpadding="0" cellspacing="0" width="90%"

−

Daniel Quinn, Ishmael, [DQ, 12]

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+

Thus, in asking ''why'', I was trying to puzzle out why life should be divided in this way, half of it interesting and pleasant and half of it boring and unpleasant.

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|-

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| align="right" | Daniel Quinn, ''Ishmael'', [DQ, 12]

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|}

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So let me dispense for the moment, even if this dispensation has to be carried out for now in the flippant manner and the fugal mannerisms of the foregoing counterpoint of discussion, with what I earnestly desire, all in good time and by means of well tempered arguments, to dispense with once and for all: The notion that individual words, sentences, paragraphs, articles, and so on up the scale can be anything like the final arbiters of thought and anything approaching the units of thought of ultimate interest to inquiry. But I want to do this without giving up the spirit of analysis altogether, merely by looking for forms of analysis that are fit to address the ''text of inquiry'' (TOI) in its full integrity.

−

~~So let me dispense for the moment, even if this dispensation has to be carried~~ out for now in the flippant manner and the fugal mannerisms of the foregoing counterpoint of discussion, with what I earnestly desire, all in good time and by means of well tempered arguments, to dispense with once and for all: The notion that ~~individual words~~, ~~sentences~~, ~~paragraphs~~, articles, and so on up the scale can be anything like the final arbiters of thought and anything approaching the units of thought of ultimate interest to inquiry. But I want to do this without giving up the spirit of analysis altogether, merely by looking for forms of analysis that are fit to address the "text of inquiry" (TOI) in its full integrity.

+

{| align="center" cellpadding="0" cellspacing="0" width="90%"

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It was in puzzling out such small matters as these that my interior life began — quite unnoticed.

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|-

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| align="right" | Daniel Quinn, ''Ishmael'', [DQ, 12]

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|}

−

~~It was in puzzling out such small matters as these~~ that ~~my interior life began — quite unnoticed~~.

+

In the process of elucidating the pragmatic point of view and applying it to the present array of problems, it soon becomes useful to examine the very notion of a ''point of view'' (POV). As reflections on the idea of a POV gradually mount up, the analysis of the general conception of a POV begins not only to take on a definite shape for itself, that is, with respect to the conditions it needs for its continued progress, but also to give a determinate, if slightly schematic, form to its object. Eventually, a sufficient confidence in the accumulated developments of the concept of a POV can lead this analysis to the point of suggesting provisional definitions and even to the point of attempting a specific formalization of POVs in general. This series of developments occurs concurrently throughout the construction of the current or any RIF, the necessity of which ought to be clear from the fact that the sequence of POVs from which one reflects is critical to the result and the success of any process of reflection.

−

~~Daniel Quinn~~, ~~Ishmael~~, ~~[DQ, 12]~~

−

~~In the process of elucidating the pragmatic point of view and applying it to the present array of problems, it soon becomes useful to examine the very notion of a~~ "~~point of view~~" (POV). As reflections on the idea of a POV gradually mount up, the analysis of the general conception of a POV begins not only to take on a definite shape for itself, that is, with respect to the conditions it needs for its continued progress, but also to give a determinate, if slightly schematic, form to its object. Eventually, a sufficient confidence in the accumulated developments of the concept of a POV can lead this analysis to the point of suggesting provisional definitions and even to the point of attempting a specific formalization of POV's in general. This series of developments occurs concurrently throughout the construction of the current or any RIF, the necessity of which ought to be clear from the fact that the sequence of POV's from which one reflects is critical to the result and the success of any process of reflection.

+

{| align="center" cellpadding="0" cellspacing="0" width="90%"

−

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−

A child hears it said that the stove is hot. But it is not, he says; and, indeed, that central body is not touching it, and only what that touches is hot or cold. But he touches it, and finds the testimony confirmed in a striking way. Thus, he becomes aware of ignorance, and it is necessary to suppose a self in which this ignorance can inhere. ~~...~~

+

A child hears it said that the stove is hot. But it is not, he says; and, indeed, that central body is not touching it, and only what that touches is hot or cold. But he touches it, and finds the testimony confirmed in a striking way. Thus, he becomes aware of ignorance, and it is necessary to suppose a ''self'' in which this ignorance can inhere. …

−

In short, error appears, and it can be explained only by supposing a self which is fallible.

+

In short, ''error'' appears, and it can be explained only by supposing a ''self'' which is fallible.

−

Ignorance and error are all that distinguish our private selves from the absolute ego of pure apperception.

+

Ignorance and error are all that distinguish our private selves from the absolute ''ego'' of pure apperception.

−

(Peirce, CP 5.233 235).

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| align="right" | (Peirce, CP 5.233–235)

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|}

Peirce makes the point that one's first awareness of a personal existence arises in reaction to the brute impact of experience and is ultimately compounded by way of reflection on its imports. Taking this to echo the exchange between Brutus and Cassius, I have the points that I need to stake out and to sound out a significant portion of the RIF that I intend to discuss.

