Changes

Line 1,285: Line 1,285:  
=====1.3.9.1.  The Informal Context=====
 
=====1.3.9.1.  The Informal Context=====
    +
<br>
 
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
 
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
 
| colspan="3" | On either side the river lie
 
| colspan="3" | On either side the river lie
Line 1,308: Line 1,309:  
| width="10%" | &nbsp;
 
| width="10%" | &nbsp;
 
| width="40%" | &nbsp;
 
| width="40%" | &nbsp;
| Tennyson, The Lady of Shalott, [Ten, 17]
+
| Tennyson, ''The Lady of Shalott'', [Ten, 17]
 
|}
 
|}
 
<br>
 
<br>
Line 1,317: Line 1,318:  
Inquiry is an activity that still takes place largely in the informal context.  Accordingly, much of what people instinctively and intuitively do in carrying out an inquiry is done without a fully explicit idea of why they proceed that way, or even a thorough reflection on what they hope to gain by their efforts.  It may come as a shock to realize this, since most people regard their scientific inquiries, at least, as rational procedures that are founded on explicit knowledge and follow a host of established models.  But the standard of rigor that I have in mind here refers to the kind of fully thorough formalization that it would take to create autonomous computer programs for inquiry, ones that are capable of carrying out significant aspects of complete inquiries on their own.  The remoteness of that goal quickly becomes evident to any programmer who sets out in the general direction of trying to achieve it.
 
Inquiry is an activity that still takes place largely in the informal context.  Accordingly, much of what people instinctively and intuitively do in carrying out an inquiry is done without a fully explicit idea of why they proceed that way, or even a thorough reflection on what they hope to gain by their efforts.  It may come as a shock to realize this, since most people regard their scientific inquiries, at least, as rational procedures that are founded on explicit knowledge and follow a host of established models.  But the standard of rigor that I have in mind here refers to the kind of fully thorough formalization that it would take to create autonomous computer programs for inquiry, ones that are capable of carrying out significant aspects of complete inquiries on their own.  The remoteness of that goal quickly becomes evident to any programmer who sets out in the general direction of trying to achieve it.
   −
<blockquote>
+
<br>
Willows whiten, aspens quiver,
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
Little breezes dusk and shiver
+
| colspan="3" | Willows whiten, aspens quiver,
Thro' the wave that runs forever
+
|-
By the island in the river
+
| colspan="3" | Little breezes dusk and shiver
Flowing down to Camelot.
+
|-
Four gray walls, and four gray towers,
+
| colspan="3" | Thro' the wave that runs forever
Overlook a space of flowers,
+
|-
And the silent isle imbowers
+
| colspan="3" | By the island in the river
The Lady of Shalott.
+
|-
Tennyson, The Lady of Shalott, [Ten, 17]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | Flowing down to Camelot.
 +
|-
 +
| colspan="3" | Four gray walls, and four gray towers,
 +
|-
 +
| colspan="3" | Overlook a space of flowers,
 +
|-
 +
| colspan="3" | And the silent isle imbowers
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | The Lady of Shalott.
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 17]
 +
|}
 +
<br>
    
Nothing says that everything can be formalized.  Nothing says even that every intellectual process has a formal analogue, at least, nothing yet.  Indeed, one is obliged to formulate the question whether every inquiry can be formalized, and one has to be prepared for the possibility that an informal inquiry may lead one to the ultimate conclusion that not every inquiry has a formalization.  But how can these questions be any clearer than the terms "inquiry" and "formalization" that they invoke?  At this point it does not appear that further clarity can be achieved until specific notions of inquiry and formalization are set forth.
 
Nothing says that everything can be formalized.  Nothing says even that every intellectual process has a formal analogue, at least, nothing yet.  Indeed, one is obliged to formulate the question whether every inquiry can be formalized, and one has to be prepared for the possibility that an informal inquiry may lead one to the ultimate conclusion that not every inquiry has a formalization.  But how can these questions be any clearer than the terms "inquiry" and "formalization" that they invoke?  At this point it does not appear that further clarity can be achieved until specific notions of inquiry and formalization are set forth.
Line 1,349: Line 1,365:  
iii. How does it evolve over time?
 
iii. How does it evolve over time?
   −
<blockquote>
+
<br>
By the margin, willow-veil'd,
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
Slide the heavy barges trail'd
+
| colspan="3" | By the margin, willow-veil'd,
By slow horses;  and unhail'd
+
|-
The shallop flitteth silken-sail'd
+
| colspan="3" | Slide the heavy barges trail'd
Skimming down to Camelot:
+
|-
But who hath seen her wave her hand?
+
| colspan="3" | By slow horses;  and unhail'd
Or at the casement seen her stand?
+
|-
Or is she known in all the land,
+
| colspan="3" | The shallop flitteth silken-sail'd
The Lady of Shalott?
+
|-
Tennyson, The Lady of Shalott, [Ten, 17]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | Skimming down to Camelot:
 +
|-
 +
| colspan="3" | But who hath seen her wave her hand?
 +
|-
 +
| colspan="3" | Or at the casement seen her stand?
 +
|-
 +
| colspan="3" | Or is she known in all the land,
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | The Lady of Shalott?
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 17]
 +
|}
 +
<br>
    
I begin with the idea that a question is an unclear sign.  The question can express a problematic situation or a surprising phenomenon, but of course it expresses it only obscurely, or else the inquiry is at an end.  Answering the question is, generally speaking, a task of converting or replacing the initial sign with a clearer but logically equivalent sign, usually proceeding until a maximally clear sign or a sufficiently clear sign is achieved, or else until some convincing indication is developed that the initial sign has no meaning at all, or no sense worth pursuing.
 
I begin with the idea that a question is an unclear sign.  The question can express a problematic situation or a surprising phenomenon, but of course it expresses it only obscurely, or else the inquiry is at an end.  Answering the question is, generally speaking, a task of converting or replacing the initial sign with a clearer but logically equivalent sign, usually proceeding until a maximally clear sign or a sufficiently clear sign is achieved, or else until some convincing indication is developed that the initial sign has no meaning at all, or no sense worth pursuing.
Line 1,369: Line 1,400:  
An inquiry viewed as a recursive procedure seeks to compute, to find, or to generate a satisfactory answer to a hard question by working its way back to related but easier questions, component questions on which the whole original question appears to depend, until a set of questions are found that are so basic and whose answers are so easy, so evident, or so obvious that the agent of inquiry already knows their answers or is quickly able to obtain them, whence the agent of the procedure can continue by building up an adequate answer to the instigating question in terms of its answers to these fundamental questions.  The couple of phases that can be distinguished on logical grounds to be taking place within this process, whether in point of actual practice they proceed in exclusively serial, interactively dialectic, or independently parallel fashions, are usually described as the "analytic descent" (AD) and the "synthetic ascent" (SA) of the recursion in question.
 
