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=====5.1.2.12. Recursions : Possible, Actual, Necessary=====
=====5.1.2.12. Recursions : Possible, Actual, Necessary=====
<pre>
Is there a whim inspired fool,
Owre fast for thought, owre hot for rule,
Owre blate to seek, owre proud to snool?
Let him draw near;
And owre this grassy heap sing dool,
And drap a tear.
Robert Burns, A Bard's Epitaph, [CPW, 220]
The purpose of a sign, for instance, a name, expression, program, or text, is to denote and possibly to describe an object, for instance, a thing, situation, mode of being, or activity in the world. In cases of practical interest, the object is usually very complex and the sign is usually very simple. Indeed, the intention of the whole descriptive enterprise is take objects as complex and as subtle as possible and to arrive at signs as simple and as concrete as the agent can conceive of fashioning to describe that object. Not surprisingly, the value of this exercise to the agent that carries it out is measured by the degree of difference in the apparent complexities of the object and the sign, or the proportion of success in this project is the measure of its value to the agent involved in it. In the cases of ultimate interest, the sorts of objects that the agent is charged to describe begin with something like the natural and social world itself, moves on to the natural and social language that avails itself to describe this world, and ends up with the natural and social mind that evolves in association with this language and with this world. In effect, a "trialogue", a three way dialogue or a threefold dialectic.
When the reality to be described is infinitely more complex than the typically finite resources that an agent has to describe it, then any number of elliptic, multiple, and repeated uses of these resources are bound to occur, leading to the strategies of approximation, abstraction, and recursion, respectively. All of these techniques have in common the fact that a "systematic ambiguity" in the use of signs is introduced and tolerated, necessitating a new order of context sensitivity, discernment, intelligence, or just plain good sense in the conduct of interpretations. A "systematic ambiguity" or a "controlled equivocation" occurs when the same sign is used for many different things or when the same sign is used at many different stages of a process.
Although the elliptic strategy of approximation is tantamount to simply "leaving off" from the effort to describe a difficult object, in effect, "throwing up one's hands" in exasperation, exhaustion, supplication, or surrender, by this means hoping to escape from the self imposed part of the requirement to describe it more closely, and finally "giving up" the attempted description with the significance of the data already recorded, no matter how much the "broken off" approach "falls short" of its goal, the closely related strategies of abstraction and recursion are rather more persistent in their tries at describing the object.
Is there a Bard of rustic song,
Who, noteless, steals the crowds among,
That weekly this area throng?
O, pass not by!
But, with a frater feeling strong,
Here, heave a sigh.
Robert Burns, A Bard's Epitaph, [CPW, 220]
In effect, so long as an agent sticks to the object and persists in the purpose of describing it / this kind of object, ... In other words, an agent is forced to resort to the stratagems of abstraction and recursion, where the same sign is used for many different objects and when the same sign is used to mark the progress of an activity at many different stages of its process, respectively. The underlying principle involved here is a kind of "pragmatic pigeonhole principle" (P3)
Is there a man, whose judgment clear
Can others teach the course to steer,
Yet runs, himself, life's mad career,
Wild as the wave?
Here pause and, thro the starting tear,
Survey this grave.
Robert Burns, A Bard's Epitaph, [CPW, 220]
A "resilient enough system of interpretation" (RESOI), if driven to the point of distraction by the task of describing an inexhaustibly complex reality, makes several strategies available to its interpretive agent, either for preventing its being driven over the edge or for recovering from the inevitale lapses of attention that nevertheless happen to occur. The most salient of these strategies can be organized for discussion in the following manner:
Approximation. In resorting to approximation, one accepts the variety of natural bounds that apply to one's capacities for significant denotation, acknowledges the practical constraints that affect one's abilities for attending to detail and retaining exact records, and acts accordingly. This means recognizing the limitations of one's capacity for attention, recording the amounts that one can at the levels of accuracy that are feasible, and restricting one's intentions appropriately to capturing an aspect of one's object or representing a fraction of its reality.
Abstraction. In resorting to abstraction, one is trying to escape the limitations of a "strict democracy" in one's representations, otherwise known as the "one object, one sign" rule. Abstraction occurs when the same sign is used to refer to many different things, often conceived to form a class or a set of objects. In effect, abstraction introduces a common name or a general concept that denotes each individual object in a multitude of particular objects. Typically and most effectively, this comes about in recognition of a common attribute, a general feature, or a universal property that all of these objects share, giving the process of abstraction the beneficial side effect that the abstract sign can be newly re interpreted as referring to the abstract property in question.
Depending on the kinds of entities that are covered by an abstraction and the orders of logical complexity that are involved in this coverage, abstractions can be classified according to their domains of application and qualified according to their manners of construction and derivation. The next topics for discussion are two varieties of abstraction, called "recursion" and "polymorphism", that are especially important for the purpose of building computational models of interpretation and that deserve special mention in the present inquiry.
The poor inhabitant below
Was quick to learn and wise to know,
And keenly felt the friendly glow,
And softer flame;
But thoughtless follies laid him low,
And stain'd his name!
Robert Burns, A Bard's Epitaph, [CPW, 220]
"Recursion" occurs when the same sign is used at different stages of a designated process, referring to different amounts of work to be done, marking the different amounts of work already done that establish the different settings of work going on, and often appearing at different levels of the agenda, charge, or mission that plots out this process. When a process is described by a text, that is, by a recorded agenda, outline, program, recipe, or script, then the recursion is typically reflected in the recursive sign's appearance at different structural levels of the text that serves to recapitulate or specify the process. For instance, a recursive sign can show up initially in the heading and then turn up at least one more time in the body of a text that codes a specification of a procedure, a text that formulates a definition of a function, or a text that constitutes a program, routine, or subprogram.
"Polymorphism" is a type of higher order abstraction that occurs when the same sign is used to denote elements of many different conceptual classes or objects of many distinct logical types. Comprehending the possible options calls for many alternative "conventions of intention", many heterogeneous "directions of connotation", and many splintered if still overlapping "moments of interpretation" to sort out the profusion of senses that is engendered. In the intermediate time frame, this type of diversity can appear to require a panoply of intellectual conceptions to organize the resulting multitude of meanings and to demand a variety of connotative planes to arrange their separate senses across, but it ultimately leads to a richer idea of the original aim or the intended object, as the potential for interpretation can be attributed to it.
Reader, attend! whether thy soul
Soars Fancy's flights beyond the pole,
Or darkling grubs in this earthly hole,
In low pursuit;
Know, prudent, cautious, self control
Is wisdom's root.
Robert Burns, A Bard's Epitaph, [CPW, 220]
One of the aims of this work as a whole is to explain the use of sign relations in the interpretation of complex texts, for instance, this sentence, this paragraph, this entire work, just to name a few of the most obvious examples among the many that are conceivable. As the text I produce to explain the pragmatic theory of sign relations is itself just a sign in a sign relation to which the theory is intended to apply, the encounter with self reference, in both the senses of a self referent text and a self referent writer, cannot be avoided. Among the questions that this encounter brings in its train are the issues of self indicating signs, texts, and interpreters, bringing the following topics to a head:
1. "Indexical signs" are signs that indicate their own interpretive context.
2. "Reflexive signs" are signs that indicate themselves or their issuer.
3. "Recursive signs" are signs that embody, enclose, or invoke themselves, that count themselves among their own parts or that include references to these parts within their own compositions, for instance, texts that incorporate references to their own headings, subtitles, or titles.
</pre>
=====5.1.2.13. Ostensibly Recursive Texts=====
=====5.1.2.13. Ostensibly Recursive Texts=====