Line 2,557: Line 2,702:

Before passing over the subject of the JE, in order to continue with a sketch of reflection, it is useful to notice a couple of features that affect this style of movement, as recapitulated in this strophe, and that determine the prospective turns of events, as predicated on its action. In one sense the motion is reversible, since the boundary in the basic state space, once crossed, is easily crossed again. In another sense the transition is irreversible, since what is learned from a single crossing, assuming the agent is capable of acquiring knowledge in the process, is neither so quickly forgotten nor so easily lost.

−

It is the usual thing, in contemplating the forms of development that are epitomized by the figure of the JE, to find the images of winding gyres and helical ascents coming to mind, in other words, the trajectories of open curves in an extended space that project onto closed curves in a more basic space. In anticipation of later developments, I propose to attribute the "basic" and the "extended" aspects of this strophic segue to its "dynamic" and its "symbolic" components, respectively.

+

It is the usual thing, in contemplating the forms of development that are epitomized by the figure of the JE, to find the images of winding gyres and helical ascents coming to mind, in other words, the trajectories of open curves in an extended space that project onto closed curves in a more basic space. In anticipation of later developments, I propose to attribute the ''basic'' and the ''extended'' aspects of this strophic segue to its ''dynamic'' and its ''symbolic'' components, respectively.

If it is important, at first sight, to recognize the JE as an irreducible primitive, inscribing its expression of its own being in the self signed tokens of a uniquely traced but perfectly typical autograph, all along personalizing its form of possession with an irrepressible panache, and leaving its legacy in an otherwise irreproducible style of paraph, it is just as important, on second thought, to try various schemes of analysis on it, with the aim, however artificially, of articulating, approximating, or explaining its form.

Line 2,563: Line 2,708:

A number of questions arise at this point, concerning the justification of these moves, not just to justify the initial JE but to rationalize all of the ensuing action that is predicated on it. Just to name a few:

−

1. What justifies a particular way of leading experience to reflect on itself?

+

# What justifies a particular way of leading experience to reflect on itself?

−

+

# What justifies a particular way of causing reflection to comment on itself?

−

2. What justifies a particular way of causing reflection to comment on itself?

If it is asked, with respect to the legitimacy of all such questions, what is the justification for imposing extraneous ventures and superimposing foreign notions on the otherwise natural course of things, the answer has to be that, otherwise, it could not be articulated at all, and that, once reflected, the naturalness of expression that affected the original intention cannot be recovered without some risk of artificiality.

Line 2,573: Line 2,717:

To deal with the relationship between the dynamic and the symbolic aspects of the JE, I try a couple of strategies, ranging in character from the casual to the formal.

−

1. To start, I adapt an informal distinction between the "matter" of a thought and the "manner" of thinking it. For example, in the effort to think about uncertainty one hopes to develop a certain concept of it. So, even though one continues to think about uncertainty, one hopes to become fairly certain about it. Here, the matter or content of one's thinking is fixed on uncertainty while the manner or conduct of one's thinking is hoped to change from the dubious to the certain.

+

# To start, I adapt an informal distinction between the ''matter'' of a thought and the ''manner'' of thinking it. For example, in the effort to think about uncertainty one hopes to develop a certain concept of it. So, even though one continues to think about uncertainty, one hopes to become fairly certain about it. Here, the matter or content of one's thinking is fixed on uncertainty while the manner or conduct of one's thinking is hoped to change from the dubious to the certain.

+

# Eventually, it is necessary to develop a formal concept and even a mathematical model of this relationship. To do this, I adopt the intuitive notions of a ''point of view'' (POV) and its ''point of development'' (POD), gradually turning them into formal concepts of a very general character. This requires distinguishing between two kinds of propositions that are associated with POVs and PODs, namely: (a) the propositions that are ''attached to'' or ''contained in'' them, and (b) the propositions that are ''applied to'' or ''maintained about'' them.

−

~~2. Eventually~~, ~~it is necessary~~ to ~~develop~~ a ~~formal concept and even~~ a ~~mathematical model~~ of ~~this relationship~~. ~~To do~~ this, ~~I adopt~~ the ~~intuitive notions~~ of a ~~"point of view" (~~POV~~) and its "point~~ of ~~development" (POD)~~, ~~gradually turning them into formal concepts of~~ a ~~very general character. This requires distinguishing between two kinds~~ of ~~propositions that are associated~~ with ~~POV's~~ and ~~POD's~~, ~~namely:~~ (a) the ~~propositions that are "attached~~ to~~" or "contained in" them~~, ~~and (b) the propositions that are "applied to" or "maintained about" them~~.

