Changes

=====1.2.2.3.  Pragmatic Theory of Signs=====

=====1.2.2.3.  Pragmatic Theory of Signs=====

The theory of signs that I find most useful was developed over several decades in the last century by C.S. Peirce, the founder of modern American pragmatism.  Signs are defined pragmatically, not by any essential substance, but by the role they play within a three-part relationship of signs, interpreting signs, and referent objects.  It is a tenet of pragmatism that all thought takes place in signs. Thought is not placed under any preconceived limitation or prior restriction to symbolic domains.  It is merely noted that a certain analysis of the processes of perception and reasoning finds them to resolve into formal elements which possess the characters and participate in the relations that a definition will identify as distinctive of signs.

The theory of signs that I find most useful was developed

over several decades in the last century by C.S. Peirce,

the founder of modern American pragmatism.  Signs are

defined pragmatically, not by any essential substance,

but by the role they play within a three-part relationship

of signs, interpreting signs, and referent objects.  It is

a tenet of pragmatism that all thought takes place in signs.

Thought is not placed under any preconceived limitation or

prior restriction to symbolic domains.  It is merely noted

that a certain analysis of the processes of perception and

reasoning finds them to resolve into formal elements which

possess the characters and participate in the relations

that a definition will identify as distinctive of signs.

One version of Peirce's sign definition is especially useful for

One version of Peirce's sign definition is especially useful for the present purpose.  It establishes for signs a fundamental role in logic and is stated in terms of abstract relational properties that are flexible enough to be interpreted in the materials of dynamic systems.  Peirce gave this definition of signs in his 1902 "Application to the Carnegie Institution":

the present purpose.  It establishes for signs a fundamental role

in logic and is stated in terms of abstract relational properties

that are flexible enough to be interpreted in the materials of  

dynamic systems.  Peirce gave this definition of signs in his

1902 "Application to the Carnegie Institution":

| Logic is 'formal semiotic'.  A sign is something, 'A', which brings

| something, 'B', its 'interpretant' sign, determined or created by it,

<p>Logic is ''formal semiotic''.  A sign is something, ''A'', which brings something, ''B'', its ''interpretant'' sign, determined or created by it, into the same sort of correspondence (or a lower implied sort) with something, ''C'', its ''object'', as that in which itself stands to ''C''. This definition no more involves any reference to human thought than does the definition of a line as the place within which a particle lies during a lapse of time.  (Peirce, NEM 4, 54).</p>

| into the same sort of correspondence (or a lower implied sort) with

| something, 'C', its 'object', as that in which itself stands to 'C'.

| This definition no more involves any reference to human thought than

| does the definition of a line as the place within which a particle lies

| during a lapse of time.  (Peirce, NEM 4, 54).

A placement and appreciation of this theory in a philosophical context

<p>It is from this definition, together with a definition of "formal", that I deduce mathematically the principles of logic.  I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non-psychological conception of logic has ''virtually'' been quite generally held, though not generally recognized.  (Peirce, NEM 4, 21).</p>

that extends from Aristotle's early treatise 'On Interpretation' through

John Dewey's later elaborations and applications (Dewey, 1910, 1929, 1938)

is the topic of (Awbrey & Awbrey, 1992). Here, only a few features of

One characteristic of Peirce's definition is crucial in supplying

A placement and appreciation of this theory in a philosophical context that extends from Aristotle's early treatise ''On Interpretation'' through John Dewey's later elaborations and applications (Dewey, 1910, 1929, 1938) is the topic of (Awbrey & Awbrey, 1992).  Here, only a few features of this definition will be noted that are especially relevant to the goal of implementing intelligent interpreters.

a flexible infrastructure that makes the formal and mathematical

treatment of sign relations possible.  Namely, this definition

equivalent in their information content.  Namely, objects of signs,

they fall  under this definition, allow themselves to be reconstituted

or correspondence that is preserved in passing from initial signs to

between signs and the world into a relation interior to the world of signs

the foreshortening and planar projections that are used in perspective drawing.

This definition takes as its subject a certain three-place relation,

One characteristic of Peirce's definition is crucial in supplying a flexible infrastructure that makes the formal and mathematical treatment of sign relations possible.  Namely, this definition allows objects to be characterized in two alternative ways that are substantially different in the domains they involve but roughly equivalent in their information content.  Namely, objects of signs, that may exist in a reality exterior to the sign domain, insofar as they fall  under this definition, allow themselves to be reconstituted nominally or reconstructed rationally as equivalence classes of signs.  This transforms the actual relation of signs to objects, the relation or correspondence that is preserved in passing from initial signs to interpreting signs, into the membership relation that signs bear to their semantic equivalence classes.  This transformation of a relation between signs and the world into a relation interior to the world of signs may be regarded as a kind of representational reduction in dimensions, like the foreshortening and planar projections that are used in perspective drawing.

the sign relation proper, envisioned to consist of a certain set of

three-tuples.  The pattern of the data in this set of three-tuples,

the extension of the sign relation, is expressed here in the form:

<Object, Sign, Interpretant>.  As a schematic notation for various

sign relations, the letters "s", "o", "i" serve as typical variables

ranging over the relational domains of signs, objects, interpretants,

respectively.  There are two customary ways of understanding this

abstract sign relation as its structure affects concrete systems.