An inquiry viewed as a recursive procedure seeks to compute, to find, or to generate a satisfactory answer to a hard question by working its way back to related but easier questions, component questions on which the whole original question appears to depend, until a set of questions are found that are so basic and whose answers are so easy, so evident, or so obvious that the agent of inquiry already knows their answers or is quickly able to obtain them, whence the agent of the procedure can continue by building up an adequate answer to the instigating question in terms of its answers to these fundamental questions.  The couple of phases that can be distinguished on logical grounds to be taking place within this process, whether in point of actual practice they proceed in exclusively serial, interactively dialectic, or independently parallel fashions, are usually described as the "analytic descent" (AD) and the "synthetic ascent" (SA) of the recursion in question.
   −
<blockquote>
+
<br>
Only reapers, reaping early
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
In among the bearded barley,
+
| colspan="3" | Only reapers, reaping early
Hear a song that echoes cheerly
+
|-
From the river winding clearly,
+
| colspan="3" | In among the bearded barley,
Down to tower'd Camelot:
+
|-
And by the moon the reaper weary,
+
| colspan="3" | Hear a song that echoes cheerly
Piling sheaves in uplands airy,
+
|-
Listening, whispers, "'T is the fairy
+
| colspan="3" | From the river winding clearly,
Lady of Shalott."
+
|-
Tennyson, The Lady of Shalott, [Ten, 17]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | Down to tower'd Camelot:
 +
|-
 +
| colspan="3" | And by the moon the reaper weary,
 +
|-
 +
| colspan="3" | Piling sheaves in uplands airy,
 +
|-
 +
| colspan="3" | Listening, whispers, "'T is the fairy
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | Lady of Shalott."
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 17]
 +
|}
 +
<br>
    
One of the continuing claims of this work is that the formal structures of sign relations are not only adequate to address the needs of building a basic commerce among objects, signs, and ideas but are ideally suited to the task of linking vastly different realms of objective realities and widely disparate realms of interpretive contexts.  What accounts for the utility that sign relations enjoy as a staple element for this job, not only for establishing the connectivity and maintaining the integrity of the mind in the world, but for holding the world and the mind together?
 
One of the continuing claims of this work is that the formal structures of sign relations are not only adequate to address the needs of building a basic commerce among objects, signs, and ideas but are ideally suited to the task of linking vastly different realms of objective realities and widely disparate realms of interpretive contexts.  What accounts for the utility that sign relations enjoy as a staple element for this job, not only for establishing the connectivity and maintaining the integrity of the mind in the world, but for holding the world and the mind together?
Line 1,388: Line 1,434:  
In view of this distinction, the issue for this inquiry is not so much a question about the bare facts of sign relation use themselves as it is a question about the abilities of sign-using agents to accomplish anything amounting to, analogous to, or approaching an awareness of these facts.  This is a question about an additional aptitude of sign-bearing agents, an extra capacity for the articulation and the expression of the facts and the factors that affect their very bearing as agents, and it amounts to an aptness for "reflection" on the facilities, the facticities, and the faculties that factor into making up their own sign use.  If nothing else, these reflections serve to settle the question of a name, permitting this ability to be called "reflection", however little else is known about it.
 
In view of this distinction, the issue for this inquiry is not so much a question about the bare facts of sign relation use themselves as it is a question about the abilities of sign-using agents to accomplish anything amounting to, analogous to, or approaching an awareness of these facts.  This is a question about an additional aptitude of sign-bearing agents, an extra capacity for the articulation and the expression of the facts and the factors that affect their very bearing as agents, and it amounts to an aptness for "reflection" on the facilities, the facticities, and the faculties that factor into making up their own sign use.  If nothing else, these reflections serve to settle the question of a name, permitting this ability to be called "reflection", however little else is known about it.
   −
<blockquote>
+
<br>
There she weaves by night and day
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
A magic web with colors gay.
+
| colspan="3" | There she weaves by night and day
She has heard a whisper say,
+
|-
A curse is on her if she stay
+
| colspan="3" | A magic web with colors gay.
To look down to Camelot.
+
|-
She knows not what the curse may be,
+
| colspan="3" | She has heard a whisper say,
And so she weaveth steadily,
+
|-
And little other care hath she,
+
| colspan="3" | A curse is on her if she stay
The Lady of Shalott.
+
|-
Tennyson, The Lady of Shalott, [Ten, 17]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | To look down to Camelot.
 +
|-
 +
| colspan="3" | She knows not what the curse may be,
 +
|-
 +
| colspan="3" | And so she weaveth steadily,
 +
|-
 +
| colspan="3" | And little other care hath she,
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | The Lady of Shalott.
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 17]
 +
|}
 +
<br>
    
The purpose of a sign, for instance, a name, an expression, a program, or a text, is to denote and possibly to describe an object, for instance, a thing, a situation, or an activity in the world.  When the reality to be described is infinitely more complex than the typically finite resources that one has to describe it, then strategic uses of these resources are bound to occur.  For example, elliptic, multiple, and repeated uses of signs are almost bound to be called for, involving the strategies of approximation, abstraction, and recursion, respectively.
 
The purpose of a sign, for instance, a name, an expression, a program, or a text, is to denote and possibly to describe an object, for instance, a thing, a situation, or an activity in the world.  When the reality to be described is infinitely more complex than the typically finite resources that one has to describe it, then strategic uses of these resources are bound to occur.  For example, elliptic, multiple, and repeated uses of signs are almost bound to be called for, involving the strategies of approximation, abstraction, and recursion, respectively.
 
The agent of a system of interpretation that is driven to the point of distraction by the task of describing an inexhaustibly complex reality has several strategies, aside from dropping the task altogether, that are available to it for recovering from a lapse of attention to its object:
 
The agent of a system of interpretation that is driven to the point of distraction by the task of describing an inexhaustibly complex reality has several strategies, aside from dropping the task altogether, that are available to it for recovering from a lapse of attention to its object:
 +
 
# The agent can resort to approximation.  This involves accepting the limitations of attention and restricting one's intention to capturing, describing, or representing merely the most salient aspect, facet, fraction, or fragment of the objective reality.
 
# The agent can resort to approximation.  This involves accepting the limitations of attention and restricting one's intention to capturing, describing, or representing merely the most salient aspect, facet, fraction, or fragment of the objective reality.
 
# The agent can resort to abstraction.  ...
 
# The agent can resort to abstraction.  ...
Line 1,409: Line 1,471:  
A common feature of these techniques is the creation of a formal domain, a context that contains the conceptually manageable images of objective reality, a circumscribed arena for thought, one that the mind can range over without an intolerable fear of being overwhelmed by its complexity.  In short, a formal arena, for all the strife that remains to it and for all the tension that it maintains with its informal surroundings, still affords a space for thought in which various forms of complete analysis and full comprehension are at least conceivable in principle.  For all their illusory character, these meager comforts are not to be despised.
 
A common feature of these techniques is the creation of a formal domain, a context that contains the conceptually manageable images of objective reality, a circumscribed arena for thought, one that the mind can range over without an intolerable fear of being overwhelmed by its complexity.  In short, a formal arena, for all the strife that remains to it and for all the tension that it maintains with its informal surroundings, still affords a space for thought in which various forms of complete analysis and full comprehension are at least conceivable in principle.  For all their illusory character, these meager comforts are not to be despised.
   −
<blockquote>
+
<br>
And moving thro' a mirror clear
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
That hangs before her all the year,
+
| colspan="3" | And moving thro' a mirror clear
Shadows of the world appear.
+
|-
There she sees the highway near
+
| colspan="3" | That hangs before her all the year,
Winding down to Camelot:
+
|-
There the river eddy whirls,
+
| colspan="3" | Shadows of the world appear.
And there the surly village-churls,
+
|-
And the red cloaks of market girls,
+
| colspan="3" | There she sees the highway near
Pass onward from Shalott.
+
|-
Tennyson, The Lady of Shalott, [Ten, 17-18]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | Winding down to Camelot:
 +
|-
 +
| colspan="3" | There the river eddy whirls,
 +
|-
 +
| colspan="3" | And there the surly village-churls,
 +
|-
 +
| colspan="3" | And the red cloaks of market girls,
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | Pass onward from Shalott.
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 17–18]
 +
|}
 +
<br>
    
The formal plane stands like a mirror in relation to the informal scene.  If it did not reflect the interests and represent the objects that endure within the informal context, no matter how dimly and slightly it is able to portray them, then what goes on in a formal domain would lose all its fascination.  At least, it would have little hold on a healthy mentality.  The various formal domains that an individual agent is able to grasp are set within the informal sphere like so many myriads of mirrored facets that are available to be cut on a complex gemstone.  Each formal domain affords a medium for reflection and transmission, a momentary sliver of selective clarity that allows an agent who realizes it to reflect and to represent, if always a bit obscurely and partially, a miniscule share of the wealth of formal possibilities that is there to be apportioned out.
 