+

Just to give a rough idea of how these two distinctions relate to each other, the ''matter'' of a thought corresponds to an ''attached'' proposition, ''in'' a POV or ''at'' a POD, while the ''manner'' of a thought corresponds to an ''applied'' proposition, ''on'' a POV or ''about'' a POD. Employing this language to describe the case of an inquiry successfully self-applied, one can say the following things. An agent of inquiry has a POV that changes from one POD to the next in a series of developments, and this can be a POV that concerns itself with the question of inquiry, among other things, and thus with the topics of uncertainty and certainty, or doubt and belief. In such a case, as the POV moves from an initial POD to a terminal POD, a part of its matter stays fixed on ''doubt'', while its whole manner is transformed from one of ''doubt'' toward one of ''belief''.

−

~~Just~~ to ~~give~~ a ~~rough idea~~ of ~~how these two distinctions relate~~ to ~~each other,~~ the ~~matter~~ of ~~a thought corresponds to an "attached" proposition~~, ~~"in"~~ a POV or ~~"at" a POD, while~~ the ~~manner~~ of ~~a thought corresponds to an "applied" proposition, "on" a POV or "about" a POD~~. ~~Employing this language~~ to ~~describe~~ the ~~case~~ of ~~an inquiry successfully self applied~~, ~~one can say~~ the ~~following things~~. ~~An agent~~ of ~~inquiry has a POV that changes from one POD to~~ the ~~next~~ in a series ~~of developments~~, ~~and this can be a POV that concerns itself with~~ the ~~question of inquiry, among other things, and thus with the topics of uncertainty and certainty~~, or ~~doubt and belief. In such a case, as the~~ POV ~~moves from an initial POD to a terminal POD, a part of its matter stays fixed on "doubt", while its whole manner is transformed from one of "doubt" toward one of "belief"~~.

+

It is not always necessary to distinguish a POV from each of its PODs, except when one needs to emphasize the dynamic aspect of these ideas, especially the fact that a single POV can pass through or incorporate many different PODs in the course of its development. It is legitimate to say that the POV is present at each of its PODs, or that the PODs are incorporated in their overall POV. Accordingly, it is not always necessary to lose sight of the successive PODs in a series, so long as they are amenable to being incorporated in the last POD, or final POV.

−

It is ~~not~~ always ~~necessary to distinguish~~ a POV ~~from each~~ of its ~~POD's~~, ~~except when one needs to emphasize the dynamic aspect of these ideas~~, ~~especially the fact~~ that a ~~single POV can pass through or incorporate many different~~ POD~~'s in the course~~ of ~~its development~~. ~~It is legitimate~~ to ~~say~~ that ~~the POV is present~~ at ~~each of its~~ POD's, or that the ~~POD~~'~~s are incorporated in their overall POV. Accordingly~~, ~~it is not always necessary~~ to ~~lose sight~~ of ~~the successive POD's in a series~~, ~~so long~~ as ~~they are amenable~~ to ~~being incorporated in~~ the ~~last~~ POD~~, or final POV~~.

+

When one says that a POV is associated with a particular proposition, whether containing it or instancing it, one always means a POV as it exists at a particular POD, or through a particular range of its PODs. For example, if I say <math>{}^{\backprime\backprime}J ~\text{thinks}~ K ~\text{is smarter than}~ L{}^{\prime\prime},\!</math> then I am implicating a POV that <math>J\!</math> has at a particular POD, assumed to be capable of specification. Moreover, I am relying on the specific information inherent in this POD to index the particular persons <math>K\!</math> and <math>L\!</math> that I am assuming <math>J\!</math> has in mind at that POD. In technical terms, this requires the “intentional context” that is signaled by the verb ''thinks'', normally “opaque” to all distributions of contextual information from any point outside its frame, to be treated as “transparent” to the packet of information that is assumed to be represented by the POD in question.

−

When one says that a POV is associated with a particular proposition, whether containing it or instancing it, one always means a POV as it exists at a particular POD, or through a particular range of its POD's. For example, if I say that "J thinks K is smarter than L", then I am implicating a POV that J has at a particular POD, assumed to be capable of specification. Moreover, I am relying on the specific information inherent in this POD to index the particular persons named "K" and "L" that I am assuming J has in mind at that POD. In technical terms, this requires the "intentional context" that is signaled by the verb "thinks", normally "opaque" to all distributions of contextual information from any point outside its frame, to be treated as "transparent" to the packet of information that is assumed to be represented by the POD in question.