In the first version the agency of a particular interpreter

This definition takes as its subject a certain three-place relation, the sign relation proper, envisioned to consist of a certain set of three-tuples. The pattern of the data in this set of three-tuples, the extension of the sign relation, is expressed here in the form: ‹Object,&nbsp;Sign,&nbsp;Interpretant›.  As a schematic notation for various sign relations, the letters "s", "o", "i" serve as typical variables ranging over the relational domains of signs, objects, interpretants, respectively.  There are two customary ways of understanding this abstract sign relation as its structure affects concrete systems.

is taken into account as an implicit parameter of the relation.

As used here, the concept of interpreter includes everything about

the context of a sign's interpretation that affects its determination.

In this view a specification of the two elements of sign and interpreter

is considered to be equivalent information to knowing the interpreting or

the interpretant sign, that is, the affect that is produced 'in' or the

effect that is produced 'on' the interpreting system. Reference to an

object or to an objective, whether it is successful or not, involves

by affects 'in' and effects 'on' the interpreter.  Schematically,

a lower case "j" can be used to represent the role of a particular

interpreter.  Thus, in this first view of the sign relation the

represented in the form <o, s, j> or <s, o, j>, as one chooses.

In the second version of the sign relation the interpreter

In the first version the agency of a particular interpreter is taken into account as an implicit parameter of the relation.  As used here, the concept of interpreter includes everything about the context of a sign's interpretation that affects its determination.  In this view a specification of the two elements of sign and interpreter is considered to be equivalent information to knowing the interpreting or the interpretant sign, that is, the affect that is produced ''in'' or the effect that is produced ''on'' the interpreting system. Reference to an object or to an objective, whether it is successful or not, involves an orientation of the interpreting system and is therefore mediated by affects ''in'' and effects ''on'' the interpreter.  Schematically, a lower case "j" can be used to represent the role of a particular interpreter.  Thus, in this first view of the sign relation the fundamental pattern of data that determines the relation can be represented in the form ‹o,&nbsp;s,&nbsp;j› or ‹s,&nbsp;o,&nbsp;j›, as one chooses.

is considered to be a hypostatic abstraction from the actual

process of sign transformation.  In other words, the interpreter

is regarded as a convenient construct that helps to personify the

as a process involving successive signs.  An interpretant sign is  

merely the sign that succeeds another in a continuing sequence.

What keeps this view from falling into sheer nominalism is the

relation with objects that is preserved throughout the process

of transformation.  Thus, in this view of the sign relation the

fundamental pattern of data that constitutes the relationship

can be indicated by the optional forms <o, s, i> or <s, i, o>.

In the second version of the sign relation the interpreter is considered to be a hypostatic abstraction from the actual process of sign transformation. In other words, the interpreter is regarded as a convenient construct that helps to personify the action but adds nothing informative to what is more simply observed as a process involving successive signs.  An interpretant sign is merely the sign that succeeds another in a continuing sequence.  What keeps this view from falling into sheer nominalism is the relation with objects that is preserved throughout the process of transformation.  Thus, in this view of the sign relation the fundamental pattern of data that constitutes the relationship can be indicated by the optional forms ‹o,&nbsp;s,&nbsp;i› or ‹s,&nbsp;i,&nbsp;o›.

of all of those conceivable moments -- past, present, prospective, or

when something means something about something, in the pattern <s, i, o>.

But this ultimate sign relation is not often explicitly needed, and it

could easily turn out to be logically and set-theoretically ill-defined.

In physics, it is important for theoretical completeness to regard the

whole universe as a single physical system, but more common to work with

"isolated" subsystems.  Likewise in the theory of signs, only particular

and well-bounded subsystems of the ultimate sign relation are likely to

be the subjects of sensible discussion.