The formal plane stands like a mirror in relation to the informal scene.  If it did not reflect the interests and represent the objects that endure within the informal context, no matter how dimly and slightly it is able to portray them, then what goes on in a formal domain would lose all its fascination.  At least, it would have little hold on a healthy mentality.  The various formal domains that an individual agent is able to grasp are set within the informal sphere like so many myriads of mirrored facets that are available to be cut on a complex gemstone.  Each formal domain affords a medium for reflection and transmission, a momentary sliver of selective clarity that allows an agent who realizes it to reflect and to represent, if always a bit obscurely and partially, a miniscule share of the wealth of formal possibilities that is there to be apportioned out.
Line 1,428: Line 1,505:  
In other images, aside from a mirror, a formal domain can be compared to a circus arena, a theatrical stage, a motion picture, television, or other sort of projective screen, a congressional forum, indeed, to that greatest of all three-ring circuses, the government of certain republics that we all know and love.  If the clonish characters, clownish figures, and other colonial representatives that carry on in the formal arena did not mimic in variously diverting and enlightenting ways the concerns of their spectators in the stands, then there would hardly be much reason for attending to their antics.  Even when the action in a formal arena appears to be designed as a contrast, more diverting than enlightening, or a recreation, more a comic relief from their momentary intensity than a serious resolution of the troubles that prevail in the ordinary realm, it still amounts to a strategic way of dealing with a problematic tension in the informal context.
 
In other images, aside from a mirror, a formal domain can be compared to a circus arena, a theatrical stage, a motion picture, television, or other sort of projective screen, a congressional forum, indeed, to that greatest of all three-ring circuses, the government of certain republics that we all know and love.  If the clonish characters, clownish figures, and other colonial representatives that carry on in the formal arena did not mimic in variously diverting and enlightenting ways the concerns of their spectators in the stands, then there would hardly be much reason for attending to their antics.  Even when the action in a formal arena appears to be designed as a contrast, more diverting than enlightening, or a recreation, more a comic relief from their momentary intensity than a serious resolution of the troubles that prevail in the ordinary realm, it still amounts to a strategic way of dealing with a problematic tension in the informal context.
   −
<blockquote>
+
<br>
Sometimes a troop of damsels glad,
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
An abbot on an ambling pad,
+
| colspan="3" | Sometimes a troop of damsels glad,
Sometimes a curly shepherd-lad,
+
|-
Or long-hair'd page in crimson clad,
+
| colspan="3" | An abbot on an ambling pad,
Goes by to tower'd Camelot;
+
|-
And sometimes thro' the mirror blue
+
| colspan="3" | Sometimes a curly shepherd-lad,
The knights come riding two and two:
+
|-
She hath no loyal knight and true,
+
| colspan="3" | Or long-hair'd page in crimson clad,
The Lady of Shalott.
+
|-
Tennyson, The Lady of Shalott, [Ten, 18]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | Goes by to tower'd Camelot;
 +
|-
 +
| colspan="3" | And sometimes thro' the mirror blue
 +
|-
 +
| colspan="3" | The knights come riding two and two:
 +
|-
 +
| colspan="3" | She hath no loyal knight and true,
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | The Lady of Shalott.
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 18]
 +
|}
 +
<br>
    
Before I can continue any further, it is necessary to discuss a question of terminology that continues to bedevil this discussion with ambiguities:  Is a "context" still a "text", and thus composed of signs throughout, or is it something else again, an object among objects of another order, or the incidental setting of an interpreter's referent and significant acts?
 
Before I can continue any further, it is necessary to discuss a question of terminology that continues to bedevil this discussion with ambiguities:  Is a "context" still a "text", and thus composed of signs throughout, or is it something else again, an object among objects of another order, or the incidental setting of an interpreter's referent and significant acts?
Line 1,447: Line 1,539:  
All human interests arise in and return to the informal context, an openly vague region of indefinite duration and ever-expanding scope.  That is to say, all of the objectives that people instinctively value and all of the phenomena that people genuinely wish to understand are things that arise in informal conduct, are carried on in pursuit of it, develop in connection with it, and ultimately have their bearing on it.  Indeed, the wellsprings that nourish a human interest in abstract forms are never in danger of escaping the watersheds of the informal sphere, and they promise by dint of their very nature never to totally inundate nor to wholly overflow the landscape that renders itself visible there.  This fact is apparent from the circumstance that every formal domain is originally instituted as a flawed inclusion within the informal context, continues to develop its constitution as a wholly-dependent subsidiary of it, and sustains itself as worthy of attention only so long as it remains a sustaining contributor to it.
 
All human interests arise in and return to the informal context, an openly vague region of indefinite duration and ever-expanding scope.  That is to say, all of the objectives that people instinctively value and all of the phenomena that people genuinely wish to understand are things that arise in informal conduct, are carried on in pursuit of it, develop in connection with it, and ultimately have their bearing on it.  Indeed, the wellsprings that nourish a human interest in abstract forms are never in danger of escaping the watersheds of the informal sphere, and they promise by dint of their very nature never to totally inundate nor to wholly overflow the landscape that renders itself visible there.  This fact is apparent from the circumstance that every formal domain is originally instituted as a flawed inclusion within the informal context, continues to develop its constitution as a wholly-dependent subsidiary of it, and sustains itself as worthy of attention only so long as it remains a sustaining contributor to it.
   −
<blockquote>
+
<br>
But in her web she still delights
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
To weave the mirror's magic sights,
+
| colspan="3" | But in her web she still delights
For often thro' the silent nights
+
|-
A funeral, with plumes and lights,
+
| colspan="3" | To weave the mirror's magic sights,
And music, went to Camelot:
+
|-
Or when the moon was overhead,
+
| colspan="3" | For often thro' the silent nights
Came two young lovers lately wed;
+
|-
"I am half-sick of shadows," said
+
| colspan="3" | A funeral, with plumes and lights,
The Lady of Shalott.
+
|-
Tennyson, The Lady of Shalott, [Ten, 18]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | And music, went to Camelot:
 +
|-
 +
| colspan="3" | Or when the moon was overhead,
 +
|-
 +
| colspan="3" | Came two young lovers lately wed;
 +
|-
 +
| colspan="3" | "I am half-sick of shadows," said
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | The Lady of Shalott.
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 18]
 +
|}
 +
<br>
    
To describe the question that instigates an inquiry in the language of the pragmatic theory of signs, the original situation of the inquirer is constituted by an "elementary sign relation", taking the form <o, s, i>.  In other words, the initial state of an inquiry is constellated by an ordered triple of the form <o, s, i>, a triadic element that is known in this case to exist as a member of an otherwise unknown sign relation, if the truth were told, a sign relation that defines the whole conceivable world of the interpreter along with the nature of the interpreter itself.  Given that the initial situation of an inquiry has this structure, there are just three different "directions of recursion" (DOR's) that the agent of the inquiry can take out of it.
 
To describe the question that instigates an inquiry in the language of the pragmatic theory of signs, the original situation of the inquirer is constituted by an "elementary sign relation", taking the form <o, s, i>.  In other words, the initial state of an inquiry is constellated by an ordered triple of the form <o, s, i>, a triadic element that is known in this case to exist as a member of an otherwise unknown sign relation, if the truth were told, a sign relation that defines the whole conceivable world of the interpreter along with the nature of the interpreter itself.  Given that the initial situation of an inquiry has this structure, there are just three different "directions of recursion" (DOR's) that the agent of the inquiry can take out of it.
Line 1,464: Line 1,571:  
On occasion, it is useful to consider a DOR as outlined by two factors:  (1) There is the "line of recursion" (LOR) that extends more generally in a couple of directions, conventionally referred to as "up" and "down".  (2) There is the "arrow of recursion" (AOR), a binary feature that is frequently but quite arbitrarily depicted as "positive" or "negative", and that picks out one of the two possible directions, "up" or "down", respectively.  Since one is usually more concerned with the devolution of a complex power, that is, with the direction of analytic descent, the downward development, or the reductive progress of the recursion, it is common practice to point to DOR's and to advert to LOR's in a welter of loosely ambivalent ways, letting context determine the appropriate sense.
 