+

In the application of mediate interest to this project, a POV corresponds to a computational system, while a POD corresponds to one of its states. It is desirable to have a way of referring to the system as a whole, but in ways that are implicitly quantified by the relevant classes of states. For example, I want to have a system of interpretation in place where it is possible to write <math>{}^{\backprime\backprime}j : x = y{}^{\prime\prime}\!</math> to mean that <math>{}^{\backprime\backprime}j ~\text{sets}~ x ~\text{equal to}~ y{}^{\prime\prime},\!</math> to read this as a statement about a system <math>j\!</math> and two of its stores <math>x\!</math> and <math>y,\!</math> and to understand this as a statement that implicitly refers to a set of states that makes it true. Further, I want to recognize this statement as the active voice, attributed account, or authorized version of the more familiar, but passive, anonymous, or unavowed species of assignment statement <math>{}^{\backprime\backprime}x := y{}^{\prime\prime}.\!</math>

−

In the application of mediate interest to this project, a POV corresponds to a computational system, while a POD corresponds to one of its states. It is desirable to have a way of referring to the system as a whole, but in ways that are implicitly quantified by the relevant classes of states. For example, I want to have a system of interpretation in place where it is possible to write "j : x = y" to mean that "j sets x equal to y", to read this as a statement about a system j and two of its stores x and y, and to understand this as a statement that implicitly refers to a set of states that makes it true. Further, I want to recognize this statement as the "active" voice, "attributed" account, or "authorized" version of the more familiar, but "passive", "anonymous", or "unavowed" species of assignment statement "x := y".

The rudimentary parallels between these different distinctions should not be treated too rigidly, as a number of finer points about their true relationship remain to be sorted out. The next few remarks are given just to provide a hint of what is involved.

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Nevertheless, it is important to appreciate that all of these distinctions can become increasingly and divergently relativized as higher orders of reflection on the initial domain of objects turn wider circles of signs around it and heap higher towers of ideas upon it. When this happens, any initial portion of the objective and lower order syntactic domains can form the matter of a thought, while any final portion of the higher order syntactic domains can embody the manner of a thought.

−

Here is the critical point. A conceptual distinction is not absolute, but relative to the POV that sees it, makes it, draws it, or uses it. Indeed, one of the reasons for introducing the concept of a POV is to formalize this general insight and thereby to permit reflection on specific ~~POV's~~. But the intention of this move is to include any distinction that can be made in the process of an inquiry and found essential to its progress. Accordingly, the aim of this insight marks an intention to comprehend, not just the distinctions between previously identified predicates, like the attributes "dubious" and "certain" already mentioned, but also any future distinctions that might be discovered as necessary to inquiry. Almost immediately, for instance, the distinction just made by way of formalizing the concept of a POV, between the "propositions at" and the "propositions about" a POV, falls into the category of distinctions in question, at least, put under examination for the purposes of a review.

+

Here is the critical point. A conceptual distinction is not absolute, but relative to the POV that sees it, makes it, draws it, or uses it. Indeed, one of the reasons for introducing the concept of a POV is to formalize this general insight and thereby to permit reflection on specific POVs. But the intention of this move is to include any distinction that can be made in the process of an inquiry and found essential to its progress. Accordingly, the aim of this insight marks an intention to comprehend, not just the distinctions between previously identified predicates, like the attributes ''dubious'' and ''certain'' already mentioned, but also any future distinctions that might be discovered as necessary to inquiry. Almost immediately, for instance, the distinction just made by way of formalizing the concept of a POV, between the ''propositions at'' and the ''propositions about'' a POV, falls into the category of distinctions in question, at least, put under examination for the purposes of a review.

−

Consciousness is a movement which continually annihilates its starting point and can guarantee itself only at the end. In other words, it is something that has meaning only in later figures, since the meaning of a given figure is deferred until the appearance of a new figure.

+

{| align="center" cellpadding="0" cellspacing="0" width="90%"

−

Paul Ricoeur, The Conflict of Interpretations, [Ric, 113]

+

|

+

Consciousness is a movement which continually annihilates its starting point and can guarantee itself only at the end. In other words, it is something that has meaning only in later figures, since the meaning of a given figure is deferred until the appearance of a new figure.

+

|-

+

| align="right" | Paul Ricoeur, ''The Conflict of Interpretations'', [Ric, 113]

+

|}

−

In a sense, knowledge shrinks as wisdom grows: for details are swallowed up in principles. The details of knowledge which are important will be picked up ad hoc in each avocation of life, but the habit of the active utilisation of well understood principles is the final possession of wisdom.

+

{| align="center" cellpadding="0" cellspacing="0" width="90%"

−

~~A.N.~~ Whitehead, The Aims of Education, [ANW, 46]

+

|

−

cited in S.R. Covey, First Things First, [CMM, 71]

+

In a sense, knowledge shrinks as wisdom grows: for details are swallowed up in principles. The details of knowledge which are important will be picked up ad hoc in each avocation of life, but the habit of the active utilisation of well-understood principles is the final possession of wisdom.