It is helpful to view the definition of individual sign relations

Viewed as a totality, a complete sign relation would have to consist of all of those conceivable moments — past, present, prospective, or in whatever variety of parallel universes that one may care to admit — when something means something to somebody, in the pattern ‹s,&nbsp;o,&nbsp;j›, or when something means something about something, in the pattern ‹s,&nbsp;i,&nbsp;o›.  But this ultimate sign relation is not often explicitly needed, and it could easily turn out to be logically and set-theoretically ill-defined.  In physics, it is important for theoretical completeness to regard the whole universe as a single physical system, but more common to work with "isolated" subsystems.  Likewise in the theory of signs, only particular and well-bounded subsystems of the ultimate sign relation are likely to be the subjects of sensible discussion.

on analogy with another important class of three-place relations

of broad significance in mathematics and far-reaching application

in physics:  namely, the binary operations or ternary relations that

fall under the definition of abstract groups.  Viewed as a definition

would call highly non-categorical, that is, not every two models are

isomorphic (Wilder, p. 36).  But viewing the category of groups as

a whole, if indeed it can be said to form a whole (MacLane, 1971),

the definition allows a vast number of non-isomorphic objects,

namely, the individual groups.

In mathematical inquiry the closure property of abstract groups

It is helpful to view the definition of individual sign relations on analogy with another important class of three-place relations of broad significance in mathematics and far-reaching application in physics:  namely, the binary operations or ternary relations that fall under the definition of abstract groups.  Viewed as a definition of individual groups, the axioms defining a group are what logicians would call highly non-categorical, that is, not every two models are isomorphic (Wilder, p. 36).  But viewing the category of groups as a whole, if indeed it can be said to form a whole (MacLane, 1971), the definition allows a vast number of non-isomorphic objects, namely, the individual groups.

mitigates most of the difficulties that might otherwise attach

to the precision of their individual definition.  But in physics

the application of mathematical structures to the unknown nature

of the enveloping world is always tentative.  Starting from the

most elemental levels of instrumental trial and error, this kind

the risk of physical pain.  The act of abstracting a particular

It becomes, in effect, a hypothesis, a guess, a bet on what is

thought to be the most relevant aspect of a current, potentially

dangerous, and always ever-insistently pressing reality. And this

its character.  Consequently, due to the abyss of ignorance that always

remains to our kind and the chaos that can result from acting on what

little is actually known, risk and pain accompany the extraction of

particular structures, attempts to isolate particular forms, or

guesses at viable factorizations of phenomena.

Likewise in semiotics, it is hard to find any examples of autonomous

In mathematical inquiry the closure property of abstract groups mitigates most of the difficulties that might otherwise attach to the precision of their individual definition.  But in physics the application of mathematical structures to the unknown nature of the enveloping world is always tentative.  Starting from the most elemental levels of instrumental trial and error, this kind of application is fraught with intellectual difficulty and even the risk of physical pain.  The act of abstracting a particular structure from a concrete situation is no longer merely abstract.  It becomes, in effect, a hypothesis, a guess, a bet on what is thought to be the most relevant aspect of a current, potentially dangerous, and always ever-insistently pressing reality.  And this hypothesis is not a paper belief but determines action in accord with its character.  Consequently, due to the abyss of ignorance that always remains to our kind and the chaos that can result from acting on what little is actually known, risk and pain accompany the extraction of particular structures, attempts to isolate particular forms, or guesses at viable factorizations of phenomena.

sign relations and to isolate them from their ulterior entanglements.

This kind of extraction is often more painful because the full analysis

of each element in a particular sign relation may involve references to

other object-, sign-, or interpretant-systems outside of its ostensible,

initially secure bounds.  As a result, it is even more difficult with

sign systems than with the simpler physical systems to find coherent

subassemblies that can be studied in isolation from the rest of the

enveloping universe.

These remarks should be enough to convey the plan of this work.

Progress can be made toward new resettlements of ancient regions

 

where only turmoil has reigned to date.  Existing structures can

These remarks should be enough to convey the plan of this work. Progress can be made toward new resettlements of ancient regions where only turmoil has reigned to date.  Existing structures can be rehabilitated by continuing to unify the terms licensing AI representations with the terms leasing free space over dynamic manifolds.  A large section of habitable space for dynamically intelligent systems could be extended in the following fashion: The images of state and the agents of change that are customary in symbolic AI could be related to the elements and the operators which form familiar planks in the tangent spaces of dynamic systems. The higher order concepts that fill out AI could be connected with the more complex constructions that are accessible from the moving platforms of these tangent spaces.

be rehabilitated by continuing to unify the terms licensing AI

representations with the terms leasing free space over dynamic

manifolds.  A large section of habitable space for dynamically

intelligent systems could be extended in the following fashion:

The images of state and the agents of change that are customary

in symbolic AI could be related to the elements and the operators

which form familiar planks in the tangent spaces of dynamic systems.

The higher order concepts that fill out AI could be connected with the

more complex constructions that are accessible from the moving platforms

of these tangent spaces.

====1.2.3.  Architecture of Inquiry====

====1.2.3.  Architecture of Inquiry====