On occasion, it is useful to consider a DOR as outlined by two factors:  (1) There is the "line of recursion" (LOR) that extends more generally in a couple of directions, conventionally referred to as "up" and "down".  (2) There is the "arrow of recursion" (AOR), a binary feature that is frequently but quite arbitrarily depicted as "positive" or "negative", and that picks out one of the two possible directions, "up" or "down", respectively.  Since one is usually more concerned with the devolution of a complex power, that is, with the direction of analytic descent, the downward development, or the reductive progress of the recursion, it is common practice to point to DOR's and to advert to LOR's in a welter of loosely ambivalent ways, letting context determine the appropriate sense.
   −
<blockquote>
+
<br>
A bow-shot from her bower-eaves,
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
He rode between the barley sheaves,
+
| colspan="3" | A bow-shot from her bower-eaves,
The sun came dazzling thro' the leaves,
+
|-
And flamed upon the brazen greaves
+
| colspan="3" | He rode between the barley sheaves,
Of bold Sir Lancelot.
+
|-
A redcross knight forever kneel'd
+
| colspan="3" | The sun came dazzling thro' the leaves,
To a lady in his shield,
+
|-
That sparkled on the yellow field,
+
| colspan="3" | And flamed upon the brazen greaves
Beside remote Shalott.
+
|-
Tennyson, The Lady of Shalott, [Ten, 18]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | Of bold Sir Lancelot.
 +
|-
 +
| colspan="3" | A redcross knight forever kneel'd
 +
|-
 +
| colspan="3" | To a lady in his shield,
 +
|-
 +
| colspan="3" | That sparkled on the yellow field,
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | Beside remote Shalott.
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 18]
 +
|}
 +
<br>
    
A process of interpretation can appear to be working solely and steadily on the signs that occupy a formal context - to emblaze it as an emblem:  on an island, in a mirror, and all through the texture of a tapestry - at least, it can appear this way to an insufficiently attentive onlooker.  But an agent of interpretation is obliged to keep a private counsel, to maintain a frame that adumbrates the limits of a personal scope, and so an interpreter recurs in addition to a boundary on, a connection to, or an interface with the informal context - returning to the figure blazed:  every interloper on the scene silently resorts to the facile musings and the potentially delusive inspirations of looking down the road toward the secret aims of the finished text:  its ideal reader, its eventual critique, its imagined interest, its hidden intention, and its ultimate importance.  An interpreter keeps at this work within this confine and keeps at this station within this horizon only so long as the counsel that is kept in the depths of the self keeps on appearing as a consistent entity in and of itself and just so long as it comports with continuing to do so.
 
A process of interpretation can appear to be working solely and steadily on the signs that occupy a formal context - to emblaze it as an emblem:  on an island, in a mirror, and all through the texture of a tapestry - at least, it can appear this way to an insufficiently attentive onlooker.  But an agent of interpretation is obliged to keep a private counsel, to maintain a frame that adumbrates the limits of a personal scope, and so an interpreter recurs in addition to a boundary on, a connection to, or an interface with the informal context - returning to the figure blazed:  every interloper on the scene silently resorts to the facile musings and the potentially delusive inspirations of looking down the road toward the secret aims of the finished text:  its ideal reader, its eventual critique, its imagined interest, its hidden intention, and its ultimate importance.  An interpreter keeps at this work within this confine and keeps at this station within this horizon only so long as the counsel that is kept in the depths of the self keeps on appearing as a consistent entity in and of itself and just so long as it comports with continuing to do so.
Line 1,483: Line 1,605:  
A recursion can "lead to" a resource in two senses:  (1) It can have recourse to a resource as power that is meant to be used in carrying out another action, and merely in the pursuit of a more remote object, that is, as an ancillary, assumed, implicit, incidental, instrumental, mediate, or subservient power.  (2) It can be brought face to face with the fact or the question of this power, as an entity that is explicitly mentioned or recognized as a problem, and thus be forced to reflect on the nature of this putative resource in and of itself.
 
A recursion can "lead to" a resource in two senses:  (1) It can have recourse to a resource as power that is meant to be used in carrying out another action, and merely in the pursuit of a more remote object, that is, as an ancillary, assumed, implicit, incidental, instrumental, mediate, or subservient power.  (2) It can be brought face to face with the fact or the question of this power, as an entity that is explicitly mentioned or recognized as a problem, and thus be forced to reflect on the nature of this putative resource in and of itself.
   −
<blockquote>
+
<br>
The gemmy bridle glitter'd free,
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
Like to some branch of stars we see
+
| colspan="3" | The gemmy bridle glitter'd free,
Hung in the golden Galaxy.
+
|-
The bridle bells rang merrily
+
| colspan="3" | Like to some branch of stars we see
As he rode down to Camelot:
+
|-
And from his blazon'd baldric slung
+
| colspan="3" | Hung in the golden Galaxy.
A mighty silver bugle hung,
+
|-
And as he rode his armor rung,
+
| colspan="3" | The bridle bells rang merrily
Beside remote Shalott.
+
|-
Tennyson, The Lady of Shalott, [Ten, 18]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | As he rode down to Camelot:
 +
|-
 +
| colspan="3" | And from his blazon'd baldric slung
 +
|-
 +
| colspan="3" | A mighty silver bugle hung,
 +
|-
 +
| colspan="3" | And as he rode his armor rung,
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | Beside remote Shalott.
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 18]
 +
|}
 +
<br>
    
Any attempt to present the informal context in anything approaching its full detail is likely to lead to so much conflict and confusion that it begins to appear more akin to a chaotic context or a formless void than it chances to resemble a merely casual or a purely incidental environ.  For all intents and purposes, the informal context is a coalescence of many forces and influences and a loose coalition of disparate ambitions.  These forces impact on the individual thinker in what can appear like a random fashion, especially at the beginnings of individual development.  Broadly speaking, if one considers the "ways of thinking" (WOT's) that are made available to a thinker, then these factors can be divvied up according to their bearing on two wide divisons of their full array:
 
Any attempt to present the informal context in anything approaching its full detail is likely to lead to so much conflict and confusion that it begins to appear more akin to a chaotic context or a formless void than it chances to resemble a merely casual or a purely incidental environ.  For all intents and purposes, the informal context is a coalescence of many forces and influences and a loose coalition of disparate ambitions.  These forces impact on the individual thinker in what can appear like a random fashion, especially at the beginnings of individual development.  Broadly speaking, if one considers the "ways of thinking" (WOT's) that are made available to a thinker, then these factors can be divvied up according to their bearing on two wide divisons of their full array:
Line 1,505: Line 1,642:  
The informal context enfolds a multitude of formal arenas, to selections of which the particular interpreters usually prefer to attach themselves.  It transforms a space into a medium of reflection, a respite, a retreat, or a final resort that affords the agent of interpretation a stance from which to review the action and to reflect on its many possible meanings.  The informal context is so much broader in scope than the formal arenas of discourse that are located within it that it does not matter if one styles it with the definite article "the" or the indefinite article "an", since no one imagines that a unique definition could ever be implied by the vagueness of its sweeping intension or imposed on the vastness of its continuing extension.  It is in the informal context that a problem arising spontaneously is most likely to meet with its first expression, and if a writer is looking for a common stock of images and signs that can permit communication with the randomly encountered reader, then it is here that the author has the best chance of finding such a resource.
 