+

|-

+

| align="right" |

+

Alfred North Whitehead, ''The Aims of Education'', [ANW, 46]

+

cited in Stephen R. Covey, ''First Things First'', [CMM, 71]

+

|}

If I reflect on my own POV, it becomes evident that the critical focus and main interest of this inquiry is on the kinds of inquiry that cross a certain threshold, that of becoming deliberately conducted and critically controlled. But in order to remain critical and reflective I have to be interested in both sides of this distinction. This is the usual pattern of the circumspect transition that I just personified in the form of the JE. But here it seems to lead to the disconcerting conclusion that reason is founded on unreason, and that this reason is justified by the end that it leads to, not by the state that it starts in. This sounds ominous and dangerous, but I think that the difficulties it raises are partly verbal, the fault of ambiguities that are quick to right themselves on reflection, but more seriously, partly due to misleading theory of what constitutes a foundation, a theory that tends to be applied on the modern scene as an uncritical reflex of that very same and everyday modern POV.

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One thing is apparent: If reflective inquiry, based on the rationality of the intellectual share of reason, addresses instinctive inquiry, based on the sensibility of the affective, emotional, and motivational portion, as something wholly other, indeed, as its logical opposite, then it obstructs the eventuality and even precludes the possibility of discovering their compatibilities and continuities, and it interferes with the chances of seeing how each form of inquiry completes and extends the other.

−

~~</pre>~~

−

====The Light in the Clearing====

+

====5.3.2. The Light in the Clearing====

{| align="center" cellpadding="0" cellspacing="0" width="90%"

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|-

| align="right" |

−

Paul Ricoeur, ''The Conflict of Interpretations'', [Ric, 222],

+

Paul Ricoeur, ''The Conflict of Interpretations'', [Ric, 222]

−

quoting Jean Nabert, ''Elements for an Ethic'', [Nab, 77].

+

quoting Jean Nabert, ''Elements for an Ethic'', [Nab, 77]

|}

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If one accepts the idea that all of these excerpts are expressions of one and the same POV, but considered at different points of development, as enunciated, as reviewed, and as revised over an interval of many years, then they can be taken to illustrate the diverse kinds of changes that occur in the formulation, the development, and the clarification of a continuing POV.

−

====The Face in the Mirror====

+

====5.3.3. The Face in the Mirror====

{| align="center" cellpadding="0" cellspacing="0" width="90%"

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To draw the conclusion: To say that death is the end of life, in the sense of a goal, is obviously going a bit too far. Death is merely the contingent end of life as form of action, not the intentional end of life as a form of conduct, and all the rest of the confusion is merely verbal equivocation around and about these two senses of an end. In the light of the distinction between action and conduct it is easy to see that death is just a bit beyond the true end of life.

−

<~~pre~~>

+

{| align="center" cellpadding="0" cellspacing="0" width="90%"

−

In the same way as it is not sufficient, before beginning to rebuild the house in which one lives, only to pull it down and to provide material and architects, or oneself to try one's hand at architecture, and moreover, to have drawn the plan carefully, but one must also provide oneself with some other accommodation in which to be lodged conveniently while the work is going on, so, also, in order that I might not remain irresolute in my actions during the time that my reason would oblige me to be so in my judgements, and so that I would not cease to live from that time forward as happily as I could, I formed a provisional moral code which consisted of only three or four maxims, which I am willing to disclose.

+

|

−

Rene Descartes, Discourse on Method, [Des, 45]

+

In the same way as it is not sufficient, before beginning to rebuild the house in which one lives, only to pull it down and to provide material and architects, or oneself to try one's hand at architecture, and moreover, to have drawn the plan carefully, but one must also provide oneself with some other accommodation in which to be lodged conveniently while the work is going on, so, also, in order that I might not remain irresolute in my actions during the time that my reason would oblige me to be so in my judgements, and so that I would not cease to live from that time forward as happily as I could, I formed a provisional moral code which consisted of only three or four maxims, which I am willing to disclose.

+

|-

+

| align="right" | Rene Descartes, ''Discourse on Method'', [Des, 45]

+

|}

−

The advisability of justifying one's actions as much as one can is clear, but the problems that arise in trying to do so are not trivial, ~~...~~

+

The advisability of justifying one's actions as much as one can is clear, but the problems that arise in trying to do so are not trivial, …

−

In view of these problems, it is necessary to examine the formation of the JE and to consider its import for the "justification of inquiry" (JOI). It is useful to begin with a traditional idea or a received sense of what a JOI must be. The default justification, that almost everyone seems to fall back on, even when deliberately trying to be critical and reflective, arises from the common notion of a "foundation" as something that forms a necessary prerequisite to all attempts at reasoning.

+

In view of these problems, it is necessary to examine the formation of the JE and to consider its import for the ''justification of inquiry'' (JOI). It is useful to begin with a traditional idea or a received sense of what a JOI must be. The default justification, that almost everyone seems to fall back on, even when deliberately trying to be critical and reflective, arises from the common notion of a “foundation” as something that forms a necessary prerequisite to all attempts at reasoning.

−

After giving a critical account of the standard model in the light of a few additional reflections, I review the question of what a real JOI must be like, at least, if it is to allow for inquiry into inquiry and to account for the other features of inquiry already observed. At last, I renew the quest for those ~~JOI's~~ that befit a pragmatic perspective and that can be found within its survey.

