Changes

=====5.1.2.12. Recursions : Possible, Actual, Necessary=====

=====5.1.2.12. Recursions : Possible, Actual, Necessary=====

Is there a whim inspired fool,

| colspan="2" | Is there a whim-inspired fool,

Owre fast for thought, owre hot for rule,

Owre blate to seek, owre proud to snool?

| colspan="2" | Owre fast for thought, owre hot for rule,

Let him draw near;

And owre this grassy heap sing dool,

| colspan="2" | Owre blate to seek, owre proud to snool?

And drap a tear.

Robert Burns, A Bard's Epitaph, [CPW, 220]

| width="5%"  |   || Let him draw near;

| colspan="2" | And owre this grassy heap sing dool,

| width="5%"  |   || And drap a tear.

| colspan="2" align="right" | — 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.

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.

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.

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,

Is there a Bard of rustic song,

Who, noteless, steals the crowds among,

Who, noteless, steals the crowds among,