The informal context enfolds a multitude of formal arenas, to selections of which the particular interpreters usually prefer to attach themselves.  It transforms a space into a medium of reflection, a respite, a retreat, or a final resort that affords the agent of interpretation a stance from which to review the action and to reflect on its many possible meanings.  The informal context is so much broader in scope than the formal arenas of discourse that are located within it that it does not matter if one styles it with the definite article "the" or the indefinite article "an", since no one imagines that a unique definition could ever be implied by the vagueness of its sweeping intension or imposed on the vastness of its continuing extension.  It is in the informal context that a problem arising spontaneously is most likely to meet with its first expression, and if a writer is looking for a common stock of images and signs that can permit communication with the randomly encountered reader, then it is here that the author has the best chance of finding such a resource.
   −
<blockquote>
+
<br>
All in the blue unclouded weather
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
Thick-jewell'd shone the saddle-leather,
+
| colspan="3" | All in the blue unclouded weather
The helmet and the helmet-feather
+
|-
Burn'd like one burning flame together,
+
| colspan="3" | Thick-jewell'd shone the saddle-leather,
As he rode down to Camelot.
+
|-
As often thro' the purple night,
+
| colspan="3" | The helmet and the helmet-feather
Below the starry clusters bright,
+
|-
Some bearded meteor, trailing light,
+
| colspan="3" | Burn'd like one burning flame together,
Moves over still Shalott.
+
|-
Tennyson, The Lady of Shalott, [Ten, 18]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | As he rode down to Camelot.
 +
|-
 +
| colspan="3" | As often thro' the purple night,
 +
|-
 +
| colspan="3" | Below the starry clusters bright,
 +
|-
 +
| colspan="3" | Some bearded meteor, trailing light,
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | Moves over still Shalott.
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 18]
 +
|}
 +
<br>
    
There is a "form of recursion" (FOR) that is a FOR for itself, that seeks above all to perpetuate itself, that never quite terminates by design and never quite reaches its end on purpose, but merely seizes the occasional diaeresis to pause for a while while a state of dynamic equilibrium or a moment of dialectical equipoise is achieved between its formal focus and the informal context.  The FOR for itself recurs not to an absolute state or a static absolute but to a relationship between the ego and the entire world, between the fictional character or the hypostatic personality that is hypothesized to explain the occurrence of specific localized phenomena and something else again, a whole that is larger, more global, and better integrated, however elusive and undifferentiated it is in its integrity.   
 
There is a "form of recursion" (FOR) that is a FOR for itself, that seeks above all to perpetuate itself, that never quite terminates by design and never quite reaches its end on purpose, but merely seizes the occasional diaeresis to pause for a while while a state of dynamic equilibrium or a moment of dialectical equipoise is achieved between its formal focus and the informal context.  The FOR for itself recurs not to an absolute state or a static absolute but to a relationship between the ego and the entire world, between the fictional character or the hypostatic personality that is hypothesized to explain the occurrence of specific localized phenomena and something else again, a whole that is larger, more global, and better integrated, however elusive and undifferentiated it is in its integrity.   
Line 1,522: Line 1,674:  
This "inclusive other" can be referred to as "nature", so long as this nature is understood as a form of being that is not alien to the ego and not wholly external to the agent, and it can be identified as the "self", so long as this identity is understood as a relation that is not alone a property of the ego and not wholly internal to the mind of the agent.
 
This "inclusive other" can be referred to as "nature", so long as this nature is understood as a form of being that is not alien to the ego and not wholly external to the agent, and it can be identified as the "self", so long as this identity is understood as a relation that is not alone a property of the ego and not wholly internal to the mind of the agent.
   −
<blockquote>
+
<br>
His broad clear brow in sunlight glow'd;
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
On burnish'd hooves his war-horse trode;
+
| colspan="3" | His broad clear brow in sunlight glow'd;
From underneath his helmet flow'd
+
|-
His coal-black curls as on he rode,
+
| colspan="3" | On burnish'd hooves his war-horse trode;
As he rode down to Camelot.
+
|-
From the bank and from the river
+
| colspan="3" | From underneath his helmet flow'd
He flash'd into the crystal mirror,
+
|-
"Tirra lirra," by the river
+
| colspan="3" | His coal-black curls as on he rode,
Sang Sir Lancelot.
+
|-
Tennyson, The Lady of Shalott, [Ten, 18]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | As he rode down to Camelot.
 +
|-
 +
| colspan="3" | From the bank and from the river
 +
|-
 +
| colspan="3" | He flash'd into the crystal mirror,
 +
|-
 +
| colspan="3" | "Tirra lirra," by the river
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | Sang Sir Lancelot.
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 18]
 +
|}
 +
<br>
    
There is a FOR for another whose nature is never to quit in its quest until its aim is within its clasp, though it knows how much chance there is for success, and it knows the reason why its reach exceeds its grasp.  This FOR, too, never rests in and of itself, but unlike the FOR for itself it can be satisfied by achieving a particular alternative state that is distinct from its initial condition, by reaching another besides itself.  This FOR, too, short of reaching its specific end, never quite terminates in its own right, not of its essence, nor by its intent, nor does it relent through any deliberate purpose of its own, but only by accident of an unforseen circumstance or by dint of an incidental misfortune.
 
There is a FOR for another whose nature is never to quit in its quest until its aim is within its clasp, though it knows how much chance there is for success, and it knows the reason why its reach exceeds its grasp.  This FOR, too, never rests in and of itself, but unlike the FOR for itself it can be satisfied by achieving a particular alternative state that is distinct from its initial condition, by reaching another besides itself.  This FOR, too, short of reaching its specific end, never quite terminates in its own right, not of its essence, nor by its intent, nor does it relent through any deliberate purpose of its own, but only by accident of an unforseen circumstance or by dint of an incidental misfortune.
Line 1,539: Line 1,706:  
It needs to be examined whether this state of dynamic equilibrium, this condition of balance, equanimity, harmony, and peace can be described as an aim, an end, a goal, or a good that even the FOR for itself can take for itself.
 
It needs to be examined whether this state of dynamic equilibrium, this condition of balance, equanimity, harmony, and peace can be described as an aim, an end, a goal, or a good that even the FOR for itself can take for itself.
   −
<blockquote>
+
<br>
She left the web, she left the loom,
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
She made three paces thro' the room,
+
| colspan="3" | She left the web, she left the loom,
She saw the water-lily bloom,
+
|-
She saw the helmet and the plume,
+
| colspan="3" | She made three paces thro' the room,
She look'd down to Camelot.
+
|-
Out flew the web and floated wide;
+
| colspan="3" | She saw the water-lily bloom,
The mirror crack'd from side to side;
+
|-
"The curse is come upon me," cried
+
| colspan="3" | She saw the helmet and the plume,
The Lady of Shalott.
+
|-
Tennyson, The Lady of Shalott, [Ten, 18]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | She look'd down to Camelot.
 +
|-
 +
| colspan="3" | Out flew the web and floated wide;
 +
|-
 +
| colspan="3" | The mirror crack'd from side to side;
 +
|-
 +
| colspan="3" | "The curse is come upon me," cried
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | The Lady of Shalott.
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 18]
 +
|}
 +
<br>
    
In stepping back from a "formally engaged existence" (FEE) to reflect on the activities that normally take place within its formal arena, in stepping away from the peculiar concerns that normally take precedence within its jurisdiction to those that prevail in more ordinary contexts - and unless one is empowered by some miracle of discursive transport to jump from one charmed circle of discussion to another without entailing the usual repercussions:  of causing a considerable loss of continuity, or of suffering a significant shock of dissociation - then one commonly enters on, as an intervening stage of discourse, and passes through, as a transitional phase of discussion, a context that is convenient to call a "higher order level of discourse" (HOLOD).  This new level of discussion allows for a fresh supply of signs and ideas that can serve to reinforce an agent's inherent but transient capacity for reflection, qualifying an observant agent as a deliberate interpreter of the events under survey.
 