+

After giving a critical account of the standard model in the light of a few additional reflections, I review the question of what a real JOI must be like, at least, if it is to allow for inquiry into inquiry and to account for the other features of inquiry already observed. At last, I renew the quest for those JOIs that befit a pragmatic perspective and that can be found within its survey.

−

There is a standard sort of proposal to justify inquiry that attempts to place its foundations at the beginning of its process and that insists on making them out as certain. I think it is fitting to describe this as a variety of "fundamentalism". If this form of understanding is submitted to reflection, it begins to look inconsistent, or at least hypocritical, since it promises a distinct JOI, but one that it can just as easily tell, by the right reflection at the outset, is not forthcoming by these means. In essence, it claims to have a different sort of justification for itself than every other claim to one's allegiance, but a careful examination of its more finely printed disclaimers begins to turn up the evidence that this, too, is ultimately on a par with every other belief system, with the technical exception that it demands unquestioning faith at the level of a method rather than on the grounds of a doctrine. Even here, it leaves one wondering how to discern these levels in practice, or whether they can be distinguished in principle.

+

There is a standard sort of proposal to justify inquiry that attempts to place its foundations at the beginning of its process and that insists on making them out as certain. I think it is fitting to describe this as a variety of ''fundamentalism''. If this form of understanding is submitted to reflection, it begins to look inconsistent, or at least hypocritical, since it promises a distinct JOI, but one that it can just as easily tell, by the right reflection at the outset, is not forthcoming by these means. In essence, it claims to have a different sort of justification for itself than every other claim to one's allegiance, but a careful examination of its more finely printed disclaimers begins to turn up the evidence that this, too, is ultimately on a par with every other belief system, with the technical exception that it demands unquestioning faith at the level of a method rather than on the grounds of a doctrine. Even here, it leaves one wondering how to discern these levels in practice, or whether they can be distinguished in principle.

On this fundamental model of inquiry, any appearance of a passage from doubt to certainty has its authenticity placed in doubt, and begins to have its pretensions of creatively discovering new knowledge fall into question, looking more like the illusions of a derivative performance. Indeed, every semblance of a genuine inquiry is parasitic on the host of axioms and methods already taken for granted, and it creates no greater capital of knowledge than the fund of certainty already established in a prior method of inquiry. In effect, this prior method is taken on faith, since it begs to be imitated in a ritual fashion and to have its formulas, while invoked without question, to be invested with blind forms of trust.

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In fine, the default manner of approaching the question of foundations makes inquiry into inquiry a moot question, an otiose endeavor that is neither possible to pursue in a bona fide way nor necessary to venture. Given the fundamentalist understanding of inquiry, the application of inquiry to itself can neither accomplish any real purpose nor achieve any goal that is actually at risk. The pretense of establishing the integrity of inquiry under a self-application of its principles always results in something of a put up job, a kangaroo court, or a show trial.

−

Under these conditions, the proceedings that declaim themselves to be engaged in honest inquiry are nothing more than a hypocritical display. They imitate the exterior form of a due process, but their judgment is fixed in advance and their conclusion but extravagantly reconstructs a previously settled system of belief, one that is never really doubted or put in question. The outer inquiry in the self-application is not a live inquiry but a "frame" that is prefabricated to isolate the object inquiry. Whether expertly or inertly, it is designed ahead of time to contain and to delimit a picture of inquiry that may or may not already be painted.

+

Under these conditions, the proceedings that declaim themselves to be engaged in honest inquiry are nothing more than a hypocritical display. They imitate the exterior form of a due process, but their judgment is fixed in advance and their conclusion but extravagantly reconstructs a previously settled system of belief, one that is never really doubted or put in question. The outer inquiry in the self-application is not a live inquiry but a ''frame'' that is prefabricated to isolate the object inquiry. Whether expertly or inertly, it is designed ahead of time to contain and to delimit a picture of inquiry that may or may not already be painted.

Notice that this is not a question of whether the original inquiry is genuine or not. The object inquiry, typically ignited by an external phenomenon, is commonly taken up in good faith, that is, with honest doubts at stake. But when there is never any doubt about what method to use, or about how to use it, or about the chances of its leading to a satisfactory end of the doubts inflamed in the first place, then there is never any need for inquiry into inquiry, and all show of it is vanity.

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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.

−

Could great men thunder

+

−

As Jove himself does, Jove would never be quiet,

+

−

For every pelting petty officer

+

{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"

−

Would use his heaven for thunder, nothing but thunder.

+

| colspan="2" | Could great men thunder

−

Merciful heaven,

+

|-

−

Thou rather with thy sharp and sulphurous bolt

+

| colspan="2" | As Jove himself does, Jove would never be quiet,

−

Split'st the unwedgeable and gnarled oak

+

|-

−

Than the soft myrtle. But man, proud man,

+

| colspan="2" | For every pelting petty officer

−

Dressed in a little brief authority,

+

|-

−

Most ignorant of what he's most assured,

+

| colspan="2" | Would use his heaven for thunder, nothing but thunder.

