ONT Sign Relations
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| Document History:
|
| Project: Intelligent Dynamic Systems Engineering
| Subject: Systems Engineering Interest Statement
| Contact: Jon Awbrey <jawbrey@oakland.edu>
| Version: 6.0
| Created: 12-Nov-1991
| Revised: 01-Sep-1992
| Revised: 01-Sep-2001
| Setting: Oakland University, Rochester, Michigan, USA
| Excerpt: Subsection 1.2.2.3 (Pragmatic Theory of Signs)
Systems Engineering: Interest Statement
Jon Awbrey, September 1, 1992
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 that 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 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,
| 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).
|
| 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).
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.
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.
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, 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
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, s, j> or <s, o, j>, as one chooses.
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, s, i> or <s, i, o>.
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, o, j>, 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
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.
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.
Likewise in semiotics, it is hard to find any examples of autonomous
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
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.
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