In stepping back from a "formally engaged existence" (FEE) to reflect on the activities that normally take place within its formal arena, in stepping away from the peculiar concerns that normally take precedence within its jurisdiction to those that prevail in more ordinary contexts - and unless one is empowered by some miracle of discursive transport to jump from one charmed circle of discussion to another without entailing the usual repercussions:  of causing a considerable loss of continuity, or of suffering a significant shock of dissociation - then one commonly enters on, as an intervening stage of discourse, and passes through, as a transitional phase of discussion, a context that is convenient to call a "higher order level of discourse" (HOLOD).  This new level of discussion allows for a fresh supply of signs and ideas that can serve to reinforce an agent's inherent but transient capacity for reflection, qualifying an observant agent as a deliberate interpreter of the events under survey.
Line 1,557: Line 1,739:  
In forming a HOLOD one reaches into the informal context for the images and the methods to do so.  As long as one is restricted by availability or habit to dyadic relations one tends to pay attention to either one of two complementary features of the situation at the expense of the other.  One can attend to either (1) the transitions that occur between entities at a single level of discourse, or (2) the distinctions that exist between entities at different levels of discourse.
 
In forming a HOLOD one reaches into the informal context for the images and the methods to do so.  As long as one is restricted by availability or habit to dyadic relations one tends to pay attention to either one of two complementary features of the situation at the expense of the other.  One can attend to either (1) the transitions that occur between entities at a single level of discourse, or (2) the distinctions that exist between entities at different levels of discourse.
   −
<blockquote>
+
<br>
In the stormy east-wind straining,
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
The pale yellow woods were waning,
+
| colspan="3" | In the stormy east-wind straining,
The broad stream in his banks complaining,
+
|-
Heavily the low sky raining
+
| colspan="3" | The pale yellow woods were waning,
Over tower'd Camelot;
+
|-
Down she came and found a boat
+
| colspan="3" | The broad stream in his banks complaining,
Beneath a willow left afloat,
+
|-
And round about the prow she wrote
+
| colspan="3" | Heavily the low sky raining
The Lady of Shalott.
+
|-
Tennyson, The Lady of Shalott, [Ten, 18]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | Over tower'd Camelot;
 +
|-
 +
| colspan="3" | Down she came and found a boat
 +
|-
 +
| colspan="3" | Beneath a willow left afloat,
 +
|-
 +
| colspan="3" | And round about the prow she wrote
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | ''The Lady of Shalott''.
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 18]
 +
|}
 +
<br>
    
An "ostensibly recursive text" (ORT) is a text that cites itself by title at some site within its body.  A "wholly ostensibly recursive literature" (WORL) is a litany, a liturgy, or any other body of texts that names its entire collective corpus at some locus of citation within its interior.  I am using the words "cite" and "site" to emphasize the superficially syntactic character of these definitions, where the title of a text is conventionally indicated by capitals, by italics, by quotation, or by underscoring.  If a text has a definite subject or an explicit theme, for instance, an object or a state of affairs to which it makes a denotative reference, then it is not unusual for this reference to be reused as the title of the text, but this is only the rudimentary beginnings of a true self-reference in the text.  Although a genuine self-reference can take its inspiration from a text being named after something that it denotes, the reference in the text to the text itself becomes complete only when the name of the subject or the title of the theme is stretched to serve as the explicit denoter of the entire text.
 
An "ostensibly recursive text" (ORT) is a text that cites itself by title at some site within its body.  A "wholly ostensibly recursive literature" (WORL) is a litany, a liturgy, or any other body of texts that names its entire collective corpus at some locus of citation within its interior.  I am using the words "cite" and "site" to emphasize the superficially syntactic character of these definitions, where the title of a text is conventionally indicated by capitals, by italics, by quotation, or by underscoring.  If a text has a definite subject or an explicit theme, for instance, an object or a state of affairs to which it makes a denotative reference, then it is not unusual for this reference to be reused as the title of the text, but this is only the rudimentary beginnings of a true self-reference in the text.  Although a genuine self-reference can take its inspiration from a text being named after something that it denotes, the reference in the text to the text itself becomes complete only when the name of the subject or the title of the theme is stretched to serve as the explicit denoter of the entire text.
Line 1,576: Line 1,773:  
In reading the signs of ostensible recursion that appear within a text of this sort an interpreter is empowered, if not always explicitly entitled, to pick out a personal way of refining their implications from among the plenitude of possible options:  to gloss them over or to read them anew, to reform the masses of their solid associations into a manifold body of interpenetrating interpretations or to refuse the resplendence of their canonical suggestions in the fires of freshly refulgent convictions and by dint of the impressions that redound from a host of novel directions, to regard their indications in the light of wholly familiar conventions or to regale their invitations in the hopes of a rather more sumptuous symposium, to reinforce their established denominations with a ruthless redundancy or to riddle their resorts to the rarefied reaches of rhyme and reason with repeated petitions for their reconciliation and restless researches to reconstruct the rationales of their resources until they are honeycombed with an array of rich connotations, to subtilize or to subvert, in short, to choose between thoroughly undermining or more thoroughly understanding the suggestions of its WORL.
 
In reading the signs of ostensible recursion that appear within a text of this sort an interpreter is empowered, if not always explicitly entitled, to pick out a personal way of refining their implications from among the plenitude of possible options:  to gloss them over or to read them anew, to reform the masses of their solid associations into a manifold body of interpenetrating interpretations or to refuse the resplendence of their canonical suggestions in the fires of freshly refulgent convictions and by dint of the impressions that redound from a host of novel directions, to regard their indications in the light of wholly familiar conventions or to regale their invitations in the hopes of a rather more sumptuous symposium, to reinforce their established denominations with a ruthless redundancy or to riddle their resorts to the rarefied reaches of rhyme and reason with repeated petitions for their reconciliation and restless researches to reconstruct the rationales of their resources until they are honeycombed with an array of rich connotations, to subtilize or to subvert, in short, to choose between thoroughly undermining or more thoroughly understanding the suggestions of its WORL.
   −
<blockquote>
+
<br>
And down the river's dim expanse -
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
Like some bold seer in a trance,
+
| colspan="3" | And down the river's dim expanse
Seeing all his own mischance -
+
|-
With a glassy countenance
+
| colspan="3" | Like some bold seer in a trance,
Did she look to Camelot.
+
|-
And at the closing of the day
+
| colspan="3" | Seeing all his own mischance
She loosed the chain, and down she lay;
+
|-
The broad stream bore her far away,
+
| colspan="3" | With a glassy countenance
The Lady of Shalott.
+
|-
Tennyson, The Lady of Shalott, [Ten, 18]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | Did she look to Camelot.
 +
|-
 +
| colspan="3" | And at the closing of the day
 +
|-
 +
| colspan="3" | She loosed the chain, and down she lay;
 +
|-
 +
| colspan="3" | The broad stream bore her far away,
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | The Lady of Shalott.
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 18]
 +
|}
 +
<br>
    
Given the benefit of hindsight, or with some measure of due reflection, it is perhaps fair to say that no one should ever have expected that a property which is delimited solely on syntactic grounds would turn out to be anything more than ultimately shallow.  But this recognition only leaves the true nature of recursion yet to be described.  This is a task that can be duly inaugurated here but that has to be left unfinished in its present shape, as it occupies the greater body of the current work.
 