−

His glassy essence, like an angry ape

+

|-

−

Plays such fantastic tricks before high heaven

+

| colspan="2" | Merciful heaven,

−

As makes the angels weep, who, with our spleens,

+

|-

−

Would all themselves laugh mortal.

+

| colspan="2" | Thou rather with thy sharp and sulphurous bolt

−

Measure for Measure~~: Isabella—2~~.2.113-126

+

|-

+

| 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

+

|}

+

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.

−

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:

−

1. 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.

+

# 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.

−

~~2. 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~~.

+

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.

−

3. In ~~effect~~, ~~"founded or grounded" (FOG) systems require absolute certainty with respect to some~~ of ~~their~~ points, the points ~~on which they are said~~ to ~~rest~~. ~~It is as if these fixed points put them in contact with an infinite source~~ of ~~knowledge or connect them 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.~~

+

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:

−

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.

+

# 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.

−

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:

−

1. 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.

−

2. 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.

−

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?

−

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.

−

~~There's a double meaning in that.~~

+

−

~~Much Ado About Nothing: Benedick—2.3.246~~

−

~~(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.)

+

{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"

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| colspan="2" | There's a double meaning in that.

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|-

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| width="50%" |  

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| ''Much Ado About Nothing'', 2.3.246

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|}

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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.

+

−

Covey, Merrill, & Merrill, First Things First, [CMM, 59]

+

(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.)

+

{| align="center" cellpadding="0" cellspacing="0" width="90%"

+

|

+

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="right" | Covey, Merrill, and Merrill, ''First Things First'', [CMM, 59]

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|}

−

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.

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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.

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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.

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{| align="center" cellpadding="0" cellspacing="0" width="90%"

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Paul Ricoeur, The Conflict of Interpretations, [Ric, 13]

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|

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This circumscription of expressions with a double meaning properly constitutes the hermeneutic field.

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|-

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| align="right" | Paul Ricoeur, ''The Conflict of Interpretations'', [Ric, 13]

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|}

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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.

−

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.

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.

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~~</pre>~~

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====Points Forward====

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====5.3.4. Points Forward====

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~~<pre>~~

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'''Point 1.'''     Thought takes place in signs.

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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 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.

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Point 2. Thinking is a form of conduct.

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'''Point 2.'''     Thinking is a form of conduct.

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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.

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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.

−

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.

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~~bearing~~ on the order of the normative sciences:

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(Bearing on the order of the normative sciences : logic < ethics < aesthetics?)

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logic < ethics < aesthetics

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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.

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Point 4.

+

'''Point 4.'''     Conduct = (Act, End) = (State1, State2, State3).

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.

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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.

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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.

−

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 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.

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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, …

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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.

−

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.

−

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.

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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.

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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.

+

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.

+

If quotation were the only mechanism for introducing HO signs, then each new round of HO signs would require for its primary registration only the same constant amount of memory capacity. The laying down of each new order of signs over the original foundation would take up an increment of memory equal to that used by the initial domain of signs.

+

But tagging sign processes and sign relations with signs that actually stick to them requires an agent to catch them first. In other words, the generation of signs for sign processes and signs for sign relations demands that an agent be able to perceive them or conceive them amidst the flow of an ongoing sign process that is itself governed by the law of a prevailing sign relation. This involves a contribution from the higher faculties of reasoning, in particular, taking steps of synthetic inference to introduce or invent the necessary signs. Since it resorts to the processes of inductive and abductive reasoning, this is naturally much more difficult to achieve.

+

In order to reflect on sign processes it is necessary to have signs for sign processes. One needs to start with signs for sign transitions, that is, signs for ordered pairs of signs, and work up to signs for arbitrary sequences of signs. As an empirical matter, every transition between signs that actually appears in experience is worth noting. By extension, it is useful to note as many sequences of transitions from sign to sign as actually occur, so long as one can spare the capacity to record them. If one also attends to the objects with regard to which these transitions occur, then one has the material of an empirical sign relation.

+

But this is a tricky matter, much less obvious than it seems at first. Pragmatic objects are more than just the physically compacted objects that happen to be present in a given situation, at, during, or in causal relation to a particular transition. In general, a pragmatic object is a hypothetical object, one whose presence in a situation, relevance to a transition, or association with a system of interpretation has to be hypothesized. But a hypothesis incurs a risk of error that goes beyond the elementary faults of observation and recording. The hypothesis has to be tested in subsequent experience and corrected by future inquiry. What this all comes down to is the circumstance that not even the raw empirical matter of a theory of signs can be panned from the pure stream of consciousness without a good admixture of speculation.

