Changes

=====1.3.4.6. The "Meta" Question=====

=====1.3.4.6. The "Meta" Question=====

There is one point of common contention that I finessed from play in my handling of the discussion between A and B, even though it lies in plain view on both their Tables.  This is the troubling business, recalcitrant to analysis precisely because its operations race on so heedlessly ahead of thought and grind on so routinely beneath its notice, that concerns the placement of object languages within the frame of a meta-language.

There is one point of common contention that I finessed from play in my handling of the discussion between <math>\text{A}</math> and <math>\text{B}</math>, even though it lies in plain view on both their Tables.  This is the troubling business, recalcitrant to analysis precisely because its operations race on so heedlessly ahead of thought and grind on so routinely beneath its notice, that concerns the placement of object languages within the frame of a meta-language.

 

Numerous bars to insight appear to interlock here.  Each one is forged with a good aim in mind, if a bit single-minded in its coverage of the scene, and the whole gang is set to work innocently enough in the unavoidable circumstances of informal discussion.  But a failure to absorb their amalgamated impact on the figurative representations and the analytic intentions of sign relations can lead to several types of false impression, both about the true characters of the tables presented here and about the proper utilities of their graphical equivalents to be implemented as data structures in the computer.  The next few remarks are put forth in hopes of averting these brands of misreading.

Numerous bars to insight appear to interlock here.  Each one is forged with a good aim in mind, if a bit single-minded in its coverage of the scene, and the whole gang is set to work innocently enough in the unavoidable circumstances of informal discussion.  But a failure to absorb their amalgamated impact on the figurative representations and the analytic intentions of sign relations can lead to several types of false impression, both about the true characters of the tables presented here and about the proper utilities of their graphical equivalents to be implemented as data structures in the computer.  The next few remarks are put forth in hopes of averting these brands of misreading.

The general character of this question can be expressed in the schematic terms that were used earlier to give a rough sketch of the modeling activity as a whole.  How do the isolated SOI's of A and B relate to the interpretive framework that I am using to present them, and how does this IF operate, not only to objectify A and B as models of interpretation (MOI's), but simultaneously to embrace the present and the prospective SOI's of the current narrative, the implicit systems of interpretation that embody in turn the initial conditions and the final intentions of this whole discussion?

The general character of this question can be expressed in the schematic terms that were used earlier to give a rough sketch of the modeling activity as a whole.  How do the isolated SOIs of <math>\text{A}</math> and <math>\text{B}</math> relate to the interpretive framework that I am using to present them, and how does this IF operate, not only to objectify <math>\text{A}</math> and <math>\text{B}</math> as models of interpretation (MOIs), but simultaneously to embrace the present and the prospective SOIs of the current narrative, the implicit systems of interpretation that embody in turn the initial conditions and the final intentions of this whole discussion?

One way to see how this issue arises in the discussion of A and B is to recognize that each table of a sign relation is a complex sign in itself, each of whose syntactic constituents plays the role of a simpler sign.  In other words, there is nothing but text to be seen on the page.  In comparison to what it represents, the table is like a sign relation that has undergone a step of ''semantic ascent''.  It is as if the entire contents of the original sign relation have been transposed up a notch on the scale that registers levels of indirectness in reference, each item passing from a more objective to a more symbolic mode of presentation.

One way to see how this issue arises in the discussion of <math>\text{A}</math> and <math>\text{B}</math> is to recognize that each table of a sign relation is a complex sign in itself, each of whose syntactic constituents plays the role of a simpler sign.  In other words, there is nothing but text to be seen on the page.  In comparison to what it represents, the table is like a sign relation that has undergone a step of ''semantic ascent''.  It is as if the entire contents of the original sign relation have been transposed up a notch on the scale that registers levels of indirectness in reference, each item passing from a more objective to a more symbolic mode of presentation.

Sign relations themselves, like any real objects of discussion, are either too abstract or too concrete to reside in the medium of communication, but can only find themselves represented there.  The tables and graphs that are used to represent sign relations are themselves complex signs, involving a step of denotation to reach the sign relation intended.  The intricacies of this step demand interpretive agents who are able, over and above executing all the rudimentary steps of denotation, to orchestrate the requisite kinds of concerted steps.  This performance in turn requires a whole array of techniques to match the connotations of complex signs and to test their alternative styles of representation for semiotic equivalence.  Analogous to the ways that matrices represent linear transformations and that multiplication tables represent group operations, a large part of the usefulness of these complex signs comes from the fact that they are not just conventional symbols for their objects but iconic representations of their structure.

Sign relations themselves, like any real objects of discussion, are either too abstract or too concrete to reside in the medium of communication, but can only find themselves represented there.  The tables and graphs that are used to represent sign relations are themselves complex signs, involving a step of denotation to reach the sign relation intended.  The intricacies of this step demand interpretive agents who are able, over and above executing all the rudimentary steps of denotation, to orchestrate the requisite kinds of concerted steps.  This performance in turn requires a whole array of techniques to match the connotations of complex signs and to test their alternative styles of representation for semiotic equivalence.  Analogous to the ways that matrices represent linear transformations and that multiplication tables represent group operations, a large part of the usefulness of these complex signs comes from the fact that they are not just conventional symbols for their objects but iconic representations of their structure.