Given the benefit of hindsight, or with some measure of due reflection, it is perhaps fair to say that no one should ever have expected that a property which is delimited solely on syntactic grounds would turn out to be anything more than ultimately shallow.  But this recognition only leaves the true nature of recursion yet to be described.  This is a task that can be duly inaugurated here but that has to be left unfinished in its present shape, as it occupies the greater body of the current work.
Line 1,596: Line 1,808:  
Now there is a form of conduct or a pattern of activity that naturally accompanies a text, no matter how inert its images may be, and this is the action of reading.  If the act of reading can be led to induce work on a larger scale, then reading becomes akin to heeding.  In the medium of an active interpretation a reading can inspire a form of performance, and legislative declarations acquire the executive force that is needed to constitute commands, injunctions, instructions, prescriptions, recipes, and programs.  Under these conditions an ostensible recursion, the mere repetition of a sign in a context subordinate to its initial appearance, as in a title role, can serve to codify a perpetual process, a potential infinitude of action, all in a finite text, where only the details of a determinate application and the discretion of an individual interpreter can bring the perennating roots of life to bear fruit in a finite time.
 
Now there is a form of conduct or a pattern of activity that naturally accompanies a text, no matter how inert its images may be, and this is the action of reading.  If the act of reading can be led to induce work on a larger scale, then reading becomes akin to heeding.  In the medium of an active interpretation a reading can inspire a form of performance, and legislative declarations acquire the executive force that is needed to constitute commands, injunctions, instructions, prescriptions, recipes, and programs.  Under these conditions an ostensible recursion, the mere repetition of a sign in a context subordinate to its initial appearance, as in a title role, can serve to codify a perpetual process, a potential infinitude of action, all in a finite text, where only the details of a determinate application and the discretion of an individual interpreter can bring the perennating roots of life to bear fruit in a finite time.
   −
<blockquote>
+
<br>
Lying, robed in snowy white
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
That loosely flew to left and right -
+
| colspan="3" | Lying, robed in snowy white
The leaves upon her falling light -
+
|-
Thro' the noises of the night
+
| colspan="3" | That loosely flew to left and right
She floated down to Camelot:
+
|-
And as the boat-head wound along
+
| colspan="3" | The leaves upon her falling light
The willowy hills and fields among,
+
|-
They heard her singing her last song,
+
| colspan="3" | Thro' the noises of the night
The Lady of Shalott.
+
|-
Tennyson, The Lady of Shalott, [Ten, 18-19]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | She floated down to Camelot:
 +
|-
 +
| colspan="3" | And as the boat-head wound along
 +
|-
 +
| colspan="3" | The willowy hills and fields among,
 +
|-
 +
| colspan="3" | They heard her singing her last song,
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | The Lady of Shalott.
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 18–19]
 +
|}
 +
<br>
    
It is time to discuss a text of a type that bears a kinship to the ORT, whose cut as a whole is likened to the reclusive cousins of this caste, each one lying just within reach of a related ORT but keeping itself a pace away, staying at a discreet remove, reserving the full implications of its potential recursion against the day of a suitable interpretation, and all in all residing in similar manors of meaning to the ORT, though not so ostentatiously.  Even if the manifold ways of reading the senses of such a text are not as conspicuous as those of an ORT, and if it is a fair complaint to say that the deliberate design that keeps it from being obvious can also keep it from ever becoming clear, there is in principle a key to unlocking its meaning, and the ulterior purpose of the text is simply to pass on this key.
 
It is time to discuss a text of a type that bears a kinship to the ORT, whose cut as a whole is likened to the reclusive cousins of this caste, each one lying just within reach of a related ORT but keeping itself a pace away, staying at a discreet remove, reserving the full implications of its potential recursion against the day of a suitable interpretation, and all in all residing in similar manors of meaning to the ORT, though not so ostentatiously.  Even if the manifold ways of reading the senses of such a text are not as conspicuous as those of an ORT, and if it is a fair complaint to say that the deliberate design that keeps it from being obvious can also keep it from ever becoming clear, there is in principle a key to unlocking its meaning, and the ulterior purpose of the text is simply to pass on this key.
 
For the lack of a better name, let the type of text that devolves in evidence here be called a "pseud-ORT" (PORT) or a "quasi-ORT" (QORT).  These acronyms inherit the hedge word "ostensibly" from the ORT's that their individual namesakes beget, once they are interpreted as doing so.  It is the main qualification of the indicated PORT's or QORT's, and the one that continues to be borne by them as the sole inherent property of their bearing.  As before, this qualification is intended to serve as a caution to the reader that the properties ordinarily imputed to the text do not actually belong to the matter of the text, but that they properly belong to the agent and the process of the active interpretation, namely, the one that is actually carried out on the material supplied by the text.  The adjoined pair of weasel words "pseudo" and "quasi" are intended to remind the reader that a PORT or a QORT falls short of even the order of specious recursion that is afforded by an ORT, but has to be nudged in the general direction of this development or this evolution through the intercession of artificial distortions or specialized modulations of the semantics that is applied to the text.  Whether these extra epithets exacerbate the spurious character of the putative recursion or whether they take the edge off the order of ostentation that already occurs in an ORT is a question that can be deferred to a future time.
 
For the lack of a better name, let the type of text that devolves in evidence here be called a "pseud-ORT" (PORT) or a "quasi-ORT" (QORT).  These acronyms inherit the hedge word "ostensibly" from the ORT's that their individual namesakes beget, once they are interpreted as doing so.  It is the main qualification of the indicated PORT's or QORT's, and the one that continues to be borne by them as the sole inherent property of their bearing.  As before, this qualification is intended to serve as a caution to the reader that the properties ordinarily imputed to the text do not actually belong to the matter of the text, but that they properly belong to the agent and the process of the active interpretation, namely, the one that is actually carried out on the material supplied by the text.  The adjoined pair of weasel words "pseudo" and "quasi" are intended to remind the reader that a PORT or a QORT falls short of even the order of specious recursion that is afforded by an ORT, but has to be nudged in the general direction of this development or this evolution through the intercession of artificial distortions or specialized modulations of the semantics that is applied to the text.  Whether these extra epithets exacerbate the spurious character of the putative recursion or whether they take the edge off the order of ostentation that already occurs in an ORT is a question that can be deferred to a future time.
   −
<blockquote>
+
<br>
Heard a carol, mournful, holy,
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
Chanted loudly, chanted lowly,
+
| colspan="3" | Heard a carol, mournful, holy,
Till her blood was frozen slowly,
+
|-
And her eyes were darken'd wholly,
+
| colspan="3" | Chanted loudly, chanted lowly,
Turn'd to tower'd Camelot;
+
|-
For ere she reach'd upon the tide
+
| colspan="3" | Till her blood was frozen slowly,
The first house by the water-side,
+
|-
Singing in her song she died,
+
| colspan="3" | And her eyes were darken'd wholly,
The Lady of Shalott.
+
|-
Tennyson, The Lady of Shalott, [Ten, 19]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | Turn'd to tower'd Camelot;
 +
|-
 +
| colspan="3" | For ere she reach'd upon the tide
 +
|-
 +
| colspan="3" | The first house by the water-side,
 +
|-
 +
| colspan="3" | Singing in her song she died,
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | The Lady of Shalott.
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 19]
 +
|}
 +
<br>
    
If its ways are kept in the way intended, lacking only a fitting key to be unlocked, then the PORT or the QORT in question leads an interloper into a recursion only whenever the significance of certain analogies, comparisons, metaphors, or similes is recognized by that interpreter.  Generally speaking, this happens only when the interpreter discovers that a set of "semiotic equations" (SEQ's), applying to signs that can be picked out from the text in specific senses, is conceivably in force.  Expressed another way, the recursive or self-referent interpretation is actualized when the interpreter hypothesizes that the text in question bears up under a certain kind of additional intention, namely, that a system of "qualified identifications" (QUI's) ought to be applied to selected signs in the text.
 