+

To amplify this point, in many cases the objects of a sign relation cannot be pointed out with any sense of clarity or resolve until the semantic equivalence classes are fairly and adequately sampled and the semantic partition that mirrors the structure of the object domain is at least partially reconstructed in the experience of an interpretive agent.

+

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 …

+

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.

−

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 15.'''     Pragmatic incapacities have practical consequences.

−

~~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.

+

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

−

~~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~~.

+

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

−

+

−

~~If quotation were~~ the ~~only mechanism~~ for ~~introducing HO signs~~, ~~then each new round~~ of ~~HO signs would require for its primary registration only the same constant amount~~ of ~~memory capacity~~. ~~The laying down of each new order of signs over the original foundation would take up an increment of memory equal~~ to ~~that used by the initial domain of signs.~~

+

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.

−

+

−

~~But tagging sign processes~~ and ~~sign relations~~ with ~~signs that actually stick~~ to ~~them requires an agent to catch them first~~. In ~~other words,~~ the ~~generation~~ of ~~signs for sign processes and signs for sign relations demands that~~ an agent ~~be able~~ to ~~perceive them or conceive them amidst~~ the ~~flow~~ of ~~an ongoing sign process that is itself governed by~~ the ~~law~~ of ~~a prevailing sign relation~~. ~~This involves a contribution from~~ the ~~higher faculties~~ of ~~reasoning~~, ~~in particular, taking steps~~ of ~~synthetic inference to introduce~~ or ~~invent~~ the ~~necessary signs~~. ~~Since~~ it ~~resorts~~ to ~~the processes of inductive and abductive reasoning~~, ~~this is naturally much more difficult to achieve~~.

+

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.

−

+

−

In ~~order to reflect~~ on ~~sign processes it is necessary to have~~ signs ~~for sign processes. One needs to start~~ with signs ~~for sign transitions,~~ that ~~is, signs for ordered pairs~~ of ~~signs, and work up~~ to ~~signs for arbitrary sequences of signs~~. ~~As an empirical matter~~, ~~every transition between signs that actually appears in experience is worth noting. By extension~~, ~~it is useful to note~~ as ~~many sequences~~ of ~~transitions from sign to sign as actually occur~~, ~~so long as one~~ can ~~spare~~ the ~~capacity to record them~~. ~~If one also attends to the objects with regard to which these transitions occur~~, ~~then one has~~ the ~~material~~ of ~~an empirical sign relation.~~

+

'''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.

−

+

−

~~But this is~~ a ~~tricky matter, much less obvious than it seems at first~~. ~~Pragmatic objects are more than just the physically compacted objects that happen~~ to ~~be present~~ in ~~a given situation, at, during~~, or ~~in causal relation to a particular transition. In general~~, ~~a pragmatic object is a hypothetical object~~, ~~one whose presence in a situation, relevance~~ to ~~a transition~~, ~~or association with a system of interpretation has to be hypothesized. But a hypothesis incurs a risk of error that goes beyond~~ the ~~elementary faults of observation and recording. The hypothesis has to~~ be ~~tested in subsequent experience and corrected by future inquiry~~. ~~What~~ this ~~all comes down to is the circumstance that not even the raw empirical matter~~ of ~~a theory~~ of ~~signs~~ can be ~~panned from the pure stream of consciousness without~~ a ~~good admixture of speculation~~.

+

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.

−

+

−

~~To amplify this point, in many cases the objects~~ of a ~~sign relation cannot be pointed out with any sense~~ of ~~clarity or resolve until the semantic equivalence classes are fairly and adequately sampled and the semantic partition~~ that ~~mirrors the structure of the object domain~~ is ~~at least partially reconstructed in the experience~~ of ~~an interpretive agent~~.

+

'''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.

−

+

−

~~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~~.

+

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”.

−

+

−

~~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 ...~~

+

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

−

+

−

~~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.~~

+

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

+

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.

−

~~Point 15. Pragmatic incapacities have practical consequences~~.

−

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

+

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

−

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

+

# 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,

−

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.

+

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

−

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.~~

−

~~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.~~

−

~~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".

−

~~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 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.

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.

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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.

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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.

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

−

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

+

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

−

+

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

−

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

−

Point 22. Intelligent inquiry involves inquiry into inquiry.

+

'''Point 22.'''     Intelligent inquiry involves inquiry into inquiry.

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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.

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Point 23.

+

'''Point 23.'''     Inquiry into inquiry involves integrating independent inquiries.

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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.

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Point 24.

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

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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.

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Point 25.

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'''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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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>

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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.

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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.

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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?

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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.

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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.

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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.

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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''.

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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.

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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.

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Point 27.

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'''Point 27.'''

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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.

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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~~).

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'''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).

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Point 29.

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'''Point 29.'''

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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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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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~~</pre>~~

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~~ <sharethis />~~

[[Category:Artificial Intelligence]]

Jon Awbrey

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