Changes

So long as one expects to deal with only a few sign relations at a time, managing to use only a few conventional names to denote each of them, then one's participation in a higher order sign relation hardly ever becomes too problematic, and it rarely needs to be formalized in order for one to cope with the duties of serving as its unofficial interpreter.  Once a reflective involvement with higher order sign relations gets started, however, there will be difficulties that continue to grow and lurk just beneath the apparently conversant surface of their all too facile fluency.

So long as one expects to deal with only a few sign relations at a time, managing to use only a few conventional names to denote each of them, then one's participation in a higher order sign relation hardly ever becomes too problematic, and it rarely needs to be formalized in order for one to cope with the duties of serving as its unofficial interpreter.  Once a reflective involvement with higher order sign relations gets started, however, there will be difficulties that continue to grow and lurk just beneath the apparently conversant surface of their all too facile fluency.

By way of example, a singular sign that denotes an entire sign relation refers by extension to a class of elementary sign relations, or a set of ''transaction triples'' <math>(o, s, i).\!</math>  So far, this is still not too much of a problem.  But when one begins to develop large numbers of conventional symbols and complicated formulas for referring to the same classes of sign transactions, then considerations of effective and efficient interpretation will demand that these symbols and formulas be organized into semantic equivalence classes with recognizable characters.  That is, one is forced to find computable types of similarity relations defined on pairs of symbols and pairs of formulas that tell whether they refer to the same class of sign transactions or not.  It is almost inevitable in such a situation that canonical representatives of these equivalence classes will have to be developed, and a means for transforming arbitrarily complex and obscure expressions into optimally simple and clear equivalents will also become necessary.

By way of example, a singular sign that denotes an entire sign relation refers by extension to a class of elementary sign relations, or a set of "transaction triples" <o, s, i>. So far, this is still not too much of a problem.  But when one begins to develop large numbers of conventional symbols and complicated formulas for referring to the same classes of sign transactions, then considerations of effective and efficient interpretation will demand that these symbols and formulas be organized into semantic equivalence classes with recognizable characters.  That is, one is forced to find computable types of similarity relations defined on pairs of symbols and formulas that tell whether they refer to the same class of sign transactions or not.  It is almost inevitable in such a situation that canonical representatives of these equivalence classes will have to be developed, and a means for transforming arbitrarily complex and obscure expressions into optimally simple and clear equivalents will also become necessary.

At this stage one is brought face to face with the task of implementing a full fledged interpreter for a particular HO sign relation, summarized as follows:

At this stage one is brought face to face with the task of implementing a full fledged interpreter for a particular higher order sign relation, summarized as follows:

1. The objects of Q are the abstract classes of transactions that constitute the sign relations in question.

# The objects of <math>Q\!</math> are the abstract classes of transactions that constitute the sign relations in question.

 

# The signs of <math>Q\!</math> are the collection of symbols and formulas used as conventional names and analytic expressions for the sign relations in question.

2. The signs of Q are the collection of symbols and formulas used as conventional names and analytic expressions for the sign relations in question.

# The interpretants of <math>Q\!</math> &hellip;

 

3. The interpretants of Q ...

But a generic name intended to reference a whole class of sign relations is another matter altogether, especially when it comes into play in a comparative study of many different orders of relations.

But a generic name intended to reference a whole class of sign relations is another matter altogether, especially when it comes into play in a comparative study of many different orders of relations.

===6.30. Connected, Integrated, Reflective Symbols===

===6.30. Connected, Integrated, Reflective Symbols===