If its ways are kept in the way intended, lacking only a fitting key to be unlocked, then the PORT or the QORT in question leads an interloper into a recursion only whenever the significance of certain analogies, comparisons, metaphors, or similes is recognized by that interpreter.  Generally speaking, this happens only when the interpreter discovers that a set of "semiotic equations" (SEQ's), applying to signs that can be picked out from the text in specific senses, is conceivably in force.  Expressed another way, the recursive or self-referent interpretation is actualized when the interpreter hypothesizes that the text in question bears up under a certain kind of additional intention, namely, that a system of "qualified identifications" (QUI's) ought to be applied to selected signs in the text.
Line 1,633: Line 1,875:  
The writer borrows a vehicle from the informal context, adapts its forms to the current conditions, adopts the guises appurtenant to it, and aims to appropriate to a private advantage what appears as if it is asking to assist or is long ago abandoned along a public way.  The writer instills this open form with a living significance, invests it with a new lease of meaning, inscribes it perhaps with a personal title or a suitable envoi, and sends it on its way, through whatever medium avails itself and to whatever party awaits it, without knowing how the sense of the message is destined to be appreciated when life in the ordinary sense is passed from its limbs and long after the flashes of its creation are frozen in the shapes of its reception.  All in all, the writer has no choice but to assume the good graces of eventually finding a charitable interpretation.
 
The writer borrows a vehicle from the informal context, adapts its forms to the current conditions, adopts the guises appurtenant to it, and aims to appropriate to a private advantage what appears as if it is asking to assist or is long ago abandoned along a public way.  The writer instills this open form with a living significance, invests it with a new lease of meaning, inscribes it perhaps with a personal title or a suitable envoi, and sends it on its way, through whatever medium avails itself and to whatever party awaits it, without knowing how the sense of the message is destined to be appreciated when life in the ordinary sense is passed from its limbs and long after the flashes of its creation are frozen in the shapes of its reception.  All in all, the writer has no choice but to assume the good graces of eventually finding a charitable interpretation.
   −
<blockquote>
+
<br>
Under tower and balcony,
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
By garden-wall and gallery,
+
| colspan="3" | Under tower and balcony,
A gleaming shape she floated by,
+
|-
A corse between the houses high,
+
| colspan="3" | By garden-wall and gallery,
Silent into Camelot.
+
|-
Out upon the wharfs they came,
+
| colspan="3" | A gleaming shape she floated by,
Knight and burgher, lord and dame,
+
|-
And round the prow they read her name,
+
| colspan="3" | A corse between the houses high,
The Lady of Shalott.
+
|-
Tennyson, The Lady of Shalott, [Ten, 19]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | Silent into Camelot.
 +
|-
 +
| colspan="3" | Out upon the wharfs they came,
 +
|-
 +
| colspan="3" | Knight and burgher, lord and dame,
 +
|-
 +
| colspan="3" | And round the prow they read her name,
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | ''The Lady of Shalott''.
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 19]
 +
|}
 +
<br>
    
I assume that the reader has gleaned the existence of something beyond a purely accidental relation that runs between the text and the epitext, between the prose discussion and the succession of epigraphs, that are interwoven with each other throughout the course of this presentation.  In general, it is best to let these incidental counterpoints develop in a loosely parallel but rough independence from each other, and to let them run through their corresponding paces not too strenuously interlocked.  The rule is thus to lay out the principal lines of their generic motives, their arguments, plans, plots, and themes, without incurring the fear of inadvertent intersections looming near, and thus to string the beads of their selective articulations along the strands of their envisioned text without invoking the undue force of a final collusion among their mass.  In spite of all that, I take the chance of bringing the various threads together at this point, in order to sound out their accords and discords, and to make a bolder exegesis of the relationships that they display.
 
I assume that the reader has gleaned the existence of something beyond a purely accidental relation that runs between the text and the epitext, between the prose discussion and the succession of epigraphs, that are interwoven with each other throughout the course of this presentation.  In general, it is best to let these incidental counterpoints develop in a loosely parallel but rough independence from each other, and to let them run through their corresponding paces not too strenuously interlocked.  The rule is thus to lay out the principal lines of their generic motives, their arguments, plans, plots, and themes, without incurring the fear of inadvertent intersections looming near, and thus to string the beads of their selective articulations along the strands of their envisioned text without invoking the undue force of a final collusion among their mass.  In spite of all that, I take the chance of bringing the various threads together at this point, in order to sound out their accords and discords, and to make a bolder exegesis of the relationships that they display.
Line 1,651: Line 1,908:  
Given the complexity and the subtlety of the epitext in this subsection, it makes sense to begin the detailed analysis of ORT's and their ilk with a much simpler example, and one that exemplifies a straightforward ORT.  These preparations are undertaken at the beginning of the next section, after which it is feasible to return to the present example, to consider the formal analysis of PORT's and QORT's, to explain how the effects of meaning that are achieved in this general type of text are supported by its sign-theoretic structure, and to discuss how these semantic intents are facilitated by the infrastructure of the language that is employed.
 
Given the complexity and the subtlety of the epitext in this subsection, it makes sense to begin the detailed analysis of ORT's and their ilk with a much simpler example, and one that exemplifies a straightforward ORT.  These preparations are undertaken at the beginning of the next section, after which it is feasible to return to the present example, to consider the formal analysis of PORT's and QORT's, to explain how the effects of meaning that are achieved in this general type of text are supported by its sign-theoretic structure, and to discuss how these semantic intents are facilitated by the infrastructure of the language that is employed.
   −
<blockquote>
+
<br>
Who is this?  and what is here?
+
{| align="center" border="0" cellpadding="0" cellspacing="0" style="text-align:left; width:90%"
And in the lighted palace near
+
| colspan="3" | Who is this?  and what is here?
Died the sound of royal cheer;
+
|-
And they cross'd themselves for fear,
+
| colspan="3" | And in the lighted palace near
All the knights at Camelot:
+
|-
But Lancelot mused a little space;
+
| colspan="3" | Died the sound of royal cheer;
He said, "She has a lovely face;
+
|-
God in his mercy lend her grace,
+
| colspan="3" | And they cross'd themselves for fear,
The Lady of Shalott."
+
|-
Tennyson, The Lady of Shalott, [Ten, 19]
+
| width="10%" | &nbsp;
</blockquote>
+
| colspan="2" | All the knights at Camelot:
 +
|-
 +
| colspan="3" | But Lancelot mused a little space;
 +
|-
 +
| colspan="3" | He said, "She has a lovely face;
 +
|-
 +
| colspan="3" | God in his mercy lend her grace,
 +
|-
 +
| width="10%" | &nbsp;
 +
| colspan="2" | The Lady of Shalott."
 +
|-
 +
| width="10%" | &nbsp;
 +
| width="40%" | &nbsp;
 +
| Tennyson, ''The Lady of Shalott'', [Ten, 19]
 +
|}
 +
<br>
    
As it happens, many a text in literature or science that concerns itself with hypothetical creatures, mythical entities, or speculative figures, that contents itself with idealized models of actual situations, indulges itself with idle idylls that barely allude to the serious threats against human peace and social well-being that they betray, or satisfies itself with romantic images of real enough but unknown perils of the soul - none of these would hold the level of interest that it actually has if it did not make itself available to many different levels of interpretation, readings that go far beyond the levels of discourse where it ostensibly presents itself at first sight.
 
As it happens, many a text in literature or science that concerns itself with hypothetical creatures, mythical entities, or speculative figures, that contents itself with idealized models of actual situations, indulges itself with idle idylls that barely allude to the serious threats against human peace and social well-being that they betray, or satisfies itself with romantic images of real enough but unknown perils of the soul - none of these would hold the level of interest that it actually has if it did not make itself available to many different levels of interpretation, readings that go far beyond the levels of discourse where it ostensibly presents itself at first sight.
12,080

edits